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astro-ph9806269

i

a search for unresolved white dwarfs in binary systems with optically brighter normal stellar companions has been conducted with iue during its final year of operation . targets were chosen among the fainter and still un - identified euv sources in the rosat 2re catalogue ( pye et al . one new system was discovered ( re j0500@xmath1364 , da@xmath2f6/7v ) , which appears to lie in a direction of low interstellar neutral hydrogen volume density . if this star is really as distant as @xmath0500 - 1000pc , then it may represent a lower limit to the size of the @xmath3 cma tunnel of low density neutral gas stretching away from the local bubble in that direction . including the independently identified hd27483 ( da@xmath2f6v , bhm - vitense 1993 ) , this new discovery brings the total number of such systems found in the rosat and euve surveys to nineteen . these two satellites have , therefore , been very successful in helping us to identify these kinds of binary systems , which have never been seen optically and could only have been identified through such satellite surveys . however , these stars still represent @xmath1020% of the hot white dwarfs identified in the euv . the demise of iue , which suffered a gyro failure in february 1996 , limiting it to observe only targets with bright guide stars ( the mission was finally terminated in september 1996 ) , effectively cut short our programme . the loss of iue means that this particular method of searching for these important systems is no longer available . although hst can observe the same wavelength region , it is of course much harder to obtain the time required for this kind of search . it is likely , therefore , that very few new examples of these systems will be discovered in the near future . the results presented in this paper seem to suggest that this search , using the euv catalogues as a basis from which to identify potential systems , has been fairly exhaustive ( we have identified only one new system from thirteen targets ) . however , the identification by vennes et al . ( 1997 ) of a hot white dwarf companion to a previously catalogued euv - bright active star , re j0702@xmath2129 ( k0ve ) , instead suggests that , in fact , some systems may have been completely overlooked . re j0702@xmath2129 was classified as active by mason et al . ( 1995 ) in their optical follow - up programme to identify the euv sources found in the rosat wfc survey , and was not , therefore , included on any of our target lists for the iue search . this raises the question of how many of the @xmath5200 ` active ' stars in the wfc and euve catalogues really are the source , or at least the only source , of the euv radiation . until each star has been observed and analysed in detail , the suspicion remains that there are more of these binary systems in the survey waiting to be identified . for example , the rosat wfc catalogue includes @xmath4120 isolated white dwarfs , and @xmath460 in some kind of binary , e.g. classic sirius - type systems , cvs , non - interacting da@xmath2 dm systems , and visual binaries . conservatively , then , we might assume that we have already identified the majority of the white dwarf binaries to be found in the survey . however , if as many as 80% of stars reside in binary or multiple systems , another 30 might be awaiting discovery . these could include double degenerate systems as well as further examples of sirius - type systems ( e.g. the apparantly isolated da re j0512@xmath1007 has a mass , [email protected]@xmath15 , too low for it to be the result of single star evolution , and may have a degenerate companion ) . what is really needed to try to find more sirius - type binaries is an all - sky uv survey . none has been undertaken since the td-1 survey of 1972/73 , which originally appeared to have only detected sirius b among these systems . subsequently , though , landsman , simon and bergeron ( 1996 ) found white dwarf companions to 56 persei and hr3643 as a result of the uv excess detected by td-1 . the recently approved _ galex _ mission ( bianchi 1998 ) , which will survey the sky at uv wavelengths and follow - up some targets spectroscopically , may reveal many more of these binaries . in the meantime , follow - up observations of these nineteen new euv - bright systems are required . in particular , it is important to determine whether these systems are wide , or close enough that they must have undergone common envelope evolution . this information will help to place constraints on theoretical models of binary evolution ( e.g. de kool and ritter 1993 ) . detailed studies of the normal stellar companions may also reveal evidence of past interaction ( e.g. jeffries and stevens 1996 ) , and stars with possible abundance anomalies that may be the progenitors of the barium and carbon giants ( e.g. jeffries and smalley 1996 ) . in addition , the forthcoming _ fuse _ mission ( far ultra - violet spectroscopic explorer ) will , for the first time , allow us to unambiguously determine the temperatures and surface gravities of the white dwarfs in these systems ( and hence their masses and radii ) , through modelling of the h lyman absorption series down to 912 .

one new system , re j0500 ( daf6/7v ) , has been identified . the very low line - of - sight neutral hydrogen volume density to this object could place a lower limit on the length of the cma interstellar tunnel of diffuse gas , which stretches away from the local bubble in a similar direction to re j0500 . in this paper

the rosat wide field camera ( wfc ) survey of the extreme ultraviolet ( euv ) has provided us with evidence for the existence of a previously unidentified sample of hot white dwarfs in unresolved , detached binary systems . these stars are invisible at optical wavelengths due to the close proximity of their much more luminous companions ( spectral type k or earlier ) . however , for companions of spectral typea5 or later the white dwarfs are easily visible at far - ultraviolet ( far - uv ) wavelengths , and can be identified in spectra taken by iue . sixteen such systems have been discovered in this way through rosat , euve and iue observations , including four identified by us in paper i ( burleigh , barstow and fleming 1997 ) . in this paper we report the results of our continuing search during the final year of iue operations . one new system , re j0500 ( daf6/7v ) , has been identified . this star appears to lie at a distance of betweenpc , making it one of the most distant white dwarfs , if not the most distant , to be detected in the euv surveys . the very low line - of - sight neutral hydrogen volume density to this object could place a lower limit on the length of the cma interstellar tunnel of diffuse gas , which stretches away from the local bubble in a similar direction to re j0500 . in this paper we also analyse a number of the stars observed where no white dwarf companion was found . some of these objects show evidence for chromospheric and coronal activity . finally , we present an analysis of the previously known wdactive f6v binary hd27483 ( bhm - vitense 1993 ) , and show that , at t,000k , the white dwarf may be contributing significantly to the observed euv flux . if so , it is one of the coolest such stars to be detected in the euv surveys . -1_td-1 _ stars : binaries stars : white dwarfs x - ray : stars ultra - violet : stars ism : general .

1604.04868

i

@xcite conducted a comparison project of numerical simulations of the formation of a massive cluster of galaxies in a cold dark matter ( cdm ) universe in which the results of twelve independent simulation codes were compared . both eulerian mesh codes and lagrangian smoothed particle hydrodynamics ( hereafter sph ; * ? ? ? * ; * ? ? ? * ) codes were used in this comparison project . in this project , they took into account only gravity and hydrodynamics so that the comparison was simplified . this project is known as the `` santa barbara cluster comparison project '' . although most of global properties reasonably converged , there was a systematic difference in entropy profiles of the clusters in simulations with different methods . the results of the eulerian mesh codes showed the central core in entropy profiles , whereas those of sph codes did not ( see figure 18 in their paper ) . later studies confirmed this tendency ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite interpreted that this difference might reflect the difference in the treatment of shocks of sph and mesh codes . @xcite pointed out that there are `` fundamental differences '' between eulerian mesh and lagrangian sph codes ( see also * ? ? ? * ; * ? ? ? this difference is originated from the fact that the standard formulation of sph ( hereafter ssph , where @xmath0 and @xmath1 are the mass and density of a particle , as the discrete volume element for the discretization of the equations . ] ) has difficulties when dealing with contact discontinuities . since ssph requires the differentiability of the density field , the density around a contact discontinuity has a large error . in particular , the density of particles in the low - density side of the contact discontinuity is overestimated by a large factor . this error propagates to the pressure evaluation , resulting in the _ unphysical surface tension _ and the suppression of fluid instabilities ( see figure 1 in * ? ? ? we can solve this problem by using the volume element which does not depend on the density @xcite , by introducing extra dissipation terms @xcite , by using the integration form to evaluate the derivatives of physical quantities @xcite , by employing the non - standard equation of motion which breaks newton s third law @xcite , and by adopting the godunov sph @xcite where physical quantities are smoothed twice @xcite . @xcite used a diffusive quantity , @xmath2 , instead of the mass and mass density , to formulate the sph approximation . each particle has the @xmath3 , and from that its density is calculated using the usual formula to calculate mass density from mass of particles in sph . since all of the sph codes used in the santa barbara cluster comparison project were based on ssph , the cuspy entropy profile obtained with sph codes might be , at least partly , the artifact caused by the unphysical surface tension . in the hierarchical structure formation scenario , a cluster of galaxies grows through mergers of a number of small building blocks which contain cold , low - entropy gas . the unphysical surface tension of ssph tends to protect cold gas clumps in the building blocks against the fluid instabilities and the ram - pressure stripping , as demonstrated by the `` blob test '' of @xcite . as a result , cold clumps might reach the center of the cluster due to the dynamical friction with keeping their low entropy state , resulting in a cuspy entropy profile of the cluster . some of techniques described above have been applied to the cluster formation simulations in order to investigate their effect on the central entropy structure . @xcite added a diffusion term to the energy equation which mimics the turbulence mixing and performed the santa barbara cluster simulations . they found that the entropy core could be formed , but the size and depth of the entropy core depended strongly on the diffusion coefficient and numerical resolutions ( see their figures 12 and 13 ) . @xcite carried out a set of comparison tests of the cluster formation in a @xmath4cdm universe with sph and an adaptive mesh refinement ( amr ) codes , focusing on the formation of the entropy core . in their comparison tests , they used not only ssph but also their new sph , sphs @xcite which avoids multivalues of physical quantities by artificial diffusion terms with a higher order dissipation switch and increases the force accuracy by adopting a higher order kernel with a large number of neighbor particles . in sphs runs , the entropy core was formed in the cluster center and its size was consistent to that obtained by an amr code , ramses @xcite . this good agreement is achieved when the maximum dissipation parameter @xmath5 ( see their figure 6 ) . on the other hand , in the case with @xmath6 , the entropy profile has a core , but it is smaller and the core entropy is lower than those with converged values . in the case with @xmath7 , it is close to that found with ssph . recently , @xcite reported a new comparison test of a numerical cluster in a @xmath4cdm universe . they showed that sph codes with the artificial conductivity ( hereafter ac ) term and sphs give entropy profiles which are close to those given by amrs ( i.e. , cored profiles ) , although they did not provide the results of the parameter tests . the agreement with the results of amr calculations does not guarantee the validity of the results , since eulerian schemes have their own limitations . an obvious one comes from its eulerian nature . in order to integrate the motion and internal energy of fast - moving cold gas clump , very high accuracy is required . the internal energy of a gas clump can be many orders of magnitudes smaller than its kinetic energy in the reference frame of the mesh . numerical error comes from the kinetic energy , but it affects the internal energy of the clump . consider the case that a molecular cloud moves in a galaxy following the galactic potential . the typical temperature of the cloud is @xmath8 while the virial temperature which corresponds to the typical kinematic energy is @xmath9 for a galaxy of the milky way size . the energy difference between the thermal and kinetic energies of the cloud becomes about five orders of magnitude . very high accuracy is , thus , required to keep the structure of the clump , and this requirement in turn results in the requirement of high spacial resolution and small time step . otherwise , a large error is induced by the loss of significant digits and/or negative pressure . a remedy for this problem is the dual energy formulation @xcite . in this formulation , both total ( @xmath10 ) and internal ( @xmath11 ) energies are solved independently . then , either @xmath11 or @xmath12 , where @xmath13 is the kinetic energy , is used to evaluate pressure , depending on the fraction of the thermal energy . for the high mach number fluid , e.g. , @xmath14 , @xmath11 is adopted to evaluate pressure . otherwise , since @xmath15 , the loss of significant digits occurs . another difficulty is that the eulerian formulation is not the galilean invariant , which leads to the numerical diffusion . an example of this problem can be seen in figure 14 of @xcite . in eulerian codes , an initially hydrostatic cluster decays after 1 gyr evolution , in particular in enzo @xcite with zeus @xcite and flash @xcite , when a translational velocity was added . in principle , by going to higher spatial resolution , we can reduce the rate of decay by reducing the effect of the numerical dissipation @xcite . nevertheless , compared to lagrangian codes with the same effective accuracy , the computational cost would be much higher . the other way is to adopt higher spatial order schemes , such as essentially non - oscillatory polynomial interpolation ( eno ; * ? ? ? * ) , weighted eno ( weno ; * ? ? ? * ) , and constrained interpolation profile ( cip ; * ? ? ? * ) schemes . however , these schemes are computationally expensive and it is difficult to combine high - order schemes with amr in a consistent way . the latter is serious because joint interfaces of finer and coarse meshes lose their accurracy @xcite and thus careful treatment is necessary . recently , novel numerical schemes have been developed and used in the field of numerical astrophysics . @xcite developed a moving mesh scheme which is free from the above problem of the eulerian mesh codes . in @xcite , he carried out simulations of the santa barbara cluster with `` arepo '' , an implementation of his moving mesh scheme , and reported that the entropy core was formed . the size of the core is smaller than those obtained by amr simulations and the entropy at the core is lower than those obtained by amr simulations . @xcite developed a new code `` gizmo '' which implemented a meshless method and found that in cluster simulations with gizmo entropy cores similar to those of arepo is formed . these results are quite encouraging . however these two codes use similar approaches , such as quasi - lagrangian nature using riemann solvers . further tests with different schemes are important . in this paper , we report the results of santa barbara cluster simulations obtained with the density independent formulation of sph ( disph ) @xcite . since disph is free from the unphysical surface tension , we can expect that it gives better results compared to ssph . in addition , since disph do not introduce artificial dissipations , we can expect that the result is not affected by free parameters . the structure of this paper is as follows . in [ sec : disph ] we give a brief review of the formulation of ssph and disph and their advantages and disadvantages . we then describe the initial condition and our numerical methods in [ sec : method ] . the comparison is carried out in [ sec : results ] and discussion is given in [ sec : discussion ] .

the santa barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by eulerian mesh and lagrangian smoothed particle hydrodynamics ( sph ) codes : mesh codes gave a core with a constant entropy whereas sph codes did not . one possible reason for this difference is that mesh codes are not galilean invariant . the size of the core is , however , significantly smaller than those obtained with mesh simulations , and is comparable to those obtained with quasi - lagrangian schemes such as `` moving mesh '' and `` mesh free '' schemes . we conclude that both the standard sph without artificial conductivity and eulerian mesh codes have serious problems even such an idealized simulation , while disph , sph with artificial conductivity , and quasi - lagrangian schemes have sufficient capability to deal with it .

the santa barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by eulerian mesh and lagrangian smoothed particle hydrodynamics ( sph ) codes : mesh codes gave a core with a constant entropy whereas sph codes did not . one possible reason for this difference is that mesh codes are not galilean invariant . another possible reason is the problem of the sph method , which might give too much `` protection '' to cold clumps because of the unphysical surface tension induced at contact discontinuities . in this paper , we apply the density independent formulation of sph ( disph ) , which can handle contact discontinuities accurately , to simulations of a cluster of galaxies , and compare the results with those with the standard sph . we obtained the entropy core when we adopt disph . the size of the core is , however , significantly smaller than those obtained with mesh simulations , and is comparable to those obtained with quasi - lagrangian schemes such as `` moving mesh '' and `` mesh free '' schemes . we conclude that both the standard sph without artificial conductivity and eulerian mesh codes have serious problems even such an idealized simulation , while disph , sph with artificial conductivity , and quasi - lagrangian schemes have sufficient capability to deal with it .

1604.04868

r

in this section , we compare the properties of the santa barbara cluster obtained by simulations with ssph and disph , and then investigate the origin of the difference in the entropy profile . we first describe the global properties of the santa barbara cluster in [ sec : results : globalproperties ] . the density , temperature and entropy distributions in the clusters obtained by simulations with ssph and disph at @xmath61 are compared in [ sec : results : snapshots ] . in [ sec : results : radialprofile ] , we compare radial profiles . we investigate how the central entropy core / cusp formed in [ sec : results : entropy : formation ] . in [ sec : results : ac ] , we investigate the contribution of the ac term for the cluster entropy profile . in order to avoid confusion , we use the label `` sph '' to indicate the results of ssph on figures and `` disph '' for the results of disph . the average of virial radii of the santa barbara clusters of the four runs ( the high- and low - resolution runs with ssph and disph ) is @xmath62 . this radius is somewhat larger than those obtained in previous studies @xcite . the total mass within @xmath59 is @xmath63 which is @xmath64 larger than those obtained by @xcite . these differences are probably due to the difference in the treatment of the boundary condition . we used the open boundary condition , while all runs in @xcite adopted the periodic boundary condition . since the radius of the initially imposed overdensity region is @xmath65 , the cut - off radius of @xmath45 would be insufficient to remove boundary effects . nonetheless , as we see later , the central region of the cluster does not seem to be affected by the boundary condition . in the following , we call the santa barbara cluster just `` cluster '' , for brevity . we found that the clusters obtained by disph contain more gas than those obtained by ssph . the gas fractions of the cluster with disph are @xmath66 which are close to the results of high resolution mesh codes in @xcite and also the cosmic averaged value of @xmath67 for this model . on the other hand , those of ssph are @xmath68 which are close to those of ssph runs in @xcite , @xmath69 . figure [ fig : virial : density ] shows the gas density maps of the four runs within @xmath59 at @xmath61 . these density maps are not very different . however , when we inspect these maps carefully , we find several differences . first , we can see that the central densities in runs with ssph are higher than those with disph . the density of the innermost regions of the clusters with ssph is one order of magnitude higher than that with disph . second , for both of ssph and disph runs , the central density of the cluster is higher for runs with high mass resolution ( large number of particles ) . figure [ fig : virial : temperature ] shows the temperature distribution within the cluster of four runs . we can see that the clusters of ssph runs contain more small - scale substructures compared to those of disph runs . figure [ fig : virial : entropy ] shows the entropy distributions ; the definition of the entropy we adopted in this paper is @xmath70 where @xmath71 and @xmath1 are the temperature in the unit of kelvin and the density in the unit of @xmath72 , respectively , and this definition is the same as that used in @xcite . it is obvious that the values of the central entropy in ssph runs are much lower than those in disph runs . the clusters in disph runs have no or a little amount of gas with entropy below @xmath73 , while the clusters in ssph runs have significant amounts of such gas at the center . it is also clear that the entropy distributions of the cluster in disph runs are smoother than those of clusters in ssph runs . in other words , the entropy distribution indicates that the gas in the clusters of ssph runs is not well mixed . figure [ fig : radialprofiles ] shows the radial profiles of the cluster at @xmath61 . in this figure , we used two high - resolution results . in this plots , `` sb '' denotes the averaged profiles in @xcite , `` arepo '' is the result of a moving mesh code arepo by @xcite . as expected , with this formalism the entropy generation is slightly suppressed @xcite . on the other hand , @xcite pointed out that spurious heating from riemann solver errors affects an entropy profile when this formalism turned off . hence , we adopt the original data shown in @xcite . ] , and `` nyx '' denotes the result of an amr code nyx by @xcite . -body / gas dynamics code designed for large scale cosmological simulations . in this code , the fluid evolution is solved by a finite volume method with a block structured amr . the dual energy formulation is used . the riemann solver is used for the evaluation of fluxes . according to these features , nyx is one of good representatives of the state - of - the - art amr codes . the entropy profile of the santa barbara cluster with nyx is almost identical to those with enzo @xcite and art @xcite . ] we note that these data were taken from figures in their papers : figure 18 in @xcite for sb , figure 45 in @xcite for arepo ( we adopt the result labeled @xmath41 ) , and figure 7 in @xcite for nyx . we also note that the entropy profile with gizmo reported by @xcite is comparable to that with arepo . the density profiles of dm ( the top - left panel of figure [ fig : radialprofiles ] ) of all four runs agree very well . the central density of gas of the ssph run is significantly higher than those of the other three runs . here , `` sb '' , `` arepo '' and our disph results seem to agree well . note , however , that the `` sb '' plot is the average of 7 sph and 5 mesh - based scheme runs , and sph models in @xcite gave the result similar to our ssph run , while the mesh runs gave a central density even lower than arepo / disph results . thus , the agreement between our disph result and the arepo result is rather good , whereas all ssph runs gave high central densities and amr runs , lower density . from the temperature profile ( the left - bottom panel of figure [ fig : radialprofiles ] ) and density profile ( the top - right panel ) of the gas component , we can see that the standard sph gives a central cusp with the temperature decreasing inward , while arepo and disph give constant - density , constant - temperature cores . mesh runs in @xcite also gave constant - density cores , but their cores are systematically larger than those obtained by arepo and our disph . the averaged `` sb '' profile of the temperature shows a sign of central decrease , since it is the average of sph ( decreasing ) and mesh ( increasing ) profiles . we can see the same tendency in the entropy profile ( the bottom - right panel ) . in figure [ fig : entropy : comparison ] , we plot the entropy profiles of our low - resolution runs , as well as those of our high - resolution runs and three results from the literature ( `` sb '' , `` arepo '' and `` nyx '' ) . we can see that for disph runs , the difference in resolution does not make much difference in the entropy profile ; the entropy profiles with disph are consistent with that obtained by a moving mesh code arepo . on the other hand , our low - resolution ssph run gave a central entropy significantly higher than that of our high - resolution ssph run . our low - resolution ssph result is similar to those of the ssph simulations in @xcite and @xcite . thus , it is clear that the `` core '' in these previous ssph results is due to the limitations in the numerical resolution . from this figure , we find that the central entropy in the high - resolution disph run is slightly higher than that in the low - resolution disph run , although we saw the opposite sense from the entropy maps ( figure [ fig : virial : entropy ] ) . this is because there is an offset of @xmath74 between the position of the entropy minimum and the plot center ( the density weighted center ) in the high - resolution disph run , and it makes the rather flatter central entropy profile . thus , there is no discrepancy . in order to assess which parameters , i.e. , mass and spatial resolutions , are more crucial to the final entropy profile of the cluster , we carried out two extra models with disph and ssph which mix resolutions ; ( 1 ) with the high mass / low spatial resolutions ( `` mixed resolution 1 '' ) and ( 2 ) with the low mass / high spatial resolutions ( `` mixed resolution 2 '' ) . as shown in figure [ fig : entropy : mixed ] , the former run reproduced the entropy profile of the high - resolution ssph run , while the latter run did that of the low - resolution ssph run . a slight difference is found only in the very central region ( @xmath75 ) . hence , in the ssph runs , the central structure of the entropy profile is sensitive to the small scale power of the initial density fluctuations . there is no significant influence on the results with disph . the good agreement between results with disph , arepo , and gizmo is quite encouraging . however , the analysis so far is only limited at the date of @xmath61 . in the next subsection , we compare the results obtained by disph and ssph methods deeply , by focusing on the formation process of the cluster . the cluster grew rapidly while @xmath76 , and then experienced a major merger around @xmath77 , and evolved mildly until @xmath61 . we follow these typical phases of evolution to understand how and when the entropy core and cusp are established . figure [ fig : entropy : threeepochs ] shows the radial entropy and density profiles for the high - resolution disph and ssph runs . we here plot them for three epochs , before the major merger ( @xmath78 ) , after the major merger ( @xmath79 ) , and at the end of the simulation ( @xmath61 ) . for the run with disph , at @xmath78 , the entropy profile has a relatively small core . then , the core entropy and core size increase and these quantities are kept unchanged until @xmath61 . the entropy profile at @xmath79 is comparable to that at @xmath61 ; the last major merger event triggers this core entropy increase ( see below ) . the entropy of the intermediate region of @xmath80 slightly increased during @xmath81 . the evolution of the density profile is similar , but in the opposite direction . the core density decreases by almost a factor of three from @xmath78 to @xmath79 , and it remains unchanged until @xmath61 . the evolution of the radial profile in the ssph run is quite different from that in the disph run . at @xmath78 , the entropy profile with ssph has a small core which is comparable to that of the disph run . this entropy core becomes larger until @xmath79 . however the core entropy is much lower than that with the disph run . at @xmath61 , the entropy core vanishes nearly . the density profile follows this evolution similarly but in the opposite direction . at the end of the simulation the density profile has a cusp . evolution of the radius of the entropy core and the averaged core entropy in the runs with disph and ssph are shown in figures [ fig : entropy : coreradius ] and [ fig : entropy : coreentropy ] . the definition of the core radius is described in appendix [ sec : method : core ] . the averaged core entropy is measured using the entropy of gas in the core radius . their evolutions can be divided into two phases and the transition takes place after the major merger epoch ( @xmath82 ) . in the disph runs , two results agree with each other very well . in the early phase ( @xmath83 ) , the radius of the entropy core increases from @xmath84 ( @xmath85 ) to @xmath86 ( @xmath82 ) and the averaged core entropy increases from @xmath87 ( @xmath85 ) to @xmath88 ( @xmath82 ) . then the growth of the core radius is stopped and the core is essentially unchanged until @xmath61 . in the ssph runs , the evolution is completely different from those of disph runs . when we compare the high resolution runs , the core radius of the ssph run is smaller than that of the disph run in the initial phase ( @xmath89 ) . major merger triggered the rapid increase , but at @xmath82 the core is still smaller than that of disph runs . second , the core size shrinks and the averaged core entropy decreases in the late phase ( @xmath90 ) . these figures suggest that the low - entropy material is supplied to the central region , most likely via minor mergers in the late phase . the low resolution ssph run follows the evolution of the high resolution one , although its goes between disph runs and the high resolution ssph runs because of lower resolution . in [ sec : majormerger ] and [ sec : minormerger ] , we further investigate the evolution of the cluster s central entropy induced by the major and minor mergers . figure [ fig : entropy : merger : disph ] shows the evolution of the distributions of pressure and entropy in the cluster in the high resolution disph run during the major merger phase ( @xmath91 ) . a smaller cluster consisting of the low - entropy material approaches from the top - right corner ( @xmath92 ) , it merges with the main cluster ( @xmath93 ) and after several crossing times these two clusters completely merge to form a single cluster with the relaxed structure ( @xmath94 and @xmath95 ) . in this run , the entropy at the cluster center increases due to shocks ( see bottom panels ) . before the merging event , the central entropy is lower than @xmath73 , but it becomes higher than @xmath73 after the merger event ( see also figure [ fig : entropy : coreentropy ] , @xmath96 at @xmath97 whereas @xmath98 at @xmath82 ) . the pressure maps are smooth throughout this event ( top panels ) . in the ssph run , we also observe the increase of the central entropy whereas the absolute value is lower than that in the disph run , as we see figure [ fig : entropy : merger : ssph ] . there are sharp edges in the distribution of the low - entropy ( cold ) gas clumps , and therefore the mixing of low- and high - entropy components is much weaker in the ssph run compared to that in the disph run . pressure maps show sharp gaps which are not found in those in the disph run . thus , these gaps are outcomes of the unphysical surface tension of ssph , resulting in the suppression of the entropy generation due to shocks . here , we focus on the late stage of the evolution of the cluster . figure [ fig : entropy : merger : minor ] shows the evolution of the radial entropy distribution . the main sequence of the entropy distribution , where the relative fraction is high , corresponds to the radial entropy profile we saw in , e.g. , figure [ fig : entropy : comparison ] . in addition to the main sequence , there are a number of low entropy components . these low - entropy components are clumps in and around the cluster . the evolution of the cold gas clumps are quite different in the disph run and ssph run . in the case of ssph run ( bottom panels ) , there are many clumps with minimum entropy around @xmath99 , within the distance range @xmath100 . on the other hand , in the case of the disph run , there are only a few clumps within the distance @xmath101 , and their minimum entropy is much higher . thus , in the case of the ssph runs , cold gas clumps survive in the cluster and fall to the cluster center , forming low - entropy core , while in the case of the disph run , cold gas clumps are disrupted before they reach to the center of the cluster . in order to clarify the difference of the late stage evolution of the disph run and that of the ssph run , we here focus on the evolution of one clump . for this analysis , we first pick up low entropy component within @xmath59 . the threshold entropy is @xmath102 which is slightly lower than the core entropy of the disph runs at @xmath61 . with this threshold , we found a number of low entropy clumps . in order to select one representative clump from them , we imposed the following conditions : ( 1 ) the clump is approaching to the cluster center , ( 2 ) the mass is sufficiently large so that we can track its evolution , ( 3 ) the clump reaches to the center of the cluster before @xmath61 , and ( 4 ) the clump can be found in both runs at the same position . the representative clump we picked up is found at @xmath103 and its total mass is @xmath104 at @xmath105 . figure [ fig : target : disph ] shows the evolution of this low - entropy clump in the high - resolution disph run . from the particle distribution maps ( upper panels ) , we can see that this representative clump enters the cluster center forming a bow - shock . its front surface is being stripped due to fluid instabilities , resulting in the complete destruction of the clump by @xmath106 ( recall the blob test in * ? ? ? the pressure distribution across the interface between the clump and the intracluster medium is always smooth . figure [ fig : target : ssph ] shows the evolution of the same clump in the high - resolution ssph run . there is a clear gap both in the particle and pressure distributions in the front of the clump . this gap is induced by the unphysical surface tension , protecting this clump from the development of fluid instabilities at the surface and ram - pressure stripping . thus , the low entropy gas in this clump can sink to the cluster center . we compare the evolutions of this representative clump in disph and ssph runs in figure [ fig : target : evolutions ] . top , middle , and bottom panels are the distance from the cluster center , the size , and the averaged entropy of the gas particles of the clump , respectively . before the pericenter passage , clumps in two runs are almost identical . when it passed the pericenter , the orbital decay starts . the orbital decay in the ssph run is much faster than that in the disph run . clumps expand when passing the pericenter . the clump in the disph run is more extended compared to that in the ssph run . these two results tell us that the clump in the ssph run keeps a compact structure much longer . the increase of the mean entropy starts slightly before the pericenter passage in both runs . at @xmath61 , the mean entropy of the clump in disph is @xmath107 higher than that in ssph . this indicates that the shock heating is more efficient in the disph run . however , behind the fact that ssph has unphysical surface tension , we should say that the shock heating in ssph is more inefficient . disph can capture the intrinsic shocks . this difference in the shock heating efficiency explains why cold gas clumps can reach to the center of the cluster in the ssph run but are disrupted in the disph run . this tendency that the clumps in the ssph run survive longer at the center of the cluster compared to those in the disph run can be seen in figure [ fig : target : stack ] . here , we used subfind clumps ( see appendix [ sec : method : subfind ] ) and stacked data during @xmath108 ( total 17 snapshots ) . generally , as clumps move closer to the center of the cluster , they loose their masses due to tidal and ram - pressure stripping . at the same distance from the cluster center , in particular for @xmath109 , we can see the clear tendency that clumps in ssph are more massive than those in disph . thus , the evolution of the inner part of the cluster strongly affected by the choice of the sph scheme . while clump surviving time is different , there is no significant difference in mass functions with different sph schemes ( see appendix [ sec : results : massfunction ] ) . it has been pointed out by @xcite that the cluster core entropy decreased at the low-@xmath110 with ssph . they measured the evolution of entropy at the central region ( @xmath111 ) of clusters of galaxies in a @xmath4cdm universe . they found that the core entropy of the ssph run decreased continuously for @xmath112 whereas those of amr and sphs runs were roughly constant . although they did not follow the individual clumps , they explained that the change of the central entropy found in low-@xmath110 period is due to the accretion of the low - entropy clumps induced by the minor mergers . our study supports their result and this process works in the evolution of the santa barbara cluster in previous studies as well . recently , the ac term has become widely used in sph simulations in order to remove the unphysical surface tension ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? , we investigate the effects of ac on the cluster formation and evolution . similar studies are found in the literature ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? according to the numerical experiments by @xcite and @xcite , it is expected that the entropy core appears if the ac term is introduced into ssph and the core size and core entropy depend on the maximum value of the conduction control parameter @xmath113 . thus , in this section , we highlight the contribution of @xmath113 to the thermal structure and the entropy profile . here , we adopt the following functional form for the ac : @xmath114 where @xmath115 , @xmath116 , @xmath117 is pressure , and @xmath118 $ ] . following @xcite , we evaluate the ac coefficient of particle @xmath25 , @xmath119 using the following equation ; @xmath120 where @xmath121 is evaluated by the sph manner and @xmath119 is allowed to evolve from @xmath122 to @xmath113 . this ac term is essentially the same as those adopted in the previous studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? we tested several functional forms and switches and found that the conclusion in this subsection does not affected by them . we show five high - resolution ssph runs with different values of @xmath123 : @xmath124 and @xmath125 . figure [ fig : ac : temp ] shows the temperature maps of five runs with the ac term , as well as that of the run without ac . from this figure , we can see that the temperature structure gets blurred when @xmath113 increases . we find that there is a similar effect in both the density and entropy maps . this blurring effect has an influence on the entropy profile of the cluster , as we see next . figure [ fig : ac : entropy ] shows the radial entropy profiles with and without ac . apparently , the entropy profile is affected by ac . the entropy profile with @xmath126 is cuspy ; it has a slightly higher entropy than that without ac in @xmath127 . on the other hand , those with @xmath128 have cores . these core entropies increase with increasing @xmath129 and the increase stalls when @xmath130 . the core entropy with @xmath131 is comparable to those with disph and arepo whereas that with @xmath132 is rather close to that obtained by a mesh code . in our test , unlike previous study @xcite , the core entropies with @xmath130 are slightly lower than those obtained by mesh codes . this difference might come from the detailed implementations . time evolutions of averaged core entropies for five ac runs are shown in figure [ fig : ac : entropy : core ] . the overall evolutions of the runs with @xmath133 are similar to those of disph runs ; the increase of the core entropy is fast until @xmath82 and then it stops . on the other hand , the evolution with @xmath134 is close to that without ac , whereas this run has a slightly higher entropy within @xmath135 . the final core sizes are @xmath136@xmath137 for the runs with @xmath138 ( recall that they are @xmath139 in disph runs ) . although ssph runs with ac ( @xmath138 ) have slightly larger entropy cores , the effect of the ac term looks similar to that of disph ; the essential difference is that ac requires the new free parameter @xmath123 . since the numerical results depend on this parameter , one needs to pay attention to determine its value . it is of course possible that the calibrated @xmath113 for one experiment is inadequate for another experiment .

another possible reason is the problem of the sph method , which might give too much `` protection '' to cold clumps because of the unphysical surface tension induced at contact discontinuities . in this paper , we apply the density independent formulation of sph ( disph ) , which can handle contact discontinuities accurately , to simulations of a cluster of galaxies , and compare the results with those with the standard sph .

the santa barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by eulerian mesh and lagrangian smoothed particle hydrodynamics ( sph ) codes : mesh codes gave a core with a constant entropy whereas sph codes did not . one possible reason for this difference is that mesh codes are not galilean invariant . another possible reason is the problem of the sph method , which might give too much `` protection '' to cold clumps because of the unphysical surface tension induced at contact discontinuities . in this paper , we apply the density independent formulation of sph ( disph ) , which can handle contact discontinuities accurately , to simulations of a cluster of galaxies , and compare the results with those with the standard sph . we obtained the entropy core when we adopt disph . the size of the core is , however , significantly smaller than those obtained with mesh simulations , and is comparable to those obtained with quasi - lagrangian schemes such as `` moving mesh '' and `` mesh free '' schemes . we conclude that both the standard sph without artificial conductivity and eulerian mesh codes have serious problems even such an idealized simulation , while disph , sph with artificial conductivity , and quasi - lagrangian schemes have sufficient capability to deal with it .

gr-qc0107078

i

the de sitter s 1917 solution of the vacuum einstein equations with a positive cosmological constant @xmath0 , in which freely moving test particles accelerate away from one another , played a crucial role in the acceptance of expanding standard cosmological models at the end of the 1920s @xcite . it reappeared as the basic arena in steady - state cosmology in the 1950s , and it has been resurrected in cosmology again in the context of inflationary theory since the 1980 s @xcite . de sitter spacetime represents the of cosmological models with @xmath1 @xcite . since de sitter space shares with minkowski space the property of being maximally symmetric but has a nonvanishing constant positive curvature and nontrivial global properties , it has been widely used in numerous works studying the effects of curvature in quantum field theory and particle physics ( see , e.g. , ref . @xcite for references ) . recently , its counterpart with a constant negative curvature , anti de sitter space , has received much attention again from quantum field and string theorists ( e.g. ref . @xcite ) . these three maximally symmetric spacetimes of constant curvature also played a most important role in gaining many valuable insights in mathematical relativity . for example , both the particle ( cosmological ) horizons and the event horizons for geodesic observers occur in de sitter spacetime , and the cauchy horizons in anti de sitter space ( e.g. ref . the existence of the past event horizons of the worldlines of sources producing fields on de sitter background is of crucial significance for the structure of the fields . the existence of the particle and event horizons is intimately related to the fact that de sitter spacetime has , in contrast with minkowski spacetime , two _ spacelike _ infinities past and future at which all timelike and null worldlines start and end @xcite . since the pioneering work of penrose @xcite it has been well known that minkowski , de sitter , and anti de sitter spacetimes , being conformally flat , can be represented as parts of the ( conformally flat ) einstein static universe . however , the causal structure of these three spaces is globally very different . the causal character of the conformal boundary @xmath2 to the physical spacetime that represents the endpoints at infinity reached by infinitely extended null geodesics , depends on the sign of @xmath0 . in minkowski space , these are _ null _ hypersurfaces future and past null infinity , @xmath3 and @xmath4 . in de sitter space , both @xmath3 and @xmath4 are _ spacelike _ ; in anti de sitter space the conformal infinity @xmath2 is not the disjoint union of two hypersurfaces , and it is timelike . towards the end of his 1963 les houches lectures @xcite , penrose discusses briefly the zero rest - mass free fields with spin @xmath5 in cosmological ( not necessarily de sitter ) backgrounds . at a given point @xmath6 , not too far from @xmath4 , say , the field can be expressed as an integral over quantities defined on the intersection of the past null cone of @xmath6 and @xmath4 ( ) plus contributions from sources whose worldlines intersect the past null cone . however , the concept of at @xmath4 depends on the position of @xmath6 if @xmath4 is spacelike @xcite . if there should be no incoming radiation at @xmath4 with respect to all , all components of the fields must vanish at @xmath4 . imagine that spacelike @xmath4 is met by the worldlines of discrete sources . then there will be points @xmath6 near @xmath4 whose past null cones will not cross the worldlines see fig . [ fig : penrose ] . the field at @xmath6 should vanish if an incoming field is absent . this , however , is not possible since the part of the field of the sources can not vanish there ( as follows from gauss s law ) . penrose @xcite thus concludes that `` if there is a particle horizon , then purely retarded fields of spin @xmath7 do not exist for general source distributions . '' and advanced fields . ] ( the restriction on @xmath5 follows from the number of arbitrarily specifiable initial data for the field with spin @xmath5 see ref . penrose also emphasized that the result depends on the definition of advanced and retarded fields , and `` the application of the result to actual physical models is not at all clear cut ... . '' this observation was reported in a somewhat more detail at the meeting on `` the nature of time '' @xcite , with an appended discussion ( in which , among others , bondi , feynman , and wheeler participated ) but technically it was not developed futher since 1963 . in a much later monograph penrose and rindler @xcite discuss ( see p. 363 in vol . ii ) the fact that the radiation field is defined when @xmath2 is spacelike than when it is null , but no comments or references are given there on the absence of [ fig : penrose ] one of the purposes of this paper is to study the properties of fields of pointlike sources the de sitter universe across spacelike @xmath4 . we thus provide a specific physical model on which penrose s observation can be demonstrated and analyzed . we assume the sources and their fields to be weak enough so that they do not change the de sitter background . in de sitter space we identify retarded ( advanced ) fields of a source as those which are in general nonvanishing only in the future ( past ) domain of influence of the source . as a consequence , purely retarded ( advanced ) fields have to vanish at the past ( future ) infinity . adopting this definition we shall see that indeed purely retarded fields produced by pointlike sources can not be smooth or even do not exist . we find this general conclusion to be true not only for charges ( monopoles and dipoles ) producing electromagnetic fields @xmath8 but , to some degree , also for scalar fields @xmath9 produced by scalar charges . in general , purely retarded fields of monopoles and dipoles become singular on the past horizons ( ) of the particle s worldlines . a singularity at the particle s creation light cone can be understood similarly to a cauchy horizon instability inside a black hole ( see , e.g. , ref . @xcite ) ; an observer crossing the creation light cone sees an infinitely long history of the source in a finite interval of proper time . in the scalar field case ( not considered by penrose ) no constraints exist and retarded fields can be constructed . however , we shall see that the strength of the retarded field ( the gradient of the field ) of a scalar monopole has a @xmath10-function character on the creation light cone so that , for example , its energy - momentum tensor can not be evaluated there . in the electromagnetic case it is not even possible to construct a purely retarded field of a single monopole one has to allow additional sources on the creation light cone to find a consistent retarded solution vanishing outside the future domain of influence of the sources . in both our somewhat different explanation of the nonexistence of purely retarded fields of general sources , and in penrose s original discussion , the main cause of difficulties is the spacelike character of @xmath4 and the consequential existence of the past horizons , respectively , it was only after we constructed the various types of fields produced by sources on de sitter background and analyzed their behavior when we noticed penrose s general considerations in ref . our original motivation has been to understand fields of accelerated sources , and in particular , the electromagnetic field of uniformly accelerated charges in de sitter spacetime . the question of electromagnetic field and its radiative properties produced by a charge with hyperbolic motion in minkowski spacetime has perhaps been one of the most discussed of classical electrodynamics if not of all classical physics in the 20th century . here let us only notice that the december 2000 issue of annals of physics contains the series of three papers ( covering 80 pp . ) by eriksen and grn @xcite , which study in depth and detail various aspects of `` electrodynamics of hyperbolically accelerated charges '' ; the papers also contain many ( though not all ) references on the subject . the electromagnetic field of a uniformly accelerated charge along the @xmath11 axis , say , is symmetrical not only with respect to the rotations around the axis , but also with respect to the boosts along the axis . now spacetimes with boost - rotation symmetry play an important role in full general relativity ( see , e.g. , ref . @xcite , and references therein ) . they represent the only explicitly known exact solutions of the einstein vacuum field equations , which describe moving accelerated singularities or black holes emitting gravitational waves , and which are asymptotically flat in the sense that they admit global , though not complete , smooth null infinity @xmath4 . their radiative character is best manifested in a nonvanishing bondi s news function , which is an analog of the radiative part of the poynting vector in electrodynamics . the general structure of all vacuum boost - rotation symmetric spacetimes with hypersurface orthogonal killing vectors was analyzed in detail in ref . one of the best known examples is the @xmath12-metric , describing uniformly accelerated black holes attached to conical singularities ( or ) along the axis of symmetry . there exists also the generalization of the @xmath12-metric including a nonvanishing @xmath0 @xcite . it has been used to study the pair creation of black holes @xcite ; its interpretation as uniformly accelerating black holes in a de sitter space has been discussed recently @xcite . however , no general framework is available to analyze the whole class of boost - rotation symmetric spacetimes , which are asymptotically approaching a de sitter ( or anti de sitter ) spacetime as it is given in ref . @xcite for @xmath13 . before developing such a framework in full general relativity , we wish to gain an understanding of fields produced by ( uniformly ) accelerated sources in a de sitter background . this has been our original motivation for this work . although it has been widely known and used in various contexts that there exists a conformal transformation between de sitter and minkowski spacetimes , this fact does not seem to be employed for constructing the fields of specific sources . in the following we make use of this conformal relation to find scalar and electromagnetic fields of the scalar and electric charges in de sitter spacetime . the plan of the paper is as follows . in section [ sc : confinv ] , we will analyze the behavior of scalar and electromagnetic field equations with source terms under general conformal transformations . few points contained here appear to be new , like the behavior of scalar sources in a general , @xmath14-dimensional spacetime , but the main purpose of this section is to review results and introduce notation needed in subsequent parts . in section [ sc : minkdscompact ] , the compactification of minkowski and de sitter spacetimes and their conformal properties are discussed . again , all main ideas are known , especially from works of penrose . but we need the detailed picture of the complete compactification of both spaces and explicit formulas connecting them in various coordinate systems , in order to be able to appropriate motion of the sources and their fields from minkowski into de sitter spacetime . the worldlines of uniformly accelerated particles in de sitter space are defined , found , and their relation to the corresponding worldlines in minkowski space under the conformal mapping is discussed in section [ sc : pointpart ] . in general , a single worldline in minkowski space gets transformed into two worldlines in de sitter space . in section [ sc : symfield ] , by using the conformal transformation of simple boosted spherically symmetric fields of sources in minkowski spacetime , we construct the fields of uniformly accelerated monopole sources in de sitter spacetime . in particular , with both the scalar and electromagnetic fields , we obtain what we call they are analytic everywhere outside the sources and can be written as a linear combination of retarded and advanced fields from both particles . from the symmetric fields we wish to construct purely retarded fields that are nonvanishing only in the future domain of influence of particles worldlines . for the scalar field , this is accomplished in section [ sc : sfretfield ] . we do find the retarded field , but its strength contains a @xmath15-function term located on the particle s past horizon ( creation light cone ) . in section [ sc : emretfield ] , the retarded electromagnetic fields are analyzed for free ( unaccelerated ) monopoles ( subsection [ ssc : freemon ] ) , for ( subsection [ ssc : rigdip ] ) , consisting of two close , uniformly accelerated charges of opposite sign , and for ( subsection [ ssc : geoddip ] ) , made of two free opposite charges moving along geodesics . in subsection [ ssc : emconstr ] the role of the constraints , which electromagnetic fields and charges have to satisfy on any spacelike hypersurface , is emphasized . these constraints in de sitter space with compact spatial slicings require the total charge to be zero . as is well known , there can be no net charge in a closed universe ( see , e.g. , ref . however , we find out that the constraints imply even _ local _ conditions on the charge distribution if @xmath4 is spacelike and purely retarded fields are only admitted . in the case of an unaccelerated electromagnetic monopole , we discover that the solution resembling retarded field represents not only the monopole charge but also a spherical shell of charges moving with the velocity of light along the creation light cone of the monopole . the total charge of the shell is precisely opposite to that of the monopole . retarded fields of both rigid and geodesic dipoles blow up along the creation light cone since , by restricting ourselves to the fields nonvanishing in the future domain of influence , we the field lines produced by the dipoles into their past horizon ( creation light cone ) . we do not discuss the radiative character of the fields obtained . the problem of radiation is not a straightforward issue since the conformal transformation does not map an infinity onto an infinity and , thus , one has to analyze carefully the falloff ( ) of the fields along appropriate null geodesics going to future , respectively , past spacelike infinity . a detailed discussion of the radiative properties of the solutions found here and of some additional fields will be given in a forthcoming publication @xcite . a brief discussion in section [ sc : summary ] concludes the paper . some details concerning coordinate systems on de sitter space are relegated to the appendix .

special attention is paid to new effects arising in spacetimes which , like de sitter space , have _ spacelike _ conformal infinities . under the presence of particle and event horizons , purely retarded fields ( appropriately defined ) we construct smooth ( outside the sources ) fields involving both retarded and advanced effects , and analyze the fields in detail in case of ( i ) scalar monopoles , ( ii ) electromagnetic monopoles , and ( iii ) electromagnetic rigid and geodesic dipoles . pacs : 04.20.-q , 04.40.-b , 98.80.hw , 03.50.-z

the scalar and electromagnetic fields produced by the geodesic and uniformly accelerated discrete charges in de sitter spacetime are constructed by employing the conformal relation between de sitter and minkowski space . special attention is paid to new effects arising in spacetimes which , like de sitter space , have _ spacelike _ conformal infinities . under the presence of particle and event horizons , purely retarded fields ( appropriately defined ) become necessarily singular or even can not be constructed at the future light cones of the at which the sources the universe . we construct smooth ( outside the sources ) fields involving both retarded and advanced effects , and analyze the fields in detail in case of ( i ) scalar monopoles , ( ii ) electromagnetic monopoles , and ( iii ) electromagnetic rigid and geodesic dipoles . pacs : 04.20.-q , 04.40.-b , 98.80.hw , 03.50.-z

quant-ph9803014

i

in this paper we are concerned with quantum fields in _ open _ cavities the obvious example of ultimate interest would be electromagnetic fields in optical cavities @xcite and the associated problem of cavity quantum electrodynamics ( cqed ) . such systems are open because energy leaks to the outside ( e.g. , via output coupling ) , and as dissipative systems can not normally be quantized on their own @xcite ; rather , one must also consider the bath into which energy escapes , so that the total universe is conservative . thus such cavities , say of linear dimension @xmath0 , can be embedded in a universe of dimension @xmath1 . one can then quantize on the modes of the universe , which are labeled by a wavenumber @xmath2 spaced by @xmath3 . the field quanta are then created or destroyed by operators @xmath4 and @xmath5 , and higher - order processes involve integrals @xmath6 . on the other hand , these cavities often have a very small amount of leakage , characterized by a parameter @xmath7 , where the quality factor of the cavity can be as high as @xmath8 or more . if this is the case , the intuition developed from a _ closed _ cavity , also of length @xmath0 , should be relevant . a closed cavity is a conservative system , with normal modes ( nms ) labeled by a _ index @xmath9 , where the wavenumber is @xmath10 , @xmath11 . field quanta in such a closed cavity are created and destroyed by operators @xmath12 and @xmath13 , and higher - order processes involve discrete sums @xmath14 . can quantum fields in an _ open _ cavity be described in a similar way in terms of discrete modes and the corresponding operators ? if this is possible , computations will be simplified and will correspond to physical intuition , with each term @xmath15 associated with a cavity mode " . the connection with the limit of a closed cavity ( @xmath16 ) would also become manifest . quantization of a closed system relies on its nms ; the counterparts in an open system are the quasinormal modes ( qnms ) , which are again factorized solutions @xmath17 where @xmath18 because of the loss of energy . each qnm corresponds to a resonance , with a width @xmath19 . the purpose of this paper , in short , is to develop a formalism whereby field quantization can be implemented in terms of these qnms , and to define and study operators @xmath12 , @xmath20 for these modes . specifically , one wishes to express field correlation functions , feynman propagators and other quantities in terms of the qnms . the dissipative nature of the system is then contained in the qnms themselves . the advantages for cqed would be obvious . the simplest phenomenon to which such a formalism can apply is the well - known enhancement ( or suppression ) of spontaneous decay rates when the emitted radiation falls on ( or between ) resonances @xcite . resonance domination of these processes has been discussed starting with the heuristic argument due to purcell @xcite . he proposed that the fermi golden rule should be generalized : the density of states per unit volume , instead of the usual @xmath21 for vacuum ( where @xmath22 is the velocity of light ) , is to be replaced by @xmath23 for a @xmath24-fold degenerate qnm of width @xmath25 in a cavity of volume @xmath26 . this leads to an enhancement factor of @xmath27 for spontaneous emission on resonance , where @xmath28 is the wavelength of light emitted and @xmath29 is the quality factor of the cavity . the essence of this argument is that each resonance counts as one state , i.e. , in a suitable sense it carries unit weight . while intuitively plausible , this statement is difficult to justify formally since the entire concept of a state , i.e. , an nm , falls apart in an open system . however , this argument , and its many variants and extensions , would find natural expression in a framework that quantizes on the qnms , and we shall in particular show explicitly below that each resonance carries unit weight . in section [ class ] , the qnm expansion of _ classical _ fields outgoing from a cavity is reviewed . the classical results may be organized into two levels . first , under conditions to be specified , the green s function @xmath30 can be expanded in terms of qnms . second , one can try to expand the outgoing classical fields @xmath31 in terms of qnms , and to establish a linear space structure similar to that for conservative systems . in order to do so , it turns out to be necessary to make use of a two - component formalism , dealing with @xmath31 and the conjugate momentum @xmath32 at the same time . the linear space formalism is more elegant , but in its simplest form is limited to only 1 d. the quantum formalism can likewise be approached in two ways . in the first , which we shall call the green s function method ( section [ 1comp ] ) , one focuses on @xmath22-number correlation functions and propagators without explicitly expanding the field operator @xmath31 in terms of qnms . the key idea is that the retarded propagator @xmath33 of the quantum theory is exactly the same as the classical green s function @xmath30 , and the latter has a qnm expansion . once @xmath33 is obtained , it is straightforward to derive a qnm expansion for the correlation function @xmath34 as well . in the second , which we shall call the field expansion method , one tries to establish an expansion of the quantum field @xmath31 , in parallel with the linear space structure established for classical fields this allows us to interpret the expansion coefficients @xmath12 and @xmath13 , roughly speaking , as generalized creation and annihilation operators for the discrete qnms @xmath15 . however , before doing so , it has to be recognized that quantum fields can not be constrained by the outgoing wave condition for the simple reason that zero - point ( and thermal ) fluctuations must contain an incoming component . thus , the first step in developing this method , presented in section [ incoming ] , is to generalize the field expansion to handle _ incoming _ waves as well . with this generalization , one can then subject the fields to canonical quantization in section [ quant ] . this is done by starting with the universe , a closed hermitian system for which the quantization is unambiguously defined . then , in parallel with the usual removal of bath oscillators @xcite , the outside degrees of freedom are eliminated from the equations of motion @xcite . the results will be equations of motion and commutation relations for the _ discrete _ operators @xmath12 and @xmath13 , in which the effects of the outside bath are clearly displayed : the loss of energy of each mode by leakage , and the pumping of each mode by the thermal or quantum fluctuations from the outside . the formalism is then used to evaluate the correlation function @xmath34 in section [ correl ] , and the results are compared with those obtained from the green s function method . interestingly , the results appear to be different those derived from the green s function method contain a single sum @xmath35 over the qnms , while the field expansion method yields a double sum @xmath36 with off - diagonal terms . the two are , however , shown to be equal through an identity on @xmath33 . recalling that the expansion of the classical field is unique only when the second component @xmath32 is considered at the same time , we next show that the expansion of the correlation function @xmath34 is also unique if we consider @xmath32 as well , giving the non - diagonal form . the density of states @xmath37 , which is intimately related to the correlation function , is also expressed in terms of qnms ; in particular it is shown that up to corrections of @xmath38 , each resonance carries unit weight in the density of states . the results on the correlation function are then used , in section [ feyn ] , to evaluate and discuss the feynman propagator @xmath39 , which is the fundamental building block for cqed . again , equivalent diagonal and non - diagonal forms are obtained . particular attention is paid to the equal space propagator @xmath40 , whose imaginary part is related to the life - time of an excited atom placed at @xmath41 . this quantity is discussed in the approximation of domination by a single resonance , providing justification for purcell s heuristic argument @xcite on the enhancement of spontaneous decay rates . the advantage of using the non - diagonal expression is again emphasized . in section [ example ] , a very simple example is studied explicitly , and its correlation function and energy density are expressed in terms of a sum over qnm contributions . some final remarks are then given in section [ remarks ] . we stress that this paper is concerned entirely with _ free _ fields , either as a model of the free electromagnetic field in an optical cavity , or as the zeroth - order building blocks in an interacting theory , e.g. , the propagators as ingredients in higher - order feynman diagrams . the development of the interacting theory and its application to cqed phenomena will be given elsewhere @xcite . a partial account of the present theory has been given in @xcite .

the second - quantization of a scalar field in an open cavity is formulated , from first principles , in terms of the quasinormal modes ( qnms ) , which are the eigensolutions of the evolution equation that decay exponentially in time as energy leaks to the outside . thermal correlation functions and cavity feynman propagators are thus expressed in terms of the qnms , labeled by a discrete index rather than a continuous momentum .

the second - quantization of a scalar field in an open cavity is formulated , from first principles , in terms of the quasinormal modes ( qnms ) , which are the eigensolutions of the evolution equation that decay exponentially in time as energy leaks to the outside . this formulation provides a description involving the cavity degrees of freedom only , with the outside acting as a ( thermal or driven ) source . thermal correlation functions and cavity feynman propagators are thus expressed in terms of the qnms , labeled by a discrete index rather than a continuous momentum . single - resonance domination of the density of states and the spontaneous decay rate is then given a proper foundation . this is a first essential step towards the application of qnms to cavity qed phenomena , to be reported elsewhere .

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the @xmath0 and @xmath1 cmds of stars in the thin disk field are shown in the right hand panels of figures 5 and 6 . the @xmath1 cmd in figure 6 is in many respects similar to the cmds of the ngc 55 fields studied by davidge ( 1998 ) , one of which overlaps with the area observed with the cfhtir . in particular , the prominent vertical sequence in the davidge ( 1998 ) cmds have a peak @xmath46band brightness and @xmath36 color that matches the cmd in the right hand panel of figure 6 . however , the cfhtir cmd goes deeper and has less scatter than the davidge ( 1998 ) cmds , due to the larger aperture of the cfht and better image quality . the @xmath1 and @xmath0 cmds both broaden towards the faint end . the standard deviation along the color axis for stars with @xmath27 between 17.75 and 18.25 is @xmath47 mag in @xmath48 and @xmath49 mag in @xmath36 . for comparison , the artificial star experiments predict that random photometric errors introduce a scatter of @xmath50 mag in @xmath48 and @xmath51 mag in @xmath36 at @xmath39 . given that the scatter in both cmds exceeds the random photometric error predictions , it thus appears that the broadening of the cmds near the faint end is due to a real spread in stellar content . later in this section it is demonstrated that this spread is due to agb stars having a range of ages . the objects along the vertical sequence in the right hand panels of figures 5 and 6 with @xmath52 are rsgs , while the sources on this sequence with @xmath53 are evolving on the agb ( see below ) . the nature of the stars in the thin disk field can be investigated further by examining their broad - band near - infrared spectral - energy distributions ( seds ) . this is done in the upper panel of figure 7 , which shows the @xmath54 two - color diagram ( tcd ) of stars in the thin disk with @xmath55 . the majority of stars have seds that are suggestive of m giants , although the seds of some are consistent with k and m dwarfs , indicating that they may be foreground objects . the stars with @xmath56 tend to scatter around the lmc lpv sequence , and there are some objects with @xmath57 , which is a color range dominated by c stars in the lmc ( hughes & wood 1990 ) . the narrow - band co and k continuum observations were used to measure the co index of the brightest stars in the southernmost tile of the cfhtir strip , and the @xmath58 cmd and @xmath59 tcd of stars in the thin disk field are shown in figures 8 and 9 . the stars fall along a single sequence in the cmd , and tend to have co indices that are consistent with them being m giants , although some have co indices that are indicative of rsgs . the brightest star in the thin disk field has a co index near 0 , suggesting that it may be a foreground dwarf . the @xmath60 cmd of the thin disk is shown in the right hand panel of figure 10 . a distance modulus of @xmath61 , based on the rgb - tip brightness measured from the gmos data ( 4.2 ) , has been adopted . foreground reddening is negligible towards ngc 55 ( burstein & heiles 1984 ) , and so no reddening correction was applied . also shown in figure 10 are isochrones from girardi et al . given the overall similarities between ngc 55 and the lmc , a metallicity of z = 0.008 ( [ fe / h ] @xmath62 ) , which is comparable to the peak in the metallicity distribution function of giants in the lmc ( larsen , clausen , & storm 2000 ) , might be appropriate for ngc 55 . in fact , hii regions in ngc 55 have oxygen abundances that are similar to those in the lmc , although ngc 55 may be deficient in nitrogen with respect to the lmc ( webster & smith 1983 ) . tllmann et al . ( 2003 ) argues that the typical disk metallicity of ngc 55 is z = @xmath63 , based on the central hii region . thus , the isochrones plotted in figure 10 have z = 0.008 . the log(t ) = 8.15 isochrone is significant as it marks the onset of the agb , and this isochrone comes close to matching the color of the agb plume in ngc 55 . the predicted peak agb brightness also falls close to a discontinuity in the number counts along the vertical sequence in the cmd , although matching the agb - tip brightness is problematic , as many bright agb stars are photometric variables , with the brightest being observed near the peak of their light curves . the peak agb brightness also has a slight metallicity sensitivity , such that m@xmath64 if z = 0.008 , which is 0.1 mag brighter than the predicted peak z=0.004 brightness . in any event , it appears that a significant number of agb stars in the thin disk of ngc 55 have progenitor masses that are close to that needed for the agb to form . these are accompanied by a sizeable population of fainter agb stars with colors and brightnesses that are consistent with log(t ) @xmath65 , indicating that this portion of ngc 55 has been an area of active star formation for at least the last 1 gyr . the comparison with the isochrones in figure 10 indicate that stars with m@xmath66 are rsgs , and it is evident that the rsg sequence in the thin disk extends to m@xmath67 . this peak rsg brightness is roughly consistent with what is seen in other star - forming disk - dominated systems , although there is considerable galaxy - to - galaxy scatter . late - type galaxies with integrated brightnesses comparable to ngc 55 have peak m@xmath68 stellar brightnesses between 11 and 12 ( e.g. rozanski & rowan - robinson 1994 ) , while the brightest rsgs in the magellanic clouds have m@xmath69 and @xmath70 ( elias , frogel , & humphreys 1985 ) . the age of the brightest rsgs can be estimated from their luminosities . the @xmath46band bolometric correction for rsgs with @xmath70 is bc@xmath71 ( elias et al . 1985 ) , and so rsgs with m@xmath67 have m@xmath72 , or log(l / l@xmath73 . this corresponds to stars with progenitor masses near 25 m@xmath74 , or ages of @xmath75 myr based on the models computed by fagotto et al . the bright rsgs are thus the result of very recent star formation throughout the disk of ngc 55 . the integrated near - infrared broad - band colors of the thin disk were measured to permit comparisons with other galaxies . there are prominent dust lanes in the area separating clusters 1 and 2 , and so the integrated colors were measured in a semi - circular annulus with a width of 10 arcsec that samples the disk to the north , south , and west of cluster 1 , but avoids the region between the two clusters . caution must be exercised in making integrated photometric measurements of this nature , as the presence of a handful of very bright stars may unduly influence aperture photometry . therefore , rather than compute the mean flux in the area described above , the median flux was computed instead . the location of the thin disk field on the tcd is shown in figure 11 , along with models for simple stellar systems from leitherer et al . the location of the thin disk field on the tcd is appropriate for an intermediate - age system . this is not an unexpected result given the preponderance of agb stars in the near - infrared cmds of the thin disk field . the integrated colors of sb(s)m systems in the 2mass large galaxy atlas ( jarrett et al . 2003 ) , as computed from the total brightness measurements , are also shown in figure 11 . the sb(s)m galaxies form a sequence that cuts diagnonally across figure 11 , and the ngc 55 thin disk field falls along this sequence . this comparison indicates that the sed of the thin disk field , and thus the stellar content , is consistent with what is seen in other galaxies of similar morphological type . the outer regions of the thin disk skirt the north east corner of the gmos field , and the @xmath76 cmd of this portion of the gmos dataset is shown in the left hand panel of figure 12 . the @xmath76 cmd of the corresponding region of the control field is shown in left hand panel of figure 13 . the control field contains a mixture of foreground stars and background galaxies , with the latter dominating near the bright end . the gmos data sample intrinsically fainter stars than the cfhtir data because they were recorded with a much larger telescope and have better image quality . the @xmath76 cmd of the thin disk is dominated by rgb and agb stars , with the rgb - tip near @xmath9 ( 4.2 ) ; the properties of the rgb in the thin disk are not discussed here because of the crowded nature of this part of the gmos image , and a detailed discussion of the rgb in ngc 55 is deferred to 4.2 . however , it is worth noting that the color of the rgb in the thin disk portion of the gmos data is similar to what is seen in the thick disk , suggesting similar metallicities . the @xmath76 cmd of the thin disk portion of the gmos field is populated by stars spanning a range of ages , indicating that this portion of the thin disk has formed stars over an extended period of time . a population of blue stars with @xmath77 and @xmath78 is present , and these likely belong to the youngest populations in this portion of ngc 55 . applying the transformation equations from fukugita et al . ( 1996 ) indicates that the brightest blue stars have @xmath79 , or m@xmath80 . these stars are thus near the bright end of the main sequence ( e.g. humphreys & mcelroy 1984 ) , and so may be very massive and have ages consistent with , or even younger than , the rsgs discussed in 3.1 and 3.2 . there are two agb sequences in the gmos thin disk cmd . one sequence forms a plume with @xmath81 that extends roughly from the rgb - tip to @xmath82 , while the other has @xmath83 , and bends towards larger @xmath84 colours , becoming difficult to track when @xmath85 . the nature of these agb sequences is investigated in figure 14 , which shows the @xmath86 cmd of the thin disk and the corresponding portion of the control field . a distance modulus of @xmath61 has been assumed ( 4.2 ) . also shown are z=0.001 and z=0.008 isochrones from girardi et al . ( 2002 ) , which were transformed into the sdss filter system using relations from fukugita et al . ( 1996 ) . the log(t@xmath4 ) = 8.15 isochrone roughly follows the vertical agb plume . given the number of objects in the control field cmd , it is likely that the bulk of stars with m@xmath87 are agb stars in ngc 55 , and not background or foreground contaminants . as for the fainter agb sequence , while the log(t@xmath4 ) = 10 models with z=0.001 and z=0.008 have very different colors , it is clear that the upper envelope of the fainter agb stars on the @xmath86 cmds is consistent with log(t@xmath4 ) = 10.0 . therefore , the thin disk of ngc 55 contains stars that formed early in the life of the galaxy . stars fall between the z=0.008 log(t@xmath4 ) = 8.15 and 10.0 sequences , indicating that star formation continued during intermediate epochs . the bolometric lf of agb stars provides another means of probing the star - forming history of the thin disk of ngc 55 . to construct such a lf from the gmos data , agb stars were selected based on ( 1 ) brightness , such that @xmath88 , so as to be brighter than the rgb - tip , and ( 2 ) color , such that @xmath89 to avoid main sequence stars and include the blue edge of the agb plume . while the thin disk of ngc 55 contains rsgs , these will have @xmath90 , and no such objects are seen in the gmos field . following davidge ( 2003 ) , the @xmath84 colors and @xmath20 brightnesses were transformed into @xmath91 and @xmath92 , where @xmath93 and @xmath92 are in the kron - cousins system , using relations from fukugita et al . ( 1996 ) and the relation between @xmath94 and @xmath91 for solar neighborhood giants from bessell ( 1979 ) . bolometric magnitudes were then computed using @xmath13band bolometric corrections for agb stars from bessell & wood ( 1984 ) . this procedure was also applied to objects in the thin disk portion of the control field , and the result was subtracted from the lf constructed from the ngc 55 thin disk field . the final bolometric agb lf of the thin disk , corrected for objects in the control field , is shown in figure 15 . the lf does not follow a single power - law , and there is a clear break near m@xmath95 . the majority of stars with m@xmath96 are on the agb immediately above and to the right of the rgb - tip in the @xmath76 cmd . the location of these stars on the cmd is consistent with log(t@xmath97 , indicating that they have ` old ' ages ( see above ) . the break in the lf thus suggests that the star formation rate in this region of the ngc 55 disk dropped at some point during the past @xmath5 gyr , and that a large fraction of the stars in the thin disk formed during early epochs . davidge ( 1998 ) investigated the bolometric lf of two areas in the disk of ngc 55 , and it is of interest to see if a break occurs in those lfs near m@xmath95 . unfortunately , after adjusting the lfs in figure 11 of davidge ( 1998 ) to the distance modulus adopted here , incompleteness becomes significant when m@xmath98 , and so these data do not go faint enough to determine if a break is present . pritchet et al . ( 1987 ) also investigated the bolometric lf of agb stars in ngc 55 . after adjusting their lf to the distance modulus adopted here , the faint limit of the pritchet et al . ( 1987 ) lf is m@xmath99 , and so these data also do not go faint enough to sample the discontinuity seen in the lf constructed from the gmos data . the @xmath0 and @xmath1 cmds of clusters 1 and 2 are shown in the left hand and middle panels of figures 5 and 6 . the cluster cmds show more scatter and are shallower than the thin disk cmds , due to the higher stellar densities in the clusters . indeed , cluster 1 is more crowded than cluster 2 , and the cmds of the former show a greater amount of scatter than the latter . it is likely that some of the stars in the cluster cmds may be interlopers from the thin disk field . this being said , the brightest stars in the clusters are @xmath42 mag in @xmath27 fainter than in the thin disk field , and this leads to only a modest difference in age ( see below ) . the @xmath54 tcd of stars with @xmath55 in both clusters is shown in the upper panel of figure 7 . as was the case in the thin disk , the majority of stars within the cluster boundaries have near - infrared seds that are similar to those of solar neighborhood m giants . there is considerable scatter among stars in both clusters with @xmath100 , which is the color interval occupied by lpvs in the lmc . some stars in cluster 1 fall in a region of the @xmath54 tcd where @xmath57 , indicating that they may be c stars . the @xmath58 cmds of stars in clusters 1 and 2 are shown in the left hand and middle panels of figure 8 , while the @xmath59 tcd of stars with @xmath34 in clusters 1 and 2 is shown in the upper panel of figure 9 . the brightest stars in clusters 1 and 2 define a relatively tight sequence in figure 8 , with @xmath101 when @xmath34 . the stars in cluster 2 fall in a region of the @xmath59 tcd that is occupied by m giants , while many of the stars in cluster 1 have co indices that are consistent with them being rsgs . there is one star in cluster 1 with @xmath102 that has a co index that is comparable to those of milky - way c stars . finally , the brightest star in cluster 2 has co = 0.0 , which is much weaker than the co indices of the majority of stars in either cluster . based on this weak co index , it is likely that this object is a foreground star , and not a real member of the cluster . the @xmath60 cmds of clusters 1 and 2 are shown in the left hand and middle panels of figure 10 . the ideal means of measuring the age of clusters 1 and 2 would be to use the brightness of the main sequence turn - off . while some bright blue stars are seen in the cmds of both clusters near m@xmath103 , there are not enough objects on which to base a reliable age determination , and these could be blue supergiants . therefore , as with the thin disk field , the ages of clusters 1 and 2 are estimated from the properties of the rsgs . the rsgs with m@xmath104 have m@xmath105 , or log(l / l@xmath106 . this corresponds to stars with progenitor masses near 20 m@xmath74 , or an age of @xmath5 myr based on the fagotto et al . ( 1994 ) models . hence , although the brightest rsgs in the thin disk field are @xmath42 mag brighter in @xmath27 than their counterparts in clusters 1 and 2 , this leads to only a 2 myr difference in age . the young age inferred for these clusters is consistent with them being sites of h@xmath45 emission ( tllmann et al . 2003 ) . the integrated near - infrared photometric properties of clusters 1 and 2 can be used to check the age estimated from the rsgs . following the procedure described in 3.1 for the thin disk field , the integrated colors of the clusters were computed from median flux measurements to suppress the effects of individual bright stars . the background was measured in a 2 arcsec wide annulus immediately around each cluster . the location of clusters 1 and 2 on the @xmath54 tcd is shown in figure 11 . a comparison with models from leitherer et al . ( 1999 ) indicates that both clusters have near - infrared seds that are consistent with them being simple stellar systems with log(t@xmath107 and a@xmath108 between 1 and 2 magnitudes ; thus , the integrated near - infrared colors of cluster 1 and 2 are broadly consistent with the age inferred from the rsgs . davidge ( 2004 ) detected a population of young clusters near the center of the star - forming galaxy ngc 3077 . the young ngc 3077 clusters discovered by davidge ( 2004 ) , which are also shown in figure 11 , form a relatively tight sequence on the tcd that roughly parallels the reddening vector . clusters 1 and 2 have near - infrared seds that are similar to those of the ngc 3077 clusters , but with 1 2 magnitudes less extinction in @xmath109 . tllmann et al . ( 2003 ) discovered two star - forming regions that have projected distances of 1 1.5 kpc from the ngc 55 disk plane . one of these , ehr 1 , falls within the boundaries of the thin disk region and was imaged with cfhtir . individual sources were not resolved in this object . however , the integrated brightness of ehr 1 in a 2.5 arcsec radius aperture is @xmath110 , with @xmath111 and @xmath112 . the near - infrared sed of ehr 1 is consistent with it being a very young system , and this is demonstrated in figure 11 , which shows the location of ehr 1 on the near - infrared tcd . ehr 1 falls on the ngc 3077 young cluster sequence in figure 11 , and a comparison with the leitherer et al . ( 1999 ) models indicates that ehr 1 has an age of a few myr , with a@xmath113 magnitudes .

comparisons with stellar evolution models suggest that the brightest rsgs have an age near 8 myr . a well - defined plume , which stellar evolution models suggest contains stars with masses near the rsg it is concluded that star formation in the thin disk of ngc 55 has ocurred at a significant rate for at least the past 0.1 0.2 gyr , and this is consistent with other indicators . the mean metallicity of rgb stars is in excellent agreement with that measured in the extraplanar hii regions ehr 1 and 2 , suggesting that the age - metallicity relation in this part of ngc 55 has been flat for at least a few gyr .

the stellar content of the nearby sb(s)m galaxy ngc 55 is investigated using images obtained with the gemini south and canada - france - hawaii telescopes . the and color - magnitude diagrams ( cmds ) of stars near the plane of the disk reveal signatures of large scale star formation during recent and intermediate epochs in the form of red supergiants ( rsgs ) with m , and an asymptotic giant branch ( agb ) that peaks near m . comparisons with stellar evolution models suggest that the brightest rsgs have an age near 8 myr . a well - defined plume , which stellar evolution models suggest contains stars with masses near the rsg agb transition , is detected in cmds constructed both from infrared and visible wavelength observations . it is concluded that star formation in the thin disk of ngc 55 has ocurred at a significant rate for at least the past 0.1 0.2 gyr , and this is consistent with other indicators . the near - infrared spectral - energy distribution ( sed ) of the integrated light near the center of the galaxy is consistent with that in other magellanic irregular galaxies , indicating that the star - forming history of ngc 55 , when averaged over timescales of 0.1 1 gyr , has likely not been peculiar when compared with other late - type systems . evidence is also presented that the disk contains a large population of old ( log(t ) ) stars , and it is argued that a stable disk has been in place in ngc 55 for a significant fraction of the age of the universe . at projected distances in excess of 2 kpc off of the disk plane the brightest agb stars have ages gyr . thus , despite indications that dust and gas are present in the envelope surrounding the ngc 55 disk , the agb content suggests that recently formed stars do not occur in large numbers in the extraplanar region . the colors of the rgb in the extraplanar region are consistent with [ fe / h ] between 2.2 and 0.7 , with the majority of stars having [ fe / h ] , and the mean metallicity inferred from the rgb color does not change with distance above the disk plane . thus , the stellar component in the extraplanar envelope is well mixed , at least in terms of metallicity . the mean metallicity of rgb stars is in excellent agreement with that measured in the extraplanar hii regions ehr 1 and 2 , suggesting that the age - metallicity relation in this part of ngc 55 has been flat for at least a few gyr . finally , the rgb - tip occurs near in the extraplanar region , and a distance modulus of 26.5 is computed from this feature .

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the @xmath0 , and @xmath1 cmds of the thick disk and halo portions of the cfhtir strip are shown in figures 16 and 17 . there is a concentration of stars in the thick disk cmds when @xmath114 , which is due to stars evolving on the agb . in constrast , the cmds of the halo region lack an obvious concentration of agb stars . the numbers of stars with @xmath115 in the thick disk and halo cmds are similar , suggesting that the objects at this brightness likely do not belong to ngc 55 . this is consistent with the near - infrared seds of these objects . the @xmath54 tcd of stars with @xmath55 in the thick disk and halo is shown in the lower panel of figure 7 . while the majority of stars in the thin disk have near - infrared seds that are consistent with them being evolved giants , and hence are likely at the distance of ngc 55 , many of the bright sources in the thick disk and halo regions fall systematically below the giant sequences on the tcd . in fact , the stars with @xmath116 occupy a portion of the tcd that suggests they are k and m main sequence stars , and so are likely foreground objects . some of the brighter objects in the halo field have obvious extended morphologies , indicating that they are background galaxies . the @xmath60 cmds of the thick disk and halo are shown in figure 18 . based on the number of objects in each cmd , an excess population of stars in the thick disk with respect to the halo region only occurs when m@xmath117 , and so m@xmath118 is adopted as the agb - tip brightness in the thick disk . the majority of resolved rgb stars in this portion of ngc 55 have metallicities between z = 0.001 and 0.004 ( 4.2 ) , and so the isochrones in figure 18 have these metallicities . given an agb - tip brightness of m@xmath118 , the isochrones in figure 18 indicate that the resolved stars in the thick disk have an age that is close to log(t@xmath4 ) = 10 . the stellar contents of the thin disk and the thick disk thus appear to differ , in that the latter lacks the young and intermediate age populations seen in the former . the @xmath76 cmds of the thick disk and halo portions of the ngc 55 gmos field are shown in the middle and right hand panels of figure 12 ; the cmds of the corresponding regions of the control field are shown in figure 13 . the number of objects with @xmath119 in the control field is comparable to that in the thick disk and halo cmds , indicating that many of the sources with @xmath119 in the thick disk and halo are probably foreground and background objects . the bright main sequence stars and vertical agb plume that were conspicuous in the thin disk are thus abscent in detectable numbers , and this is consistent with what is seen in the cfhtir data ( 4.1 ) . stars evolving on the rgb and agb dominate the faint end of the thick disk and halo cmds . the giant branch in the thick disk is much wider than predicted solely from photometric errors . indeed , the standard deviation in @xmath84 for stars with @xmath20 between 22.75 and 23.25 is @xmath120 mag , whereas the artificial star experiments predict a scatter due to photometric errors of only @xmath121 magnitudes . thus , there is a real variation in stellar content among bright giants , and later in this section this is shown to be due to a spread in metallicity . the brightness of the rgb - tip is a standard candle , and the rgb - tip brightness was measured from the thick disk data . the number counts in the thick disk cmd drop noticeably near @xmath122 , indicating that the rgb - tip occurs close to this brightness . a better estimate of the rgb - tip brightness can be obtained from the @xmath20 lf of rgb stars in the thick disk , which is shown in figure 19 . the final lf was constructed by restricting the sample to objects with @xmath84 between 0.5 and 1.5 and then correcting for objects falling in the same color interval in the corresponding region of the control field . the conventional means of measuring the brightness of the rgb - tip is to convolve the lf with a stobel edge - detection kernel ( e.g. lee , freedman , & madore 1993 ) . however , given the significant spray of agb stars above the rgb - tip , it was decided to apply a different technique , which judges the position of the rgb - tip based on the departure from the power - law nature of the lf , as defined by rgb stars below the rgb - tip . the ngc 55 lf shown in the lower panel of figure 19 follows a power - law at the faint end . a power - law was fit to the lf bins between @xmath123 and 25.0 , which is an interval where the uncertainties in individual bins are modest and the artificial star experiments predict that incompleteness is not significant . a least squares fit to the thick disk lf entries in this brightness interval gives an exponent @xmath124 , which is within the range seen in globular clusters ( e.g. davidge 2000 ) . the fitted power - law is compared with the data in the lower panel of figure 19 . the lf departs significantly from the fitted relation at @xmath125 , and this is adopted as the brightness of the rgb - tip . lee et al . ( 1993 ) calibrated the rgb - tip as a standard candle in the i filter . following davidge et al . ( 2002 ) , the relations computed by fukugita et al . ( 1996 ) were used to transform the @xmath20 brightness of the rgb - tip into i , with the result that i@xmath126 for ngc 55 . adopting m@xmath127 ( lee et al . 1993 ) , which holds for populations with [ fe / h ] @xmath128 , then the distance to ngc 55 computed from the rgb - tip is @xmath129 . no correction is applied for foreground extinction , as this appears to be small ( burstein & heiles 1984 ) . with the distance to ngc 55 established from the brightness of the rgb - tip then the metallicity of the thick disk and halo can be estimated from the colors of rgb stars in the @xmath76 cmd . in figure 20 the @xmath130 cmd of rgb stars in the thick disk and halo are compared with log(t@xmath4 ) = 10 sequences from girardi et al . ( 2002 ) , transformed into the sdss system using relations from fukugita et al . the isochrones match the rgb - tip brightness and shape of the upper rgb in both the thick disk and halo regions . the majority of rgb stars in the thick disk appear to have a metallicity between z = 0.001 and z = 0.003 , although there are also stars that may be as metal - poor as z = 0.0001 . the rgb stars in the halo have a similar range of metallicities to those in the thick disk , and so there is no evidence for a metallicity gradient off of the disk plane . there is a spray of objects above the rgb - tip in the thick disk cmd , and these are analogous to the agb stars in the @xmath1 cmd that were discussed in 4.1 . the agb stars in the left hand panel of figure 20 are nicely bracketed by the log(t@xmath4 ) = 10 isochrones with z=0.001 and z = 0.004 ; in fact , the upper envelope of the agb population in the left hand panel of figure 20 is well matched by a line that connects the ends of the z=0.001 and z=0.004 log(t@xmath4 ) = 10.0 agb sequences . the inferred old age for the agb stars is consistent with what was established from the cfhtir data in 4.1 . what is the uncertainty in the age estimate determined from the comparisons in figure 20 ? the age estimate is subject to uncertainties ( 1 ) in the models , ( 2 ) in the ability to locate the upper envelope of the agb population on the cmd due to photometric variability , and ( 3 ) in the assumed distance to ngc 55 . the uncertainties in the models are difficult to assess , and an error of @xmath131 mag is ( arbitrarily ) assigned to this component . the scatter in the upper envelope of the thick disk agb sequence on the cmd suggests that stellar variability may contribute a @xmath131 mag uncertainty . the errors in the distance estimates are more easily quantifiable , and are likely on the order of @xmath131 mag , which is one half of the binning interval in figure 19 . if all three components are combined in quadrature then the total uncertainty in m@xmath132 is @xmath133 mag . the z = 0.001 agb isochrones are more - or - less vertical in the @xmath86 cmd , and hence are well suited for assessing how an error in the agb - tip brightness propogates into an uncertainty in the age estimate . the z=0.001 sequences from girardi et al . ( 2002 ) indicate that a 0.2 mag change in m@xmath132 translates into a 0.1 dex change in log(t@xmath4 ) near log(t@xmath4 ) = 10 , and so a @xmath131 uncertainty is assigned to log(t@xmath4 ) estimated from the agb - tip brightness . a lower limit to the age of the dominant stellar component in the envelope surrounding ngc 55 is thus 8 gyr , while an upper limit is 13 gyr . while an agb sequence is not seen above the rgb in the halo cmd , this does not mean that these stars are abscent ; rather , they may have a density that is sufficiently low to make their detection difficult . in fact , the @xmath20 lf of stars in the halo , corrected for sources in the control field , contains a modest population of stars that extend up to 0.6 mag in @xmath20 above the rgb - tip , indicating that agb stars brighter than the rgb - tip do occur in this field . based on the similar metallicities and age properties inferred from the cmds , it appears that the halo and thick disk regions as defined here are not physically distinct entities ; rather , they are part of the same structure . dalcanton & bernstein ( 2002 ) find that the envelopes that surround their sample of undisturbed , bulgeless , edge - on disk galaxies have many properties in common . in particular , there is a distinct break between the main disk bodies and the surrounding envelopes , while the integrated colors of the thick disks indicate that the envelopes tend to have a metallicity that is comparable to the thin disk , and contain stars that formed @xmath134 gyr in the past . finally , the envelopes also tend to be homogeneous stellar systems , in the sense that there is no evidence for age or metallicity gradients at moderately large distances off of the disk plane ( e.g. figure 10 of dalcanton & bernstein 2002 ) . while the properties of the envelope around ngc 55 are reminiscent of those in the dalcanton & bernstein ( 2002 ) sample , few envelopes in that sample have [ fe / h ] as low as @xmath135 , and ages as old as 10 gyr . the dalcanton & bernstein ( 2002 ) analysis relies on integrated photometric measurements , and so may be affected by the well known age - metallicity degeneracy . this degeneracy works in the sense that higher metallicities may be misinterpreted as older ages , with the result that if metallicity is overestimated then ages will be underestimated . thus , if the metallicities of the envelopes in the dalcanton & bernstein ( 2002 ) sample were fixed at lower values then older ages would be predicted . this would then give results that are consistent with the ngc 55 envelope properties established here from resolved stars .

kpc off of the disk plane the brightest agb stars have ages gyr . the colors of the rgb in the extraplanar region are consistent with [ fe / h ] between 2.2 and 0.7 , with the majority of stars having [ fe / h ] , and the mean metallicity inferred from the rgb color does not change with distance above the disk plane . thus , the stellar component in the extraplanar envelope is well mixed , at least in terms of metallicity .

the stellar content of the nearby sb(s)m galaxy ngc 55 is investigated using images obtained with the gemini south and canada - france - hawaii telescopes . the and color - magnitude diagrams ( cmds ) of stars near the plane of the disk reveal signatures of large scale star formation during recent and intermediate epochs in the form of red supergiants ( rsgs ) with m , and an asymptotic giant branch ( agb ) that peaks near m . comparisons with stellar evolution models suggest that the brightest rsgs have an age near 8 myr . a well - defined plume , which stellar evolution models suggest contains stars with masses near the rsg agb transition , is detected in cmds constructed both from infrared and visible wavelength observations . it is concluded that star formation in the thin disk of ngc 55 has ocurred at a significant rate for at least the past 0.1 0.2 gyr , and this is consistent with other indicators . the near - infrared spectral - energy distribution ( sed ) of the integrated light near the center of the galaxy is consistent with that in other magellanic irregular galaxies , indicating that the star - forming history of ngc 55 , when averaged over timescales of 0.1 1 gyr , has likely not been peculiar when compared with other late - type systems . evidence is also presented that the disk contains a large population of old ( log(t ) ) stars , and it is argued that a stable disk has been in place in ngc 55 for a significant fraction of the age of the universe . at projected distances in excess of 2 kpc off of the disk plane the brightest agb stars have ages gyr . thus , despite indications that dust and gas are present in the envelope surrounding the ngc 55 disk , the agb content suggests that recently formed stars do not occur in large numbers in the extraplanar region . the colors of the rgb in the extraplanar region are consistent with [ fe / h ] between 2.2 and 0.7 , with the majority of stars having [ fe / h ] , and the mean metallicity inferred from the rgb color does not change with distance above the disk plane . thus , the stellar component in the extraplanar envelope is well mixed , at least in terms of metallicity . the mean metallicity of rgb stars is in excellent agreement with that measured in the extraplanar hii regions ehr 1 and 2 , suggesting that the age - metallicity relation in this part of ngc 55 has been flat for at least a few gyr . finally , the rgb - tip occurs near in the extraplanar region , and a distance modulus of 26.5 is computed from this feature .

astro-ph0501173

c

moderately deep red and near - infrared images that were obtained with the cfhtir imager on the cfht and the gmos imaging spectrograph on gs have been used to probe the stellar content of the nearby galaxy ngc 55 . the data are used to investigate the stellar content along the disk plane and in the extraplanar region using evolved red stars as probes . the results of this investigation provide insight into the past history of the galaxy . in 3.1 it was shown that the integrated near - infrared sed of the disk near the center of ngc 55 is similar to the seds of other magellanic irregular galaxies , and is consistent with significant recent star formation . in fact , the thin disk field contains a population of rsgs that have brightnesses consistent with very young ages , indicating that the region near the center of ngc 55 has been the site of large scale star formation within the past 8 myr . there are also two large clusters that have ages near 10 myr . the cfhtir data samples the disk near the main light concentration in ngc 55 . the presence of very young stars in this portion of the ngc 55 disk may not be surprising if the main light concentration is a bar viewed end - on ( de vaucouleurs 1961 ) , as the ends of bars in magellanic - type galaxies tend to be sites of very recent star formation ( elmegreen & elmegreen 1980 ) . a substrate of luminous agb stars is seen throughout the thin disk , and comparisons with models from girardi et al . ( 2002 ) indicate that these objects span a range of ages . a prominent feature in the cmds constructed from both the cfhtir and gmos data is a plume that appears to contain stars with masses close to that needed to commence evolution on the agb . a plume of stars with a similar color and peak brightness is seen in the cmds of the two ngc 55 fields studied by davidge ( 1998 ) . one of the davidge ( 1998 ) fields samples a region of the ngc 55 disk that is , like the regions observed with gmos , well offset from the optical center of the galaxy . thus , the stars on the agb plume occur throughout the disk of ngc 55 . the detection of large numbers of stars with masses near the rsg agb evolutionary transition provides clues into the star - forming history of ngc 55 during recent epochs . one possibility is that ngc 55 is being viewed at a fortuitous time following an isolated episode of star formation when the rsg agb transition just happens to be occuring . however , it is more likely that the detection of significant numbers of stars with masses close to those needed to evolve on the agb indicates that there has been vigorous star formation during the past 0.1 0.2 gyr . in fact , data from other sources indicate that the sfr in ngc 55 during the past 0.1 - 1 gyr has been at least as high as that at the present day , and that it is more likely that the star formation rate ( sfr ) of ngc 55 has recently dropped . a number of indicators support a present - day sfr of at most a few tenths of a m@xmath74 year@xmath30 . the fir luminosity and radio continuum emission from ngc 55 suggest that the present - day sfr is 0.3 m@xmath74 year@xmath30 ( dettmar & heithausen 1989 ) , while the integrated h@xmath45 flux of ngc 55 is consistent with a sfr of 0.16 m@xmath74 year@xmath30 ( ferguson et al . the sfr computed from x - ray flux measurements ranges between 0.06 and 0.18 m@xmath74 year@xmath30 , based on equations 14 and 15 of ranali , comastri , & setti ( 2003 ) . recent fir flux measurements from the spitzer space telescope yield a sfr of 0.22 m@xmath74 year@xmath30 ( engelbracht et al . these various estimates of the present - day sfr are significantly lower than what is computed from the blue luminosity , which is a measure of the sfr averaged over the past gyr , and which predicts a sfr of 1.6 m@xmath74 year@xmath30 in ngc 55 ( dettmar & heithausen 1989 ) . further evidence that the sfr has dropped during the past @xmath136 years comes from the high sne rate needed to explain the extended x - ray emission around the galaxy ( oshima et al . there may have been brief lulls in star - forming activity , as tllmann et al . ( 2003 ) argue that breaks in the sfr may be needed to allow gas in the extraplanar region to cool sufficiently for stars to form , as has happened in ehr 1 and 2 . the stellar content throughout the thin disk of ngc 55 appears to be well mixed . for example , the distribution of the @xmath36 colors of stars with @xmath27 between 16.0 and 17.5 does not change with distance from the disk plane ; a gradient in the color distribution would be expected if mean age changed with height above the disk plane . the ratio of objects with seds consistent with m giants to stars with seds similar to lmc lpvs also does not change with distance above the disk plane in the thin disk region . adopting @xmath137 as the dividing line between m giants and lpvs in the tcd , then the ratio of m giants to lpvs is 11/8 @xmath138 in the portion of the thin disk between 1.1 and 2.2 arcmin from the disk plane , compared with 162/125 @xmath139 for stars within 1.1 arcmin of the disk plane . the similarity in the stellar contents of the regions probed with the cfhtir , which samples the disk plane , and gmos , which samples the edge of the thin disk , further suggests that the disk of ngc 55 has experienced a remarkably uniform star - forming history . however , it should be kept in mind that ngc 55 is viewed nearly edge - on , and so any given site line samples stars from a large range in galactocentric distances . a high inclination can thus introduce an apparent uniformity in stellar content , as the star - forming history is smoothed over large portions of the galaxy . this also makes it easier to detect rare features in cmds , such as the onset of the agb , as the projected density of objects is higher than in other orientations . we close this portion of the discussion by noting that the contribution made by c stars to the total agb luminosity peaks near log(t@xmath140 in moderately metal - poor systems ( maraston 1998 ) ; therefore , a large c star population might be expected in ngc 55 based on the star - forming history inferred from various sources , including the cfht and gmos data . however , figure 9 of pritchet et al . ( 1987 ) suggests that the c star frequency in ngc 55 may be relatively low given the integrated brightness of the galaxy . it is thus worth noting that candidate c stars with @xmath55 are seen in the @xmath54 tcd of thin disk stars . these c stars may well be the tip of the iceberg , and their presence suggests that a rich c star population remains to be discovered in the disk of ngc 55 . the cfhtir and gmos data sample the extraplanar stellar content of ngc 55 , and both datasets support an old age for this region of the galaxy ; more specifically , based on the peak brightnesses of stars on the agb there is no evidence for a young or intermediate age component outside of the region that is defined here as the thin disk . this result is perhaps surprising given the presence of gas and dust outside of the disk plane ( e.g. ferguson et al . 1996 ) . of course , the extraplanar region is not completely devoid of young stars , as there are some pockets of recent star formation ( tllmann et al . nevertheless , it appears that extraplanar star - forming regions like ehr 1 and ehr 2 have not contributed significantly to the stellar content of the envelope surrounding ngc 55 . the metallicities of ehr 1 and 2 suggest that they formed from material that did not originate in the thin disk ( tllmann et al . in fact , the metallicities of these hii regions are in excellent agreement with the mean metallicity among rgb stars in the extraplanar region . this suggests that the age - metallicity relation in the extraplanar region may have been flat over a large fraction of the age of the universe , after an initial period of rapid enrichment ( see below ) . this could occur if the envelope has not been the site of large scale star formation for the past 10 gyr or if it is unable to retain processed material . another possibility is that there has been infall of metal - poor material at a rate that has fortuitously maintained the mean metallicity of the gas in the extraplanar region at a constant value . the results of this study have implications for understanding the early evolution of ngc 55 in the context of the hierarchal formation model , although whether the envelope formed from the disruption of an early proto - disk or from the violent relaxation of proto - galactic gas clouds remains a matter of speculation . the absence of obvious metallicity gradients indicates that the envelope formed in a highly coherent manner or has been well mixed since its formation . it is perhaps worth noting that the mean metallicity of the envelope around ngc 55 coincides with the point where the dynamical properties of the globular cluster system in the milky - way changes from orbits that are indicative of a pressure - supported system to one that has a significant rotational component ( zinn 1985 ) , and this provides indirect evidence for a disk origin . efforts to study the shape of the envelope will help constrain the origin of this structure . if the envelope originated from the disruption of a protodisk then it should not have a markedly flattened distribution . the issue of how the envelope formed notwithstanding , that the rgb stars in the extraplanar region are old and typically have [ fe / h ] @xmath141 indicates that they likely formed from material that experienced rapid early enrichment . this is broadly consistent with the age - metallicity relation of the lmc during early epochs , which de vaucouleurs ( 1961 ) argues is a galaxy that is structurally similar to ngc 55 . the lmc age - metallicity relation climbs from [ fe / h ] @xmath142 to 1 over a 3 gyr period during early epochs ( hill et al . 2000 ) , and an age dispersion of this size would affect the agb - tip brightness in @xmath27 in ngc 55 by only @xmath143 mag ( 4.2 ) , making it difficult to detect . if the age - metallicity relations of ngc 55 and the lmc are similar then the absence of stars with [ fe / h ] @xmath144 would indicate that there should be no stars with ages less than @xmath5 gyr in the envelope around ngc 55 , and this is consistent with the age inferred from the agb - tip . the chemical content of stars in the envelope around ngc 55 will provide additional clues into the origin of this structure . while there are as yet no abundance measurements of stars in the outer envelope of ngc 55 , measurements of this nature have been made for metal - poor giants in the lmc , and the results are of interest in the context of the early evolution of magellanic irregular galaxies . hill et al . ( 2000 ) find that the metal - poor giants in the lmc fall along the trend between [ o / h ] and [ fe / h ] defined by galactic giants , suggesting that the metal - poor stars in the lmc may have formed in an environment similar to that from which the galactic halo formed . however , the number of lmc giants in the hill et al . ( 2000 ) sample is tiny , amounting to only four objects . the globular cluster content of ngc 55 may present a problem for models in which the envelope around ngc 55 formed as the result of an early , violent collapse . if globular clusters form in supergiant molecular clouds ( e.g. harris & pudritz 1994 ) that are associated with the major collapse events that are expected to produce rapid chemical enrichment , then a number of globular clusters might be expected in ngc 55 given the age and metallicity properties of stars in the envelope . indeed , the lmc contains ten globular clusters with ages older than 10 gyr ( e.g. geisler et al . 1997 ) , and the majority of these are metal - poor , with [ fe / h ] @xmath145 ( e.g. hill et al . 2000 ) . it appears that ngc 55 does not contain a large cluster population , and may have a globular cluster content that differs from that of the lmc . da costa & graham ( 1982 ) found three cluster candidates , one of which was identified as a young globular cluster , while liller & alcaino ( 1983 ) found five candidate clusters . however , the nature of the clusters detected in these early surveys is in doubt , as beasley & sharples ( 2000 ) obtained spectra of a number of globular cluster candidates and concluded that the vast majority of these are background galaxies , with only one being a bona fide globular cluster . the origin of the envelope around ngc 55 notwithstanding , the absence of a large population of young or intermediate age stars in the envelope indicates that the disk of ngc 55 has not been disrupted by major merger activity for a large fraction of the hubble time ; the conditions for a stable disk to form in this galaxy were evidently in place early on . in fact , ngc 55 is in a relatively isolated environment . it is one of four galaxies that are on the near side of the sculptor group , and the largest member of this mini - group is ngc 300 . the crossing time of this four galaxy ensemble is almost 19 gyr ( karachentsev et al . 2003 ) ; consequently , the number of galaxy - to - galaxy interactions is expected to be small . nevertheless , there are hints that ngc 55 may have been involved in recent interactions . the hi disk of ngc 55 is warped ( hummel et al . 1986 ) , while ngc 55 is a barred galaxy , and bars are difficult to form without an external trigger , such as tidal interactions ( e.g. bottema 2003 ) . this being said , the bar of the lmc contains a large population of stars with ages of at least a few gyr ( ardeberg et al . 1997 ; smecker - hane et al . 2002 ) , suggesting that the bars in magellanic irregular galaxies can be long - lived , and so may not be indicative of recent interactions . the rgb - tip occurs near @xmath9 in the thick disk of ngc 55 , indicating that the distance modulus of this galaxy is 26.5 . this distance measurement is likely not affected by dust internal to ngc 55 , as the brightness of the rgb - tip does not change with distance off of the disk , and any dust will likely be concentrated close to the disk plane . the distance modulus of ngc 55 measured from the rgb - tip is larger than that computed previously from other indicators ( 1 ) . nevertheless , given the distances to other nearby galaxies in this part of the sky ( karachentsev et al . 2003 ) , the distance estimated from the rgb - tip still makes ngc 55 one of the nearest members of the sculptor group . oshima , t. , mitsuda , k. , ota , n. , & yamasaki , n. y. 2003 in proceedings of the workshop on galaxies and clusters of galaxies , held at shunzenji , october 2002 , japan society for the promotion of science , p. 33

the near - infrared spectral - energy distribution ( sed ) of the integrated light near the center of the galaxy is consistent with that in other magellanic irregular galaxies , indicating that the star - forming history of ngc 55 , when averaged over timescales of 0.1 1 gyr , has likely not been peculiar when compared with other late - type systems . evidence is also presented that the disk contains a large population of old ( log(t ) ) stars , and it is argued that a stable disk has been in place in ngc 55 for a significant fraction of the age of the universe . at projected distances in excess of 2 finally , the rgb - tip occurs near in the extraplanar region , and a distance modulus of 26.5 is computed from this feature .

the stellar content of the nearby sb(s)m galaxy ngc 55 is investigated using images obtained with the gemini south and canada - france - hawaii telescopes . the and color - magnitude diagrams ( cmds ) of stars near the plane of the disk reveal signatures of large scale star formation during recent and intermediate epochs in the form of red supergiants ( rsgs ) with m , and an asymptotic giant branch ( agb ) that peaks near m . comparisons with stellar evolution models suggest that the brightest rsgs have an age near 8 myr . a well - defined plume , which stellar evolution models suggest contains stars with masses near the rsg agb transition , is detected in cmds constructed both from infrared and visible wavelength observations . it is concluded that star formation in the thin disk of ngc 55 has ocurred at a significant rate for at least the past 0.1 0.2 gyr , and this is consistent with other indicators . the near - infrared spectral - energy distribution ( sed ) of the integrated light near the center of the galaxy is consistent with that in other magellanic irregular galaxies , indicating that the star - forming history of ngc 55 , when averaged over timescales of 0.1 1 gyr , has likely not been peculiar when compared with other late - type systems . evidence is also presented that the disk contains a large population of old ( log(t ) ) stars , and it is argued that a stable disk has been in place in ngc 55 for a significant fraction of the age of the universe . at projected distances in excess of 2 kpc off of the disk plane the brightest agb stars have ages gyr . thus , despite indications that dust and gas are present in the envelope surrounding the ngc 55 disk , the agb content suggests that recently formed stars do not occur in large numbers in the extraplanar region . the colors of the rgb in the extraplanar region are consistent with [ fe / h ] between 2.2 and 0.7 , with the majority of stars having [ fe / h ] , and the mean metallicity inferred from the rgb color does not change with distance above the disk plane . thus , the stellar component in the extraplanar envelope is well mixed , at least in terms of metallicity . the mean metallicity of rgb stars is in excellent agreement with that measured in the extraplanar hii regions ehr 1 and 2 , suggesting that the age - metallicity relation in this part of ngc 55 has been flat for at least a few gyr . finally , the rgb - tip occurs near in the extraplanar region , and a distance modulus of 26.5 is computed from this feature .

1408.2154

i

social networking services are widely used in modern society as illustrated by the alexa s top 500 global sites statistics where _ facebook _ and _ linkedin _ rank @xmath18nd and @xmath19th respectively in 2014 . such popularity has enabled governments and third - party enterprises to massively collect social network data , which eventually can be released for mining and analysis purposes . the power of social network analysis is questionless . it might uncover previously unknown knowledge such as community - based problem , media use , individual engagement , amongst others . sociology is a trivial example of a field that certainly benefits from social graphs publication . many other fields ( _ e.g. , _ economics , geography , or political science ) and systems ( _ e.g. , _ service - oriented systems , advertisers , or recommended systems ) improve their decisions , processes , and services , based on users interaction . however , all these benefits are not cost - free . an adversary can compromise users privacy using the published social network , which results in the disclosure of sensitive data such as e - mails , instant messages , or relationships . a simple and popular approach to prevent this privacy problem is _ anonymization _ by means of removing potential identifying attributes . doing so , aggregate knowledge still can be inferred ( _ e.g. , _ connectivity , distance , or node degrees ) while the `` who '' information has been removed . in practice , however , this naive approach is not enough for protecting users privacy . what makes social network anonymization a challenging problem is the combination of the adversary s background knowledge with the released structure of the network . considering a social network as a simple graph , in which individuals are represented by vertices and their bidirectional relationships by edges , the adversary s background knowledge about a victim may take many forms , _ e.g. , _ vertex degrees , connectivity , or local neighborhood . this structural knowledge , together with the released graph , is often enough to perform _ passive attacks _ where the users and their relationships are re - identified @xcite . other privacy attacks exist . in 2007 , backstrom _ et al . _ @xcite introduced _ active attacks _ based on the creation and insertion in the network of _ attacker nodes _ controlled by the adversary . the attacker nodes could be either new accounts with pseudonymous or spoofed identities ( sybil nodes ) , or legitimate users in the network who collude with the adversary . attacker nodes establish links with other nodes in the network ( also between themselves ) aiming at creating a sort of fingerprint in the network . once the social graph is released , the adversary just need to retrieve such a fingerprint ( the attacker nodes ) and use it as a hub to re - identify other nodes in the network . backstrom et . al . proved that @xmath20 attacker nodes in the network can compromise the privacy of arbitrary targeted nodes with high probability , which makes active attack particularly dangerous . several active attacks to social graphs have been proposed . they could even target random nodes in the network as recently shown in @xcite . however , to the best of our knowledge , no privacy measure aimed at evaluating the resistance of a social graph to this kind of attack exists . the lack of such a measure prevents the development of privacy - preserving methods with theoretically proven privacy guarantees . in this article we define _ @xmath0-anonymity _ ; a privacy measure that can be applied to real - life social graphs in order to measure their resistance to active attacks . the proposed privacy measure copes with adversaries whose background knowledge concerning a node @xmath21 and a subset @xmath5 of attacker nodes is the metric representation of @xmath21 with respect to @xmath5 . @xmath0-anonymity turns out to be based on a new problem in graph theory : the _ @xmath1-metric antidimension_. we propose a true - biased algorithm whose computational complexity and success rate can be adjusted . empirical results show that our algorithm finds @xmath1-antiresolving basis in random graphs of order at most @xmath16 with a success rate above @xmath15 . our algorithm has been also used to determine the privacy offered by two real - life social graphs against active attacks . finally , we provide theoretical results on the @xmath1-metric antidimension of graphs , such as paths , cycles , complete bipartite graphs and trees . the rest of this article is structured as follows . section [ sec_related_work ] briefly reviews the literature on privacy - preserving publication of social network data . section [ sec_antiresolving_sets ] presents the metric representation as a reasonable definition of the adversary s background knowledge . it also introduces the @xmath1-metric antidimension as the basis for the privacy measure @xmath0-anonymity . in section [ sect - algo ] we present a true - biased algorithm for computing the @xmath1-metric antidimension of a graph , and evaluate the proposed algorithm through experiments . preliminary results ( mathematical properties ) on the new problem ( the @xmath1-metric antidimension ) are provided in sections [ sec_metric_antidimension ] and [ section - trees ] ( the later specifically addresses the case of tree graphs ) . section [ sec_conclusions ] draws conclusions and future work .

, we introduce-anonymity ; a novel privacy measure aimed at evaluating the resistance of social graphs to active attacks . -anonymity is based on a new problem in graph theory , the _ the proposed algorithm is used to determine the privacy guarantees offered by two real - life social graphs with respect to-anonymity . in particular , we focus on paths , cycles , complete bipartite graphs and trees . anonymity , active attack , social network , graph , resolving set ,-metric antidimension

the study and analysis of social graphs impacts on a wide range of applications , such as community decision making support and recommender systems . with the boom of _ online _ social networks , such analyses are benefiting from a massive collection and publication of social graphs at large scale . unfortunately , individuals privacy right might be inadvertently violated when publishing this type of data . in this article , we introduce-anonymity ; a novel privacy measure aimed at evaluating the resistance of social graphs to active attacks . -anonymity is based on a new problem in graph theory , the _ -metric antidimension _ defined as follows . let be a simple connected graph and an ordered subset of vertices . the metric representation of a vertex with respect to is the-vector , where represents the length of a shortest path in . we call a-antiresolving set if is the largest positive integer such that for every vertex there exist other different vertices with . the-metric antidimension of is the minimum cardinality among all the-antiresolving sets for . we address the-metric antidimension problem by proposing a true - biased algorithm with success rate above when considering random graphs of size at most . the proposed algorithm is used to determine the privacy guarantees offered by two real - life social graphs with respect to-anonymity . we also investigate theoretical properties of the-metric antidimension of graphs . in particular , we focus on paths , cycles , complete bipartite graphs and trees . anonymity , active attack , social network , graph , resolving set ,-metric antidimension

astro-ph0111591

i

in the currently standard interpretation of gamma - ray bursts ( grbs ) , the central engine gives rise to a highly relativistic outflow , the ` fireball ' . although the presence of relativistic outflows in grbs has been amply demonstrated by multiwavelength observations of afterglows ( piran 1999 , van paradijs , kouveliotou & wijers 2000 , mszros 2001 ) , the nature of the central engine itself is still a great mystery . one model of the central engine that has recently gained attention is the ` supranova ' model of vietri & stella ( 1998 , hereafter vs98 ) , in which a massive star ends up in a supernova ( sn ) , but the subsequent black hole formation and grb event is delayed by some time @xmath2 , typically expected to be a few months to years . the sn is assumed to leave behind a rotationally - supported , ` supramassive ' neutron star ( smns ; hereafter also referred to simply as ` pulsar ' ) which then slowly shrinks by shedding angular momentum via a magnetospheric wind ( and/or gravitational radiation ; see [ sec : sum ] ) . after a spin - down time @xmath2 when roughly half its initial angular momentum has been lost , the configuration becomes unstable and collapses to a black hole , possibly with a surrounding disk , leading to the grb proper . the model s major advantage lies in the potential realization of a very baryon - clean pre - grb environment ( mandatory for generating sufficiently relativistic fireballs ) : first the sn ejects the majority of the outlying mass of the progenitor star , and second the smns driven - wind effectively sweeps up remaining baryonic matter in the vicinity of the central object . support for this model comes from recent detections of strong fe emission features in the x - ray afterglow spectra of some grbs ( piro et al . 1999 , antonelli et al . 2001 , yoshida et al . 2001 ) , particularly that of grb991216 ( piro et al . 2000 ) , as well as a transient fe absorption feature in the prompt emission of grb990705 ( amati et al . 2000 ) , indicating surprisingly large amounts of fe - rich material existing nearby , yet relatively removed from the grb site . observational constraints on its location , quantity , density and velocity are compatible with the pre - ejected shell sn remnant ( snr ) in the supranova model ( lazzati et al . 1999 , vietri et al . 2001 , lazzati et al . 2001 ) , but may be difficult to accomodate in other models ( see however rees & mszros 2000 , mszros & rees 2001 , bttcher & fryer 2001 , mclaughlin et al . 2002 ) . the precursor pulsar wind should be extremely powerful . before collapsing , the smns must inevitably expel a substantial fraction of its rotational energy @xmath3 as a magnetically - driven wind , @xmath4 where @xmath5 and @xmath6 are the smns s mass and angular velocity , @xmath7 is its angular momentum in units of @xmath8 , and the numbers are typical smns model values ( salgado et al . 1994 , cook , shapiro & teukolsky 1994 , vs98 ) . the spin - down time ( i.e. the sn - grb delay time ) and corresponding wind luminosity can be estimated from the magnetic dipole formula ( pacini 1967 , vs98 ) @xmath9 and @xmath10 where @xmath11 is a typical smns equatorial radius . the surface magnetic field @xmath12 is unconstrained from model calculations and can be considered a free parameter . equivalently , we may take @xmath2 as the free parameter , and vary @xmath13 accordingly with @xmath3 fixed as in eq.[eqn : ep ] ; the fiducial value we choose below is @xmath14 ( implying @xmath15 ) so as to be consistent with observations of grb991216 ( see [ sec : aftenv ] ) . during @xmath2 , @xmath16 is expected to be relatively constant , and the wind should energize a plerionic nebula in the pre - grb surroundings , a more compact yet much more luminous version of the crab nebula . the consequences of such a precursor plerion in the supranova scenario has not been considered previously , and this paper addresses some important dynamical and radiative effects it may induce , each providing important observational diagnostics for the supranova model . we discuss the acceleration and fragmentation of the sn ejecta material by the plerion - snr interaction and its implications for fe line emission in [ sec : snr ] , and inverse compton scattering of the ambient plerion radiation field in the grb external shock and the resulting high - energy afterglow emission in [ sec : ec ] . a brief consideration of the direct detection and identification of the precursor plerion emission is given in [ sec : dir ] . we will assume a flat lambda cosmology with @xmath17 , @xmath18 and @xmath19 . after this paper was submitted , we became aware of the work of knigl and granot ( 2002 , hereafter kg02 ) , who also investigated the properties of grb afterglows occurring inside plerionic nebulae in the context of the supranova model . they stressed the advantages of such a picture in realizing the relatively high magnetic fields and electron injection efficiencies required in the grb blastwave to explain observed afterglows , and demonstrated this by constructing magnetohydrodynamical ( mhd ) models for the plerion under various assumptions . here we are interested in some characteristic observable effects caused by the precursor plerionic activity which are peculiar to the supranova model and through which the model may be tested by future observations . the emphasis of this paper will be on the relevant radiative processes and their observational implications ; we choose to keep the discussion of the plerion dynamics relatively simple and leave more detailed modeling of this aspect to future studies . a study following our approach but with a more realistic treatment of the plerion has recently been carried out by guetta & granot ( 2002 ) .

we discuss some observational consequences of this precursor plerion , which should provide important tests for the supranova model : 1 ) the fragmentation of the outlying sn ejecta material by the plerion and its implications for fe line emission ; and 2 ) the effect of inverse compton cooling and emission in the grb external shock due to the plerion radiation field . the prospects for direct detection and identification of the precursor plerion emission are also briefly considered .

the supranova model of gamma - ray bursts ( grbs ) , in which the grb event is preceded by a supernova ( sn ) explosion by a few months to years , has recently gained support from fe line detections in the x - ray afterglows of some grbs . a crucial ingredient of this model yet to be studied is the fast - rotating pulsar that should be active during the time interval between the sn and the grb , driving a powerful wind and a luminous plerionic nebula . we discuss some observational consequences of this precursor plerion , which should provide important tests for the supranova model : 1 ) the fragmentation of the outlying sn ejecta material by the plerion and its implications for fe line emission ; and 2 ) the effect of inverse compton cooling and emission in the grb external shock due to the plerion radiation field . the plerion - induced inverse compton emission can dominate in the gev - tev energy range during the afterglow , being detectable by glast from redshifts and by agile from redshifts , and distinguishable from self - compton emission by its spectrum and light curve . the prospects for direct detection and identification of the precursor plerion emission are also briefly considered . naoj - th - ap 2001 , no.66

astro-ph0111591

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we summarize the salient points of our work . in the supranova model of grbs , the fast - rotating smns active during the time between the sn and the grb should drive a luminous plerionic nebula into the preburst environment , with a number of important consequences for the ensuing grb afterglow . rayleigh - taylor instabilities acting at the plerion - sn ejecta interface may induce significant filamentary clumping of the ejecta material , allowing a favorable geometry and enhanced emissivity for the afterglow fe line emission . the plerion radiation field can act as seeds for ec cooling and emission in the grb external shock , leading to prominent gev - tev gamma - rays during the afterglow , which is detectable by glast out to typical grb redshifts , and distinguishable from ssc emission by its characteristic spectrum and light curve . a direct search for the plerion emission prior to the grb may be conducted through accurate grb positions and concurrent wide field surveys , e.g. in the optical and x - rays . all of these should provide critical tests for the supranova model in the near future . the ability of the plerion to effectively fragment the snr and penetrate between the ejecta material is an uncertain aspect of our scenario . we may therefore consider the consequences of the plerion being completely confined inside the snr shell instead . in the case of a spherical geometry , such a circumstance would be at odds with constraints derived from the observed fe lines , since : 1 ) the snr would likely be optically thick to thomson scattering at the time of the grb , so that no prompt or afterglow emission can be seen ( eq.[eqn : nes ] ) ; 2 ) the snr shell , as well as the plerionic bubble material , would be dense enough to decelerate the grb blastwave in a time shorter than the observed afterglow ; and 3 ) the radiation density of the plerion would be so large as to cause excessively fast cooling of electrons in the afterglow blastwave . a possible alternative is a snr - confined plerion with a globally anisotropic geometry , being elongated in the direction of the grb beam , as discussed by kg02 and guetta & granot ( 2002 ) . the true efficacy of rt instabilities at the snr - plerion interface should be clarified through future high - resolution numerical simulations including all the relevant microphysics . arons ( 2002 ) has recently discussed in more detail the plausibility of a powerful pulsar wind shredding the surrounding snr in the context of a model for cosmic ray acceleration by magnetars . although we have concentrated on the case of the pulsar spinning down exclusively via a magnetospheric wind , there is a possibility that significant spindown can also occur through gravitational wave emission , such as those driven by r - mode instabilities ( e.g. andersson et al . 2000 , stergioulas & font 2001 , lindblom , tohline & vallisneri 2001 and references therein ) . however , many aspects of the present theoretical calculations regarding gravitational waves are uncertain ( fryer & woosley 2001 ) . our work can be viewed as exploring the maximum possible effects of electromagnetic spindown , which can be modeled with some more confidence . in reality , both effects could be important to varying degrees , and we leave an investigation of such cases to the future . we are thankful to m. salvati for an initial suggestion leading to the present work , and e. amato , j. granot , d. lazzati , n. omodei and m. vietri for helpful discussions . s.i . also expresses his heartfelt thanks to members of the arcetri astrophysical observatory for a very pleasant and hospitable environment where part of this work was carried out . this work was partly supported by a grant from the italian ministry of university and research ( cofin-99 - 02 - 02 ) . amati , l. et al . 2000 , sci . , 290 , 953 amato , e. , salvati , m. , bandiera , r. , pacini , f. & woltjer , l. 2000 , , 359 , 1107 andersson , n. , jones , d. i. , kokkotas , k. & stergioulas , n. 2000 , , 534 , l75 antonelli , l. a. et al . 2001 , , 545 , l39 arons , j. 2002 , submitted to apj ( astro - ph/0208444 ) ballantyne , d. r. & ramirez - ruiz , e. 2001 , , 559 , l83 bandiera , r. , pacini , f. & salvati , m. 1983 , , 126 , 7 bandiera , r. , pacini , f. & salvati , m. 1984 , , 285 , 134 blandford , r. d. & mckee , c. f. 1976 , phys . fluids , 19 , 1130 bloom , j. s. et al . 1999 , , 401 , 453 bloom , j. s. et al . 2002 , , 572 , l45 bttcher , m. & dermer , c. d. 1999 , astropart . phys . , 11 , 113 bttcher , m. & dermer , c. d. 2000 , , 532 , 281 bttcher , m. & fryer , c. l. 2001 , , 547 , 338 bttcher , m. , fryer , c. l. & dermer , c. d. 2002 , , 567 , 441 chevalier , r. a. 1977 , in supernovae , ed . d. n. schramm , ( dordrecht : reidel ) 53 chevalier , r. a. 2000 , , 539 , l45 chevalier , r. a. & fransson , c. 1992 , , 395 , 540 cook , g. b. , shapiro , s. l. & teukolsky , s. a. 1994 , , 424 , 823 davidson , k. & fesen , r. a. 1985 , , 23 , 119 dermer , c. d. 1995 , , 446 , l63 frail , d. a. et al . 2000 , , 538 , l129 frail , d. a. et al . 2001 , , 562 , l55 fryer , c. & woosley , s. 2001 , , 411 , 31 galama , t. j. et al . 2000 , , 536 , 185 granot , j. , piran , t. & sari , r. 2000 , , 534 , l163 guetta , d. & granot , j. 2002 , submitted to ( astro - 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the plerion - induced inverse compton emission can dominate in the gev - tev energy range during the afterglow , being detectable by glast from redshifts and by agile from redshifts , and distinguishable from self - compton emission by its spectrum and light curve . naoj - th - ap 2001 , no.66

the supranova model of gamma - ray bursts ( grbs ) , in which the grb event is preceded by a supernova ( sn ) explosion by a few months to years , has recently gained support from fe line detections in the x - ray afterglows of some grbs . a crucial ingredient of this model yet to be studied is the fast - rotating pulsar that should be active during the time interval between the sn and the grb , driving a powerful wind and a luminous plerionic nebula . we discuss some observational consequences of this precursor plerion , which should provide important tests for the supranova model : 1 ) the fragmentation of the outlying sn ejecta material by the plerion and its implications for fe line emission ; and 2 ) the effect of inverse compton cooling and emission in the grb external shock due to the plerion radiation field . the plerion - induced inverse compton emission can dominate in the gev - tev energy range during the afterglow , being detectable by glast from redshifts and by agile from redshifts , and distinguishable from self - compton emission by its spectrum and light curve . the prospects for direct detection and identification of the precursor plerion emission are also briefly considered . naoj - th - ap 2001 , no.66

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* proof * : * if part * : assume that the controllable part @xmath52 is @xmath72-dissipative and the assumption in the theorem is satisfied . by propositions [ lmiunctrb ] and [ graphneutral ] , to prove that the behavior @xmath16 is dissipative , it suffices to show the existence of a @xmath259 such that the corresponding graph subspace is an @xmath158-dimensional , @xmath159-invariant , @xmath106-neutral subspace . to show the existence of such a @xmath125 , we use lemma [ invariant ] to construct a c - set such that the corresponding @xmath158-dimensional @xmath159-invariant , @xmath106-neutral subspace is also a graph subspace of @xmath125 . this @xmath125 is the solution to the are and storage function for the whole behavior would then be defined as @xmath260 , thus completing the proof . as the unmixing assumption on uncontrollable modes is assumed , @xmath261 means that @xmath262 and @xmath263 . as we have assumed that the controllable part is @xmath72-dissipative , from lemma [ evenpartial ] , the partial multiplicities of real eigenvalues of @xmath264 are all even . using this fact , lemma [ invariant ] can be used to infer that there exists a unique @xmath158-dimensional @xmath159-invariant , @xmath106-neutral subspace for every c - set . now , it remains to show the existence of a c - set such that the corresponding @xmath158-dimensional , @xmath159-invariant , @xmath106-neutral subspace is also a graph subspace . we choose a c - set @xmath190 such that @xmath265 and show that the corresponding @xmath158-dimensional , @xmath159-invariant , @xmath106-neutral subspace is a graph subspace . let @xmath266 be the @xmath158-dimensional , @xmath106-neutral , @xmath159-invariant subspace of @xmath163 corresponding to the c - set @xmath190 and suppose @xmath267 \label{eq : l}\ ] ] for matrices @xmath268 and @xmath269 @xmath270 . in order to prove that @xmath266 is a graph subspace it is enough to prove that @xmath268 is invertible . this is proved using contradiction : we assume @xmath268 is singular and show that we get a contradiction to the unmixing assumption on @xmath55 . this constitutes the rest of the proof of the ` if part ' . we prove this along the lines of @xcite . @xmath159-invariance of @xmath266 implies that @xmath271 \left [ \begin{array}{c } x_1 \\ \end{array } \right ] = \left [ \begin{array}{c } x_1 \\ x_2 \\ \end{array } \right ] t \nonumber\ ] ] for @xmath272 . in other words , @xmath273 then as @xmath266 is @xmath106-neutral @xmath274 \left [ \begin{array}{cc } -\tilde{c } & \tilde{a}^\ast \\ \tilde{a } & \tilde{d } \\ \end{array } \right ] \left[\begin{array}{c } x_1 \\ x_2 \\ \end{array } \right ] = 0 , \label{eq : neutral1}\ ] ] i.e. @xmath275 now suppose @xmath268 is singular . let @xmath276 . from , for every @xmath277 we have , @xmath278 which implies @xmath279 since @xmath280 , @xmath281 , i.e. , @xmath282 . now , for every @xmath277 , from equations we have , @xmath283 that is , @xmath284 this implies @xmath285 is @xmath286-invariant . hence there exists a non - zero @xmath287 which is an eigenvector of t such that @xmath288 corresponding to eigenvalue , say @xmath54 . we claim that @xmath54 can not be a real eigenvalue and prove this below . post - multiplying the second equation of by @xmath287 we get , @xmath289 @xmath290 this implies that @xmath291 is a left eigenvector of @xmath292 with eigenvalue @xmath293 and from equation we have @xmath294 . this means that @xmath293 is an uncontrollable eigenvalue of @xmath292 and @xmath295 , i.e. , @xmath296 . now , if @xmath54 were a real eigenvalue , then @xmath293 and @xmath297 belong to @xmath55 and contradicts the unmixing assumption @xmath298 . since @xmath299 ( by proposition [ invariant ] ) , @xmath300 . we now have @xmath301 but @xmath302 can not belong to @xmath190 . but we have @xmath296 and thus @xmath303 which is a contradiction by definition of c - set . this completes the proof for the if part . * only if part : * assume @xmath16 is @xmath72-dissipative . then there exists a storage function @xmath304 such that @xmath305 integrating both sides for every @xmath306 , @xmath307 which implies that @xmath52 is @xmath72-dissipative . this completes the proof of theorem [ main ] . the above proof is constructive in the sense that if a behavior @xmath71 satisfies the three conditions : * uncontrollable poles are unmixed , i.e. no two of them add to zero * the controllable part @xmath140 is dissipative , * the controllable part @xmath140 is ` strictly dissipative ' at infinity , i.e. @xmath138 where @xmath308 is the feed - through term of the transfer function , then we construct a storage function that satisfies the dissipation inequality for the whole behavior @xmath26 . further , the storage function we construct is equal to @xmath124 where @xmath125 is a solution to the corresponding algebraic riccati equation . further , we constructed the storage function by starting with a state representation in which the state @xmath92 is _ observable _ from the manifest variable @xmath13 . these facts lead to the following important corollary . let @xmath71 be an uncontrollable behavior whose uncontrollable poles @xmath55 are unmixed , i.e. @xmath309 . consider @xmath72 partitioned in accordance with the input cardinality of @xmath26 as @xmath310 suppose @xmath140 , the controllable part of @xmath26 , has an observable image representation , @xmath311 , where @xmath44 is partitioned as @xmath312 , w_2 \in \mathbb{r}^{(\texttt{p+q } ) \times \texttt{m}}\left [ \xi \right].\ ] ] let @xmath313 and @xmath314 . assume @xmath52 is such that @xmath138 . then , the following are equivalent . 1 . @xmath140 is dissipative . 2 . there exists a @xmath315}$ ] such that @xmath316 is a storage function , i.e. @xmath317 for all @xmath318 . 3 . there exists a matrix @xmath125 and an observable state variable @xmath92 such that @xmath319 for all @xmath318 . statement 2 tells that the storage function can be expressed as a quadratic function of the manifest variables @xmath13 and their derivatives . statement 3 says that the storage function is a ` state function ' , i.e. a static function of the states , and hence storage of energy requires no more memory of past evolution of trajectories than required for arbitrary concatenation of any two system trajectories .

for various reasons , in the context of uncontrollable systems / behaviors , a more appropriate definition of dissipativity is in terms of the dissipation inequality , namely the _ existence _ of a storage function . we first assume that the storage function can be expressed in terms of the external variables and their derivatives only and prove our first main result that , assuming the uncontrollable poles are unmixed , i.e. no pair of uncontrollable poles add to zero , and assuming a strictness of dissipativity at the infinity frequency , the dissipativities of a system and its controllable part are equivalent ; in other words once the autonomous subsystem satisfies a lyapunov equation solvability - like condition , it does not interfere with the dissipativity of the system .

the theory of dissipativity has been primarily developed for controllable systems / behaviors . for various reasons , in the context of uncontrollable systems / behaviors , a more appropriate definition of dissipativity is in terms of the dissipation inequality , namely the _ existence _ of a storage function . a storage function is a function such that along every system trajectory , the rate of increase of the storage function does not exceed the power supplied . while the power supplied is always expressed in terms of only the external variables , whether or not the storage function should be allowed to depend on only the external variables and their derivatives or also unobservable / hidden variables has various consequences on the notion of dissipativity : this paper thoroughly investigates the key aspects of both cases , and also proposes another intuitive definition of dissipativity . we first assume that the storage function can be expressed in terms of the external variables and their derivatives only and prove our first main result that , assuming the uncontrollable poles are unmixed , i.e. no pair of uncontrollable poles add to zero , and assuming a strictness of dissipativity at the infinity frequency , the dissipativities of a system and its controllable part are equivalent ; in other words once the autonomous subsystem satisfies a lyapunov equation solvability - like condition , it does not interfere with the dissipativity of the system . we also show that the storage function in this case is a static state function . this main result proof involves new results about solvability of the algebraic riccati equation , and uses techniques from indefinite linear algebra and hamiltonian matrix properties . we then investigate the utility of unobservable / hidden variables in the definition of storage function : we prove that lossless uncontrollable behaviors are ones which require storage function to be expressed in terms of variables that are unobservable from the external variables . we next propose another intuitive definition : a behavior is called dissipative if it can be embedded in a controllable dissipative _ super - behavior_. we show that this definition imposes a constraint on the number of inputs and thus explains unintuitive examples from the literature in the context of lossless / orthogonal behaviors . these results are finally related to rlc realizability of passive networks , specifically to the nonrealizability of the nullator one - port circuit using rlc elements .

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we briefly review the main results in this paper . we first used the existence of an observable storage function as the definition of a system s dissipativity and proved that the dissipativities of a behavior and its controllable part are equivalent assuming the uncontrollable poles are unmixed and the dissipativity at infinity frequency is strict . this result s proof involved new results in the solvability of are and used indefinite linear algebra results . we showed that for lossless autonomous dissipative systems , the storage function can not be observable , thus motivating the need for unobservable storage functions . we then studied orthogonality / lossless behaviors in the context of using the definition of existence of a controllable dissipative superbehavior as a definition of dissipativity . in addition to results about the smallest controllable superbehavior , we showed necessary conditions on the number of inputs for embeddability of lossless / orthogonal behaviors in larger controllable such behaviors . in the context of embeddability as a definition of dissipativity , we showed that one can always find behaviors that can be embedded in both a strictly dissipative behavior and a strictly ` anti - dissipative ' behavior , thus raising a question on the embeddability definition . we related this question to the well - known result that the nullator one - port circuit is not realizable using only rlc elements . j. c. willems , dissipative dynamical systems - part i : general theory , part ii : linear systems with quadratic supply rates , _ archive for rational mechanics and analysis _ , 45 , pages 321351 , 352393 , 1972 ,

this main result proof involves new results about solvability of the algebraic riccati equation , and uses techniques from indefinite linear algebra and hamiltonian matrix properties . these results are finally related to rlc realizability of passive networks , specifically to the nonrealizability of the nullator one - port circuit using rlc elements .

the theory of dissipativity has been primarily developed for controllable systems / behaviors . for various reasons , in the context of uncontrollable systems / behaviors , a more appropriate definition of dissipativity is in terms of the dissipation inequality , namely the _ existence _ of a storage function . a storage function is a function such that along every system trajectory , the rate of increase of the storage function does not exceed the power supplied . while the power supplied is always expressed in terms of only the external variables , whether or not the storage function should be allowed to depend on only the external variables and their derivatives or also unobservable / hidden variables has various consequences on the notion of dissipativity : this paper thoroughly investigates the key aspects of both cases , and also proposes another intuitive definition of dissipativity . we first assume that the storage function can be expressed in terms of the external variables and their derivatives only and prove our first main result that , assuming the uncontrollable poles are unmixed , i.e. no pair of uncontrollable poles add to zero , and assuming a strictness of dissipativity at the infinity frequency , the dissipativities of a system and its controllable part are equivalent ; in other words once the autonomous subsystem satisfies a lyapunov equation solvability - like condition , it does not interfere with the dissipativity of the system . we also show that the storage function in this case is a static state function . this main result proof involves new results about solvability of the algebraic riccati equation , and uses techniques from indefinite linear algebra and hamiltonian matrix properties . we then investigate the utility of unobservable / hidden variables in the definition of storage function : we prove that lossless uncontrollable behaviors are ones which require storage function to be expressed in terms of variables that are unobservable from the external variables . we next propose another intuitive definition : a behavior is called dissipative if it can be embedded in a controllable dissipative _ super - behavior_. we show that this definition imposes a constraint on the number of inputs and thus explains unintuitive examples from the literature in the context of lossless / orthogonal behaviors . these results are finally related to rlc realizability of passive networks , specifically to the nonrealizability of the nullator one - port circuit using rlc elements .

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molecular motors are proteins that transform the free energy released from chemical reactions into mechanical work . in this article we consider a special class of motor proteins , namely cytoskeletal motors which perform directed walks along cytoskeletal filaments as reviewed in @xcite . in the cell , these motors have different functions related , e.g. , to vesicle transport and cell division . the best studied examples are kinesins , which walk along microtubules , and certain types of myosins , which walk along actin filaments . after a certain walking time , such a motor unbinds from its filament because its binding energy is finite and can be overcome by thermal activation . for kinesins , this typically happens after 100150 steps or after a walking time of about 1.21.8 seconds , see , e.g. , @xcite . in many motility assays , the filaments are immobilized on a substrate and are in contact with an aqueous solution . in such a situation , the unbound motors diffuse in the surrounding fluid until they eventually reattach to the same or another filament . recently , we have introduced lattice models to study the motors random walks , which consist of many diffusional encounters between motors and filaments in open and closed compartments @xcite . if many motors are placed in such a compartment , hard core exclusion between the motors has to be taken into account , since the motors are strongly attracted to the binding sites of the filaments , so that the filaments get overcrowded . these models are new variants of driven lattice gas models and exclusion processes , for which the active processes which drive the particles are localized to the filaments . lattice models of driven diffusive systems have been studied extensively in the last years , see e.g. @xcite . the simplest model is the asymmetric simple exclusion process ( asep ) in one dimension , where particles hop on a one - dimensional lattice with a strong bias towards one direction ( in the simplest case there are no backward steps at all ) and the only interaction of the particles is hard core exclusion , i.e. , steps to occupied lattice sites are forbidden . when coupled to open boundaries , this simple model already exhibits a complex phase diagram , see e.g. @xcite , which we will review below in some detail . the first model for the 1dimensional asep was introduced more than 30 years ago by macdonald _ @xcite in the context of protein synthesis by ribosomes on messenger rna ( mrna ) . at that time it was solved using a mean field approach and used to explain results of radioactive labeling experiments @xcite which showed that protein synthesis gets slower as the ribosome moves on the mrna template . the model of macdonald _ et al . _ explained this by the steric hindrance between successive ribosomes along the mrna track . two years later the same model was discussed by spitzer as a simple example for interacting particles in probability theory @xcite . since then , the asymmetric simple exclusion process ( and variants ) has been studied extensively as a generic model for non - equilibrium phase transitions @xcite and interacting stochastic systems @xcite as well as in other applications such as traffic flow @xcite . many properties of the 1dimensional asep are known exactly . as mentioned , the lattice models for random walks of molecular motors differs from the driven lattice gas models in an important way : walks of molecular motors are only driven as long as the motor is attached to a cytoskeletal filament , hence driving is localized to one or several lines . it can therefore be viewed as an asep which has the additional property , that particles ( molecular motors ) can unbind from the track with a small probability , diffuse in the surroundings and reattach to the same or another filament . in more mathematical terms , the asep is coupled to a _ symmetric _ exclusion process via adsorption and desorption of particles onto filaments . boundary conditions play an important role in driven systems . this becomes apparent , e.g. , if one compares a tube like system with periodic boundary conditions with one with closed boundaries . in the system with closed boundaries , a traffic jam of motors arises at one end of the system and the current of motors bound to the filament is balanced by diffusive currents of unbound motors as first shown in @xcite . with periodic boundary conditions , motors arriving at the right end of the system just restart their walk from the left end and a net current through the systems is obtained . in this article , we study the stationary states of tube - like compartments with open boundaries . these compartments have the shape of a cylinder and contain one filament which is placed along the cylinder axis in order to obtain the simplest possible geometry . the bound motors move along the filament and the unbound motors diffuse within the cylinder , see fig . [ fig : motor_tube_geom ] . at the ends of the tube , motors are inserted and extracted . such a system is accessible to _ in vitro _ experiments using standard motility assays , but it can also be viewed as a strongly simplified model for motor based transport in an axon @xcite , if these motors , which are synthesized in the cell body , are at least partly degraded at the axon terminal @xcite , a situation that can be mimicked by insertion and extraction of motors at the ends of a tube . the stationary states depend strongly on the way , in which the motors are inserted and extracted at the boundaries as we will explicitly demonstrate for three different types of boundary conditions , see fig . [ fig : motor_tube_randbed ] . our article is organized as follows . after introducing the model in section [ sec : model ] , we start in section [ sec : periodic_tube ] with periodic boundary conditions . this case can be solved exactly , since it satisfies local balance of currents in the radial direction , see appendix [ app_rdb ] . in section [ sec : open_tube ] , we discuss the situation in which the density of bound motors on the filament is fixed at the boundaries . finally , in section [ sec : bounddiff ] , we consider the case where the filament is shorter than the tube and the motors diffuse into and out of the tube . the main tool to study the open systems are monte carlo simulations . these are supplemented by dynamical considerations and self - consistent or mean field calculations . some details of the latter calculations are presented in appendix [ app_mf ] .

these models exhibit boundary - induced phase transitions related to those of the asymmetric simple exclusion process ( asep ) in one dimension . ( b ) fixed motor densities at the two tube ends where radial equilibrium holds locally ; and ( c ) diffusive motor injection at one end and diffusive motor extraction at the other end .

the traffic of molecular motors through open tube - like compartments is studied using lattice models . these models exhibit boundary - induced phase transitions related to those of the asymmetric simple exclusion process ( asep ) in one dimension . the location of the transition lines depends on the boundary conditions at the two ends of the tubes . three types of boundary conditions are studied : ( a ) periodic boundary conditions which correspond to a closed torus like tube . ( b ) fixed motor densities at the two tube ends where radial equilibrium holds locally ; and ( c ) diffusive motor injection at one end and diffusive motor extraction at the other end . in addition to the phase diagrams , we also determine the profiles for the bound and unbound motor densities using mean field approximations and monte carlo simulations . our theoretical predictions are accessible to experiments .

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let us summarize the main results and add a few comments . we have studied a lattice model for the motion of many molecular motors in an open tube which contains a single filament . when bound to the filament , the motor particles undergo an asymmetric simple exclusion process ( asep ) . in addition , motors can unbind from the filament and then diffuse freely in the tube . as for the asep in one dimension , the motor traffic in open tubes can exhibit three different phases : high density and low density phases which are characterized by an exponential decay of the density deviations from their bulk values and maximal current phases characterized by an algebraic decay . therefore , the molecular motor traffic in open tubes are promising candidates for the experimental observation of boundary induced non equilibrium phase transitions . in general , the location of the transition lines is found to depend on the precise choice of the boundary conditions . apart from periodic boundary conditions , case ( a ) , we studied two different boundary conditions ( b ) and ( c ) for an open tube . in case ( b ) , the bound and unbound densities are kept fixed at the boundaries and satisfy radial equilibrium . for this case , the location of the transition lines is independent of the model parameters , and the phase diagram of the asep in one dimension is recovered . in case ( c ) , the active compartment of the tube is bounded by two compartments where the transport is purely diffusive . in this latter case , the phase diagram depends on the geometry of the tube and on the transport properties in the bound and unbound motor states . in many cases , the maximal current phase is completely suppressed by the coupling to the diffusive compartments which act as bottle necks for the transport . the theoretical results described here should be accessible to experiments on cytoskeletal filaments and motors . in particular , the motor traffic through open tubes as discussed here provides new opportunities to study the transport properties of aseps by systematic experiments .

the traffic of molecular motors through open tube - like compartments is studied using lattice models . the location of the transition lines depends on the boundary conditions at the two ends of the tubes . three types of boundary conditions are studied : ( a ) periodic boundary conditions which correspond to a closed torus like tube . our theoretical predictions are accessible to experiments .

the traffic of molecular motors through open tube - like compartments is studied using lattice models . these models exhibit boundary - induced phase transitions related to those of the asymmetric simple exclusion process ( asep ) in one dimension . the location of the transition lines depends on the boundary conditions at the two ends of the tubes . three types of boundary conditions are studied : ( a ) periodic boundary conditions which correspond to a closed torus like tube . ( b ) fixed motor densities at the two tube ends where radial equilibrium holds locally ; and ( c ) diffusive motor injection at one end and diffusive motor extraction at the other end . in addition to the phase diagrams , we also determine the profiles for the bound and unbound motor densities using mean field approximations and monte carlo simulations . our theoretical predictions are accessible to experiments .

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local spectral analysis of the solar wind ( sw ) magnetic fields reveals strong time variations in the power level of the turbulent field fluctuations . this variability of the power level of the field fluctuations is responsible for the strong non - gaussianity of the observed pdfs of field variations associated with intermittency ( ragot 2013 ) . the strong non - gaussianity of the observed pdfs of field variations is unlikely to be the only observable consequence of the power - level variability . here , we investigate the magnetic field orientations as functions of the highly varying power level of turbulence in the fast sw , and vice versa , where the power level of turbulence is defined with the field fluctuations normalized to the medium - scale ( @xmath2min ) average background field . sw magnetic fields @xmath3 are measured along sw flow lines and the time series of these in situ field measurements can be averaged on a timescale @xmath4 to obtain mean `` magnetic field vectors '' @xmath5 . if @xmath6 is the time resolution of the measurements and @xmath7 , ( t , t ) = 1 n+1 _ n =- n/2^n/2 ( t+n t ) . [ bav ] what is the meaning of these mean `` magnetic field vectors '' @xmath8 ? do they somehow give the direction of a real magnetic field within the sw ? how do they relate to the direction of `` real '' magnetic field lines ? the answer depends on how much magnetic field lines diverge from each other , locally , and on how much transport they undergo collectively . if the directions of neighboring field lines strongly deviate from each other rather than being dominated by one common direction of transport , then it is dubious that the mean `` magnetic field vectors '' @xmath9 can be ascribed any other meaning than that of time averages of in situ magnetic fields along sw flow lines . however , if the directions of neighboring field lines mostly run `` parallel '' to each other , being dominated by one common direction of transport , then the mean `` magnetic field vectors '' @xmath9 give the mean local common direction of transport , or mean local direction of a field line that passes through one of the measurement points . in a magnetic turbulence with background field @xmath10 , such as the sw , both the field - line dispersal ( relative field - line divergence ) and global field - line transport ( common transport ) can be assessed theoretically and modeled ( e.g. , ragot 1999 , 2006a , 2006b , 2009 , 2010a , 2010b , 2011 ) . field - line dispersal and global field - line transport are measured by the variations in field - line separations and by the field - line displacements across the background - field direction , or cross - field displacements , @xmath11 , respectively . it appears that in slow and fast sw streams , the association between time - averaged field vector direction and mean direction of an actual field line is justified on most timescales because the cross - field displacements @xmath11 far exceed the variations in field - line separations on the background field - aligned length scales @xmath12 cm ( e.g. , ragot 2010b , knowing that @xmath13 on these @xmath14 scales).@xmath15 cm apart may grow tenfold on a @xmath14 scale of @xmath16 cm , or even hundredfold on a @xmath14 scale of @xmath17 cm ( see figures 3 and 5 of ragot 2011 ) , and statistically , by factors of @xmath18 and 20 ( from figures 1 , 2 and 4 of ragot 2011 ) , but the variation of that separation remains only a small fraction of the cross - field displacements undergone by both field lines on these @xmath14 scales , here about 0.9 and 3.6 percent at @xmath19 and @xmath17 cm , respectively , in the flux - tube simulation of ragot ( 2011 ) , and only 0.4 and 0.7 percent , statistically ( from figure 1 of ragot 2006b , @xmath20 and @xmath21 cm at @xmath19 and @xmath17 cm , respectively ) . ] for a sw speed @xmath22 , the length scales @xmath14 relate to the timescales @xmath4 through @xmath23 , the angle @xmath24 between parker spiral and radial direction being defined below in equation ( [ spiral ] ) . the time - averaged field directions obtained by integrating in situ fast sw magnetic fields over time intervals of duration @xmath25s ( depending on @xmath22 ) should therefore match the local field - line directions on the background field - aligned length scale @xmath26 cm . and the angles @xmath1 [ see equation ( [ tan_a ] ) in section 4 ] between these time - averaged in situ fields and the background field @xmath10 should match the angles between the mean directions of local individual field - line segments of @xmath10-projection @xmath14 and @xmath10 , whose tangents are given by the ratios @xmath27 . again , this would not be the case if the field lines were too strongly diverging from each other . these premises are at the basis of the modeling of section 4 for the pdfs of the angles @xmath1 at the scale @xmath28 cm . a first - order approximation for the large - scale geometry of the sw magnetic fields is given by the parker - spiral model for interplanetary magnetic fields ( parker 1958 , 1963 ) . the angle @xmath24 of the parker spiral to the radial direction at heliocentric distance @xmath29 is related to the solar rotation rate @xmath30 and sw speed @xmath22 through ( e.g. , burlaga 1995 ) _ r . [ spiral ] the local magnetic fields actually deviate from the parker spiral by large angles , but the parker spiral direction generally represents a good axis of symmetry for long statistics of the fields . pdfs of the azimuthal angles of the magnetic fields in - ecliptic projections were determined from in situ measurements early on ( ness & wilcox 1966 ; hirshberg 1969 ; see also , burlaga & ness 1997 ) . more recently , pdfs of the angles between sw magnetic fields and parker spiral ( or background field ) were also determined both in three- and two - dimensional space from in situ measurements , and using the measured fourier spectra of magnetic fluctuations , also theoretically and numerically ( ragot 2006b ) . these determinations , however , were made from only one single sw stream in each of four sw conditions ( slow and fast sw at @xmath31 and @xmath32au ) , and the time variability of the power level of turbulence was not considered . here we focus on the fast sw near @xmath33au and extend our analysis to a large set of streams ( over one hundred ) observed onboard _ ace _ and _ stereo a _ and _ b_. most importantly , we analyze the directions of the local magnetic fields as functions of the local level of turbulence , rather than a characteristic average value of that level . an earlier study by podesta ( 2009 ) showed that the turbulent energy observed in fast sw streams is on the average higher when the local magnetic field is normal to the sw flow . the conclusion of that earlier study was that the higher levels of turbulent energy seen when the local magnetic field is normal to the sw flow are indicative of anisotropic turbulence with a wavevector distribution dominated by the wavevectors normal to the field . we are somewhat skeptical of this conclusion that variations of turbulent energy with magnetic field angles necessarily reflect an anisotropy of the wavevector distribution . our skepticism is driven by the facts that ( 1 ) the variations in the turbulent energy and turbulence level are actually so much greater than the variations seen in the above anisotropy argument ( orders of magnitude , to be compared to a factor of the order of a few ) , and ( 2 ) the orientation of the local magnetic field is in large measure determined by the turbulent energy and turbulence level ( see abstract , next paragraph and section 3 for a definition of the power level of turbulence or turbulence level ) , as we confirm here through our analysis and modeling of the field orientations for a broad range of turbulence levels . through our analysis and modeling , we will test whether a turbulence model of isotropic wavevector distribution could account for the observed pdfs of local field angles at any of the measured turbulence levels . we will also test whether the pdfs of angles relative to the radial can be recovered from the pdfs of angles relative to the background under an assumption of axisymmetry and parker - spiral background field . here , we distinguish between turbulent energy and turbulence level . the turbulent energy is basically the power level of the magnetic field fluctuations , computed at either one frequency or integrated over a broader frequency range . by contrast , to anticipate our discussion of section 3.5 , the turbulence level is the power level of the magnetic field fluctuations _ normalized to the medium - scale average background field . _ while the turbulent energy does say little about the stochasticity of the fields and the amount of field - line wandering actually taking place in the sw , especially if the background field undergoes strong fluctuations , the turbulence level tightly parametrizes field stochasticity and field - line wandering . in fast sw streams , it appears that the background field does undergo strong fluctuations . therefore , the turbulence level as defined above and in greater detail in section 3.5 , is a far better ordering parameter for the orientations of the fast sw magnetic fields . whether the turbulence level is defined at one frequency , integrated over a range of frequencies , or involves a more complex combination of frequencies through the formula for the mean cross - field displacement ( see sections 3.4 and 3.5 ) does not affect that basic fact . our data selection is presented in section 2 and the variations in the power level of magnetic fluctuations are shown in section 3 , where the power level of intermittent turbulence is also defined . in section 4 , through modeling of the pdfs of field - line directions , we model the pdfs of the angles @xmath1 between local and background ( or parker spiral ) fields at series of stable levels of turbulence . section 5 deals with the transition from the @xmath1 angles to the angles @xmath0 between local fields and radial direction . section 6 presents some consequences of the power variability on the field orientations and the apparent `` anisotropy '' of the turbulence . the conclusion follows in section 7 .

the power level of turbulence , roughly defined as the power in the transverse field fluctuations normalized to the medium - scale average background field , tightly orders the location of the peaks in the probability distribution functions ( pdfs ) of the angles between local fields and parker spiral . as a result ,

the turbulent magnetic fields of a large set of fast solar wind streams measured onboard _ ace _ and _ stereo a _ and _ b _ are analyzed in an effort to identify the effects of the turbulence - level broad variations on the orientations of the local , time - averaged magnetic fields . the power level of turbulence , roughly defined as the power in the transverse field fluctuations normalized to the medium - scale average background field , tightly orders the location of the peaks in the probability distribution functions ( pdfs ) of the angles between local fields and parker spiral . as a result , the broad variations in the power level of turbulence cause a steep dependence of the average power level of turbulence on the angle of the local field to the parker spiral , with the highest turbulence levels found near the normal to the parker spiral and the lowest levels near the parker spiral direction . generalized quasilinear estimates of the mean cross - field displacements adapted to intermittent time - varying turbulence lead to accurate fits of the observed angle pdfs at all stable levels of turbulence , supporting the idea that isotropic turbulence could account for the observed angle pdfs . modeling of the angles between local fields and radial direction , from the pdfs of the angles between local and background fields under an assumption of axisymmetry of the turbulent fields around a background field in or near the direction of the parker spiral , also produces fairly good fits of the observed pdfs of , thereby validating the assumption . finally , local field reversals are found to be quite common even within very broad streams of `` unipolar '' fast solar wind .

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in an effort to identify the effects of the broad variations in turbulence levels on the orientations of the local mean fields , we have analyzed the turbulent magnetic fields of a large set of fast sw streams measured onboard _ ace _ and _ stereo a _ and _ b_. our multiscale fourier analysis of the transverse turbulent fields reveals time variations of the spectral power at all frequencies and on many timescales . the higher the time resolution of the spectral analysis is , the stronger the fluctuations of the power level are . the higher - resolution fluctuations far exceed the lower - resolution fluctuations , but roughly follow them in their time average ( see figures 1@xmath383 ) . from this multiscale fourier analysis , we estimate as a linear combination of the fourier amplitudes @xmath88 ( see figure 3 ) the gql mean cross - field displacement of the magnetic field lines in the time - varying intermittent turbulence . this estimate of the mean cross - field displacement in intermittent turbulence is given by the square root of equation ( [ dr ] ) with a local medium - scale ( @xmath201min ) average background field @xmath113 substituting for the stream average @xmath110 . it includes the effects of all turbulent scales and fluctuates on many timescales . this estimate of the mean cross - field displacement , once divided by the field - aligned scale @xmath14 , defines the square root @xmath117 of the power level of the intermittent turbulence in equation ( [ c ] ) , and the related angle , @xmath202 , used throughout the paper to parametrize the power level of the intermittent turbulence . provided `` compressibility effects '' are included at the lowest power levels of turbulence ( @xmath203 ) , modeling the pdfs of the angles @xmath1 between local and background fields produces satisfactory fits of the observed pdfs at all stable power levels of turbulence ( see figures 8 , 10 and 11 ) , that is , on all time intervals with variations in the power level of turbulence that are sufficiently slow . because the highest power levels of turbulence happen in short bursts , the statistics for stable power levels are biased toward the lower turbulence levels and smaller angles ( see figures 6@xmath389 ) . but the fits remain quite accurate at all levels @xmath46 , even for the very low statistics of the higher @xmath46 . because our gql modeling does not assume anything about the three - dimensional distribution of wavevectors in the turbulence , and therefore does not preclude an isotropic distribution of wavevectors , it follows from these fits that an isotropic turbulence could account for the measured pdfs of the angles @xmath1 between local and background fields at all stable levels of turbulence . both the direct measure of the field projection on the background field ( parker spiral direction ) and the pdfs of the measured angles @xmath1 between local and background fields reveal local field reversals that are quite common even within very broad streams of `` unipolar '' fast sw ( see figures 5 and 12 ) . on the whole , they happen some 4 to 10 percent of the time , but at the highest levels of turbulence , short - scale reversals are so frequent that on the scale of @xmath103 cm , reversed fields are practically as common as normal - polarity fields . modeling through monte - carlo simulation the pdfs of the angles @xmath0 between local fields and radial direction from the measured pdfs of the angles @xmath1 , we find that axisymmetry of the turbulent fields around a background field in or near the direction of the parker spiral is a reasonably good assumption . the modeling made under this simple assumption does indeed produce fairly accurate fits of the measured pdfs of @xmath0 angles , away from the lowest turbulence levels where @xmath45 fluctuations become dominant , that is , above @xmath174 . at the highest turbulence levels , above @xmath204 , both the model and observed @xmath0 pdfs are nearly flat on a broad range of angles @xmath0 between @xmath168 and @xmath169 ( see figure 12 ) . unsurprisingly , magnetic fields near the normal to the background field or parker spiral dominate at the highest turbulence levels , while magnetic fields close to the parker spiral direction dominate at the lowest turbulence levels @xmath46 , with a peak of the @xmath1 ( @xmath46 ) angle pdfs smoothly shifting from the parallel to the normal direction ( from the low to the high turbulence levels ) as @xmath46 ( @xmath1 ) increases [ figure 12 ( 13 ) ] . this results in a very steep dependence of the average power level of turbulence @xmath205 of equation ( [ cav ] ) on the angle to the parker spiral , and in a more moderate dependence on the angle to the radial ( figure 17 ) . the steeper dependence on @xmath1 is due to the fact that the @xmath1 pdfs remain peaked at all @xmath46 whereas the @xmath0 pdfs , due to the broad and nearly axisymmetric pdfs of the field directions relative to the background , become flat at the higher @xmath46 . the dependence is found to be even steeper for the higher - frequency amplitudes @xmath206 ( figure 18 ) , but strongly reduced for @xmath199 ( figure 19 ) . our conclusion that magnetic fields near the normal to the background parker spiral dominate at the highest turbulence levels , while magnetic fields close to the parker spiral direction dominate at the lowest turbulence levels is not modified by the use of a single - frequency turbulence - level definition @xmath207 in the place of @xmath208 ( figures 1416 ) . we do not presume to know whether the @xmath0 `` anisotropy '' of @xmath199 presented in figure 19 is a residual effect of the strong variability in the power level of turbulence . but we can certainly conclude that the extreme `` anisotropy '' seen in figures 17 and 18 is unambiguously caused by the time variability in that power level of turbulence , and not by any anisotropy in the wavevector distribution of the turbulence . clearly , a purely isotropic model of turbulence , that is , a model of turbulence with an isotropic distribution of wavevectors @xmath80 , _ can _ reproduce the pdfs of the angles @xmath1 and @xmath0 between local and background fields and between local field and radial direction presented in this paper for series of the power level of turbulence . by this we mean that an isotropic model of turbulence can not be excluded on the basis of the observed dependences of the angle pdfs on the power level of turbulence , or of the average power levels of turbulence on the angles . these dependences are entirely imputable to the time variability in the power level of turbulence observed in the fast sw streams . these results are consistent with the near isotropy found by narita et al . ( 2010 ) from four - point magnetic field measurements of the cluster spacecraft at the turbulence scales close to @xmath103 cm in the sw . the parameter @xmath46 defined by equations ( [ c ] ) and ( [ xi ] ) does order the directions of the local fields best because it physically represents the local _ statistical _ average directions . this tight ordering of the local field directions with the parameter @xmath46 brings the observed `` anisotropies '' of the average power level of turbulence to extremes much higher than otherwise found with the power level _ undivided _ by the local background field . but again , we argue that the power level has to be divided by the squared magnitude of the background magnetic field because in itself , the power in @xmath177 tells us nothing about turbulence , it is the power in @xmath178 that does . no matter how high the power in @xmath177 , if @xmath113 is high enough , it will `` quench '' the turbulence . the variations of @xmath113 itself are likely caused , in large part , by the non - uniformity of the emerging fields within each of the coronal holes at the source of the fast sw streams . we suggest that some of the variations of @xmath113 , in particular the local field reversals ( figure 5 ; section 3.6 ) , may also be signs of intermixed magnetic fields of opposite polarity , originating from a different sw stream , perhaps even signs of ongoing reconnection with these opposite - polarity fields , or remnants of reconnections that took place earlier . though it is of course also possible and even likely that some of these local field reversals are due to the reconnection , at the basis of the corona , within coronal holes , of open field lines with closed magnetic loops . this research was funded by nsf under the grant 0940976 of the solar terrestrial research program . the _ ace _ mag and _ stereo _ impact / mag data were downloaded from the _ ace _ science center at www.srl.caltech.edu/ace/asc and from sprg.ssl.berkeley.edu/impact .

the turbulent magnetic fields of a large set of fast solar wind streams measured onboard _ ace _ and _ stereo a _ and _ b _ are analyzed in an effort to identify the effects of the turbulence - level broad variations on the orientations of the local , time - averaged magnetic fields . the broad variations in the power level of turbulence cause a steep dependence of the average power level of turbulence on the angle of the local field to the parker spiral , with the highest turbulence levels found near the normal to the parker spiral and the lowest levels near the parker spiral direction . generalized quasilinear estimates of the mean cross - field displacements adapted to intermittent time - varying turbulence lead to accurate fits of the observed angle pdfs at all stable levels of turbulence , supporting the idea that isotropic turbulence could account for the observed angle pdfs . modeling of the angles between local fields and radial direction , from the pdfs of the angles between local and background fields under an assumption of axisymmetry of the turbulent fields around a background field in or near the direction of the parker spiral , also produces fairly good fits of the observed pdfs of , thereby validating the assumption . finally , local field reversals are found to be quite common even within very broad streams of `` unipolar '' fast solar wind .

the turbulent magnetic fields of a large set of fast solar wind streams measured onboard _ ace _ and _ stereo a _ and _ b _ are analyzed in an effort to identify the effects of the turbulence - level broad variations on the orientations of the local , time - averaged magnetic fields . the power level of turbulence , roughly defined as the power in the transverse field fluctuations normalized to the medium - scale average background field , tightly orders the location of the peaks in the probability distribution functions ( pdfs ) of the angles between local fields and parker spiral . as a result , the broad variations in the power level of turbulence cause a steep dependence of the average power level of turbulence on the angle of the local field to the parker spiral , with the highest turbulence levels found near the normal to the parker spiral and the lowest levels near the parker spiral direction . generalized quasilinear estimates of the mean cross - field displacements adapted to intermittent time - varying turbulence lead to accurate fits of the observed angle pdfs at all stable levels of turbulence , supporting the idea that isotropic turbulence could account for the observed angle pdfs . modeling of the angles between local fields and radial direction , from the pdfs of the angles between local and background fields under an assumption of axisymmetry of the turbulent fields around a background field in or near the direction of the parker spiral , also produces fairly good fits of the observed pdfs of , thereby validating the assumption . finally , local field reversals are found to be quite common even within very broad streams of `` unipolar '' fast solar wind .

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i

nuclear structure has been discussed mostly in the context of the liquid drop and shell models . these models have been extremely useful in explaining many observed nuclear properties . however , they are based on macroscopic concepts , and do not address the simplest nuclei , hydrogen and helium . furthermore , recent @xmath22 experiments @xcite have indicated that in heavier near - closed - shell nuclei , less than @xmath23 of the nucleons are in the single - particle orbitals that would be fully occupied in the simple shell model . to obtain a more microscopic description of nuclear structure , we may regard the nucleus as a collection of interacting nucleons described by the hamiltonian @xcite @xmath24 the interactions @xmath25 and @xmath26 are not exactly known , but @xmath25 is well constrained by the available scattering data , and binding energies and theoretical considerations place important constraints on @xmath26 . the structure of the ground - state wave function @xmath27 at small interparticle distances is influenced by the repulsive core and tensor parts of @xmath25 . most realistic models of @xmath25 contain these components and , for example , the reid @xcite , paris @xcite , urbana @xcite and new argonne @xmath28 @xcite models seem to predict similar structures . the three - nucleon interaction @xmath26 is much weaker than the @xmath25 . due to a large cancellation between kinetic and two - body interaction energies , it has a significant effect on nuclear binding energies @xcite but its effect on the structure of @xmath27 is much less than that of the better known @xmath25 . due to the strong spin - isospin dependence of @xmath25 and @xmath26 it is difficult to solve the schrdinger equation with the hamiltonian ( 1.1 ) . only recently it has been possible to obtain accurate solutions for @xmath29 nuclei @xcite with the green s function monte carlo ( gfmc ) method . accurate variational wave functions @xmath30 , which contain less than @xmath31 admixture of excited states are known for @xmath32 = 3 and 4 nuclei @xcite . the available @xmath30 for @xmath6li @xcite and @xmath7o @xcite are certainly not as accurate as those for @xmath32 = 3 and 4 , nevertheless they presumably contain most of the important structure of the @xmath27 . in this paper we examine the short - range structure of @xmath4h , @xmath5he , @xmath6li and @xmath7o by calculating the two - nucleon density distributions in states with isospin @xmath33 , spin @xmath1 , and spin projection @xmath2 . since the deuteron has only two nucleons , its one- and two - body density distributions are trivially related . variational wave functions @xmath30 and monte carlo methods are used for @xmath34 . the two - nucleon distributions in the @xmath20 states have a strong dependence on the spin projection @xmath2 . the equidensity surfaces , spanning the top three quarters of the density range in @xmath2=0 states , have toroidal shape . these tori are produced by the joint action of the repulsive core and tensor interactions . in contrast the equidensity shapes in the @xmath2=@xmath31 have dumbbell shapes , which have been studied earlier in the deuteron @xcite . a brief description of the two - nucleon interaction in @xmath20 states is given in section ii , and the density distribution of the deuteron is discussed in detail in section iii , where we show that the dumbbell - shaped distributions in @xmath2=@xmath31 states are produced by rotating tori . commonly used models of @xmath25 predict that the maximum density torus has a diameter of @xmath171 fm , and the half - maximum density torus has a thickness of @xmath170.9 fm . in section iii we relate these dimensions of the toroidal distribution to the observed electromagnetic form factors of the deuteron . the structures are rather dense ; current models predict the maximum one - body density of the torus inside the deuteron to be @xmath35 @xmath36 , i.e. , approximately twice nuclear matter density . the two - nucleon @xmath20 , @xmath37 density distributions in @xmath5he , @xmath6li and @xmath7o are compared with those of the deuteron in section iv . the distributions for @xmath8 fm differ only by a single scale factor . they indicate that in the @xmath0 state , the tensor correlations have near maximal strength for @xmath8 fm in all these nuclei . the scale factor is identified as the levinger - bethe quasi - deuteron number , and its value is compared to the ratios of total photon ( @xmath38 = 80 to 120 mev ) and pion ( @xmath39115 mev ) absorption cross sections . in order to study the nature of many - body structures induced by these compact two - body structures we study the @xmath9 , @xmath10 and @xmath11 overlaps with the @xmath30 of @xmath14he , @xmath15he and @xmath16li in section v. these depend strongly on the spin projection @xmath40 of the deuteron and indicate the presence of anisotropic structures in all these nuclei . experiments to probe these structures are suggested . pair distribution functions in other @xmath41 states are discussed in section vi . those in @xmath42 , @xmath43 states are anisotropic as expected from the pion - exchange tensor force . we also find that the number of @xmath44 pairs in a nucleus is reduced due to many - body effects involving the strong @xmath45 tensor correlations . this reduction gives a significant contribution to the saturation of nuclear binding energies . the skyrme field theory @xcite , related to qcd in the limit of large number of colors @xmath46 , has predicted toroidal shapes for the deuteron @xcite in the classical limit . density distributions of the ground states with 3 to 6 baryons have also been calculated @xcite in this limit . in the last section , vii , we summarize our results , obtained with conventional nuclear many - body theory , and indicate their relation to those of the skyrme field theory in the classical limit , and of the constituent quark model .

the two - nucleon density distributions in states with isospin , spin=1 and projection=0 and are studied inh ,he ,li ando . the dumbbell shapes are generated by rotating tori . the toroidal shapes indicate that the tensor correlations have near maximal strength at fm in all these nuclei . the toroidal distribution has a maximum - density diameter of fm and a half - maximum density thickness of.9 fm . , it could have a revealing relation to certain aspects of qcd . experiments to probe this structure and its effects in nuclei are suggested . pair distribution functions in other channels are also discussed ; those in have anisotropies expected from one - pion exchange interactions . = 10000

the two - nucleon density distributions in states with isospin , spin=1 and projection=0 and are studied inh ,he ,li ando . the equidensity surfaces for=0 distributions are found to be toroidal in shape , while those of= have dumbbell shapes at large density . the dumbbell shapes are generated by rotating tori . the toroidal shapes indicate that the tensor correlations have near maximal strength at fm in all these nuclei . they provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron , the quasi - deuteron model , and the , and=2 (-wave ) components inhe ,he andli . the toroidal distribution has a maximum - density diameter of fm and a half - maximum density thickness of.9 fm . many realistic models of nuclear forces predict these values , which are supported by the observed electromagnetic form factors of the deuteron , and also predicted by classical skyrme effective lagrangians , related to qcd in the limit of infinite colors . due to the rather small size of this structure , it could have a revealing relation to certain aspects of qcd . experiments to probe this structure and its effects in nuclei are suggested . pair distribution functions in other channels are also discussed ; those in have anisotropies expected from one - pion exchange interactions . the tensor correlations in states are found to deplete the number of pairs in nuclei and cause a reduction in nuclear binding energies via many - body effects . = 10000

nucl-th9603035

c

the main conclusions of this study of nuclear structure , as predicted by realistic models of nuclear forces , are : \(i ) the static part of the two - nucleon potential in @xmath409 state has a large angular dependence due to the tensor interaction dominated by one - pion exchange . at @xmath410 fm the difference between this potential at @xmath55 = @xmath58 and 0 is @xmath411 mev in most models ( fig . [ potfig ] ) . it confines @xmath409 pairs to the small @xmath55 region producing toroidal distributions . the central hole in these tori is due to the repulsive core in @xmath69 interaction . the maximum density in the tori is large , due to which the peak one - body density in deuterium exceeds 0.3 @xmath36 in most models . \(iii ) the diameter of the maximum density torus , and the thickness of the half - maximum density torus are predicted to be @xmath413 and 0.9 fm , respectively ; these values are supported by the observed elastic electron - deuteron scattering . \(v ) the pair distribution functions in @xmath20 and 1,0 states in different nuclei , can be scaled to lie on universal surfaces for @xmath414 fm . these universal surfaces are predicted by the density distributions of the deuteron and the @xmath415 virtual bound state . the scaling factor @xmath235 for the @xmath20 densities provides a rigorous definition of the levinger - bethe quasi - deuteron number of the nucleus . the calculated values of @xmath235 are significantly different from estimates based on independent - particle models , and in qualitative agreement with photon and pion absorption data . \(vi ) the many - body distribution functions are also predicted to be anisotropic . in particular the anisotropies of the @xmath329 , @xmath416 , and @xmath417 distributions in @xmath14he , @xmath15he and @xmath16li are strongly influenced by the toroidal structure of the deuteron . \(vii ) tensor correlations convert @xmath33=1 pairs of nucleons from @xmath1=0 to @xmath1=1 state . this many - body effect reduces the binding energies of nuclei . it does not appear as if many - body effects reduce the magnitude of tensor correlations for the range of nuclei studied here : @xmath4h to @xmath7o . due to the small size of this toroidal structure it may be worthwhile to attempt to understand it from the more basic quark degrees of freedom . within the constituent quark model @xcite it requires a solution of the six - quark problem with a suitably chosen hamiltonian . many attempts have been made ( see refs . @xcite for example ) to calculate the nucleon - nucleon interaction from approximate solutions of the six - quark hamiltonian . a direct coupling of the pions to the quarks is used to obtain the tensor part of the interaction . the toroidal structure is presumably very sensitive to this coupling and to the tensor part of the quark - quark interaction in the framework of the constituent quark model . as is well known , toroidal structure for the ground state of the deuteron was predicted many years ago @xcite using classical skyrme field theory @xcite related to qcd in the @xmath46 limit . in the classical limit one obtains a toroidal shape of @xmath418 fm in size and a binding energy of @xmath419 mev . from fig . [ potfig ] it is obvious that in the classical limit realistic models of nuclear forces would also give a deuteron binding energy in the 100 to 200 mev range . there have been attempts to include quantum corrections to this theory . a recent calculation @xcite obtains an energy of 6.18 mev for the deuteron in this model . ground states of the classical skyrme field with baryon numbers 3 to 6 have also been studied @xcite . the baryon equidensity surfaces of these classical solutions are highly anisotropic . however , the nucleon equidensity surfaces of the @xmath420 and @xmath421 @xmath14he and @xmath15he must be spherically symmetric , thus a direct comparison is not possible . nevertheless the anisotropic @xmath329 and @xmath416 distributions in @xmath14he and @xmath15he may have some relation to the baryon density distributions in the skyrme model . the authors wish to thank brian pudliner for many interesting discussions . wishes to thank a. m. eir for useful discussions on the two - cluster overlap functions . r.b.w . wishes to thank dieter kurath for useful comments on constructing wave functions for @xmath6li . the calculations were made possible by grants of computer time from the mathematics and computer science division of argonne national laboratory , the pittsburgh supercomputing center , the cornell theory center and the national energy research supercomputer center . the work of j.l.f , v.r.p . and a.a . has been partially supported by u.s . national science foundation via grant no . phy94 - 21309 , that of s.c.p . and r.b.w . by the u.s . department of energy , nuclear physics division under contract no . e-31 - 109-eng-38 , that of a.a . by universidade de lisboa , junta de investigao cientfica e tecnolgica under contract no . pbic / c / cen/1108/92 , and that of r.s . by the u.s . department of energy . electronic address : [email protected] electronic address : [email protected] electronic address : [email protected] electronic address : [email protected] electronic address : [email protected] electronic address : [email protected] r. g. arnold _ et al_. , phys . lett . * 35 * , 776 ( 1975 ) . g. g. simon , ch . schmitt , and v. h. walther , nucl . * a364 * , 285 ( 1981 ) . r. cramer _ et al_. , z. phys . c * 29 * , 513 ( 1985 ) . s. platchkov _ et al_. , nucl . phys . * a510 * , 740 ( 1990 ) . s. auffret _ et al_. , phys . lett . * 54 * , 649 ( 1985 ) . r. g. arnold _ et al_. , phys . rev . * 58 * , 1723 ( 1987 ) . m. e. schulze _ et al_. , phys . * 52 * , 597 ( 1984 ) . i. the _ et al_. , phys . rev . * 67 * , 173 ( 1991 ) . v. f. dmitriev _ et al_. , phys . * 157b * , 143 ( 1985 ) . r. gilman _ et al_. , phys . lett . * 65 * , 1733 ( 1990 ) . w. fabian and h. arenhvel , nucl * a258 * , 461 ( 1976 ) . e. hummel and j. a. tjon , phys . lett . * 63 * , 1788 ( 1989 ) . r. schiavilla and d. o. riska , phys . c * 43 * , 437 ( 1991 ) . j. w. van orden , n. devine , and f. gross , phys . lett . * 75 * , 4369 ( 1995 ) . cdddddd @xmath422nucleus & @xmath235 & @xmath423 & @xmath424 & @xmath425 & + & & & & & ip & @xmath30 + @xmath14he & 2.0 & 2.1 & 2.4(1 ) & @xmath172 & 1.5 & 1.49 + @xmath15he & 4.7 & 5.1 & 4.3(6 ) & @xmath174 & 3 . & 2.99 + @xmath16li & 6.3 & 6.3 & & & 5.5 & 5.46 + @xmath259li & 7.2 & 7.8 & & 6.5(5 ) & 6.75 & 6.73 + @xmath7o & 18.8 & 22 & 17(3 ) & 16(3 ) & 30 . & 30.1 + cddddddddd @xmath422nucleus & @xmath426 & & @xmath427 & & @xmath379 & + & & ip & & & ip & & & ip & + @xmath14he & 0.087 & 1.5 & 1.35 & 0.0016 & 0 . & 0.01 & 0.012 & 0 . & 0.14 + @xmath15he & 0.22 & 3 . & 2.5 & 0.0085 & 0 . & 0.01 & 0.060 & 0 . & 0.47 + @xmath16li & 0.24 & 4.5 & 4.0 & 0.061 & 0.5 & 0.52 & 0.104 & 4.5 & 4.96 + @xmath259li & 0.37 & 6.75 & 6.1 & 0.118 & 0.75 & 0.77 & 0.18 & 6.75 & 7.41 + @xmath7o & 1 . & 30 . & 28.5 & 1 . & 6 . & 6.05 & 1 . & 54 . & 55.5 +

many realistic models of nuclear forces predict these values , which are supported by the observed electromagnetic form factors of the deuteron , and also predicted by classical skyrme effective lagrangians , related to qcd in the limit of infinite colors . due to the rather small size of this structure the tensor correlations in states are found to deplete the number of pairs in nuclei and cause a reduction in nuclear binding energies via many - body effects .

the two - nucleon density distributions in states with isospin , spin=1 and projection=0 and are studied inh ,he ,li ando . the equidensity surfaces for=0 distributions are found to be toroidal in shape , while those of= have dumbbell shapes at large density . the dumbbell shapes are generated by rotating tori . the toroidal shapes indicate that the tensor correlations have near maximal strength at fm in all these nuclei . they provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron , the quasi - deuteron model , and the , and=2 (-wave ) components inhe ,he andli . the toroidal distribution has a maximum - density diameter of fm and a half - maximum density thickness of.9 fm . many realistic models of nuclear forces predict these values , which are supported by the observed electromagnetic form factors of the deuteron , and also predicted by classical skyrme effective lagrangians , related to qcd in the limit of infinite colors . due to the rather small size of this structure , it could have a revealing relation to certain aspects of qcd . experiments to probe this structure and its effects in nuclei are suggested . pair distribution functions in other channels are also discussed ; those in have anisotropies expected from one - pion exchange interactions . the tensor correlations in states are found to deplete the number of pairs in nuclei and cause a reduction in nuclear binding energies via many - body effects . = 10000

1408.0788

i

inference for graphical models is a topic of contemporary interest , and in this regard , various tools for inference have been proposed in the statistics literature , including establishing sufficient and/or necessary conditions for existence of high dimensional estimators . one important contribution in the area are the families of type i and type ii graphical wishart distributions introduced by letac and massam ( lm ) @xcite . the families of graphical wishart type distributions of letac - massam have the distinct advantage of being standard conjugate for gaussian graphical models , have attractive hyper markov properties , and have multiple shape parameters . this is in contrast with the classical wishart distribution which has just one shape parameter that is restricted to the one dimensional gindikin set - see . these multi - parameter graphical wishart distributions are therefore useful for flexible high dimensional inference @xcite , and have also been used as flat conjugate priors for objective bayesian inference . since the domain of integrability of these high dimensional priors are not fully identified , it is not clear when these distributions yield proper priors . the lm conjecture aims to address this question formally . the lm conjecture is also critical for understanding when these priors lead to well - defined bayes estimators , since this is not always guaranteed in high dimensional , sample starved settings . in this sense resolving the lm conjecture can be viewed as a bayesian analogue of the frequentist problem of identifying sufficient and necessary conditions for the existence of the maximum likelihood estimator for gaussian graphical models . the primary goal of this paper is therefore to resolve a conjecture of letac and massam ( henceforth the lm conjecture ) which concerns identifying the parameter sets for the families of the so - called type i and type ii wishart distributions . a definitive solution to the lm conjecture has remained elusive to the graphical models community ever since it was formally posed by letac and massam about ten years ago . the conjecture also has deep and profound connections to gindikin s result @xcite on the region of integrability of the p - variate gamma function . this domain is referred to as the gindikin set and is given as follows : @xmath0 though the main goal of this paper is to resolve the lm conjecture , we note that understanding the domain of integrability of these graphical wishart distributions is important for two other reasons beyond bayesian inference and model selection : 1 ) these two classes of distributions also serve as statistical models in their own right for matrix - variate distributions defined on sparse subsets of the cone , and 2 ) the integrals of these graphical wishart densities are extensions of the gamma and multivariate gamma functions on sparse manifolds . thus understanding the domains of integrability of these graphical wishart distributions is of independent mathematical interest that is closely linked to generalizations of the gindikin set . in what follows we shall employ the notation introduced in the work of letac and massam @xcite . the type i wishart and type ii wishart are defined , respectively , on the cones @xmath1 and @xmath2 associated with a decomposable graph @xmath3 , i.e. , an undirected graph that that has no induced cycle of length greater than or equal to four . these cones naturally arise as the set of covariance and inverse - covariance parameters for a gaussian undirected graph model over @xmath3 . i.e. , the family of multivariate gaussian distributions that obey the pairwise or global markov property with respect to @xmath3 @xcite . it is well known that if the vertices of @xmath3 are labeled @xmath4 , then a p - variate gaussian distribution @xmath5 obeys the global markov property with respect to @xmath3 if @xmath6 whenever there exists no edge between @xmath7 and @xmath8 . this property gives a simple characterization of the associated inverse - covariance matrices , i.e. , the elements of the cone @xmath2 . the cone @xmath1 is the dual cone of @xmath2 and its elements are incomplete covariance matrices where only the entries along the edges of @xmath3 are specified , and the rest of the entries are unspecified . however , the specified entries are also the only functionally independent entries of the covariance matrix parameter , and uniquely determine the rest of the entries ( the unspecified entries that is ) . in particular , the space of covariance matrices for the gaussian inverse - covariance graph model over @xmath3 can be identified with the cone @xmath9 . when @xmath3 is complete , i.e. , in the full model , type i and type ii wishart distributions are identical to the classical wishart distribution . moreover by restricting the multi - parameters to a specific one dimensional space , these distributions reduce to the hyper wishart distribution introduced by dawid and lauritzen @xcite and the g - wishart defined by roverato in @xcite respectively ( see @xcite for more details ) . although having multiple shape parameters allow the type i wishart and type ii wishart distributions to be more flexible as prior distributions , there is a trade - off : the sets of multi - parameters are not completely identified . in an attempt to identify the set of multi - parameterss of the type i wisharts , denoted by @xmath10 , and that of type ii wisharts , denoted by @xmath11 , in ( * ? ? ? * section 3.3 ) letac and massam first consider the case when @xmath3 is homogeneous , i.e. , @xmath3 is decomposable and has no induced paths of length greater than or equal to 4 . when @xmath3 is homogeneous letac and massam are able to completely identify @xmath10 and @xmath11 and , furthermore , give algebraic expressions for the elements of both sets . if @xmath3 is non - homogeneous , however , in ( * section 3.4 ) the authors are able to only partially identify the sets @xmath10 and @xmath11 . more specifically , for each perfect order @xmath12 of @xmath3 , they identify a subset @xmath13 of @xmath10 and a subset @xmath14 of @xmath11 . the authors then proceed to conjecture that @xmath10 and @xmath11 are indeed the union of @xmath13 and @xmath14 over all perfect orders of the cliques of @xmath15 , respectively . they demonstrate that the conjecture holds when @xmath3 is the 4-path , the simplest non - homogeneous decomposable graph , @xmath16 . they note that a similar calculation for the 5-path appears insurmountable . on a different route , but motivated by the recent work of letac and massam @xcite and rajaratnam et al . @xcite for concentration graph models , and khare and rajaratnam @xcite for covariance graph models , the authors of this paper undertook a parallel analysis in @xcite for directed acyclic graph models , abbreviated dag models , or bayesian networks . in @xcite , we introduce a new class of multi - parameter wishart type distributions , useful for bayesian inference for gaussian dag models . one of its advantages is that the framework in @xcite applies to all directed acyclic graph models and not just the narrower class of perfect dags . furthermore the normalizing constant for these dag wisharts is available in closed form for all dags . it is also well - known fact that the family of inverse - covariance graph model over a decomposable graph @xmath3 is markov equivalent to the family of dag models over a perfect dag version of @xmath3 . as we shall demonstrate later , this , in particular , implies that both the type ii wisharts of letac - massam in @xcite and the dag wisharts in @xcite are indeed defined on the same cone @xmath2 . therefore , a relevant question is how the functional form and the multi - parameter set of the type ii wishart density compare with those of the dag wishart . a similar comparison arises between the type i wisharts of letac - massam and the riez distributions for decomposable graphs introduced by andersson and klein in @xcite . such comparisons shed light on the lm conjecture since the domains of integrability of the dag wisharts are fully specified in @xcite . in this paper we develop tools which allows a careful comparison of these two types of wisharts on @xmath2 and @xmath1 , leading to counterexamples , which in turn can then be used to conclude that the lm conjecture does not hold in general . the primary key to resolving the part of the lm conjecture that concerns the type ii wishart is theorem [ thm : comparison ] of this paper . in this theorem we show that for any non - homogeneous decomposable graph @xmath15 there exists a perfect order @xmath17 and a perfect dag version of @xmath15 , associated with this order , such that the type ii wishart distribution on @xmath14 is a special case of the dag wishart distribution . using this observation , and depending on the perfect dag version of the underlying graph @xmath3 , we derive a condition in proposition [ prop : b1 ] , which when satisfied , can lead to counterexamples to the lm conjecture . we then proceed to present two graphs ( with their respective perfect dag versions ) where the stated condition in proposition [ prop : b1 ] is satisfied and lead to counterexamples to the lm conjecture . the counterexample to the other part of the lm conjecture concerning the type i wishart distribution is given after proposition [ prop : a1 ] where we prove that the same condition as that in proposition [ prop : b1 ] can lead to resolving the lm conjecture . in addition to disproving the lm conjecture , we also prove that not only for non - homogeneous decomposable graphs , but also for homogeneous graphs , the family of type ii wisharts are a subclass of the family of dag wisharts . the organization of the paper is as follows . in [ sec : pre ] we recall some fundamental notation and concepts in graphical models and , in particular , for gaussian undirected graphical models . in [ sec : wishart_for_decomposable graph ] we provide the reader with definition of type i and type ii wishart distributions and formally state the letac - massam conjecture . in [ subsec : gaussian_over_d ] and [ sub : dag_wishart ] we give a short introduction to guassian dag models and the families of dag wisharts . the main results of the paper are presented in the ensuing four sections . in [ sub : comparison_non_hom ] and [ sub : typeii_dag_wish_hom ] , we develop tools which enable a detailed comparison between type ii wisharts on one hand , and on the other hand , dag wisharts for the corresponding dag versions of the associated undirected graphs . moreover , tools are developed for comparisons of both decomposable and homogeneous type ii wisharts to their dag wishart counterparts . using the tools developed in [ sub : comparison_non_hom ] and [ sub : typeii_dag_wish_hom ] , we formally resolve the letac - massam conjecture in [ sub : lm_partb ] and [ sub : lm_parta ] by providing counterexamples .

the wishart distribution , defined on the open convex positive definite cone , plays a central role in multivariate analysis and multivariate distribution theory . its domain of integrability is often referred to as the gindikin set . in recent years , a variety of useful extensions of the wishart have been proposed in the literature for the purposes of studying markov random fields / graphical models . in particular , generalizations of the wishart , referred to as type i and type ii wishart distributions , have been introduced by letac and massam ( _ annals of statistics _ ) and play important roles in both frequentist and bayesian inference for gaussian graphical models . these distributions have been especially useful in high - dimensional settings due to the flexibility offered by their multiple shape parameters . the domain of integrability of these graphical wisharts are however not fully identified , despite its critical role in determining existence of high dimensional bayes estimators and specifying diffuse proper priors for gaussian graphical models . moreover , these graphical wisharts also serve as statistical models in their own right for matrix - variate distributions defined on sparse convex subsets of the cone . besides its statistical motivation , understanding the domain of integrability is also of independent mathematical interest as these graphical wisharts are extensions of the gamma function on sparse manifolds . in this paper we resolve a long - standing conjecture of letac and massam ( lm ) concerning the domains of the multi - parameters of graphical wishart type distributions . this conjecture , posed in _ annals of statistics _ , also relates fundamentally to the existence of bayes estimators corresponding to these high dimensional priors . to achieve our goal , we first develop novel theory in the context of probabilistic analysis of graphical models . using these tools , and a recently introduced class of wishart distributions for directed acyclic graph ( dag ) models , we proceed to give counterexamples to the lm conjecture , thus completely resolving the problem . our analysis also proceeds to give useful insights on graphical wishart distributions with implications for bayesian inference for such models .

the wishart distribution , defined on the open convex positive definite cone , plays a central role in multivariate analysis and multivariate distribution theory . its domain of integrability is often referred to as the gindikin set . in recent years , a variety of useful extensions of the wishart have been proposed in the literature for the purposes of studying markov random fields / graphical models . in particular , generalizations of the wishart , referred to as type i and type ii wishart distributions , have been introduced by letac and massam ( _ annals of statistics _ ) and play important roles in both frequentist and bayesian inference for gaussian graphical models . these distributions have been especially useful in high - dimensional settings due to the flexibility offered by their multiple shape parameters . the domain of integrability of these graphical wisharts are however not fully identified , despite its critical role in determining existence of high dimensional bayes estimators and specifying diffuse proper priors for gaussian graphical models . moreover , these graphical wisharts also serve as statistical models in their own right for matrix - variate distributions defined on sparse convex subsets of the cone . besides its statistical motivation , understanding the domain of integrability is also of independent mathematical interest as these graphical wisharts are extensions of the gamma function on sparse manifolds . in this paper we resolve a long - standing conjecture of letac and massam ( lm ) concerning the domains of the multi - parameters of graphical wishart type distributions . this conjecture , posed in _ annals of statistics _ , also relates fundamentally to the existence of bayes estimators corresponding to these high dimensional priors . to achieve our goal , we first develop novel theory in the context of probabilistic analysis of graphical models . using these tools , and a recently introduced class of wishart distributions for directed acyclic graph ( dag ) models , we proceed to give counterexamples to the lm conjecture , thus completely resolving the problem . our analysis also proceeds to give useful insights on graphical wishart distributions with implications for bayesian inference for such models .

math-ph0612075

i

a _ point process _ in a set @xmath3 is a random collection of points in @xmath3 , whose distribution is described by a probability measure @xmath12 on the set of all possible point collections . here we will take @xmath3 to be @xmath13 , a lattice such as @xmath14 , the torus @xmath15 , a lattice on the torus , or an open subset of any of these . we always assume that any bounded subset of @xmath3 contains only finitely many points of the collection ( this is of course automatically true if @xmath3 is a lattice ) ; the collection of points is then necessarily countable and we will write it as @xmath16 , with the understanding that the @xmath17 are all distinct . well known examples of point processes are gibbs measures for equilibrium systems of statistical mechanics . the points of the process are then interpreted as the positions of particles ; because the particle configuration is identified with a subset of physical space , the models satisfy an exclusion principle : no two particles can occupy the same position . point processes are also used to model phenomena other than those of statistical mechanics , such as trains of neural spikes @xcite , departure times from queues @xcite , and positions of stars in galaxies @xcite . in many of these cases the quantities of primary interest , partly because they are the ones most accessible to experiment , are the low order correlations , such as the one particle density @xmath18 and the pair density @xmath19 . these may be defined in terms of expectations ( averages ) , with respect to the measure @xmath12 , of products of the ( random ) _ empirical field _ @xmath20 describing the process . for continuum systems , i.e. , when @xmath3 is @xmath13 or an open subset of @xmath13 , @xmath20 is defined by @xmath21 where @xmath22 is the dirac delta function and the @xmath17 s are as above the ( random ) positions of the points of the process . then , with @xmath23 denoting expectation with respect to @xmath12 , @xmath24 and so on ; in general , @xmath25 equation ( [ defrhon ] ) defines @xmath26 as a measure , and we will always assume that this measure assigns finite mass to any bounded set in @xmath27 ( which means that the number of particles in a bounded set in @xmath13 is a random variable with finite moments up to order @xmath28 ) . in many cases this measure is absolutely continuous with respect to lebesgue measure and we identify @xmath29 with its density , i.e. , @xmath30 is the probability of finding a particle in the infinitesimal box @xmath31 at @xmath32 for @xmath33 . we will assume that , whenever possible , @xmath26 is extended by continuity to be defined at points where two of its arguments coincide . the @xmath26 , here and in the lattice case discussed in the next paragraph , are often referred to as the @xmath28-particle distribution functions or correlation functions . when @xmath3 is discrete , a finite set or a lattice , we will also use the notation ( [ eta ] ) and the definitions ( [ defrho1])([defrhon ] ) , interpreting @xmath34 as the kronecker delta @xmath35 , so that @xmath36 has value 0 or 1 , depending on whether the site @xmath37 is empty or occupied . note that if @xmath38 then @xmath29 , @xmath39 , vanishes whenever @xmath40 for some @xmath41 , and that for distinct sites @xmath42 , @xmath29 is the probability of having particles at these sites . in this paper we shall study the following _ realizability problem : _ given functions @xmath18 , @xmath43 , @xmath44 , @xmath45 , nonnegative and symmetric , does there exist a point process for which these are the correlations ? since only a finite number of correlations are prescribed , the problem may be regarded as an infinite dimensional version of the standard truncated moment problem @xcite . the full realizability problem , in which all the correlations @xmath4 , @xmath46 are given , was studied by a. lenard @xcite . realizability , and the related question of fully describing the realizing process , are long standing problems in the classical theory of fluids @xcite , @xcite , and @xcite , recently revived by torquato , stillinger , et al . this problem has been also investigated in the context of the quantum system see e.g. @xcite , @xcite , and @xcite . an important ingredient in that theory is the introduction of various approximation schemes for computing @xmath47 , such as the percus - yevick and hyper - netted chain approximations @xcite . it is then of primary interest to determine whether or not the resulting functions @xmath48 in fact correspond to any point process , that is , are in some sense internally consistent . if so they can provide rigorous bounds for the entropy of the system under consideration . a novel application of the realizability problem to the determination of the maximal density of sphere packing in high dimensions is discussed in @xcite . applications of the problem of describing a point process from its low order correlations occur in other contexts , for example , in the study of neural spikes @xcite . in this and other physical situations it is natural to consider a closely related problem in which the @xmath4 , @xmath49 , are specified only on part of the domain @xmath3 ; for example , on the lattice we might only specify the nearest neighbor correlations . see @xcite for a similar problem in error correcting codes . we will not consider this case further here , except for some comments at the end of section 6 . an important special case is that in which @xmath3 is @xmath13 , @xmath14 , or a periodic version of one of these ( a torus ) , and the point process is translation invariant . the specified correlation functions will then also be translation invariant and may be written in the form @xmath50 as we often work with @xmath51 , we write @xmath52 . we will often state our arguments and results in the translation invariant case , but these may frequently be extended to the more general situation ; when we do not impose translation invariance we will use a notation similar to ( [ g ] ) : @xmath53 we now make some general remarks in order to put the realizability problem in context . first , we observe that if the correlations ( [ rho])([g ] ) can be realized for some density @xmath8 , then they can also be realized , for the same functions @xmath54 , for any @xmath55 with @xmath56 @xcite . to see this , note that if @xmath57 is the empirical field with density @xmath8 , then @xmath58 , where the @xmath59 are independent , identically distributed bernoulli random variables with expectation @xmath60 , is a field with density @xmath55 having the same value for all @xmath61 s . in other words , the new measure is constructed by independently choosing to delete or retain each point in a configuration , keeping a point with probability @xmath60 . ( we will refer to this construction as _ thinning_. ) in this light it is thus natural to pose the realizability problem in the following form : given the @xmath61 , @xmath62 , what is the least upper bound @xmath63 of the densities for which they can be realized ? it is of course possible in the continuum case to have @xmath64 ; for example , if @xmath65 for @xmath66 then for any density @xmath67 a poisson process realizes the correlations . for the lattice systems considered here , on the other hand , we always have @xmath68 . lacking a full answer to this question , one may of course ask rather for upper and lower bounds on @xmath63 . a lower bound @xmath69 may be obtained by the construction of a process at density @xmath70 ; we discuss such constructions in sections [ lowrho][subseclee ] and show that @xmath71 under reasonable restrictions on the @xmath61 in ( [ g ] ) . upper bounds on @xmath63 may be obtained from necessary conditions for realizability , some of which are described in section [ secneccond ] . beyond the question of realizability one may ask about the number or more generally about the types of measures which give rise to a specified set of correlations @xmath4 , @xmath2 . a natural question in the theory of fluids , for example , is whether any of these measures are gibbsian for interactions in a particular class ; for example , given @xmath72 and @xmath9 , is there a gibbs measure realizing these correlations which involves only pair interactions ? this question is considered in section [ gibbs ] , where we discuss the nature of the realizing measure @xmath12 which maximizes the gibbs - shannon entropy . the outline of the rest of this paper is as follows . in section [ secneccond ] , we discuss some necessary conditions for realizability . ( in a separate paper @xcite we will present general necessary and sufficient conditions . ) sections [ lowrho ] , [ triplet ] , and [ subseclee ] cover proofs of realizability : in section [ lowrho ] we prove a theorem , a generalization of one proven by r. v. ambartzumian and h. s. sukiasian @xcite , showing that if @xmath73 is absolutely integrable and @xmath74 satisfies a certain stability condition then the pair @xmath75 is realizable for sufficiently small @xmath8 , with explicitly given higher correlations . in section [ triplet ] we show that the construction can be extended to the case in which the third correlation function @xmath76 is also specified , showing in particular that the realization determined by @xmath75 alone is not unique ; in fact since @xmath76 can take an uncountable number of values there are at low values of @xmath8 an uncountable number of measures realizing @xmath75 . we note also possible extensions to higher order @xmath61 . in section [ subseclee ] we give a variant construction for lattice systems , based on the lee - yang theorem @xcite . in section [ gibbs ] we show that a problem with specified @xmath75 , on a finite set , e.g. , a periodic lattice , may be realized by a gibbs measure with just one- and two - particle potentials whenever @xmath77 . we make some concluding remarks in section [ conclude ] , and in the appendices discuss in some detail an illustrative one - dimensional example and give some technical proofs .

we describe some necessary and sufficient conditions on the s for this to be true . our primary examples are , , and an arbitrary finite set . in particular , we extend a result by ambartzumian and sukiasian showing realizability at sufficiently small densities . we also investigate in detail a simple example in which a uniform density and translation invariant are specified on ; there is a gap between our best upper bound on possible values of and the largest for which realizability can be established .

there are various situations in which it is natural to ask whether a given collection of functions , , , defined on a set , are the first correlation functions of a point process on . here we describe some necessary and sufficient conditions on the s for this to be true . our primary examples are , , and an arbitrary finite set . in particular , we extend a result by ambartzumian and sukiasian showing realizability at sufficiently small densities . typically if any realizing process exists there will be many ( even an uncountable number ) ; in this case we prove , when is a finite set , the existence of a realizing gibbs measure with body potentials which maximizes the entropy among all realizing measures . we also investigate in detail a simple example in which a uniform density and translation invariant are specified on ; there is a gap between our best upper bound on possible values of and the largest for which realizability can be established . * realizability of point processes * t. kuna , j. l. lebowitz , and e. r. speer

hep-th0110007

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we begin these lectures with one of our favorite equations @xmath1 this is the bekenstein - hawking area - entropy law , which says that the entropy @xmath2 associated with an event horizon is its area @xmath3 divided by @xmath4 , where @xmath5 is newton s constant @xcite . this is a macroscopic formula . it should be viewed in the same light as the macroscopic thermodynamic formulae that were first studied in the 18th and 19th centuries . it describes how properties of event horizons in general relativity change as their parameters are varied . this behavior can be succinctly summarized by ascribing to them an entropy given by ( [ bh ] ) . one of the surprising and impressive features of this formula is its universality . it applies to all kinds of black holes with all kinds of charges , shapes and rotation , as well as to black strings and to all of the strange new objects we ve found in string theory . it also applies to cosmological horizons , like the event horizon in de sitter space @xcite . after boltzmann s work we tend to think of entropy in microscopic statistical terms as something which counts the number of microstates of a system . such an interpretation for the entropy ( [ bh ] ) was not given at the time that the law was discovered in the early 70s . a complete understanding of this law , and in particular of the statistical origin of this law , is undoubtedly one of the main keys to understanding what quantum gravity is and what the new notions are that replace space and time in quantum gravity . there has been some definite but still limited progress in understanding the microscopic origin of ( [ bh ] ) in very special cases of black holes which can be embedded into string theory @xcite . that little piece of ( [ bh ] ) that we have managed to understand has led to all kinds of interesting insights , ultimately culminating in the ads / cft correspondence @xcite . nevertheless the progress towards a complete understanding of ( [ bh ] ) is still very limited , because we only understand special kinds of black holes among which schwarzschild black holes are not included and we certainly do nt understand much about cosmological event horizons , such as the horizon in de sitter space . in some ways cosmological horizons are much more puzzling than black hole horizons because in the black hole case one may expect that the black hole is a localized object with some quantum microstates . then if you could provide the correct description of that localized object , you would be able to count those microstates and compare your result to the bekenstein - hawking formula and see that they agree . in some stringy cases this agreement has been achieved . on the other hand in de sitter space the event horizon is observer dependent , and it is difficult even to see where the quantum microstates that we would like to count are supposed to be . why has there been significant progress in understanding black hole entropy , but almost no progress in understanding the entropy of de sitter space ? one reason is that one of the principal tools we ve used for understanding black hole entropy is supersymmetry . black holes can be supersymmetric , and indeed the first black holes whose entropy was counted microscopically were supersymmetric . since then we ve managed to creep away from the supersymmetric limit a little bit , but not very far , and certainly we never managed to get all the way to schwarzschild black holes . so supersymmetry is a crutch that we will need to throw away before we can do anything about de sitter space . indeed there is a very simple observation @xcite that de sitter space is inconsistent with supersymmetry in the sense that there is no supergroup that includes the isometries of de sitter space and has unitary representations . a second , related , obstacle to progress in understanding de sitter space is that so far we have not been able to embed it in a fully satisfactory manner into string theory . while the importance of understanding de sitter quantum gravity has been evident for decades , it has recently been receiving more attention@xcite . one reason for this is the recent astronomical observations which indicate that the cosmological constant in our universe is positive @xcite . a second reason is that recent progress in string theory and black holes provides new tools and suggests potentially fruitful new angles . so perhaps de sitter quantum gravity is a nut ready to be cracked . these lectures are mostly an elementary discussion of the background material relevant to the problem of de sitter quantum gravity . the classical geometry of de sitter space is described in section [ secclassical ] . scalar quantum field theory in a fixed de sitter background is in section [ secqft ] . finally , in section [ secqg ] we turn to some recent work on de sitter quantum gravity . a pedagogical derivation is given of the appearance of the the two dimensional conformal group in three dimensional de sitter space , which leads to the ds / cft correspondence @xcite . this section also contains a derivation , missing in previous treatments , of the asymptotically de sitter boundary conditions on the metric . the appendix contains a calculation of the asymptotic form of the brown - york stress tensor .

these lectures present an elementary discussion of some background material relevant to the problem of de sitter quantum gravity . the final lecture contains a pedagogical discussion of the appearance of the conformal group as an asymptotic symmetry group , which is central to the ds / cft correspondence . a ( previously lacking ) derivation of asymptotically de sitter boundary conditions is also given .

these lectures present an elementary discussion of some background material relevant to the problem of de sitter quantum gravity . the first two lectures discuss the classical geometry of de sitter space and properties of quantum field theory on de sitter space , especially the temperature and entropy of de sitter space . the final lecture contains a pedagogical discussion of the appearance of the conformal group as an asymptotic symmetry group , which is central to the ds / cft correspondence . a ( previously lacking ) derivation of asymptotically de sitter boundary conditions is also given . ( 0,0)(0,0 ) ( 300,205)pupt-2015 ( 300,220)hep - th/0110007 0.25 in _ department of physics _ _ princeton university _ _ princeton , nj 08544 _ 0.5 in

1412.4142

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since the work of arratia @xcite on annihilating random walks , it is known that , when starting with infinitely many supporters of each opinion , the one - dimensional voter model fluctuates , i.e. , the number of opinion changes at each vertex is almost surely infinite . in contrast , as a consequence of irreducibility , the process on finite connected graphs fixates to a configuration in which all the vertices share the same opinion . the objective of this paper is to study the dichotomy between fluctuation and fixation for a general class of opinion models with confidence threshold . the main novelty is to equip the set of opinions with the structure of a connected graph and use the induced graph distance to define mathematically a level of disagreement among individuals . based on this modeling approach , some of the most popular models of opinion dynamics can be recovered by choosing the structure of the opinion space suitably : the constrained voter model , independently introduced in @xcite , is obtained by assuming that the opinion space is a path , while the axelrod model for the dissemination of cultures @xcite and the discrete deffuant model @xcite are closely related to our models when the opinion space is a hamming graph and a hypercube , respectively . * model description * the class of models considered in this article are examples of interacting particle systems inspired from the voter model @xcite for the dynamics of opinions . individuals are located on the vertex set of a connected graph and characterized by their opinion , with the set of opinions being identified with the vertex set of another connected graph . the former graph represents the underlying spatial structure and is used to determine the interaction neighborhood of each individual . the latter graph , that we call the opinion graph , represents the structure of the opinion space and is used to determine the distance between two opinions and the level of disagreement between two individuals . from now on , we call spatial distance the graph distance induced by the spatial structure and opinion distance the graph distance induced by the opinion graph . individuals interact with each of their neighbors at rate one . as the result of an interaction , an individual imitates her neighbor if and only if the distance between their opinions just before the interaction does not exceed some confidence threshold @xmath0 . more formally , we let @xmath1 be two connected graphs , where @xmath2 is also assumed to be finite . then , our opinion model is the continuous - time markov chain whose state at time @xmath3 is a spatial configuration @xmath4 and with transition rates at vertex @xmath5 given by @xmath6 here , the set @xmath7 denotes the interaction neighborhood of vertex @xmath8 , i.e. , all the vertices which are at spatial distance one from @xmath8 , while @xmath9 refers to the opinion distance between @xmath10 and @xmath11 , which is the length of the shortest path connecting both opinions on the opinion graph . note that the classical voter model is simply obtained by assuming that the opinion graph consists of two vertices connected by an edge and that the confidence threshold equals one . the general class of opinion models described by the transition rates where the opinion space is represented by a finite connected graph equipped with its graph distance has been recently introduced in @xcite . * main results * the main question about the general model is whether the system fluctuates and clusters , leading ultimately the population to a global consensus , or fixates in a highly fragmented configuration . recall that the process is said to * * fluctuate * when @xmath12 for all @xmath5 , * * fixate * when @xmath13 for all @xmath5 , * * cluster * when @xmath14 as @xmath15 for all @xmath16 . note that whether the system fluctuates and clusters or fixates in a fragmented configuration is very sensitive to the initial configuration . also , throughout this paper , we assume that the process starts from a product measure with densities which are constant across space , i.e. , @xmath17 only depends on opinion @xmath11 but not on site @xmath8 . to avoid trivialities , these densities are assumed to be positive . sometimes , we will make the stronger assumption that all the opinions are equally likely at time zero . these two hypotheses correspond to the following two conditions : @xmath18 where @xmath19 refers to the total number of opinions . key quantities to understand the long - term behavior of the system are the radius and the diameter of the opinion graph defined respectively as the minimum and maximum eccentricity of any vertex : @xmath20 to state our first theorem , we also introduce the subset @xmath21 that we shall call the * @xmath22-center * of the opinion graph . the next result states that , whenever the confidence threshold is at least equal to the radius of the opinion graph , the infinite one - dimensional system fluctuates and clusters while the probability that the finite system reaches ultimately a consensus , i.e. , fixates in a configuration where all the individuals share the same opinion , is bounded from below by a positive constant that does not depend on the size of the spatial structure . here , infinite one - dimensional means that the spatial structure is the graph with vertex set @xmath23 and where each vertex is connected to its two nearest neighbors . [ th : fluctuation ] assume . then , 1 . the process on @xmath23 fluctuates whenever @xmath24 assume in addition that @xmath25 . then , 1 . the process on @xmath23 clusters and 2 . the probability of consensus on any finite connected graph satisfies @xmath26 we will show that the @xmath22-center is nonempty if and only if the threshold is at least equal to the radius so the probability of consensus in the last part is indeed positive . in fact , except when the threshold is at least equal to the diameter , in which case all three conclusions of the theorem turn out to be trivial , when the threshold is at least equal to the radius , both the @xmath22-center and its complement are nonempty , and therefore form a partition that satisfies . in particular , fluctuation also holds when the radius is not more than the threshold . we also point out that the last part of the theorem implies that the average domain length in the final absorbing state scales like the population size , namely @xmath27 . this result applies in particular to the constrained voter model where the opinion graph is a path with three vertices interpreted as leftists , centrists and rightists , thus contradicting the conjecture on domain length scaling in @xcite . we now seek for sufficient conditions for fixation of the infinite one - dimensional system , beginning with general opinion graphs . at least for the process starting from the uniform product measure , these conditions can be expressed using @xmath28 which is the number of pairs of opinions at opinion distance @xmath29 of each other . in the statement of the next theorem , the function @xmath30 refers to the ceiling function . [ th : fixation ] for the opinion model on @xmath23 , fixation occurs 1 . when holds and @xmath31 2 . for some initial distributions when @xmath32 . combining theorems [ th : fluctuation].a and [ th : fixation].b shows that these two results are sharp when @xmath33 , which holds for opinion graphs such as paths and stars : for such graphs , the one - dimensional system fluctuates starting from any initial distribution if and only if @xmath25 . our last theorem , which is also the most challenging result of this paper , gives a significant improvement of the previous condition for fixation for * distance - regular * opinion graphs . this class of graphs is defined mathematically as follows : let @xmath34 be the * distance partition * of the vertex set @xmath35 for some @xmath36 . then , the opinion graph is said to be a distance - regular graph when the so - called * intersection numbers * @xmath37 only depend on the distance @xmath38 but not on the particular choice of @xmath39 and @xmath40 . this implies that , for distance - regular opinion graphs , the number of vertices @xmath41 does not depend on vertex @xmath10 . to state our last theorem , we let @xmath42 where by convention an empty sum is equal to zero and an empty product is equal to one , and where the coefficients @xmath43 and @xmath44 are defined in terms of the intersection numbers as @xmath45 then , we have the following sufficient condition for fixation . [ th : dist - reg ] assume and . then , the process on @xmath23 fixates when @xmath46 to understand the coefficients @xmath43 and @xmath44 , we note that , letting @xmath39 and @xmath11 be two opinions at opinion distance @xmath47 of each other , we have the following interpretation : @xmath48 * outline of the proofs * the lower bound for the probability of consensus on finite connected graphs follows from the optional stopping theorem after proving that the process that keeps track of the number of supporters of opinions belonging to the @xmath22-center is a martingale . the analysis of the infinite system is more challenging . the first key to all our proofs is to use the formal machinery introduced in @xcite that consists in keeping track of the disagreements along the edges of the spatial structure . this technique has also been used in @xcite to study related models . in the context of our general opinion model , we put a pile of @xmath29 particles on edges that connect individuals who are at opinion distance @xmath29 of each other , i.e. , we set @xmath49 the definition of the confidence threshold implies that , piles with at most @xmath22 particles , that we call active , evolve according to symmetric random walks , while larger piles , that we call frozen , are static . in addition , the jump of an active pile onto another pile results in part of the particles being annihilated . the main idea to prove fluctuation is to show that , after identifying opinions that belong to the same member of the partition , the process reduces to the voter model , and use that the one - dimensional voter model fluctuates according to @xcite . fluctuation , together with the stronger assumption @xmath25 , implies that the frozen piles , and ultimately all the piles of particles , go extinct , which is equivalent to clustering of the opinion model . in contrast , fixation occurs when the frozen piles have a positive probability of never being reduced , which is more difficult to establish . to briefly explain our approach to prove fixation , we say that the pile at @xmath50 is of order @xmath51 when @xmath52 to begin with , we use a construction due to @xcite to obtain an implicit condition for fixation in terms of the initial number of piles of any given order in a large interval . large deviation estimates for the number of such piles are then proved and used to turn this implicit condition into the explicit condition . to derive this condition , we use that at least @xmath53 active piles must jump onto a pile initially of order @xmath54 to turn this pile into an active pile . condition is obtained assuming the worst case scenario when the number of particles that annihilate is maximal . to show the improved condition for fixation for distance - regular opinion graphs , we use the same approach but count more carefully the number of annihilating events . first , we use duality - like techniques to prove that , when the opinion graph is distance - regular , the system of piles becomes markov . this is used to prove that the jump of an active pile onto a pile of order @xmath55 reduces / increases its order with respective probabilities at most @xmath43 and at least @xmath44 . this implies that the number of active piles that must jump onto a pile initially of order @xmath54 to turn it into an active pile is stochastically larger than the first hitting time to state 1 of a certain discrete - time birth and death process . this hitting time is equal in distribution to @xmath56 the probabilities @xmath43 and @xmath44 are respectively the death parameter and the birth parameter of the discrete - time birth and death process while the integer @xmath57 is the number of states of this process , which is also the maximum order of a pile . * application to concrete opinion graphs * we now apply our general results to particular opinion graphs , namely the ones which are represented in figure [ fig : graphs ] . first , we look at paths and more generally stars with @xmath58 branches of equal length . for paths , one can think of the individuals as being characterized by their position about one issue , ranging from strongly agree to strongly disagree . for stars , individuals are offered @xmath58 alternatives : the center represents undecided individuals while vertices far from the center are more extremist in their position . these graphs are not distance - regular so we can only apply theorem [ th : fixation ] to study fixation of the infinite system . this theorem combined with theorem [ th : fluctuation ] gives the following two corollaries . [ cor : path ] when @xmath2 is the path with @xmath59 vertices , * the system fluctuates when holds and @xmath60 whereas * the system fixates when holds and @xmath61 . [ cor : star ] when @xmath2 is the star with @xmath58 branches of length @xmath62 , * the system fluctuates when holds and @xmath63 whereas * the system fixates when holds , @xmath64 and @xmath65 to illustrate theorem [ th : dist - reg ] , we now look at distance - regular graphs , starting with the five convex regular polyhedra also known as the platonic solids . these graphs are natural mathematically though we do not have any specific interpretation from the point of view of social sciences except , as explained below , for the cube and more generally hypercubes . for these five graphs , theorems [ th : fluctuation ] and [ th : dist - reg ] give sharp results with the exact value of the critical threshold except for the dodecahedron for which the behavior when @xmath66 remains an open problem . [ cor : polyhedron ] assume . then , * the tetrahedral model fluctuates for all @xmath67 , * the cubic model fluctuates when @xmath68 and fixates when @xmath69 , * the octahedral model fluctuates for all @xmath67 , * the dodecahedral model fluctuates when @xmath70 and fixates when @xmath71 , * the icosahedral model fluctuates when @xmath68 and fixates when @xmath69 . next , we look at the case where the individuals are characterized by some preferences represented by the set of vertices of a cycle . for instance , as explained in @xcite , all strict orderings of three alternatives can be represented by the cycle with @xmath72 vertices . [ cor : cycle ] when @xmath2 is the cycle with @xmath59 vertices , * the system fluctuates when holds and @xmath73 whereas * the system fixates when hold and @xmath74 . finally , we look at hypercubes with @xmath75 vertices , which are generalizations of the three - dimensional cube . in this case , the individuals are characterized by their position in favor or against about @xmath76 different issues , and the opinion distance between two individuals is equal to the number of issues they disagree on . theorem [ th : dist - reg ] gives the following result . [ cor : hypercube ] when @xmath2 is the hypercube with @xmath77 vertices , * the system fluctuates when holds and @xmath78 whereas * the system fixates when holds and @xmath79 or when @xmath80 with @xmath22 large . cccccc opinion graph & radius & diameter & fluctuation & fix . ( @xmath81 ) & fix . ( @xmath22 large ) + path & @xmath82 & @xmath83 & @xmath60 & @xmath84 & @xmath85 + star ( @xmath86 ) & @xmath87 & @xmath88 & @xmath63 & @xmath89 & @xmath90 + star ( @xmath91 ) & @xmath87 & @xmath88 & @xmath63 & @xmath89 & @xmath92 + cycle & @xmath82 & @xmath93 & @xmath73 & @xmath84 & @xmath94 + hypercube & @xmath95 & @xmath96 & @xmath78 & @xmath97 & @xmath80 + opinion graph & radius & diameter & fluctuation & + tetrahedron & @xmath98 & @xmath99 & @xmath67 & + cube & @xmath100 & @xmath101 & @xmath68 & + octahedron & @xmath102 & @xmath103 & @xmath67 & + dodecahedron & @xmath104 & @xmath105 & @xmath70 & + icosahedron & @xmath100 & @xmath101 & @xmath68 & + table [ tab : summary ] summarizes our results for the graphs of figure [ fig : graphs ] . the second and third columns give the value of the radius and the diameter . the conditions in the fourth column are the conditions for fluctuation of the infinite system obtained from the corollaries . for opinion graphs with a variable number of vertices , the last two columns give sufficient conditions for fixation in the two extreme cases when the confidence threshold is one and when the confidence threshold is large . to explain the last column for paths and stars , note that the opinion model fixates whenever @xmath106 is larger than the largest root of the polynomials @xmath107 and the diameter of the opinion graph is sufficiently large . these polynomials are obtained from the conditions in corollaries [ cor : path][cor : star ] by only keeping the terms with degree two .

this article is concerned with a general class of stochastic spatial models for the dynamics of opinions . like in the voter model , individuals are located on the vertex set of a connected graph and update their opinion at a constant rate based on the opinion of their neighbors . when the confidence threshold is at least equal to the radius of the opinion graph , we prove that the one - dimensional process fluctuates and clusters and give a universal lower bound for the probability of consensus of the process on finite connected graphs . we also establish a general sufficient condition for fixation of the infinite system based on the structure of the opinion graph , which we then significantly improve for opinion graphs which are distance - regular .

this article is concerned with a general class of stochastic spatial models for the dynamics of opinions . like in the voter model , individuals are located on the vertex set of a connected graph and update their opinion at a constant rate based on the opinion of their neighbors . however , unlike in the voter model , the set of opinions is represented by the set of vertices of another connected graph that we call the opinion graph : when an individual interacts with a neighbor , she imitates this neighbor if and only if the distance between their opinions , defined as the graph distance induced by the opinion graph , does not exceed a certain confidence threshold . when the confidence threshold is at least equal to the radius of the opinion graph , we prove that the one - dimensional process fluctuates and clusters and give a universal lower bound for the probability of consensus of the process on finite connected graphs . we also establish a general sufficient condition for fixation of the infinite system based on the structure of the opinion graph , which we then significantly improve for opinion graphs which are distance - regular . our general results are used to understand the dynamics of the system for various examples of opinion graphs : paths and stars , which are not distance - regular , and cycles , hypercubes and the five platonic solids , which are distance - regular .

1107.5515

i

studies of rr lyrae stars in the milky way globular clusters reveal what is traditionally known as the oosterhoff dichotomy ; the tendency for these clusters to be either oosterhoff i ( oo - i ) or oosterhoff ii ( oo - ii ) objects with a relatively clear zone of avoidance between these two groups . the left panel of figure 5 in @xcite strikingly illustrates the oosterhoff dichotomy in a plot of the average period of the rr lyrae stars of bailey type ab ( rrab ) versus cluster metallicity for milky way globular clusters . when one looks at the nearby dwarf galaxies and their globular clusters , one does not see an oosterhoff dichotomy as these objects fall not only into the oo - i / ii groups but also into the gap between those two groups . in fact the distribution of these extragalactic objects seems to peak in the zone of avoidance @xcite . the existence of oosterhoff - intermediate objects ( oo - int ) , objects that fall into the zone of avoidance , in the nearby dwarf galaxies poses a significant challenge to the hierarchical merger model for the formation of the milky way halo . the lack of oo - int clusters in the halo means that the objects that were accreted to form the halo could not have had properties entirely like the present - day nearby dwarf galaxies . this is the first of a series of papers focusing on variable stars in globular clusters in the large magellanic cloud ( lmc ) . the goal of this series is to better understand how the rr lyrae stars in oo - int systems compare to those in oo - i / ii systems . the lmc is an ideal place for this study because of the large number of oo - int clusters that it contains @xcite ; of the twelve lmc globular clusters that contain at least @xmath10 rrab variables , five of these clusters are oo - int ( ngc 1466 , ngc 1853 , ngc 2019 , ngc 2210 , and ngc 2257 ) . in this paper we identify , classify , and discuss the variable stars found in the lmc globular cluster ngc 1466 . subsequent papers will focus on the variable stars in other lmc globular clusters . ngc 1466 is an old globular cluster that is located relatively far from the center of the lmc . it has a metal abundance of [ fe / h ] @xmath11 , see discussion in section [ sec : abprop ] , and is not very reddened , e(b - v ) = @xmath12 @xcite . @xcite used color - magnitude diagrams obtained with the hubble space telescope to determine that the age of ngc 1466 is within @xmath6 gyr of the ages of the milky way globular clusters m3 ( ngc 5272 ) and m92 ( ngc 6341 ) . ngc 1466 features a well - populated horizontal branch that extends through the instability strip ( see figure 5 in walker 1992 ) ; thus it is expected to contain a significant number of rr lyrae stars . rr lyrae stars were first found in ngc 1466 by @xcite , and additional rr lyrae were discovered by @xcite . the most recent study of variables in ngc 1466 was conducted by @xcite , who found @xmath13 rr lyrae stars ; @xmath14 rrab and @xmath15 rrc stars . due to the density of unresolved stars in the cluster core , walker did not perform photometry of stars within a radius of @xmath16 arcsec from the cluster center , suggesting that there are probably additional rr lyrae stars that could not be detected in his study . the core radius of ngc 1466 is @xmath17 arcsec , as measured by @xcite using images from the hubble space telescope , which is entirely within the region of the cluster where walker was unable to perform photometry . advances in instrument resolution and image - subtraction techniques now make it easier for us to search for variable stars in more crowded regions . in this paper we present the results of a new search for variable stars in ngc 1466 and use the rr lyrae in ngc 1466 to confirm the distance modulus and oosterhoff classification of the cluster . we also present fourier fits to the light curves and derive physical properties for the stars from these fits .

this is the first in a series of papers studying the variable stars in large magellanic cloud globular clusters . the primary goal of this series is to better understand how the rr lyrae stars in oosterhoff - intermediate systems compare to those in oosterhoff i / ii systems . in this paper we present the results of our new time - series photometric study of ngc 1466 . we present photometric parameters for these variables . for the rr lyrae stars the rr lyrae stars were used to determine a reddening - corrected distance modulus of . we discuss several different indicators of oosterhoff type and find ngc 1466 to be an oosterhoff - intermediate object .

this is the first in a series of papers studying the variable stars in large magellanic cloud globular clusters . the primary goal of this series is to better understand how the rr lyrae stars in oosterhoff - intermediate systems compare to those in oosterhoff i / ii systems . in this paper we present the results of our new time - series photometric study of ngc 1466 . a total of variables were identified in the cluster , of which are new discoveries . the variables include rrab stars , rrc s , rrd s , candidate rr lyrae , long - period variables , potential anomalous cepheid , and variables of undetermined classification . we present photometric parameters for these variables . for the rr lyrae stars physical properties derived from fourier analysis of their light curves are presented . the rr lyrae stars were used to determine a reddening - corrected distance modulus of . we discuss several different indicators of oosterhoff type and find ngc 1466 to be an oosterhoff - intermediate object .

1506.00395

i

the progress in three - dimensional ( 3d ) modeling research has been rapid and hectic , fueled by recent breakthroughs in keypoint detection and matching , the advances in computational power of desktop and mobile devices , the advent of digital photography and the subsequent availability of large datasets of public images . today , the goal of definitively bridging the gap between physical reality and the digital world seems within reach given the magnitude , breadth and scope of current 3d modeling systems . three dimensional modeling is the process of recovering the properties of the environment and optionally of the sensing instrument from a series of measures . this generic definition is wide enough to accommodate very diverse methodologies , such as time - of - flight laser scanning , photometric stereo or satellite triangulation . the structure - and - motion(a.k.a . structure - from - motion ) field of research is concerned with the recovery of the three dimensional geometry of the scene ( the structure ) when observed through a moving camera ( the motion ) . sensor data is either a video or a set of exposures ; additional informations , such as the calibration parameters , can be used if available . this paper describes our contributions to the problem of structure - and - motionrecovery from unordered , uncalibrated images i.e , the problem of building a three dimensional model of a scene given a set of exposures . the sought result ( the `` model '' ) is generally a 3d point - cloud consisting of the points whose projection was identified and matched in the images and a set of camera matrices , identifying position and attitude of each image with respect to an arbitrary reference frame . the main challenges to be solved are computational efficiency ( in order to be able to deal with more and more images ) and generality , i.e. , the amount of ancillary information that is required . to address the efficiency issue we propose to describe the entire structure - and - motionprocess as a binary tree ( called _ dendrogram _ ) constructed by agglomerative clustering over the set of images . each leaf corresponds to a single image , while internal nodes represent partial models obtained by merging the left and right sub - nodes . computation proceeds from bottom to top , starting from several seed couples and eventually reaching the root node , corresponding to the complete model . this scheme provably cuts the computational complexity by one order of magnitude ( provided that the dendrogram is well balanced ) , and it is less sensitive to typical problems of sequential approaches , namely sensitivity to initialization @xcite and drift @xcite . it is also scalable and efficient , since it partitions the problem into smaller instances and combines them hierarchically , making it inherently parallelizable . on the side of generality , our aim is to push the `` pure '' structure - and - motiontechnique as far as possible , to investigate what can be achieved without including any auxiliary information . current structure - and - motionresearch has partly sidestepped this issue using ancillary data such as exif tags embedded in conventional image formats . their presence or consistency , however , is not guaranteed . we describe our approach to autocalibration , which is the process of automatic estimation from images of the internal parameters of the cameras that captured them , and we therefore demonstrate the first structure - and - motionpipeline capable of using unordered , uncalibrated images . the main issue to address in structure - and - motionis the computational complexity , which is dominated by the bundle adjustment phase , followed by feature extraction and matching . a class of solutions that have been proposed are the so - called partitioning methods @xcite . they reduce the structure - and - motionproblem into smaller and better conditioned subproblems which can be effectively optimized . within this approach , two main strategies can be distinguished . the first one is to tackle directly the bundle adjustment algorithm , exploiting its properties and regularities . the idea is to split the optimization problem into smaller , more tractable components . the subproblems can be selected analytically as in @xcite , where spectral partitioning has been applied to structure - and - motion , or they can emerge from the underlying 3d structure of the problem , as described in @xcite . the computational gain of such methods is obtained by limiting the combinatorial explosion of the algorithm complexity as the number of images and points increases . the second strategy is to select a subset of the input images and points that subsumes the entire solution . hierarchical sub - sampling was pioneered by @xcite , using a balanced tree of trifocal tensors over a video sequence . the approach was subsequently refined by @xcite , adding heuristics for redundant frames suppression and tensor triplet selection . in @xcite the sequence is divided into segments , which are resolved locally . they are subsequently merged hierarchically , eventually using a representative subset of the segment frames . a similar approach is followed in @xcite , focusing on obtaining a well behaved segment subdivision and on the robustness of the following merging step . the advantage of these methods over their sequential counterparts lies in the fact that they improve error distribution on the entire dataset and bridge over degenerate configurations . in any case , they work for video sequences , so they can not be applied to unordered , sparse images . the approach of @xcite works with sparse datasets and is based on selecting a subset of images whose model provably approximates the one obtained using the entire set . this considerably lowers the computational requirements by controllably removing redundancy from the dataset . even in this case , however , the images selected are processed incrementally . moreover , this method does not avoid computing the epipolar geometry between all pairs of images . within the solutions aimed at reducing the impact of the bundle adjustment phase , hierarchical approaches include @xcite and this paper . the first can be considered as the first paper where the idea has been set forth : a spanning tree is built to establish in which order the images must be processed . after that , however , the images are processed in a standard incremental way . the approach described in @xcite is based on recursive partitioning of the problem into fully - constrained sub - problems , exploiting the bipartite structure of the visibility graph . the partitioning operates on the problem variables , whereas our approach works on the input images . orthogonally to the aforementioned approaches , a solution to the the computational complexity of structure - and - motionis to throw additional computational power at the problem @xcite . within such a framework , the former algorithmic challenges are substituted by load balancing and subdivision of tasks . such a direction of research strongly suggest that the current monolithic pipelines should be modified to accommodate ways to parallelize and optimally split the workflow of structure - and - motiontasks . in @xcite image selection ( via clustering ) is combined with a highly parallel implementation that exploits graphic processors and multi - core architectures . the impact of the bundle adjustment phase can also be reduced by adopting a different paradigm in which _ first _ the motion is recovered and _ then _ the structure is computed . all these methods start from the relative orientation of a subset of camera pairs ( or triplets ) , computed from point correspondences , then solve for the absolute orientation of all the cameras ( _ globally _ ) , reconstruct 3d points by intersection , and finally run a single bundle adjustment to refine the reconstruction . camera internal parameters are required . the method described in @xcite solves a homogeneous linear system based on a novel decomposition of the essential matrix that involves the absolute parameters only . in @xcite nonlinear optimization is performed to recover camera translations given a network of both noisy relative translation directions and 3d point observations . this step is preceded by outlier removal among relative translations by solving simpler low - dimensional subproblems . the authors of @xcite propose a discrete markov random field formulation in combination with levenberg - marquardt minimization . this technique requires additional information as input , such as geotag locations and vanishing points . other approaches ( e.g. @xcite ) compute translations together with the structure , involving a significant number of unknowns . the method presented in @xcite proposes a fast spectral solution by casting translation recovery in a graph embedding problem . govindu in @xcite derives a homogeneous linear system of equations in which the unknown epipolar scaling factors are eliminated by using cross products , and this solution is refined through iterative reweighted least squares . the authors of @xcite propose a linear algorithm based on an approximate geometric error in camera triplets . moulon et al . @xcite extract accurate relative translations by using an a - contrario trifocal tensor estimation method , and then recover simultaneously camera positions and scaling factors by using an @xmath0-norm approach . similarly to @xcite , this method requires a graph covered by contiguous camera triplets . the authors of @xcite propose a two - stage method in which relative translation directions are extracted from point correspondences by using robust subspace optimization , and then absolute translations are recovered through semidefinite programming . another relevant issue in structure - and - motionis the level of generality , i.e. , the number of assumption that are made concerning the input images , or , equivalently the amount of extra information that is required in addition to pixel values . existing pipelines either assume known internal parameters @xcite , or constant internal parameters @xcite , or rely on exif data plus external information ( camera ccd dimensions ) @xcite . methods working in large scale environments usually rely on a lot of additional information , such as camera calibration and gps / ins navigation systems @xcite or geotags @xcite . autocalibration ( a.k.a . self - calibration ) has generated a lot of theoretical interest since its introduction in the seminal paper by maybank and faugeras @xcite . the attention created by the problem however is inherently practical , since it eliminates the need for off - line calibration and enables the use of content acquired in an uncontrolled setting . modern computer vision has partly sidestepped the issue by using ancillary information , such as exif tags embedded in some image formats . unfortunately it is not always guaranteed that such data will be present or consistent with its medium , and do not eliminate the need for reliable autocalibration procedures . a great deal of published methods rely on equations involving the dual image of the absolute quadric ( diaq ) , introduced by triggs in @xcite . earlier approaches for variable focal lengths were based on linear , weighted systems @xcite , solved directly or iteratively @xcite . their reliability has been improved by more recent algorithms , such as @xcite , solving super - linear systems while directly forcing the positive definiteness of the diaq . such enhancements were necessary because of the structural non - linearity of the task : for this reason the problem has also been approached using branch and bound schemes , based either on the kruppa equations @xcite , dual linear autocalibration @xcite or the modulus constraint @xcite . the algorithm described in @xcite shares , with the branch and bound approaches , the guarantee of convergence ; the non - linear part , corresponding to the localization of the plane at infinity , is solved exhaustively after having used the cheiral inequalities to compute explicit bounds on its location . this paper describes a hierarchical and parallelizable scheme for structure - and - motion ; please refer to fig . [ fig : schema ] for a graphical overview . the front end of the pipeline is keypoint extraction and matching ( sec . [ sec : match ] ) , where the latter is subdivided into two stages : the first ( `` broad phase '' ) is devoted to discovering the tentative topology of the epipolar graph , while the second ( `` narrow phase '' ) performs the fine matching and computes the epipolar geometry . images are then organized into a dendrogram by clustering them according to their overlap ( sec . [ sec : dendro ] ) . a new clustering strategy , derived from the simple linkage , is introduced ( sec . [ sec : balance ] ) that makes the dendrogram more balanced , thereby approaching the best - case complexity of the method . the structure - and - motioncomputation proceeds hierarchically along this tree , from the leaves to the root ( sec . [ sec : hierarchical ] ) . images are stored in the leaves , whereas partial models correspond to internal nodes . according to the type of node , three operations are possible : stereo modeling ( image - image ) , resection - intersection ( image - model ) or merging ( model - model ) . bundle adjustment is run at every node , possibly in its `` local '' form ( sec . [ sec : localba ] ) . we demonstrate that this paradigm has several advantages over the sequential one , both in terms of computational performance ( which improves by one order of magnitude on average ) and overall error containment . autocalibration ( sec . [ sec : urec ] ) is performed on partial models during the dendrogram traversal . first , the location of the plane at infinity is derived given two perspective projection matrices and a guess on their internal parameters , and subsequently this procedure is used to iterate through the space of internal parameters looking for the best collineation that makes the remaining cameras euclidean . this approach has several advantages : it is fast , easy to implement and reliable , since a reasonable solution can always be found in non - degenerate configurations , even in extreme cases such as when autocalibrating just two cameras . being conscious that `` the devil is in the detail '' , section [ sec : devil ] reports implementation details and heuristics for setting the parameters of the pipeline . the experimental results reported in sec . [ sec : exp ] are exhaustive and analyze the output of the pipeline in terms of accuracy , convergence and speed . we report here on the latest version of our pipeline , called samantha . previous variants have been described in @xcite and @xcite respectively . the main improvements are in the matching phase and in the autocalibration that now integrates the method described in @xcite . the geometric stage has been carefully revised to make it more robust , to the point where in some cases bundle adjustment is not needed any more except at the end of the process . most efforts have been made in the direction of a robust and automatic approach , avoiding unnecessary parameter tuning and user intervention .

this paper addresses the structure - and - motionproblem , that requires to find camera motion and 3d structure from point matches . moreover , a practical autocalibration procedure allows to process images without ancillary information . experiments with real data assess the accuracy and the computational efficiency of the method . structure and motion ; image orientation ; bundle adjustment ; autocalibration ; 3d

this paper addresses the structure - and - motionproblem , that requires to find camera motion and 3d structure from point matches . a new pipeline , dubbed samantha , is presented , that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach . this method has several advantages , like a provably lower computational complexity , which is necessary to achieve true scalability , and better error containment , leading to more stability and less drift . moreover , a practical autocalibration procedure allows to process images without ancillary information . experiments with real data assess the accuracy and the computational efficiency of the method . structure and motion ; image orientation ; bundle adjustment ; autocalibration ; 3d

1010.1979

i

spectropolarimetry continues to be a valuable technique for a broad range of astrophysical studies ( e.g. , adamson 2005 ; bastian 2010 ) , including applications for circumstellar envelopes . advances in technology and access to larger telescopes means an ever growing body of high quality spectropolarimetric data . it is therefore important that the arsenal of diagnostic methods and theoretical models in different astrophysical scenarios keep pace . this paper represents the fifth in a series devoted toward developing the hanle effect as tool for measuring magnetic fields in circumstellar media from resonance line scattering polarization . the observational requirements for the effects examined in this series are ambitious : high signal - to - noise ( s / n ) data and high spectral resolving power . however , these demands are being met , as illustrated by harrington & kuhn ( 2009a ) in a spectropolarimetric survey of circumstellar disks at h@xmath0 . there are numerous effects that can influence the polarization across resolved lines . a number of researchers have investigated the effects of line opacity for polarization from thomson scattering ( wood , brown , & fox 1993 ; harries 2000 ; vink , harries , drew 2005 ; wang & wheeler 2008 ; hole , kasen , & nordsieck 2010 ) . scattering by resonance lines can generate polarization similar to dipole scattering ( e.g. , ignace 2000a ) . with high s / n and high spectral resolution , harrington & kuhn ( 2009b ) have identified a new polarizing effect for lines that coincides with line absorption . an explanation for this previously unobserved effect in stars is discussed by kuhn ( 2007 ) and is attributed to the same dichroic processes detailed by trujillo bueno & landi deglinnocenti ( 1997 ) for interpreting polarizations in some solar spectral lines . generally associated with circular polarization , the zeeman effect has received acute attention of late as a result of techniques that co - add many lines ( donati 1997 ) . the method has been used successfully in many studies ( see the review of donati & landstreet 2009 ) . in relation to massive stars , the technique has led to the detection of magnetism in several stars ( e.g. , donati 2002 , 2006a , 2006b ; neiner 2003 ; grunhut 2009 ) . in fact , there exists a large collaborative effort called the mimes collaboration ( e.g. , wade 2009 ) to increase the sample of massive stars with well - studied magnetic fields . another method that has been used productively in studies of solar magnetic fields involves the hanle effect ( hanle 1924 ) . this is a weak zeeman effect that operates when the zeeman splitting is roughly comparable to the natural line broadening . monographs that deal with atomic physics and polarized radiative transfer provide excellent treatments of the hanle effect , including stenflo ( 1994 ) and landi deglinnocenti & landolfi ( 2004 ) . this contribution extends a series of theoretical papers that has enlarged the scope of its general use with circumstellar envelopes . building on work developed in the solar physics community , and using expressions for resonance line scattering with the hanle effect ( e.g. , from stenflo 1994 ) , ignace , nordsieck , & cassinelli ( 1997 ; paper i ) provided an introduction of the hanle effect for use in studies of circumstellar envelopes . ignace , cassinelli , & nordsieck ( 1999 , paper ii ) considered its use in simplified models of disks with constant radial expansion or solid body rotation as pedagogic examples . both of these papers approximated the star as a point source of illumination . ignace ( 2001 ; paper iii ) then incorporated the finite source depolarization factor of cassinelli , nordsieck , & murison ( 1987 ) into the treatment of the source functions for the hanle effect in circumstellar envelopes . finally , ignace , nordsieck , & cassinelli ( 2004 , paper iv ) calculated the hanle effect in p cygni wind lines using an approximate treatment for line optical depth effects . the focus of this fifth paper in the series is the hanle effect in polarized lines from keplerian disks , of relevance for accretion disks and be star disks ( e.g. , cranmer 2009 ) . as in previous papers of this series , the sobolev approximation ( sobolev 1960 ) for optically thin scattering lines is adopted for exploring the run of polarization with velocity shift across line profiles . this paper adopts the notation laid out in paper ii . the results of paper ii are expanded for keplerian rotation with the inclusion of finite source depolarization ( ala paper iii ) and stellar occultation . resonance line scattering polarization from such disks were explored in ignace ( 2000a ) for unmagnetized disks without consideration of the hanle effect . drawing on these previous works , methods for computing the polarization of line profiles will be briefly reviewed in section [ sec : lines ] . in section [ sec : hanle ] , results for the hanle effect from disk lines are described . there are three applications that will be considered : purely axial fields ( i.e. , normal to the disk plane ) , purely toroidal fields ( i.e. , azimuthal in the disk plane ) , and field topologies that can arise from the magnetorotational instability , or mri ( balbus & hawley 1991 ) . conclusions of this study and observational prospects are presented in section [ sec : conc ] . appendices detail analytic derivations for special cases of the hanle effect in keplerian disks .

model line profiles are calculated for simple field topologies of axial fields ( i.e. , vertical to the disk plane ) and toroidal fields ( i.e. , purely azimuthal ) . a scheme for discerning field strengths and geometries in disks is developed based on stokes q - u diagrams for the run of polarization across line profiles that are doppler broadened by the disk rotation . the hanle effect does not suffer from this impediment , and so a multi - line analysis could be used to constrain field strengths in disks dominated by the mri .

this paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks . optically thin lines from keplerian planar disks are considered . model line profiles are calculated for simple field topologies of axial fields ( i.e. , vertical to the disk plane ) and toroidal fields ( i.e. , purely azimuthal ) . a scheme for discerning field strengths and geometries in disks is developed based on stokes q - u diagrams for the run of polarization across line profiles that are doppler broadened by the disk rotation . a discussion of the hanle effect for magnetized disks in which the magnetorotational instability ( mri ) is operating is also presented . given that the mri has a tendency to mix the vector field orientation , it may be difficult to detect the disk fields with the longitudinal zeeman effect , since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer . the hanle effect does not suffer from this impediment , and so a multi - line analysis could be used to constrain field strengths in disks dominated by the mri .

1010.1979

c

polarized line profile shapes from magnetized keplerian disks have been calculated under a number of simplifying assumptions : the disk is geometrically thin ; the scattering lines are optically thin ; primarily simple fields were considered ( axial or toroidal ) ; and no account was taken of photospheric absorption lines . on the other hand , the model profiles do include finite source depolarization and the effects of stellar occultation . the presentation of results focused on the polarimetric `` efficiencies '' and with a description of how to identify the occurrence of the hanle effect in scattering lines from disks . in addition , a discussion was presented for the hanle effect from a magnetized disk in which the mri mechanism is operating . one of the main conclusions from this work is that axial and toroidal fields in disks are easily distinguishable through an analysis of - figures for the run of stokes polarizations across line profiles . although a profile does exist even without the hanle effect , owing to stellar occultation , its amplitude is quite small . the strongest profiles result when much of the inner disk , where most of the scattered light is produced , has values of @xmath123 of order a few . if the inner disk is mostly in the saturated limit of the hanle effect , the profile becomes a null profile for both axial and toroidal fields . one should bear in mind that the polarized efficiencies are upper limits to the polarizations that would actually be measured , since the efficiencies are with reference to the scattered light only and do not take account of the direct starlight from the system . since this starlight is expected to be largely unpolarized , its contribution acts to `` dilute '' the polarization substantially below the efficiency levels reported here . for example , if the line is relatively weak at 20% of the continuum level , then the expected measured polarizations would have fractional values at about 1/5 of the efficiency values , resulting in line polarizations of around 1%2% for and 0.5% or less for . as percent polarizations , such values would appear to be easily measurable , but in practice there are several challenges . first , a spectral resolution yielding several points across the polarized profile is needed . circumstellar disks have rotation speeds of order 500 km s@xmath124 . a requisite velocity resolution of perhaps 50 km s@xmath124 would then be needed , implying a resolving power of @xmath125 . harrington & kuhn ( 2009a ) have demonstrated that such resolving powers can be achieved in spectropolarimetry ; however , the next requirement is that of finding suitable scattering lines . the very interesting effects seen in the sample of harrington & kuhn ( 2009a ) exploits a relatively new effect of enhanced polarization that is coincident with regions of higher line absorption , a consequence of optical pumping effects . for the hanle effect , or even for non - magnetic resonance scattering , lines that are predominantly scattering are needed . for hot star disks , such as the disks of be stars , resonance scattering lines are generally to be found at uv wavelengths . this requires space - borne spectropolarimeters . although the wisconsin ultraviolet photo - polarimeter experiment ( wuppe ) obtained exciting new results from uv polarimetry , its resolving power was only about 200 ( nordsieck 1994 ) . a new uv spectropolarimeter called the far - ultraviolet spectropolarimeter ( fusp ) is a sounding rocket payload that will have a resolving power of about 1800 ( nordsieck 1998 ) . although possibly two low for circumstellar disks , it will be suitable for studying scattering line polarizations from high velocity stellar wind sources . as a matter of practical analysis , how should spectropolarimetric data best be managed to measure a hanle effect ? plotting the velocity shifted polarizations in the - space appears to be most promising . the sequencing of the analysis for scattering lines from disk sources might proceed as follows : * subtract off the continuum polarization in the vicinity of the line of interest . this will counter the effects of both interstellar polarization and any other broadband source polarization , such as may arise from thomson scattering in the disk . * plot the q and u line _ fluxes _ , not fractional or percent polarizations that would be derived through normalization by the total i - flux . the reason for plotting polarized fluxes is that many common uv resonance lines are doublets ( e.g. , nv , siiv , and civ uv resonance doublets ) . the shorter wavelength component ( `` blue '' ) has @xmath78 , and the long wavelength component ( `` red '' ) has @xmath126 ( e.g. , tab . 1 of paper ii ) . if the lines are thin , then the polarized flux from the red line will not be influenced by the blue one . however , if the lines are sufficiently closely spaced , then will be a blend , and normalization by that blend would artificially skew the q - u figure shape , making interpretation more difficult . if the doublet components are well separated , then relative polarizations could also be used in what follows . * determine whether the resultant figure for the line polarization shows any axis of symmetry . if so , then either ( a ) there is no hanle effect , or ( b ) there is a hanle effect with a dominant toroidal component . for an axis of symmetry , a rotation of the figure from observer q - u axes to a source set of axes q-u could be accomplished with a mueller rotation matrix . after rectifying the figure in this way , the relative amplitude of should be compared to . if @xmath127 , then there is likely little hanle effect or the disk is in the saturated limit of the hanle effect . if @xmath128 , then a hanle effect is required with @xmath129 few in the disk where the bulk of scattered light is produced this means @xmath130 . * if there is no symmetry axis to the q - u figure , then a hanle effect involving an axial field is most likely the culprit . recall that a radial field could be present , but this would give no hanle effect by itself . * for identifying a field distribution arising from mri , things are more complicated . if the hanle effect is in operation , then the stokes - u flux is likely driven to zero , even if @xmath131 . a net profile should survive ; however , it may not be symmetric . using an oversimplification , each isovelocity zone can be considered to have a different effective @xmath110 value . this is already the case in the pure axial or toroidal field case that is axisymmetric , but the variation of the effective @xmath110 with velocity shift is monotonic ( in a flux - weighted sense ) . with mri , one expects non - monotonicity from fluctuations of the field strength . this amounts to the introduction of amplitude fluctuations across the polarized line . there are complications to the above approach . for example , in the case of the be star disks , there is substantial evidence for one - armed spiral density wave patterns that make the disk density non - axisymmetric ( e.g. , okazaki 1997 ; papaloizou & savonije 2006 ) . for thin thomson scattering , there is little observational consequence of this effect which is mainly a redistribution of disk scatterers in a point antisymmetric pattern ( e.g. , ignace 2000b ) . however , with resolved line profiles , the non - axisymmetric density distribution will produce asymmetry in the profile and will be a new source of net signal , also asymmetric . certainly it will be important to model the profile self - consistently along with the polarized profiles . note that there may be some concern about the choice adopted for the radial distribution of the field strength through the disk . the choice of @xmath132 is perhaps the most shallow distribution that one could expect . a steeper gradient of the field strength will restrict the operation of the hanle effect to a more restricted range of radii in the disk . if the interval in radius where @xmath133 becomes narrow in relation to where most of the scattered light is produced , then the hanle effect will be irrelevant for the observed polarization . what are the next steps in formulating better diagnostics of the density and magnetic field structure in disks ? most of work considered in this series of papers has focused on optically thin lines in an attempt to gain a better understanding of how the hanle effect influences line polarizations that form in circumstellar media . in paper iv the issue of optical depth effects for p cygni lines from stellar winds were considered by treating regions of high optical as contributing no polarization at all . although simplistic , insight was gained into how optical depth effects provide an additional spatial `` filter '' in terms of where bulk of line polarization will be produced . naturally , rigorous radiative transfer and a more realistic disk model ( i.e. , not simply planar ) is badly needed to extend the considerations of this paper . even with thin line scattering , it would be useful to explore how non - axisymmetric disk models , such as the one - armed spiral density wave pattern for be disks , will modify the line polarization . moreover , winds driven off magnetized disks ( e.g. , knigl 1989 ; proga , stone , & drew 1998 ; proga , stone , & kallman 2000 ) have been ignored entirely in this work . these are all new calculations that will need to be considered in the future . the author is indebted to the anonymous referee whose comments have improved this manuscript . appreciation is expressed to ken gayley , joe cassinelli , and gary henson for engaging conversations about line polarizations and the zeeman and hanle effects . this work was supported by a grant from the national science foundation ( ast-0807664 ) .

this paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks . optically thin lines from keplerian planar disks are considered . a discussion of the hanle effect for magnetized disks in which the magnetorotational instability ( mri ) is operating is also presented . given that the mri has a tendency to mix the vector field orientation

this paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks . optically thin lines from keplerian planar disks are considered . model line profiles are calculated for simple field topologies of axial fields ( i.e. , vertical to the disk plane ) and toroidal fields ( i.e. , purely azimuthal ) . a scheme for discerning field strengths and geometries in disks is developed based on stokes q - u diagrams for the run of polarization across line profiles that are doppler broadened by the disk rotation . a discussion of the hanle effect for magnetized disks in which the magnetorotational instability ( mri ) is operating is also presented . given that the mri has a tendency to mix the vector field orientation , it may be difficult to detect the disk fields with the longitudinal zeeman effect , since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer . the hanle effect does not suffer from this impediment , and so a multi - line analysis could be used to constrain field strengths in disks dominated by the mri .

1102.3160

i

this article is an offshoot of the authors forthcoming work @xcite . in that paper we will combine a detailed geometric examination of the lagrangian correspondences between symmetric products of riemann surfaces , studied by the second author in @xcite , with the @xmath1 quilted floer theory of mau wehrheim woodward @xcite and the functoriality principle of @xcite ( see also @xcite ) . by doing so , we will extend the package of heegaard floer cohomology invariants @xcite from closed 3-manifolds to compact 3-manifolds with boundary . to be precise , we construct invariants for compact , oriented , connected 3-manifolds with precisely two boundary components , marked as ` incoming ' and ` outgoing ' . when these are both spherical , our invariants capture the heegaard floer cochains of the capped - off 3-manifold . we refer to auroux s work @xcite for the relationship of this theory to bordered heegaard floer theory @xcite . the format of our invariants is alarmingly abstract : they take the form of @xmath1-functors between @xmath1-categories associated with the boundary surfaces , satisfying a composition law under sewing of cobordisms . enthusiasts for extended tqft will approve of this formulation , but geometric topologists will want to know how to extract topological information from it . in this article , we examine the next - to - simplest case of the theory by applying it to manifolds @xmath5 with incoming boundary of genus @xmath6 ( which we cap off to form @xmath7 ) and outgoing boundary of genus @xmath8 . the relevant @xmath1-categories are certain versions of the fukaya category of a symplectic 2-torus @xmath9 with a distinguished point @xmath10 . the simplest version of the invariant for @xmath11 is * an @xmath1-module @xmath12 over the fukaya category + @xmath13 of exact , embedded curves in @xmath14 . * this module evaluates on each object @xmath15 ( which is a circle @xmath16 with an exactness constraint and certain decorations ) to give a cochain complex @xmath17 . this complex is quasi - isomorphic to the heegaard floer cochains @xmath18 , where @xmath19 is the solid torus in which the circle @xmath15 bounds a disc . the different objects @xmath15 correspond to different dehn fillings of @xmath11 . we illustrate our theory by showing how it leads to a proof of the dehn surgery exact triangle in heegaard floer cohomology @xcite ( theorem [ exacttri ] , corollary [ surgery ] ) . by working with the modules @xmath12 rather than the heegaard floer cochain complexes , one can legitimately work on the genus 1 boundary rather than on the @xmath20-fold symmetric product of a genus @xmath20 heegaard surface . this makes the proof technically straightforward and also makes the signs , on which the proof depends , transparent . to better understand the nature of our invariants , we need to understand the structure of @xmath13 . this category is closely related to the one studied in @xmath21 ( see @xcite for a deformation - theoretic approach to the latter category ) , but the differences are significant . it follows from the surgery exact triangle ( theorem [ exacttri ] ) that @xmath13 ( whose objects we declare to be exact , oriented lagrangians with _ non - trivial _ spin structures ) is generated by two objects curves @xmath22 and @xmath23 that meet transversely at a point , generating a full @xmath1-subcategory @xmath24 . that is , the inclusion @xmath25 induces a quasi - equivalence of the triangulated envelopes @xmath26 ( ` @xmath27 ' stands for twisted complexes ; see ( * ? ? ? * ( 3l ) ) ) . this in turn induces an equivalence of triangulated categories between the derived categories @xmath28 and @xmath29 ) . the @xmath1-structure of @xmath24 can be transferred to an @xmath1-structure on the cohomology algebra @xmath30 . this structure is governed by the hochschild cochain complex @xmath31 , with its bigrading and gerstenhaber bracket . we show that over a field @xmath32 in which 6 is invertible gauge - equivalence classes of @xmath1-structures in @xmath2 determine and are determined by two parameters , @xmath33 and @xmath34 . the ` moduli space ' @xmath35 is parametrized by the invariants @xmath3 of dg algebras associated with a pair of sheaves the structure sheaf and the skyscraper at @xmath36$]on the weierstrass curves @xmath37 ( prop . [ weierstrass ] ) for @xmath38 . the value of @xmath39 is non - zero ( theorem [ m6 ] ) . our expectation is that @xmath24 is quasi - isomorphic to the dg algebra for a _ nodal _ cubic . [ [ note . ] ] note . + + + + + the topics we have chosen do not rely on detailed information about our general theory . most of the theorems proved in this article are independent of it ; the sole exception , corollary [ surgery ] , invokes a general feature of the theory . the section on hochschild cohomology can be read on its own . we invoke the definition of the fukaya category from @xcite . we refer to that book for points of homological algebra , but recommend ( * ? ? ? * section 3 ) as a briefer alternative reference .

this paper is a companion to the authors forthcoming work extending heegaard floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted floer cohomology . we describe the first interesting case of this theory : the invariants of 3-manifolds bounding , regarded as modules over the fukaya category of the punctured 2-torus . we extract a short proof of exactness of the dehn surgery triangle in heegaard floer homology .

this paper is a companion to the authors forthcoming work extending heegaard floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted floer cohomology . we describe the first interesting case of this theory : the invariants of 3-manifolds bounding , regarded as modules over the fukaya category of the punctured 2-torus . we extract a short proof of exactness of the dehn surgery triangle in heegaard floer homology . we show that-structures on the graded algebra formed by the cohomology of two basic objects in the fukaya category of the punctured 2-torus are governed by just two parameters , extracted from the hochschild cohomology of . for the fukaya category itself , .

1505.07531

i

a discrete sturm - liouville problem ( briefly , slp ) considered in the present paper consists of a discrete sturm - liouville equation ( briefly , sle ) @xmath0,\ ] ] and the boundary condition ( briefly , bc ) @xmath1 where @xmath2 is an integer , @xmath3 and @xmath4 are the forward and backward difference operators , respectively , i.e. , @xmath5 and @xmath6 ; @xmath7 , @xmath8 and @xmath9 are complex - valued sequences such that @xmath10 , \;\;w_n\neq0\;{\rm for}\ ; n\in [ 1,n];\ ] ] @xmath11 is the spectral parameter ; the interval @xmath12 $ ] denotes the set of integers @xmath13 ; and @xmath14 and @xmath15 are @xmath16 complex matrices such that @xmath17 throughout this paper , by @xmath18 , @xmath19 , and @xmath20 denote the sets of the complex numbers , real numbers , and integer numbers , respectively ; and by @xmath21 denotes the complex conjugate of @xmath22 . moreover , when a capital latin letter stands for a matrix , the entries of the matrix are denoted by the corresponding lower case letter with two indices . for example , the entries of a matrix @xmath23 are @xmath24 s . the dependence of the continuous sturm - liouville eigenvalues on the problems and its applications have been extensively studied ( cf . , @xcite ) . in @xcite , kong and zettl proved that the eigenvalues of continuous slps depend not only continuously but also smoothly on problems and then gave an expression for the derivative of the @xmath25-th eigenvalue with respect to a given parameter in the continuous slp . later , they , together with wu , gave a natural geometric structure on the space of bcs of continuous slps in @xcite . this structure is the base for studying the dependence of sturm - liouville eigenvalues on the bcs . in addition , they investigated the differentiability of continuous eigenvalue branches based on this structure , and discussed the relationships between the algebraic and geometric multiplicities of an eigenvalue . along another line , research on discrete spectral problems and their inverse problems has been of growing interest in recent years ( cf . , e.g.@xcite ) . atkinson @xcite and jirari @xcite studied spectral problems of second - order discrete scalar self - adjoint slps with separate bcs . in @xcite , the third author of the present paper with her coauthor chen investigated the following vector difference equation @xmath26,\;\;\;n\geq2,\ ] ] with the general boundary condition @xmath27 where @xmath28)$ ] , @xmath29 , and @xmath30(@xmath31 $ ] ) are hermitian @xmath32 matrices , @xmath33 and @xmath34 are nonsingular , @xmath35 for @xmath31 $ ] ; r and s are @xmath36 matrices with @xmath37 . it is evident that the bc is included in the bc . the spectral results obtained in @xcite will be used in the study of the multiplicity of eigenvalues in the present paper . further , the third author of the present paper with her coauthor lv studied error estimate of eigenvalues of perturbed problems , sufficiently close to a given sturm - liouville problem and , by some variational properties of the eigenvalues under a certain non - singularity condition in @xcite . so we obtained the continuous dependence of eigenvalues on problems under the nonsingularity condition . in chapter 2 of @xcite , kato investigated perturbation problems for linear operators in finite - dimensional spaces . he studied how the eigenvalues change with the operator , in particular when the operator analytically depends on a parameter . his method is based on function - theoretic study of the corresponding resolvent . obviously , the eigenvalue problem of the self - adjoint discrete slps consisting of - corresponds to that of an operator in a finite - dimensional space . note that the operator defined by - may be multi - valued since @xmath38 and @xmath39 may not be uniquely determined by the bc , and the problem discussed in the present paper is dependent on multi - parameters . however , the operators are all single - valued and their perturbations are only referred to one single parameter in @xcite . so the results in @xcite can not be directly available in our study . in the present paper , we shall investigate dependence of eigenvalues on the slp consisting of and . there are two main motivations for our study . firstly , it is helpful to clarify the common features and differences between the class of continuous slps and that of discrete slps . secondly , it is hoped that findings of such work will form a theoretical foundation for numerical works on discrete slps and their inverse problems , and such numerical works will shed light on numerical works on continuous slps and their inverse problems . many results in the continuous case may be obtained from the corresponding results in the discrete case , via certain limit procedures , but not vice verse ; while some results in the discrete case have relatively direct proofs . in this way , shorter proofs of results in the continuous case may be found . this paper is organized as follows . in section 2 , we give topologies and geometric structures on various spaces of discrete slps , which are fundamental for further developments . in section 3 , we first discuss properties of the analytic and geometric multiplicities of eigenvalues of the discrete slps and their relationships , and then study continuous dependence of eigenvalues on the problems . in section 4 , we investigate some fundamental properties of continuous eigenvalue branches including their analyticity , differentiability and monotonicity . finally , several examples illustrating results of these sections are presented in section 5 . [ r11 ] we shall apply the results obtained in the present paper to study some other topics about discrete sturm - liouville problems , including dependence of the @xmath25-th eigenvalue on problems , inequalities among eigenvalues for different problems , and index problems for eigenvalues in our forthcoming papers .

this paper is concerned with dependence of discrete sturm - liouville eigenvalues on problems . topologies and geometric structures on various spaces of such problems are firstly introduced . it is shown that all problems sufficiently close to a given problem have eigenvalues near each eigenvalue of the given problem .

this paper is concerned with dependence of discrete sturm - liouville eigenvalues on problems . topologies and geometric structures on various spaces of such problems are firstly introduced . then , relationships between the analytic and geometric multiplicities of an eigenvalue are discussed . it is shown that all problems sufficiently close to a given problem have eigenvalues near each eigenvalue of the given problem . so , all the simple eigenvalues live in so - called continuous simple eigenvalue branches over the space of problems , and all the eigenvalues live in continuous eigenvalue branches over the space of self - adjoint problems . the analyticity , differentiability and monotonicity of continuous eigenvalue branches are further studied .

0907.1354

i

the sources of ultra - high energy cosmic rays have remained elusive in spite of the enormous progress reached on the experimental side , with present day detectors reaching apertures @xmath6km@xmath7 sr yr . the differential energy spectrum , the chemical composition and the distribution of arrival directions on the sky are as many clues to the nature of the source . there is now a consensus on the existence of the gzk cut - off ( greisen 1966 ; zatsepin & kuzmin 1966 ) , which has been observed by two different experiments ( abbasi et al . 2008 , abraham et al . the existence of this gzk cut - off puts on solid ground the models which attribute the origin of ultra - high energy cosmic rays to powerful astrophysical objects distributed on cosmological scales , such as powerful radio - galaxies ( rachen & biermann 1993 ) , gamma - ray bursts ( milgrom & usov 1995 , vietri 1995 , waxman 1995 ) , or magnetars ( arons 2003 ) . experimental results on the chemical composition and anisotropies are however far more confusing . while the most recent analysis of hires data points to a proton composition above the ankle ( abbasi et al . 2005 , belz 2009 ) , the fluorescence data of the pierre auger observatory ( pao ) rather indicates an increasingly heavier composition above this energy , with the last data points at @xmath8eev close to expectations for iron ( unger et al . 2007 , wahlberg et al . 2009 ) . regarding the distribution of arrival directions on the sky , there exist various contradictory claims , see for instance the correlation with the super - galactic plane reported by stanev et al . ( 1995 ) , contradicted by the results of the agasa experiment ( takeda et al . 1999 ) ; the claim for a correlation with bl lac objects in tinyakov & tkachev ( 2001 , 2002 ) , gorbunov et al . ( 2002 , 2004 ) , which has been debated ( evans , ferrer & sarkar 2003 , 2004 ; tinyakov & tkachev 2004 ) ; as well as the possible detections of multiplets in various datasets , e.g. takeda et al . ( 1999 ) , uchihori et al . ( 2000 ) , farrar , berlind & hogg ( 2006 ) , the significance of which is questioned in abbasi et al . ( 2004 ) and finley & westerhoff ( 2004 ) ; or , finally , the recent data of the pao , which reveal a correlation with nearby active galactic nuclei ( agn ) , the maximal signal being obtained for a search radius of @xmath9 around agn located closer than 75 mpc and for energies above @xmath10eev ( abraham et al . 2007 , 2008b ) . in general , these issues of anisotropies and chemical composition are discussed separately . however , as we argue in the present paper , one can construct a powerful test of the chemical composition by using the anisotropy signal at various energies . this becomes particularly interesting when one notes that measurements of chemical composition are relatively sensitive to the details of the shower reconstruction , in particular to the extrapolation of hadronic models at energies beyond those currently tested in accelerators ( see wibig 2008 , ulrich et al . 2009a , b and wibig 2009 for recent discussions of this issue ) . moreover , measurements of chemical composition rely on the use of fluorescence detectors whose duty cycle is rather low and can not be made event by event , so that they are limited by statistics . the essence of the test proposed in this paper is to exploit the fact that a source in the sky emitting heavy nuclei of charge @xmath0 at an energy @xmath11 is expected to produce a similar anisotropy pattern at energies @xmath12 via the proton component which is expected to be associated with the same source . our expectation for the existence of a proton component relies on the theoretical expectation , that if protons are present in the plasma in which particle acceleration takes place , then they should be accelerated along side with the heavy nuclei . as discussed in some detail at the end of [ sec : test - chem ] , a source accelerating heavy nuclei to energy @xmath11 is quite generally expected to accelerate protons to energy @xmath12 . although the isotropic background `` noise '' increases at lower energies , we show in [ sec : test - chem ] that the signal - to - noise ratio for the detection of the anisotropy also increases . this prediction does not depend at all on the modelling of astrophysical magnetic fields as it only relies on the property that protons of energy @xmath12 follow the same path in the intervening magnetic fields and produce the same angular image as heavy nuclei of charge @xmath0 and energy @xmath11 . the proposed test is discussed in more detail in section [ sec : test - chem ] . when applied to the most recent data of the pao ( section [ sec : pao ] ) , it shows that the signal that is responsible for the apparent anisotropy pattern at energies @xmath13eev must not be heavy but light nuclei , provided this anisotropy is confirmed by future data , and provided the pao does not see evidence for anisotropy at lower energies , as seems to be the case ( abraham et al . 2007 ) . we discuss the implications of these results in the last two sections . in section [ sec : agn ] , we argue that local agn ( including fr i radio - galaxies ) do not possess the power required to accelerate protons to ultra - high energies . when combined with the previous conclusions , this leads to the conclusion that the current pao data do not support agn as sources of the highest energy cosmic rays . finally , section [ sec : disc ] summarizes the findings and concludes that the current data on composition and anisotropy suggest one of the following : ( i ) the shower modelling or , what would be more interesting , the hadronic theoretical models of shower reconstruction are in error at high energy ; ( ii ) the composition switches abruptly from heavy to light above @xmath14eev ; ( iii ) the source injects primarily heavy nuclei ( which seems unlikely ) ; ( iv ) the anisotropy seen by the pao is a statistical artefact .

, we show that if one records an anisotropy signal produced by heavy nuclei of charge above an energy , one should record an even stronger ( possibly much stronger ) anisotropy at energies due to the proton component that is expected to be associated with the sources of the heavy nuclei . this conclusion remains robust with respect to the parameters characterizing the sources and it does not depend at all on the modelling of astrophysical magnetic fields . as a concrete example , we apply this test to the most recent data of the pierre auger observatory . assuming that the anisotropy reported above 55 eev is not a statistical accident , and that no significant anisotropy has been observed at energieseev , we show that the apparent clustering toward cen a can not be attributed to heavy nuclei . similar conclusions are drawn regarding the apparent excess correlation with nearby active galactic nuclei . , we argue that the current pao data does not support the model of cosmic ray origin in active radio - quiet or even radio - loud galaxies .

this paper proposes and discusses a test of the chemical composition of ultra - high energy cosmic rays that relies on the anisotropy patterns measured as a function of energy . in particular , we show that if one records an anisotropy signal produced by heavy nuclei of charge above an energy , one should record an even stronger ( possibly much stronger ) anisotropy at energies due to the proton component that is expected to be associated with the sources of the heavy nuclei . this conclusion remains robust with respect to the parameters characterizing the sources and it does not depend at all on the modelling of astrophysical magnetic fields . as a concrete example , we apply this test to the most recent data of the pierre auger observatory . assuming that the anisotropy reported above 55 eev is not a statistical accident , and that no significant anisotropy has been observed at energieseev , we show that the apparent clustering toward cen a can not be attributed to heavy nuclei . similar conclusions are drawn regarding the apparent excess correlation with nearby active galactic nuclei . we then discuss a robust lower bound to the magnetic luminosity that a source must possess in order to be able to accelerate particles of charge up toeev ,erg / s . using this bound in conjunction with the above conclusions , we argue that the current pao data does not support the model of cosmic ray origin in active radio - quiet or even radio - loud galaxies . finally , we demonstrate that the apparent clustering in the direction of cen a can be explained by the contribution of the last few gamma - ray bursts or magnetars in the host galaxy thanks to the scattering of the cosmic rays on the magnetized lobes .

0907.1354

c

let us start by summarizing the results obtained so far . we have discussed how one can can test the chemical composition of ultra - high rays on the sky by comparing the anisotropy signals at various energies . our main result is to show that if anisotropies are observed above some energy @xmath1 and the composition is assumed to be heavy at that energy ( nuclei of charge @xmath0 ) , one should observe at energies @xmath2 a substantially stronger anisotropy signal , which is associated with the proton component emitted by the sources that are responsible for the anisotropy pattern . these conclusions do not depend at all on the modelling of the intervening magnetic fields and they are robust with respect to the parameters characterizing the sources . we have then applied this test to the most recent data of the pao . we find that , if these data are taken at face value ( and if the pao arrival directions around the ankle appear isotropic ) , the events that are responsible for the anisotropy signal reported toward cen a and toward the nearby agn should not be heavy nuclei . interestingly , this result appears to be at odds with the current pao results on the chemical composition at the highest energies . one can not exclude at the present time that the observed anisotropies are statistical accidents ; only the acquisition of a larger set of data will tell . one can not exclude either that the composition switches abruptly from heavy to light at @xmath232eev . finally , one can not exclude that a systematic bias affects the composition measurements of the pao . in any case , the present discussion indicates that , if both the anisotropy and the heavy composition are confirmed by future data , some possibly important information is to be extracted out of this apparent contradiction . the theoretical and experimental uncertainties in the extrapolation of the @xmath233 cross - section to center - of - mass energies @xmath234tev are one of the possible sources of biases in shower reconstruction . recently , it has been argued that , if this cross - section were underestimated by some @xmath235% at these energies , one might reconcile the existing @xmath236 measurements with a pure proton composition at energies above the ankle ( ulrich et al . 2009a , 2009b ; see however wibig 2009 ) . in this respect , and in the light of the above discussion , the apparent anisotropy towards cen a offers a very valuable opportunity to test this possibility . it suffices , in principle , to test the anisotropy pattern against a future ( independent ) data set at various energies by comparing the number of events detected within a predetermined solid angle in a predetermined direction to the expected number for isotropic arrival directions ; at the same time , one needs to perform a dedicated composition measurement for cosmic rays from this particular region of the sky , in order to avoid as much as possible the contamination due to the isotropic contribution to the all - sky flux . then , one should apply the test discussed above . the natural question that follows is what can be inferred about the sources of ultra - high energy cosmic rays if , following the anisotropy results of pao and the above discussion , one assumes that most ultra - high energy cosmic rays are protons . let us now explore this line of reasoning . first of all , one concludes that the existing data of the pao disfavor the agn model of ultra - high energy cosmic ray origin . indeed , we have discussed in section [ sec : agn ] a robust lower bound to the magnetic luminosity that a source must possess in order to be able to accelerate particles of charge @xmath0 up to @xmath58ev , @xmath237erg / s . this bound allows to rule out the local radio quiet agn as sources of @xmath58ev protons . we have also argued that , while fr i radio - galaxies do not seem to possess the required luminosity to accelerate protons up to @xmath58ev , fr ii radio - galaxies and blazars do not correlate with the highest energy events . although radio - loud galaxies could possibly accelerate heavy nuclei up to energies close to the gzk cut - off , as we have discussed they would produce an anisotropy pattern predominantly at @xmath238eev energies rather than at ultra - high energies , in conflict with the pao results . we have discussed the particular case of cen a in some detail , as this source has recently received a lot of attention due to the observed clustering of events around it . we have provided a critical discussion of acceleration in this object and argued that its agn / jet / lobe system can not produce protons at the energies required , in good agreement with the general expectations from the above luminosity bound . that being said , the excess clustering in this particular direction , if real , remains to be interpreted . first , if sources are distributed according to the large scale structure , one expects a certain number of events to coincide accidentally with the direction of cen a , because of the location of the centaurus and shapley superclusters in this direction . using the pscz catalog of galaxies as a proxy for the distribution of the sources , with a depth of @xmath239mpc , and accounting for the pao exposure , one expects @xmath240 events above @xmath51eev within @xmath241 of cen a nucleus ( and @xmath242 for isotropic arrival directions ) for @xmath243 observed , or @xmath244 events within @xmath82 ( and @xmath86 for isotropic arrival directions ) for @xmath81 observed . note that the large scale structure is poorly sampled in the proximity of cen a due to its low galactic latitude . nevertheless , the above numbers already indicate that the contamination from the surrounding large scale structure in the direction to cen a is substantial . in particular , at the present level of statistics , one can not claim observing a significant departure from a model in which the sources are distributed as the large scale structure . it should also be recalled here that the pao analysis of clustering around cen a is an a posteriori one , hence one may not therefore assign a reliable significance to the detection of the anisotropy . moreover , if sources are gamma - ray bursts or magnetars , one should include in the flux prediction the contribution of such sources located in the cen a host galaxy itself . it is well known that the probability of detecting ultra - high energy cosmic rays from nearby gamma - ray bursts is extremely small unless the arrival times of these ultra - high energy cosmic rays are sufficiently dispersed ( waxman 1995 , waxman & miralda - escud 1996 ) . consider for instance gamma - ray bursts with rate of occurence @xmath245 in cen a ; these can be seen if either of their jets points into a solid angle @xmath246 where @xmath89 is the typical deflection acquired by the cosmic ray en route to the detector , giving a detection probability @xmath247 , with @xmath248 ; @xmath249 represents the spread of arrival times and @xmath250 the angular deflection for particles of energy @xmath251eev traveling from cen a to the detector through a magnetic field of strength @xmath252 g and coherence length @xmath253kpc ( waxman & miralda - escud 1996 ) . the above probability suggests that one should not detect events from gamma - ray bursts emitted directly toward the observed . however , if the jet of the gamma - ray burst hits one of the lobes of cen a , the particles can be redistributed in all directions , in particular towards the detector . the magnetic field inside the lobe , @xmath254 g is indeed sufficient to impart a deflection of order unity on the lobe distance scale @xmath48kpc to protons of @xmath255eev . in this case , the expected time delay and time dispersion are of the order of the travel time to the lobes , @xmath256yr , so that the expected number of gamma - ray bursts that one can see at any time , through rescattering of the particles on the lobes of cen a is : @xmath257 for an apparent solid angle of the lobes @xmath258 as viewed from the host galaxy of cen a , which is close to @xmath259 . the last gamma - ray burst(s ) of cen a may then contribute to the flux above the gzk cut - off up to : @xmath260 with @xmath261yrs , @xmath262 for an injection spectrum with @xmath263 , and @xmath264ergs the energy injected by one gamma - ray burst in ultra - high energy cosmic rays . this flux should be spread over the angular scale of the lobes , @xmath265 . at @xmath255eev , pao records a diffuse flux @xmath266 . after correcting for the solid angle of the cen a image and the pao aperture towards cen a , one finds that the last gamma - ray bursts in cen a should contribute up to @xmath267% of the observed pao flux , well within the range of the observed anisotropy . we also note that this contribution from sources inside cen a would improve the overall correlation of all the pao data above @xmath51eev with sources distributed as the local large scale structure . finally , we remark that the above effect of rescattering on the lobes provides a clear example of the possible biases discussed in kotera & lemoine ( 2008 ) , namely that the pao could be preferentially observing the last scattering centers ( in the present case , the lobes of cen a ) rather than the source itself ( the gamma - ray bursts located in the core of cen a ) . abbasi , r. u. , et al . 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this paper proposes and discusses a test of the chemical composition of ultra - high energy cosmic rays that relies on the anisotropy patterns measured as a function of energy . in particular we then discuss a robust lower bound to the magnetic luminosity that a source must possess in order to be able to accelerate particles of charge up toeev ,erg / s . using this bound in conjunction with the above conclusions finally , we demonstrate that the apparent clustering in the direction of cen a can be explained by the contribution of the last few gamma - ray bursts or magnetars in the host galaxy thanks to the scattering of the cosmic rays on the magnetized lobes .

this paper proposes and discusses a test of the chemical composition of ultra - high energy cosmic rays that relies on the anisotropy patterns measured as a function of energy . in particular , we show that if one records an anisotropy signal produced by heavy nuclei of charge above an energy , one should record an even stronger ( possibly much stronger ) anisotropy at energies due to the proton component that is expected to be associated with the sources of the heavy nuclei . this conclusion remains robust with respect to the parameters characterizing the sources and it does not depend at all on the modelling of astrophysical magnetic fields . as a concrete example , we apply this test to the most recent data of the pierre auger observatory . assuming that the anisotropy reported above 55 eev is not a statistical accident , and that no significant anisotropy has been observed at energieseev , we show that the apparent clustering toward cen a can not be attributed to heavy nuclei . similar conclusions are drawn regarding the apparent excess correlation with nearby active galactic nuclei . we then discuss a robust lower bound to the magnetic luminosity that a source must possess in order to be able to accelerate particles of charge up toeev ,erg / s . using this bound in conjunction with the above conclusions , we argue that the current pao data does not support the model of cosmic ray origin in active radio - quiet or even radio - loud galaxies . finally , we demonstrate that the apparent clustering in the direction of cen a can be explained by the contribution of the last few gamma - ray bursts or magnetars in the host galaxy thanks to the scattering of the cosmic rays on the magnetized lobes .

1507.03072

i

in protein synthesis , the genetic information is deciphered into proteins by molecular machines called ribosomes that attach themselves at the start end of mrna , move along the chain in a unidirectional manner and finally detach at the stop end @xcite . each translation step requires the binding of a freely diffusing transfer - rna ( trna ) molecule , carrying the amino acid specific to each codon @xcite . the important factor affecting the ribosome translation rate is relative concentrations of trna , which may vary from codon to codon . the codons with lower concentrations of trna reduce the protein synthesis rate and thus plays the role of an inhomogeneity in a homogeneous system @xcite . apart from this , inhomogeneities also occur naturally in many other transport systems such as vehicular traffic @xcite , blood flow @xcite and flow of data in a von neumann architecture @xcite . in traffic flow , the ongoing construction on roads , a slow moving vehicle or an accident can lead to slow down the flow rate on highways and can lead to congestion . further , the separation of the cpu and the memory in computers creates von neumann bottleneck , which limits the performance of the computer via limited bandwidth between the cpu and the memory . totally asymmetric simple exclusion process ( tasep ) @xcite is well known to be a paradigmatic model for studying stochastic transport in many - particle systems . both single - channel and multi - channel taseps have been well explored theoretically as well as using monte carlo simulations @xcite . further , one has to take into account the fact that the proteins as molecular motors can also attach from the bulk reservoir or detach from it ( langmuir kinetics ( lk ) ) @xcite . in contrast to tasep , where total number of particles remain conserved , the additional attachment - detachment dynamics ( lk dynamics ) violate the particle conservation and leads to many interesting phenomena @xcite . in literature , the consequences of coupling of the two different dynamics : tasep and lk have been well analyzed in single - channel @xcite as well as two - channel homogeneous systems @xcite . the idea of slowing down of particles at certain defect positions can be incorporated in the form of a set of inhomogeneous lattice sites ( bottleneck ) , either as a single unit or randomly distributed over the whole lattice in tasep . this type of disorder is known as site - wise disorder . another type of disorder studied in literature is particle - wise , where a slow moving particle itself acts as an inhomogeneity in the system . the present work focuses on site - wise disorder which is suitable to model the inhomogeneities present in transport of molecular motors . although a lot of work has been done on homogeneous taseps , the effect of disorder on the steady - state dynamics of such systems is not well understood . several studies have been performed on single - channel inhomogeneous taseps with @xcite as well as without lk @xcite . while investigating the role of a bottleneck in a closed tasep @xcite , it was found that even the presence of a single bottleneck site can produce shock profile and a plateau in the fundamental current - density relation . later , kolomeisky @xcite examined even richer case of single - channel open system and explored the consequences of the inhomogeneity with both faster and slower transition rates . he divided the system into two homogeneous taseps coupled at the single bottleneck site ( defect mean - field theory ( dmft ) ) and proved analytically that a fast site has no effect on the phase diagram ; whereas a slow site leads to shifting of the phase boundaries only . he also tested the theoretical results with monte carlo simulations and found a good agreement in low density ( ld ) and high density ( hd ) phases ; while a little deviation in maximal current ( mc ) phase . another analytical approach namely finite - segment mean - field theory ( fsmft ) was introduced by chou and laktaos @xcite to study clusters of slow codons in protein synthesis . they found that ribosome density profiles near neighboring clusters of slow codons suppress the proteins synthesis . dong et al . @xcite generalized the dmft to study the effect of two bottlenecks on the protein production rate and also performed extensive monte carlo simulations to conclude that the location as well as spacing between the bottlenecks affect the production rate , pointing out an important phenomenon namely _ edge effect_. the investigation into edge effects was further carried out by greulich and scadshneider @xcite to generate the phase diagrams of inhomogeneous tasep using interacting subsystem approximation ( isa ) . they could successfully explain the interactions of defects with the boundaries of the single - channel system . the more complex case of inhomogeneous tasep in the presence of langmuir kinetics was studied by qiu et al . they calculated phase diagrams and density profiles by adopting the concept of dmft and also studied the effect of slow hopping rate and detachment rate on the phase diagram . pierobon et al . @xcite provided a detailed study on the role of a bottleneck in a tasep with lk , using an effective mean - field theory and monte carlo simulations . they introduced the concept of carrying capacity to identify various novel phases called bottleneck phases . importantly , all of the above studies focused on single - channel inhomogeneous systems . parallel to the inhomogeneous single - channel systems , particles in multi - channel transport systems @xcite may also confront a bottleneck , present in either one or in more than one channels . the importance of studying the multi - channel system lies in the fact that it can act as a framework for extending the analysis to networks . due to the complexity in dynamics generating from the interactions between different channels , it is difficult to examine the effects of inhomogeneity in a multi - channel open system . up to our knowledge , the only contribution in this direction has been made by wang et al . @xcite , which explored the effect of a local inhomogeneity in one of the lanes of a two - lane tasep with lk under a symmetric lane changing rule . they extended the dmft to a two - channel system by incorporating the concept of effective injection and removal rates at the inhomogeneous lattice site . despite a good agreement between the solution of the mean - field equations and monte carlo simulations in ref . @xcite , this approach fails to produce the steady - state phase diagrams of the two - channel system . moreover , it is not feasible to analyze the role played by various parameters such as lane - changing rate , attachment - detachment rate and strength of bottleneck on the steady - state dynamics . one can infer from here that though dmft is capable to provide analytic solutions for single - channel inhomogeneous taseps with @xcite as well as without lk @xcite , it lacks some important ingredients to generate a complete picture of the dynamics of the corresponding two - channel system as discussed in section [ sec:3 ] . this motivates us to develop a new approach to handle the bottleneck in a two - channel tasep with lk , which not only overcomes the existing limitations , but also demonstrates the unexplored dynamics of two - channel inhomogeneous systems . the objective of the proposed study is two - fold , to develop a general theoretical approach , which is capable to produce the phase diagrams and to study the effect of various system parameters on the steady - state phases . in this paper , we attempt to provide a complete picture of the dynamics of two - channel symmetrically coupled tasep with lk in the presence of a single localized bottleneck in one of the two channels by adopting a new and simplified approach , called the _ hybrid approach_. we have also validated the theoretical results with monte carlo simulations . the paper is organized as follows . in section [ sec:2 ] , we define the model under examination and the governing dynamical rules . we briefly discuss the limitations of the earlier approaches in sec . [ sec:3 ] . the theoretical hybrid approach and monte carlo simulations are covered in section [ sec:4 ] and section [ sec:5 ] . a thorough analysis of the stationary properties of the model is discussed in section [ sec:6 ] . in the concluding section [ sec:7 ] , we summarize the results and future prospectives of our work .

this work is devoted to the development of a novel theoretical approach , named _ hybrid approach _ , to handle a localized bottleneck in a symmetrically coupled two - channel totally asymmetric simple exclusion process with langmuir kinetics . hybrid approach , bottleneck , monte carlo simulations , langmuir kinetics

this work is devoted to the development of a novel theoretical approach , named _ hybrid approach _ , to handle a localized bottleneck in a symmetrically coupled two - channel totally asymmetric simple exclusion process with langmuir kinetics . the hybrid approach is combined with singular perturbation technique to get steady - state phase diagrams and density profiles . we have thoroughly examined the role played by the strength of bottleneck , binding constant and lane - changing rate in the system dynamics . the appearances of bottleneck - induced shock , a bottleneck phase and meissner phase are explained . further , the critical values of bottleneck rate are identified , which signify the changes in the topology of phase diagram . it is also found that increase in lane - changing rate as well as unequal attachment , detachment rates weaken the bottleneck effect . our theoretical arguments are in good agreement with extensively performed monte carlo simulations . hybrid approach , bottleneck , monte carlo simulations , langmuir kinetics

1507.03072

r

in this section , we provide a detailed discussion of the steady - state properties of the proposed model , with emphasis on the resulting phase diagrams and analyze the effects of bottleneck strength , lane - changing rate and binding constant . for simplicity , we assume that the bottleneck in lane a is located exactly at the middle i.e. @xmath100 . the steady - state phase diagrams as well as density profiles are obtained from hybrid mean - field approach and validated using extensive monte carlo simulations . when there is no bottleneck , i.e. @xmath101 , the present model reduces to the homogeneous two - channel tasep with lk . under symmetric coupling conditions , the two - channel homogeneous tasep with lk is analogous to its single - channel counterpart , which has been studied well in literature @xcite . for @xmath102 , we call the defect to be _ fast defect _ as the bottleneck rate is more than the usual horizontal particle hopping rate in the system . clearly , a single fast defect does not affect the steady - state dynamics as the rate - limiting hoppings occurring with rate @xmath103 dominate the whole lattice @xcite . thus , it is appropriate to focus on the situation where the bottleneck acts as a slow defect i.e. @xmath104 . it is well known that the steady - state dynamics of exclusion process are significantly affected by the binding constant . so , we proceed by segmenting the analysis into two subcases viz . ( i ) @xmath105 , and ( ii ) @xmath106 . the other parameters are kept fixed to @xmath107 and @xmath99 . we examine the steady - state dynamics for different strengths of bottleneck by gradually decreasing the value of @xmath26 . no significant qualitative changes are found in the phase diagram till @xmath108 , below which one notices the effect of bottleneck more clearly . [ fig:2 ] shows the phase diagram of the system with @xmath109 and @xmath110 . specifically , fig . [ fig:2](a ) shows the complete characterization of various phases in terms of the boundary layers . the solid and dashed lines denote the bulk and surface transitions , respectively . as an illustration , the notation ( tanh - r , tanh - r ) signifies that there is a right boundary layer in lane a as well as lane b of the kind tanh - r , given by eq . and @xmath111 denotes the shock phase . for a detailed understanding of the bulk and surface transitions , we refer the readers to references @xcite . as discussed in previous section that a surface transition is responsible for the change in slope of the boundary layer only and does not affect the bulk density , henceforth , our focus will be only on bulk transitions to avoid any complexities in the phase diagrams . [ fig:2](b ) represents the bulk phase transitions only corresponding to fig . [ fig:2](a ) . , @xmath107 , @xmath110 and @xmath99 , ( a ) phase diagram showing bulk as well as surface transitions and classification according to the boundary layers , nbl denotes no boundary layer , ( b ) phase diagram showing qualitative nature of phases with no surface transitions . notations:- m : meissner phase , 1 : ( @xmath112-ld / mc / hd , ld / hd / ld / mc / hd ) , 2 : ( ld / mc / hd - ld / mc / hd , ld / mc / hd / ld / mc / hd ) , 3 : ( ld / mc / hd - s , ld / mc / hd / ld / hd ) , 4 : ( @xmath112-s , ld / hd / ld / hd ) , 5 : ( @xmath112-ld / mc , ld / hd / ld / mc ) , 6 : ( ld / mc / hd - ld / mc , ld / mc / hd / ld / mc ) , 7:(mc / hd - ld / mc , mc / hd / ld / mc ) , 8 : ( mc / hd - ld / mc / hd , mc / hd / ld / mc / hd ) and 9 : ( mc / hd - s , mc / hd / ld / hd ) . solid and dashed lines denote bulk and surface transitions , respectively.,title="fig:",width=255,height=219 ] , @xmath107 , @xmath110 and @xmath99 , ( a ) phase diagram showing bulk as well as surface transitions and classification according to the boundary layers , nbl denotes no boundary layer , ( b ) phase diagram showing qualitative nature of phases with no surface transitions . notations:- m : meissner phase , 1 : ( @xmath112-ld / mc / hd , ld / hd / ld / mc / hd ) , 2 : ( ld / mc / hd - ld / mc / hd , ld / mc / hd / ld / mc / hd ) , 3 : ( ld / mc / hd - s , ld / mc / hd / ld / hd ) , 4 : ( @xmath112-s , ld / hd / ld / hd ) , 5 : ( @xmath112-ld / mc , ld / hd / ld / mc ) , 6 : ( ld / mc / hd - ld / mc , ld / mc / hd / ld / mc ) , 7:(mc / hd - ld / mc , mc / hd / ld / mc ) , 8 : ( mc / hd - ld / mc / hd , mc / hd / ld / mc / hd ) and 9 : ( mc / hd - s , mc / hd / ld / hd ) . solid and dashed lines denote bulk and surface transitions , respectively.,title="fig:",width=255,height=219 ] to understand the dynamics in a better way , we introduce an appropriate notation @xmath113 denoting the kind of stationary phase in the two - channel system . here , @xmath114 denotes the type of stationary phase in left ( right ) subsystem of lane a ; while @xmath115 denotes the stationary phase in lane b. for example , the phase ( ld - s , s ) denotes that the region left to the bottleneck is low density ( ld ) with a shock present in the right subsystem in lane a and a shock is also present in lane b. , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] + , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] + , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] , @xmath107 , @xmath110 and @xmath99 . ( a ) ( ld - ld , ld / ld ) phase for @xmath116 , ( b ) ( ld - s , ld / s ) phase for @xmath117 , ( c)(hd - hd , hd / hd ) for @xmath118 , ( d ) ( s - hd , s / hd ) phase for @xmath119 , ( e ) ( mc / hd - ld / mc , mc / hd / ld / mc ) phase for @xmath120 and ( f ) ( @xmath112-s , ld / hd / ld / hd ) phase for @xmath121.,title="fig:",width=198,height=179 ] we list important features of the steady - state dynamics under the current choice of parameters . 1 . _ meissner phase and bottleneck affected region : _ in the upper right quadrant ( @xmath122 , shaded blue ) , the bulk densities in each lane becomes independent of entrance as well as exit rates . this effect is similar to the behavior of the meissner phase found in superconducting materials @xcite . therefore , we also adopt the name meissner phase ( denoted by m ) to identify boundary independent behavior of two - channel system . it is important to mention that meissner phase is actually a part of certain existing phase , denoted by phase @xmath123 in fig . [ fig:2](b ) . meissner phase is also reported in the literature for a homogeneous single - channel tasep with lk @xcite . note that the density profiles get significantly influenced by bottleneck for a specific range of @xmath124 . the corresponding region in phase - plane is marked with red dots and referred as bottleneck phase throughout this paper . similar results also exist for single - channel inhomogeneous tasep with lk , in which bottleneck phase is identified and analyzed in terms of carrying capacity @xcite . in contrast , for low entrance and exit rates one recovers the tasep / lk density profiles perturbed by a local spike or a dip , which will be discussed as we proceed in this paper . 2 . _ phase transitions and mixed phases : _ to gain an intuitive understanding of the steady - state dynamics of the system , it is important to analyze the phase transitions . across the bulk transition line between ( ld - ld , ld)(fig . [ fig:3](a ) ) and ( ld - s , s ) ( fig . [ fig:3](b ) ) phases , one finds the formation of a shock through deconfinement of the right boundary layer @xcite . it is evident from fig . [ fig:2](b ) that @xmath125 and @xmath126 for @xmath127 are the lines of deconfinement of shock from right boundary layer ( ld phase ) and left boundary layer ( hd phase ) , respectively . interestingly , these are also the corresponding lines of deconfinement in analogous single - channel homogeneous system @xcite . from here , one can infer that the phase diagram under a weak bottleneck has almost similar topological structure as for the one with no bottleneck ( @xmath101 ) @xcite though some of the phases differ in their qualitative nature . actually , a weak bottleneck is incapable of affecting the steady - state dynamics of a symmetrically coupled two - channel tasep with lk system globally . the only effects can be seen in the vicinity of the bottleneck . this point is evident from the density profiles in fig . [ fig:3 ] , which will be discussed in detail subsequently . + as one can see from fig . [ fig:3](b ) , a shock is present in both the lanes in ( ld - s , s ) phase . on decreasing @xmath12 , the shock in both the lanes moves leftwards and reaches exactly at @xmath128 on the line @xmath129 ; @xmath130 . this line corresponds to the phase transition between ( ld - s , s ) and ( s - hd , s ) phases . a further reduction in magnitude of @xmath12 moves the shock upstream to the bottleneck giving rise to ( s - hd , s ) phase . the bulk phase transition from ( hd - hd , hd)(fig . [ fig:3](c))to ( s - hd , s)(fig . [ fig:3](d ) ) can also be understood on the similar lines . rest of the phase transitions in fig . [ fig:2](b ) are due to gradual changes in the magnitude of densities with respect to entrance and exit rates . + note that lane b has exactly the same density as that in lane a everywhere , except in the vicinity of the bottleneck ( see fig . [ fig:3 ] ) . interestingly , this slight difference in density near the bottleneck is able to produce peculiar kinds of density profiles , giving rise to a number of coexistence ( or mixed ) phases such as ( ld / mc / hd - s , ld / mc / hd / ld / hd ) and ( mc / hd - ld / mc , mc / hd / ld / mc ) etc . an illustration of a mixed phase is shown in fig . [ fig:3](e ) . formation of upward and downward spikes : _ consider the ld phase in left subsystem of lane a , where the particles have enough space to move along the lattice and the presence of a weak bottleneck does not affect the particle motion significantly . here , the density profile in lane a incurs a local perturbation in the form of an upward spike as shown in fig . [ fig:3](a ) . due to comparatively slower particle hopping rate at the bottleneck , the particles coming from the left feels a little congestion before entering the bottleneck . due to this , the density in lane a rises slightly just upstream to the bottleneck , leading to formation of an upward spike in the density profile . importantly , lane b remains unaffected in this phase . similarly , one can understand the formation of a downward spike shown in fig . [ fig:3](b ) ) in hd phase . this can be attributed to particle - hole symmetry . when a particle comes out of the bottleneck in a highly packed situation , it experiences a sudden increase in its hopping rate . this leads to formation of a lower density region just downstream to the bottleneck . similar findings have been reported in literature @xcite . 4 . _ transition to bottleneck - induced shock : _ now we discuss an important feature of our system dynamics i.e. the formation of a bottleneck - induced shock . with ld in lane a , an increase in entrance rate @xmath9 increases the number of particles in left subsystem of lane a , which ultimately increases height of the existing upward spike . at a particular @xmath131 , this local density perturbation converts into a shock , which travels in the left subsystem in lane a for further increase in @xmath9 . since this shock emerges due to bottleneck only , we call this shock as _ bottleneck - induced shock _ and denote it by @xmath112 . the formation of bottleneck - induced shock is also observed for a single - channel inhomogeneous tasep with lk @xcite . the presence of bottleneck - induced shock leads to the existence of three new phases ( @xmath112-s , ld / hd / ld / hd ) , ( @xmath112-ld / mc / hd , ld / hd / ld / mc ) and ( @xmath112-ld / mc / hd , ld / hd / ld/ mc / hd ) in the phase - plane as shown in fig . [ fig:2](b ) . the existence of mixed phases in lane b indicates the effect of bottleneck in homogeneous lane as well . interestingly , there exist two shocks in lane a in ( @xmath112-s , ld / hd / ld / hd ) phase ( see fig . [ fig:3](f ) ) , the left one being bottleneck - induced ; whereas the right one is formed due to deconfinement of right boundary layer . we propose a terminology to identify the strength of the bottleneck as shown in table [ tab:1 ] . we also provide the number of steady - state phases observed under each case , the details of which follow in the text . cccc & & + & & & + no bottleneck & @xmath132 & 4 & 7 + weak & @xmath133 & 2 & 13 + moderate & @xmath134 & 2 & 9 + strong & & & 14 + blockage & @xmath135 & 3 & 14 + _ weak bottleneck : _ so far , we have discussed the steady - state dynamics for a weak bottleneck and pointed out important features such as appearance of meissner phase , bottleneck phase and bottleneck - induced shock etc . clearly , the number of steady - state phases under a weak bottleneck is more than in homogenous case , which is due to the appearance of mixed phases . now , we will gradually change the strength of bottleneck from weak to moderate and then to strong and see whether the same trend continues or not ? _ moderate strength : _ in the range of moderate strength of bottleneck , we have chosen @xmath136 to generate the phase diagram . it is found that for a moderate bottleneck , the phase diagram ( see fig . [ fig:4](a ) ) is qualitatively as well as quantitatively different from the one with weaker bottleneck ( see fig . [ fig:2](b ) ) . an important distinguishing feature of the phase diagram is the appearance of bottleneck - induced shock in lane b as well . this can be seen from fig . [ fig:4](a ) , which identifies ( @xmath112-s,@xmath112/s ) as a new phase . while the nature of bottleneck - induced shock in lane a has already been discussed , one needs to investigate the occurrence of two shocks in lane b. clearly one located in the right is due to the deconfinement of right boundary layer ; while other is because of the indirect impact of bottleneck in lane a , whose origin can be understood as follows . actually , the presence of a bottleneck - induced shock in lane a produces a local high - density region there , making it difficult to accommodate incoming particles from lane b. as a result , the density in the left subsystem of lane b rises and converts into a shock with an increase in entrance rate @xmath9 . the shock produced in lane b , due to the effect of bottleneck in lane a , is also called as bottleneck - induced shock . , @xmath110 and @xmath99 with ( a)@xmath136 , 1:(@xmath112-s , s ) , and ( b)density profile in ( @xmath112-s,@xmath112/s ) phase with @xmath137 , @xmath138 and @xmath136 , and ( c ) phase diagram for @xmath139 , i : ( @xmath112-s,@xmath112/s ) , ii : ( @xmath112-ld,@xmath112/s ) , iii : ( hd - ld,@xmath112/s ) and iv : ( hd - s,@xmath112/s ) . increase in height of upward spike ( shown in magnified inset ) and conversion of spike into bottleneck - induced shock with a decrease in @xmath26,title="fig:",width=170,height=160 ] , @xmath110 and @xmath99 with ( a)@xmath136 , 1:(@xmath112-s , s ) , and ( b)density profile in ( @xmath112-s,@xmath112/s ) phase with @xmath137 , @xmath138 and @xmath136 , and ( c ) phase diagram for @xmath139 , i : ( @xmath112-s,@xmath112/s ) , ii : ( @xmath112-ld,@xmath112/s ) , iii : ( hd - ld,@xmath112/s ) and iv : ( hd - s,@xmath112/s ) . increase in height of upward spike ( shown in magnified inset ) and conversion of spike into bottleneck - induced shock with a decrease in @xmath26,title="fig:",width=170,height=160 ] , @xmath110 and @xmath99 with ( a)@xmath136 , 1:(@xmath112-s , s ) , and ( b)density profile in ( @xmath112-s,@xmath112/s ) phase with @xmath137 , @xmath138 and @xmath136 , and ( c ) phase diagram for @xmath139 , i : ( @xmath112-s,@xmath112/s ) , ii : ( @xmath112-ld,@xmath112/s ) , iii : ( hd - ld,@xmath112/s ) and iv : ( hd - s,@xmath112/s ) . increase in height of upward spike ( shown in magnified inset ) and conversion of spike into bottleneck - induced shock with a decrease in @xmath26,title="fig:",width=170,height=160 ] on moving from weak to moderate bottleneck , the phase diagram gets simplified resulting into a reduction in number of phases . the coexistence phases ( mc / hd - ld / mc , mc / hd / ld / mc ) , ( mc / hd - s , mc / hd / ld / hd ) and ( @xmath112-ld / mc , ld / hd / ld / mc ) , observed in fig . [ fig:2](b ) , are replaced by ( hd - ld , hd / ld ) , ( hd - s , s ) and ( @xmath112-ld , s ) , respectively . this shows that mc phase , either as a whole or as a part of density profile , does not exist for moderate bottleneck , contrary to the weak bottleneck case . this result is analogous to the one found for single - channel tasep with lk with a single bottleneck @xcite . further , the bottleneck phase ( dotted region ) enlarges , as expected for a stronger bottleneck ; whereas the phases ( ld - ld , ld),(ld - s , s ) , ( s - hd , s ) and ( hd - hd , hd ) shrink . meissner phase remains unaffected with increase in bottleneck strength . _ strong bottleneck : _ fig . [ fig:4](c ) shows the phase diagram for the present system with @xmath139 , a strong bottleneck . it can be seen that topology of the phase diagram is significantly changed in comparison to the one with moderate bottleneck . here , the bottleneck effect is sufficiently strong to increase the density difference between two lanes up to a level that we have a complex phase diagram structure as shown in fig . [ fig:4](c ) . one can see that ld phase does not exist in the left subsystem to the bottleneck in lane a. this is physically justified as the extremely slow hopping rate at bottleneck obstructs the incoming particles , leading to formation of either a shock or a hd region in left subsystem . similar argument and particle - hole symmetry accounts for the non - existence of hd phase downstream to the bottleneck in lane a. it further accounts for the enlargement of ( hd - ld , hd / ld ) phase with a decrease in @xmath26 . note that the bottleneck phase ( dotted region ) further enlarges to maximum extent and covers the whole @xmath95 plane . we have also checked the results for the case of complete blockage at the bottleneck i.e. @xmath140 . the phase diagram for @xmath140 remains essentially similar to the one for @xmath139 . the only change is shifting of the phase boundaries , which leads to expansion of ( hd - ld , hd / ld ) phase ( following the similar trend as explained above ) and shrinkage of rest of the phases . .,width=245,height=198 ] fig . [ fig:5 ] shows the transition of upward spike into bottleneck - induced shock with respect to an increase in bottleneck strength . firstly the height of upward spike in lane a at @xmath128 increases in moderate bottleneck case(clearly seen in the inset ) , then the spike converts into shock for strong bottleneck . a further decrease in value of @xmath26 pulls the shock leftwards . so far , we have investigated the system dynamics under different bottleneck strengths , but for fixed lane - changing rate at @xmath110 . since coupling strength has always been an important parameter in two - channel systems , it is necessary to examine its role for the proposed model . in literature , it is well explored @xcite that higher orders of lane - changing rate does not affect the dynamics of a symmetrically coupled homogeneous two - channel tasep with / without lk because the system decouples into two independent single - channel homogeneous systems . but , in our model , this is not the case as our system is inhomogeneous . so , we thoroughly investigate the effect of coupling strength on the dynamics of the proposed inhomogeneous model under different strengths of bottleneck systematically . our aim is to discuss the important topological changes in the phase diagram induced by higher order of lane - changing rate ( for definition of order , please see @xcite ) . for a weak bottleneck , the effect of lane - changing rate on the phase diagram is insignificant till @xmath141 . only little quantitative differences are seen on density profiles in both the lanes . when @xmath142 , we notice significant changes in the density profiles of both the lanes leading to some qualitative changes in the nature of certain phases . [ fig:6](a ) shows the phase diagram for @xmath109 with @xmath143 . for higher orders of @xmath144 , we have found that the number of stationary phases remain same . interestingly , some of the existing phases get transformed into new phases without a noticeable change in the phase boundaries . for example , the phases ( ld / mc / hd - ld / mc , ld / mc / hd / ld / mc ) , ( mc / hd - ld / mc , mc / hd / ld / mc ) and ( @xmath112-s , ld / hd / ld / hd ) change to ( ld / hd - mc , ld / hd / mc ) , ( mc / hd - mc , mc / hd / mc ) , ( @xmath112-hd,@xmath112/hd ) , respectively on moving from @xmath110 to @xmath143 . the effect of increasing the order of @xmath144 on a moderate bottleneck is similar to the one discussed for weak bottleneck . therefore , we skip the phase diagrams for this case at higher orders of @xmath144 . moving our attention towards strong bottleneck , we analyze the phase diagram for @xmath139 . no structural changes in the phase diagram are seen till @xmath145 , except minor translation of various phase boundaries . as an example , the ( @xmath112-s , s ) phase expands ; while ( hd - ld , hd / ld ) phase shrinks . an important phenomenon occurs at @xmath146 , where the density difference between both the lanes , in the vicinity of the bottleneck , decreases . as a result , the complexity of the phase diagram reduces as shown in fig . [ fig:6](b ) . importantly , four new phases ( ld - ld , ld ) , ( ld - s , s ) , ( s - hd , s ) and ( hd - hd , hd ) appear . the effect of bottleneck , despite its higher strength at @xmath139 , reduces because the bottleneck phase covers comparatively smaller region in @xmath95 plane . further increase in lane - changing rate does not produce any subsequent changes in the phase diagram for @xmath139 . this happens due to the weakening of bottleneck effect by an increase in lane - changing rate , which is discussed as follows . , and @xmath99 with ( a ) @xmath109 , @xmath143 , notations:- 1 : ( @xmath112-ld / mc / hd,@xmath112/ld / mc / hd ) , 2 : ( ld / hd - ld / mc / hd , ld / hd / ld / mc / hd ) , 3 : ( ld / hd - hd , ld / hd ) and 4 : ( @xmath112-hd,@xmath112/hd).(b ) @xmath139 with @xmath147 . , title="fig:",width=255,height=219 ] , and @xmath99 with ( a ) @xmath109 , @xmath143 , notations:- 1 : ( @xmath112-ld / mc / hd,@xmath112/ld / mc / hd ) , 2 : ( ld / hd - ld / mc / hd , ld / hd / ld / mc / hd ) , 3 : ( ld / hd - hd , ld / hd ) and 4 : ( @xmath112-hd,@xmath112/hd).(b ) @xmath139 with @xmath147 . , title="fig:",width=255,height=219 ] _ weakening of bottleneck effect _ it can be seen from figs . [ fig:2 ] , [ fig:4 ] and [ fig:6 ] that the bottleneck affected region ( dotted region ) shrinks at higher orders of lane - changing rate in comparison to the one for lower orders of @xmath144 under all values of @xmath26 . specifically , the weakening of bottleneck effect occurs for lower values of @xmath9 and @xmath12 with an increase in lane - changing rate @xmath144 . this is further justified from fig . [ fig:7 ] , which shows a monotonic reduction in peak s height of upward spike at bottleneck with respect to an increase in @xmath144 . an obvious explanation of this effect is that the particles in lane a , feeling hindered due to the bottleneck , would shift to other lane more frequently . as a result , the congestion in lane a gets slightly reduced as one increase the lane - changing rate . similar kind of effect is also reported in literature @xcite . the insets in fig . [ fig:7 ] shows the similar effect for downward spike as well . , ( b ) @xmath136 and ( c ) @xmath139 . here , @xmath148 , @xmath149 for upward spike in ld phase and @xmath150 , @xmath151 for downward spike in hd phase.,width=255,height=219 ] since the methodology of the proposed hybrid mean - field approach is general and applicable for any value of binding constant @xmath153 , we follow same lines to discuss the case where attachment and detachment rates differ , @xmath154 , i.e. @xmath155 . , @xmath107 and @xmath156 with different @xmath26 : ( a ) @xmath109 , ( b ) @xmath157 , and ( c ) @xmath139 . notations , m : meissner phase ( shaded blue ) and bp : bottleneck phase ( shaded with red dots),title="fig:",width=170,height=160 ] , @xmath107 and @xmath156 with different @xmath26 : ( a ) @xmath109 , ( b ) @xmath157 , and ( c ) @xmath139 . notations , m : meissner phase ( shaded blue ) and bp : bottleneck phase ( shaded with red dots),title="fig:",width=170,height=160 ] , @xmath107 and @xmath156 with different @xmath26 : ( a ) @xmath109 , ( b ) @xmath157 , and ( c ) @xmath139 . notations , m : meissner phase ( shaded blue ) and bp : bottleneck phase ( shaded with red dots),title="fig:",width=170,height=160 ] fig . [ fig:8 ] shows the steady - state phase diagrams with @xmath158 . comparing fig . [ fig:8 ] with figs . [ fig:2 ] and [ fig:4 ] , we notice that the complexity of the phase diagrams reduces tremendously for @xmath158 under all values of @xmath26 . the number of steady - state phases is shown in table [ tab:1 ] . note that due to the increased attachment rate in comparison to detachment rate , the density in both the lanes increases , leading to a complete absence of ld phase in the system . for weaker bottleneck , the phase diagram is much simple consisting of only two stationary phases ( s - hd , s ) and ( hd - hd , hd ) as shown in fig . [ fig:8](a ) . quite surprisingly , no density profile in @xmath95 plane is significantly affected by bottleneck , excluding the presence of a downward spike at @xmath128 . this is in sharp contrast to the parallel case with @xmath105 ( see fig . [ fig:2](b ) ) . consequently , one does not get a bottleneck - induced shock here for any values of @xmath9 and @xmath12 . further decrease in the value of @xmath26 does not change the structure of phase diagram but increases the height of downward spike in hd phase . this trend continues till one reaches @xmath159 , at which the perturbation of downward spike enters the right subsystem in lane a in the form of a shock , called as bottleneck - induced shock . its emergence leads to formation of new steady - state phases such as ( @xmath160 ) and ( hd-@xmath112,hd ) as shown in fig . [ fig:8](b ) . a part of phase - plane ( shaded with red dots ) is strongly influenced by the bottleneck - induced shock called as bottleneck phase , which was absent for @xmath161 ( see fig . [ fig:8](a ) ) . on the other hand , the value of @xmath26 does not influence the meissner phase . a further decrease in value of @xmath26 below @xmath162 leads to significant changes in the steady - state dynamics . the emergence of a new phase ( hd-@xmath112,s ) is seen at another critical value @xmath163 as shown in fig . [ fig:8](c ) . additionally two of the earlier existing phases ( s - hd , s ) and ( hd - hd , hd ) disappear completely ; while the bottleneck phase covers the whole @xmath95 plane reflecting the profound effect of strong bottleneck . we have also investigated the effect of lane - changing rates on the dynamics of the proposed system under case @xmath164 . for @xmath165 , no significant changes are seen except shifting of phase boundaries for any value of @xmath26 . we focus on the situation when @xmath166 . it is found that the steady - state phase diagram for weak bottlenecks remains unchanged and has a structure similar to the one seen in fig . [ fig:8](a ) . but the height of downward spike at @xmath128 decreases with respect to increase in lane - changing rate , analogously to the parallel case @xmath105 . one can infer from here that an increase in lane - changing rate weakens the bottleneck effect with @xmath155 as well . the extent of weakening effect is up to a level that we do not get a bottleneck - induced shock till @xmath167 , which means the global effects of the disturbance caused by bottleneck can be captured only for a very strong bottleneck . as an illustration , we provide the phase diagram for @xmath139 in fig . [ fig:9](a ) , which consists of four new stationary phases . moreover , the bottleneck phase shrinks in its size , which once again indicates the weakening of the bottleneck s effect with respect to an increases in @xmath144 . , @xmath158 , @xmath143 and ( b)@xmath168 , @xmath169 , @xmath170.,title="fig:",width=198,height=179 ] , @xmath158 , @xmath143 and ( b)@xmath168 , @xmath169 , @xmath170.,title="fig:",width=198,height=179 ] we have observed that an increase in lane - changing rate weakens the bottleneck effect and as a result the bottleneck affected region in @xmath95 plane shrinks with respect to an increase in @xmath144 . comparing the two cases @xmath105 and @xmath164 , one can infer that the effect of bottleneck is further reduced when @xmath155 . the above two statements generate interest to know whether there exist some values of @xmath153 and/or @xmath144 , at which we do not get a bottleneck - induced shock even for a strong bottleneck . a thorough analysis of our study has revealed that for @xmath169 and @xmath170 with a very strong bottleneck ( @xmath168 , almost a blockage ) , we get a steady - state situation free of any bottleneck - induced shock . the resulting steady - state phase diagram is shown in fig . [ fig:9](b ) . although we do have a downward spike in the density profiles , yet the non - existence of a bottleneck - induced shock is an important outcome . such dynamics further opens up new challenges to dig deeply into the shock dynamics of the proposed model , which will be undertaken in our future study .

we have thoroughly examined the role played by the strength of bottleneck , binding constant and lane - changing rate in the system dynamics . the appearances of bottleneck - induced shock , a bottleneck phase and meissner phase are explained . further , the critical values of bottleneck rate are identified , which signify the changes in the topology of phase diagram . it is also found that increase in lane - changing rate as well as unequal attachment , detachment rates weaken the bottleneck effect .

this work is devoted to the development of a novel theoretical approach , named _ hybrid approach _ , to handle a localized bottleneck in a symmetrically coupled two - channel totally asymmetric simple exclusion process with langmuir kinetics . the hybrid approach is combined with singular perturbation technique to get steady - state phase diagrams and density profiles . we have thoroughly examined the role played by the strength of bottleneck , binding constant and lane - changing rate in the system dynamics . the appearances of bottleneck - induced shock , a bottleneck phase and meissner phase are explained . further , the critical values of bottleneck rate are identified , which signify the changes in the topology of phase diagram . it is also found that increase in lane - changing rate as well as unequal attachment , detachment rates weaken the bottleneck effect . our theoretical arguments are in good agreement with extensively performed monte carlo simulations . hybrid approach , bottleneck , monte carlo simulations , langmuir kinetics

1406.2717

i

merging and mass - transferring white dwarfs ( wds ) are responsible for the creation of a variety of exotic astrophysical systems and events . among these are isolated sdb / sdo stars ( likely created by the merger of two he wds ; saio & jeffery 2000 ; han et al . 2002 ; heber 2009 ) , r crb stars ( likely created by the merger of a co and he wd ; webbink 1984 ; iben et al . 1996 ; jeffery et al . 2011 ; clayton 2012 ) , am cvn binaries ( possibly created by stable mass transfer from a he wd onto a co wd ; warner 1995 ; tutukov & yungelson 1996 ; han & webbink 1999 ; nelemans et al . 2001a ) , and possibly high - mass neutron stars and magnetars ( created by the accretion - induced collapse of merging co wds or accreting o - ne - mg wds ; saio & nomoto 1985 ; nomoto & kondo 1991 ; saio & nomoto 2004 ) . more importantly , merging or accreting co wds may be the progenitors of type ia supernovae ( iben & tutukov 1984 ; webbink 1984 , di stefano 2010 ; gilfanov & bogdan 2010 ; maoz et al . 2010 ; li et al . 2011 ; bloom et al . 2012 ; gonzalez hernandez et al . 2012 ; schaefer & pagnotta 2012 ) , although the pre - supernova conditions of the wd are still a subject of intense investigation . compact wd binaries ( with periods in the range of minutes to hours ) are also being discovered at an accelerating pace ( e.g. mullally et al . 2009 ; kulkarni & van kerkwijk 2010 ; steinfadt et al . 2010 ; brown et al . 2012 ; kilic et al . 2012 ; kilic et al . 2013 , see marsh 2011 for a review ) . these systems will begin mass transfer within a hubble time , although it is not always clear which observed wd systems will result in which phenomena . recent simulations ( e.g. , segretain et al . 1997 ; yoon et al . 2007 ; loren - aguilar et al . 2009 ; van kerkwijk et al . 2010 ; dan et al . 2012 ; raskin et al . 2012 , dan et al . 2013 ) have shed new light on the outcome of wd mergers , however , the initial conditions of these simulations are predicated upon the tidal effects that precede ( and may ultimately determine the stability of ) the mass transfer process . it is thus crucial to understand how tides operate up to the moment of roche - lobe overflow . it is also important to quantify the rate of tidal dissipation once mass transfer begins . previous works ( nelemans et al . 2001b , marsh et al . 2004 ) have shown that the strength of tidal torques may be important in determining the stability of mass transfer . low mass ratio systems with @xmath0 are expected to have stable mass transfer , while high mass ratio systems with @xmath1 are expected to be unstable and merge . the fates of intermediate mass ratio systems with @xmath2 ( such as the recently discovered 12.75 minute binary , brown et al . 2011 ) are less certain . the stability of mass transfer in these systems may depend on the rate at which tidal torques can transfer rotational angular momentum from the accretor back to the orbit . this paper is the fifth in a series ( see fuller & lai 2011,2012a,2012b,2013 , hereafter papers i - iv ) dedicated to the physics of tidal interactions and their observational consequences in compact wd binaries . in these previous works , we examined the tidal excitation , propagation , and dissipation of gravity waves ( g - waves ) that are restored by buoyancy forces within co and he wds . the waves dissipate energy and angular momentum , leading to the rotational synchronization and tidal heating of wds in compact systems . we found that gravity waves are excited at compositional gradients within the wds and propagate toward the surface where they become highly non - linear , causing them to break and locally deposit their angular momentum . this results in strong tidal heating in the outer layers of the wd , and causes the wds to be spun up from the outside in . tides in white dwarfs have also been examined in several previous works using parameterized tidal dissipation laws ( iben et al . 1998 , piro 2011 , dallosso & rossi 2013 ) and in calculations of the tidal excitation of oscillation modes ( willems et al . 2010 , valsecchi et al . encouragingly , the detailed study of wd tides by burkart et al . 2013 utilizes techniques comparable to papers i and ii , and reaches generally similar conclusions . however , these works ( and all previous works that we know of ) have ignored the influence of rotation on the wave dynamics . while this approximation works for slowly spinning wds at the beginning of the tidal spin up process , it breaks down for wds nearing synchronous rotation in which the tidal forcing frequency becomes comparable to the spin frequency . the approximation is even worse for wds being spun up to super - synchronous rotation via mass transfer . in this study , we attempt to quantify the effect of the coriolis force on the efficiency of tidal angular momentum transport . to do this , we employ the so - called traditional " approximation frequently used to study the influence of rotation on gravity waves ( see e.g. , chapman & lindzen 1970 , bildsten et al . 1996 , lee & saio 1997 , townsend 2003 ) . the coriolis force modifies the angular dependence of the gravity waves , confining them to the equatorial region of the star . this affects their overlap with the ( predominantly quadrupolar ) tidal potential that excites them . moreover , the coriolis force modifies the radial wavelength of gravity waves , which in turn affects the amplitude to which they are excited . finally , the coriolis force allows for the existence of inertial and rossby waves ( r - waves ) , which are especially important in super - synchronously rotating wds in which tidal dissipation occurs through the excitation of retrograde waves ( i.e. , the wave pattern propagates opposite to the direction of the spin in a frame co - rotating with the wd ) . this paper is organized as follows . in section [ traditional ] , we review the influence of rotation under the traditional approximation , and we examine its effect on tidally excited gravito - inertial waves . in section [ tidal ] , we investigate the effects of rotation on the excitation of the dynamical tide and discuss how the dynamical tide transports energy angular momentum . in section [ torque ] , we present our numerical results of tidal dissipation rates in rotating wds and analyze its effect on the orbital and spin evolution of compact wd binaries . finally , in section [ conc ] , we discuss the implications of our results , and how they may affect wds in various types of compact binary systems .

however , rotation strongly alters retrograde gravity waves and inertial waves , with important consequences for the tidal spin - down of accreting wds . additionally , we discuss the impact of stokes drift currents on the wave angular momentum flux . finally , we speculate on how tidal interactions will affect super - synchronously rotating wds in accreting systems .

tidal interactions play an important role in the evolution and ultimate fate of compact white dwarf ( wd ) binaries . not only do tides affect the pre - merger state ( such as temperature and rotation rate ) of the wds , but they may also determine which systems merge and which undergo stable mass transfer . in this paper , we attempt to quantify the effects of rotation on tidal angular momentum transport in binary stars , with specific calculations applied to wd stellar models . we incorporate the effect of rotation using the traditional approximation , in which the dynamically excited gravity waves within the wds are transformed into gravito - inertial hough waves . the coriolis force has only a minor effect on prograde gravity waves , and previous results predicting the tidal spin - up and heating of inspiraling wds are not significantly modified . however , rotation strongly alters retrograde gravity waves and inertial waves , with important consequences for the tidal spin - down of accreting wds . we identify new dynamical tidal forcing terms that arise from a proper separation of the equilibrium and dynamical tide components ; these new forcing terms are very important for systems near synchronous rotation . additionally , we discuss the impact of stokes drift currents on the wave angular momentum flux . finally , we speculate on how tidal interactions will affect super - synchronously rotating wds in accreting systems . [ firstpage ] white dwarfs hydrodynamics waves

1406.2717

c

we have examined the effect of the coriolis force on the excitation of dynamical tides in rotating stars , with specific application to white dwarfs in compact binary systems . in particular , we study the dependence of the tidal dissipation on the tidal forcing frequency @xmath133 and rotational parameter @xmath98 . we utilize the traditional approximation to examine the effect of the coriolis force , which applies well to the gravito - inertial waves important for tidal dissipation in wds . as one might expect , the coriolis force is negligible when @xmath55 and important when @xmath31 . there are four primary effects of the coriolis force . first , it alters the angular profile of g - waves propagating in stars , changing their effective angular wavenumber @xmath23 and their angular overlap with the tidal potential . second , the changing value of @xmath23 also changes the radial wavelength of the waves , modifying their radial overlap with the tidal potential . third , the coriolis force introduces new classes of waves ( inertial waves and r - waves ) which rotationally mix with g - waves and provide strong tidal dissipation in certain regions of parameter space . fourth , the coupling of the equilibrium tidal distortion with the coriolis force introduces new tidal forcing terms , which dominate the tidal response of the star when @xmath57 . we find that the coriolis force has a small qualitative effect on tidal dynamics in sub - synchronous wds in which prograde g - waves create most of the tidal torque . for these waves , the value of @xmath23 is not very dependent on @xmath30 , and thus the angular and radial structure of the waves is not strongly affected . moreover , in the traditional approximation , no prograde r - wave branches obtain positive values of @xmath23 , and thus there are no additional types of prograde waves that can propagate through the stably stratified interiors of wds and cause tidal dissipation . by contrast , the coriolis force has a large effect on the tidal dynamics of super - synchronous wds in which retrograde g - waves and r - waves dominate the tidal torque . the retrograde @xmath37 , @xmath60 g - waves ( which correspond to @xmath134 , @xmath60 waves for a slowly spinning star ) that dominate tidal dissipation at small values of @xmath30 are strongly altered by the coriolis force . their angular wave number increases as @xmath135 , causing their radial wavelength to decrease , strongly reducing their overlap with the tidal potential and making them irrelevant for tidal dissipation when @xmath57 . however , the coriolis force also introduces an r - wave branch of solutions for @xmath43 , which obtains positive @xmath23 for @xmath136 ( for the @xmath45 r - waves , under the traditional approximation ) , leading to g - wave - like behavior . the r - waves maintain a small but positive value of @xmath23 for @xmath57 , allowing them to couple strongly with the tidal potential and dominate tidal dissipation in this region of parameter space . the above mentioned waves have also been identified in previous works . in the language of pantillon et al . ( 2007 ) and mathis et al . ( 2008 ) , the prograde ( @xmath58 , @xmath37 ) waves are the @xmath137 kelvin waves ( note the opposite definition of the sign of @xmath4 in those works ) . the retrograde g - waves ( @xmath60 , @xmath37 ) are @xmath138 gravito - inertial waves , and the retrograde r - waves ( @xmath60 , @xmath45 ) are @xmath138 rossby waves . the yanai waves discussed in the above works are anti - symmetric across the equator and thus not relevant to our problem , but may be relevant for tidal dissipation when the spin and orbital axes are misaligned . it is also important to address the limitations of the traditional approximation , namely , that it does not accurately characterize the oscillation mode spectrum of a star for @xmath43 , as pointed out by mathis et al . ( 2008 ) and examined in detail by dintrans et al . ( 1999 ) and dintrans & rieutord ( 2000 ) . modes of dintrans et al . 1999 , for @xmath139 , and to the @xmath140 modes for @xmath43 . similar to figure 1c of dintrans et al . 1999 , g - waves in the traditional approximation are confined to the equatorial regions of the star . it may be possible that modes similar to the @xmath141 and @xmath142 modes of dintrans et al . 1999 can exist near the core of the star where @xmath143 . ] for @xmath43 , the oscillation equations become of a mixed hyperbolic and elliptic type , with the solutions exhibiting wave attractors such that the waves are focused onto rays where dissipation becomes very large . we have partially circumvented this problem because we consider outgoing waves which are not reflected from an outer boundary , and which can not exhibit the periodic orbits and singularities discussed in dintrans et al . ( 1999 ) . since the solutions we consider for @xmath43 do not directly violate any of the assumptions of the traditional approximation ( this applies to the r - wave branch so long as we consider regions with a positive eigenvalue @xmath23 ) , it appears that our results remain qualitatively and quantitatively accurate . however , we can not rule out the possibility that additional forms of dissipation exist , e.g. , due to dynamical tides composed of waves which are able to reflect near the surface of the wd and are focused onto wave attractors . we have used our results to calculate the orbital and spin evolution of wds in tight binary systems . since the coriolis force does not strongly modify the prograde g - waves that induce tidal dissipation in sub - synchronously rotating inspiraling wds , the general conclusions of papers ii - iv and burkart et al . ( 2013 ) remain valid . thus , compact wds whose orbits decay via gravitational radiation should be spun up nearly to synchronization by the time roche - lobe overflow occurs , with the tidal forcing frequency @xmath3 and effective tidal @xmath101 remaining nearly constant for orbital periods less than approximately 1 hour . we can also speculate on the tidal dynamics of a wd accreting material from a companion such that the wd begins to spin super - synchronously . our analysis indicates that the retrograde r - wave branch is capable of producing strong tidal dissipation as the wd is spun up and the tidal forcing frequency @xmath123 increases . thus , we do not expect wds accreting in compact systems ( e.g. , am cvn systems ) to be spun up to near break up , as tidal dissipation will likely transfer some of the accreted angular momentum back to the orbit of the donor star . the spin evolution of an accreting wd in a cv system is less certain because the companion is more distant and the g - waves / r - waves may remain linear , in which case the excitation of discrete g - modes studied in paper i and burkart et al . ( 2013 ) become important ( although these discrete g - modes must be modified to account for rotational effects ) . whether tides can act fast enough to stabilize the mass transfer from a degenerate companion ( as suggested in nelemans et al . 2001b and marsh et al . 2004 ) remains unclear , as this scenario hinges on a delicate balance of several physical mechanisms ( e.g. , the gravitational - wave - induced orbital decay , the mass - transfer induced orbital expansion , the tidal torque on the orbit , and the response of the donor star to mass loss ) . we plan to investigate this issue in a future paper .

tidal interactions play an important role in the evolution and ultimate fate of compact white dwarf ( wd ) binaries . not only do tides affect the pre - merger state ( such as temperature and rotation rate ) of the wds , but they may also determine which systems merge and which undergo stable mass transfer . in this paper , we attempt to quantify the effects of rotation on tidal angular momentum transport in binary stars , with specific calculations applied to wd stellar models . we incorporate the effect of rotation using the traditional approximation , in which the dynamically excited gravity waves within the wds are transformed into gravito - inertial hough waves . the coriolis force has only a minor effect on prograde gravity waves , and previous results predicting the tidal spin - up and heating of inspiraling wds are not significantly modified . we identify new dynamical tidal forcing terms that arise from a proper separation of the equilibrium and dynamical tide components ; these new forcing terms are very important for systems near synchronous rotation . [ firstpage ] white dwarfs hydrodynamics waves

tidal interactions play an important role in the evolution and ultimate fate of compact white dwarf ( wd ) binaries . not only do tides affect the pre - merger state ( such as temperature and rotation rate ) of the wds , but they may also determine which systems merge and which undergo stable mass transfer . in this paper , we attempt to quantify the effects of rotation on tidal angular momentum transport in binary stars , with specific calculations applied to wd stellar models . we incorporate the effect of rotation using the traditional approximation , in which the dynamically excited gravity waves within the wds are transformed into gravito - inertial hough waves . the coriolis force has only a minor effect on prograde gravity waves , and previous results predicting the tidal spin - up and heating of inspiraling wds are not significantly modified . however , rotation strongly alters retrograde gravity waves and inertial waves , with important consequences for the tidal spin - down of accreting wds . we identify new dynamical tidal forcing terms that arise from a proper separation of the equilibrium and dynamical tide components ; these new forcing terms are very important for systems near synchronous rotation . additionally , we discuss the impact of stokes drift currents on the wave angular momentum flux . finally , we speculate on how tidal interactions will affect super - synchronously rotating wds in accreting systems . [ firstpage ] white dwarfs hydrodynamics waves

1302.6091

m

the basic necessity for a good spectral analysis of grb pulses is wide band coverage to identify additional spectral components . the gamma - ray burst monitor ( gbm ) on board the fermi satellite , with its wide band width and excellent sensitivity , provides a good data base for such studies . it has two scintillation detectors : the sodium iodide ( nai ) detector is sensitive in the @xmath6 8 kev to @xmath7 900 kev range while the bgo energy range is @xmath7 200 kev to @xmath7 40 mev ( meegan et al . 2009 ) . we examined the nava catalog ( nava et al . 2011 ) of fermi/ gbm grbs and found that there are 112 bright ( fluence @xmath8 erg ) , long ( @xmath9 s ) grbs and 11 of these grbs have single/ separable pulses . grb 081221 is the brightest among them . in figure [ lc ] , we have plotted the light curve ( lc ) of this grb with norris model ( norris et al . 2005 ) fitted for the two pulses . we have also made a systematic analysis of the other 10 grbs and the time - integrated spectral analysis for all of them is given later . we use the cspec data for time - integrated study and the time tag event ( tte ) data for the time - resolved spectral analysis . we choose 2 or more nai detectors having high count rate and one/ both bgo detector ( s ) . for source selection and background subtraction , we use the _ rmfit v3.3pr7 _ tool , developed by user contributions of fermi science support center ( fssc ) . the background exposure time is chosen before and after the burst . this background is modelled by a polynomial of different degrees , according to the need . the pha files are binned in energy channels so as to get a minimum count in each spectral bin . typically , the nai detectors are binned by minimum count @xmath10 , while the bgo detectors are binned by requiring a minimum count of @xmath11 . first , we perform time - integrated analysis for all the 11 bright , long grbs having single/ separable pulses . we implement both c - stat and @xmath12 minimization methods in _ rmfit_. we fit either band or cut - off powerlaw ( cpl ) model . in table 1 , we report the best fit parameter values along with the corresponding 3@xmath13 errors . the reduced c - stat and @xmath14 with degrees of freedom ( dof ) are also reported . for comparison , we quote the results of nava et al . ( 2011 ) for these grbs . it is clearly seen that all these values are matching quite well . the sources of very minor deviations between the values of this work , done by c - stat minimisation and nava et al . ( 2011 ) are : ( i ) mismatch between actual start and stop time , ( ii ) exact background selection and modelling and , ( iii ) the exact number of detectors and the channels used . comparing the deviation of the parameter values , it is clear that the deviation due to using different statistics other than c - stat , i.e. @xmath12 minimisation , is much less than that due to these other reasons . hence , we conclude that the statistics plays a minimal role in actual parameter estimation . in fact , the grbs taken in our analysis are all bright grbs ( fluence @xmath8 erg ) . hence , by default , the @xmath12 minimisation is a correct technique for parameter estimation of grbs with high count rates . we select four models for the spectral study : a ) band model , b ) blackbody with a power - law , c ) a modified blackbody with a power - law and d ) two blackbodies with a power - law . the band function can be written in terms of the spectral indices ( @xmath2 and @xmath15 ) and the peak energy ( @xmath16 ) as : here , @xmath18 is the normalisation constant . a model consisting of thermal ( blackbody with temperature kt ) and non - thermal ( power law with index @xmath19 ) components has been used earlier ( see , e.g. , ryde 2004 , ryde et al . 2006 , ryde and peer 2009 , peer and ryde 2011 ) . we name this function as bbpl . this can be written as : @xmath20}+k_{2}e^{-\gamma } \label{bbpl}\ ] ] where k1 and k2 are normalisation constants . there are suggestions ( e.g. , ryde et al . 2010 ) in the literature of a modified blackbody ( mbb ) , which may exist due to angular dependence of the optical depth and the observed temperature ( peer 2008 ) . hence , we also investigate this model with a powerlaw ( mbbpl ) . the mbb model is a multi - colour blackbody disk model ; the local disk temperature kt(r ) is proportional to @xmath21 . in several grbs there are distinct additional thermal components ( see eg . shirasaki et al . 2008 ) and further , if the grb spectrum is due to thermal inverse compton ( ic ) of seed photons , then there may be , in principle , multiple photon baths . for brevity , we take one more bb component and call it 2bbpl model . this has essentially two bbs with two temperatures @xmath22 and @xmath23 and two normalisations @xmath24 and @xmath25 . we use all the four models for our subsequent analysis . we note here that it is also possible to have combinations of the above models ( like band+pl , band + bb + pl ) , but , at this juncture , we consider only these four generic models . this is essentially because of the fact that the time resolved spectra of grbs generally consists of a broad peak with wings , which can be adequately captured by any of the above four models . time - resolved spectral studies require a large number of parameters . if ` n ' is the number of time bins , then a four - parameter model , such as band or bbpl , requires 4n parameters for a full description . our motivation , in this study , is to reduce the number of parameters with some reasonable assumptions . the basic assumption we make is that the temperature ( kt ) and the peak energy ( @xmath26 ) follow smooth time evolution . this evolution has a break at the peak of the pulse ( see also ryde and peer 2009 ) . in the following discussion we shall refer to them as two episodes rising and falling part . we assume that the time evolution law of kt and @xmath26 is simple powerlaw of time i.e. , @xmath27 , with different @xmath28 in different episodes . if ` m ' and ` n ' are the number of time bins in these two episodes , respectively , then this parametrization reduces the number of free parameters by ` m+n-2 ' . note that , ideally one should use one more parameter to account for the start time , but we have chosen it to be zero for all the cases , except for the rising part of grb 090618 , where the pulse starts from -1 sec . hence , only for this case , we have chosen this start time to be -10 sec . as the parametrization is not corrected for the actual start time , the actual values of @xmath28 are not unique and hence , these values should not be used to compare different pulses . we also assume that for the band model the photon indices ( @xmath2 and @xmath15 ) are constants in each episode . their values can be determined by simultaneously fitting all the time - resolved spectra in an episode , with the photon indices tied . for bbpl model , we assume that the index ( @xmath19 ) of the powerlaw ( pl ) is constant in each episode . this index can be determined in the similar way as the photon indices of the band . the parametrization of the norm of bbpl model is more complicated , as , unlike band , we have two norms . in the band model , norm is a free parameter . in order to have equal number of parameters as band , either we can use an overall free norm with suitable parametrization of bbpl norms , or , we can parametrize one of the norms and treat the other as a free parameter . ryde and peer ( 2009 ) have shown that the parameter @xmath29 either increases with time or remains constant . if we assume that the observed flux of the bb varies as a simple function of time as @xmath30 , then the variation of @xmath31 can be parametrized as @xmath32 . for @xmath33 , @xmath31 will show the expected behaviors . the bb flux variation can be translated to the norm variation of equation [ bbpl ] as @xmath34 . now , if we parametrize the bb norm and treat the powerlaw ( pl ) norm as a free parameter of the model , we have the same number of free parameters as band model . but , this makes the bbpl more constrained , in the sense that the overall norm is not a free parameter , as in the case of band model . to overcome this difficulty , let us assume ( which will be justified later ) that the powerlaw ( pl ) component has norm variation as smooth as that of bb , i.e. , @xmath35 . then the overall norm ( k ) can be made a free parameter by parametrizing the ratio of the bb norm and pl norm as @xmath36 . thus , both band and bbpl models have equal number of free parameters ` m+n+8 ' . for band model , ` m+n ' are norms of band function in ` m+n ' time bins . the other 8 parameters are @xmath2 , @xmath15 , @xmath28 and the @xmath26 at the starting bin , @xmath37 , in the two episodes . peak energy at any time ` t ' is determined by @xmath38 . for the bbpl model , ` m+n ' are overall norms ( k ) and the other four parameters are powerlaw index ( @xmath19 ) , @xmath28 , @xmath39 and kt at the initial bin , kt(@xmath40 ) , in the two episodes . for mbbpl model , we have an added parameter , namely , p , in each episode . hence , the number of parameters is ` m+n+10 ' . for 2bbpl model , the photons are boosted by the same material , hence , the bb parameters can not be arbitrary . we assume that the ratio of temperatures and norms of these bbs are fixed , which should be determined by tying the ratios in all bins . hence , the number of parameters in this model is ` m+n+12 ' . as an example , if there are 5 time bins preceding to the peak of a pulse and 10 bins afterwards , then the parametrization for band and bbpl reduces the number of free parameters from 60 to 23 ; for a total of 25 bins this factor is 100 to 33 and so on . to compare the significance of a model with respect to another , we have performed the f - test . the f value is defined in most general case as , @xmath41 , where index 1 is used for the primary model , while 2 is used for the alternative model . we compute the probably ( p ) of a given f value and thereby find the @xmath13 significance ( and the % confidence level ) of the alternative model preferred over the primary model . if the primary model is a subset of the alternative model , then the f value is defined as , @xmath42 and the difference between the dofs ( m ) is deemed as the dof of the primary model .

we choose , from the literature , a set of possible models which includes the band model , blackbody with a power - law ( bbpl ) , a collection of black bodies with a smoothly varying temperature profile , along with a power - law ( mbbpl ) , and two blackbodies with a power - law ( 2bbpl ) . first , we perform time - resolved study to confirm the spectral parameter variations , and then construct the new model to perform a joint spectral fit .

time - resolved spectral analysis , though a very promising method to understand the emission mechanism of gamma - ray bursts ( grbs ) , is difficult to implement in practice because of poor statistics . we present a new method for pulse - wise time - resolved spectral study of the individual pulses of grbs , using the fact that many spectral parameters are either constants or smooth functions of time . we use this method for the two pulses of grb 081221 , the brightest grb with separable pulses . we choose , from the literature , a set of possible models which includes the band model , blackbody with a power - law ( bbpl ) , a collection of black bodies with a smoothly varying temperature profile , along with a power - law ( mbbpl ) , and two blackbodies with a power - law ( 2bbpl ) . first , we perform time - resolved study to confirm the spectral parameter variations , and then construct the new model to perform a joint spectral fit . we find that any photospheric emission in terms of black bodies is required mainly in the rising parts of the pulses and the falling part can be adequately explained in terms of the band model , with the low energy photon index within the regime of synchrotron model . interestingly , we find that 2bbpl is comparable or sometimes even better , though marginally , than the band model , in all episodes . consistent results are also obtained for the brightest grb of fermi era grb 090618 . we point out that the method is generic enough to test any spectral model with well defined parameter variations .

1302.6091

c

from purely data analysis point of view , there are essentially two parts in a grb spectrum the peak of the spectrum and the wings , which extend to very low and very high energies . the fundamental difference between a band only model and the models with thermal and non - thermal parts is : while band accounts for the peak position , with exponential fall in the wings , the other models have thermal component to account for the peak position , and a powerlaw , falling slower than an exponent , holding the spectra at the wings . in principle , all these spectra should be equally good at the peak position , except for the fact that band and mbb have broader peak than simple bb , while 2bbpl has double hump . hence , the difference between these models arises mainly in the wings . the bb is inferior to the others if the peak is not narrow . as photon count at the peak is larger , the residual should show up immediately . but , this is not easy to see if the difference occurs in the wings . consequently , the three very different models , namely , band , mbbpl and 2bbpl show comparable @xmath12 , while fitting time - resolved data . hence , re - binning at these wings plays a very important role to pin down the correct model . however , we can not expect an order of magnitude improvement in the @xmath12 , because , binning in these wings gives 6 - 8 broad bins ( see section 3.3.1 ) with large errors , while the major statistics comes from the peak position . we have found , in our analysis , that the spectrum changes from one pulse to the other , and even within a pulse . the fact that one of these four models is superior than the others , in a particular episode , points to the fundamental radiation mechanism . we see that this change of superiority is not random . for example , the first pulse of both the grbs have shown that a mbbpl model is better , though marginally , than band in the rising part . for grb 081221 , this could be described even by bbpl model in the rising part , which is really pointing towards the thermal origin of radiation in the first pulses . similar observations are reported in the literature e.g. , ryde et al . ( 2009 ) showed , in the 1 - 3 s time bin of batse detected grb 981021 , that a bbpl is better fit than a band model . note that the low energy photon index ( @xmath2 ) of the band model crosses the synchrotron limit in the rising part , where the thermal models are adequate . however , in the falling part of all the pulses , where band is better than mbbpl , @xmath2 is consistent with the synchrotron limit . hence , we can safely conclude that the radiation mechanism starts with a thermal origin , but is rapidly overtaken by synchrotron mechanism . the first pulse may be dominated by the photospheric emission in all episode , but the second pulse is mostly synchrotron dominated . the second pulse may or may not have a thermal origin . for example , the second pulse of grb 081221 shows a mbbpl model in the rising part , which then becomes synchrotron dominated in the falling part . on the other hand , the second pulse of 090618 is always synchrotron dominated . hence , the transition between these different radiation paradigms is smooth and repeatable . in comparison to the mbbpl model , we note that the 2bbpl is particularly better in all episodes . this model sometimes shows superiority to the band model , even at the falling part of a pulse , except for the second pulse of grb 090618 , though we can not rule out the possibility of two highly overlapping pulses in this particular case . softer component than band were reported for a few batse grbs by preece et al . shirasaki et al . ( 2008 ) , using the time - resolved spectral data of grb 041006 , detected by hete-2 ( 2 kev to 400 kev ) , found multiple spectral components , each having characteristic evolution . after the launch of fermi satellite , these earlier claims were reconfirmed in some cases . for example , guiriec et al . ( 2011 ) , fitting the time - integrated spectrum of grb 100724b , have shown the presence of an additional blackbody ( bb ) component along with the traditional band spectrum ( also see burgess et al . in our analysis , we have used two blackbodies to account for the softer components . the origin of these two components is speculative . they might be different locations of the boosted front of the fireball having same temperature , but different boosting factors . alternatively , they can be different seed photon baths , up - scattered by the bulk material . irrespective of its origin , this model shows superiority to all other models in all episodes . note that , though 2bbpl model has double hump in the peak , one of the peaks may occur in the lower wing ( i.e. , < 15 kev ) . hence , it is easy to identify this model , only if the difference occurs at the peak . figure [ spectrum ] clearly shows the double hump in the residuals of the bbpl fit . hence , it is easy to visualise the 2bbpl model from this figure . the band model , however , has similar residuals as the 2bbpl model . hence , the data are not sufficient to distinguish between these two models , except when we perform a parametrized joint fit . in figure [ spectrum_compare ] , we have shown the marginal superiority of the 2bbpl fit over the band model as a case study of the rising part of the first pulse ( -1.0 to 2.15 s ) of grb 081221 . in the right panels , we have plotted the fitted data neglecting the 30 - 40 kev channels . the upper panels are 2bbpl fits , while the lower panels are band model fits . residuals of the band model shows structures with excesses in 15 kev , 50 - 60 kev , and 150 kev regions . these are not present in the residuals of the 2bbpl model . of course , the difference is not as prominent as the case of figure [ spectrum ] . the 2bbpl model is preferred over the band model at 1.04 @xmath13 ( p=0.298 , 70.17% confidence ) . hence , 2bbpl is only marginally better than the band model . to visualise the evolution of the lower black body component , we have plotted in figure [ lower_bb ] , the residuals of 2bbpl fit , with the lower bb omitted . this technique is well known for finding iron line profile in the inner accretion disks of black holes ( see e.g. , miller 2007 ) . we fit the spectrum with the 2bbpl model and then omit the lower bb . the residual ( expressed as normalized counts kev@xmath72 s@xmath72 ) of the fit clearly shows this bb component . residuals of different detectors are shown by different markers . we have overplotted the lower bb model ( in terms of normalized counts kev@xmath72 s@xmath72 ) on the residual to guide the eye . we have plotted these residuals for second , sixth and ninth time bins from top to bottom panels to show that the bb peaks at lower energies at later times . in summary , we have rigorously used the evolution of parameters in the pulses of a grb to construct various spectral models with a minimum number of parameters . we have constructed band model with parametrized peak evolution and tied photon indices , bbpl with parametrized norm ratio of the bb and pl , parametrized temperature , and tied pl indices . apart from these , we have used mbbpl and 2bbpl , which , other than the parametrizations of bbpl , have tied p indices , and tied ratios of temperatures and norms , respectively . this new method is quite general in the sense that any such model can be incorporated with suitable parametrization . the fact that the parametrization works demands a close look into the theoretical predictions of various radiation models . these models , irrespective of their complexities , should produce such smooth variations of parameters within a pulse of a grb . also , if there is really a transition from one radiation mechanism to another , one should correctly model the mechanism of such transition . the fact that the synchrotron model is applicable at the falling part of the pulses , without invoking any other component , is really intriguing and demands a close look at the predictions of the internal shock model . one of the surprising result obtained in this work is that the 2bbpl model is statistically superior to the other models in most of the episodes in these two grbs . basak & rao ( 2012c ) have used this model for grb 090902b . the residual of bbpl fit clearly shows double humps ( see figure 3 of basak & rao 2012c ) which are taken care by the two peaks of the 2bbpl model . we selected this model purely in a phenomenological and data analysis perspective : distinct blackbody components ( apart from the main peak in the spectrum ) are seen in a few grbs and while looking at the residuals , two humps are clearly discernible in a few time bins . since these two are the brightest grbs for such analysis ( grb 081221 is the brightest grb in the category of grbs with single/ separable pulses and grb 090618 is the brightest grb in the fermi era ) , it is unlikely that we can reinforce this result by analysing data from other grbs . one method could be to get the pulse - wise spectral parameters of a sample of grbs and relate them to other properties of grbs like redshift , afterglow properties etc . this will not only help us to identify the most appropriate spectral description but also to identify the emission mechanism operating during the prompt emission .

we use this method for the two pulses of grb 081221 , the brightest grb with separable pulses . we find that any photospheric emission in terms of black bodies is required mainly in the rising parts of the pulses and the falling part can be adequately explained in terms of the band model , with the low energy photon index within the regime of synchrotron model . interestingly , we find that 2bbpl is comparable or sometimes even better , though marginally , than the band model , in all episodes . consistent results are also obtained for the brightest grb of fermi era grb 090618 . we point out that the method is generic enough to test any spectral model with well defined parameter variations .

time - resolved spectral analysis , though a very promising method to understand the emission mechanism of gamma - ray bursts ( grbs ) , is difficult to implement in practice because of poor statistics . we present a new method for pulse - wise time - resolved spectral study of the individual pulses of grbs , using the fact that many spectral parameters are either constants or smooth functions of time . we use this method for the two pulses of grb 081221 , the brightest grb with separable pulses . we choose , from the literature , a set of possible models which includes the band model , blackbody with a power - law ( bbpl ) , a collection of black bodies with a smoothly varying temperature profile , along with a power - law ( mbbpl ) , and two blackbodies with a power - law ( 2bbpl ) . first , we perform time - resolved study to confirm the spectral parameter variations , and then construct the new model to perform a joint spectral fit . we find that any photospheric emission in terms of black bodies is required mainly in the rising parts of the pulses and the falling part can be adequately explained in terms of the band model , with the low energy photon index within the regime of synchrotron model . interestingly , we find that 2bbpl is comparable or sometimes even better , though marginally , than the band model , in all episodes . consistent results are also obtained for the brightest grb of fermi era grb 090618 . we point out that the method is generic enough to test any spectral model with well defined parameter variations .

1310.3642

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[ tbl : summary ] llllll object & type & p@xmath25 & p@xmath30 & @xmath4 & remarks + & & ( d ) & ( d ) & & + css0116 + 09 & dn & 0.06582(@xmath75 ) & - & 18.9@xmath62 , 17.1@xmath63 & eclipsing , [email protected] mag + css0411 - 09 & su & - & 0.06633(@xmath71 ) & 15.4@xmath10 & superhump + css0438 + 00 & dn & 0.06546(@xmath79 ) & - & 19.3@xmath62 & eclipsing , depth@xmath51 mag + css0449 - 18 & dn & 0.15554(@xmath74 ) & - & 17.9@xmath62 & eclipsing , [email protected] mag + sss0501 - 48 & dn & - & - & 17.3@xmath64 & + css0558 + 00 & dn & 0.06808(@xmath71 ) & - & 19.3@xmath64 & + css0902 - 11 & dn & 0.2758(@xmath74)@xmath65 & - & 17.7@xmath64 , 16.5@xmath10 & + css0942 - 19 & su ? & 0.147(@xmath71 ) & - & 19.5@xmath64 & + css1052 - 06 & su & - & 0.07938(@xmath73 ) & 16.2@xmath10 , 18.7@xmath64 & superhump + sss1128 - 34 & dn & 0.0985(@xmath71 ) & - & 18.7@xmath64 , 16@xmath10 & + css1221 - 10 & dn & 0.14615(@xmath71 ) & - & 19.4@xmath66 & eclipsing , [email protected] mag + sss1224 - 41 & dn & 0.25367(@xmath73 ) & - & 19.3@xmath66 & eclipsing , [email protected] mag + sss1340 - 35 & dn & 0.059(@xmath71 ) & - & 18.4@xmath66 & eclipsing , [email protected] mag + css1417 - 18 & su & 0.0845(@xmath71 ) & - & 17.8@xmath10 , 19.9@xmath64 & fast decline from outburst + css1556 - 08 & su & - & 0.089309(@xmath753)@xmath67 & 16.9@xmath10 , 18.2@xmath64 & + css1727 + 13 & dn & - & - & 19.5@xmath64 & + sss1944 - 42 & p & 0.06385(@xmath72 ) & - & 17.4@xmath64 & + sss2003 - 28 & su & 0.05871(@xmath74 ) & - & 19.1@xmath66 , 16.4@xmath68 & eclipsing , [email protected] mag + css2054 - 19 & su & - & 0.09598(@xmath78)@xmath69 & 16.8@xmath10 & superhump + css2108 - 03 & dn & 0.15699(@xmath75)@xmath70 & - & 17.7@xmath66 & eclipsing , [email protected] mag + + we observed 20 cvs identified by the crts with the aim of classifying them , determining orbital periods and selecting targets for further observations with large telescopes . of these 20 systems , only 6 have been observed prior to this work . four systems were confirmed to be cvs by means of spectra and standardized photometry and a superhump period was determined for one of these ( css1556 - 08 , @xcite ) . css0902 - 11 has been followed - up in detail with time - series spectroscopy @xcite and css2108 - 03 was observed photometrically by @xcite . the results are summarised in tab . we determined 12 new orbital periods and independently discovered periods for a further two cvs , namely css0902 - 11 and css2108 - 03 . for three of the systems ( css0411 - 09 , css1052 - 06 and css2054 - 19 ) , we determined superhump periods . css1556 - 08 had a pre - determined superhump period ( @xcite and @xcite ) , but we could not determine an orbital period from our photometry . the remaining 2 cvs did not show any periodic modulations . most of the cvs were dne systems . this is as we should expect , as the crts identifies transients based on their variability . there was also a polar in the sample ( sss1944 - 42 ) , that was picked up by the crts because it showed high and low states that differed by more than a magnitude . the orbital periods of these cvs fall predominantly below the period gap ( see @xcite and @xcite ) , but there were two within the gap ( sss1128 - 34 and possibly css2054 - 19 ) and six above it . the predominance of cvs with periods below the period gap in the crts dataset is not fully explained . @xcite discussed this bias . they compared the cumulative distribution functions of the outburst amplitudes of the crts cvs and those in the survey region that were listed in rkcat @xcite that were not detected by the crts . they found that the crts shows a bias against low amplitude outbursts up to 6@xmath0mag . cvs with larger outburst amplitudes spend more time above the 2@xmath0mag cut - off limit that the crts employs and are thus more likely to be detected . furthermore , they plotted the outburst amplitude versus the orbital period for cvs within the crts footprint ( values from rkcat ) and found a trend for short period dne to have larger outbursts . combined , these two findings indicate that there is a bias in the crts towards shorter period systems @xcite . eight of the cvs in this sample were eclipsing systems . as mentioned in section [ sec : observations ] , the long - term crts light curves of the deeply eclipsing systems sometimes give indications of the eclipses . as each field is observed three times at 10-min intervals , it is possible that one or two of the observations are taken in eclipse . if it is sufficiently deep , these points can show up on the long - term light curve at a magnitude or more below the quiescent level . of the five systems with eclipse depths of more than 0.9@xmath0mag in our sample , four showed these characteristics . a number of the cvs presented in this paper provide promising targets for more in - depth studies with larger telescopes - such as the eclipsing systems ( css0116 + 09 , css0438 + 00 , css0449 - 18 , css1221 - 10 , sss1224 - 41 , sss1340 - 35 , sss2003 - 28 and css2108 - 03 ) , which through eclipse deconvolution can yield parameters such as the inclination and mass ratio . css1417 - 18 shows an unusually fast decline from outburst . the new orbital periods will also contribute towards population and evolutionary studies .

14 of these systems have not been observed previously and only two have been examined in - depth . from the observations we determined 12 new orbital periods and independently found a further two . eight of the cvs are eclipsing systems , five of which have eclipse depths of more than 0.9 mag . included in the sample are six su uma systems ( three of which show superhumps in our photometry ) , a polar ( sss1944 - 42 ) and one system ( css1417 - 18 ) that displays an abnormally fast decline from outburst .

time series photometry of 20 cataclysmic variables detected by the catalina real - time transient survey is presented . 14 of these systems have not been observed previously and only two have been examined in - depth . from the observations we determined 12 new orbital periods and independently found a further two . eight of the cvs are eclipsing systems , five of which have eclipse depths of more than 0.9 mag . included in the sample are six su uma systems ( three of which show superhumps in our photometry ) , a polar ( sss1944 - 42 ) and one system ( css1417 - 18 ) that displays an abnormally fast decline from outburst . [ firstpage ] techniques : photometric - binaries : close , eclipsing - stars : novae , cataclysmic variables , dwarf novae

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the past few years have seen a large increase in the interest for modeling dynamic interactions between individuals . while many real world data contain continuous - time information on the interactions , as e.g. email exchanges between employees in a company @xcite or face - to - face contact between individuals measured through sensors @xcite , most models are discrete in time . commonly , data are aggregated on predefined time intervals to obtain a sequence of snapshots of interaction random graphs . besides the loss of information induced by data aggregation , the specific choice of the time intervals has a direct impact on the results , which is most often overlooked . thus , developing models of interaction that exploit the continuous - time aspect of the data either called _ longitudinal networks , interaction event data , link streams _ or _ temporal networks _ is an important research issue . statistical methods for the analysis of longitudinal networks form a huge corpus , especially in social sciences and we do not pretend to provide an exhaustive bibliography on this topic . we refer to the very nice and recent review by @xcite for a more complete view on temporal networks . a natural way of modeling temporal event data is based on stochastic point processes . an important line of research involves continuous - time markov processes with seminal works on dyad - independent models @xcite up to the development of so - called stochastic actor oriented models ( e.g. * ? ? ? * ; * ? ? ? * ) . in these works observations consist in a series of time intervals of interaction and interactions are assumed to last during the whole corresponding time interval . here , we focus on a rather different setup where each interaction is identified with a time point . furthermore , we consider a model that allows for dependencies of the processes modeling the interactions of pairs of individuals . the analysis of event data is an old and important area in statistics ( see e.g. * ? ? ? generally a multivariate counting process @xmath0 is considered , that counts the number of interactions of each pair @xmath1 of individuals up to time @xmath2 . in @xcite counting processes have been introduced in the context of _ action _ data , which are a set of time - stamped directed interactions between individuals that , in addition , are marked by a label ( representing a behavioral event ) . the model may be viewed as an instance of cox s multiplicative hazard model with time - dependent covariates and constant baseline function . in the same vein , @xcite propose a general regression - based modeling of the intensity of non recurrent interaction events . they consider two different frameworks : cox s multiplicative and aalen s additive hazard rates ( see e. g. * ? ? ? @xcite propose another variant of cox s multiplicative intensity model for recurrent interaction events where the baseline function is specific to each individual . in the above mentioned works a set of statistics is chosen by the user as potential candidates that modulate the interactions . as in any regression framework , the choice of these statistics might raise some issues : increasing their number potentially leads to a high - dimensional problem , and interpretation of the results might be blurred by the correlation between these statistics . the approaches by @xcite , @xcite , @xcite and others are based on conditional poisson processes characterized by random intensities , also known as doubly stochastic poisson processes or cox processes . a particular instance of the conditional poisson process is the hawkes process , which is a collection of point processes with some background rate , where each event adds a nonnegative impulse to the intensity of all other processes . @xcite develop a model for spatial - temporal networks with missing information , based on such self - exciting point processes for temporal dynamics combined with a gaussian mixture for the spatial dynamics . similarly , @xcite combine temporal hawkes processes with latent distance models for implicit networks that can not be observed directly . clustering individuals based on interaction data represents a well - established technique for taking into account the intrinsic heterogeneity and summarizing information . in the context of dynamic random graphs , where a discrete - time sequence of graphs is observed , recent approaches propose to generalize the so - called stochastic block model to a dynamic context @xcite . stochastic block models posit that each individual belongs to a latent group and interactions between two individuals are conditionally independent of the interactions of any other pair , given the latent groups of the interacting individuals . another attempt to use stochastic block models in the context of interaction events appears in @xcite generalizing the approach of @xcite by adding discrete latent variables on the individuals . in this work a semiparametric stochastic block model for recurrent interaction events in continuous time is introduced , to which we refer as the poisson process stochastic block model . this is a stochastic block model where interactions are modeled by conditional inhomogeneous poisson processes , whose intensities only depend on the latent groups of the interacting individuals . in contrast to many other works , we do not rely on a parametric model where intensities are modulated by predefined network statistics , but intensities are modeled and estimated in a nonparametric way . the model is shown to be identifiable . our estimation and clustering approach is a semiparametric version of the variational expectation - maximization algorithm , where the maximization step is replaced by nonparametric estimators of the intensities . semiparametric generalizations of the classical expectation - maximization ( ` em ` ) algorithm have been proposed in many different contexts ( see e.g. @xcite for semiparametric mixtures or @xcite for a semiparametric hidden markov model ) . however , we are not aware of other attempts to incorporate nonparametric estimates in a variational approximation of ` em ` . two versions are developed for the nonparametric part of the model : a histogram approach based on the work of @xcite and a kernel estimator based on @xcite . for the histogram approach , an integrated classification likelihood criterion is proposed to select the number of latent groups adaptively . synthetic experiments enlighten both the clustering capacities of our method as well as the performance of the nonparametric estimation of the different intensities . moreover , the analysis of several real datasets illustrates the strengths and weaknesses of our approach . the supplementary material , whose references appear as s.xx , provides the proofs of all theoretical results , technical details on the algorithm and more detailed results of the analysis of the real data examples .

to model recurrent interaction events in continuous time , we propose an extension of the stochastic block model where each individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous poisson process whose intensity is driven by the individuals latent groups . the model is shown to be identifiable and an estimation procedure is proposed based on a semiparametric variational expectation - maximization algorithm . two versions of the method are developed , using either a nonparametric histogram approach ( with an adaptive choice of the partition size ) or kernel intensity estimators . finally , we demonstrate the performance of our procedure on synthetic experiments and the analysis of several real datasets illustrates the utility of our approach .

to model recurrent interaction events in continuous time , we propose an extension of the stochastic block model where each individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous poisson process whose intensity is driven by the individuals latent groups . the model is shown to be identifiable and an estimation procedure is proposed based on a semiparametric variational expectation - maximization algorithm . two versions of the method are developed , using either a nonparametric histogram approach ( with an adaptive choice of the partition size ) or kernel intensity estimators . the number of latent groups can be selected by an integrated classification likelihood criterion . finally , we demonstrate the performance of our procedure on synthetic experiments and the analysis of several real datasets illustrates the utility of our approach . * keywords : * dynamic interactions ; expectation - maximization algorithm ; integrated classification likelihood ; link streams ; longitudinal network ; semiparametric model ; stochastic block model ; variational approximation .

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according to the generally accepted recycling scenario suggested by @xcite , millisecond pulsars ( msps ) are descendants of neutron stars ( nss ) , which were spun up by accretion from roche - lobe filling companion stars in low - mass x - ray binaries ( lmxbs ) . this scenario has been extensively studied in the literature with the main emphasis at the neutron star spin frequency , evolution of the companion star , and parameters of the binary system ( e.g. , @xcite and references therein ) . ns temperature has not been typically considered as an important parameter for neutron star recycling , and is not even mentioned in most of the papers in the field . however , ns temperature is crucial for the instability of r - modes ( similar to rossby waves controlled by the coriolis force ) driven by chandrasekhar - friedman - schutz ( cfs , @xcite ) mechanism due to emission of gravitational waves ( @xcite ) . namely , if a rapidly rotating ns is hot enough , it becomes unstable with respect to excitation of r - modes ( see , e.g. , @xcite ; the corresponding region of ns temperatures and spin frequencies is often referred to as ` the instability window ' ) . this instability is known to modify the ns evolution in lmxbs dramatically ( see section [ sec_minmod ] and , e.g. , @xcite ) . in particular , it can limit rotation frequencies of nss ( @xcite ) . furthermore , we ( @xcite ) argued that the r - mode instability can lead to additional channel of ns recycling : formation of a new class of nss hot widows / hofnars ( from hot and fast non - accreting rotators ) in addition to msps . thus , accurate account for the r - mode instability should be important for the recycling scenario ; conversely , verification of the recycling scenario can put stringent constraints on the r - mode instability and , therefore , on the properties of superdense matter . in this paper we analyse constraints on the r - mode instability within the recycling scenario . we base our analysis on the following observations : * x - ray observations of transiently accreting neutron stars in lmxbs ( section [ sec_xray ] ) ; * timing of msps ( section [ sec_timing ] ) ; * x - ray and uv observations of msps ( section [ sec_xray_msp ] ) . we do not take into consideration observational data on binary system parameters ( orbital period , eccentricity etc . ) , because they seem to be determined by the evolution of binary system ( e.g. , @xcite ) and not affected directly by the r - mode instability . the set of observations ( a ) allows one to estimate the surface temperatures ( in the quiescent state , see , e.g. , @xcite ) and spin frequencies ( e.g. , @xcite ) for a number of accreting nss . it has been shown to be a crucial test of the r - mode instability theory ( @xcite ) . in particular , those references has demonstrated that the ` minimal ' model of r - mode instability window , suggested by @xcite ( ns has a nucleonic core , r - mode damping is associated with shear and bulk viscosities , see section [ sec_minmod ] ) , should be supplemented by additional damping mechanism at redshifted internal temperatures @xmath5 k , rather than by the local temperature @xmath6 , because it is @xmath7 , which is constant throughout the star . ] ( alternatively , saturation amplitude for r - modes should be extremely small , the so called ` tiny r - mode amplitude scenario ' , see section [ sec_tiny ] and , e.g. , @xcite ) . a number of papers is devoted to identification of the required damping mechanism ( see the recent review by @xcite ) . in particular , @xcite argues that finite temperature effects in superfluid ns cores can lead to resonance mode coupling and suppression of the r - mode instability at certain stellar temperatures . as a result , the instability window is splitted up by ` stability peaks ' in the vicinity of these temperatures . @xcite discuss evolution of nss in lmxbs within this model and suggest a ` resonance uplift scenario ' , which allows them to explain the observational set ( a ) . other ideas about the required additional damping include enhanced mutual friction ( e.g. , @xcite ) , crust - core coupling ( e.g. , @xcite ) , and exotic core composition ( e.g. , @xcite ) . concerning the observational set ( a ) we point out that any successful theory should not only stabilize the observed nss in lmxbs , but also explain their temperatures . msp timing [ set of observations ( b ) ; see section [ sec_timing ] ] has also been used to constrain the r - mode instability . @xcite discuss formation of msps assuming bulk viscosity driven suppression of r - mode instability . they predict that spin down of the fastest msps can be affected by r - modes . furthermore , these nss should have internal temperatures @xmath8 k , being the sources of thermal x - rays . @xcite analyse formation of recycled nss within the resonance uplift scenario and concluded that it does not contradict the idea that msps are descendants of nss in lmxbs . they also predict that the most rapidly rotating msps should be rather hot ( with internal temperatures @xmath9 k ) due to r - mode heating . @xcite argue that the minimal instability model requires extremely small r - mode saturation amplitudes to match the observed pulsars spin - down . @xcite discuss msp formation and conclude that compact stars with the cores composed of ` ungapped interacting quark matter ' are consistent with observations of lmxbs and msps ( see a critique of this statement in section [ sec_bulk ] ) . they also confirm that additional damping is required to describe msps by the models with nucleonic core composition . in this paper ( section [ sec_timing ] ) we present an independent argument in favour of enhanced r - mode damping at low temperatures , based on the msp internal heating mechanisms : superfluid vortex creep ( @xcite ) , rotochemical heating ( @xcite ) , and rotation - induced deep crustal heating ( @xcite ) . the x - ray and uv observations [ set ( c ) , section [ sec_xray_msp ] ] attract less attention in the r - mode literature , because the data for most of the observed msps do not require thermal emission from the whole surface ( but only from hot spots , see , e.g. , @xcite ) and the surface temperature is measured only for psr j0437 - 4715 by @xcite . for other msps the surface temperature is thought of as generally unknown ( see , e.g. , @xcite ) or not too high ( e.g. , @xcite ) . in this paper we argue that x - ray and uv observations allow one to put an upper limit on the redshifted surface temperature of msps , @xmath10 , and argue that @xmath11 k can be chosen as a fiducial value , applicable to all msps ( otherwise thermal emission from the whole surface should be observed , see section [ sec_xray_msp ] ) . it corresponds to an upper limit on the internal temperatures of msps : @xmath12 k ( here and below , to estimate internal temperatures of nss , we consider a canonical ns with the mass @xmath13 and @xmath14 km , and use the accreted envelope model from @xcite ) . this constraint is crucial for r - mode instability models , because any successful model should not only stabilize nss at these temperatures ( in the opposite case r - mode instability heats msps up to higher temperatures ) , but also explain how they came into this temperature region . in sections [ sec_tiny]-[sec_gen ] we apply observations ( a - c ) to constrain the r - mode instability parameters . namely , in section [ sec_tiny ] we improve constraints on the tiny r - mode amplitude scenario . in section [ sec_bulk ] we analyse models based on an enhanced bulk viscosity , in particular , the ungapped interacting quark matter model , suggested by @xcite , and conclude that it can hardly explain temperatures of the hottest nss in lmxbs . in section [ sec_reson ] we analyse the resonance uplift scenario . we demonstrate that low - temperature stability peaks at @xmath15 k are required by observations , and those resonances are likely to be broad . these results are extended to a quite general class of r - mode instability models in section [ sec_gen ] . we conclude in section [ sec_consl ] . during the final stage of the preparation of this manuscript we became aware of the work by @xcite , who also use x - ray observations to constrain msp temperatures and derive upper bounds on the r - mode amplitudes for these sources . the results of our section [ sec_tiny ] qualitatively agree with those of @xcite . the preliminary results of this work were presented by one of us ( aic ) at the two conferences : ( i ) ` the modern physics of compact stars and relativistic gravity 2015 ' ( september 30 october 3 , yerevan , armenia , 2015 ) ; and ( ii ) ` the international workshop on quark phase transition in compact objects and multimessenger astronomy : neutrino signals , supernovae and gamma - ray bursts ' ( october 7 october 14 , nizhnij arkhyz & terskol , russia , 2015 ) .

we also demonstrate that the observational set ( b ) requires enhanced r - mode dissipation at low temperatures , k. observational set ( c ) allows us to set an upper limit on the red - shifted internal temperatures of msps , k ( assuming a canonical ns with the accreted crust ) . [ firstpage ]

to put new constraints on the r - mode instability window , we analyse formation of millisecond pulsars ( msps ) within the recycling scenario , making use of three sets of observations : ( a ) x - ray observations of neutron stars ( nss ) in low - mass x - ray binaries ; ( b ) timing of millisecond pulsars ( msps ) ; and ( c ) x - ray and uv observations of msps . as shown in previous works , r - mode dissipation by shear viscosity is not sufficient to explain observational set ( a ) , and enhanced r - mode dissipation at internal temperatures k is required to stabilize the observed nss . here we argue , that models with enhanced bulk viscosity can hardly lead to a self - consistent explanation of observational set ( a ) due to strong neutrino emission , which is typical for these models ( unrealistically powerful energy source is required to keep nss at the observed temperatures ) . we also demonstrate that the observational set ( b ) requires enhanced r - mode dissipation at low temperatures , k. observational set ( c ) allows us to set an upper limit on the red - shifted internal temperatures of msps , k ( assuming a canonical ns with the accreted crust ) . recycling scenario can produce msps at these temperatures only if r - mode instability is suppressed in the whole msp spin frequency range ( hz ) at temperatures k , providing thus a new constraint on the r - mode instability window . these observational constraints are analysed in more details in application to the resonance uplift scenario of . [ firstpage ]

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we put new constraints on the shape of the r - mode instability window . they follow from the recycling scenario and observations of ( a ) nss in lmxbs ( section [ sec_xray ] ) , ( b ) msp timing ( section [ sec_timing ] ) and ( c ) uv and x - ray observations of msps ( section [ sec_xray_msp ] ) . analysing the observational sets ( a ) and ( b ) , which have already been used to put an upper bound on the r - mode instability by several authors , we emphasize the importance of two points : ( i ) any successful model should not only suppress the instability for nss observed in lmxbs , but also explain their temperatures ( this is especially important for models based on an enhanced bulk viscosity , see section [ sec_bulk ] ) ; ( ii ) observations of psr b1937 + 21 provide a new evidence of additional dissipation of r - modes at low temperatures , because the internal heating mechanisms [ superfluid vortex creep ( @xcite ) , rotochemical heating ( @xcite ) , and rotation - induced deep crustal heating ( @xcite ) ] are likely to be strong enough for psr b1937 + 21 to make it unstable within the minimal r - mode instability model . additional constraint comes from the observational set ( c ) , which allows us to put an upper limit on the internal msp temperature , @xmath243 k , limiting thus the maximum possible r - mode amplitude in msps ( section [ sec_tiny ] ) . these results qualitatively agree with similar conclusions of @xcite . combined with the recycling scenario of msp formation , the temperature upper limit ( [ tmax ] ) allow us to conclude that the r - mode instability should be suppressed in the whole msp frequency range ( @xmath233 hz ) at temperatures @xmath244 k ( see cross - hatched region in fig . [ fig_uplift](b ) and section [ sec_gen ] for details ) . this necessary condition can be used to quickly check for consistency various instability windows available in the literature . in particular , it can be fulfilled in the resonance uplift scenario suggested by @xcite ( see section [ sec_reson ] for a detailed analysis ) . it is worth noting , that constraining the surface temperature of the fastest msps by detailed analysis of x - ray and uv observational data can be a very interesting task . it is very likely that such analysis can put much more stringent upper limits on the surface temperatures of individual sources , than our general upper limit @xmath245 k ( see section [ sec_xray_msp ] , and @xcite ) . this can make the r - mode instability even more tightly constrained . in the opposite case , if one observes an msp with higher temperature , it will be even more important , because it will present an almost direct evidence of r - mode instability in such pulsar : the thermal emission from the surface @xmath246 ergs@xmath52 should have an energy source and the r - mode instability seems to be the most natural ` energy supplier ' in the absence of accretion . ( see @xcite ) , producing @xmath247 ergs@xmath52 even for msps with the highest spin down power , @xmath209ergs@xmath52 . ]

to put new constraints on the r - mode instability window , we analyse formation of millisecond pulsars ( msps ) within the recycling scenario , making use of three sets of observations : ( a ) x - ray observations of neutron stars ( nss ) in low - mass x - ray binaries ; ( b ) timing of millisecond pulsars ( msps ) ; and ( c ) x - ray and uv observations of msps . as shown in previous works , r - mode dissipation by shear viscosity is not sufficient to explain observational set ( a ) , and enhanced r - mode dissipation at internal temperatures k is required to stabilize the observed nss . here recycling scenario can produce msps at these temperatures only if r - mode instability is suppressed in the whole msp spin frequency range ( hz ) at temperatures k , providing thus a new constraint on the r - mode instability window .

to put new constraints on the r - mode instability window , we analyse formation of millisecond pulsars ( msps ) within the recycling scenario , making use of three sets of observations : ( a ) x - ray observations of neutron stars ( nss ) in low - mass x - ray binaries ; ( b ) timing of millisecond pulsars ( msps ) ; and ( c ) x - ray and uv observations of msps . as shown in previous works , r - mode dissipation by shear viscosity is not sufficient to explain observational set ( a ) , and enhanced r - mode dissipation at internal temperatures k is required to stabilize the observed nss . here we argue , that models with enhanced bulk viscosity can hardly lead to a self - consistent explanation of observational set ( a ) due to strong neutrino emission , which is typical for these models ( unrealistically powerful energy source is required to keep nss at the observed temperatures ) . we also demonstrate that the observational set ( b ) requires enhanced r - mode dissipation at low temperatures , k. observational set ( c ) allows us to set an upper limit on the red - shifted internal temperatures of msps , k ( assuming a canonical ns with the accreted crust ) . recycling scenario can produce msps at these temperatures only if r - mode instability is suppressed in the whole msp spin frequency range ( hz ) at temperatures k , providing thus a new constraint on the r - mode instability window . these observational constraints are analysed in more details in application to the resonance uplift scenario of . [ firstpage ]

cond-mat0003218

i

communication through a noisy channel is a central problem in information theory @xcite . error correcting codes are a widespread method for compensating the information corruption due to the noise , by cleverly increasing the redundancy of the message . turbo codes @xcite are a recently invented class of error correcting codes with nearly optimal performances . they allows reliable communication ( i.e. very low error per bit probability ) with practical communication rates . it is known , since the work of sourlas @xcite , that there exists a close relationship between the statistical behavior of error correcting codes and the physics of some disordered spin models . recently the tools developed in statistical physics have been employed in studying gallager - type codes @xcite . in ref . @xcite the equivalence discovered by sourlas is extended to turbo codes , and the basic features of the corresponding spin models are outlined . a remarkable property of a large family of turbo codes , presented in ref . @xcite , is the existence of a no - error phase . in other words the error probability per bit vanishes beyond some critical ( finite ) signal to noise ratio . in ref . @xcite some intuitive arguments supporting this thesis are given . some analytical results concerning the critical value of the signal to noise ratio are announced without giving any derivation . these results are compared with numerical simulations . in this paper we present the analytical results in their full generality , and explain their derivation . we prove the existence of the no - error phase and find the condition for its local stability . this condition is derived in two different approaches . in the first one we study the asymptotic dynamics of the decoding algorithm . in the second approach we use replicas and establish the condition for stability in the full replica space . local stability is a necessary but not sufficient condition for the stability of the no - error phase . the critical signal to noise ratio obtained from local stability is the correct one only if the phase transition is a second order one : in the general case it is only a lower bound . the spin models which are equivalent to turbo codes have the following statistical weight @xcite : @xmath0 the dynamical variables of the model are the spins @xmath1 with @xmath2 . we shall choose them to be ising spins , that is @xmath3 . the spins enters in the hamiltonians @xmath4 through the local interaction terms @xmath5 and @xmath6 which are products of @xmath7 s . their exact form can be encoded in two set of numbers @xmath8 and @xmath9 as follows : @xmath10 and @xmath11 . in order to fix completely our notation we set @xmath12 . the quenched variables are : * the couplings @xmath13 , whose distribution @xmath14 satisfies the conditions @xmath15 and @xmath16 ; * the permutation @xmath17 , which has uniform distribution . it is convenient to impose a fixed boundary condition at one end of the chain ( i.e. @xmath18 for @xmath19 ) and a free boundary condition at the other end . the model is composed by two one dimensional substructures ( chains ) , which interact through the kronecker delta functions in eq . ( [ models1 ] ) . when the average over permutations is taken into account this interaction turns into a mean field one . this interplay between the two subsystems , each one possessing a one dimensional structure , and the mean field interaction which couples them is clearly displayed by the analytical calculations . for further explanations on eqs . ( [ models1]-[models2 ] ) and their motivation we refer to @xcite . the paper is organised as follows . in sections [ withoutreplicas1 ] and [ withoutreplicas2 ] we present a first derivation of the stability condition . we write a `` mean field '' equation which describes the dynamics of the decoding algorithm ( sec . [ withoutreplicas1 ] ) , we show that it possesses a no - error fixed point and then study its behavior in a neighbourhood of this fixed point ( sec . [ withoutreplicas2 ] ) . thanks to this derivation we will understand how this fixed point is reached . in section [ withreplicas ] replicas are introduced in order to compute the average over the permutations . we exhibit the no - error saddle point . in section [ stability ] the stability of the no - error saddle point is studied by diagonalizing the second derivative of the free energy . finally in section [ conclusion ] the validity of our calculations is discussed . appendix [ appendicealgebra ] collects some useful ( although simple ) facts of algebra . in appendix [ appendiceprobabilita ] the type of integral equations which appear in section [ withoutreplicas2 ] is studied in detail .

turbo codes are a very efficient method for communicating reliably through a noisy channel . they are mapped onto a class of disordered spin models . the analytical calculations concerning these models are reported here . we prove the existence of a no - error phase and compute its local stability threshold . as a byproduct lptens 00/13

turbo codes are a very efficient method for communicating reliably through a noisy channel . there is no theoretical understanding of their effectiveness . in ref . they are mapped onto a class of disordered spin models . the analytical calculations concerning these models are reported here . we prove the existence of a no - error phase and compute its local stability threshold . as a byproduct , we gain some insight into the dynamics of the decoding algorithm . lptens 00/13

1408.2501

i

the concept of topological order @xcite was initiated in the 80 s with the discovery of the fractional quantum hall effect and high temperature superconductivity @xcite . since then it has also been seen in short range resonating valence bond states @xcite and in quantum spin liquids @xcite . once it s usefulness was realized in solid state quantum computation @xcite several exactly solvable models have been constructed achieving this . the classic example emerged when kitaev wrote down the toric code hamiltonian in two dimensions @xcite . these systems are examples of lattice models which host anyons @xcite as part of their low energy excitations . they can also be thought of as particular phases of the @xmath2 lattice gauge theory which host these deconfined excitations with anyonic statistics . they posses ground states with degeneracies which are topological invariants . this degeneracy is stable up to the addition of weak perturbations . this feature makes this model a probable candidate for fault tolerant quantum computation @xcite . these models have been extended to other discrete groups and involutary hopf algebras as well @xcite . in these cases they can be thought of as arising from lattice gauge theories based on these discrete groups or involutary hopf algebras @xcite . earlier works showing the existence of anyons in two dimensional discrete gauge theories can be found in @xcite . discrete gauge theories emerge in these models when a continuous gauge group breaks down to one via spontaneous symmetry breaking @xcite . these systems are usually perturbed by adding qudit terms to act on the edges of the lattice which carry the gauge degrees of freedom . they drive the system out of the topological phase @xcite . the resulting models are rendered unsolvable analytically and are thus subject to study using numerical methods . however by considering restricted plaquette and vertex operators they can be made solvable . such studies were carried out in @xcite . this resulted in condensed phases of the quantum double model . these works were crucial in understanding the stability of these topological phase represented by the quantum double model . it is thus an important problem to find exactly solvable models which remain in topological phases in the presence of these perturbations . in this spirit we introduce exactly solvable models which are constructed by looking at possible hamiltonians that can be generated using the transfer matrices of such systems . we show exactly solvable models which include the single qudit perturbations . the cases of abelian and non - abelian groups are studied separately . it is shown that in the abelian case the system remains in the topological phase corresponding to the quantum double model . the situation turns out different for the non - abelian cases . we find that the model remains in a topological phase but it is in a modified version with respect to the corresponding topological phase of the quantum double model . these are seen by studying the examples of the group algebras of @xmath0 and @xmath1 denoted by @xmath3 and @xmath4 respectively . we then go beyond the transfer matrices of lattice gauge theories by introducing more parameters in the transfer matrix of lattice gauge theories to find other topological phases . this transfer matrix is made up of two - qudit operators apart from the usual operators making up the transfer matrix of lattice gauge theories . we work with the @xmath5 case to show how one can obtain the double semion phase from such considerations . for more general groups these transfer matrices contain the twisted quantum double models as defined in @xcite . such models were also defined in @xcite while considering trivial global symmetry groups . the paper is organized as follows . section 2 describes the transfer matrices of two dimensional lattice gauge theories . the local operators used to build these transfer matrices and the parameters used to study phase transitions between different phases is explained here . hamiltonians of two dimensional lattice models are obtained from these transfer matrices by taking their logarithms . this can be done in different ways resulting in several models . these include exactly solvable models and models which can not be solved analytically . the models of interest are presented in section 3 . their excitations along with their braiding statistics and fusion rules are studied in section 4 . section 5 shows the construction of the double semion model from the transfer matrix picture . section 6 makes up our concluding remarks .

we modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase , thus nullifying the effect of the perturbation . the implementation of these models can possibly improve the use of quantum double models for fault tolerant quantum computation . more generally for other discrete groups these transfer matrices contain the twisted quantum double models . these transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories .

two dimensional lattice models such as the quantum double models , which includes the toric code , can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups . these transfer matrices are built out of local operators acting on links , vertices and plaquettes and are parametrized by the center of the gauge group algebra and its dual . for general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase towards a paramagnetic phase . these perturbations can be thought of as magnetic fields added to the system which destroy the exact solvability of the quantum double model . we modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase , thus nullifying the effect of the perturbation . the algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra . the abelian cases are shown to be in the quantum double phase whereas the non - abelian phases are shown to be in a modified phase of the corresponding quantum double phase . this is shown by working with the groups and for the abelian and non - abelian cases respectively . the quantum phases are determined by studying the excitations of these systems . the fusion rules and the statistics of these anyons indicate the quantum phases of these models . the implementation of these models can possibly improve the use of quantum double models for fault tolerant quantum computation . we then construct theories which arise from transfer matrices that are not the transfer matrices of lattice gauge theories . in particular we show that for the case this contains the double semion model . more generally for other discrete groups these transfer matrices contain the twisted quantum double models . these transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories . these parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice . as in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties .

astro-ph0204162

i

it has long been known that the redshifts derived from different quasar emission lines often do not agree with each other within typical measurement errors . ( 1982 ) performed the first detailed study of this phenomenon and concluded that high - ionization , broad , emission lines such as are shifted by a few hundred @xmath2 blueward of the redshifts determined from low - ionization , broad , emission lines such as . subsequent studies ( wilkes 1984 ; espey et al . 1989 ; corbin 1990 ; tytler & fan 1992 ; mcintosh et al . 1999 ; sulentic , marziani , & dultzin - hacyan 2000 ) have confirmed these shifts beyond any shadow of a doubt . using a sample of over 2200 active galactic nuclei ( agn ) , ( 2001 ) demonstrated that these effects are also present in the sample of quasars from the sloan digital sky survey ( sdss ; 2000 ) . these shifts affect many of the most important issues in quasar - related science ( both directly and indirectly ) . the most obvious area of research that is affected is in the modeling of the phenomena of agn , particularly the broad emission line region ( belr ; 1997 ; krolik 1999 ) . belr models based upon accretion disk winds ( murray & chiang 1997 ; proga , stone , & kallman 2000 ) will have different dynamics than cloud - based models ( blumenthal & mathews 1975 ; capriotti , foltz , & byard 1980 ) . these differences affect the line profiles and their locations in ways that should be testable . in addition to investigations of the belr , investigations regarding associated absorption ( foltz et al . 1986 ) , broad absorption lines ( weymann et al . 1991 ) , and the cosmic uv and x - ray background are affected by the apparent blueshift of the emission line . we will comment on each of these issues in turn . determining the nature of the so - called `` associated absorber '' ( foltz et al . 1986 ) population ( @xmath3 ) , requires understanding the velocity shift of the emission line in quasars . some associated absorbers are observed to have redshifts greater than the quasar redshift as determined from the emission line peak . however , as many authors have suggested , these apparent redshifts could simply be the result of the blueshift of the emission line relative to the systemic redshift of the quasar . given the average observed blueshift of the emission line , it is clear that the population of truly @xmath4 systems is smaller than it would appear , but it remains unclear if these systems can be completely explained as outflows that only appear to be infalling because of the observed shift of the emission line peak . in addition to the narrower associated absorbers , emission line shifts are important for broad absorption line ( bal ) quasars . previous investigations of the velocity shifts of quasar emission lines , such as that of ( 1990 ) , suggest a correlation between the velocity shift of the emission lines and the broad absorption line troughs observed in at least 10% of all quasars ( weymann 1997 ) . however , ( 1991 ) saw no such effect . whether or not the velocity shifts are an orientation effect has strong implications for bal quasars . if we can determine the nature of the emission line shifts , we can likely settle the issue of how bals are distributed relative to the plane of the accretion disk that is thought to feed agn . are bal flows found preferentially in the plane of the accretion disk , or are the flows more spherically symmetric in their distribution ? in addition to the more obvious problems associated with our inability to determine accurate redshifts for quasars , we must also consider the effect that the apparent inconsistency of emission line redshifts has on indirect quasar science . for example , the blueshift of the emission line causes an over - estimation of the ionizing flux in the inter - galactic medium , such as is described by ( 1999 ) . the issue of emission blueshift takes on even more importance if these shifts are correlated with the line of sight orientation of quasars , or with an orientation - type parameter such as the opening angle of a disk - wind . the most obvious ramification of such a possibility is the ability to determine orientation angles for radio - quiet quasars : until now , only a small percentage of quasars with distinct radio properties could be analyzed in terms of orientation . if a measure of orientation for radio - quiet quasars could be found and is robust ( whether it be related to the emission line shifts or not ) , it would likely revolutionize the study of quasars . the format of the paper is as follows . in 2 , we describe the data used in this analysis . throughout this paper we will follow ( 2002 ) and use a cosmology where @xmath5 . we also adopt a quasar - centered coordinate system in which outflows from the quasar along our line of sight ( which appear blueshifted ) have _ positive _ velocities . section 3 presents an analysis of the data in terms of composite quasar spectra , and the radio and x - ray properties of our sample . in 4 , we discuss the implications of our findings for modeling of the belr , the baldwin effect , the origin of intrinsic absorption , and orientation measures . we also give suggestions for future work . finally , 5 presents a summary of our results .

using a sample of 3814 quasars from the early data release of the sloan digital sky survey , we confirm that high - ionization , broad , emission lines such as are significantly blueshifted with respect to low - ionization , broad , emission lines , such as , which are thought to be close to the systemic redshift . we find a possible correlation between the emission line shifts and the radio properties of the quasars that is suggestive of orientation as the cause of the velocity shifts .

using a sample of 3814 quasars from the early data release of the sloan digital sky survey , we confirm that high - ionization , broad , emission lines such as are significantly blueshifted with respect to low - ionization , broad , emission lines , such as , which are thought to be close to the systemic redshift . we examine the velocity shifts of the and emission lines with respect to [ ] and , respectively . emission line peaks have a range of shifts from a redshift of to blueshifts well in excess of as compared to . we confirm previous results that suggest an anti - correlation between the shift of the emission line peak and the rest equivalent width of the emission line . furthermore , by creating composite quasar spectra as a function of shift , we are able to study , in detail , the profiles of the line as a function of velocity shift . we find that the apparent shift of the emission line peak is not a shift so much as it is a lack of flux in the red wing for the composite with the largest apparent shift . this observation should strongly constrain models for the broad emission line region in quasars . the emission line blueshift and equivalent width of are also discussed in light of the well - known anti - correlation between the equivalent width of emission and continuum luminosity , otherwise known as the baldwin effect . we further discuss the emission line shift as a function of other quasar properties such as spectral index , radio and x - ray detection . we find a possible correlation between the emission line shifts and the radio properties of the quasars that is suggestive of orientation as the cause of the velocity shifts . finally , we explore whether the emission line blueshifts correlate with the presence of broad absorption line absorption troughs or with narrow , `` associated '' absorption and how these might be related to orientation .

astro-ph0204162

c

the results presented herein will help to constrain models for the belr , in particular , it should be clear that there can not be any doubt as to the reality of the systematic blueshift of emission lines ; this shift _ must _ be accounted for in any agn models . this could be considered a strike against the model of ( 2000 ) , in which the blueshift of high - ionization emission lines relative to low - ionization emission lines has `` no obvious interpretation '' . however , it is equally important that these models incorporate the new results herein , primarily that the blueshift does not seem to be a net blueshift , but rather a blueshift resulting from a lack of flux in the red wing of the emission line . for cloud models , the similar blue wings of emission in the different composites would appear to favor an intrinsically isotropic velocity field in an isotropically - emitting belr , plus obscuration that preferentially removes flux from the red wing of however , such preferential obscuration may be difficult to produce . unfortunately , the parameter space available to belr models is huge , and it becomes difficult to distinguish between using observations to constrain a model and fine tuning a model to match the observations ex post facto . thus , a detailed discussion of how our results constrain belr models is beyond the scope of this paper . however , we briefly comment on the subject . first , we make two general assumptions : 1 ) that the belr region is stratified in ionization , specifically that the low - ionization region is located farther from the continuum source than the high - ionization region ( peterson 1993 ) , but see ( 1998 ) ; and 2 ) that an optically thick accretion disk is interior to both regions . we then hypothesize that the differences between composite a and d are an orientation effect with composite a representing a face - on configuration and composite d representing a more edge - on configuration . further assuming a cloud model for the belr with a roughly isotropic distribution of _ outflowing _ clouds , one possible ( but perhaps unlikely ) scenario could involve an equatorial screen that is optically thin in the face - on direction , but becomes optically thick to clouds on the side of the accretion disk facing away from the observer in the edge - on direction ( figure [ fig : fig9 ] ) . the high - ionization clouds are assumed to be outflowing faster than the low - ionization clouds , and the dust layer is assumed to be located mostly interior to the typical emission radius . such a `` model '' could produce emission profiles similar to those that we observe . however , if the clouds were infalling , it is difficult to imagine a way for obscuration to produce the observed results . we must also consider disk - like belr geometries , such as discussed by & kartje ( 1994 ) , ( 1997 ) , & chiang ( 1998 ) , and others . if we invoke a disk - wind type model instead of a spherically symmetric cloud model , then the situation may be quite different . in this case , the flow is not purely radial : the velocity differences can be due purely to orientation and a screen is not needed . however , since we observe that the emission line profiles are not simply shifted , but also they are weaker , a screen may still be necessary . for such a disk - wind model the most obvious source of a blueshift would be an outflow in the plane of the disk . in this case , a face - on orientation would yield no net shift , whereas an edge - on orientation could produce a net shift if the far side of the disk were obscured . however , we would still have to account for the fact that our observations suggest that there is not a net blueshift , just an apparent blueshift . in addition , although our hypothesis assumes that the proposed orientation effect is a result of the orientation of the disk itself , it could instead result from a change in the opening angle of the disk - wind , see [ sec : orientation ] for further discussion . we note that & chiang ( 1997 ) were able to use a varying outer radius for the emission line gas in a disk - wind model to explain the emission profiles in ( 1993 ) . & chiang ( 1997 ) also found that additionally varying the inclination angle did not produce a better fit . however , the ( 1993 ) composites all place the peak of the emission profile at zero velocity . since the emission line profiles of our four composites are so similar to theirs , it seems quite likely that their `` composite 4 '' should be blueshifted in a similar manner to our `` composite d '' ( and so on for the other composites ) . thus , a varying outer radius can not be the whole picture , and it would be interesting to re - address this issue . in any case , it should be obvious that these observations and further study of both cloud and disk - wind models , combined with the results of reverberation mapping data and analysis ( e.g. , korista et al . 1995 ; done & krolik 1996 ) will lead to a significantly better understanding of the broad line region in agn . the baldwin effect was originally defined as an anti - correlation between the equivalent width of emission and the continuum luminosity at @xmath67 in the spectra of quasars ( baldwin 1977 ) . while the original definition is still the dominant one , the baldwin effect has come to mean any anti - correlation between quasar luminosity or absolute magnitude and the strength of the broad emission lines . since our sample shows a very clear evolution of equivalent width from large equivalent width in sample a to a much smaller equivalent width in sample d , a discussion of how the baldwin effect might relate to our results is warranted . although the mean absolute magnitudes of our sample and a histogram of the individual absolute magnitudes in each sample ( not shown ) are quite similar , we were surprised to find that there is a significant difference between the samples in terms of their absolute magnitudes . the mean values of @xmath68 for samples a and d are @xmath69 and @xmath70 , respectively . this difference has a student s @xmath71 ( press et al . 1992 ) of @xmath72 with a probability of @xmath73 , indicating a significant difference between the samples . the differences between the adjacent samples ( e.g. , a and b ) are only marginally significant . to determine if our results are influenced by luminosity , we have created control samples by constraining the absolute magnitude distributions for sub - samples of each sample . we first bin the absolute magnitudes in bins of 0.5 mag , then count how many quasars are in each bin for each sample . we then created a sub - sample for each sample with only the minimum number of quasars in each bin . in this way , we create sub - samples with the same absolute magnitude distributions . a student s @xmath71 test confirms the similarity of the sub - samples in terms of their mean absolute @xmath35-band magnitudes . using these absolute magnitude normalized subsamples , we have recreated figure [ fig : fig4 ] and find no qualitative differences as compared to the full samples . we thus conclude that changes in @xmath68 are not driving the differences between the original samples . nevertheless , a better analysis in terms of the baldwin effect is still needed . our @xmath68 values sample both the continuum and emission line flux at @xmath74 , whereas the baldwin effect is usually in terms of the continuum flux at @xmath75 . more work is clearly needed to understand the exact relationship between our observations and the balwin effect . it is particularly interesting to note that the lines that show the most differences between samples a and d are also the ones that have the strongest reported baldwin effects , in particular , and ( osmer , porter , & green 1994 ) . we also see no strong differences in the profiles or blueshifts ; no baldwin effect is observed for this line ( osmer et al . these observations are unusual in the sense that both and are high ionization lines with very similar chemical structure . finally , if the baldwin effect and the blueshifts of quasar emission lines are related , one must take the blueshifts into account when determining the luminosity of the quasars . large blueshifts will cause the redshift and thus the luminosity of the quasar to be systematically underestimated . since we have shown that those quasars with large blueshifts also have weaker emission , large emission line blueshifts will cause the the baldwin effect to appear weaker than it should . since the troughs in bal quasars removes some of the emission flux , it is nearly impossible to ask whether individual bal quasars have small or large emission line blueshifts . however , we can study how the ensemble average of bals compares to the composites that we have created . first , we divide the bals into two types : low - ionization ( lobals ) and high - ionization ( hibals ) , where , in addition to absorption by , lobals show absorption in and other low - ionization lines . the hibal composite was created by combining all of the non - lobal bal - like objects that were originally rejected from our sample ; the redshifts are all taken from as they were for our sample . the lobal composite includes the lobals from the hibal sample and includes some lobals outside of the redshift range studied in the sample in order to improve the signal - to - noise of the composite spectrum . these bal composite spectra were created in exactly the same manner as composites a , b , c , and d. the composite bal spectra were then scaled as follows . a composite spectrum ( vanden berk et al . 2001 ) was fitted to each of them in the rest wavelength frame by minimizing a weighted @xmath17 merit function , normalized in the region @xmath76 . the spectral index and reddening , @xmath77 , were allowed to vary , using a reddening law with @xmath78 ( see , whiting , & webster 2000 ) , where @xmath79 is in @xmath80 and @xmath81 . the @xmath17 function was weighted at certain wavelengths to eliminate or reduce the effects of several emission and absorption features . the weight was 0 for the major emission lines from lyman-@xmath49 to , and also for the lyman-@xmath49 forest ; 0.5 for the region between and where bal troughs are most likely to be found ; and 1 for other wavelengths . the chi - square function was then minimized using a quasi - newton method , yielding best - fit values of the spectral index and reddening . see reichard et al . ( 2002 , in preparation ) for a more detailed discussion . in order to compare the bal composites to our a , b , c , and d composites , we also scale composites a , b , c , and d in the same manner as above . thus the composites from samples a , b , c , and d will have roughly the same ( overall ) continuum slope and shape as the bal composites , which allows comparison of their emission line features . from figure [ fig : fig10 ] , it is quite clear that the lobal composite is most similar to composite d : the red wing of matches quite well as does the ] blend . in addition , the lobal composite also shows a clear weakening of emission . the hibal composite is most similar to composite c ; the and ] emission line profiles are good matches . also note that , based upon the upper left - hand panel , it would appear that the bal outflows begin right at zero velocity with respect to the systemic redshift ( as defined by ) . since the viewing angles of bals are generally thought to be constrained to a relatively small angle from the accretion disk plane , that the lobal composite best matches composite d is consistent with the idea that composite d is composed of quasars that are preferentially observed in an edge - on configuration . the fact that the hibal composite is most similar to composite c is also consistent with the orientation hypothesis : hibals may differ from lobals in that the line of sight passes through somewhat less dense gas clouds that are more highly ionized . these correlations would seem to be inconsistent with , but do not necessarily rule out , the idea that bals may ( also ) be an evolutionary stage of all quasars ( becker et al . 2000 ) . not only does the blueshift of the emission line affect the study of bal absorption , it also affects our understanding of narrow , `` associated '' absorption ( foltz et al . these are absorption systems that are preferentially within @xmath82 of the quasar redshift ; they occur at a much higher rate ( per unit redshift ) than absorbers which are thought to be caused by intervening galaxies at redshifts much smaller than the quasars . since their discovery , two hypotheses have dominated the possible explanations , ( 1986 ) suggested that 1 ) they are due to outflows , similar to , but weaker than bals , or 2 ) they are due to a virialized cluster - like velocity dispersion . however , the fact that the emission line can be blueshifted changes the situation significantly ( mcintosh et al . 1999 ) . a full analysis of this issue is beyond the scope of this work ; however , we have performed a simple test that helps to shed light on this subject . one of us ( gtr ) examined the emission line regions of all the spectra that comprise composites a and d , and two samples of quasars ( one each from samples a and d ) with good signal - to - noise and strong associated absorption were constructed . these samples were further restricted to those objects showing the largest associated absorption redshifts ( i.e. , towards or in the red wing of ) . we present the emission line regions of some of the quasars from these biased sub - samples in figure [ fig : fig11 ] . the quasars on the left - hand - side are from sample a and have small emission line blueshifts with respect to , whereas the quasars on the right - hand - side are from sample d and have larger emission line blueshifts with respect to . what is interesting about figure [ fig : fig11 ] is that , in almost every case , the associated absorption is at or shortward of the systemic redshift ( dashed line , as measured from ) , and thus are consistent with outflows . large virial velocities are not necessary to explain the `` infalling '' absorbers . furthermore , in only one sample a case does the absorption occur entirely in the red wing of the emission profile . for this one exception , we suspect that a blueshift that has a larger error than normal is to blame ; when we remeasured the redshift by hand , we found that the redshift from the automated code was too small by @xmath83 . the expected location of using the revised redshift is indicated by the dotted line in the bottom panel on the left - hand side of figure [ fig : fig11 ] . however , given the expected errors in the individual measurements , it it unlikely that the errors will produce a symmetric distribution around the line center , but quite possible that the errors could explain any of the remaining apparent inflows . that is , if the velocity shifts of associated absorption lines were always referenced to the systemic redshift , we might find that associated absorbers are all outflows . since ( 1986 ) and others ( e.g. , richards et al . 2001 ) have found that the strong associated absorbers are predominantly found in steep - spectrum radio - loud quasars , it is interesting to think about them in terms of an orientation hypothesis . first , we note that the presence of associated absorption in our sample a quasars may be an argument _ against _ an orientation interpretation for the emission line blueshifts . steep - spectrum quasars are thought to have a more edge - on orientation , whereas flat - spectrum quasars are thought to be more face - on . thus the observation that associated absorbers are predominantly found in steep - spectrum quasars and that our hypothesized face - on quasars can have strong associated absorption is apparently inconsistent . however , it may be possible to reconcile this problem in the following manner . if we define `` associated absorption '' as any absorption that occurs within the profile of ( say within @xmath84 of the emission line peak regardless of whether the peak is blueshifted or not ) , _ and _ we assume that the associated absorbers are purely outflows , then we would expect to see a higher density of associated absorption per unit velocity in the objects in sample d ( assuming that they are seen edge - on ) . this is because there is a bigger range of velocities in which the absorbers can be found in sample d quasars , since the emission line is blueshifted . for example , in a quasar with no blueshift of the emission line , the observable range of associated absorption velocities is only @xmath40 , but in a quasar where the emission line is blueshifted by @xmath40 , the observable range of associated absorption is @xmath85 ; in both cases we _ assume _ that the full range over which associated absorption can be seen is @xmath85 , so a sample of quasars with blueshifted emission lines would be expected to have a higher density of associated absorption . if sample d objects tend to be steep - spectrum , lobe - dominated objects when they are radio sources , this could explain the excess of associated absorbers seen in steep - spectrum , lobe - dominated radio - loud quasars . if associated absorbers are really outflows , then they may be present at velocities much larger than @xmath40 from the emission redshift of the quasar , as was suggested by ( 2001 ) . thus , there may be a large population of narrow , intrinsic absorption systems in flat - spectrum face - on quasars , see ( 2001 ) and references therein . what causes the blueshifted emission lines in quasars and other similar phenomena ( e.g. , the baldwin effect ) ? orientation , specifically orientation of the plane of the accretion disk is certainly one possibility . we have presented some results that are consistent with this hypothesis . we have shown that bal quasars are most similar to the quasars from samples c and d. since most models of bals have the bal clouds confined to a region within a small angle of the disk ( or the disk - wind ) , this observation may be consistent with an orientation effect . the case for associated absorption , which is preferentially seen in steep - spectrum ( edge - on ) quasars , is less clear , but could also be consistent with an orientation effect . the radio properties of our sample may also support the hypothesis that orientation plays a key role in the blueshifting of the emission line . we find that there are significantly more radio - detected quasars in sample a than sample d and that the sample a objects are brighter at radio wavelengths . if the sdss+first matching algorithm is failing to find lobe dominated quasars , or if first is failing to detect some lobe dominated quasars , an orientation effect might explain the lack of radio - detected sources in sample d. furthermore that the sample a sources are bright , whereas the sample d sources are faint could be the result of an orientation - related beaming effect . an edge - on orientation for the largest shifts may also be consistent with the reduced emission and the lack of emission . these are both high - ionization lines that are likely to be formed closer to the source of ionizing radiation than low - ionization lines and thus would be easier to obscure than the low - ionization lines which are presumably formed further out . if the obscuration is restricted to the plane of the presumed accretion disk , then we might expect that some of the high - ionization lines would be completely or partially obscured in an edge - on orientation . furthermore , if the disk - wind model for the belr is true , then we might expect a broadening of the lines with increasing disk inclination angle as seen in h@xmath33 by & browne ( 1986 ) . , wilkes , & barthel ( 2000 ) find that systems which appear to be inclined according to their radio properties have broader emission line wings , which is consistent with the material being seen in a preferred direction . we do indeed see an increase in the fwhm of with an increase in our proposed viewing angle ( see table 2 ) . however , as we discussed earlier , it is not clear that this broadening of the line is real ; it may instead be due to partial obscuration of the line . a possible argument _ against _ the orientation hypothesis is the fact that & hunstead ( 1995 ) found significant differences in the strength of the @xmath56 bump between composite spectra that are core- and lobe - dominated ( core - dominated having stronger @xmath56 bump emission ) . in their sample , the @xmath56 bump is barely visible for steep - spectrum quasars and virtually disappears for _ compact _ steep - spectrum quasars . since core - dominance is thought to be correlated with orientation in radio - loud quasars , this change in @xmath56 bump strength may also be related to orientation . although we do see some differences in the strength of @xmath86 bump between composites a and d , they do not appear to be anywhere near as apparent as those found by & hunstead ( 1995 ) . if both our effects and the & hunstead ( 1995 ) effects are caused by orientation , we might expect to see a bigger difference in the fluxes between composites a and d. although the unified model ( e.g. , urry & padovani 1995 ) is well - established , more and more emphasis is being placed on properties other than orientation in terms of explaining differences between quasars . these include luminosity , the eddington ratio , accretion rate , black hole mass , black hole spin and age ( e.g. , laor 2000 ) . for example , & green ( 1992 ) argue that the first eigenvector from their principal component analysis ( `` eigenvector 1 '' which illuminates some correlations between intrinsic quasar properties ) is driven by something other than external orientation . even though the properties of our sample are very similar to the `` eigenvector 1 '' properties ( see & francis 1999 , table 2 ) , we prefer orientation as an explanation . however , this orientation effect need not be specific to the orientation of the accretion disk ( i.e. external orientation ) , but rather it could be related to the opening angle of a disk wind ( such as in 2000 , figure 7 ) , where some other quasar property is causing the opening angle of the disk wind to change , thus producing an orientation type effect ( i.e. internal orientation ) . a strong argument for this type of behavior ( or against orientation entirely depending on how you look at it ) is the intrinsic baldwin effect ( pogge & peterson 1992 ) . since a baldwin type effect is seen in individual quasars as their continuum luminosity varies ( but with a different slope than the `` external '' baldwin effect ) , the baldwin effect can not be entirely due to the orientation of the accretion disk ; the same is true for the emission line blueshifts if they are related to the baldwin effect . however , if the orientation effect is really the wind opening angle or the angle the wind makes with the disk axis and these angles can change on reasonably short timescales , then this might account for the major differences in quasar spectra . in any case , it is certainly possible that the size of the emission line blueshift may be a function of the orientation of the quasar . whether the orientation in question is external or internal remains to be seen . further study , particularly with regard to radio and x - ray properties , is needed to determine if this is really the case . some areas of future work are beyond the scope of this paper , but are clearly appropriate , including the following : \1 ) ideally , we would like to know the velocity offset between the and [ ] emission lines , which requires that we obtain ir spectra of the [ ] emission line region for those quasars where we already cover and . \2 ) similarly , we should attempt to extend our low redshift sample to cover the emission line region by obtaining uv spectra of these quasars . \3 ) uv spectra would also be appropriate for those objects where we can not see the lyman-@xmath49 emission line , since the profile of lyman-@xmath49 may be helpful in constraining belr models ( kallman & krolik 1986 ) . \4 ) if we could find a way to know how large the blueshift is likely to be without looking at the emission line , it would be possible to study how the blueshifts correlate with broad absorption line properties . \5 ) a detailed study of associated absorbers among the quasars studied herein is clearly in order . in many cases , this will mean getting higher signal - to - noise spectra . \6 ) since the blueshifts so strongly correlate with the equivalent width of the emission lines , a more detailed investigation of how this affects the baldwin effect is in order . \7 ) it is possible that emission from and could be influencing some of the changes that we attribute to other species . removing the iron emission complexes using the & wilkes ( 2001 ) iron template would address this issue . we have not chosen to attempt this procedure here , in part because the & wilkes ( 2001 ) iron template is not complete in the critical regions near and emission . \8 ) last , but perhaps most important , is that future agn `` models '' must not fail to take into account these emission line blueshifts . furthermore , they must be able to explain the emission line profiles . these should be key ingredients to any model .

the emission line blueshift and equivalent width of are also discussed in light of the well - known anti - correlation between the equivalent width of emission and continuum luminosity , otherwise known as the baldwin effect . finally , we explore whether the emission line blueshifts correlate with the presence of broad absorption line absorption troughs or with narrow , `` associated '' absorption and how these might be related to orientation .

using a sample of 3814 quasars from the early data release of the sloan digital sky survey , we confirm that high - ionization , broad , emission lines such as are significantly blueshifted with respect to low - ionization , broad , emission lines , such as , which are thought to be close to the systemic redshift . we examine the velocity shifts of the and emission lines with respect to [ ] and , respectively . emission line peaks have a range of shifts from a redshift of to blueshifts well in excess of as compared to . we confirm previous results that suggest an anti - correlation between the shift of the emission line peak and the rest equivalent width of the emission line . furthermore , by creating composite quasar spectra as a function of shift , we are able to study , in detail , the profiles of the line as a function of velocity shift . we find that the apparent shift of the emission line peak is not a shift so much as it is a lack of flux in the red wing for the composite with the largest apparent shift . this observation should strongly constrain models for the broad emission line region in quasars . the emission line blueshift and equivalent width of are also discussed in light of the well - known anti - correlation between the equivalent width of emission and continuum luminosity , otherwise known as the baldwin effect . we further discuss the emission line shift as a function of other quasar properties such as spectral index , radio and x - ray detection . we find a possible correlation between the emission line shifts and the radio properties of the quasars that is suggestive of orientation as the cause of the velocity shifts . finally , we explore whether the emission line blueshifts correlate with the presence of broad absorption line absorption troughs or with narrow , `` associated '' absorption and how these might be related to orientation .

1603.03665

i

momentum space topology is becoming the important tool for the study of the ground states of condensed matter systems ( for the review see @xcite ) . in particular , the momentum space topological invariants protect gapless fermions on the boundaries of topological insulators @xcite . topological invariants in momentum space protect also the bulk gapless fermions in dirac and weyl semi - metals @xcite . the large variety of topological defects and textures exist in the fermionic superfluids , and the gapless fermions associated with these objects are described by momentum space topology @xcite . momentum space topology was also discussed in the context of relativistic quantum field theory ( qft ) @xcite . in @xcite the topological invariants in momentum space have been considered for the lattice regularization of qft with wilson fermions . appearance of the massless fermions at the intermediate values of bare mass parameter was related to the jump of the introduced momentum space topological invariant . this invariant may actually be used for the description of a certain class of topological insulators . in @xcite the model with overlap fermions has been considered on the same grounds . in particular , the possible physical meaning of the zeros of the green function has been discussed . the appearance of zeros of the green function , in turn , has been discussed in the context of condensed matter physics ( see , for example , @xcite ) . the momentum space topological invariants are expressed in terms of the green functions . therefore , they are applicable both to the non - interacting and to the interacting systems @xcite . suppose , that we start from the model without interactions . when the interactions are turned on , the value of the topological invariant is not changed until the phase transition is encountered . this means , that the properties of the system described by the given topological invariant are robust to the introduction of interactions . the more simple non - interacting model may be investigated in order to describe such properties of the complicated interacting system . in the present paper we apply momentum space topology to the description of the anomalous quantum hall effect ( aqhe ) in topological insulators and weyl semimetals . in @xcite we considered the chiral magnetic effect ( cme ) ( mainly , in the framework of relativistic quantum field theory ) using the approach based on momentum space topology . here we briefly repeat our proof of the absence of the equilibrium bulk cme with the emphasis in the application to the solid state systems . actually , momentum space topology with topological invariants expressed through the green functions represents the alternative to the less powerful but more popular technique of berry curvature proposed to describe the qhe in @xcite and developed later in a number of publications ( see , for example , @xcite and references therein ) . the technique of berry curvature may be applied to the noninteracting condensed matter systems with green function of the form @xmath2 , where @xmath3 is the imaginary frequency while @xmath4 is the hamiltonian . unfortunately , this formalism does not allow to deal in a similar way with the interacting systems with more complicated dependence of the green function on the imaginary frequency . besides , in spite of all its advantages , the berry curvature formalism does not allow to describe the response of the system to the external magnetic ( rather than electric ) field . finally , the bulk - boundary correspondence remains out of this formalism . those three points are improved in the technique that utilizes the topological invariants composed directly of the green functions . it was proposed first by g.e.volovik ( see @xcite and references therein ) . following @xcite in the present paper we develop this technique and give the relation between the electromagnetic response of electric current and the topological invariants in momentum space of both @xmath0d and @xmath1d systems . in the present paper we emphasise , that those topological invariants are constructed of the wigner transform of the two - point green functions , which allows to apply the proposed methodology to the direct description of bulk - boundary correspondence . as for the berry curvature formalism , we demonstrate that it follows from our approach as a particular case . the family of the non - dissipative transport effects related to chiral anomaly has been widely discussed recently both in the context of the high energy physics and in the context of condensed matter theory @xcite . in particular , the possible appearance of such effects in the recently discovered dirac and weyl semimetals has been considered @xcite . besides , the possibility to observe those effects in relativistic heavy - ion collisions was proposed @xcite . the chiral magnetic effect ( cme ) is the generation of electric current in the presence of external magnetic field and chiral chemical potential @xcite . the quantum hall effect in the @xmath0 d and the @xmath1 d systems is the appearance of electric current in the direction orthogonal to the direction of the applied electric field . the anomalous quantum hall effect ( aqhe ) is such an effect that takes place due to the internal properties of the system rather than due to the external magnetic field . recently its possible appearance in weyl semimetals has been widely discussed @xcite . the aqhe was also discussed in the @xmath1d topological insulators @xcite . in the present paper we consider aqhe within the lattice regularized quantum field theory and within the tight - binding models of the solid state physics . the expression of the hall current ( through the topological invariant in momentum space @xmath5 ) in the quasi two dimensional condensed matter systems is well - known @xcite . we reproduce this result basing on the technique of the derivative expansion applied to the wigner transform of the two - point green function . next , we apply the same technique to the aqhe in the @xmath1 d lattice models . the obtained expression relates the aqhe current to the new topological invariant . the technique of its calculation is developed . our methodology allows to predict the appearance of the aqhe both in the weyl semi - metals and in certain topological insulators . we represent here the consideration of the equilibrium cme , which was based on the same technique . it appears , that the resulting current is also proportional to the topological invariant in momentum space . unlike the case of the naive continuum fermions for the considered lattice models with regular fermionic green function the value of the mentioned topological invariant does not depend on the chiral chemical potential . we consider the case , when the lattice dirac fermions are massive . however , the limit , when the physical dirac mass tends to zero , does not change our conclusion . this indicates , that the equilibrium bulk cme current is absent for the lattice regularized quantum field theory and in the certain class of solids . notice , that our conclusions on aqhe and cme are in accordance with the recent consideration of the particular lattice model of weyl semimetals @xcite . the conclusion on the absence of the equilibrium bulk cme is in line with the recent numerical calculations made using the particular lattice models @xcite . it also does not contradict to the consideration of the effective continuum field theoretic description of weyl / dirac semimetals @xcite and the consideration of dirac semimetals in the framework of the semi - classical approach @xcite . besides , this conclusion is in accordance with the bloch theorem @xcite . we incorporate the slowly varying external gauge field directly to the momentum space representation of the lattice model@xcite . in this representation it appears as a pseudo - differential operator @xmath6 , where @xmath7 determines the functional dependence of the gauge field on coordinates , while @xmath8 is the derivative over momentum . such an introduction of the gauge field to the lattice model deforms it at small distances ( of the order of the lattice spacing ) . however , the gauge invariance remains intact , and at large distances the theory is indistinguishable from the lattice model with the external gauge field introduced in a conventional way . therefore , the given way to introduce the electromagnetic field satisfies all requirements to be imposed on the lattice regularization of the qft . we also consider this appropriate to apply this method to the lattice models of solid state physics if the long range phenomena are to be investigated . we demonstrate explicitly , that in the particular case of the noninteracting condensed matter system our formalism allows to reproduce the expression for the hall conductivity as an integral over the berry curvature ( the green function of such system has the form @xmath2 , where @xmath3 is the imaginary frequency while @xmath4 is the hamiltonian ) . the paper is organized as follows . in sections [ sectgaugelat ] , [ sectwignlat ] , [ sectlinlat ] we describe the formalism proposed to be used @xcite . in sect . [ sectgaugelat ] we describe the way to introduce the slowly varying external gauge field to the momentum space formulation of lattice model . in sect . [ sectwignlat ] we consider the wigner transformation of the two - point green function in momentum space . the linear response of electric current to external field strength is considered in sect . [ sectlinlat ] . in sect . [ secthall ] we reproduce the expression for the qhe current in the @xmath0 d systems using the developed methodology . in sect . [ sectberry ] we demonstrate , how the formalism of berry curvature follows from our expressions . in sect . [ secthall3d ] we consider the aqhe in the @xmath1d systems . in sect . [ bulkboundary ] we discuss bulk - boundary correspondence for the topological insulators with aqhe . the considerations of sect . [ secthall3d ] are illustrated by two particular models of insulators in sect . [ sectins ] , and by two particular models of weyl semimetal in sect . [ sectweylsem ] . in sect . [ sectcme ] we analyse using this methodology the cme , and demonstrate , that it is absent in the considered systems . in sect . [ sectconcl ] we end with the conclusions .

using derivative expansion applied to the wigner transform of the two - point green function we analyse the anomalous quantum hall effect ( aqhe ) , and the chiral magnetic effect ( cme ) . the corresponding currents are proportional to the momentum space topological invariants . we reproduce the conventional expression for the hall conductivity in d. in d our analysis allows to explain systematically the aqhe in topological insulators and weyl semimetals . at the same time using this method it may be proved , that the equilibrium cme is absent in the wide class of solids , as well as in the properly regularized relativistic quantum field theory .

using derivative expansion applied to the wigner transform of the two - point green function we analyse the anomalous quantum hall effect ( aqhe ) , and the chiral magnetic effect ( cme ) . the corresponding currents are proportional to the momentum space topological invariants . we reproduce the conventional expression for the hall conductivity in d. in d our analysis allows to explain systematically the aqhe in topological insulators and weyl semimetals . at the same time using this method it may be proved , that the equilibrium cme is absent in the wide class of solids , as well as in the properly regularized relativistic quantum field theory .

0912.5491

i

giant star radii have been measured in the past using various interferometers , including the mark iii ( 85 giants and supergiants , * ? ? ? * ) , the palomar testbed interferometer ( 69 giants and supergiants , * ? ? ? * ) , the navy prototype optical interferometer ( 50 giants and supergiants , * ? ? ? * ) , and the center for high angular resolution astronomy ( chara ) array ( 4 hyades giants , * ? ? ? these measurements are valuable because these are the stars populating the coolest , most luminous part of the hertzsprung - russell ( h - r ) diagram @xcite . what makes the sample of giant stars under consideration here particularly interesting is that they are potential exoplanet hosts , and planetary candidates have been discovered around six of the stars already . two important characteristics of a star are its mass and radius . for giant stars , the determination of these parameters is indirect and heavily model dependent . in practice , spectroscopic observations to measure the surface gravities ( log @xmath0 ) , effective temperatures ( @xmath1 ) , and iron abundances ( [ fe / h ] ) can be combined with a distance measurement to derive the stellar radius . fitting evolutionary tracks to the position of the star in the h - r diagram then yields the mass . the reliability of these measurements depend both on the validity of the model atmospheres and the stellar evolution code . unfortunately this is an uncertain process because the evolutionary tracks of stars with a wide range of masses all converge to near the same region of the h - r diagram as they evolve up the giant branch . in particular the mass estimates derived from evolutionary tracks depend critically on several parameters hidden in the tracks , such as the mixing length parameter and its assumed constancy for all stars , the unknown helium content in the core , and uncertainties about the nature of the convection zone . as a result , using different tracks can produce different masses , and in the absence of good calibrating objects no set of tracks can be claimed to provide the best results . on the other hand , if one can test and calibrate these evolutionary tracks by comparing the theoretically - determined mass and radius to observed values , then one can have some faith in applying these tracks to stars for which direct measurements of these stellar parameters is not possible . a star s mass is not only important for its evolution , but it should play an important role in the type of planetary system a star will form . there are a number of doppler surveys searching for planets around evolved giant stars with stellar masses of 1 to 2 @xmath2 . all are plagued by the same problem in that they rely on evolutionary tracks to determine the stellar mass . until these are calibrated both the mass of the host star and the planet are uncertain . a more reliable means of calculating the stellar mass independent of evolutionary tracks and model atmospheres is using stellar oscillation observations , as the frequency of stellar oscillations is related to the mean density of the star . if one has an accurate stellar radius it is simple to compute a stellar mass from the oscillation frequencies that is model independent . depending on the accuracy of the diameter measurements , the masses can be measured to an accuracy of @xmath32@xmath4 to @xmath315@xmath4 @xcite . there is increasing evidence that most and possibly all giant stars show stellar oscillations , which are due to p - mode oscillations where pressure is the restoring force . thus giant stars are an ideal class of objects for deriving fundamental stellar parameters . they are abundant , they have large angular diameters suitable for interferometric measurements , and they exhibit stellar oscillations with radial velocity amplitudes of a few to several tens of m / s , which are easily measurable by state - of - the - art techniques . the observed oscillation frequencies constrain the internal structure of the star @xcite and interferometry measures the star s size , and the combination leads to the mass of the star . once stellar isochrones have been refined and calibrated for these evolved stars , they can be used to determine the masses of all planet - hosting giant stars . because collecting data on the oscillation frequencies requires considerable telescope resources and can only be done for relatively few stars , we first present our results on interferometric measurements on a larger sample of giant stars . the advantage interferometry provides is the ability to directly measure stellar angular diameters . once the angular diameters are known for these giant stars , physical radii and effective temperatures can be calculated when combined with other parameters , such as the parallax , bolometric flux , interstellar absorption , and bolometric corrections . the radii and effective temperatures are important values that characterize the parent star as well as the environment in which the exoplanet resides for those stars hosting planets . section 2 describes the spectroscopic measurements of @xmath1 and log @xmath0 for the sample , @xmath53 discusses the interferometric observations , @xmath54 explains how the angular diameters , linear radii , and @xmath1 were determined , and @xmath55 explores the physical implications of the interferometric observations .

using georgia state university s chara array interferometer , we measured angular diameters for 25 giant stars , six of which host exoplanets . our values do not match those derived from spectroscopic observations as well , perhaps due to the inherent properties of the methods used or because of a missing source of extinction in the stellar models that would affect the spectroscopic temperatures .

using georgia state university s chara array interferometer , we measured angular diameters for 25 giant stars , six of which host exoplanets . the combination of these measurements and _ hipparcos _ parallaxes produce physical linear radii for the sample . except for two outliers , our values match angular diameters and physical radii estimated using photometric methods to within the associated errors with the advantage that our uncertainties are significantly lower . we also calculated the effective temperatures for the stars using the newly - measured diameters . our values do not match those derived from spectroscopic observations as well , perhaps due to the inherent properties of the methods used or because of a missing source of extinction in the stellar models that would affect the spectroscopic temperatures .

0905.0410

i

the fundamental concepts in the fields of cosmology and galaxy formation hinge on the one defining characteristic of galaxies , their age . however , a galaxy s age is a difficult parameter to define observationally . for example , in the current cold dark matter paradigm ( @xmath3cdm , bahcall 1999 ) , a galaxy s age is the point in time when the non - baryonic matter becomes gravitational bound . these dark matter halos , then , induce the infall of baryonic material , that forms the luminous galaxies that we observe . typically , a collection of raw dark and baryonic matter is impossible to date as they contain no signatures of age ( i.e. an observable clock ) . only if , and when , the baryonic matter collapses and initiates star formation do we have any measure of the amount of time since the formation epoch . a complication arises if the time of initial star formation does not immediate follow the epoch of gravitational collapse . if star formation is delayed , the age of the stellar population will not coincide with the formation age . fortunately , studies of globular clusters have revealed that there do exist stars in our own galaxy with ages that are nearly equal to the age of the universe ( marin - franch 2008 ; salaris & weiss 2002 ) . therefore , even if star formation is ongoing through a galaxy s life , it may be possible to isolate the oldest stars and use their ages as a lower limit to the age of the entire galaxy system and , by inference , the epoch of galaxy formation . in addition to a possible mismatch between the epoch of formation and the epoch of initial star formation , there is also the possibility that the stars in a galaxy do not form instantaneously as one unit . for example , in our own galaxy there is a range of stellar ages ( twarog 1980 ) , although the halo population is uniformly old ( de angeli 2005 ) . this problem can be minimized by focusing our studies on galaxies where there is no evidence of current or recent star formation . early - type galaxies satisfy this condition with their lack of molecular gas and spectra profiles that are dominated by evolved stars suggesting a majority are older than a few gyr ( see trager 2005 for a dissenting view ) . the age of a galaxy s stellar population has become an increasingly important parameter in the last decade with the introduction of hierarchical models of galaxy formation . under the original scenarios of galaxy formation ( referred to as the monolithic model , larson 1974 ; kodama & arimoto 1997 ) , a galaxy forms quickly , with an intense epoch of star formation at high redshifts followed by a short phase of galactic winds . the rapid initial star formation produces a stellar population that is nearly singular in age and uniform in its chemical composition . the epoch of galactic winds is controlled by a galaxy s mass ( i.e. depth of its gravitational potential ) and , thereby , its total metallicity . under hierarchical models , the formation epochs are extended to lower redshifts , assumingly with later epochs of star formation and thereby younger stellar ages ( white & frenk 1991 ) . the history of determining the age of a galaxy s stellar population is long and rich in observational techniques ( see thomas 2005 for a review ) . early studies focused on the direct comparison between integrated galaxy colors and colors of galactic clusters ( sandage & vishvanathan 1977 ; burstein 1987 ) . these early results supported a view where early - type galaxy stellar populations were similar to globular clusters in their evolutionary state , but with higher metallicities ( burstein 1984 ) . improved technology led to the matching of colors with various spectral indices ( gonzalez 1993 ; trager 2000 ) . and improved spectroenergy distribution ( sed ) models led to the use of spectral indices alone to calculate the age and metallicity of underlying stellar populations ( kuntschner 2000 ; trager 2000 ) . the method of determining age and metallicity of a galaxy matured with the introduction of the lick system that , primarily , depends on fe ( notably fe5270 and fe5335 ) , mg @xmath4 and h@xmath2 lines to deduce mean age and metallicity ( trager 2000 ) . a surprising result from the spectroscopic surveys ( e.g. , gallazzi 2006 ) is that a significant fraction of early - type galaxies have mean ages younger than expected from monolithic scenarios ( see schiavon 2007 for a review ) . this result would support hierarchical models of galaxy formation ( kauffmann , white & guiderdoni 1993 ; cowie 1996 ) . a range of ages for early - type galaxies is not necessarily a problem for their optical and near - ir colors as a stellar population s color evolution is expected to proceed at a rapid pace for the first 1 to 2 gyr after initial star formation , but color changes over the next 10 gyr are small ( bower 1992 ) . however , a significant number of early - type galaxies with ages less than 8 gyr would challenge our understanding of the thinness of the fundamental plane ( macarthur 2008 ; cappellari 2006 , where galaxies greater than @xmath5 have formation redshifts of greater than 2 ) ; the detection of evolved galaxies at high redshifts ( mei 2009 , andreon 2008 , where both studies find passive evolution with redshifts of formation beyond 3 ) ; and the passive evolution of galaxies at intermediate redshifts ( kelson 2001 , rakos & schombert 1995 , where both studies find colors and spectral indices agree with passive evolution models to redshifts of 0.8 ) . the goal of this paper is to examine the impact of young stellar population age by comparison of expected colors for galaxies with spectroscopically determined ages and metallicity against the color - magnitude relation ( cmr ) . due to the known lack of uniqueness in age and metallicity for broadband color systems ( i.e. johnson @xmath6 or sdss @xmath7 , worthey 1994 ) , we compare the sed model generated colors to a special narrowband color system that focuses on spectral regions near the 4000 break . to achieve this goal , we have divided our analysis into three parts . first , we examine the behavior of the cmr in our color system and compare its slope and zeropoint to other cmr s . second , we outline the selected sed models and their input parameters . lastly , we construct cmr s from actual spectroscopic samples and compare their colors with our observations . anticipating that the derived colors , across all wavelengths , will be too blue to reproduce the observed cmr , we will also examine the color - h@xmath2 phase space in order to isolate the magnitude of the discrepancies .

using new narrowband color observations of early - type galaxies in clusters , we reconstruct the color - magnitude relation ( cmr ) with a higher degree of accuracy than previous work . we find that the cmr can not by reproduced by the spectroscopically determined ages and metallicities in any of the samples despite the high internal accuracies to the spectroscopic indices .

using new narrowband color observations of early - type galaxies in clusters , we reconstruct the color - magnitude relation ( cmr ) with a higher degree of accuracy than previous work . we then use the spectroscopically determined ages and metallicities from three samples ( trager 2008 , thomas 2005 , gallazzi 2006 ) , combined with multi - metallicity sed models , to compare predicted colors for galaxies with young ages ( less than 8 gyr ) with the known cmr . we find that the cmr can not by reproduced by the spectroscopically determined ages and metallicities in any of the samples despite the high internal accuracies to the spectroscopic indices . in contrast , using only thefe index to determine [ fe / h ] , and assuming a mean age of 12 gyr for a galaxy s stellar population , we derive colors that exactly match not only the color zeropoint of the cmr but also its slope . we consider the source of young age estimates , the h index , and examine the conflict between red continuum colors and large h values in galaxy spectra . we conclude that our current understanding of stellar populations is insufficient to correctly interpret h values and that the sum of our galaxy observations supports an old and monolithic scenario of galaxy formation . _ this result has a devastating impact on every study that has used the h index to calculate galaxy age , as the use of the h versus mgfe diagram will result in incorrectly deduced young ages_.

0905.0410

c

using a narrowband color system , we have examined the impact of the deduced younger ages for early - type galaxies in clusters proposed by numerous spectroscopic surveys under the lick system . the color - magnitude diagram is the tool of choice for testing sed model colors as one axis ( magnitude ) is limited in its explanation ( i.e. , galaxy stellar mass ) leaving only galaxy color as open for interpretation . * the cmr for our narrowband color system is well defined and consistent with the known changes in broadband colors . the slope is steepest for the @xmath17 ` metallicity ' color , that also has the lowest internal errors and intrinsic scatter . * sed models have reached a level of sophistication that now allow for detailed testing of integrated colors as a function of age and metallicity . however , as expected , a range of model parameters ( in terms of stellar population age and metallicity ) can reproduce the various color - color diagrams in our filter system . of course , the converse is not true , a pair of age and metallicity values will correspond to a unique galaxy color . we can use this effect to test the integrity of ages and metallicities determined by spectroscopic values by comparing predicted model colors with a one parameter relation such as the cmr . as these models contain the same assumptions and calculations as the models in which the spectroscopic groups use to convert their indices into age and metallicity , then the results should be the same . * converting the ages and metallicities from the trager ( 2008 ) and thomas ( 2005 ) spectroscopic samples into colors , then comparing them to the observed cmr , demonstrates that spectroscopically determined ages are sharply discordant with cmr ( see figure 5 ) . this discrepancy is visible in all colors ( broadband and narrowband ) , but has the strongest signature in our narrowband system , mostly due to the high sensitivity to metallicity and age effects in our narrowband system and the fact that our colors bracket the region of a galaxy s spectrum containing the h@xmath2 feature . most importantly , this discrepancy is resolved if model ages of 12 gyr are assumed ( see figure 7 ) . using spectroscopic ages , yet varying metallicity , requires unrealistic super - solar global metallicity values for galaxies . * any possibility that inaccurate spectroscopic values are responsible for young ages is removed when the high resolution keck data for coma is considered ( trager 2008 ) . this dataset has the highest s / n of any spectroscopic survey , particularly for the critical h@xmath2 index , and still display the same inconsistent colors for a stellar population of assumed young age ( see figure 8) . * on the other hand , using the same coma data , with matching narrowband colors , finds excellent agreement between spectral indices , such as @xmath0fe@xmath1 and colors . the conflict only arises between the h@xmath2 index and colors . there is a strong correlation between h@xmath2 and color ( bluer colors result in higher h@xmath2 values ) ; however , none of our experiments to add a hot stellar component to an underlying old stellar population can raise the sed h@xmath2 values without introducing discordant blue colors . we are left with the conclusion that the unusual aspect to ellipticals is not a young stellar age , but rather their high h@xmath2 values without a significant hot component to their underlying stellar population to explain these values . and our numerical experiments demonstrate that if you adopt @xmath0fe@xmath1 values calibrated to [ fe / h ] then you can reproduce the cmr with no need for galaxy mean ages of less than 10 gyr . there are only two possible interpretations for this dilemma , either 1 ) the h@xmath2 index is incorrectly interpreted and the galaxies are composed of old ( greater than 10 gyr ) stellar populations to match their colors and metallicities as given by metal indices or , 2 ) our sed models correctly map the h@xmath2 values into age - metallicity space and the spectroscopic results are correct , i.e. , many galaxies have young stellar populations , but then the sed models incorrectly predict all narrowband and broadband colors . nearly every spectroscopic study of ellipticals has revealed a significant fraction with large h@xmath2 indices ( greater than 1.6 ) which implies a young mean stellar population age through interpretation by the most basic sed models ( cervantes & vazdekis 2008 ; caldwell , rose & concannon 2003 ) . however , galaxies with ages less than 8 gyr would challenge our understanding of passive color evolution of galaxies at intermediate redshifts ( rakos & schombert 1995 ) . while galaxy colors redden quickly and stabilize after 8 gyrs ( rakos , schombert & odell 2008 ) , ages less than 8 gyrs , as seen in many spectroscopic studies , are impossible to reconcile with the observed colors at redshifts of 0.2 to 0.4 . for example , rakos & schombert ( 2005 ) find the colors of a2218 ( @xmath54=0.18 ) are consistent with a lookback time of 2 gyr . however , if the mean ages from the spectroscopic study of coma are extrapolated to a2218 , the mean colors would be 0.2 mags bluer than those observed . this has serious consequences to current state of our field of galaxy evolution as every spectroscopic study of galaxies using the lick system has , therefore , incorrectly deduced galaxy age . this ranges from individual spectroscopic surveys ( e.g. smith 2007 ; sanchez - blazquez 2006 ) to large sdss programs ( e.g. clemens 2008 ) . as these age datasets are used to test our galaxy formation scenarios , a great deal of our conclusions on the star formation history of ellipticals is in error . _ note on astro - ph version _ : this version of our work released on astro - ph deviates slightly from the version that will be published . this is due to , what we believe , is a repressive editorial policy that allows an anonymous referee to replace our conclusions to match their personal views . thus , we have restored several sections of text to re - enforce , more strongly , our results based on our data . since no one ever references our work , we find the possible confusion in bibliography s to be moot . financial support from austrian fonds zur foerderung der wissenschaftlichen forschung and nsf grant ast-0307508 is gratefully acknowledged . we also acknowledge all the telescope time granted this project from noao ( north and south ) , as well as eso . this research has made extensive use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . andreon , s. , puddu , e. , de propris , r. , & cuillandre , j .- c . 2008 , , 385 , 979 andreon , s. 2003 , , 285 , 143 bahcall , n. a. 1999 , in mouro , a. m. , pimenta , m. & s , p. , eds , new worlds in astroparticle physics ii , world scientific publishers , 77 baldry , i. k. , glazebrook , k. , brinkmann , j. , ivezi , . , lupton , r. h. , nichol , r. c. , & szalay , a. s. 2004 , , 600 , 681 baldry , i. k. , balogh , m. l. , bower , r. g. , glazebrook , k. , nichol , r. c. , bamford , s. p. , & budavari , t. 2006 , , 373 , 469 , 2002 , , 566 , 123 balogh , m. l. , baldry , i. k. , nichol , r. , miller , c. , bower , r. , & glazebrook , k. 2004 , , 615 , l101 bernardi , m. , 2003 , , 125 , 1866 bower , r. g. , lucey , j. r. , & ellis , r. s. 1992 , , 254 , 601 bruzual , g. , & charlot , s. 2003 , , 344 , 1000 burstein , d. , faber , s. m. , gaskell , c. m. , & krumm , n. 1984 , , 287 , 586 burstein , d. , davies , r. l. , dressler , a. , faber , s. m. , stone , r. p. s. , lynden - 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ph/0610832 matteucci , f. , & tornambe , a. 1987 , , 185 , 51 mei , s. , et al . 2009 , , 690 , 42 odell , a. p. , schombert , j. , & rakos , k. 2002 , , 124 , 3061 percival , s. m. , salaris , m. , cassisi , s. , & pietrinferni , a. 2009 , , 690 , 427 rakos , k. , & fiala , n. 1983 , , 95 , 594 rakos , k. , & schombert , j. m. 1995 , , 439 , 47 rakos , k. , & schombert , j. 2004 , , 127 , 1502 rakos , k. , & schombert , j. 2005 , , 117 , 245 rakos , k. , schombert , j. m. , odell , a. p. , & steindling , s. 2000 , , 540 , 715 rakos , k. d. , odell , a. p. , & schombert , j. m. 1997 , , 490 , 194 rakos , k. , schombert , j. , & odell , a. 2007 , , 658 , 929 rakos , k. , schombert , j. , & odell , a. 2008 , , 677 , 1019 rose , j. a. 1985 , , 90 , 1927 salaris , m. , & weiss , a. 2002 , , 388 , 492 snchez - blzquez , p. , gorgas , j. , cardiel , n. , & gonzlez , j. j. 2006 , , 457 , 809 schiavon , r. p. 2007 , , 171 , 146 schombert , j. , & rakos , k. 2009 , , 137 , 528 schulz , j. , fritze - v . alvensleben , u. , mller , c. s. , & fricke , k. j. 2002 , , 392 , 1 thomas , d. , maraston , c. , bender , r. , & mendes de oliveira , c. 2005 , , 621 , 673 trager , s. c. , faber , s. m. , worthey , g. , & gonzlez , j. j. 2000 , , 120 , 165 trager , s. c. , worthey , g. , faber , s. m. , & dressler , a. 2005 , , 362 , 2 trager , s. c. , faber , s. m. , & dressler , a. 2008 , , 386 , 715 twarog , b. a. 1980 , , 242 , 242 van dokkum , p. g. , & van der marel , r. p. 2007 , , 655 , 30 visvanathan , n. , & sandage , a. 1977 , , 216 , 214 white , s. d. m. , & frenk , c. s. 1991 , , 379 , 52 worthey , g. , faber , s. m. , & gonzalez , j. j. 1992 , , 398 , 69 worthey , g. , trager , s. c. , & faber , s. m. 1995 , in buzzoni , a. & renzini , a. and serrano , a. , astronomical society of the pacific conference series , fresh views of elliptical galaxies , astronomical society of the pacific , 86 , 203 worthey , g. , espaa , a. , macarthur , l. a. , & courteau , s. 2005 , , 631 , 820 worthey , g. 1994 , , 95 , 107 wyder , t. , 2007 , , 173 , 293 wyse , r. f. g. , & gilmore , g. 1995 , , 110 , 2771 yi , s. k. 2008 , in heber , u. , jeffery , c. s. & napiwotzki , r. , astronomical society of the pacific conference series , 392 , 3 rccccccccc -0.7 & 0.614 & 0.289 & 0.202 & 0.201 & 0.725 & 2.387 & 1.587 & 2.174 & 2.053 -0.4 & 0.646 & 0.378 & 0.229 & 0.280 & 0.773 & 2.569 & 1.937 & 2.307 & 2.149 0.0 & 0.712 & 0.535 & 0.276 & 0.431 & 0.855 & 2.867 & 2.458 & 2.894 & 2.080 + 0.4 & 0.794 & 0.712 & 0.332 & 0.595 & 0.958 & 3.317 & 2.900 & 3.763 & 1.711 -0.7 & 0.628 & 0.418 & 0.238 & 0.289 & 0.799 & 2.522 & 1.814 & 2.846 & 1.561 -0.4 & 0.690 & 0.540 & 0.278 & 0.415 & 0.867 & 2.813 & 2.191 & 2.933 & 1.640 0.0 & 0.783 & 0.711 & 0.329 & 0.594 & 0.954 & 3.116 & 2.817 & 3.565 & 1.610 + 0.4 & 0.909 & 0.902 & 0.381 & 0.797 & 1.054 & 3.504 & 3.219 & 4.316 & 1.272 -0.7 & 0.622 & 0.263 & 0.200 & 0.185 & 0.711 & 2.363 & 1.506 & 1.995 & 2.174 -0.4 & 0.643 & 0.342 & 0.222 & 0.251 & 0.755 & 2.539 & 1.811 & 2.264 & 2.144 0.0 & 0.686 & 0.464 & 0.260 & 0.357 & 0.823 & 2.851 & 2.231 & 2.753 & 2.046 + 0.4 & 0.737 & 0.593 & 0.303 & 0.467 & 0.899 & 3.245 & 2.610 & 3.380 & 1.819 -0.7 & 0.633 & 0.388 & 0.238 & 0.267 & 0.785 & 2.515 & 1.710 & 2.577 & 1.702 -0.4 & 0.671 & 0.486 & 0.266 & 0.360 & 0.839 & 2.744 & 2.059 & 2.876 & 1.660 0.0 & 0.738 & 0.625 & 0.308 & 0.494 & 0.915 & 3.066 & 2.523 & 3.362 & 1.574 + 0.4 & 0.811 & 0.762 & 0.349 & 0.624 & 0.991 & 3.413 & 2.890 & 3.918 & 1.370

we then use the spectroscopically determined ages and metallicities from three samples ( trager 2008 , thomas 2005 , gallazzi 2006 ) , combined with multi - metallicity sed models , to compare predicted colors for galaxies with young ages ( less than 8 gyr ) with the known cmr . we consider the source of young age estimates , the h index , and examine the conflict between red continuum colors and large h values in galaxy spectra . we conclude that our current understanding of stellar populations is insufficient to correctly interpret h values and that the sum of our galaxy observations supports an old and monolithic scenario of galaxy formation . _ this result has a devastating impact on every study that has used the h index to calculate galaxy age , as the use of the h versus mgfe diagram will result in incorrectly deduced young ages_.

using new narrowband color observations of early - type galaxies in clusters , we reconstruct the color - magnitude relation ( cmr ) with a higher degree of accuracy than previous work . we then use the spectroscopically determined ages and metallicities from three samples ( trager 2008 , thomas 2005 , gallazzi 2006 ) , combined with multi - metallicity sed models , to compare predicted colors for galaxies with young ages ( less than 8 gyr ) with the known cmr . we find that the cmr can not by reproduced by the spectroscopically determined ages and metallicities in any of the samples despite the high internal accuracies to the spectroscopic indices . in contrast , using only thefe index to determine [ fe / h ] , and assuming a mean age of 12 gyr for a galaxy s stellar population , we derive colors that exactly match not only the color zeropoint of the cmr but also its slope . we consider the source of young age estimates , the h index , and examine the conflict between red continuum colors and large h values in galaxy spectra . we conclude that our current understanding of stellar populations is insufficient to correctly interpret h values and that the sum of our galaxy observations supports an old and monolithic scenario of galaxy formation . _ this result has a devastating impact on every study that has used the h index to calculate galaxy age , as the use of the h versus mgfe diagram will result in incorrectly deduced young ages_.

1404.0012

c

we used the physically motivated , self - consistent spherical absorption model of @xcite and the mytorus model @xcite to unravel the complexities of the x - ray reprocessor in 19 type 2 [ oiii]-selected agn , 9 of which are seyfert 2 galaxies and 10 of which are obscured quasar candidates . we report , for the first time for an agn sample , reliable measurements of the global , as well as line - of - sight , column densities . * along the line - of - sight , 1 sy2 and 1 qso2 are mildly obscured ( @xmath13 @xmath5 ) , 1 sy2 and 4 qso2s are moderately obscured ( @xmath14 @xmath181 n@xmath182 @xmath5 ) , 4 sy2s and 2 qso2s are heavily obscured ( @xmath175 @xmath181 n@xmath183 @xmath5 ) , and 2 sy2s and 3 qso2s are heavily - obscured to compton - thick ( @xmath184 @xmath5 ) . one source is unabsorbed . * 13 objects have evidence of scattering of the intrinsic agn continuum off a distant medium . the scattering fraction is largely under 2% , but reaches between @xmath172 7 - 9% for individual sources . * in 4 agn , we measure global column densities that are significantly different from the line - of - sight column density . in one of these objects , sdss j082443.28 + 295923.5 , the line - of - sight column density is compton - thin while the global column density is compton - thick , while in 1 other object , sdss j093952.74 + 355358.0 , the line - of - sight column density is heavily - obscured to compton thick with a compton - thin global column density . * we identified a candidate changing - look agn or naked sy2 galaxy , mrk 0609 . if mrk 0609 is a true sy2 , both its bolometric luminosity and eddington rate exceed the predicted critical values of disk - wind models that explain such sources @xcite . we are pursuing simultaneous x - ray and optical observations to test this possibility . * the spectral features of sdss j093952.74 + 355358.0 indicate that the line - of - sight obscuration is in the form of compton - thick toroidal ring which is embedded in a compton - thin global matter distribution . this is the first type 2 qso where this geometry has been observed . * the ratio of the intrinsic 2 - 10 kev luminosity to the [ oiii ] luminosity , [email protected] dex , is basically equivalent to that for type 1 agn @xcite , affirming that these sophisticated models reliably measure the circumnuclear column density , allowing the inherent x - ray luminosity to be revealed . * we find a significant correlation between the fe k@xmath3 and [ oiii ] luminosities , though with wide scatter . estimating the fe k@xmath3 luminosity from the [ oiii ] luminosity can lead to errors of over an order of magnitude . * we compared n@xmath48 and n@xmath33 with obscuration diagnostics used often in the literature from _ ad hoc _ spectral modeling , i.e. , l@xmath174/l@xmath179}$ ] and the fe k@xmath3 ew ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , where lower values of the former ( i.e. , @xmath1851 ) and higher values of the latter ( i.e. , @xmath1721 kev ) imply heavy - to - compton - thick obscuration . sources that are flagged as heavily obscured via these proxies do indeed have measured column densities consistent with heavy or compton - thick obscuration , but a couple of objects with values similar to unabsorbed agn also have measured n@xmath48 indicative of heavy obscuration . * though a larger percentage of the sy2s are more heavily obscured than the qso2s , no trend exists between line - of - sight or global obscuration and agn luminosity , parametrized here as the intrinsic , rest - frame 2 - 10 kev luminosity . we also find no relationship between n@xmath48 or n@xmath33 and scattering fraction , n@xmath48 or n@xmath33 and redshift , scattering fraction and redshift , and scattering fraction and l@xmath174/l@xmath179}$ ] . we reiterate that these results hold for the objects we studied here which are not necessarily representative of type 2 agn in general .

using self - consistent , physically motivated models , we investigate the x - ray obscuration in 19 type 2 [ oiii ] 5007 selected agn , 9 of which are local seyfert 2 galaxies and 10 of which are type 2 quasar candidates . we derive reliable line - of - sight and global column densities for these objects , which is the first time this has been reported for an agn sample ; 4 agn have significantly different global and line - of - sight column densities .

using self - consistent , physically motivated models , we investigate the x - ray obscuration in 19 type 2 [ oiii ] 5007 selected agn , 9 of which are local seyfert 2 galaxies and 10 of which are type 2 quasar candidates . we derive reliable line - of - sight and global column densities for these objects , which is the first time this has been reported for an agn sample ; 4 agn have significantly different global and line - of - sight column densities . five sources are heavily obscured to compton - thick . we comment on interesting sources revealed by our spectral modeling , including a candidate `` naked '' sy2 . after correcting for absorption , we find that the ratio of the rest - frame , 2 - 10 kev luminosity ( l ) to l}$ ] is 1.54 0.49 dex which is essentially identical to the mean type 1 agn value . the fe k luminosity is significantly correlated with l}$ ] , but with substantial scatter . finally , we do not find a trend between l and global or line - of - sight column density , between column density and redshift , between column density and scattering fraction or between scattering fraction and redshift .

1507.06872

r

we employ the theoretical framework presented above to study thermal effects on the @xmath9 and @xmath10 cross sections for two sample nuclei , @xmath121 and @xmath122 . the iron isotope is among the most abundant nuclei at the early stage of the core - collapse , while the neutron - rich germanium isotope can be considered as the average nucleus at later stages @xcite . to describe charge - changing transitions in a hot nucleus we use the same phenomenological nuclear hamiltonian as in @xcite . the hamiltonian consists of spherically symmetric woods - saxon potentials for protons and neutrons , bcs pairing interactions , and separable multipole and spin - multipole residuals interaction in the particle - hole channel . we neglect particle - particle interactions except for the bcs pairing forces . this hamiltonian is usually referred to as the quasiparticle - phonon model ( qpm ) @xcite . for the two nuclei considered , the parameters of the qpm hamiltonian are fixed in the same manner as in @xcite . here we just mention that solving the bcs equations at zero temperature we get the following proton and neutron pairing gaps : @xmath123 mev for @xmath0fe and @xmath124 mev for @xmath1ge . thus , the critical temperature ( @xmath125 ) when the pairing phase transition occurs is @xmath126 mev for the iron isotope and @xmath127 mev for the germanium isotope . a separable form of the residual interaction allows us to reduce the tqrpa equations to a secular equation . the explicit form for charge - changing excitations as well as expressions for transition strengths are given in @xcite . moreover , it has been proved in ref . @xcite that the tqrpa fulfills the ikeda sum rule for allowed fermi and gt transitions . as in @xcite , before proceeding to discuss thermal effects on neutrino - nucleus absorption cross sections , we consider the ground - state ( @xmath128 ) cross sections for @xmath129 , @xmath130 , @xmath131 , and @xmath132 reactions and compare the our results with those available from other theoretical studies . in fig [ gs_crsect ] , the calculated total cross sections are shown as functions of the incident ( anti)neutrino energy @xmath133 . we find that for @xmath134 the reactions considered are dominated by the multipole transitions @xmath135 , while contributions from higher multipoles are only a few percent of the total cross sections . for @xmath0fe the cross sections increase sharply as @xmath133 approaches the reaction threshold @xmath136 mev for @xmath11-absorption and @xmath137 mev for @xmath12-absorption ( @xmath138 , where @xmath139 are the masses of the parent and daughter nuclei ) . as the neutron number increases , the threshold energy for @xmath11-absorption decreases . for the neutron - rich nucleus @xmath122 the @xmath140-value becomes negative ( @xmath141 mev ) allowing neutrino absorption for all energies . contrary to this , for the @xmath10 reactions the @xmath142-values become less favorable with increasing neutron excess . the antineutrino has to overcome a noticeable threshold ( @xmath143 mev ) to be absorbed by @xmath122 and the corresponding cross section is considerably lower in comparison to the neutrino one . in addition to the total cross sections , contributions from the @xmath112 multipole channel are shown in fig . [ gs_crsect ] . referring to the plots in fig . [ gs_crsect ] for the @xmath129 , @xmath130 , @xmath131 reactions the cross sections are dominated by allowed @xmath112 transitions for energies up to @xmath144 mev , with contributions from other multipoles being much smaller . in the @xmath132 cross section , however , the @xmath112 contribution is negligible and forbidden transitions dominate the reaction . we find that @xmath145 and @xmath146 transitions mainly contribute to the cross section for @xmath147 mev . in fig . [ gs_crsect ] we also analyze the effect of the full @xmath93-dependent @xmath112 transition operator instead of its long - wavelength limit . as was mentioned above , in the latter case the @xmath112 transition operator reduces to the gamow - teller operator and the ground - state cross section is given by the first term in eq . . it should be noted that to make a comparison with the shell - model calculations @xcite more transparent , we use the same quenching factor for the axial weak coupling constant , @xmath148 . by comparing in fig . [ gs_crsect ] the @xmath112 and gamow - teller contributions to the cross sections , we conclude that for energies @xmath149 mev the application of the gt operators instead of the @xmath93-dependent @xmath112 operator is fully justified . therefore , we conclude that the low - energy ground - state cross sections for the @xmath129 , @xmath130 , @xmath131 reactions are completely dominated by gt transitions . in contrast , all gt@xmath150 transitions of are essentially blocked in @xmath1ge . for nuclei with @xmath151 and @xmath152 blocking occurs because the valence protons are in the @xmath5 shell , while the valence neutrons occupy already the next major shell ( @xmath153 shell ) . in the next section it will be shown , however , that thermal effects unblock gt@xmath150 transitions in @xmath1ge and for typical supernova temperatures the low - energy @xmath132 cross sections are also dominated by the gt contributions . .total @xmath129 cross sections for selected neutrino energies @xmath133 . the present qrpa results ( second column ) are compared with those from @xcite and with the hybrid approach results @xcite . the cross sections are given in units of @xmath154 , with exponents given in parentheses . [ cols="^,^,^,^",options="header " , ] [ 56fe_antineutrino ] in tables [ 56fe_neutrino ] and [ 56fe_antineutrino ] , we compare the calculated ground - state cross sections for ( anti)neutrino absorption by @xmath0fe to those obtained from self - consistent qrpa calculations with skyrme forces @xcite and with the hybrid approach ( large - scale shell - model calculations for gt contributions and rpa for other multipoles ) @xcite . as is seen , the three models , although based on different microscopic pictures , predict rather similar neutrino absorption cross sections . we note , however , that for low energies ( @xmath155 mev ) the present results are closer to the hybrid approach results than those of ref . it is evident that the reason why the qrpa and the hybrid approach cross sections are systematically lower than those of the skyrme based calculations at @xmath155 mev is caused by differences in the gt@xmath156 strength distributions . although the authors of ref . @xcite do not provide the gt@xmath156 distribution in @xmath0fe , it seems that the skyrme based calculations result in a larger strength below the gt@xmath156 resonance compared to the other two approaches . other possible reasons for the discrepancy could be a lower energy of the gt@xmath156 resonance and a larger total gt strength obtained from the calculations with the skyrme interaction . experimental results for neutrino absorption cross sections are rather limited . the karmen collaboration has measured the flux averaged @xmath157 cross section for the neutrino spectrum from the muon decay at rest and obtains @xmath158\times10^{-42}\,\mathrm{cm}^2$]@xcite . our result , @xmath159 , is in excellent agreement with the experimental value . note , that the hybrid approach predicts @xmath160 @xcite , while the qrpa calculations with skyrme forces gives @xmath161 @xcite . to the cross section for the @xmath162 reaction at @xmath163 mev . the present qrpa results are compared with those obtained from rqrpa @xcite and skqrpa @xcite calculations . ] for @xmath0fe a detailed demonstration of the most important multipole contributions to neutrino absorption cross section is presented in fig . [ partial ] at three neutrino energies , @xmath164 mev . as expected , at relatively low neutrino energies ( @xmath165 mev ) the dominant contribution to the cross section originates from @xmath112 transitions . with increasing @xmath133 , however , contributions from other multipole transitions become important . in particular , at @xmath166 mev , the dominant contribution comes from @xmath145 transitions , but other multipoles , e.g. , @xmath112 , @xmath146 , @xmath167 , and @xmath168 , also play an important role . in fig . [ partial ] , we also compare the calculated multipole decomposition of the cross section for @xmath0fe with those from the skqrpa calculations @xcite and the relativistic qrpa ( rqrpa ) calculations @xcite . as is evident from the figure , the latter model predicts somewhat smaller cross section at high neutrino energies ( @xmath169 mev ) , whereas we observe an excellent agreement between the results of the present qrpa and the skqrpa . specifically , in accordance with ref . @xcite , we find that @xmath170 allowed transitions only marginally contribute to the @xmath129 reaction . this finding is true for other three reactions and for finite temperatures as well . for this reason , in the discussion below , we will always imply @xmath112 multipole channels when referring the allowed transitions . in discussing @xmath11 and @xmath12 absorption reactions under supernova conditions we will follow the line of our recent work @xcite and consider first thermal effects on the strength distribution of gt transitions which dominate the reactions at low energies . in fig . [ gt_56fe_temp ] , we display on a logarithmic scale the gt@xmath156 and gt@xmath150 distributions in @xmath0fe calculated for the ground - state ( @xmath128 ) and at three stellar temperatures above the critical one , @xmath171 , @xmath172 , and @xmath173 . these temperatures roughly correspond to three stages in the collapse evolution @xcite . we emphasize that the distributions are plotted with the bare gt operators @xmath174 as functions of the transition energy . for each temperature we show the value of @xmath70 in eq . as well as the total transition strengths @xmath175 and @xmath176 . note that @xmath175 and @xmath176 values calculated for the ground - state satisfy the ikeda sum rule @xmath177 ( a small deviation is caused by the incompleteness of our single - particle basis ) but noticeably overestimate the experimental data ( @xmath178 @xcite , @xmath179 @xcite ) . this overestimation is common for any qrpa calculations of gt strength and is remedied by a quenched value for the axial weak coupling constant @xmath180 . one might notice that our qrpa calculations fairly well reproduce the experimental centroid energies for both gt@xmath150 @xcite and gt@xmath156 @xcite distributions in @xmath0fe . in this respect the present calculations are consistent with the large - scale shell - model calculations @xcite . of course , in contrast to the lssm approach , the qrpa can not recover all nuclear correlations needed to reproduce the fragmentation of the gt strength . ( left panels ) and gt@xmath150 ( right panels ) strength distributions for @xmath0fe vs transition energy . the solid ( dashed ) lines refer to transitions to non - tilde ( tilde ) thermal one - phonon states . the arrows indicate the ground - state reaction thresholds for neutrino ( @xmath136 mev ) and antineutrino ( @xmath137 mev ) absorption . ] for @xmath0fe , due to a relatively small absolute value of @xmath70 , the major part of the upward ( downward ) gt strength corresponds to transitions to non - tilde ( tilde ) phonon states . according to our qrpa calculations , the principal contribution to the gt@xmath156 ( gt@xmath150 ) strength in @xmath0fe comes from the @xmath181 neutron - to - proton ( proton - to - neutron ) single - particle transition which forms a resonance peak at @xmath182 mev ( @xmath183 mev ) . because the brink hypothesis is not valid within the tqrpa , we observe an evolution of the gt resonances with temperature . namely , when the temperature is increased to @xmath184 mev , the transition energy is lowered by @xmath185 mev for the gt@xmath156 resonance and @xmath186 mev for the gt@xmath150 resonance . this decrease in energy is mainly attributed to the vanishing of pairing correlations : at temperatures above the critical one no extra energy is needed to break a proton ( neutron ) cooper pair and as a consequence the gt@xmath150 ( gt@xmath156 ) resonance moves to lower energies . however , not only pairing effects lead to downward shift of the gt resonances . it can be easily seen from the structure of the tqrpa equations @xcite that quasiparticle thermal occupations factors will appear which screen the interaction term . due to the thermal blocking of the proton - neutron repulsive residual interaction , a further increase in temperature to @xmath187 mev decreases the gt@xmath156 and gt@xmath150 resonances in @xmath0fe by @xmath188 mev and @xmath189 mev , respectively . as was mentioned in the introduction , the observed downward shift of the gt strength is not present in large - scale shell - model calculations which are partially based on brink s hypothesis . in contrast , the finite - temperature relativistic qrpa calculations in ref . @xcite and shell - model monte - carlo calculations in ref . @xcite show similar features for the changes of the gt resonance energy . finite temperature also affects the low - energy gt@xmath156 strength in @xmath0fe : due to the gradual disappearance of pairing it partially shifts below the ground - state reaction threshold and becomes more fragmented . the fragmentation arises from the thermal smearing of the nuclear fermi surface that unblocks low - energy particle - particle and hole - hole gt@xmath156 transitions . here , particle ( hole ) denotes a state above ( below ) the fermi level . moreover , in accordance with detailed balance , the temperature rise exponentially increases the strength of negative - energy downward transitions . referring to the figure , the dominant part of the downward gt@xmath156 strength around @xmath190 mev originates from a transition inverse to the gt@xmath150 resonance , that is due to the transition from the thermally populated neutron orbit @xmath191 to the lower lying proton orbit @xmath192 . in contrast , transitions inverse to the gt@xmath156 resonance are suppressed by the energy - dependent exponent in eq . and the gt@xmath150 downward strength is dominated by transitions inverse to low - energy gt@xmath156 transitions . it should be mentioned that although thermal effects unblock some new gt transitions , the total gt@xmath118 strength in @xmath0fe slightly decreases with temperature . nevertheless , the tqrpa preserves the ikeda sum rule . it is obvious that the violation of brink s hypothesis should affect the downward gt strength . in @xcite , this influence was studied thoroughly for charge - neutral gt transitions in @xmath0fe by comparing the gt running sums derived with and without brink s hypothesis . applying the same method , we find that both the shift of the gt@xmath150 resonance to lower energies and the thermal unblocking of low - lying gt@xmath156 strength enhance the gt@xmath156 and gt@xmath150 downward strengths in @xmath0fe . but for @xmath1ge . due to pauli blocking of allowed @xmath73 transitions , the total gt@xmath156 strength is many times larger than the gt@xmath150 strength and @xmath193 . ] [ gt_82ge_temp ] shows the temperature evolution of the gt strength function for the neutron - rich nucleus @xmath1ge . the distributions are displayed at the same temperatures as those for @xmath0fe in fig . [ gt_56fe_temp ] . as evident from the figure , some gt strength associated with non - tilde ( tilde ) phonon states appears at negative ( positive ) transition energies which is due to a large value of @xmath70 . the temperature rise affects the gt@xmath156 and gt@xmath150 distributions in a different way . for the gt@xmath156 distribution , a temperature increase essentially affects only the downward part , yielding some new strength below @xmath194 mev . by comparing the left and right panels in fig . [ gt_82ge_temp ] , we conclude that this thermally unblocked strength corresponds to transitions inverse to the gt@xmath150 resonance . the gt@xmath156 resonance is weakly sensitive to thermal effects . by increasing the temperature to @xmath195 mev , the excitation energy gets only lowered by @xmath189 mev . since there are no neutron pairing correlations in @xmath1ge , this lowering is solely caused by the softening of the residual interaction . in contrast , thermal effect are significant for the gt@xmath150 resonance and they clearly demonstrate a violation of the brink hypothesis within the tqrpa . namely , with rising temperature the resonance peak shifts by @xmath196 mev to lower energies and the total gt@xmath150 strength shows a nonmonotomic dependence : after an initial decrease , it gradually increases . in @xcite , a detailed investigation within the tqrpa approach was performed of thermal effects on the gt@xmath150 strength in the neutron - rich nucleus @xmath197ge . the conclusions remain valid for @xmath1ge , as well . briefly , for neutron - rich nuclei with @xmath152 and @xmath151 the independent particle model predicts that all gt@xmath150 transitions of valence protons are pauli blocked due to the complete occupation of the @xmath5 neutron orbits . however , both thermal excitations and pairing correlations promote protons to the @xmath153 shell and make possible @xmath198 particle - particle transition in @xmath1ge possible . the important point is that the transition energy drastically decreases with temperature . namely , at @xmath199 , when pairing correlations are important , the transition energy is given by @xmath200 mev , while at @xmath201 , when thermal effects become significant , it is given by @xmath202 mev . in addition , the transition strength below the gt@xmath150 resonance becomes increasingly unblocked with temperature . in particular , a strong peak due to the @xmath203 hole - hole transition appears at @xmath204 mev . both unblocking mechanisms are severely suppressed in the vicinity of the critical temperature ( @xmath127 mev in @xmath1ge ) , i.e. when pairing correlations vanish while thermal effects are not yet sufficiently strong to significantly occupy the @xmath205 proton orbit or unblock the @xmath191 neutron orbit . therefore , the total gt@xmath150 strength decreases at @xmath206 . the thermal effects on the gt@xmath150 strength in neutron - rich nuclei discussed here were predicted in @xcite and also confirmed in @xcite by calculations based on the finite - temperature relativistic qrpa . we also note that , due to the large @xmath70 , downward gt@xmath150 transitions appears to be highly suppressed in @xmath1ge . fe and @xmath1ge at three different temperatures relevant for core collapse . for comparison , the ground - state cross sections are also shown . ( middle panels ) contributions from forbidden transitions to the cross sections . ( lower panels ) temperature dependence of the ratio of exoergic absorption to the reaction cross section . ] let us now illustrate the influence of the thermal effects discussed above on the neutrino and antineutrino absorption by @xmath121 and @xmath122 . in fig . [ nnb ] , we compare the @xmath207 ground - state cross sections with those calculated at the three core - collapse temperatures . for energies @xmath208 , which are typical for supernova neutrinos , the cross sections are dominated by allowed gt@xmath156 transitions at all temperatures . this is verified in the middle panels of fig . [ nnb ] , where the overall contribution of forbidden transitions to the finite temperature cross sections is given . although the forbidden cross section increases with temperature , it contributes less than 30% all the way up to @xmath209 . the lower panels of fig . [ nnb ] show the ratio of exoergic absorption to the reaction cross section @xmath210 where @xmath108 only accounts for negative - energy downward transitions induced by neutrino absorption . when considering the @xmath211 cross section , we observe that thermal effects are unimportant for @xmath212 mev , i.e. when incoming neutrinos have sufficiently large energy to excite the gt@xmath156 resonance . note , that a downward shift of the gt@xmath156 resonance only marginally affects the cross section at such high neutrino energies . thermal effects become pronounced though for lower neutrino energies since finite temperature removes the reaction threshold and significantly enhances the cross section . for energies @xmath213 mev , the ratio @xmath214 and , hence , the observed enhancement is mostly caused by downward gt@xmath156 transitions from nuclear excited states . moreover , for @xmath215 the thermally unblocked downward transitions completely dominate the reaction , increasing the cross section by more than an order of magnitude when the temperature rises from 0.86 mev to 1.72 mev . the role of the exoergic absorption decreases with increasing neutrino energy and for intermediate energies , @xmath216 , thermal effects on the gt@xmath156 resonance and its low - energy tail become important for the cross section enhancement . referring to the right panels in fig . [ nnb ] it is shown that the @xmath217 cross section to a much lesser extent depends on temperature than that for the @xmath211 reaction . this result can be understood as follows . in @xmath122 , due to the negative @xmath140-value , the downward gt@xmath156 transitions dominate the ground - state reaction up to @xmath218 mev . as discussed above , the gt@xmath156 distribution in @xmath122 is little affected by the temperature rise , which merely causes some additional strength at @xmath219 mev . this thermally unblocked downward strength becomes competitive with the ground - state contribution only at rather low energies ( @xmath220 mev ) . as a result , thermal effects on the @xmath217 reaction are noticeably milder than in the previous case and a temperature rise from @xmath128 to 1.72 mev enhances the low - energy cross section only by a factor of about four . this observation is in line with ref . @xcite , where it was shown that the thermal enhancement of the neutrino absorption cross section is reduced the more neutron - rich the nucleus is . , but for the antineutrino absorption reaction . ] the results for @xmath12-absorption are shown in fig . [ annb ] . for the @xmath221 reaction the cross section demonstrates the same trend as discussed above for the neutrino absorption by @xmath121 : ( i ) the gap in the cross section disappears and the low - energy cross section increases with temperature . ( ii ) with increasing @xmath133 the cross sections at different temperatures converge , i.e. , thermal effects become unimportant . from the lower - left panel we conclude that a significant enhancement of the low - energy cross section relative to ground - state calculations comes from the increasing contribution of downward gt@xmath156 transitions from nuclear excited states . the ratio @xmath222 gradually reduces at @xmath223 mev , since at those energies the excitation of the gt@xmath150 resonance becomes possible . however , at @xmath195 mev the exoergic component of the cross section appears to be comparable with the endoergic one up to @xmath224 mev . of the @xmath225th negative - energy gt state to the finite - temperature cross section at @xmath226 . ] it should be noted that although the calculated @xmath227 and @xmath221 cross sections show the same trend , the observed thermal enhancement at low energies is caused by different types of downward transitions . to show that , we have calculated the relative contribution @xmath228 of different negative - energy gt states to the cross section at @xmath226 . the results are depicted in fig . [ partial_t ] . as indicated in the figure , the @xmath229-absorption is completely dominated by the thermally unblocked transition inverse to the gt@xmath150 resonance . for the @xmath230-absorption , however , the main contribution to the reaction is given by transitions inverse to the gt@xmath156 low - energy strength , while the `` inverse '' gt@xmath156 resonance is suppressed by the boltzmann factor in eq . . only at @xmath195 mev , the `` inverse '' gt@xmath156 resonance gives a noticeable contribution to the absorption of low - energy antineutrinos . as illustrated in the right panels of fig . [ annb ] , the low - energy @xmath231 cross section at finite temperature is also predominantly mediated by gt@xmath150 transitions . although the cross section remains substantially smaller as compared with the other three reactions considered , it demonstrates a strong temperature dependence for antineutrinos with @xmath232 mev , i.e. below the ground - state reaction threshold . since the downward gt@xmath150 transitions are suppressed in @xmath122 , the cross section enhancement reflects the thermal unblocking of the upward gt@xmath150 strength . because of the thermal unblocking , the energy below which the gt@xmath150 contribution is more than half of the total cross section shifts to higher values : at @xmath233 mev this energy about 15 mev , at @xmath234 mev it is about 20 mev , and at @xmath195 mev it is about 25 mev . for higher energies forbidden transitions dominate the process like at @xmath128 and the cross - section depends only weakly on temperature . , but now including the outgoing electron blocking ] as was mentioned above , during the core contraction neutrino absorption by nuclei is hindered by pauli blocking of the phase space for the outgoing electron . to study this effect within the tqrpa , following ref . @xcite , we have calculated the @xmath229-absorption cross sections by introducing a blocking factor @xmath100 defined at three different sets of temperature and chemical potential ( @xmath235 in mev ) : @xmath236 . the results are shown in fig . [ nb ] for the @xmath227 and @xmath237 reactions . as can be seen , the neutrino absorption cross sections are drastically reduced due to electron blocking in the final state . moreover , as the chemical potential increases faster than the temperature the cross sections decrease with temperature . it is obvious that the absorbtion due to de - excitation of thermally excited states is less affected by the pauli blocking since the outgoing electron gains energy . this is clearly demonstrated by the plots in the lower panels of fig . [ nb ] where the relative contribution of negative - energy transitions is shown . we thus conclude that owing to blocking effect negative energy transitions dominate the cross sections up to neutrino energies @xmath238 . another consequence of the blocking is that downward @xmath239 forbidden transitions become important with increasing @xmath235 . without pauli blocking their contribution in negligible due to a small boltzmann weight . however , as shown in the middle panels of fig . [ nb ] , for @xmath240 their contribution is comparable or even larger than those of the allowed transitions . according to our calculations this downward forbidden contribution is mainly due to @xmath241 transitions . fe calculated within the tqrpa and the lssm approach ( see ref . @xcite , fig . 1 ) . the cross sections in the upper ( lower ) panel are derived without ( with ) the final - state electron blocking . the respective temperatures and chemical potentials are given in mev . ] in fig . [ comparison ] , the @xmath129 cross sections are displayed together with the results of the large - scale shell - model calculations ( see fig . 1 in ref . even if the general behaviour of the cross sections as functions of the neutrino energy and temperature is in agreement in both approaches , the tqrpa results are noticeable larger than the lssm ones but the discrepancy reduces with increasing neutrino energies . to understand the cause of the discrepancy , let us consider first the cross sections calculated neglecting the final - state electron blocking . for @xmath213 mev the tqrpa cross sections exceed the lssm values by two to three orders of magnitude . for such low energies , in both approaches , the neutrino absorption on @xmath0fe is dominated by gt@xmath156 downward transitions from thermally excited states . the differences in the description of such transitions explain the differences between the tqrpa and shell - model results . as the tqrpa is based on the grand canonical ensemble , the upward and downward gt@xmath2 strength are connected by the detailed balance . as shown in fig . [ partial_t ] , the absorption of low - energy neutrinos on @xmath0fe is dominated by the downward gt@xmath156 transition inverse to the gt@xmath150 resonance . this corresponds to an excitation energy @xmath242 mev in the boltzmann factor of eq . . within the shell - model calculations , downward transitions are included by back - resonances , that is by inverting the gt@xmath150 strength distribution of the daughter nucleus . in @xcite , the back - resonances are built on the lowest states of @xmath0co and the bulk of the back - resonance strength in @xmath0fe is located at an excitation energy of @xmath243 mev . this excitation energy is somewhat higher than @xmath244 . moreover , within the tqrpa the downward strength concentrates in a single state , while the shell model gt@xmath150 strength for @xmath0co is highly fragmented owing to multinucleon correlations @xcite . it is clear that both these factors suppress the contribution of downward transitions within the lssm . to see whether the tqrpa reliably predicts the strength of negative - energy transitions , one must go beyond the tqrpa . for a separable residual interaction used here this can be done following the method developed within the qpm , that is by taking phonon coupling into account . on the other hand we should note that due to violation of brink s hypothesis some back - resonances built on high - lying excited states of @xmath0co may be located at the same energies as those built on the nuclear ground and low - lying states . due to an increasing density of states , the contribution of such back - resonance states may be substantial and , therefore , their inclusion into the shell - model calculations may improve the agreement between the tqrpa and shell - model results . for @xmath245 mev , thermally unblocked low - energy gt@xmath156 transitions come into play , and since such transitions do not appear within the shell - model based calculation they also cause the excess of the tqrpa cross sections over the lssm ones . at @xmath246 mev , @xmath229-absorption is dominated by the strong transition involving the gt@xmath156 resonance . with increasing @xmath133 , the cross section becomes insensitive to the energy dependence of the gt distribution and depends only on the total gt@xmath156 strength . as a result we observe excellent agreement between the results of both approaches . comparing the cross sections calculated with pauli blocking for the outgoing electron ( see the lower panel of fig . [ comparison ] ) , we note that in @xcite , only allowed gt@xmath156 transitions are taken into account when calculating neutrino absorption cross section . as is shown in fig . [ nb ] , if the pauli blocking is taken into account , forbidden downward transition become important with increasing temperature and electron chemical potential . it is apparent that such transitions along with the above discussed reasons lead to larger values for the tqrpa cross sections as compared to the shell - model results .

we perform a detailed analysis of thermal effects on the strength distribution of allowed gamow - teller transitions which dominate low - energy charged - current neutrino reactions . forfe we compare the calculated finite - temperature cross sections with those obtained from large - scale shell - model calculations .

using the thermal quasiparticle random phase approximation , we study the process of neutrino and antineutrino capture on hot nuclei in supernova environments . for the sample nucleife andge we perform a detailed analysis of thermal effects on the strength distribution of allowed gamow - teller transitions which dominate low - energy charged - current neutrino reactions . the finite temperature cross sections are calculated taking into account the contributions of both allowed and forbidden transitions . the enhancement of the low - energy cross sections is explained by considering thermal effects on the gt strength . forfe we compare the calculated finite - temperature cross sections with those obtained from large - scale shell - model calculations .

1111.0135

i

key properties of physical systems can sometimes be understood by mapping them to seemingly unrelated ones . a powerful example of this was provided by laughlin , who observed that the squared norm of his @xmath0 fractional quantum hall trial wavefunction @xmath1 ( where @xmath2 is a complex coordinate in the two - dimensional plane ) could be expressed as the boltzmann weight of a two - dimensional one - component plasma @xcite : @xmath3 where @xmath4 and @xmath5 . this mapping allows properties such as quasiparticle charge and braiding statistics to be determined by appealing to the known properties of a one - component plasma . recently , a similar plasma mapping was established @xcite for ising - type quantum hall states , such as the moore - read ( mr ) @xcite , anti - pfaffian @xcite , and bonderson - slingerland ( bs ) hierarchy @xcite states , which are likely candidates to describe hall plateaus in the second landau level , in particular at filling fraction @xmath6 @xcite . in this case , the mapping is to a two - dimensional ( 2d ) two - component plasma , where the two species of particles , @xmath7 and @xmath8 , carry not only different values of charge , but also interact through two different interactions , both of the coulomb form , so the potential energy is : @xmath9 @xmath10 where @xmath11 . the @xmath8-particles interact with each other through the first coulomb - like interaction , @xmath12 , given in eq . ( and so does not depend on the @xmath13 coordinates ) . moreover , the @xmath8-particles interact with each other and with the @xmath7-particles through the second coulomb - like interaction , through which the @xmath7-particles also interact with each other , according to @xmath14 , given in eq . . note that @xmath14 is the 2d coulomb potential of the usual two - component plasma ( where the two species carry charge @xmath15 and @xmath16 , respectively ) . the @xmath8-particles carry charge @xmath17 for the first interaction and charge @xmath15 for the second interaction . the @xmath7-particles carry charge @xmath18 for the first interaction and charge @xmath16 for the second interaction . for a plasma with @xmath19 particles of each species , neutrality is satisfied using a uniform background density of type 1 charge , as in the second term in eq . . this unconventional plasma may be considered as an ordinary neutral two - component gas with positive and negative charges of magnitude @xmath15 , where the positive charges are given an additional charge of @xmath17 that is only felt by the other positive charges and not the negative charges . an illustration of the interactions between the two species in the system is shown in fig . [ fig : interactions ] . -particles only interact by the second coulomb - like interaction with charge @xmath16 , whereas the @xmath8-particles carry charge @xmath17 for the first coulomb - like interaction and @xmath15 for the second coulomb - like interaction . thus , the intraspecies interaction among the @xmath7-particles , shown in ( a ) , and the interspecies interaction between @xmath7 and @xmath8-particles , shown in ( b ) , are given by @xmath15 only , whereas the intraspecies interaction among the @xmath8-particles , shown in ( c ) , are determined by @xmath17 in addition to @xmath15 . interactions between the @xmath8-particles and the neutralizing background are omitted from the figure . ] we are thus led to consider a class of unconventional plasmas parametrized by @xmath20 and @xmath21 . as mentioned above , for mr ising - type states with filling @xmath0 , the relevant values are @xmath22 and @xmath23 . in this plasma mapping , the @xmath24 particles in the plasma correspond to the electrons in the mr wavefunctions and the @xmath13 particles correspond to screening operators ( fictitious particles ) . the case @xmath25 , @xmath23 is relevant for the plasma mapping @xcite of 2d chiral @xmath26-wave superconductors @xcite . we note that whenever @xmath25 , our model is a special case of the well - known 2d two - component plasma of equal and opposite charges @xcite . the screening properties of multi - component 2d plasmas with multiple coulomb interactions of this kind are also important for other physical systems , such as rotating multi - component bose - einstein condensates with interspecies current - current ( andreev - bashkin ) interaction @xcite and some multi - component superconducting systems @xcite . in these systems the screening properties and phase transitions determine superfluid and rotational responses . in this paper , we fix temperature to @xmath27 and consider the two most significant values of @xmath17 , namely @xmath28 . we investigate the screening and phase transition properties of these plasmas as a function of varying @xmath15 by performing a large - scale monte carlo simulation . here , a `` screening phase '' means that the system has a screening length which is finite , and exponentially decaying effective interactions . a system with logarithmic effective interactions is one where screening is defined to be absent . as a first check , we reproduce the well - known result that , for @xmath29 , there is a berezinskii - kosterlitz - thouless ( bkt ) phase transition at @xmath30 , as expected for a 2d two - component plasma of equal and opposite charges . for @xmath31 , the charges are unbound and the plasma screens , but for @xmath32 , the charges are bound into dipoles and the interaction is not screened . thus , for @xmath33 , the value relevant to 2d chiral @xmath26-wave superconductors , the plasma screens . for @xmath34 , we again find a bkt phase transition at @xmath30 , with a plasma screening phase for @xmath31 . the first coulomb - like interaction is deep within its screening phase and appears to have a negligibly small effect on the screening of the second interaction . in both cases , the critical values @xmath35 are obtained by a finite - size scaling fit of the monte carlo data to the bkt form . our findings demonstrate that the unconventional plasma which occurs in the mapping for both a chiral @xmath26-wave superconductor and the ising - type quantum hall states is clearly in the screening phase ( for both types of coulomb interaction ) and hence allows one to discern the non - abelian braiding properties of these states , as explained in ref . . the outline of this paper is as follows . in the introductory part of section [ sec : model ] , we present the model for the unconventional plasma we will be studying in this paper . in section [ sec : ising_type_qhs ] , we connect this to the ising - type of quantum hall states . in section [ sec : rotating_becs ] , we explain its connection to two - component , two dimensional , bose - einstein condensates . in section [ sec : spherical ] , we present a formulation of the model on a sphere . in section [ sec : mc_details ] , we give details of the monte - carlo simulations , and in section [ sec : results ] , we present our results for the screening properties , as well as our findings for the character of phase transition between the dielectric non - screening phase and the metallic screening phase . in section [ sec : conclusions ] , we present our conclusions . technical details on the derivation of a generalized dielectric constant is given in appendix [ app : general_dielectric_constant ] . in appendix [ app : fourth_order_derivative ] , we give a derivation of a relevant higher order response function that we use to characterize the metal - insulator transition . in appendix [ app : weber_minnhagen ] , we present technical details on the finite - size scaling we have used .

the plasma differs fundamentally from that which is associated with the two - dimensional xy model and abelian fractional quantum hall states . we find that this unconventional plasma undergoes a berezinskii - kosterlitz - thouless phase transition from an insulator to a metal . this result verifies the required properties of the unconventional plasma used to demonstrate that ising - type quantum hall states possess quasiparticles with non - abelian braiding statistics .

utilizing large - scale monte - carlo simulations , we investigate an unconventional two - component classical plasma in two dimensions which controls the behavior of the norms and overlaps of the quantum - mechanical wavefunctions of ising - type quantum hall states . the plasma differs fundamentally from that which is associated with the two - dimensional xy model and abelian fractional quantum hall states . we find that this unconventional plasma undergoes a berezinskii - kosterlitz - thouless phase transition from an insulator to a metal . the parameter values corresponding to ising - type quantum hall states lie on the metallic side of this transition . this result verifies the required properties of the unconventional plasma used to demonstrate that ising - type quantum hall states possess quasiparticles with non - abelian braiding statistics .

1407.4985

r

as a nearby ( @xmath0320 pc ) , young ( 2 - 3 myr ) , relatively compact cluster ic 348 has proven to be a valuable laboratory for studying young stellar object variability @xcite . with over 300 cluster members , only one of which is earlier than a0 , this region of low mass star formation contains a wide variety of circumstellar structures from pre - natal envelopes to disks with many - au wide gaps @xcite . in the infrared , almost 60% of the sources with an infrared excess are variable at [ 3.6 ] , [ 4.5 ] @xcite , while 89% of the pre - main sequence stars brighter than i=14 are variable in the optical @xcite on timescales of weeks to months . the frequency of these fluctuations indicates that the majority of pre - main sequence stars experience variability on their stellar surface , probed by the optical data , and within an au of the star , probed by the infrared data . in our search for correlated x - ray and infrared variability , we focus on cluster members that have the most complete infrared and x - ray time - series data . cluster members , and their stellar properties ( l@xmath3,t@xmath4 , etc . ) , are drawn from @xcite as compiled by @xcite . there are a total of 133 cluster members detected on more than one x - ray epoch , with 107 detected on more than four epochs . we restrict ourselves to these 107 stars because they have enough epochs for studying variability . while we include x - ray fluxes from previous studies of ic 348 @xcite , our analysis focuses on the data that are contemporaneous with the infrared data . as a sub - sample of the cluster , the x - ray detected sources are incomplete below l=0.3l@xmath5 and t@xmath6=3600 k ( fig [ demographics ] ) . within ic 348 , the x - ray luminosity is typically 3 to 4 orders of magnitude lower than the bolometric luminosity @xcite . x - ray emission is known to be brighter among sources without active accretion @xcite and in our sample this will present itself as a detection efficiency that is a function of the infrared sed slope ( defined as the logarithmic slope of @xmath7 versus @xmath8 over the 3 - 8 range ) since the presence of a circumstellar disk as measured with the infrared excess is correlated with accretion . using the dereddened flux , the sed slope varies from @xmath9 for sources without a disk to @xmath10 for sources with an envelope and we use @xmath11 as the boundary between a source with or without a circumstellar disk . @xcite find that within ic 348 the median x - ray luminosity among stars with disks is @xmath00.3 dex lower than comparable stars without disks . figure [ demographics ] shows the distribution of sed slope for x - ray detections compared with the entire sample , demonstrating our inefficient sensitivity to sources with disks . for the majority of our analysis we restrict ourselves to the sources with a disk . the presence of infrared variability is assessed using the techniques described in @xcite . in short , we use the reduced chi - square statistic for each band , and well as the stetson index s , which is sensitive to correlated variability in the two irac bands . the use of the stetson index does require us to restrict the analysis to sources detected in both bands , but the added sensitivity of this index compared to the reduced chi - square offsets the reduction in sample size . a star is marked as an infrared variable if @xmath12)>3 $ ] or @xmath13)>3 $ ] or [email protected] . based on prior analysis , we are sensitive to @xmath15 of fluctuations down to 0.04 mag for sources brighter than 14th magnitude @xcite ; this sensitivity limit is relatively independent of source brightness because most of the uncertainty is due to systematic effects for these bright targets @xcite . while spitzer monitoring data is available from multiple observing campaigns , we focus on the contemporaneous fall 2011 data when assessing variability since we are mainly concerned with the behavior during the same time frame as any x - ray fluctuations . the vast majority of stars variable in one season are also variable in other seasons , and our results would not significantly change if we included the entire dataset . since the 3 - 5@xmath16 emission probed by this photometry is dominated by the inner edge of the dusty disk @xcite , we are not sensitive to the dynamics of the regions of the disk beyond this point . given that we are mainly concerned with the change in x - ray flux , rather than its overall level , we do not convert photon fluxes to luminosities , which requires assumptions about the distance to the cluster and the underlying x - ray spectrum . while the arrival time of each photon is recorded , we instead use the photon flux averaged over each 10ks observing run , with each epoch comprising one point on our light curve . we chose to do this to increase sensitivity at the expense of knowledge about the x - ray variability on very short timescales . we restrict ourselves to sources detected on at least four x - ray epochs . photon fluxes range from 1e-6 to 1e-4 photons / s/@xmath17 , or 1 to 1200 net photons per 10ks block . we can roughly estimate the x - ray luminosities by assuming an average photon energy of 1.5kev , to convert from photon flux to energy flux , and a distance of 320pc ; we find luminosities range from @xmath010@xmath18 to @xmath010@xmath19 erg / sec with a typical luminosity of @xmath010@xmath20erg / sec similar to previous studies @xcite . our final sample consists of 39 stars ( table [ var_table ] ) with circumstellar disks with sufficient x - ray photometry to examine variability , all of which were detected in the infrared . figure [ lc_examples ] show examples of light curves for stars with and without x - ray and infrared variability to demonstrate the fidelity of our data . our sensitivity to infrared variability is fairly uniform over our entire sample because the uncertainties are dominated by systematics for the vast majority of sources . this is not the case for the x - ray emission whose uncertainties are dominated by poisson statistics and scale with the square root of the flux . this leads to substantially nonuniform sensitivities throughout our sample . as with the infrared flux we use the reduced chi - square to select variable x - ray emission , using @xmath21 as the boundary between variables and non - variables this picks out variations that are significant relative to the noise , which varies substantially between the brightest and the faintest sources . as a result , the size of the fluctuations selected as variable will strongly depend on the mean x - ray flux . on average this @xmath22 boundary corresponds to a factor of 2 increase in the flux relative to the mean with fluctuations reaching close to a factor of 10 . despite the non - continuous nature of our observations and the use of different selection criteria for selecting variables as compared to these previous studies , we pick out stars with similar fluctuations . @xcite find that among stars with disks , on timescales of a week , fluctuations are typically a factor of 3 , similar to our results . overall our sample consists of 39 sources with ( 1 ) detections on four or more x - ray epochs , ( 2 ) detections in both irac bands on all epochs , ( 3 ) an infrared excess indicative of a disk . among these 39 stars , 31 have significant fluctuations in the infrared , while 28 have detectable x - ray variability . our observing cadence was designed to probe long term effects of x - ray fluctuations on disk emission , at the expense of knowledge about any short , instantaneous changes in disk emission . while very rapid changes in infrared emission have been observed @xcite , week to month long variations make up a substantial fraction of the infrared variability @xcite . the time between an x - ray epoch and the nearest infrared observation ranges from 0.1 to 2.1 days ( 12 - 180 ks ) and we are completely insensitive to changes in infrared emission on timescale shorter than this . we instead focus on responses that cover more than 2 infrared epochs ( @xmath14300ks = 4 days ) . this caveat should be kept in mind when interpreting our results , especially as they apply to physical connections between x - ray and infrared variability . we first look at the 28 stars with disks that are variable in both the x - ray and infrared to see if the light curves themselves are correlated . this is assessed using the kendall s tau and spearman s rho statistics . both of these coefficients serve as non - parametric tests of whether increases or decreases in the x - ray are mirrored in infrared . we find no significant correlation between the x - ray and infrared light curves suggesting that there is no strong correlation between the infrared and x - ray variability . we also find that the size of the infrared fluctuations is not correlated with the size of the x - ray fluctuations among these variable stars . @xcite find correlated variations in optical flux and soft , but not hard , x - ray flux of ctts in ngc 2264 between observations separated by two weeks , suggesting that there is a difference between the behavior of the soft and hard x - ray emission . we examine how the median x - ray photon energy changes over the course of the light curve to see if it changes in concert with the infrared emission . if the soft x - ray emission tracks the infrared emission while the hard x - ray flux is constant , then the median photon energy will decrease as the infrared emission increases . given that we typically only detect 24 photons per source per 10ks block we use the median flux instead of just the soft x - ray photons to reduce the errors and maximize our sensitivity to fluctuations . using both the kendall s tau and spearman s rho metrics , we do not find a correlation between the median photon energy and the infrared flux in any of our disk - bearing targets . we also find no significant correlation in the size of the infrared variability and the size of the variability in median photon energy . among the two brightest x - ray sources , lrll 2 and 6 , for which we measure @xmath0400 photons per 10 ks , while there is some evidence for a change in median photon energy this change does not track with the infrared emission . the kendall s tau and spearman s rho statistics are effective at selecting correlated variations when there is no time - delay between the infrared and x - ray fluctuations and if the light curve is monotonic . @xcite find that roughly a tenth of the stars in orion with known optical periods have detectable x - ray periods and any corresponding , but phase shifted , variability in the infrared would be missed by the previous metrics . to account for a time delay between the two light curves we employ the cross - correlation function , defined as : @xmath23[y(t_i-\tau)-\bar{y}]}{\sigma_x\sigma_y}\ ] ] where @xmath24 and @xmath25 represent the x - ray and infrared light curves , @xmath26 , @xmath27 , @xmath28 , @xmath29 are the respective means and standard deviations of the two light curves and @xmath30 is the time lag between the two light curves @xcite . this effectively shifts the infrared light curves by @xmath30 days and calculates how well the two light curves match after this shift . a positive value of @xmath30 implies that the ir light curve leads the x - ray light curve , while a negative lag corresponds to the x - ray light curve leading the ir light curve . such an effect might be expected if there is an appreciable time delay between the occurrence of an x - ray fluctuation and the response of the disk or if the x - ray and infrared flux show a rotational modulation that is out of phase . given that the data are not continuously sampled , we interpolate the more heavily sampled infrared light curve onto the x - ray light curve in our analysis . we assess the uncertainty in the ccf at different lags by computing the ccf of a particular x - ray light curve with infrared light curves from 100 random cluster members , and use the dispersion in the value of the ccf at each lag as its uncertainty . figure [ ccf ] shows our results for lrl 5 and 58 as examples . when examining all 28 cluster members with variability in both the x - ray and infrared , we find no evidence of a strong cross - correlation signal between a lag of -20 and 20 days , with our strongest sensitivity to lags between -10 and 10 days . again there is no strong evidence for a direct connection between the infrared and x - ray variability . the ccf , while effective at picking out light curves with a time lag , breaks down in the presence of flares . @xcite find that roughly a quarter of stars within taurus exhibit flares , with these flaring sources making up half of the variable sample . while these outlier points within a light curve can easily disrupt any underlying correlation , they could also be a source of changes in infrared emission if the flare is powerful enough . we define a source as having a flare if it is variable in the x - ray ( @xmath31 ) and it has one epoch whose flux is greater than three times larger than the median flux . we can also look for x - ray flares within a single 10 ks epoch among the brightest sources since each photon is tracked when taking x - ray observation . only one source ( lrll 36 ) shows evidence for an x - ray flare during one of these epochs , and this star has been included in our analysis . there are a total of 13 cluster members with an x - ray flare , all but one of which is variable in the infrared . in none of these stars do we see strong evidence for an extended change in the ir flux following the x - ray flare . figure [ flare ] shows the x - ray and infrared light curves of one star with an x - ray flare demonstrating the lack of response in the infrared light curve . if the infrared flux is changing before the flare , it continues along its course after the flare . we examine in detail the change in ir flux associated with an x - ray flare by calculating the change in [ 3.6 ] and [ 4.5 ] magnitude between the two epochs ( i.e. about 2 days ) surrounding the x - ray flare and comparing this to all consecutive epoch magnitude changes in the infrared light curve . figure [ flare ] shows an example of this analysis . this allows us to quantify the infrared fluctuation closest to the x - ray flare and how it compares to the fluctuations seen at other times . in none of the light curves do we see evidence that the ir fluctuation near the x - ray flare is substantially different than what is seen in any other part of the light curve . this is consistent with our visual inspection which found no evidence for a change in infrared flux in response to an x - ray flare . again we note that given our observing cadence we are severely limited in assessing the immediate response of the infrared flux to an x - ray flare . the time between an x - ray epoch and an infrared epoch ranges from 0.1 to 2.1 days ( 12 - 180ks ) . the majority of x - ray flares have decay times less than 60ks with an average decay time of 10ks @xcite and almost all x - ray flares would have decayed away by the time the system was observed in the infrared . ysos typically exhibit one flare per star per 500ks with the time between bright flares ( l@xmath32erg / sec ) a factor of a few longer than this @xcite . @xcite find similar results for solar - type stars , with roughly one flare per star per 650ks . a theory for the week to month long infrared variability that relies solely on x - ray flares would require the infrared response to last at least @xmath0500ks(=5.8days ) to extend the infrared variability throughout the quiescent period between flares . even with our limited cadence we can exclude these types of large , long infrared responses .

variability in the infrared emission from disks around pre - main sequence stars over the course of days to weeks appears to be common , but the physical cause of the changes in disk structure are not constrained . we obtained ten epochs of chandra acis photometry over a period of 30 days with a roughly 3 day cadence contemporaneous with 20 epochs of spitzer [ 3.6],[4.5 ] photometry over 40 days with a roughly 2 day cadence of the ic 348 cluster . this cadence allows us to search for week to month long responses of the infrared emission to changes in the high - energy flux .

variability in the infrared emission from disks around pre - main sequence stars over the course of days to weeks appears to be common , but the physical cause of the changes in disk structure are not constrained . here we present coordinated monitoring of one young cluster with the _ spitzer _ and _ chandra _ space telescopes aimed at studying the physical source of the variability . in fall 2011 we obtained ten epochs of chandra acis photometry over a period of 30 days with a roughly 3 day cadence contemporaneous with 20 epochs of spitzer [ 3.6],[4.5 ] photometry over 40 days with a roughly 2 day cadence of the ic 348 cluster . this cadence allows us to search for week to month long responses of the infrared emission to changes in the high - energy flux . we find no strong evidence for a direct link between the x - ray and infrared variability on these timescales among 39 cluster members with circumstellar disks . there is no significant correlation between the shape of the infrared and x - ray light curves , or between the size of the x - ray and infrared variability . among the stars with an x - ray flare none showed evidence of a correlated change in the infrared photometry on timescales of days to weeks following the flare . this lack of connection implies that x - ray heating of the planet forming region of the disk is not significant , although we can not rule out rapid or instantaneous changes in infrared emission .

1407.4985

c

we find no evidence for an increased frequency of infrared variability among stars with x - ray variability . we see no correlation in the shape of the light curves in stars that exhibit variability in both bands , which is especially true in the stars with moderate x - ray flares for which we see no evidence for a change in infrared flux in response to the flare . we put limits on the relation between x - ray variability and the week to month long infrared variability of dust at the inner edge of the disk that is common among young stellar objects . based on the observational evidence , the influence of x - ray heating on the temperature of the dust close to the star is relatively minor , which in turn has implications for the overall structure of the inner edge of the disk . below z / [email protected] the densities are high enough that the gas and dust temperature are highly coupled through collisions @xcite , allowing the dust temperature to set the gas temperature . the gas temperature in turn sets the pressure scale height of the disk , which is the basis of the vertical structure of the disk in a region where planet formation is expected to occur . if the x - rays can not influence the dust thermal structure , then they will not influence the overall structure in this area of the disk . compared to fuv and euv photons , x - rays have a higher penetration depth because the opacity of the gas decreases towards higher energies and if x - ray photons can not reach the dusty layers , then fuv and euv photons contribute even less to the dust temperature . the dust temperature is instead set by a combination of viscous dissipation and irradiation by stellar optical emission @xcite , at least until the disk is significantly depleted @xcite . beyond @xmath01 au , which is not probed by our infrared photometry , the x - rays may still have a strong influence on disk structure through e.g. mri turbulence @xcite . in terms of constraining the origin of the long - term infrared fluctuations , we can rule out the influence of x - ray ionization as well as interactions between the x - ray emitting plasma and the dust at the sublimation front close to the star from explaining the majority of the observed infrared variability . these factors may come into play on short timescales for a small handful of stars , or at levels below our detection limits , but generally they are not important in setting disk structure . more likely possibilities include perturbations related to accretion heating @xcite , mri driven turbulence lifting dust out of the midplane @xcite or perturbations from a companion @xcite with observations pointing toward accretion bursts , variable obscuration of the central star and changes in the inner disk structure @xcite . we would like to thank the anonymous referee for their substantive comments that greatly improved this paper . the scientific results reported in this article are based in part on observations made by the chandra x - ray observatory . support for this work was provided by the national aeronautics and space administration through chandra award number g02 - 13028a issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics space administration under contract nas8 - 03060 . this work is based in part on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa . support for the work was provided by nasa through an award issued by jpl / caltech . rg gratefully acknowledges funding support from nasa adap grants nnx11ad14 g and nnx13af08 g and caltech / jpl awards 1373081 , 142329 and 1440160 in support of spitzer space telescope observing programs . alencar , s.h.p . , et al . 2012 , , 541 , 116 alexander , f. & preibisch , t. 2012 , , 539 , 64 aresu , g. , kamp , i. , meijerink , r. , woitke , p. , thi , w .- f . , & spaans , m. 2011 , , 526 , 163 ataiee , s. , pinilla , p. , zsom , a. , dullemond , c.p . , dominik , c. , & ghanbari , j. 2013 , , 553 , l3 benz , a.o . & gdel , m. 2010 , , 48 , 241 borucki , w.j . , et al . 2011 , , 736 , 19 bouvier , j. , et al . 2007 , , 463 , 1017 caramazza , m. , flaccomio , e. , micela , g. , reale , f. , wolk , s.j . , & feigelson , e.d . 2007 , , 471 , 645 cody , a.m. , et al . 2014 , , 147 , 82 dalessio , p. , cant , j. , calvet , n. , & lizano , s. 1998 , , 500 , 411 dalessio , p. , calvet , n. , nartmann , l. , franco - 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bouwman , j. , & mor , a. 2012 , , 759 , 47 tielens , a.g.g.m . 2005 , the physics and chemistry of the interstellar medium ( cambridge , uk : cambridge university press ) turner , n.j . , carballido , a. , & sano , t. 2010 , , 708 , 188 valenti , j.a . & johns - krull , c.m . 2004 , , 292 , 619 wolk , s.j . , harnden , f.r . , jr . , flaccomio , e. , micela , g. , favata , f. , shang , h. , feigelson , e.d . 2005 , , 160 , 423 wolk , s.j . , spitzbart , b.d . , bourke , t.l . , & alves , j. 2006 , , 132 , 1100 wolk , s.j . , rice , t.s . , & aspin , c. 2013 , , 773 , 145 zanni , c. , & ferreira , j. 2013 , , 550 , 99 zhu , z. , hartmann , l. , gammie , c.f . , book , l.g . , simon , j.b . , & engelhard , e. 2010 , , 713 , 1134 ccccc 13425 & 2011 - 10 - 17 06:11:07 & 55851.3 & 9.91 & 118.1 + 13426 & 2011 - 10 - 19 22:05:11 & 55853.9 & 9.91 & 119.5 + 13427 & 2011 - 10 - 22 13:31:32 & 55856.5 & 9.91 & 121.1 + 13429 & 2011 - 10 - 28 09:52:52 & 55862.4 & 10.41 & 125.6 + 13430 & 2011 - 10 - 31 06:54:51 & 55865.3 & 9.91 & 128.3 + 13431 & 2011 - 11 - 03 09:45:09 & 55868.4 & 9.92 & 131.9 + 13432 & 2011 - 11 - 06 18:22:08 & 55871.8 & 9.91 & 136.7 + 13433 & 2011 - 11 - 10 01:35:24 & 55875.0 & 10.79 & 142.9 + 13434 & 2011 - 11 - 13 06:48:37 & 55878.3 & 9.91 & 150.6 + 13428 & 2011 - 11 - 17 05:34:13 & 55882.2 & 9.22 & 163.2 + ccc 42463744 & 2011 - 10 - 15 18:22:53 & 55849.8 + 42464000 & 2011 - 10 - 18 09:44:53 & 55852.4 + 42464256 & 2011 - 10 - 20 00:45:16 & 55854.0 + 42464512 & 2011 - 10 - 22 09:56:54 & 55856.4 + 42464768 & 2011 - 10 - 24 05:31:16 & 55858.2 + 42465024 & 2011 - 10 - 26 13:08:49 & 55860.6 + 42465280 & 2011 - 10 - 27 19:42:07 & 55861.8 + 42465536 & 2011 - 10 - 30 10:18:35 & 55864.4 + 42465792 & 2011 - 11 - 1 04:52:37 & 55866.2 + 42466048 & 2011 - 11 - 3 01:27:30 & 55868.1 + 42466304 & 2011 - 11 - 4 19:14:03 & 55869.8 + 42466560 & 2011 - 11 - 6 10:30:23 & 55871.5 + 42466816 & 2011 - 11 - 8 20:29:04 & 55873.9 + 42467072 & 2011 - 11 - 10 20:15:18 & 55875.9 + 42467328 & 2011 - 11 - 12 19:38:16 & 55877.8 + 42467584 & 2011 - 11 - 14 22:39:14 & 55880.0 + 42467840 & 2011 - 11 - 17 00:21:17 & 55882.0 + 42468096 & 2011 - 11 - 18 19:53:33 & 55883.8 + 42468352 & 2011 - 11 - 21 09:56:45 & 55886.4 + 42468608 & 2011 - 11 - 23 03:08:30 & 55888.1 + ccccccccc 2 & 03:44:35.36 & 32:10:04.6 & y & y & n & 8970 & 137 & -1.47 + 5 & 03:44:26.03 & 32:04:30.4 & y & y & n & 5520 & 9.90 & -1.24 + 6 & 03:44:36.94 & 32:06:45.4 & y & y & n & 5830 & 17.0 & -2.08 + 15 & 03:44:44.73 & 32:04:02.6 & y & y & n & 3778 & 1.90 & -1.40 + 21 & 03:44:56.15 & 32:09:15.5 & y & y & y & 5250 & 3.90 & -1.98 + 31 & 03:44:18.16 & 32:04:57.0 & y & y & y & 5945 & 9.60 & -1.85 + 32 & 03:44:37.89 & 32:08:04.2 & y & y & n & 4060 & 1.40 & -1.56 + 36 & 03:44:38.47 & 32:07:35.7 & y & y & y & 4205 & 1.50 & -0.73 + 37 & 03:44:37.99 & 32:03:29.8 & y & y & y & 4205 & 0.99 & -1.03 + 41 & 03:44:21.61 & 32:10:37.6 & y & y & y & 4060 & 0.790 & -1.72 + 55 & 03:44:31.36 & 32:00:14.7 & y & y & y & 3778 & 0.680 & -1.19 + 58 & 03:44:38.55 & 32:08:00.7 & y & y & n & 3669 & 0.720 & -1.73 + 61 & 03:44:22.29 & 32:05:42.7 & y & y & y & 3955 & 0.540 & -1.45 + 65 & 03:44:33.98 & 32:08:54.1 & y & y & n & 3850 & 0.560 & -2.41 + 67 & 03:43:44.62 & 32:08:17.9 & y & y & n & 3741 & 0.480 & -2.04 + 72 & 03:44:22.57 & 32:01:53.7 & y & y & y & 3488 & 0.510 & -2.23 + 82 & 03:44:37.41 & 32:06:11.7 & y & y & n & 4060 & 0.510 & -2.43 + 83 & 03:44:37.41 & 32:09:00.9 & y & y & y & 3705 & 0.510 & -0.84 + 90 & 03:44:33.31 & 32:09:39.6 & y & y & y & 3560 & 0.410 & -2.39 + 91 & 03:44:39.21 & 32:09:44.7 & y & y & y & 3560 & 0.390 & -1.53 + 97 & 03:44:25.56 & 32:06:17.0 & y & y & y & 3524 & 0.540 & -1.75 + 110 & 03:44:37.40 & 32:12:24.3 & y & y & y & 3560 & 0.340 & -1.59 + 116 & 03:44:21.56 & 32:10:17.4 & y & y & y & 3632 & 0.290 & -2.44 + 9024 & 03:44:35.37 & 32:07:36.2 & y & y & n & ... & ... & -1.12 + 71 & 03:44:32.58 & 32:08:55.8 & y & n & n & 3415 & 0.470 & -2.01 + 75 & 03:44:43.78 & 32:10:30.6 & y & n & n & 3669 & 0.620 & -0.53 + 103 & 03:44:44.59 & 32:08:12.7 & y & n & n & 3560 & 0.380 & -1.16 + 113 & 03:44:37.19 & 32:09:16.1 & y & n & n & 4205 & 0.320 & -1.99 + 186 & 03:44:46.33 & 32:11:16.8 & y & n & n & 3560 & 0.310 & -2.07 + 203 & 03:44:18.10 & 32:10:53.5 & y & n & n & 3741 & 0.021 & -1.42 + 1872 & 03:44:43.31 & 32:01:31.6 & y & n & n & ... & ... & 0.43 + 88 & 03:44:32.77 & 32:09:15.8 & n & y & n & 3379 & 0.360 & -2.39 + 108 & 03:44:38.70 & 32:08:56.7 & n & y & n & 3379 & 0.240 & -2.44 + 146 & 03:44:42.63 & 32:06:19.5 & n & y & n & 3705 & 0.190 & -2.48 + 226 & 03:44:31.42 & 32:11:29.4 & n & y & y & 3091 & 0.078 & -1.33 + 52 & 03:44:43.53 & 32:07:43.0 & n & n & n & 3705 & 0.920 & -2.42 + 139 & 03:44:25.31 & 32:10:12.7 & n & n & n & 3161 & 0.200 & -1.22 + 141 & 03:44:30.54 & 32:06:29.7 & n & n & n & 3778 & 0.350 & -2.32 + 1401 & 03:44:54.69 & 32:04:40.3 & n & n & n & ... & ... & 0.10 + ccccccccc 29 & 03:44:31.53 & 32:08:45.0 & y & y & y & 4900 & 2.10 & -2.88 + 45 & 03:44:24.29 & 32:10:19.4 & y & y & y & 4350 & 0.920 & -2.72 + 48 & 03:44:34.88 & 32:06:33.6 & y & y & y & 4278 & 0.990 & -2.70 + 66 & 03:44:28.47 & 32:07:22.4 & y & y & y & 4132 & 0.710 & -2.98 + 69 & 03:44:27.02 & 32:04:43.6 & y & y & n & 3705 & 0.460 & -2.95 + 86 & 03:44:27.88 & 32:07:31.6 & y & y & n & 3560 & 0.460 & -2.73 + 92 & 03:44:32.67 & 32:06:46.5 & y & y & y & 3488 & 0.390 & -2.87 + 125 & 03:44:21.66 & 32:06:24.8 & y & y & n & 3451 & 0.290 & -2.64 + 62 & 03:44:26.63 & 32:03:58.3 & y & n & n & 3161 & 0.390 & -2.88 + 105 & 03:44:11.26 & 32:06:12.1 & y & n & n & 3850 & 0.390 & -2.88 + 170 & 03:44:28.42 & 32:11:22.5 & y & n & n & 3415 & 0.190 & -2.77 + 9 & 03:44:29.17 & 32:09:18.3 & n & y & n & 5520 & 11.00 & -2.86 + 16 & 03:44:32.74 & 32:08:37.5 & n & y & n & 5700 & 0.750 & -2.72 + 23 & 03:44:38.72 & 32:08:42.0 & n & y & n & 4730 & 4.10 & -2.96 + 47 & 03:44:55.51 & 32:09:32.5 & n & y & n & 5250 & 1.90 & -2.89 + 50 & 03:44:55.63 & 32:09:20.2 & n & y & y & 4590 & 1.40 & -2.87 + 53 & 03:44:16.43 & 32:09:55.2 & n & y & y & 5250 & 1.40 & -2.80 + 74 & 03:44:34.27 & 32:10:49.7 & n & y & n & 3560 & 0.620 & -2.92 + 79 & 03:45:01.52 & 32:10:51.5 & n & y & n & 5250 & 0.940 & -2.81 + 142 & 03:43:56.20 & 32:08:36.3 & n & y & n & 3850 & 0.330 & -2.91 + 154 & 03:44:37.79 & 32:12:18.2 & n & y & n & 3198 & 0.190 & -2.79 + 171 & 03:44:44.85 & 32:11:05.8 & n & y & n & 3451 & 0.170 & -2.75 + 174 & 03:44:04.11 & 32:07:17.1 & n & y & n & 3632 & 0.180 & -2.86 + 178 & 03:44:48.83 & 32:13:22.1 & n & y & y & 3451 & 0.130 & -2.60 + 184 & 03:44:53.76 & 32:06:52.2 & n & y & y & 3270 & 0.180 & -2.96 + 188 & 03:44:56.12 & 32:05:56.7 & n & y & y & 3451 & 0.130 & -2.73 + 4 & 03:44:31.19 & 32:06:22.1 & n & n & n & 7200 & 34.00 & -2.72 + 10 & 03:44:24.66 & 32:10:15.0 & n & n & n & 6890 & 13.0 & -2.89 + 30 & 03:44:19.13 & 32:09:31.4 & n & n & n & 7200 & 6.50 & -2.84 + 33 & 03:44:32.59 & 32:08:42.5 & n & n & n & 3488 & 0.870 & -2.58 + 35 & 03:44:39.26 & 32:07:35.5 & n & n & n & 4730 & 3.60 & -2.92 + 38 & 03:44:23.99 & 32:11:00.0 & n & n & n & 6030 & 3.10 & -2.77 + 56 & 03:44:05.00 & 32:09:53.8 & n & n & n & 4660 & 0.930 & -2.87 + 59 & 03:44:40.13 & 32:11:34.3 & n & n & n & 4900 & 1.400 & -2.76 + 98 & 03:44:38.62 & 32:05:06.5 & n & n & n & 3270 & 0.330 & -2.59 + 151 & 03:44:34.83 & 32:11:18.0 & n & n & n & 3560 & 0.260 & -2.83 + 163 & 03:44:35.45 & 32:08:56.3 & n & n & n & 3091 & 0.140 & -2.67 + = 3600k and l@xmath3=0.3l@xmath5 , and are more sensitive to sources without disks ( @xmath9 ) than sources with disks.[demographics],title="fig : " ] = 3600k and l@xmath3=0.3l@xmath5 , and are more sensitive to sources without disks ( @xmath9 ) than sources with disks.[demographics],title="fig : " ] = 3600k and l@xmath3=0.3l@xmath5 , and are more sensitive to sources without disks ( @xmath9 ) than sources with disks.[demographics],title="fig : " ] per sec . points to the left of the vertical dashed line are derived from earlier chandra observations of ic 348 @xcite . the infrared light curves are shown in the corresponding bottom panels . error bars for [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) photometry are shown as the left and right vertical lines . * upper left : * lrll 31 , a source that is variable in both x - ray and infrared . * upper right : * lrll 103 , a star that is variable in the infrared , but not in the x - ray . * lower left : * lrll 108 , a star that is variable in the x - ray but not the infrared . * lower right : * lrll 141 , a star that is not variable in either the x - ray or infrared . light curves for all stars with disks are included in figure [ all_lc].[lc_examples],title="fig : " ] per sec . points to the left of the vertical dashed line are derived from earlier chandra observations of ic 348 @xcite . the infrared light curves are shown in the corresponding bottom panels . error bars for [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) photometry are shown as the left and right vertical lines . * upper left : * lrll 31 , a source that is variable in both x - ray and infrared . * upper right : * lrll 103 , a star that is variable in the infrared , but not in the x - ray . * lower left : * lrll 108 , a star that is variable in the x - ray but not the infrared . * lower right : * lrll 141 , a star that is not variable in either the x - ray or infrared . light curves for all stars with disks are included in figure [ all_lc].[lc_examples],title="fig : " ] per sec . points to the left of the vertical dashed line are derived from earlier chandra observations of ic 348 @xcite . the infrared light curves are shown in the corresponding bottom panels . error bars for [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) photometry are shown as the left and right vertical lines . * upper left : * lrll 31 , a source that is variable in both x - ray and infrared . * upper right : * lrll 103 , a star that is variable in the infrared , but not in the x - ray . * lower left : * lrll 108 , a star that is variable in the x - ray but not the infrared . * lower right : * lrll 141 , a star that is not variable in either the x - ray or infrared . light curves for all stars with disks are included in figure [ all_lc].[lc_examples],title="fig : " ] per sec . points to the left of the vertical dashed line are derived from earlier chandra observations of ic 348 @xcite . the infrared light curves are shown in the corresponding bottom panels . error bars for [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) photometry are shown as the left and right vertical lines . * upper left : * lrll 31 , a source that is variable in both x - ray and infrared . * upper right : * lrll 103 , a star that is variable in the infrared , but not in the x - ray . * lower left : * lrll 108 , a star that is variable in the x - ray but not the infrared . * lower right : * lrll 141 , a star that is not variable in either the x - ray or infrared . light curves for all stars with disks are included in figure [ all_lc].[lc_examples],title="fig : " ] and [ 4.5 ] are shown as vertical tick marks ( left and right respectively ) to the left of dotted line . while the star is variable in the infrared , its variability does not seem to change in response to the x - ray flare . ( right ) distribution of epoch - to - epoch changes in [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) magnitude for lrll 90 . the change experienced between the two epochs surrounding the x - ray flare are shown as vertical lines . the ir flux variation experienced due to the x - ray flare is not significantly different than that seen during other epochs . a similar behavior is seen in the other stars that have an x - ray flare , indicating that the observed x - ray flares do not drive large changes in infrared flux.[flare],title="fig : " ] and [ 4.5 ] are shown as vertical tick marks ( left and right respectively ) to the left of dotted line . while the star is variable in the infrared , its variability does not seem to change in response to the x - ray flare . ( right ) distribution of epoch - to - epoch changes in [ 3.6 ] ( squares ) and [ 4.5 ] ( crosses ) magnitude for lrll 90 . the change experienced between the two epochs surrounding the x - ray flare are shown as vertical lines . the ir flux variation experienced due to the x - ray flare is not significantly different than that seen during other epochs . a similar behavior is seen in the other stars that have an x - ray flare , indicating that the observed x - ray flares do not drive large changes in infrared flux.[flare],title="fig : " ]

there is no significant correlation between the shape of the infrared and x - ray light curves , or between the size of the x - ray and infrared variability . among the stars with an x - ray flare none showed evidence of a correlated change in the infrared photometry on timescales of days to weeks following the flare .

variability in the infrared emission from disks around pre - main sequence stars over the course of days to weeks appears to be common , but the physical cause of the changes in disk structure are not constrained . here we present coordinated monitoring of one young cluster with the _ spitzer _ and _ chandra _ space telescopes aimed at studying the physical source of the variability . in fall 2011 we obtained ten epochs of chandra acis photometry over a period of 30 days with a roughly 3 day cadence contemporaneous with 20 epochs of spitzer [ 3.6],[4.5 ] photometry over 40 days with a roughly 2 day cadence of the ic 348 cluster . this cadence allows us to search for week to month long responses of the infrared emission to changes in the high - energy flux . we find no strong evidence for a direct link between the x - ray and infrared variability on these timescales among 39 cluster members with circumstellar disks . there is no significant correlation between the shape of the infrared and x - ray light curves , or between the size of the x - ray and infrared variability . among the stars with an x - ray flare none showed evidence of a correlated change in the infrared photometry on timescales of days to weeks following the flare . this lack of connection implies that x - ray heating of the planet forming region of the disk is not significant , although we can not rule out rapid or instantaneous changes in infrared emission .

gr-qc0205062

i

one of the best promising methods of searching for a planetary systems around nearby stars is the high accuracy astrometric observations . sim is being designed to produce wealth of the astrometric data necessary to address exactly this problem . it is clear that the corresponding astrometric signal due to a reflex motion of a target star will be at the level of a few @xmath1as and smaller . the most successful searching techniques will have to incorporate an intelligent way of data processing almost at the astrometric noise level . another important part of this puzzle is development of the astrometric model for the instrument . this model should include all the parameters necessary to account for different phenomena affecting the light propagation , and are due to the interstellar media , the solar system dynamics , as well as due to the motion of the free - flying interferometer itself . as a result , the accuracy of astrometric observations expected with sim , will require a number of dynamical parameters to be precisely known . to do this , one will have to be able to remove ( or to correctly account for ) the signatures of all the known effects in order to study the unknown phenomena . this is necessary for minimizing probability of a false detections caused , for example , by aliasing the dynamics of objects in the solar system . actually , there will be a number of parameters introduced by the dynamics in the solar system with periods of the order of a few years . one of such a parameters is the three - dimensional vector of barycentric velocity of the spacecraft . thus , a future astrometric model will have to account not only for the effects due to the motion of the solar system bodies , but also for those that are generated by the motion of the spacecraft and corresponding errors in the spacecraft s navigation . in this paper we will discuss some important elements of dynamical model for the future astrometric observations with sim . specifically , we will address the issue of the relativistic stellar aberration . the stellar aberration is a very important problem for sim . effect of the barycentric velocity of the spacecraft is the largest term in the sim astrometric model and will amounts to @xmath2 arcsec for the earth - trailing orbit . this effect is important not only for a wide angle astrometric observations , but it will produce a measurable effect for a pairs of widely separated stars even inside the tile ( with diameter @xmath3 ) . additionally , a possible correlation of the astrometric observables with the errors in the spacecraft s velocity sky - angles suggests that in order to achieve the mission accuracy for a global astrometric observations of @xmath4as , one will have to control the barycentric velocity of the spacecraft throughout the entire mission and account for the relativistic stellar aberration inside every single tile . the outline of this paper is as follows . in section [ sec : model ] we will present a simplified model for differential astrometric observations with a free - flying interferometer with a single baseline . we will discuss a model for absolute and differential astrometric measurements and will give a three - dimensional parameterization of main observables . we will present the first order differentials , necessary to analyze the errors propagation . in section [ sec : tile ] we will discuss orientation of the tile in the sim nominal observing direction . we will present the first order equations that are governing the propagation of astrometric errors in the instrument . specifically , we address the velocity knowledge requirement , the data sampling rate and orbital position knowledge , and the spacecraft acceleration accuracy constraint . in section [ sec : req ] we will derive the set of the relativistic stellar aberration requirements for sim . we will conclude by presenting our recommendations for future attitude control for the sim spacecraft . in order to make access of the basic results of this paper easier , we will present some important ( but lengthy ! ) calculations in the appendices .

we address the issue of relativistic stellar aberration requirements for the space interferometry mission ( sim ) . motivated by the importance of this issue for sim , we have considered a problem of relative astrometric observations of two stars separated by angle on the sky with a single baseline interferometer . while a definitive answer on the stellar aberration issue may be obtained only in numerical simulations based on the accurate astrometric model of the instrument , one could still derive realistic conclusions by accounting for the main expected properties of sim .

we address the issue of relativistic stellar aberration requirements for the space interferometry mission ( sim ) . motivated by the importance of this issue for sim , we have considered a problem of relative astrometric observations of two stars separated by angle on the sky with a single baseline interferometer . while a definitive answer on the stellar aberration issue may be obtained only in numerical simulations based on the accurate astrometric model of the instrument , one could still derive realistic conclusions by accounting for the main expected properties of sim . in particular , we have analysied how the expected astrometric accuracy of determination of positions , parallaxes and proper motions will constrain the accuracy of the spaceraft navigation . we estimated the astrometric errors introduced by imperfect metrology ( variations of the calibration term across the tile of interest ) , errors in the baseline length estimations , and those due to orbital motion of the spacecraft . we also estimate requirements on the data sampling rate necessary to apply on - board in order to correct for the stellar aberration . we have shown that the worst case observation scenario is realized for the motion of the spacecraft in the direction perpendicular to the tile . this case of motion will provide the most stringent requirement on the accuracy of knowledge of the velocity s magnitude . we discuss the implication of the results obtained for the future mission analysis .

cond-mat0204303

i

in two dimensions , the dynamical equation ( [ sca ] ) for the mass profile reads @xmath330 after the change of variable @xmath331 has been effected . looking for a stationary solution , and using @xmath332 , eq . ( [ dyn2d ] ) is readily integrated leading to @xmath333 note that @xmath334 , ensuring that the whole mass is included in this solution . using @xmath335 , we find that the density profile is given by @xmath336 with @xmath337 this solution exists provided that @xmath338 , which defines the collapse temperature . we have thus recovered the result ( [ thermo11 ] ) by a slightly different method . note that the value of @xmath339 and the dependance of @xmath340 and @xmath63 with the temperature coincide with the exact results obtained within conformal field theory @xcite . in the following , @xmath47 is set constant as we have already seen that the gravothermal does not exist in the microcanonical ensemble in two dimensions . we now address the dynamics at the critical temperature @xmath342 . we note that contrary to what happens in other dimensions , the central density diverges at @xmath343 . thus , in analogy with critical phenomena , we anticipate a scaling solution for @xmath344 , of the form @xmath345 which preserves the scaling form obtained above @xmath343 , and which satisfies the boundary condition @xmath346 . the corresponding density profile is @xmath347 the central density @xmath348 is expected to diverge for @xmath76 , so that @xmath349 is also expected to diverge . inserting the _ ansatz _ eq . ( [ tc2d ] ) into eq . ( [ dyn2d ] ) shows that the left - hand term is indeed negligible compared to both terms of the right - hand side , to leading order in @xmath350 . so far , this prevents us from determining a dynamical equation for @xmath350 . in order to achieve that , we must solve eq . ( [ dyn2d ] ) to the next order in @xmath351 . we thus look for a solution of the form @xmath352 where @xmath353 is expected to be of order @xmath294 , and should satisfy @xmath354 and @xmath355 ( the total integrated mass should be 0 and 1 , respectively , for @xmath356 and @xmath357 ) , and @xmath358 , which ensures that eq . ( [ rhoa ] ) is exactly obeyed , defining @xmath349 without any ambiguity . the contribution of @xmath359 in the left - hand side of eq . ( [ dyn2d ] ) is dominated by the time derivative of eq . ( [ tc2d ] ) : @xmath360= \frac{u(1-u)}{(1+au)^2}\frac{da}{dt},\ ] ] which will be checked self - consistently hereafter . in addition , non linear terms in @xmath361 in the right - hand side are also negligible . therefore , @xmath361 satisfies @xmath362 actually , for a given time , this equation becomes an ordinary differential equation involving only one variable @xmath102 , as @xmath350 and @xmath363 appear as parameters . ( [ eqh ] ) can be integrated leading to a first order equation in @xmath361 , which can be easily solved . defining @xmath364 , we finally get @xmath365 , \nonumber\end{aligned}\ ] ] which depends on time only through the variable @xmath350 and @xmath363 . now , @xmath363 is determined by imposing the boundary condition @xmath355 , which leads to @xmath366 . \label{dadt}\ ] ] one can solve iteratively eq . ( [ dyn2d ] ) , by adding the time derivative of the above solution to the left - hand side , in order to compute an improved @xmath361 . to leading order , the solution of eq . ( [ h ] ) is preserved . however , new terms are generated which are important for @xmath367 ( @xmath368 ) , and which generate terms of order @xmath369 is the expansion for @xmath363 . this explains the form of the error term in eq . ( [ dadt ] ) . integrating eq . ( [ dadt ] ) for large time , we get the exact asymptotic expansion for large time @xmath370 . \label{at}\ ] ] for @xmath76 , the central density diverges like @xmath349 and the core radius goes to zero like @xmath371 . in addition , the scaling solution ( [ scarho2d ] ) at @xmath372 goes to a dirac peak containing the whole mass ( see eq . ( [ thermo12 ] ) ) , as the decay exponent of the scaling function is 4 , which is strictly greater than 2 . for @xmath7 , the scaling equation associated to eq . ( [ sca ] ) does not display any physical solution when numerically solved . in this section , we thus present a special treatment adapted to this case . the principal difference with other dimensions is the divergence of the central density at @xmath343 , and the occurrence of a scaling solution at this temperature . strictly below @xmath343 , we expect a finite time collapse . close to the center , the solution takes the form @xmath374 where again the left - hand side of eq . ( [ dyn2d ] ) is negligible compared to each term on the right - hand side . we thus look for a solution of the type @xmath375 where @xmath361 is now of order @xmath294 as it contains a finite fraction of the total mass , since the first term contains a mass of order @xmath376 . inserting this _ ansatz _ in the dynamical equation eq . ( [ dyn2d ] ) , we obtain @xmath377 one can look for a scaling solution of the type @xmath378 so that the mass included in this scaling profile @xmath379 . with this definition , the density profile decays for large distance as @xmath380 , with @xmath381 . inserting this _ ansatz _ in eq . ( [ ew ] ) , we obtain @xmath382\frac{da}{dt}a^{-2}=vh''+2 \left(\frac{v}{1+v}h\right)'+ 2a^{\gamma-1}h h ' , \label{scacol2d}\ ] ] where derivatives are with respect to the variable @xmath103 . we are free to choose @xmath383 , so that @xmath384 . for small @xmath103 , eq . ( [ scacol2d ] ) leads to @xmath385 eq . ( [ scacol2d ] ) has a global scaling solution only for @xmath386 . however , we know that in this case the scaling equation obtained by setting @xmath386 does not display any physical solution . thus , we conclude that there is no scaling solution obtained by imposing that all terms in eq . ( [ scacol2d ] ) scale the same way . however , as we will see in the section devoted to numerical simulations , the direct simulation of eq . ( [ dyn2d ] ) seems to display a scaling solution with @xmath387 for numerically accessible densities . strictly speaking , this is totally excluded by the above equation , except if one allows @xmath388 to very slowly depend on the density or @xmath350 . for a given @xmath350 , we thus want to solve eq . ( [ scacol2d ] ) , where the boundary conditions will ultimately select the effective value of @xmath388 , and that of @xmath363 . more precisely , once we impose @xmath384 , and the condition of eq . ( [ dadtg ] ) , we end up with a shooting problem for @xmath389 and @xmath388 . for large @xmath350 , and @xmath390 , it is clear that the non linear term of the right - hand side of eq . ( [ scacol2d ] ) becomes irrelevant , and we drop it from now on . in order to understand the origin of this shooting problem , and to obtain an accurate estimate of @xmath388 , let us solve eq . ( [ scacol2d ] ) in the limit of very large @xmath350 , in the range @xmath391 . in this regime , eq . ( [ scacol2d ] ) simplifies to the following equation @xmath392\omega = vh''+2h ' , \label{sca2dsimp}\ ] ] where @xmath393 let us now multiply this equation by @xmath394 and integrate the resulting equation . after elementary manipulations , we obtain @xmath395h=-\frac{\omega c}{4 t } v^{1-\gamma}- \frac{\omega a^{1-\gamma}}{2-\gamma}v^{-1}+(2-\gamma)(3-\gamma)v^{1-\gamma } \int_v^{+\infty}w^{\gamma-3}h(w)\,dw,\label{eqf}\ ] ] where @xmath396 , which has been defined in eq . ( [ asymf ] ) , appears here as an integration constant . then , one can integrate this differential equation which leads to the following self - consistent relation for @xmath233 : @xmath397 where @xmath398 is defined as the opposite of the right - hand side of eq . ( [ eqf ] ) : @xmath399 eq . ( [ sca2dsimp ] ) implies that @xmath400 , when @xmath401 ( of course , this apparent divergence does not occur in the full dynamical equation eq . ( [ scacol2d ] ) ) . considering the prefactor @xmath402 in eq . ( [ eqff ] ) , this behavior can be obtained if and only if @xmath403 as @xmath404 is expected to go to zero for large @xmath350 as @xmath405 ( see eq . ( [ omega ] ) ) , the dominant contribution of the integral of the third term in the definition of @xmath398 comes from the large @xmath406 region , for which @xmath233 can be replaced by its asymptotic form . hence , defining @xmath407 and @xmath408 , and using eq . ( [ omega ] ) , the condition expressed in eq . ( [ cond1 ] ) can be rewritten @xmath409 as @xmath410 is of order @xmath294 , we find that @xmath411 as @xmath412 . more precisely , in this limit , @xmath413 is the solution of the following implicit equation @xmath414 where @xmath415 . finally , we obtain @xmath416^{-1})\right ) . \label{expe}\ ] ] in conclusion , although the solution is not strictly speaking a true scaling solution , the explicit dependence of @xmath388 on @xmath350 is so weak that an apparent scaling should be seen with an effective @xmath388 almost constant for a wide range of values of @xmath350 . hence , the total density profile is the sum of the scaling profile obtained at @xmath343 with a @xmath417 weight ( behaving as a dirac peak of weight @xmath417 , at @xmath268 ) and of a pseudo - scaling solution associated to an effective scaling exponent slowly converging to @xmath2 . let us illustrate quantitatively the time dependence of @xmath381 . for example , taking arbitrarily @xmath418 ( the dependence on @xmath34 is weak and vanishes for large @xmath350 ) , eq . ( [ impe ] ) and eq . ( [ expe ] ) respectively lead to @xmath419 and @xmath420 , and to @xmath421 and @xmath422 ( note that the error between the asymptotic expansion of eq . ( [ expe ] ) and the implicit expression first grows before slowly decaying for @xmath423 ! ) . finally , for the maximum value of @xmath350 accessible numerically of order @xmath424 , we expect to observe an apparent scaling solution with @xmath425 , or @xmath426 . in this subsection , we present numerical simulations concerning the two - dimensional case . indeed , the three - dimensional case has been extensively studied in @xcite . it has been shown that the scaling function as well as the corrections to scaling ( which have been calculated for the canonical ensemble in @xcite ) are perfectly described by the theory . in addition , as the system behaves qualitatively the same for any dimension @xmath24 in both thermodynamical ensembles , we have decided to focus on the numerical study of the @xmath7 case , which displays some very rich behaviors , as exemplified in the present section . we consider the system in the canonical ensemble , as the gravitational collapse does not occur in the microcanonical ensemble . in fig . [ colld_fig1 ] , we show the scaling function at @xmath343 , as given by eq . ( [ scarho2d ] ) , finding a perfect agreement . in fig . [ colld_fig2 ] , we also display @xmath427 as a function of @xmath428 , and find an asymptotic behavior fully compatible with that given by eq . ( [ dadt ] ) . below @xmath343 , and in the accessible range of @xmath350 ( up to @xmath429 ) , we find an apparent scaling regime with @xmath430 , as predicted in sec . [ sec_tinftc ] . this is illustrated in fig . [ colld_fig3 ] , for @xmath431 . note that the effective @xmath388 or @xmath124 can also be extracted from the time evolution of @xmath349 or the central density ( see eq . ( [ dadtg ] ) ) . in fig . [ colld_fig4 ] , we show that this way of measuring @xmath388 is fully compatible with the value of the effective exponents @xmath430

finally , we solve the problem in , which displays rather rich and peculiar features . laboratoire de physique quantique ( umr 5626 du cnrs ) , universit paul sabatier , + 118 , route de narbonne , 31062 toulouse , france + e - mail : [email protected] & [email protected]_

we address the thermodynamics ( equilibrium density profiles , phase diagram , instability analysis ... ) and the collapse of a self - gravitating gas of brownian particles in dimensions , in both canonical and microcanonical ensembles . in the canonical ensemble , we derive the analytic form of the density scaling profile which decays as , with . in the microcanonical ensemble , we show that decays as , where is a non - trivial exponent . we derive exact expansions for and in the limit of large . finally , we solve the problem in , which displays rather rich and peculiar features . laboratoire de physique quantique ( umr 5626 du cnrs ) , universit paul sabatier , + 118 , route de narbonne , 31062 toulouse , france + e - mail : [email protected] & [email protected]_

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in this paper , we have studied the boltzmann - poisson equation and the smoluchowski - poisson system in various dimensions of space . our study shows in particular how the nature of the problem changes as we pass from @xmath17 to @xmath7 . we showed that the dimension @xmath7 is critical in the sense that the results obtained for @xmath24 diverge if they are naively extrapolated to @xmath7 . on a physical point of view , the two - dimensional problem differs from the @xmath24 case in two respects : in the 2d case , the central density of the equilibrium state is infinite at the critical temperature @xmath339 while it is finite at @xmath339 in higher dimensions . on the other hand , in @xmath7 , the self - similar collapse results in a dirac peak which contains a finite fraction of mass , while for @xmath24 , the mass contained in the core tends to zero at the collapse time ( but a dirac peak is always formed in the canonical ensemble after @xmath260 as discussed in appendix [ sec_cold ] ) . we have also evidenced another characteristic dimension @xmath18 at which the nature of the problem changes . for @xmath116 the classical spiral characterizing isothermal spheres in the physical three - dimensional space disappears . however , since the points in the spiral correspond to unstable states , that are therefore unphysical , this transition at @xmath18 is not so critical and indeed the nature of the self - similar collapse does not show any transition at that dimension . it is interesting to note that the dependance of the phase diagram in the @xmath461 and @xmath108 planes with the dimension of space @xmath0 shows some resemblance with the dependance of the phase diagram of confined polytropic spheres with the index @xmath210 of the polytrope @xcite . an extension of our study would be to relax the high friction limit and consider solutions of the kramers - poisson system and other relaxation equations described in ref . these equations are expected to display qualitatively similar behaviors than those described here ( i.e. gravitational collapse , finite time singularity , self - similar solutions , ... ) but their study appears to be of considerable difficulty since we now need to consider the evolution of the system in phase space . we hope to come to that problem in future publications .

we address the thermodynamics ( equilibrium density profiles , phase diagram , instability analysis ... ) and the collapse of a self - gravitating gas of brownian particles in dimensions , in both canonical and microcanonical ensembles . in the canonical ensemble , we derive the analytic form of the density scaling profile which decays as , with . in the microcanonical ensemble , we show that decays as , where is a non - trivial exponent .

we address the thermodynamics ( equilibrium density profiles , phase diagram , instability analysis ... ) and the collapse of a self - gravitating gas of brownian particles in dimensions , in both canonical and microcanonical ensembles . in the canonical ensemble , we derive the analytic form of the density scaling profile which decays as , with . in the microcanonical ensemble , we show that decays as , where is a non - trivial exponent . we derive exact expansions for and in the limit of large . finally , we solve the problem in , which displays rather rich and peculiar features . laboratoire de physique quantique ( umr 5626 du cnrs ) , universit paul sabatier , + 118 , route de narbonne , 31062 toulouse , france + e - mail : [email protected] & [email protected]_

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since the discovery of ultra - luminous infrared galaxies ( ulirgs , l@xmath3@xmath410@xmath5 ) by the _ infrared astronomical satellite _ ( _ iras _ ) in the 1980 s ( e.g. , * ? ? ? * ) , it is widely accepted that ulirgs result from strong interactions / mergers between gas - rich disk galaxies . these mergers form elliptical galaxies and ulirgs are an important intermediate stage in the process during which at least a fraction of ulirgs manifest as dust - enshrouded qsos ( see , e.g. , * ? ? ? * ; * ? ? ? in addition , active galactic nuclei ( agns ) triggered by mergers tend to appear at the final merging stages ( e.g. , @xcite , @xcite , @xcite , @xcite and reference therein ) . there is mounting evidence that qsos with far - infrared ( fir ) excess have massive starbursts in their host galaxies . for example , @xcite investigated 9 qsos with fir excess and found that their host galaxies are tidally interacting or major merger systems with obvious recent star - forming activities . from the detections of mid - infrared ( mir)/firm , fir 35 - 350 @xmath1 m , and ir 8 - 1000@xmath1 m . ] emissions for felobals ( broad absorption line qsos with low - ionisation and iron absorption lines ) by multiband imaging photometer on _ spitzer _ ( mips ; * ? ? ? * ) on board the _ spitzer space telescope _ @xcite , @xcite find that all their 9 felobals are extremely infrared ( ir ) bright , and concluded that these qsos are in transition from ulirgs to classical qsos with ongoing or recent starbursts , because the iron absorption may be from iron ejected during starbursts . @xcite studied 31 qsos / seyfert1s selected from the local ulirg samples ( termed as ir qsos for simplicity ) . by comparing the fir spectral index of ir qsos with those of optically selected palomar - green qsos ( pg qsos ; @xcite ) , they argued that the fir excess of ir qsos relative to pg qsos is from massive starbursts and inferred star formation rate ( sfr ) in the host galaxies of ir qsos . recently , from studies of z@xmath06 qsos with strong sub - mm emissions , @xcite , @xcite and @xcite concluded that massive starbursts also exist in their host galaxies . the conclusion is consistent with the results of @xcite that high redshift ( sub)mm - loud qsos follow the same trend for fir to bolometric luminosities established by low redshift ir qsos @xcite . all these studies suggest that there exists a transitional stage , during which both the central black hole and the spheroidal component of qso hosts grow rapidly in a coeval fashion . however , there is still a debate about the origin of fir emission from qsos , because one can not firmly exclude the possibility that fir emissions are from dust tori heated by central agns ( for detailed discussions see * ? ? ? moreover , from the molecular gas properties of pg qsos with ir excess and comparisons with ulirgs , @xcite find that the @xmath6 and @xmath7 ratios for pg qsos are higher than those of ulirgs , implying that agns contribute significantly to the dust heating and hence to the fir emission . therefore , other sfr indicators besides the fir emission for qsos are important for further understanding the coeval growth of supermassive black holes and their host galaxies . recently , the quest ( quasar and ulirg evolution study ) group ( see * ? ? ? * ; * ? ? ? * ) reported the detection of polycyclic aromatic hydrocarbon ( pah ) emission features in pg qsos using the infrared spectrograph ( irs ) on _ spitzer _ @xcite . for 11 out of 26 pg qsos pahs have been clearly detected . furthermore , the average spectrum of the undetected 15 pg qsos also shows pah features . since the pah emissions are closely related to star formation , not to agns ( see , e.g. , * ? ? ? * ) , such detections strongly suggest that star formation occurs widely in qsos . their analysis shows that 30% or more fir emission in these pg qsos is from starbursts . furthermore , given that the low - excitation fine - structure emission line [ neii ] 12.81@xmath1 m is one of the dominant emission lines of hii regions and that the pah molecules are easily destroyed by high energy photons from agns ( e.g. , * ? ? ? * ) , [ neii ] emission may be an alternative , perhaps even better , tracer of star formation for qsos ( see 4 ) . in this paper we study the mir spectroscopic properties of ir qsos based on _ spitzer _ irs observations , and examine their connections and evolutionary relations to ulirgs and pg qsos . the sample selection , data acquisition and reduction are described in sect . 2 and 3 . the major results and discussions are given in sect . finally we summarise our results in sect . we adopt cosmological parameters _ km s@xmath9 mpc@xmath9 , @xmath10@xmath11=0.3 , and @xmath10@xmath12=0.7 throughout this paper .

we analyse mid - infrared ( mir ) spectroscopic properties for 19 ultra - luminous infrared quasars ( ir qsos ) in the local universe based on the spectra from the infrared spectrograph on board the _ spitzer space telescope_. the mir properties of ir qsos are compared with those of optically - selected palomar - green qsos ( pg qsos ) and ultra - luminous infrared galaxies ( ulirgs ) . [ firstpage ] galaxies : active galaxies : evolution galaxies : interactions quasars : general infrared : galaxies

we analyse mid - infrared ( mir ) spectroscopic properties for 19 ultra - luminous infrared quasars ( ir qsos ) in the local universe based on the spectra from the infrared spectrograph on board the _ spitzer space telescope_. the mir properties of ir qsos are compared with those of optically - selected palomar - green qsos ( pg qsos ) and ultra - luminous infrared galaxies ( ulirgs ) . the average mir spectral features from to 30 m , including the spectral slopes , 6.2 m pah emission strengths and [ neii ] 12.81 m luminosities of ir qsos , differ from those of pg qsos . in contrast , ir qsos and ulirgs have comparable pah and [ neii ] luminosities . these results are consistent with ir qsos being at a transitional stage from ulirgs to classical qsos . we also find that the colour index(30 , 15 ) is a good indicator of the relative contribution of starbursts to agns for all qsos . correlations between the [ neii ] 12.81 m and pah 6.2 m luminosities and those between the [ neii ] , pah with 60 m luminosities for ulirgs and ir qsos indicate that both [ neii ] and pah luminosities are approximate star formation rate indicators for ir qsos and starburst - dominated galaxies ; the scatters are , however , quite large ( 0.7 to 0.8 dex ) . finally the correlation between the ew ( pah 6.2 m ) and outflow velocities suggests that star formation activities are suppressed by feedback from agns and/or supernovae . [ firstpage ] galaxies : active galaxies : evolution galaxies : interactions quasars : general infrared : galaxies

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by comparing the mir spectroscopic properties of ir qsos , ulirgs and pg qsos , we found that the indicators of relative contributions of starbursts to agns ( such as colour index @xmath2(30 , 15 ) and ew [ pah 6.2@xmath1 m ] ) for ir qsos are between those of ulirgs and pg qsos . these results are consistent with the findings of @xcite and @xcite that ( at least some ) infrared luminous qsos ( ir qsos ) are at a transitional stage from ulirgs to classical qsos . below we consider the star formation rates and agn / star formation feedback in more detail . as we argued , the agn contribution to [ neii ] emission for ulirgs and ir qsos is probably very small , and there is a tight correlation between [ neii]12.81@xmath1 m and pah 6.2@xmath1 m luminosities ( see [ sec : statis ] ) . we examine in more detail how they can be used as approximate sfr indicators for ulirgs and ir qsos . [ fig_sfr ] shows the [ neii]12.81@xmath1 m ( top panel ) and pah 6.2@xmath1 m ( bottom panel ) luminosities versus the 60@xmath1 m luminosity for ir qsos , pg qsos and ulirgs with firmly detected [ neii]12.81@xmath1 m and pah 6.2@xmath1 m emissions . a spearman rank - order analysis show that both correlations are significant at @xmath4 99.99@xmath23 level . the dashed lines in fig . [ fig_sfr ] represent the least - squares regression fits : @xmath37 @xmath38 the fitting formula ( 2 ) is consistent with that of @xcite for star - forming galaxies ( within the large errors ) . note that our sample objects have much higher @xmath39 and [ neii ] luminosities than their star - forming galaxies . thus both [ neii ] 12.81@xmath1 m and pah 6.2@xmath1 m luminosities can be used as approximate sfr indicators not only for normal star - forming galaxies , but also for galaxies with high infrared luminosities , such as ulirgs and ir qsos ( see @xcite and @xcite ) . however , the mean scatters ( about 0.7 to 0.8 dex ) in the relation of [ neii]12.81@xmath1 m , pah 6.2@xmath1 m with @xmath39 luminosities are larger than that ( about 0.6 dex ) of star - forming galaxies with lower infrared luminosity ( @xcite ) . comparing fig . [ fig_sfr ] with fig . [ fig_ne2pah ] , one can see that the scatter in the relation of [ neii]12.81@xmath1 m vs. pah 6.2@xmath1 m luminosities ( about 0.6 dex ) is smaller than that in the relations of [ neii]12.81@xmath1 m , pah 6.2@xmath1 m luminosities with l(60@xmath1 m ) . it is also clear that most large scatters are from ulirgs . this is perhaps not surprising since the range in the 9.7@xmath1 m silicate absorption depth among ulirgs is quite large ( see @xcite , @xcite ) . in short , the large scatters for ulirgs seen in the relations may be due to complicated , patchy extinctions among these galaxies in the mir band . a detailed discussion on extinction for ulirgs can be found in @xcite . one explanation for the observed correlation between spheroidal and black hole mass ( e.g. , * ? ? ? * ; * ? ? ? * ) is that star formation and the growth of central black holes may be self - regulated : agns / star formation can drive nuclear outflows which in turn suppress further cooling and star formation ( @xcite ) . while the detailed processes are still to be understood , it is now increasingly clear that feedback and outflows play an important role in galaxy formation and evolution . so far most observational evidence for agn feedback is from radio observations at the centre of clusters or groups of galaxies @xcite . on the galaxy scale , evidence is still limited . as discussed above , ir qsos have high sfrs and accretion rates @xcite , outflow properties in these objects may thus provide hints on the feedback processes on galaxy or group scale . it is well known that low - ionisation broad absorption line qsos ( lobal qsos ) comprise about 15% of bal qso population . they are defined as a subclass of bal qsos with an obvious blueshifted absorption in mg ii @xmath40@xmath402795,2802 and other low - ionisation species @xcite . such absorption troughs arise from resonance absorption by outflowing gas and dust @xcite . in addition , there is a rare class of lobal qsos , showing absorption features from excited iron ( termed as felobal qsos ) . the outflow velocities for most bal qsos span a large range , up to a few times @xmath41 kms@xmath9 , which may be formed on a scale of @xmath42 and directly associated with the wind from an accretion disk or molecular torus @xcite . however , recent spectral analyses based on keck observations for lobal qsos or felobal qsos reveal that the outflow velocities of some lobal qsos range from several hundred to several thousand kms@xmath9 and the wind is from regions of a few hundred pc ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , which is much larger than the central engine of agns , but similar to the size of the nuclear starburst region of ulirgs @xcite . on the other hand , @xcite studied four lobal qsos at [email protected] ( mrk 231 , iras 14026@xmath444341 , iras f07599 + 6508 , pg 1700 + 518 ; all four are in our sample ) and found that all are ulirgs with merging signatures . they argued that lobal qsos can not simply be explained by orientation effects , rather , they are directly related to young systems , still surrounded by gas and dust . it represents a short stage in the early life of a large fraction of qsos . moreover , @xcite reported the detections of mid / far - infrared emission from 9 felobal qsos by mips . they found that all of their objects are ir bright with infrared luminosities as high as ulirgs . thus all lobal qsos and felobal qsos with mir to fir information are infrared ultra - luminous , suggesting a link among lobal qsos , felobal qsos and ir qsos . for lobal qsos or felobal qsos , the velocities of outflows can be measured from blueshifted absorption lines . unfortunately it is still unclear whether most ir qsos are lobal qsos or felobal qsos , because not many ir qsos have been observed in the uv . however , there are measurements for the blueshifts in the permitted optical emission lines for our ir qso sample @xcite . the line profiles often contain two gaussian components , one broad and one narrow . the outflow velocities are determined by the blueshift of the broad gaussian component relative to the narrow component of permitted emission lines ( h@xmath45 ) for ir qsos ( see * ? ? ? we assume the blueshifted broad gaussian component is related to the outflow of clouds @xcite . [ fig_outflow ] shows the correlation between ew ( pah 6.2@xmath1 m ) and outflow velocities for ir qsos . as the outflow velocity increases , the ew ( pah 6.2@xmath1 m ) decreases . since the ew ( pah 6.2@xmath1 m ) expresses the relative contribution of star formation to agn in qsos ( see @xmath204.2 ) , the correlation shown in fig . [ fig_outflow ] implies that qsos with higher outflow velocities have a lower ratio of sfr to accretion rate . it may be because more energetic agns and central massive starbursts can drive faster outflows which then suppress or even quench star formation by heating up or expelling the cold gas and dust in the qso hosts , leading to a lower ratio of sfr to accretion rate . another possibility is that the higher velocity outflows are more efficient in ejecting dust cocoons of agns , leading to agns becoming the dominant source compared with starbursts . we should caution , however , that the sample shown in fig . [ fig_outflow ] is small ; a larger sample would allow us to better understand the relative importance of star formation and agn in feedback and driving outflows .

these results are consistent with ir qsos being at a transitional stage from ulirgs to classical qsos . correlations between the [ neii ] 12.81 m and pah 6.2 m luminosities and those between the [ neii ] , pah with 60 m luminosities for ulirgs and ir qsos indicate that both [ neii ] and pah luminosities are approximate star formation rate indicators for ir qsos and starburst - dominated galaxies ; the scatters are , however , quite large ( 0.7 to 0.8 dex ) . finally the correlation between the ew ( pah 6.2 m ) and outflow velocities suggests that star formation activities are suppressed by feedback from agns and/or supernovae .

we analyse mid - infrared ( mir ) spectroscopic properties for 19 ultra - luminous infrared quasars ( ir qsos ) in the local universe based on the spectra from the infrared spectrograph on board the _ spitzer space telescope_. the mir properties of ir qsos are compared with those of optically - selected palomar - green qsos ( pg qsos ) and ultra - luminous infrared galaxies ( ulirgs ) . the average mir spectral features from to 30 m , including the spectral slopes , 6.2 m pah emission strengths and [ neii ] 12.81 m luminosities of ir qsos , differ from those of pg qsos . in contrast , ir qsos and ulirgs have comparable pah and [ neii ] luminosities . these results are consistent with ir qsos being at a transitional stage from ulirgs to classical qsos . we also find that the colour index(30 , 15 ) is a good indicator of the relative contribution of starbursts to agns for all qsos . correlations between the [ neii ] 12.81 m and pah 6.2 m luminosities and those between the [ neii ] , pah with 60 m luminosities for ulirgs and ir qsos indicate that both [ neii ] and pah luminosities are approximate star formation rate indicators for ir qsos and starburst - dominated galaxies ; the scatters are , however , quite large ( 0.7 to 0.8 dex ) . finally the correlation between the ew ( pah 6.2 m ) and outflow velocities suggests that star formation activities are suppressed by feedback from agns and/or supernovae . [ firstpage ] galaxies : active galaxies : evolution galaxies : interactions quasars : general infrared : galaxies

0807.3653

i

in this work , we studied the mir spectral properties of low - redshift ir qsos based on spectroscopic observations with _ spitzer _ irs , and compared their properties with those of ulirgs and optically - selected pg qsos . the following are our main results : \1 . the average mir spectra , mir spectral slopes , 6.2@xmath1 m pah emission strengths and [ neii ] 12.81@xmath1 m luminosities of ir qsos are distinct from those of pg qsos . the mir properties of ir qsos are intermediate between ulirgs and optically - selected qsos , indicating that ir qsos are at a transitional stage from ulirgs to classical qsos . \2 . from the correlations between @xmath2(30 , 15 ) with @xmath2(60 , 25 ) , fir excess l@xmath30/l@xmath26 , and ew ( pah 6.2@xmath1 m ) for both ir qsos and pg qsos , we find that the mir colour index @xmath2(30 , 15 ) is a good indicator of the relative contribution of starbursts to agns for all qsos . both pah and [ neii]12.81@xmath1 m luminosities of ir qsos are in the same range as those of ulirgs , but are one order of magnitude higher than those of pg qsos ( see fig . [ fig_hist ] ) . from the tight correlation between pah 6.2@xmath1 m and [ neii ] 12.81@xmath1 m luminosities for ir qsos , ulirgs and pah detected pg qsos , and the fact that the l@xmath29}$]/l@xmath26 ratio for ir qsos is about one order of magnitude higher than that of classical qsos , we conclude that the [ neii ] 12.81@xmath1 m emission of ir qsos is dominated by star formation , thus their luminosity can be used as an approximate indicator of their sfrs . outflows in ir qsos play an important role in suppressing star formation by heating and/or expelling cold gas surrounding nuclei of qsos . thus ir qsos are an important observational sample to investigate agn and star formation feedback processes .

the average mir spectral features from to 30 m , including the spectral slopes , 6.2 m pah emission strengths and [ neii ] 12.81 m luminosities of ir qsos , differ from those of pg qsos . in contrast , ir qsos and ulirgs have comparable pah and [ neii ] luminosities . we also find that the colour index(30 , 15 ) is a good indicator of the relative contribution of starbursts to agns for all qsos .

we analyse mid - infrared ( mir ) spectroscopic properties for 19 ultra - luminous infrared quasars ( ir qsos ) in the local universe based on the spectra from the infrared spectrograph on board the _ spitzer space telescope_. the mir properties of ir qsos are compared with those of optically - selected palomar - green qsos ( pg qsos ) and ultra - luminous infrared galaxies ( ulirgs ) . the average mir spectral features from to 30 m , including the spectral slopes , 6.2 m pah emission strengths and [ neii ] 12.81 m luminosities of ir qsos , differ from those of pg qsos . in contrast , ir qsos and ulirgs have comparable pah and [ neii ] luminosities . these results are consistent with ir qsos being at a transitional stage from ulirgs to classical qsos . we also find that the colour index(30 , 15 ) is a good indicator of the relative contribution of starbursts to agns for all qsos . correlations between the [ neii ] 12.81 m and pah 6.2 m luminosities and those between the [ neii ] , pah with 60 m luminosities for ulirgs and ir qsos indicate that both [ neii ] and pah luminosities are approximate star formation rate indicators for ir qsos and starburst - dominated galaxies ; the scatters are , however , quite large ( 0.7 to 0.8 dex ) . finally the correlation between the ew ( pah 6.2 m ) and outflow velocities suggests that star formation activities are suppressed by feedback from agns and/or supernovae . [ firstpage ] galaxies : active galaxies : evolution galaxies : interactions quasars : general infrared : galaxies

0910.3133

i

ever since the work of lennard - jones @xcite has the interaction between atoms and surfaces been of interest in many fields of physics , chemistry and technology . the seminal work by casimir and polder @xcite demonstrated that the shift in atomic energy levels close to a conductor is a probe for the quantum fluctuations of the electromagnetic field , a key concept of quantum electrodynamics ( qed ) . in this context , a nonzero temperature becomes relevant for several aspects of the atom - surface interaction : thermally excited motion of the surface ( phonons ) and inelastic scattering of atomic beams @xcite , occupation of excited atomic energy levels , and enhancement of field fluctuations due to thermal photons @xcite . the latter aspect is usually associated with distances from the surface larger than the thermal wavelength @xmath1 , approximately @xmath2 at room temperature . the free energy of interaction typically shows a change in power law with distance around this point : generally , it is enhanced with respect to zero temperature and becomes proportional to @xmath3 . this is the classical limit where the interaction is mainly entropic in character @xcite . experimental progress in recent years has achieved the sensitivity required to detect the small energy shifts that occur at distances on the order of @xmath4 , making use of the exquisite control over the motion of atomic beams ( beam deflection @xcite , quantum reflection @xcite ) or clouds of ultracold laser - cooled atoms @xcite . the latter can be handled precisely in miniaturized traps implemented near solid state surfaces known as _ atom chips _ these devices use optical or magnetic fields for trapping and can hold atomic clouds at distances down to a few microns . here , the atom - surface interaction manifests itself typically as a distortion of the trapping potential ( loss of atoms through tunneling to the surface or change in the trap oscillation frequency ) . therefore , the design of such setups requires exact knowledge of atom - surface interactions and conversely , theory predictions can be tested experimentally with high precision . a surprising result of the research on atom chips is the importance of magnetic field fluctuations near the surface arising from thermally excited currents in the material of the chip ( johnson noise related to ohmic dissipation ) . these fluctuations couple to the spin magnetic moment of the trapped atoms and are known to provoke the loss of atoms from the trap by flipping the sign of the potential @xcite . these losses are a main obstacle for technical applications and further down - scaling of atom chips . predictions that superconducting materials reduce the spin - flip induced losses significantly have recently been backed by trap lifetime measurements @xcite . in this paper , we address the magnetic dipole contribution to the atom - surface ( casimir - polder ) interaction including nonzero temperature . one would expect this to be a small correction to the electric dipole coupling @xcite because of the smallness of the transition matrix elements @xcite . yet , the strong magnetic mode density close to a metallic surface @xcite and experimental evidence for magnetic spin flips call for a reconsideration of the magnetic contribution . in addition , the thermal occupation of photonic modes is quite relevant because magnetic transitions occur at much lower frequencies than electric ones , leading to a stronger temperature dependence . finally , it is well - known that dispersion forces between dielectric and magnetic materials can be repulsive @xcite , as has been shown for the magnetic casimir - polder interaction at @xmath5 in ref.@xcite . we were thus led to investigate whether at distances beyond @xmath4 the total atom - surface interaction might be reduced due to the magnetic contribution . in this work , we calculate the magnetic casimir - polder free energy of interaction at different temperatures and consider a few well - known models for the electromagnetic response of the surface . since ohmic losses are crucial for the thermal behavior , it is highly interesting to compare both normal metals and superconductors . the latter are described here in the frame of the two - fluid model and bardeen - cooper - schrieffer ( bcs ) theory @xcite . we demonstrate that the magnetic atom - surface coupling has very peculiar features unknown from its electrical equivalent . we find that for normal conductors at nonzero temperature , the magnetic dipole contribution to the interaction is reduced , while it is enhanced for superconductors and in certain non - equilibrium situations . this resembles the macroscopic casimir interaction between two dissipative plates , where the correct calculation of the force at large distances and nonzero temperatures has been the subject of debate @xcite . this article is organized as follows . in sec . [ atom - surface interaction ] , we give a brief review of the formalism used to calculate atom - surface interactions . section [ polarizabilities and green tensors ] presents the specific forms of the response functions and the experimental setups they describe . we also give expressions for the green s tensor in different asymptotic regimes of the distance between the atom and the surface . the magnetic casimir - polder free energy and entropy of an atom near metallic or superconducting surfaces at zero temperature is calculated in sec . [ magnetic casimir - polder ] . section [ casimir - polder interaction at nonzero temperature ] covers the effects at nonzero temperature and discusses the dissipative reduction in the interaction and questions connected to the entropy . non - thermal ( out - of - equilibrium ) states of the atoms that occur typically in experimental setups are investigated in section [ non - thermal states ] . we conclude summarizing and discussing the main results . further technical details are given in the appendices .

we analyze the magnetic dipole contribution to atom - surface dispersion forces . we use thermal response theory for the surface material and discuss both normal metals and superconductors . the asymptotes of the free energy of interaction and of the entropy are calculated analytically over a large range of distances . near a superconductor , the onset of dissipation at the phase transition strongly changes the interaction , including a discontinuous entropy . we discuss the similarities with the casimir interaction between two surfaces and suggest that precision measurements of the atom - surface interaction may shed light upon open questions around the temperature dependence of dispersion forces between lossy media .

we analyze the magnetic dipole contribution to atom - surface dispersion forces . unlike its electrical counterpart , it involves small transition frequencies that are comparable to thermal energy scales . a significant temperature dependence is found near surfaces with a nonzero dc conductivity , leading to a strong suppression of the dispersion force at . we use thermal response theory for the surface material and discuss both normal metals and superconductors . the asymptotes of the free energy of interaction and of the entropy are calculated analytically over a large range of distances . near a superconductor , the onset of dissipation at the phase transition strongly changes the interaction , including a discontinuous entropy . we discuss the similarities with the casimir interaction between two surfaces and suggest that precision measurements of the atom - surface interaction may shed light upon open questions around the temperature dependence of dispersion forces between lossy media .

1109.2680

i

the consequences of deforming the canonical commutation relation between the position and momentum operators to @xmath9 \;=\ ; i\hbar ( 1 + \beta \hat{p}^2 ) \label{commutationrelation}\ ] ] have been studied in various contexts by many authors @xcite . the main motivation behind this was to use such deformed quantum mechanical systems as models which obey the minimal length uncertainty relation ( mlur ) @xcite : @xmath10 this relation is expected on fairly generic grounds in quantum gravity @xcite , and has been observed in perturbative string theory @xcite . the mlur implies the existence of a minimal length @xmath11 below which the uncertainty in position , @xmath12 , can not be reduced . for quantum gravity , @xmath13 would be the planck scale , @xmath14 , while for string theory this would be the string length scale , @xmath15 . the investigation of said model systems could be expected to shed some light on the nature of these , and other , theories which possess a minimal length scale . as a function of @xmath3 when they obey the minimal length uncertainty relation , eq . ( [ mlur ] ) , is shown in red . the blue line indicates @xmath16 while the green line indicates @xmath17 . , width=302 ] note that the uncertainty in position which saturates the mlur bound behaves as @xmath18 for @xmath19 , while @xmath4 for @xmath20 , as illustrated in fig . [ mlurfig ] . while we are familiar with the @xmath18 behavior from canonical quantum mechanics , the @xmath4 behavior is quite novel . it behooves us to understand how it can come about , and how it can coexist with the canonical @xmath18 behavior within a single quantum mechanical system . to this end , we calculate @xmath12 and @xmath3 for the energy eigenstates of the harmonic oscillator , @xmath21 the wave - functions of which were derived explicitly in ref . we find that all of the eigenstates of this hamiltonian inhabit the @xmath2 branch , and not the other branch , as long as both the spring constant @xmath22 and the mass @xmath23 remain positive . the cross - over happens when the inverse of the mass , @xmath24 , is allowed to decrease through zero into the negative , in which case all the energy eigenstates will move smoothly over to the @xmath6 branch . the objective of this paper is to provide a detailed account of this result . in the following , we solve the schrdinger equation for the above hamiltonian without assuming a specific sign for the mass @xmath23 . the spring constant @xmath22 is kept positive throughout . we find that the ` inverted ' harmonic oscillator with @xmath25 and @xmath7 admits an infinite ladder of normalizable positive energy eigenstates provided that @xmath26 where @xmath27^{1/4 } \label{adef}\ ] ] is the characteristic length scale of the harmonic oscillator . the uncertainties @xmath12 and @xmath3 are calculated for the energy eigenstates , and the above mentioned cross - over through @xmath28 from the @xmath2 branch to the @xmath29 branch is demonstrated . we then take the classical limit of our deformed commutation relation and work out the evolution of the classical harmonic oscillator for both the positive and negative mass cases . it is found that for the ` inverted ' @xmath7 case , the time it takes for the particle to travel from @xmath30 to @xmath31 is finite , demanding the compactification of @xmath32-space , and also rendering the classical probability of finding the particle near the origin finite . this provides a classical explanation of why ` bound ' states are possible for the ` inverted ' harmonic oscillator in this modified mechanics .

we analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics , namely , that in which the commutator between the position and momentum operators is given by=i\hbar(1+\beta \hat{p}^2)$ ] . this deformed commutation relation leads to the minimal length uncertainty relation , which implies that at small while at large . we find that the uncertainties of the energy eigenstates of the normal harmonic oscillator ( ) , derived in ref . the hilbert space in the inverted case admits an infinite ladder of positive energy eigenstates provided that^{1/4}$ ] .

we analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics , namely , that in which the commutator between the position and momentum operators is given by=i\hbar(1+\beta \hat{p}^2)$ ] . this deformed commutation relation leads to the minimal length uncertainty relation , which implies that at small while at large . we find that the uncertainties of the energy eigenstates of the normal harmonic oscillator ( ) , derived in ref . , only populate the branch . the other branch , , is found to be populated by the energy eigenstates of the ` inverted ' harmonic oscillator ( ) . the hilbert space in the inverted case admits an infinite ladder of positive energy eigenstates provided that^{1/4}$ ] . correspondence with the classical limit is also discussed .

hep-th0401069

i

we have studied in detail the quantum process in which a cosmic string breaks in an anti - de sitter ( ads ) background and a pair of black holes is created at the ends of the string . the energy to materialize and accelerate the black holes comes from the strings tension . the analysis of this process in a flat background ( @xmath7 ) has been carried in @xcite , while in a de sitter background ( @xmath8 ) it has been done in @xcite . in an ads background this is the only study done in the process of production of a pair of correlated black holes with spherical topology . we remark that in principle our explicit values for the pair creation rates also apply to the process of pair creation in an external electromagnetic field , with the acceleration being provided in this case by the lorentz force instead of being furnished by the string tension . indeed , there is no ads ernst solution , and thus we can not discuss analytically the process . however , physically we could in principle consider an external electromagnetic field that supplies the same energy and acceleration as our strings and , from the results of the @xmath7 case ( where the pair creation rates in the string and electromagnetic cases agree ) , we expect that the pair creation rates found in this paper do not depend on whether the energy is being provided by an external electromagnetic field or by a string . it is well known that the ads background is attractive , i.e. , an analysis of the geodesic equations indicates that particles in this background are subjected to a potential well that attracts them ( see also appendix [ sec : a2 ] ) . therefore , if we have a virtual pair of black holes and we want to turn them real , we will have to furnish a sufficient force that overcomes this cosmological background attraction . we then expect that pair creation is possible only if the strings tension and the associated acceleration @xmath0 is higher than a critical value . we have confirmed that this is indeed the case : in the ads background , black holes can be pair produced only with an acceleration higher than @xmath1 . we have constructed the saddle point solutions that mediate the pair creation process through the analytic continuation of the ads c - metric , and we have explicitly computed the pair creation rate of the process . the ads pair creation rate reduces to the corresponding one of the flat case @xcite when we set @xmath7 . we have concluded that , for a pair of black holes that is subjected to a fixed @xmath6 and @xmath0 backgrounds , the pair creation probability decreases when the mass or charge of the black holes increases . moreover , when we fix the mass and the charge of the black holes , the probability they have to be pair created increases when the acceleration provided by the string increases . these results are physically expected , as an heuristic derivation done in appendix [ sec : a2 ] confirms . this process has also a clear analogy with a thermodynamical system , with the mass density of the string ( that is proportional to @xmath0 ) being the analogue of the temperature @xmath293 . indeed , from the boltzmann factor , @xmath294 ( where @xmath295 is the boltzmann constant ) , one knows that a higher background temperature makes the nucleation of a particle with energy @xmath296 more probable . equivalently , a higher acceleration provided by the string makes the creation of the black hole pair more probable . [ h ] general behavior of the black hole pair creation rate @xmath297 as a function of the acceleration @xmath0 provided by the strings , when a cosmic string breaks : ( a ) in a flat background ( @xmath7 ) @xcite , ( b ) in a ds background ( @xmath8 ) @xcite , and ( c ) in an ads background ( @xmath2 ) . , title="fig:",height=480 ] for the benefit of comparison , in fig . [ pc rates_ads ] we schematically represent the general behavior of the black hole pair creation rate @xmath297 as a function of the acceleration @xmath0 provided by the strings , when a cosmic string breaks in the three cosmological constant backgrounds . in a flat background [ see fig . [ pc rates_ads].(a ) ] , the pair creation rate is zero when @xmath41 @xcite . in this case , the flat c - metric reduces to a single black hole , and since we are studying the probability of pair creation , the corresponding rate is naturally zero . this does not mean that a single black hole can not be materialized from the quantum vacuum , it only means that this latter process is not described by the c - metric . the creation probability of a single black hole in a hot bath has been considered in @xcite . in a ds background [ see fig . [ pc rates_ads].(b ) ] , the pair creation rate is not zero when @xmath41 @xcite . this means that even in the absence of the string , the positive cosmological constant is enough to provide the energy to materialize the black hole pair @xcite . if in addition one has an extra energy provided by the string , the process becomes more favorable @xcite . in the ads case [ see fig . [ pc rates_ads].(c ) ] , the negative cosmological constant makes a negative contribution to the process , and black hole pair creation is possible only when the acceleration provided by the strings overcomes the ads background attraction . the branch @xmath298 represents the creation probability of a single black hole when the acceleration provided by the broken string is not enough to overcome the ads attraction , and was not studied in this paper . we have also verified that ( as occurs with pair creation in other backgrounds ) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of @xmath299 , where @xmath300 is the gravitational entropy of the black hole . it is a pleasure to acknowledge conversations with jos p. s. lemos , vitor cardoso , and alfredo b. henriques . this work was partially funded by fundao para a cincia e tecnologia ( fct ) through project cern / fis/43797/2001 and peso / pro/2000/4014 . i also acknowledge finantial support from the fct through praxis xxi programme .

we analyze the quantum process in which a cosmic string breaks in an anti - de sitter ( ads ) background , and a pair of charged or neutral black holes is produced at the ends of the strings . the energy to materialize and accelerate the pair comes from the strings tension . in an ads background the acceleration of the produced black holes is necessarily greater than , where is the cosmological constant . only in this case the instantons that describe this process are constructed through the analytical continuation of the ads c - metric . then , we explicitly compute the pair creation rate of the process , and we verify that ( as occurs with pair creation in other backgrounds ) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of , where is the black hole horizon area .

we analyze the quantum process in which a cosmic string breaks in an anti - de sitter ( ads ) background , and a pair of charged or neutral black holes is produced at the ends of the strings . the energy to materialize and accelerate the pair comes from the strings tension . in an ads background this is the only study done in the process of production of a pair of correlated black holes with spherical topology . the acceleration of the produced black holes is necessarily greater than , where is the cosmological constant . only in this case the virtual pair of black holes can overcome the attractive background ads potential well and become real . the instantons that describe this process are constructed through the analytical continuation of the ads c - metric . then , we explicitly compute the pair creation rate of the process , and we verify that ( as occurs with pair creation in other backgrounds ) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of , where is the black hole horizon area . we also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the ads , flat and de sitter cases , and our ads results reduce to the ones of the flat case when .

astro-ph0505092

c

we studied the orientation of all pne of our sample ( without separating it in regions ) and we do not see a clear preferential orientation of long axis of pn respect to the galactic plane . this distribution of gpa is similar to that observed by cam98 . we tried to double check our results by applying our analysis to the data published by cam98 , performing a suitable analysis to take over the ambiguity of the position angles ( assigned to the range @xmath52 $ ] ) . more precisely , the sample of cam98 includes 208 objects ( counting the object m2 - 55 in only one list ) ; 69 of them are in both samples ( the object that cam98 put in the list of ellipticals as pc 4 , is in fact pb 4 ) ; 85 are outside our four regions ; 50 were not measured because they are too small ; have strange morphology or circular appearance ; and 4 objects are not true pn ( bl cru , crl 2688 , m 1 - 91 , m 1 - 92 ) . 75@xmath53 of the 69 objects that are in both samples , have their gpa in good agreement ( @xmath54 ) with our measurement . moreover , the distribution of gpa from those objects from cam98 whose coordinates are in region i , shows a clear peak over 3 @xmath55 ( fig . [ fotito7 ] , 48 objects ) , whose barycenter is in @xmath56 , a position similar , within the uncertainties , to the main peak in our fig . [ fotito3 ] . this feature could not be detected by cam98 due to the way they calculated the final angles to plot . the differences could be mainly caused by the fact that they employed deep narrow - band images , as shown in fig . [ fotito8 ] . this figure shows an example of the pn th2-a dss image through r broad - band filter and 1.5 resolution . the epa was measured following the ellipsoid apparent major axis . for comparison , [ fotito8]-right shows the same object imaged with gmos at gemini - s 8 m telescope , through a [ oiii]@xmath575007 filter and with 0.7 seeing ( from daz et al . , in preparation ) . the presence of faint blue emission knots can change the major axis determination from the ellipsoid maximum diameter to an approximately perpendicular angle . therefore it can be expected that the measured geometrical properties of the objects change as distinct ionization layers are imaged through different filters , more precisely , the left peak ( e.g. we 1 - 4 ) in our broad band study could be arose in the measuring of the pn equatorial belt apparent axis instead of the faint external envelope . this should not occur in the deep narrow band images of the cam98 sample and could explain the absence of the second peak in that sample . nevertheless , the agreement between the gpa measurements in both samples is very good and the presence of the second peak can just be ascribed to the ability to detect the outer fainter details in the deep narrow band images , which are usually perpendicular to the bright equatorial belt structures more easily detected in the dss imagery . an interesting test to perform is to check if the distribution of gpa in the four regions has a distance modulation and consider objects statistically far and close . as a first order approach we separated objects in each region by its angular size : an angular diameter of 35@xmath3 divided the sample in two halves , objects with large angular size were considered closer than the ones with small angular size . assuming an average radius of 0.1pc the separating distance is 1.2kpc . the results that we obtained in the four regions show that the distribution of gpa for larger pne has the same shape than the smaller pne . so there is not evidence about a distance effect . following the same open minded search we tried to relate the pa of the long axis of pne with respect to the gould belt , the plane defined by nearby stars of young population , mainly o and b stars ( cameron et al . 1994 ) . the result found shows a noisy distribution of pa . besides , several studies have related bipolar pne with binary progenitors ( bond & livio 1990 ) but the antecedents about the orientations of the orbits of binary stars do not provide any comparable result . notwithstanding it must be remarked that a thorough analysis should be made , keeping in mind the new geometric considerations carried out in this work . we could also consider the case in which only the disk population of the pne towards the galactic center would show a preferred orientation . first , we can test the robustness of the result against the possibility of significant contamination of the pne sample toward the galactic center caused by a random orientation of bulge pne . if the bulge pne contamination were as high as 50% , then more than half of the disk pne would need to have a preferred orientation near to the galactic plane , to be detected and identified in the epa distribution . moreover , it would be necessary to disentangle the bulge objects by their radial velocities in order to verify if the preferred orientation for the disk pne is actually much larger than the one reported here . regarding the physical causes , melnick & harwitt ( 1974 ) mentioned the compression of the pne shells resulting from motion through the ism is seldom observed , remarking that the time scale of the pn expansion ( @xmath58years ) would be large enough to show systematic off - centering of the progenitor stars , which heretofore has been detected in a few lopsided objects ( borkowski , sarazin & soker 1990 ) and could be a dominant factor at the very faintest outer envelopes where the nebular density falls below a critical limit of n@xmath59@xmath60 . undoubtedly the most considered hypothesis has been that the pne could eventually expand more in the direction of the ambient or galactic magnetic field field force lines , which are approximately deployed along the milky way plane ( e.g. phillips 1997 ) . the typical energy density of the interstellar magnetic field is lower than @xmath61erg@xmath60 , whereas the energy density ( thermal , excitation and ionization ) is usually larger than @xmath62erg@xmath60 , consequently a correlation with any observable quantity related with galactic magnetic fields ( diaz & weidmann 2008 , in preparation ) would imply that this are at least one or two orders of magnitude higher in some regions towards the galactic center .

we analyze the spatial orientation of a homogenous sample of 440 elongated planetary nebulae ( pne ) in order to determine the orientation of their apparent major axis respect to the milky way plane . the global distribution of galactic position angles ( gpa ) of pne is quantitatively not very different from a random distribution of orientations in the galaxy . nevertheless we find that there is at least one region on the sky , toward the galactic center , where a weak correlation may exist between the orientation of the major axis of some pne and the galactic equator , with an excess of axes with gpa .

we analyze the spatial orientation of a homogenous sample of 440 elongated planetary nebulae ( pne ) in order to determine the orientation of their apparent major axis respect to the milky way plane . we present some important geometrical and statistical considerations that have been overlooked by the previous works on the subject . the global distribution of galactic position angles ( gpa ) of pne is quantitatively not very different from a random distribution of orientations in the galaxy . nevertheless we find that there is at least one region on the sky , toward the galactic center , where a weak correlation may exist between the orientation of the major axis of some pne and the galactic equator , with an excess of axes with gpa . therefore , we confirm that `` extrinsic '' phenomena ( i.e. , global galactic magnetic fields , shell compression from motion relative to the interstellar medium ) do not determine the morphology of pne on most of the sky , with a possible exception towards the galactic center .

1206.6116

i

the high redshift frontier has moved to @xmath11 as a result of the high resolution near - infrared ( nir ) images from the _ hubble space telescope _ ( _ hst _ ) wide field camera 3 ( wfc3 ) , and the lyman break ` dropout ' technique . the lyman break technique was first applied to select lyman break galaxies ( lbgs ) at @xmath12 @xcite , and since then it has been extensively used to select and study lbg candidates at redshifts @xmath12@xmath13 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this dropout technique has generated large samples of faint star - forming galaxy candidates at @xmath12@xmath13 . however , at highest redshifts ( @xmath4 ) , it is very difficult to understand the details of their stellar populations using current space and ground - based telescopes . their faint magnitudes make it extremely difficult to do spectroscopic studies , and limited high resolution rest - frame optical photometry make it challenging to investigate their spectral energy distributions ( seds ) . these limitations make it imperative to identify and study lbgs at lower redshifts ( @xmath14 ) . the primary reason for the lack of dropout selected lbgs at @xmath0@xmath1 is that we need highly sensitive space - based cameras to observe the mid- to near - ultraviolet ( uv ) wavelengths required to identify lyman break at @xmath0@xmath1 . the peak epoch of global star - formation rate at @xmath0@xmath1 is now accessible using the dropout technique with the wfc3 uvis channel . * hereafter h10 ) and @xcite have used the _ wfc3 with its superior sensitivity to photometrically identify lower redshift ( @xmath0@xmath1 ) lbgs . understanding the lbgs at @xmath14 is vital for two main reasons . first , we need to study the star - formation properties of these lbgs , because they are at redshifts corresponding to the peak epoch of the global star - formation rate ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? second , they are likely lower redshift counterparts of the high redshift lbgs because of their identical dropout selection and similar physical properties whose understanding will help shed light on the process of reionization in the early universe ( e.g. , * ? ? ? * ; * ? ? ? there are primarily three techniques to select star - forming galaxies at @xmath10 : ( 1 ) _ sbzk _ ( using the @xmath15 , @xmath16 , @xmath17 bands , * ? ? ? * ; * ? ? ? * ) , ( 2 ) bx / bm ( using the @xmath18 , @xmath19 , @xmath20 bands , * ? ? ? * ; * ? ? ? * ) , and ( 3 ) lbg ( using the bands which bracket the redshifted lyman limit , h10 ; * ? ? ? all these approaches select star - forming galaxies , and yield insight into the star - forming properties of these galaxies , but they have differing selection biases , and so these samples do nt completely overlap ( see * ? ? ? * ; * ? ? ? * for details ) . therefore , it is essential to apply identical selection criteria at all redshifts to properly compare galaxy samples and accurately trace their evolution . the lbg selection is widely used to select high redshift ( @xmath4 ) galaxies , and to do equal comparison with these galaxies , here we investigate physical properties of lbgs at @xmath14 . h10 used uv observations of the wfc3 science oversight committee early release science extragalactic program ( pid : 11359 , pi : oconnell ; hereafter `` ers '' ) , which covers approximately 50 arcmin@xmath2 in the northern - most part of the great observatories origins deep survey ( goods ; * ? ? ? * ) south field , to identify lbgs at @xmath0@xmath1 . the high sensitivity of the wfc3 uvis channel data @xcite , along with existing deep optical data obtained with the advanced camera for surveys ( acs ) as part of the goods program are ideal to apply dropout technique in observed uv filters to select lbg candidates at @xmath0@xmath1 . in this paper , we use this h10 sample of lbgs to investigate their physical properties by fitting stellar synthesis models to their observed seds . this paper is organized as follows : in [ data ] , we summarize the wfc3 ers observations , and discuss our lbg sample at @xmath0@xmath1 as well as the comparison sample of lbgs at @xmath21@xmath9 . in [ seds ] , we fit observed seds of lbgs at @xmath0@xmath1 and @xmath21@xmath9to stellar population synthesis models , and discuss the best - fit parameters ( redshift , uv spectral slope , stellar mass , stellar age , and star - formation rates ) obtained from these sed fits . in [ results ] , we discuss correlations between best - fit physical parameters and their implications on our understanding of lbgs . in [ conclusion ] , we conclude with a summary of our results . in the remaining sections of this paper we refer to the _ hst_/wfc3 f225w , f275w , f336w , f098 m , f125w , f160w , filters as @xmath22 , @xmath23 , @xmath24 , @xmath25 , @xmath26 , @xmath27 , to the _ hst_/acs f435w , f606w , f775w , f850lp filters as @xmath28 , @xmath29 , @xmath30 , @xmath31 , and to the _ spitzer_/irac 3.6 @xmath32 m , 4.5 @xmath32 m filters as [ 3.6 ] , [ 4.5 ] , respectively , for convenience . we assume a _ wilkinson microwave anisotropy probe _ ( wmap ) cosmology with @xmath33=0.274 , @xmath34=0.726 and @xmath35=70.5 km s@xmath36 mpc@xmath36 , in accord with the 5 year wmap estimates of @xcite . this corresponds to a look - back time of 10.4 gyr at @xmath10 . magnitudes are given in the ab@xmath37 system @xcite .

we analyze the spectral energy distributions ( seds ) of lyman break galaxies ( lbgs ) at selected using the _ hubble space telescope _ ( _ hst _ ) wide field camera 3 ( wfc3 ) uvis channel filters . these _ hst_/wfc3 observations cover about 50 arcmin in the goods - south field as a part of the wfc3 early release science program . these lbgs at are selected using dropout selection criteria similar to high redshift lbgs . this could imply that identical dropout selection technique , at all redshifts , find physically similar galaxies ; and ( 4 ) the stellar masses of these lbgs are directly proportional to their uv luminosities with a logarithmic slope of.46 , and star - formation rates are proportional to their stellar masses with a logarithmic slope of.90 .

we analyze the spectral energy distributions ( seds ) of lyman break galaxies ( lbgs ) at selected using the _ hubble space telescope _ ( _ hst _ ) wide field camera 3 ( wfc3 ) uvis channel filters . these _ hst_/wfc3 observations cover about 50 arcmin in the goods - south field as a part of the wfc3 early release science program . these lbgs at are selected using dropout selection criteria similar to high redshift lbgs . the deep multi - band photometry in this field is used to identify best - fit sed models , from which we infer the following results : ( 1 ) the photometric redshift estimate of these dropout selected lbgs is accurate to within few percent ; ( 2 ) the uv spectral slope is redder than at high redshift ( ) , where lbgs are less dusty ; ( 3 ) on average , lbgs at are massive , dustier and more highly star - forming , compared to lbgs at higher redshifts with similar luminosities ( ) , though their median values are similar within 1 uncertainties . this could imply that identical dropout selection technique , at all redshifts , find physically similar galaxies ; and ( 4 ) the stellar masses of these lbgs are directly proportional to their uv luminosities with a logarithmic slope of.46 , and star - formation rates are proportional to their stellar masses with a logarithmic slope of.90 . these relations hold true within luminosities probed in this study for lbgs from to . the star - forming galaxies selected using other color - based techniques show similar correlations at , but to avoid any selection biases , and for direct comparison with lbgs at , a true lyman break selection at is essential . the future _ hst _ uv surveys , both wider and deeper , covering a large luminosity range are important to better understand lbg properties , and their evolution .

1206.6116

i

in this paper , we investigated stellar populations of lbgs at @xmath0@xmath1 selected using _ hst_/wfc3 uvis filters in the goods - s field . we used deep multi - wavelength observations from the _ hst _ , vlt , and _ spitzer _ to compare observed seds with the spectral synthesis models to infer physical properties ( stellar masses , stellar ages , sfrs , and dust extinction ) of these lbgs . we also compared these lbgs with their higher redshift ( @xmath21@xmath9 ) counterparts with similar luminosities ( @xmath5 ) . our results can be summarized as follows : @xmath102 the uv continuum slope @xmath3 for lbgs at @xmath0@xmath1 is redder ( @xmath731.6 at @xmath38 ) compared to their higher redshift counterparts ( @xmath732.4 at @xmath74 ) , implying higher dust content in these lbgs . @xmath102 on average , lbgs at @xmath0@xmath1 are massive , dustier and more highly star - forming compared to lbgs at @xmath21@xmath9 , though their median values are very similar within estimated 1@xmath6 uncertainties . this similarity emphasizes the importance of identical lyman break selection technique at all redshifts , which selects physically similar galaxies . @xmath102 the stellar mass absolute uv magnitude relation for lbgs between @xmath8 and @xmath9 show linear correlation with a logarithmic slope of @xmath70.46 , while the sfr stellar mass relation show similar correlation with a logarithmic slope of @xmath70.90 . to properly compare and interpret such relations at higher ( @xmath4 ) redshift , and to avoid any selection biases due to different selection techniques , a true lyman break selection is required at @xmath10 . @xmath102 we need larger _ hst _ uv surveys to cover full range in luminosity / mass and better understand lbg properties , and their evolution . both deeper and wider uv surveys are needed . the wider one to probe the high mass end , while the deeper one will probe the sub-@xmath47 population . a large number of _ hst _ orbits have been used for dropout selected galaxies at @xmath4 , and the lower redshift regime needs to be explored in a comparable manner . we thank the referee for helpful comments and suggestions that significantly improved this paper . this paper is based on early release science observations made by the wfc3 scientific oversight committee . we are grateful to the director of the space telescope science institute for awarding director s discretionary time for this program . support for program # 11359 was provided by nasa through a grant hst - go-11359.08-a from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 . this research was ( partially ) supported by a grant from the american astronomical society . adelberger , k. l. , steidel , c. c. , shapley , a. e. , et al . 2004 , apj , 607 , 226 arnouts , s. , cristiani , s. , moscardini , l. , et al . 1999 , mnras , 310 , 540 atek , h. , siana , b. , scarlata , c. , et al . 2011 , apj , 743 , 121 balestra , i. , mainieri , v. , popesso , p. , et al . 2010 , a&a , 512 , 12 basu - zych , a. r. , hornschemeier , a. e. , hoversten , e. a. , lehmer , b. , & gronwall , c. 2011 , apj , 739 , 98 bertin , e. , & arnouts , s. 1996 , a&as , 117 , 393 bouwens , r. j. , illingworth , g. d. , blakeslee , j. p. , & franx , m. 2006 , apj , 653 , 53 bouwens , r. j. , illingworth , g. d. , franx , m. , & ford , h. 2007 , apj , 670 , 928 bouwens , r. j. , illingworth , g. d. , franx , m. , et al . 2009 , apj , 705 , 936 bouwens , r. j. , illingworth , g. d. , oesch , p. a. , et al . 2010 , apj , 709 , l133 bouwens , r. j. , illingworth , g. d. , oesch , p. a. , et al . 2012 , apj , 754 , 83 bruzual , g. , & charlot , s. 2003 , mnras , 344 , 1000 burgarella , d. , le floh , e. , takeuchi , t. t. , et al . 2007 , mnras , 380 , 986 calzetti , d. , kinney , a. l. , & storchi - 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fit seds of lbgs at @xmath0@xmath1 . we have used the ` le phare ` code @xcite to compute photometric redshifts and to perform sed fitting . grey concentric circles are observed magnitudes in three _ hst_/wfc3 uvis , four _ hst_/acs , three _ ir , one vlt ks , and two _ spitzer_/irac [ 3.6 ] , [ 4.5 ] bands . [ bottom panel ] same as the top panel but for the comparison sample of lbgs at @xmath21@xmath9 . stellar masses are in solar units and stellar ages are in years . ] the concentric circles indicate unreliable spectroscopic redshifts based on their quality flags . the dotted line shows the 1-to-1 relation between two redshifts . the histogram shows distribution of ( @xmath104/1+@xmath59 ) , and the 1@xmath6 uncertainties in this distribution is @xmath75% . the dot - dash lines show 3@xmath6 limits . ] to best - fit seds for two lbgs from the @xmath0@xmath1 sample . the dotted black line is the best - fit sed , while solid black line shows the estimated uv continuum slope @xmath3 . the black filled circles are observed magnitudes . we test two different rest - frame uv wavelength range ( 13001900 and 13003400 ) to address the robustness of our estimated uv continuum slope @xmath3 , and find similar median slopes within 1@xmath6 scatter . ] as a function of redshift . blue filled squares indicate the median @xmath3 values when we fit rest - frame 1300 to 1900 wavelengths , and blue open squares indicate @xmath3s when we fit 1300 to 3400 . the higher redshift ( @xmath105 ) measurements from @xcite and @xcite are also shown for comparison . ours and the @xcite uncertainties are the standard error of the mean , while uncertainties from bouwens et al . are 1@xmath6 scatter . for comparison , our 1@xmath6 uncertainties / scatter are listed in table [ tab : beta ] . ] versus best - fit sed parameters ( e(b - v ) , stellar mass , stellar age , star - formation rate ) . the size of the circle increases with redshift i.e. , the smallest circle correspond to the lowest redshift bin ( @xmath38 ) , and the largest circle correspond to @xmath21@xmath9 bin . the changes in the uv - continuum slope @xmath3 from @xmath38 to @xmath9 are most likely due to the change ( factor of @xmath72 or 0.3 dex ) in the dust content e(b v ) of the galaxies , as other parameters show smaller variation as a function of redshift . ] @xmath1 ( black ) and the comparison sample at @xmath21@xmath9 ( red ) . all four parameters are estimated from the best - fit seds . median values are shown by vertical dashed lines and 1@xmath6 uncertainties are shown by an error bar at the top of the black histogram . though the higher redshift lbgs have , on average , lower values of most of these physical parameters than lbgs at @xmath0@xmath1 , the median values are similar within estimated uncertainties . stellar ages do not show any clear evolution with redshift mainly because of higher uncertainties in their measurements ( see [ age_mass_sfr ] ) . the histograms show normalized numbers for both samples ( total number of galaxies in each sample is shown in table [ tab : beta ] ) , and a two - sided k - s test in each panel indicates a probability @xmath106 that the two distributions are drawn from the same parent distribution . ] - , @xmath23- , @xmath24-dropout samples . bottom right panel shows the same relation for the comparison sample of lbgs at @xmath21@xmath9 ( black circles for @xmath21 , and black squares for @xmath107 ) . the average uncertainties are shown in the bottom - left corner . the dotted black line is the best - fit line with a logarithmic slope of 0.46 . the dot - dash line shows the 1@xmath6 scatter ( @xmath70.3 dex ) from the best - fit linear relation . ] - , @xmath23- , @xmath24-dropout samples . bottom right panel shows the same relation for the comparison sample of lbgs at @xmath21@xmath9 ( black circles for @xmath21 , and black squares for @xmath76 ) . the average uncertainties are shown in the bottom - right corner . the dotted black line is the best - fit line with a logarithmic slope of 0.90 . the dot - dash line shows the 1@xmath6 scatter ( @xmath70.6 dex , @xmath70.4 dex for @xmath21@xmath9 ) from the best - fit linear relation . in the upper panel , few galaxies form a sharp edge towards high sfr values , which could be an artifact due to lower limits on the model parameters @xmath55 and _ t _ ( e.g. , * ? ? ? ] @xmath1 ( black ) and for the comparison sample at @xmath21@xmath9 ( red ) . median values are shown by vertical dashed lines and 1@xmath6 uncertainties are shown by an error bar at the top of the black histogram . though the higher redshift lbgs have , on average , lower values of these parameters than lbgs at @xmath0@xmath1 , the median values are similar within estimated uncertainties . the histograms show normalized numbers for both samples ( total number of galaxies in each sample is shown in table [ tab : beta ] ) , and a two - sided k - s test in each panel indicates a probability @xmath108 that the two distributions are drawn from the same parent distribution . ] 1.6 ( @xmath810.2 ) & 47 & 1.59 ( 1.67 ) & 0.29 ( 0.27 ) & 0.04 ( 0.04 ) + 2.2 ( @xmath810.3 ) & 126 & 1.71 ( 1.81 ) & 0.34 ( 0.37 ) & 0.03 ( 0.03 ) + 2.6 ( @xmath810.4 ) & 213 & 1.71 ( 1.78 ) & 0.47 ( 0.50 ) & 0.03 ( 0.03 ) + 3.8@xmath109 ( @xmath810.5 ) & 182 & 1.88 ( 1.93 ) & 0.45 ( 0.41 ) & 0.03 ( 0.03 ) +

the deep multi - band photometry in this field is used to identify best - fit sed models , from which we infer the following results : ( 1 ) the photometric redshift estimate of these dropout selected lbgs is accurate to within few percent ; ( 2 ) the uv spectral slope is redder than at high redshift ( ) , where lbgs are less dusty ; ( 3 ) on average , lbgs at are massive , dustier and more highly star - forming , compared to lbgs at higher redshifts with similar luminosities ( ) , though their median values are similar within 1 uncertainties . the star - forming galaxies selected using other color - based techniques show similar correlations at , but to avoid any selection biases , and for direct comparison with lbgs at , a true lyman break selection at is essential . the future _ hst _ uv surveys , both wider and deeper , covering a large luminosity range are important to better understand lbg properties , and their evolution .

we analyze the spectral energy distributions ( seds ) of lyman break galaxies ( lbgs ) at selected using the _ hubble space telescope _ ( _ hst _ ) wide field camera 3 ( wfc3 ) uvis channel filters . these _ hst_/wfc3 observations cover about 50 arcmin in the goods - south field as a part of the wfc3 early release science program . these lbgs at are selected using dropout selection criteria similar to high redshift lbgs . the deep multi - band photometry in this field is used to identify best - fit sed models , from which we infer the following results : ( 1 ) the photometric redshift estimate of these dropout selected lbgs is accurate to within few percent ; ( 2 ) the uv spectral slope is redder than at high redshift ( ) , where lbgs are less dusty ; ( 3 ) on average , lbgs at are massive , dustier and more highly star - forming , compared to lbgs at higher redshifts with similar luminosities ( ) , though their median values are similar within 1 uncertainties . this could imply that identical dropout selection technique , at all redshifts , find physically similar galaxies ; and ( 4 ) the stellar masses of these lbgs are directly proportional to their uv luminosities with a logarithmic slope of.46 , and star - formation rates are proportional to their stellar masses with a logarithmic slope of.90 . these relations hold true within luminosities probed in this study for lbgs from to . the star - forming galaxies selected using other color - based techniques show similar correlations at , but to avoid any selection biases , and for direct comparison with lbgs at , a true lyman break selection at is essential . the future _ hst _ uv surveys , both wider and deeper , covering a large luminosity range are important to better understand lbg properties , and their evolution .

cond-mat0502405

r

in the following we shall use reduced quantities : @xmath115 as reduced temperature , @xmath116 as reduced total density , @xmath117 as the concentration of species @xmath22 , @xmath118 as reduced pressure , @xmath119 as the reduced chemical potential of species @xmath22 , and @xmath120 as the reduced dipole moments . for our numerical analysis we consider the following choices for the lennard - jones potential parameters : @xmath121 , @xmath122 , and @xmath123 . the case @xmath124 will be discussed in subsec . iii c. the bulk phase diagrams of the binary dipolar fluid mixtures are calculated in the thermodynamic space spanned by temperature @xmath3 , pressure @xmath16 , and the difference of the chemical potentials @xmath17 of the two components . in order to obtain the phase boundaries in this space for fixed @xmath3 the corresponding phase equilibrium equations ( eq . ( [ caca ] ) ) have to be solved simultaneously under the constraint @xmath125 the pressure @xmath16 follows from eq . ( [ press ] ) . as a first step we have determined the phase diagrams of non - polar binary lennard - jones fluid mixtures ( @xmath126 ) for the aforementioned parameters . based on our systematic calculations in the thermodynamic space ( @xmath15 ) these phase diagrams take on shapes as shown schematically in fig . [ fig1](a ) . @xmath127 and @xmath128 are sheets of first - order phase transitions separating the vapor phase from the fluid phase and the a - rich liquid phase from the b - rich liquid phase , respectively . these sheets are bounded by lines @xmath129 and @xmath130 , respectively , of second - order phase transitions marking the onset of liquid - vapor separation ( @xmath129 ) and demixing ( @xmath130 ) upon lowering the temperature . the intersection of @xmath127 and @xmath128 forms the triple line @xmath131 of three - phase coexistence ending at the critical end point @xmath132 where @xmath130 hits @xmath127 . this type of phase diagrams corresponds to type ii in the classification scheme of phase diagrams of binary fluid mixtures given by scott and van konynenburg @xcite . for the non - polar binary fluid mixture fig . [ fig2 ] presents our numerical results for the pressure - temperature ( fig . [ fig2](a ) ) and the density - temperature ( fig . [ fig2](b ) ) phase diagrams for @xmath133 . at low temperatures ( @xmath134 ) the a - rich liquid coexists with the vapor . at the triple point temperature @xmath135 three phases coexist : vapor , b - rich liquid , and a - rich liquid . above @xmath136 up to the liquid - vapor critical temperature ( @xmath137 ) there is coexistence between the vapor and the b - rich liquid and between the a - rich liquid and the b - rich liquid . in the temperature range @xmath138 with @xmath139 there is only coexistence between the a - rich liquid and the b - rich liquid . + + + + + + + figure [ fig1](b ) shows the schematic phase diagram of the binary liquid mixture with the same lj parameters but with @xmath140 . the occurrence of a ferromagnetic phase gives rise to the appearance of the sheet @xmath141 which separates the isotropic liquid at high temperatures from the ferromagnetic liquid at low temperatures . the nature of this sheet @xmath141 differs from that of @xmath127 and @xmath128 in that @xmath141 is the locus of second - order phase transitions . in the thermodynamic space ( @xmath15 ) the surface @xmath141 is given by the simultaneous solution of eqs . ( [ sec2 ] ) and ( [ kont ] ) . ( with the knowledge of @xmath68 , @xmath69 , and @xmath3 eq . ( [ press ] ) gives the corresponding pressure @xmath16 , using the fact that on @xmath141 @xmath105 and @xmath106 for @xmath107 . ) the intersection of @xmath141 and @xmath127 is a line @xmath142 of critical end points . along this line the ferromagnetically critical liquid phase coexists with the isotropic vapor phase . the other line @xmath143 of critical end points is given by the intersection of the sheets @xmath128 and @xmath141 . the sheet @xmath141 divides the triple line into two parts . the upper part describes isotropic vapor isotropic b - rich liquid isotropic a - rich liquid three - phase coexistence , while the lower part describes an isotropic vapor ferromagnetic b - rich liquid ferromagnetic a - rich liquid coexistence . both critical lines @xmath129 and @xmath130 are in the isotropic part of the thermodynamic space ( @xmath15 ) . figure [ fig3 ] shows the corresponding results of our numerical calculations for a binary stockmayer fluid mixture with dipole moments @xmath140 for @xmath133 . the intersection of the plane @xmath133 with the sheet @xmath141 yields the critical ( dotted ) line in fig . [ fig3](a ) . its intersection with the first - order coexistence curve between vapor and ferromagnetic a - rich liquid is the critical end point cep with @xmath144 , @xmath145 , and @xmath146 at @xmath133 . below @xmath147 the isotropic vapor phase coexists with the ferromagnetic a - rich liquid . the critical line of second - order phase transitions divides the a - rich liquid into an isotropic a - rich liquid phase and into a ferromagnetic a - rich liquid phase . in the temperature range @xmath148 with @xmath149 the isotropic vapor coexists with an isotropic a - rich liquid phase . above the triple point temperature there is also coexistence between the isotropic b - rich liquid and the isotropic a - rich liquid . this first - order phase transition ends in the critical temperature @xmath150 . the critical temperature of the isotropic vapor isotropic b - rich liquid coexistence is @xmath151 . upon increasing the dipole moments the phase diagram shown in fig . [ fig1](b ) changes in two respects . first , the sheet @xmath141 is raised due to the strengthening of orientational ordering . second , close to the line @xmath142 the character of the ferromagnetic - isotropic phase transition on @xmath141 becomes first - order such that a line of tricritical points ( @xmath152 ) emerges from @xmath142 and separates the sheet @xmath141 into a continuous part ( back part at high @xmath16 and hatched ) and a first - order part ( front part at lower @xmath16 and unhatched ) . this implies that @xmath142 turns into a triple line @xmath153 . upon further increase of @xmath11 and @xmath12 this sheet @xmath141 , divided by the @xmath152-line , raises finally above the line @xmath130 . moreover the upper part of @xmath127 , i.e. , above @xmath153 disintegrates into a left and right part leaving a gap between them . this means that @xmath153 is split into @xmath154 and @xmath155 and @xmath129 into @xmath129 and @xmath156 in fig . [ fig1](c ) . this also generates two critical end points @xmath157 and @xmath158 which are raised above @xmath132 . figure [ fig1](c ) , corresponding to @xmath159 , displays this latter structure with @xmath160 denoting the sheet which emerged from the lower part of @xmath127 in fig . [ fig1](b ) and @xmath141 whereas the winglike structures in fig . [ fig1](c ) are the remnants of the upper part of @xmath127 in fig . [ fig1](b ) . they are connected to the sheet @xmath160 along the triple lines @xmath154 and @xmath155 and bounded by the liquid - vapor critical lines @xmath129 and @xmath156 . the isotropic vapor isotropic fluid ferromagnetic liquid triple lines @xmath154 and @xmath155 end in critical end points @xmath157 and @xmath158 . @xmath128 and @xmath160 intersect along the triple line @xmath131 which ends at the critical end point @xmath132 . figure [ fig4 ] shows the corresponding results for the projections of the triple lines and of the liquid - vapor critical lines of a binary stockmayer fluid mixture with dipole moments @xmath159 onto a plane @xmath161 . the triple line @xmath131 describes the isotropic vapor ferromagnetic a - rich liquid ferromagnetic b - rich liquid three - phase coexistence with the critical end point temperature @xmath162 . the triple lines @xmath154 and @xmath155 associated with the two winglike surfaces ( see fig . [ fig1](c ) ) describe the isotropic vapor isotropic fluid ferromagnetic a - rich liquid and isotropic vapor isotropic fluid ferromagnetic b - rich liquid three - phase coexistences with the critical end point temperatures @xmath163 and @xmath164 . figure [ fig5 ] presents our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath159 for @xmath165 . for this choice of @xmath166 at the triple point @xmath136 the following three phases coexist : vapor , isotropic fluid , and ferromagnetic liquid . at low temperatures @xmath134 with @xmath167 the ferromagnetic liquid coexists with the isotropic vapor . above the triple point temperature , two isotropic fluids coexist at low and moderate densities , becoming identical above the liquid - vapor critical temperature @xmath168 . ( the corresponding critical pressure and density are @xmath169 and @xmath170 , respectively . ) at higher densities , the isotropic liquid and magnetic liquid are separated by a first - order phase transition which becomes second order above the tricritical temperature @xmath171 . ( the corresponding tricritical pressure and density are @xmath172 and @xmath173 , respectively . ) the critical line of second - order phase transitions divides the liquid range into an isotropic liquid phase and into a ferromagnetic liquid phase . at this value of the chemical potential difference there is no a - rich liquid b - rich liquid demixing phase separation . figure [ fig6 ] shows our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath159 for @xmath174 . at the triple point temperature @xmath136 the coexisting phases are : vapor , ferromagnetic b - rich liquid , and ferromagnetic a - rich liquid . at low temperatures @xmath134 with @xmath175 the isotropic vapor phase coexists with the ferromagnetic a - rich liquid . above the triple point temperature , an isotropic vapor coexists with a ferromagnetic b - rich liquid and a ferromagnetic b - rich liquid coexists with a ferromagnetic a - rich liquid . the two ferromagnetic liquid phases become identical beyond the liquid - liquid critical point @xmath176 with @xmath177 . ( the corresponding critical pressure and density are @xmath178 and @xmath179 , respectively , at @xmath174 . ) above the ferromagnetic a - rich liquid ferromagnetic b - rich liquid critical temperature @xmath176 the isotropic liquid and ferromagnetic b - rich liquid are separated by a first - order transition which turns second order above the tricritical temperature @xmath180 . ( the corresponding tricritical pressure and density are @xmath181 and @xmath182 , respectively , at @xmath174 . ) at temperatures @xmath183 one finds second - order ferromagnetic phase transitions as given by the critical line . [ fig1](d ) shows that by further increasing the dipole moments ( @xmath184 ) the winglike surfaces associated with the isotropic liquid isotropic vapor transition disappear and only the two sheets @xmath128 and @xmath160 remain . accordingly there is only one triple line @xmath131 , which describes the isotropic vapor , ferromagnetic a - rich liquid , and ferromagnetic b - rich liquid three - phase coexistence and which ends at the critical end point @xmath132 where @xmath130 hits @xmath160 . since the sheet @xmath128 bounded by @xmath130 lies beneath the sheet @xmath160 all first - order liquid - liquid phase separations involve ferromagnetic phases . figure [ fig7 ] shows our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath184 for @xmath185 . the topology of fig . [ fig7 ] is the same as in fig . [ fig6 ] , only the numerical values for the triple , critical , and tricritical points are different . below the triple point temperature @xmath186 ( with @xmath187 at @xmath185 ) an isotropic vapor coexists with a ferromagnetic a - rich liquid . the ferromagnetic liquid - liquid critical point is given by @xmath188 , @xmath189 , and @xmath190 , while the tricritical point is given by @xmath191 , @xmath192 , and @xmath193 . in this subsection we present our results for phase diagrams of non - polar ( @xmath194 ) polar ( @xmath195 ) binary mixtures . the corresponding schematic phase diagrams are shown in fig . [ fig8 ] . in order to provide a convenient visual comparison fig . [ fig8](a ) shows again as a reference case the schematic phase diagram of a non - polar binary lennard - jones fluid mixture ( @xmath126 ) with the parameter set @xmath121 , @xmath196 and @xmath123 . figure [ fig8](b ) shows the schematic phase diagram of the binary liquid mixture with the same lj parameters but with @xmath194 and @xmath197 . similar to fig . [ fig1](b ) the occurrence of a ferromagnetic phase gives rise to the appearance of the sheet @xmath141 of second - order phase transitions which separates the isotropic liquid phase from the ferromagnetic liquid phase . the ferromagnetic phase appears only in the b - rich liquid phase and at low temperatures while the a - rich liquid phase remains isotropic even at low temperatures . this behavior reflects the polar ( @xmath7 ) and non - polar ( @xmath6 ) character of molecules . in accordance with this asymmetry the sheet @xmath141 is tilted , ends at @xmath128 and thus does not cut through the sheet @xmath128 . this leads to the line @xmath143 of critical end points . the intersection of @xmath141 and @xmath127 forms another line @xmath142 of critical end points . the triple line ( @xmath131 ) is given by the intersection of @xmath127 and @xmath128 . the line @xmath142 of critical end points divides the triple line into two parts . the upper part of the triple line describes isotropic vapor isotropic b - rich liquid isotropic a - rich liquid three - phase coexistence as in the case of symmetric dipolar mixtures with dipole moments @xmath140 ( see fig . [ fig1](b ) ) . the lower part of the triple line describes isotropic vapor ferromagnetic b - rich liquid isotropic a - rich liquid coexistence . + + + + + + figure [ fig9 ] shows our numerical findings for a binary stockmayer fluid mixture with dipole moments @xmath194 and @xmath197 for @xmath198 . figure [ fig9](a ) demonstrates that for this value of the chemical potential difference the plane @xmath198 cuts through the upper part of the triple line @xmath131 in fig . [ fig8](b ) so that the corresponding triple point @xmath136 describes an isotropic vapor a - rich isotropic liquid b - rich isotropic liquid coexistence with @xmath199 and @xmath200 . the intersection of this plane with the sheet @xmath141 yields the dotted critical line . the intersection of the plane @xmath198 with the line @xmath142 in fig . [ fig8](b ) gives the critical end point @xmath132 where an isotropic vapor coexists with a ferromagnetically critical b - rich liquid . the thermodynamic parameters of this critical end point @xmath132 are given by @xmath201 , @xmath202 , and @xmath146 , respectively , for @xmath198 . below the temperature @xmath147 the isotropic vapor phase coexists with the ferromagnetic b - rich liquid phase . between the temperatures @xmath147 and @xmath136 two phases coexist : the isotropic vapor and the b - rich isotropic liquid . above @xmath136 up to the liquid - vapor critical temperature ( @xmath203 ) coexistence is possible between the vapor and the a - rich isotropic liquid phase and between the a - rich isotropic liquid and the b - rich isotropic liquid . in the temperature range @xmath138 with @xmath204 coexistence is possible only between the isotropic a - rich and b - rich liquid phases . ( the corresponding critical densities are @xmath205 and @xmath206 , respectively . ) figure [ fig10 ] shows our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath194 and @xmath197 for @xmath207 . figure [ fig10](a ) displays that for this value of the chemical potential difference the plane @xmath207 cuts through the lower part of the triple line @xmath131 in fig . [ fig8](b ) so that the corresponding triple point @xmath136 describes an isotropic vapor a - rich isotropic liquid b - rich ferromagnetic liquid coexistence with @xmath208 and @xmath209 . below the triple temperature @xmath136 the vapor phase coexists with the b - rich ferromagnetic liquid phase . above @xmath136 up to the liquid - vapor critical temperature ( @xmath210 ) coexistence is possible between the vapor and the a - rich isotropic liquid phase and between the a - rich isotropic liquid and the b - rich ferromagnetic liquid . the critical pressure and density of liquid - vapor coexistence are @xmath211 and @xmath212 , respectively . the a - rich isotropic liquid b - rich ferromagnetic liquid phase coexistence extends to higher temperatures . the corresponding liquid - liquid critical point is not attainable at physically relevant fluid densities . ( at high densities the system freezes , but the corresponding solid phases are not captured within the framework of the present theory . ) upon increasing the dipole moment of component @xmath7 the phase diagram shown in fig . [ fig8](b ) changes considerably . first , the sheet @xmath141 moves up due to the strengthening of the dipolar interaction . like in the case of symmetrical dipolar mixtures ( @xmath159 , see fig . [ fig1](c ) ) close to the line @xmath142 the ferromagnetic - isotropic phase transition on the sheet @xmath141 becomes first order . this means that a line @xmath152 of tricritical points emerges from @xmath142 and separates the sheet @xmath141 into a continuous part and a first - order part . in turn this implies that @xmath142 turns into a triple line @xmath153 . in the next step due to the rise of the sheet @xmath141 ( divided by the @xmath152-line ) the line @xmath143 rises , too , and merges with the line @xmath130 so that @xmath141 and @xmath128 form a single sheet @xmath213 . upon a further increase of @xmath12 the upper part of @xmath127 disintegrates into a left and a right part leaving a gap between them , where @xmath127 merges with @xmath213 forming the surface @xmath214 . the remnants of the upper part of the sheet @xmath127 appear as asymmetrically winglike structures , where the triple lines @xmath154 and @xmath155 stem from the triple line @xmath153 which has split while the split line @xmath129 generates the liquid - vapor critical lines @xmath129 and @xmath156 ( see fig . [ fig8](c ) ) . the intersections of the corresponding triple and critical lines give two critical end points @xmath157 and @xmath158 . figure [ fig8](c ) corresponds to @xmath194 and @xmath215 and displays this final structure with @xmath214 denoting the surface which has emerged from the sheets @xmath127 , @xmath128 , and @xmath141 ( shown in fig . [ fig8](b ) ) upon the increase of the dipole moment @xmath12 . figure [ fig11 ] shows our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath194 and @xmath215 for @xmath216 . for this value of @xmath217 the figure displays a vertical intersection of the phase diagram shown in fig . [ fig8](c ) between the two critical end points @xmath157 and @xmath158 and close to @xmath157 . at low temperatures the b - rich isotropic fluid and the b - rich ferromagnetic fluid are separated by a first - order phase transition which becomes second order above the tricritical temperature @xmath218 . ( the tricritical pressure and density are @xmath219 and @xmath220 , respectively . ) the dotted critical line corresponds to a cut through the second - order part of the surface @xmath214 . figure [ fig12 ] shows our numerical findings for a binary stockmayer fluid mixture with dipole moments @xmath194 and @xmath215 for @xmath221 . this figure displays a vertical cut through the phase diagram in fig . [ fig8](c ) between @xmath157 and @xmath158 but close to the critical end point @xmath158 . for this value of the chemical potential difference the a - rich isotropic fluid can coexist with the b - rich ferromagnetic fluid . note that the b - rich isotropic fluid and the a - rich isotropic fluid are not separated by a demixing transition ; in fig . [ fig8](c ) both are in front of @xmath214 . the liquid - liquid critical point lies outside the physically relevant fluid densities . figure [ fig13 ] shows our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath194 and @xmath215 for @xmath222 . in this case the plane @xmath222 cuts through the wing on the right side of the surface @xmath214 in fig . [ fig8](c ) . for this choice of @xmath166 at the triple point @xmath136 the following three phases coexist : vapor , a - rich isotropic liquid , and b - rich ferromagnetic liquid . at low temperatures @xmath134 with @xmath223 ( @xmath224 ) the b - rich ferromagnetic liquid coexists with the isotropic vapor . above the triple point temperature at low densities the vapor coexists with the a - rich isotropic liquid , whereas at high densities the a - rich isotropic liquid coexists with the b - rich ferromagnetic liquid . the vapor and the a - rich isotropic liquid merge at the liquid - vapor critical point @xmath225 , @xmath226 , and @xmath227 . the a - rich isotropic liquid b - rich ferromagnetic liquid critical point occurs outside the physically relevant fluid densities . figure [ fig8](d ) shows that by further increasing the dipole moment of the component @xmath7 ( @xmath194 , @xmath228 ) the winglike structure on the left hand side in fig . [ fig8](c ) , which is associated with the b - rich isotropic liquid vapor transitions , disappears so that there remain only the two sheets @xmath214 and the wing on the right hand side associated with the a - rich isotropic liquid vapor transitions . accordingly there is only one triple line @xmath155 , which describes the isotropic vapor a - rich isotropic liquid b - rich ferromagnetic liquid three - phase coexistence . it ends at the critical end point @xmath158 where @xmath156 hits the surface @xmath214 . since the topology of the phase diagram in fig . [ fig8](d ) is the same as that of fig . [ fig8](c ) ( only the left winglike surface in fig . [ fig8](c ) is missing ) , the topologies of different cuts at given chemical potentials are in agreement with the topologies of the phase diagrams in figs . [ fig11]-[fig13 ] . therefore we refrain from presenting our detailed numerical results for stockmayer mixtures with dipole moments @xmath194 and @xmath228 . in this subsection we present phase diagrams of binary stockmayer liquid mixtures of polar particles ( @xmath229 ) of different size . since in the stockmayer interaction potential the size parameters appear in the lj contribution to the potential , we first study the effect of varying the ratio @xmath230 on the phase diagrams of binary lj fluid mixtures ( @xmath126 ) while keeping the energy parameters of the lj potential fixed . figure [ fig14 ] shows the projections of the triple lines of binary lj fluid mixtures with different particle size ratios onto a plane @xmath161 . these triple lines describe the vapor a - rich isotropic liquid b - rich isotropic liquid three - phase coexistence . the curves show that the sheet @xmath128 , which separates the a - rich and b - rich liquid phases ( see fig . [ fig1](a ) ) is increasingly tilted upon increasing the size ratio @xmath230 . the critical end point temperature increases and the chemical potential difference @xmath231 at the end point turns more negative , i.e. , it is shifted towards the region of fluid rich in the small particles . this means that for large size ratios three phase coexistence occurs for a wider range of thermodynamic parameters . + + + + + + + figure [ fig15 ] represents our numerical results for cuts through the phase diagrams of binary lj mixtures for different size ratios @xmath230 and chemical potential differences @xmath217 . for the presentation we have changed the choice for @xmath217 along with @xmath230 because there is no single value @xmath217 for which the triple points exist for the different values @xmath230=1 , 1.05 , and @xmath232 ( see fig . [ fig14 ] ) . figure [ fig15](a ) demonstrates that the liquid - vapor critical temperatures depend barely on the size ratio ( @xmath233 , @xmath234 , and @xmath235 ) while the liquid - liquid critical temperatures exhibit a stronger size ratio dependence ( @xmath236 , @xmath237 , and @xmath238 ) . the corresponding critical densities are given by @xmath239 , @xmath240 , @xmath241 and @xmath242 , @xmath243 , @xmath244 . the corresponding critical pressures of the liquid - vapor and a - rich liquid b - rich liquid critical points are @xmath245 , @xmath246 , @xmath247 and @xmath248 , @xmath249 , @xmath250 , respectively . figure [ fig15 ] shows that the a - rich liquid b - rich liquid coexistence range within the pressure - temperature plane becomes narrower while within the density - temperature plane it grows wider with increasing size ratio . we now turn to binary stockmayer fluid mixtures whose components have different dipole moments and particle sizes . this model gives a reasonable description of bidisperse ferromagnetic fluids and as such provides also a first approximation of actual polydisperse ferrocolloids . for these fluids the magnetic dipole moments of the particles are proportional to the particle volume , i.e. , @xmath26 @xmath251 @xmath252 , @xmath103 . in the following we restrict our study to binary stockmayer fluid mixtures with dipole moment ratio @xmath253 , which implies the size ratio @xmath254 . this motivates our choice of the size ratio used for the above study of the phase behavior of the binary lj fluid mixtures . for the dipole moment ratio @xmath253 in the following we compare the phase diagrams of binary stockmayer fluid mixtures composed of particles with either equal or different sizes . the corresponding schematic phase diagrams are shown in fig . [ fig16 ] . figure [ fig16](a ) displays the schematic phase diagrams of a binary stockmayer fluid mixture with dipole moments @xmath255 , @xmath215 , and with particle size ratio @xmath256 ; the lj energy parameters are the same as in fig . [ fig14 ] . the topology of this phase diagram is the same as that of shown in fig . [ fig8](c ) . this fact is not surprising because in both cases @xmath215 and the increase of @xmath257 from @xmath194 to @xmath255 causes only a small change in the dipolar interaction energy relative to the lj interaction energy . figure [ fig17 ] shows our numerical results for this binary stockmayer fluid mixture with dipole moments @xmath255 and @xmath215 , and with particle size ratio @xmath256 for @xmath222 . figure [ fig17](a ) demonstrates that the plane @xmath222 cuts through the wing attached to the right hand side of the surface @xmath214 in fig . [ fig16](a ) . in accordance with the aforementioned topological similarity the phase diagrams shown in fig . [ fig17 ] differ from those shown in fig . [ fig13 ] only quantitatively . in fig . [ fig17 ] the liquid - vapor critical point is given by @xmath258 , @xmath259 , and @xmath260 . the corresponding triple point temperature and pressure are @xmath261 and @xmath262 , respectively . for the same dipole moments ( @xmath255 and @xmath215 ) increasing the particle size ratio from @xmath256 to @xmath254 the phase diagram shown in fig . [ fig16](a ) changes considerably . the resulting phase diagram is shown in fig . [ fig16](c ) . the topology of this phase diagram is the same as in fig . [ fig8](b ) . as discussed in subsec . iii b the phase diagram shown in fig . [ fig8](b ) emerges from the phase diagram shown in fig . [ fig8](c ) by decreasing the dipole moment @xmath263 . figure [ fig16](a ) and fig . [ fig16](c ) show that the same topological change in the phase diagrams can be attained by increasing the corresponding particle size ratio . figure [ fig16](c ) tells that the dipole moment strength @xmath255 is insufficient to lead to the formation of an a - rich ferromagnetic liquid phase , so that for negative values of @xmath217 the phase remains isotropic , as in the case of non - polar polar mixtures ( see fig . [ fig8](b ) ) . figure [ fig18 ] shows our numerical findings for a binary stockmayer fluid mixture with dipole moments @xmath255 and @xmath215 , and with particle size ratio @xmath254 for @xmath264 . figure [ fig18](a ) demonstrates that the plane @xmath264 cuts through the upper part of the triple line @xmath131 in fig . [ fig16](c ) so that the corresponding triple point @xmath136 describes a vapor a - rich isotropic liquid b - rich isotropic liquid coexistence with @xmath265 and @xmath266 . the vapor - liquid and liquid - liquid critical points are given as @xmath267 , @xmath268 , @xmath269 and @xmath270 , @xmath271 , @xmath272 , respectively . the topology of these phase diagrams is the same as those of shown in fig . [ fig2 ] . increasing the dipole moments from @xmath255 and @xmath215 to @xmath273 and @xmath228 at a fixed particle size ratio @xmath256 the phase diagram shown in fig . [ fig16](a ) changes considerably leading to the phase diagram displayed in fig . [ fig16](b ) . this increase of the dipole moments causes the disappearance of the winglike structure attached to the left part of the surface @xmath214 ( see fig . [ fig16](b ) ) , which is associated with the b - rich isotropic liquid vapor transitions . moreover the winglike structure attached to the right part of the surface @xmath214 also changes due to the appearance of the sheet @xmath274 . this sheet separates the a - rich isotropic liquid at high temperatures from the a - rich ferromagnetic liquid at low temperatures . @xmath274 is the locus of second - order phase transitions and is the remnant of the sheet @xmath141 ( see fig . [ fig1](b ) ) , which together with @xmath127 and @xmath128 has formed the surface @xmath214 . figure [ fig19 ] displays our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath273 , @xmath228 , and with particle size ratio @xmath256 for @xmath275 . for this value of @xmath217 the figure shows a vertical slice through the left part of the surface @xmath214 in the phase diagram displayed in fig . [ fig16](b ) . the topology of these phase diagrams is the same as those of shown in fig . [ fig11 ] . the tricritical point is given by @xmath276 , @xmath277 , and @xmath278 . increasing the particle size ratio from @xmath256 to @xmath254 for fixed dipole moments @xmath273 and @xmath228 , the phase diagram shown in fig . [ fig16](b ) transforms into that shown in fig . [ fig16](d ) . upon the increase of the particle size ratio on the left part of the surface @xmath214 in fig . [ fig16](d ) a winglike structure appears , which is associated with b - rich isotropic liquid vapor phase transitions . through a similar topological change , the phase diagram shown in fig . [ fig8](d ) transforms into the phase diagram shown in fig . [ fig8](c ) upon a decrease of the dipole moment @xmath263 from @xmath215 to @xmath197 . figure [ fig20 ] displays our numerical results for a binary stockmayer fluid mixture with dipole moments @xmath273 , @xmath228 , and with a particle size ratio @xmath279 for @xmath275 . for this choice of @xmath217 fig . [ fig20](a ) represents a vertical slice through the left part of the surface @xmath214 in the phase diagram shown in fig . [ fig16](d ) where the attached winglike structure appears again . the corresponding liquid - vapor critical point , the tricritical point , and the triple point are given by @xmath280 , @xmath281 , @xmath282 , @xmath283 , @xmath284 , @xmath285 , and @xmath286 , @xmath287 , respectively . the topology of the phase diagrams shown in fig . [ fig20 ] is the same as of those of shown in fig .

we apply a modified mean - field density functional theory to determine the phase behavior of binary mixtures of stockmayer fluids whose spherical constituents interact according to lennard - jones ( lj ) pair potentials with embedded pointlike dipole moments . on the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three - dimensional thermodynamic space of temperature , pressure , and chemical potential difference of the two components . the vapor - liquid , isotropic liquid ferromagnetic liquid first - order phase separations are investigated .

we apply a modified mean - field density functional theory to determine the phase behavior of binary mixtures of stockmayer fluids whose spherical constituents interact according to lennard - jones ( lj ) pair potentials with embedded pointlike dipole moments . on the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three - dimensional thermodynamic space of temperature , pressure , and chemical potential difference of the two components . the vapor - liquid , isotropic liquid isotropic liquid , isotropic liquid ferromagnetic liquid , and ferromagnetic liquid ferromagnetic liquid first - order phase separations are investigated . the loci of the second - order isotropic fluid ferromagnetic fluid transition are calculated from landau theory . liquid - vapor and liquid - liquid critical lines , tricritical lines , triple lines , and lines of critical end points of the binary stockmayer mixtures are also determined . we discuss how the topology of the phase diagrams change upon varying the strengths of the two dipole moments of the two species as well as their sizes .

hep-ph0612290

i

the variety of accessible final states in @xmath12 decays to two mesons provides an abundant source of information on cp violation and flavour - changing processes . when the final state consists of two vector mesons , an angular analysis of the vector mesons decay products also provides insight into the spin structure of the flavour - changing interaction . for the @xmath13 coupling of the standard model , a specific pattern of the three helicity amplitudes is expected @xcite , such that the longitudinal polarisation fraction @xmath14 should be close to 1 . since @xmath15 was first observed @xcite for penguin - dominated strangeness - changing decays , many theoretical papers addressed the question whether this result could be explained as a strong - interaction effect , or whether it could be reproduced within specific `` new physics '' scenarios @xcite . in this paper we revisit this question using the qcd factorisation framework @xcite to deal with the strong interaction in the amplitude calculation . our study goes beyond previous ones in several respects . on the theoretical side we provide the first complete results for the hard - scattering kernels relevant to vector - vector ( @xmath16 ) final states , correcting several errors in the literature . ( in fact , the only correct calculation is @xcite . ) we also provide a more detailed discussion of the factorisation structure and power counting for the various amplitudes . it seems to have escaped attention so far that , contrary to the longitudinal polarisation amplitude and those relevant to @xmath17 and @xmath18 final states , the transverse polarisation amplitudes do not factorise even at leading power in the heavy - quark expansion . this , together with the high sensitvity to penguin weak - annihilation @xcite , implies that the calculation of polarisation observables stands on a much less solid footing than the calculation of @xmath19 decays . on the phenomenological side , we provide estimates for all @xmath20 decays ( including @xmath21 decays ) and for all parameters that enter the angular analysis . previous studies concentrated on single or a few decay modes and considered the longitudinal polarisation fraction @xmath14 only , making it often difficult to distinguish general patterns from the consequences of particular parameters choices . the organisation of the paper is as follows : in section [ sec : defs ] we summarise the definitions for the helicity amplitudes , angular variables and polarisation observables . the calculation of the @xmath20 decay amplitudes in the qcd factorisation framework is briefly reviewed in section [ sec : factorisation ] . we then discuss a few aspects of the transverse polarisation amplitudes that allow for an understanding of the main characteristics of @xmath20 phenomenology . one important conclusion from this discussion is that the analysis of @xmath1 decays will be much less rigorous and much more uncertain than the corresponding analysis of @xmath22 and @xmath1 modes @xcite . the technical results of the calculation are summarised in an appendix . section [ sec : inputs ] provides the list of input parameters , an overview of the flavour amplitude parameters with theoretical uncertainties , and a classification of the 34 @xmath1 decay channels , which guides the subsequent numerical analysis . we begin the analysis in section [ sec : tree ] with a discussion of branching fractions , cp asymmetries and polarisation observables of the nine tree - dominated decays . among these the four colour - allowed modes can be well predicted . in particular , we show that the time - dependent cp asymmetry measurement in @xmath23 leads to one of the most accurate determinations of the ckm angle @xmath4 . in section [ sec : penguin ] we turn to the 14 colour - allowed penguin - dominated decay modes . it will be seen that theoretical calculations allow for large transverse polarisation within large uncertainties . this suggests to determine the transverse penguin amplitude from data using the well - measured @xmath24 modes . this approach is used to sharpen the predictions for the remaining decay modes in this class . the analysis concludes in section [ sec : others ] with a brief discussion of the remaining penguin - dominated modes , and decays that occur only through weak annihilation . section [ sec : conclusion ] summarises our main results and conclusions .

large longitudinal polarisation is expected with certainty only for a few tree - dominated colour - allowed modes , which receive small penguin and spectator - scattering contributions . this allows for an accurate determination of the ckm angle ( or ) from resulting in we also emphasize that the system is ideal for an investigation of electroweak penguin effects .

we calculate the hard - scattering kernels relevant to the negative - helicity decay amplitude in decays to two vector mesons in the framework of qcd factorisation . we then perform a comprehensive analysis of the 34 decays , including decays and the complete set of polarisation observables . we find considerable uncertainties from weak annihilation and the non - factorisation of spectator - scattering . large longitudinal polarisation is expected with certainty only for a few tree - dominated colour - allowed modes , which receive small penguin and spectator - scattering contributions . this allows for an accurate determination of the ckm angle ( or ) from resulting in we also emphasize that the system is ideal for an investigation of electroweak penguin effects . pitha 06/13 + hep - ph/0612290 + december 21 , 2006 * branching fractions , polarisation and asymmetries + of decays * martin beneke , johannes rohrer and deshan yang + _institut fr theoretische physik e , rwth aachen , + d52056 aachen , germany +theoretical particle physics group ( eken ) , nagoya university , + furo - cho , chikusa - ku , nagoya 464 - 8602 , japan _

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baryons containing heavy quarks are interesting both from the theoretical and experimental points of view . because the bottom and charm quark masses are greater than the intrinsic energy scale of qcd , approximate heavy - quark flavor and spin symmetries constrain the spectrum and dynamics of heavy baryons @xcite . singly charmed and singly bottom baryons exhibit a similar spectrum of excitations of the light degrees of freedom . interactions with the spin of the heavy quark , and hence the hyperfine splittings , are suppressed by @xmath3 . a particularly interesting symmetry emerges for doubly heavy baryons : in the large - mass limit , the two heavy quarks are expected to form a point - like diquark that acts like a single heavy antiquark , and the light degrees of freedom behave as in a heavy - light meson @xcite . the ratio of hyperfine splittings of doubly heavy baryons ( with two equal heavy - quark flavors ) and singly heavy mesons is predicted to approach the value @xmath4 in the heavy - quark limit @xcite . finally , triply heavy baryons can be viewed as baryonic analogues of heavy quarkonia , making them very interesting systems to study in effective field theories and perturbative qcd @xcite . the masses of all low - lying singly charmed baryons with @xmath0 and @xmath1 , and of most of their singly bottom partners , are well known from experiments @xcite . in this sector , the most recent discoveries are the @xmath5 @xcite , and a state that is likely the @xmath1 @xmath6 @xcite ; the @xmath7 an @xmath8 remain to be found . the @xmath5 masses reported by d@xmath9 @xcite and cdf @xcite are inconsistent with each other , but a recent more precise measurement by the lhcb collaboration @xcite agrees with the cdf result . in contrast to the singly heavy baryons , the arena of doubly and triply heavy baryons remains experimentally unexplored to a large extent , with the only possibly observed state being the @xmath10 . the discovery of the @xmath10 was reported by the selex collaboration @xcite , but subsequent searches for this state by the focus @xcite , babar @xcite , belle @xcite , and lhcb collaborations @xcite returned negative results . nevertheless , there is still potential for discoveries of doubly and triply heavy baryons at the lhc @xcite and perhaps also at the coming generation of spectroscopy experiments at besiii @xcite , belle ii @xcite , and panda @xcite . lattice qcd can predict the masses and other properties of heavy baryons from first principles , and can help resolve experimental controversies such as those surrounding the @xmath5 and @xmath11 . for the doubly and triply heavy baryons , which may remain beyond the reach of experiments at the present time , lattice qcd results can also serve as a benchmark for other theoretical approaches , such as quark models and perturbative qcd . complete control over all sources of systematic uncertainties , including the nonzero lattice spacing and finite lattice volume , unphysical values used for the quark masses , any approximations made for the heavy quarks , as well as excited - state contamination in the correlation functions , is essential in both of these contexts . most lattice calculations of heavy baryon masses that have been published to date are still lacking in some of these aspects . the earliest studies @xcite were performed in the quenched approximation , removing the effects of sea quarks to reduce the computational cost but at the expense of connection to experiment . the first unquenched calculations were reported in refs . @xcite . since then , additional unquenched calculations have been performed with various choices of lattice actions for the light and heavy quarks @xcite ; reviews can be found in refs . @xcite . in this paper , we present the first lattice qcd determination of singly , doubly , and triply heavy baryon masses that includes both charm and bottom quarks in any combination , and also achieves good control over all major sources of systematic uncertainties . our calculation includes dynamical up , down , and strange quarks implemented with a domain - wall action @xcite , and is performed at two different lattice spacings and seven different values of the up / down quark mass corresponding to pion masses as low as 227(3 ) mev . because the masses of the charm and bottom quarks are not small in units of the lattice spacing , special heavy - quark actions are needed for them to avoid large discretization errors . we use a relativistic heavy - quark action @xcite for the charm quarks and improved nonrelativistic qcd @xcite for the bottom quarks . details of the actions and parameters are given in sec . [ sec : actions ] . the interpolating fields we use for the heavy baryons and our methodology for fitting the two - point functions are described in sec . [ sec:2pt ] . we extrapolate the results for all baryon masses to the physical pion mass and the continuum limit as explained in sec . [ sec : extrap ] . for the singly and doubly heavy baryon masses , heavy - hadron chiral perturbation theory at next - to - leading order is used to fit the light - quark mass dependence and to remove the leading finite - volume effects . because some of our data sets use valence light - quark masses lower than the sea - quark masses , we use the partially quenched extension of heavy - hadron chiral perturbation theory @xcite . for the singly heavy baryons , we generalize the expressions given in ref . @xcite to include hyperfine splittings . the final results for the baryon masses and mass splittings are presented in sec . [ sec : finalresults ] , which also includes a detailed discussion of the systematic uncertainties . we conclude in sec . [ sec : conclusions ] with a comparison of our results to the literature .

we consider all possible combinations of charm and bottom quarks , and compute a total of 36 different states with and . we use domain - wall fermions for the up , down , and strange quarks , a relativistic heavy - quark action for the charm quarks , and nonrelativistic qcd for the bottom quarks . our analysis includes results from two different lattice spacings and seven different pion masses . we perform extrapolations of the baryon masses to the continuum limit and to the physical pion mass using heavy - hadron chiral perturbation theory including and finite - volume effects . for the 14 singly heavy baryons that have already been observed , our results agree with the experimental values within the uncertainties .

we calculate the masses of baryons containing one , two , or three heavy quarks using lattice qcd . we consider all possible combinations of charm and bottom quarks , and compute a total of 36 different states with and . we use domain - wall fermions for the up , down , and strange quarks , a relativistic heavy - quark action for the charm quarks , and nonrelativistic qcd for the bottom quarks . our analysis includes results from two different lattice spacings and seven different pion masses . we perform extrapolations of the baryon masses to the continuum limit and to the physical pion mass using heavy - hadron chiral perturbation theory including and finite - volume effects . for the 14 singly heavy baryons that have already been observed , our results agree with the experimental values within the uncertainties . we compare our predictions for the hitherto unobserved states with other lattice calculations and quark - model studies . = 1

hep-ph0405232

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we calculated the dominant two - loop electroweak correction , of @xmath0 , to the partial width of the decay into two photons of the sm higgs boson in the intermediate mass range , @xmath3 , where this process is of great phenomenological relevance for the searches at hadron colliders of this elusive missing link of the sm . we evaluated the relevant feynman diagrams by application of the asymptotic - expansion technique exploiting the mass hierarchy @xmath124 . in this way , we obtained an expansion of the full @xmath0 result in the mass ratio @xmath125 through @xmath126 . the convergence property of this expansion and our experience with the analogue expansion at the born level , where the exact result is available for reference , lead us to believe that these five terms should provide a very good approximation to the exact result for @xmath127 gev . by the same token , the deviation of this approximation for the @xmath0 amplitude @xmath121 from the unknown exact result for this quantity is likely to range from 2% to 20% as the value of @xmath67 runs from 140 gev to @xmath128 . in the intermediate higgs - boson mass range , the @xmath0 electroweak correction reduces the size of @xmath97 by approximately 2.5% and thus fully cancels the positive shift due to the well - known @xmath123 qcd correction @xcite . as a by - product of our analysis , we also recovered the @xmath0 correction to the partial width of the decay into two gluon jets of the intermediate - mass higgs boson , in agreement with the literature @xcite . we thank paolo gambino for a useful communication . this work was supported in part by the bundesministerium fr bildung und forschung through grant no . 05 ht4gua/4 , by the deutsche forschungsgemeinschaft through grant no . kn 365/1 - 1 , by the helmholtz - gemeinschaft deutscher forschungszentren through grant no . vh - ng-008 , and by sun microsystems through academic equipment grant no . edud-7832 - 000332-ger . h. zheng , d. wu , phys . d 42 ( 1990 ) 3760 ; + a. djouadi , m. spira , j.j . van der bij , p.m. zerwas , phys . b 257 ( 1991 ) 187 ; + s. dawson , r.p . kauffman , phys . d 47 ( 1993 ) 1264 ; + a. djouadi , m. spira , p.m. zerwas , phys . b 311 ( 1993 ) 255 ; + k. melnikov , o.i . yakovlev , phys . b 312 ( 1993 ) 179 ; + m. inoue , r. najima , t. oka , j. saito , mod . lett . a 9 ( 1994 ) 1189 ; + j. fleischer , o.v . tarasov , z. phys . c 64 ( 1994 ) 413 ; + j. fleischer , o.v . tarasov , v.o . tarasov , phys . b 584 ( 2004 ) 294 . m. steinhauser , in : b.a . kniehl ( ed . ) , proceedings of the ringberg workshop on the higgs puzzle what can we learn from lep2 , lhc , nlc , and fmc ? , ringberg castle , germany , 813 december 1996 , world scientific , singapore , 1997 , p. 177 , report no . hep - ph/9612395 . t. seidensticker , in : g. athanasiou ( ed . ) , proceedings of the 6th international workshop on new computing techniques in physics research : software engineering , artificial intelligence , neural nets , genetic algorithms , symbolic algebra , automatic calculation ( aihenp99 ) , heraklion , greece , 12 - 16 april 1999 , spires conference no c99/04/12 , report no . hep - ph/9905298 ; + r. harlander , t. seidensticker , m. steinhauser , phys . b 426 ( 1998 ) 125 . a. djouadi , p. gambino , phys . rev . lett . 73 ( 1994 ) 2528 ; chetyrkin , b.a . kniehl , m. steinhauser , phys . rev . lett . 78 ( 1997 ) 594 ; + k.g . chetyrkin , b.a . kniehl , m. steinhauser , nucl . b 490 ( 1997 ) 19 .

we compute the dominant two - loop electroweak correction , of , to the partial width of the decay of an intermediate - mass higgs boson into a pair of photons . this correction reduces the born result by approximately 2.5% . as a by - product of our analysis , we also recover the correction to the partial width of the higgs - boson decay to two gluon jets .

we compute the dominant two - loop electroweak correction , of , to the partial width of the decay of an intermediate - mass higgs boson into a pair of photons . we use the asymptotic - expansion technique in order to extract the leading dependence on the top - quark mass plus four expansion terms that describe the dependence on the- and higgs - boson masses . this correction reduces the born result by approximately 2.5% . as a by - product of our analysis , we also recover the correction to the partial width of the higgs - boson decay to two gluon jets . pacs numbers : 12.15.ji , 12.15.lk , 14.80.bn

1504.00317

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understanding the production mechanism of low-@xmath0 quarkonia in nucleon - nucleon collisions is of fundamental importance to properly use them as probes of deconfinement or collectivity in heavy ion collisions . indeed , most of the analysis of quarkonium production in nucleus - nucleus collisions are carried out on the bulk of the cross section , namely at low @xmath0 . recently , comparisons between alice data @xcite without @xmath0 cut and cms data @xcite with @xmath0 cut in pbpb collisions at @xmath8 tev showed an unexpected suppression pattern of the charmonia , at variance with the simple picture of quarkonium melting in deconfined quark matter @xcite . however , to properly interpret this observation , it is essential to rule out the possibility that a part of the effect observed could be due to a difference in the production mechanism in individual nucleon - nucleon collisions at low and at larger @xmath0 . the propagation of a colour - octet pair in a deconfined medium certainly differs from that of a colour - singlet pair ; this can result into a different nuclear suppression ( see _ e.g. _ @xcite ) . on the contrary , as regards the bottomonia , the observation of the expected sequential - suppression pattern has been claimed by cms @xcite . further , the effect of normal nuclear matter may also significantly depend on how the pair is produced : the recently revived fractional energy loss @xcite would for instance act on long - lived colour - octet states and probably differently if the heavy quark state is already produced colourless at short distance , as postulated in the csm @xcite . saturation effects in @xmath9 collisions also do depend on the colour state of the perturbatively produced heavy - quark pair @xcite despite the possibility that nrqcd factorisation would not hold at low @xmath0 , several nrqcd analyses have thus been carried earlier to evaluate the impact of the colour - octet channels to the @xmath0-integrated @xmath3 yields @xcite . a first study of the impact of initial state radiations ( isr ) on the very low @xmath0 @xmath3 s and @xmath10 s was recently carried out successfully in nrqcd @xcite yet at the cost of introducing additional non - perturbative parameters . whereas , based on an analysis of the sole early rhic data , cooper _ et al . _ argued @xcite that the universality of nrqcd was safe and that colour - singlet contributions to the @xmath0-integrated @xmath3 yields were negligible , the global analysis of maltoni _ et al . _ at nlo showed @xcite that the colour - octet long - distance matrix elements ( ldmes ) required to describe the total prompt @xmath3 yield from fixed - target energies to rhic were _ one tenth _ of that expected from the leading - order fit of the @xmath0-differential cross sections at tevatron energies . such fits of the @xmath0-differential @xmath3 cross sections have recently been extended to nlo _i.e . _ one - loop accuracy on the prompt @xmath3 yields some of them focusing on the larger @xmath0 data and explicitly including the feed - down contributions @xcite , some enlarging the analysis beyond hadroproduction and including rather low-@xmath0 data @xcite and on the @xmath11 yields @xcite . thanks to these studies , we can significantly extend the existing nrqcd studies of the @xmath0-integrated cross section by combining in a coherent manner , the hard parts or wilson coefficients up to @xmath2 , first derived by @xcite and which we have systematically checked with fdc @xcite , with the nrqcd matrix elements fitted at nlo on the @xmath0 dependence of the yields . one can indeed consider the _ @xmath0-integrated _ and the _ @xmath0-differential _ cross sections as two different observables their born contributions involve different diagrams and such a procedure is not a all trivial physics - wise . as we detail later , our results show that the data do not allow for a global description of both the @xmath0-integrated and @xmath0-differential quarkonium yields . as a point of comparison , we also had a look at colour - evaporation - model - like ( cem ) predictions derived from nrqcd following the work of @xcite and we found out that it can not reproduce @xmath0-integrated yields using the ldmes obtained following the relations of @xcite after identifying the minimal singlet transition to that of the csm . _ a contrario _ , results obtained from the traditional cem implementation at one loop do not show a similar issue . the inability of colour - octet dominance within nrqcd to provide a global description of both low and large @xmath0 data is in line with the recent findings @xcite that the sole lo colour - singlet contributions are sufficient to account for the magnitude of the total cross section and its dependence in rapidity , @xmath12 , from rhic , tevatron all the way to lhc energies . any additional contribution in this energy range creates a surplus as compared to data . however , as we also study in a dedicated section , the total nlo csm cross section shows a weird energy dependence at lhc energies . the problem is striking for the @xmath3 , less for the @xmath10 . in any case , one should be very careful in interpreting these results . in particular , such nlo results can not be considered as a improvement of the lo ones . we also observe the same issue for @xmath13 and @xmath14 production for which there is no final - state - gluon radiation at born order . we are therefore tempted to attribute this behaviour to large loop contributions which become negative at low @xmath0 , rather than to specific effects related to the @xmath15 production _ per se_. a quick inspection of the rather concise one - loop results @xcite for @xmath13 and @xmath14 production in the tmd factorisation formalism unfortunately does not reveal any obvious negative contributions and does not help in the understanding of this rather general issue of quarkonium production in collinear factorisation . the same problems appear with some co channels as well and may therefore cast doubts on the reliability of our results in the @xmath16 region where some contributions shows a strange behaviour in particular at lhc energies . at this stage , we are not able to conclude from our observations whether these problems are indicative of the break down of nrqcd factorisation at low @xmath0 and low @xmath17 or at low @xmath17 only . however , for sure , none of the above observations can reasonably support the idea that co transitions are dominant at low @xmath0 . such a conclusion would be for the least premature . the structure of the paper is as follows . in section [ sec : x - section ] , we detail the procedure to evaluate the @xmath0-integrated yield at one - loop accuracy in nrqcd and we explain the idea underlying this first complete one - loop analysis . in section [ sec : ldmes ] , we explain our selection of ldmes determined at nlo . in section [ sec : data ] , we briefly comment on the existing world data sets for @xmath3 , @xmath18 and @xmath5 analysis of gong _ et al . _ @xcite treats the @xmath5 , @xmath19 and @xmath20 , the lack of knowledge on the @xmath21 and @xmath22 yields and their corresponding feed down to @xmath19 and @xmath20 makes the analysis of their _ direct _ yield delicate ; we have thus decided not to consider these in the present study . our choice has been confirmed by the recent lhcb result @xcite that a large fraction of the @xmath19 and @xmath20 yield actually comes from @xmath21 and @xmath22 decays up to 40% in the @xmath20 case . ] . we also explain how we estimate the direct yields . in section [ sec : results_nrqcd ] , we show and discuss our results for the first full one - loop nrqcd analysis of quarkonium hadroproduction . to go further in the interpretation of some of our results , we discuss in section [ sec : results_cem ] the prediction of nrqcd using cem - like ldmes . this is also compared with the conventional approach based on quark - hadron duality . section [ sec : results_csm ] focuses on csm results both for the @xmath15 states considered here and for the @xmath23 states for which analytical results exist . our conclusions are presented in section [ sec : conclusion ] .

we compute the energy dependence of the-integrated cross section of directly produced quarkonia in collisions at next - to - leading order ( nlo ) , namely up to , within nonrelativistic qcd ( nrqcd ) . our analysis is based on the idea that the-_integrated _ and the-_differential _ cross sections can be treated as two different observables . the colour - octet nrqcd parameters needed to predict the-integrated yield can thus be extracted from the fits of the-differential cross sections at mid and large . for the first time , the total cross section is evaluated in nrqcd at full nlo accuracy using the recent nlo fits of the-differential yields at rhic , the tevatron and the lhc . both the normalisation and the energy dependence of the , and , we obtained , are in disagreement with the data irrespective of the fit method . the same is true if one uses cem - like colour - octet nrqcd parameters . if , on the contrary , one disregards the colour - octet contribution , the existing data in the tev range are well described by the contribution in the colour - singlet model which , at , however shows an unphysical energy dependence . this may impact the interpretation of quarkonium suppression in high - energy proton - nucleus and nucleus - nucleus collisions .

we compute the energy dependence of the-integrated cross section of directly produced quarkonia in collisions at next - to - leading order ( nlo ) , namely up to , within nonrelativistic qcd ( nrqcd ) . our analysis is based on the idea that the-_integrated _ and the-_differential _ cross sections can be treated as two different observables . the colour - octet nrqcd parameters needed to predict the-integrated yield can thus be extracted from the fits of the-differential cross sections at mid and large . for the first time , the total cross section is evaluated in nrqcd at full nlo accuracy using the recent nlo fits of the-differential yields at rhic , the tevatron and the lhc . both the normalisation and the energy dependence of the , and , we obtained , are in disagreement with the data irrespective of the fit method . the same is true if one uses cem - like colour - octet nrqcd parameters . if , on the contrary , one disregards the colour - octet contribution , the existing data in the tev range are well described by the contribution in the colour - singlet model which , at , however shows an unphysical energy dependence . a similar observation is made for . this calls for a full nnlo or for a resummation of the initial - state radiation in this channel . in any case , past claims that colour - octet transitions are dominantly responsible for low- quarkonium production are not supported by our results . this may impact the interpretation of quarkonium suppression in high - energy proton - nucleus and nucleus - nucleus collisions .

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networks of processor - sharing queues with state - dependent service rates have been extensively used to model a large variety of communication and computation systems like content delivery systems @xcite , computer clusters @xcite and data networks @xcite . they are natural models for such systems as they capture the complex interactions between different jobs and also have a promise of analytical tractability of user performance when subject to stochastic loads . indeed , in the past two decades researchers have been able to obtain explicit performance expressions and bounds for several such systems , see @xcite . however , few performance results scale well with the system size . those that do rely on restrictive assumptions related to the topology or the symmetry of the system @xcite . one of the main goals of this paper is to provide scalable performance results for a class of processor - sharing systems which find applications in bandwidth - sharing networks and computer clusters . one of the key features of processor - sharing networks is the allocation of the service rates per queue in each state . a particular class of resource allocations which is more tractable for performance analysis is characterized by the balance property which constraints the relative gain in the service rate at one queue when we remove a job from another queue . processor - sharing networks where the resource allocation satisfies this property are called whittle networks @xcite . in particular , if the service rates are constrained by some capacity set , corresponding to the resources of the system considered , then there exists a unique policy which satisfies the balance property while being efficient , namely balanced fairness @xcite . in this paper we focus on networks which are constrained by a polymatroid capacity set @xcite and operate under balanced fair resource allocation policy . it was proved in @xcite that balanced fairness is pareto - efficient when it is applied in polymatroid capacity sets , which in practice yields explicit recursion formulas . however , if no further assumptions are made on the structure of the system , the complexity of these formulas is exponential with the number of queues . it was proved in @xcite that it can be made linear at the cost of strict assumptions on the overall symmetry of the capacity set and the traffic intensity at each queue . under symmetry in interaction across queues , it was shown in @xcite that the performance is robust to heterogeneity in loads and system configuration under an appropriate scaling regime . however , there is little understanding of performance for scenarios where queues themselves interact in heterogeneous fashion . in this paper , we consider a scenario where the network is divided into a finite number of parts , so that queues are exchangeable within each part and asymmetric across different parts . for such systems , that we call poly - symmetric , we obtain a performance expression with computational complexity which is polynomial in the number of queues . we demonstrate the usefulness of these bounds by applying them to tree data networks , which are representative of backhaul networks , and to randomly configured heterogeneous computer clusters . in addition , we provide a monotonicity bound which allows us to bound performance of systems with capacity regions which are ` closely ' poly - symmetric . the paper is organized as follows . section [ sec : model ] introduces the model and shows that it applies to systems as varied as tree data networks and computer clusters . we also recall known facts about balanced fairness . in section [ sec : polysymmetry ] , we introduce the notion of poly - symmetry and show that it yields explicit recursion formulas for the performance metrics which have a complexity that is polynomial in the number of queues in the network . finally , section [ sec : bounds ] gives stochastic bounds to compare the performance of different systems . we conclude in section [ sec : ccl ] .

this in turn allows us to derive stochastic bounds for a larger class of networks which satisfy less restrictive symmetry assumptions . these results are applied to practical examples of tree data networks and computer clusters . + * keyworkds : * processor - sharing networks , performance , balanced fairness , poly - symmetry

we consider a network of processor - sharing queues with state - dependent service rates . these are allocated according to balanced fairness within a polymatroid capacity set . balanced fairness is known to be both insensitive and pareto - efficient in such networks , which ensures that the performance metrics , when computable , will provide robust insights into the real performance of the system considered . we first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size when we allow for some controlled asymmetry , in the sense that the network contains a fixed number of parts wherein all queues are ` exchangeable ' . this in turn allows us to derive stochastic bounds for a larger class of networks which satisfy less restrictive symmetry assumptions . these results are applied to practical examples of tree data networks and computer clusters . + * keyworkds : * processor - sharing networks , performance , balanced fairness , poly - symmetry

1108.5490

i

it was the invention of quantum error correcting codes @xcite ( qeccs ) that opened quantum computing ( qc ) as a theoretical possibility . however , high precision required for error correction @xcite combined with the large number of auxiliary qubits necessary to implement it , have so far inhibited any practical realization beyond proof - of - the - principle demonstrations@xcite . in any qecc , one needs to perform certain many - body quantum measurements in order to decide how to correct the encoded state . the practical difficulty is that a generic code requires measurements which are both complicated and frequent at the same time . it is therefore clear that a quantum computer can only be build via a thorough optimization at every step of the design . in particular , code optimization targets codes that combine good parameters with fairly simple measurements . it is also desirable to parallelize these measurements given a specific on - chip layout of a qc architecture . to date , the main focus of the qecc - research has been on finding good codes with the traditional code parameters , which are the block length @xmath0 , code dimension @xmath1 , and code distance @xmath2 ( or code rate @xmath3 and the relative distance @xmath4 ) . for stabilizer codes @xcite , we also consider the number of encoded qubits @xmath5 . a number of stabilizer codes@xcite have been designed that meet or nearly achieve the existing bounds on distance @xmath2 for the given @xmath6 and @xmath0 . code parameters can be further refined by going beyond the family of stabilizer codes . one example is a recently introduced framework of codeword - stabilized ( cws ) quantum codes@xcite . a qubit cws code @xmath7 ( in standard form ) is determined by a graph @xmath8 and a classical binary code @xmath9 . cws codes include all stabilizer codes as a subclass ( the corresponding binary code @xmath10 must be linear ) , but also the codes which have been proved to have parameters superior to those of any stabilizer code@xcite . unfortunately , typical gains in code dimension @xmath1 correspond to a fraction of a qubit . moreover , error - correcting algorithms known for general non - additive cws codes have exponential complexity@xcite , as opposed to polynomial complexity of the stabilizer codes . even for the relatively simple additive codes , their optimization is a very difficult problem that has exponential complexity . this is one of the main reasons as to why the two relatively simple code families are almost exclusively used among stabilizer codes to estimate the threshold accuracy required for scalable quantum computation : the concatenated codes@xcite and the surface codes@xcite which originated from the toric codes@xcite . both families have very low code rates that scale as inverse powers of code distance . in this work we explore how the framework of cws codes can be used to relegate the design of quantum stabilizer codes to classical binary linear codes in order to simplify the overall design . in particular , we formulate several theorems framing the parameters of an additive cws code which can be obtained from a given graph . we also suggest a simple decomposition of the @xmath11 generator matrix corresponding to the stabilizer in terms of the graph adjacency matrix and the parity check matrix of the binary code . finally , we design several graph families corresponding to regular lattices which result in some particularly good codes . these include graphs with circulant adjacency matrix which can be used to construct single - generator cyclic additive codes , a class of codes overlooked in previous publications . in particular , we prove the existence of single - generator cyclic additive codes with the parameters @xmath12 $ ] , @xmath13 and @xmath14 $ ] ( version of toric codes ) . note that these code families have distances that are not bounded , unlike any cws code families constructed previously@xcite . the paper is organized as follows . in sec . [ sec : notations ] , we introduce the notations and briefly review some known results for quantum and classical codes . in sec . [ sec : upper - bound ] , we establish several upper bounds on general cws codes . in sec . [ sec : additive - cws ] we give a cws decomposition of the @xmath15 matrix corresponding to the stabilizer generators . in sec . [ sec : gv ] , we formulate the gilbert - varshamov ( gv ) bounds for additive cws codes which can be obtained from a given graph . cyclic additive cws and more general single - generator additive cyclic codes are considered in sec . [ sec : cyclic - cws ] where we discuss their properties and give several examples . we give our conclusions in sec . [ sec : conclusions ] .

we consider design of the quantum stabilizer codes via a two - step , low - complexity approach based on the framework of codeword - stabilized ( cws ) codes . in this framework we also consider additive cyclic cws codes and show that these codes correspond to a previously unexplored class of single - generator cyclic stabilizer codes .

we consider design of the quantum stabilizer codes via a two - step , low - complexity approach based on the framework of codeword - stabilized ( cws ) codes . in this framework , each quantum cws code can be specified by a graph and a binary code . for codes that can be obtained from a given graph , we give several upper bounds on the distance of a generic ( additive or non - additive ) cws code , and the lower gilbert - varshamov bound for the existence of additive cws codes . we also consider additive cyclic cws codes and show that these codes correspond to a previously unexplored class of single - generator cyclic stabilizer codes . we present several families of simple stabilizer codes with relatively good parameters .

0801.2413

i

in simple deterministic dynamical systems physical quantities like transport coefficients can be fractal functions of control parameters . this finding was first reported for a one - dimensional piecewise linear map lifted periodically onto the whole real line , for which the diffusion coefficient was computed by using markov partitions and topological transition matrices @xcite . a generalization of this result was obtained for a map with both drift and diffusion by deriving exact analytical solutions for the transport coefficients @xcite . further maps modeling chemical reaction - diffusion @xcite and anomalous diffusion @xcite yielded also fractal transport coefficients . recent work aimed at physically more realistic models like ( hamiltonian ) particle billiards , for which computer simulations yielded transport coefficients that are non - monotonic under parameter variation @xcite . ref . @xcite contains a summary of this line of research . these results asked for a more detailed characterization of the `` fractality '' of transport coefficients . a first attempt in this direction was reported by klages and klau @xcite , who used standard techniques from the theory of fractal dimensions for characterizing the drift and diffusion coefficients of the map studied in @xcite . they numerically computed a non - integer box counting dimension for these curves which varied with the parameter interval , leading to the notion of a `` fractal fractal dimension '' . these results were questioned by koza @xcite , who computed the oscillation of these graphs at specific markov partition parameter values . his work suggested a dimensionality of one by conjecturing that there exist non - trivial logarithmic corrections to the usual power law behaviour in the oscillation . this research reveals the need to study the parameter dependence of transport coefficients in a rigorous mathematical setting , which can be formulated as follows : given a parametrized family of chaotic dynamical systems @xmath4 on an interval @xmath5 with unique invariant physical measures @xmath6 together with a family of sufficiently regular observables @xmath7 one has , under suitable mixing assumptions on the systems @xmath8 , a law of large numbers and a central limit theorem for the partial sum processes @xmath9 , namely @xmath10 and @xmath11 where @xmath12 . for suitable choices of the observables @xmath13 , the process @xmath14 is just the deterministic random walk generated by a lift of the map @xmath15 to the real axis , and @xmath1 and @xmath2 are the drift and diffusion coefficient of this random walk respectively . there are a few rigorous results in the literature describing the dependence of @xmath6 and of quantities like @xmath1 for various classes of systems . without going into the details they can be summarized as follows : if the maps @xmath15 and the observables @xmath13 depend smoothly on @xmath16 and if the topological conjugacy class of @xmath15 is not changed when @xmath16 is varied , then @xmath6 ( and hence @xmath1 ) depends differentiably on @xmath16 @xcite . if the topological class changes , quantities like @xmath1 may behave less regular and have a modulus of continuity not better than @xmath17 , even for very simple maps @xmath15 like symmetric tent maps @xcite . on the other hand , this modulus of continuity is the rule for systems whose perron - frobenius operator ( acting on a suitable space of `` regular '' densities ) has a spectral gap @xcite . the goal of this paper is to explicitly relate these mathematical results to transport coefficients . we do so by rigorously proving continuity properties of @xmath1 and @xmath2 under parameter variation for certain classes of deterministic maps . in section [ sec : general ] we give a general estimate for families of dynamics ( deterministic or not ) , which can be described in terms of perron - frobenius operators with exponential mixing properties . the applicability of these general results to piecewise @xmath0 expanding interval maps and in particular to the class of piecewise linear maps discussed in @xcite is checked in section [ sec : checking ] . the main result is that @xmath2 has a modulus of continuity of order @xmath3 , i.e. @xmath2 is lipschitz continuous up to quadratic logarithmic corrections . in section [ sec : transport ] we summarize the general results for transport coefficients in the special case of piecewise linear maps and provide more precise estimates for special parameters . our analytical findings are verified by numerical computations in section [ sec : numerical ] , for which we use exact analytical formulas of the transport coefficients @xcite . particularly , we numerically analyze local variations of these properties . our work corrects and amends previous results reported in @xcite .

we consider families of dynamics that can be described in terms of perron - frobenius operators with exponential mixing properties . for piecewise expanding interval maps we rigorously prove continuity properties of the drift and of the diffusion coefficient under parameter variation . our main result is that has a modulus of continuity of order , i.e. is lipschitz continuous up to quadratic logarithmic corrections . for a special class of piecewise linear maps we provide more precise estimates at specific parameter values . our analytical findings are verified numerically for the latter class of maps by using exact formulas for the transport coefficients . we numerically observe strong local variations of all continuity properties .

we consider families of dynamics that can be described in terms of perron - frobenius operators with exponential mixing properties . for piecewise expanding interval maps we rigorously prove continuity properties of the drift and of the diffusion coefficient under parameter variation . our main result is that has a modulus of continuity of order , i.e. is lipschitz continuous up to quadratic logarithmic corrections . for a special class of piecewise linear maps we provide more precise estimates at specific parameter values . our analytical findings are verified numerically for the latter class of maps by using exact formulas for the transport coefficients . we numerically observe strong local variations of all continuity properties .

1103.4143

i

detailed cosmological observations made during the last decade ( see @xcite for some of the latest results ) have made it clear that the minimal cosmological model ( scdm ) based on the cosmological principle ( homogeneity , isotropy , validity of general relativity ) and with a purely radiation and matter content ( baryonic and cold dark matter ( cdm ) ) , is inconsistent with observations . the simplest extension of scdm able to reconcile it with the observed accelerated cosmic expansion ( ) involves the existence of a homogeneous , constant in time energy density that constitutes about @xmath11 of the total energy density of the universe and is known as the _ cosmological constant _ @xcite . a time - dependent generalization of this energy has been dubbed _ dark energy_. the repulsive gravitational properties of the cosmological constant dominate on large scales and may induce the observed acceleration . due to its simplicity and its consistency with most cosmological observations is currently the _ standard _ cosmological model , replacing scdm , which held that status in the early 90 s , when observational data were far less extensive and accurate . however , is also faced with some challenges , which originate from both theoretical and observational considerations . the two main theoretical challenges of the model are _ fine tuning _ and _ lack of theoretical motivation_. indeed , in order to make the model consistent with observations , the energy scale of the cosmological constant must be fine - tuned to an unnaturally small value , @xmath12 orders of magnitude smaller than the one anticipated from theoretical models of quantum field theory @xcite . from the observational point of view , even though is in agreement with the vast majority of data , there is a set of observations that appear to be mildly inconsistent with the model at the @xmath13 level . most of these observations , which we proceed to summarize , seem to be related to the existence of a preferred cosmological axis : * * planarity and alignment of the cmb low multipole moments : * it has been known since 2003 @xcite ( see @xcite for recent reviews ) that the quadrupole and octopole components of the cmb temperature perturbation maps ( the largest scale part of those maps ) are dominated by planar features which are unnaturally aligned with each other in the direction ( perpendicular to the planes ) @xmath14 @xcite . the probability that such combination of planarity and alignment occurs in a random gaussian map is less than @xmath15 @xcite . this peculiar feature has been attributed to a posteriori considerations @xcite , namely _ within a large number of features of a map , it is statistically anticipated that some of them will present large statistical fluctuations_. this type of argument would be stronger if the large fluctuations affected random uncorrelated features ( for example multipoles with @xmath16 and @xmath17 ) . in that case we would have an a posteriori arbitrary selection of features . the quadrupole - octopole moments , however , constitute _ all _ the information we have about the cmb temperature fluctuation maps on the largest angular scales . thus the observed alignment could also be restated by saying that _ the large scale features of the cmb maps are significantly more planar than anticipated for random gaussian maps_. the fact that the _ preferred _ plane is relatively close to the galactic plane ( which is usually masked due to noise , before the construction of the power spectrum is made ) is probably responsible @xcite for the relatively low values of the angular power spectrum components @xmath18 , @xmath19 , which is considered by some authors to be an independent puzzle @xcite . * * large scale velocity bulk flows : * recent studies @xcite have detected a large scale flow with a bulk velocity in the range @xmath20 $ ] km / s towards @xmath21 on scales @xmath22 . this detection is larger than the prediction and inconsistent with it at the level of @xmath23 . * * large scale alignment in the qso optical polarization data : * quasar polarization vectors are not randomly oriented over the sky with a probability often in excess of 99.9% . the alignment effect seems to be prominent along a particular axis with direction @xmath24 @xcite . * * profiles of cluster haloes : * predicts shallow , low concentration and density profiles , in contrast to some observations which point to denser cluster haloes @xcite . as announced , three of the above four puzzles are large - scale effects related to preferred cosmological directions ( cmb multipole alignments , qso polarization alignment and large scale bulk flows ) ; those directions , moreover , appear to be not far from each other , being approximately normal to the axis of the ecliptic poles @xmath25 and lying close to the ecliptic plane and the equinoxes . this coincidence has triggered investigations for possible systematic effects related to the cmb preferred axis but no significant such effects have been found @xcite . finally , it should be mentioned that , in addition to the discussed large - scale effects , the model also faces some issues on galactic scales ( missing satellites problem @xcite and the cusp / core nature of the central density profiles of dwarf galaxies @xcite ) . in spite of those problems , the construction of generalizations of has been motivated so far mainly by theoretical rather than observational considerations . some of the most popular ideas among those that go beyond are the following : * * time dependent dark energy @xcite : * within this approach , dark energy retains its homogeneous and isotropic character , but may present a time dependence . this time dependence aims at solving ( or at least alleviating ) the previously mentioned fine - tuning problem , i.e. the unnaturally small value of the current dark energy required by the observations . indeed , it turns out that a dark energy density which is larger at early times and evolves via proper dynamics to its present low value is easier to accommodate in theoretical models . a representative of this class of models is _ quintessence _ , where the role of dark energy is played by a dynamically evolving scalar field . however , for this evolution to be consistent with the observations , the scalar field must be assigned an extremely ( fine - tuned ) small mass , fact that makes the additional complexity introduced in this class of models be of questionable value . * * modified gravity : * the repulsive gravity provided by the cosmological constant on large scales can also be induced by modifications of general relativity in the context of a homogeneous and isotropic background . several such modifications have been suggested , including scalar tensor gravity @xcite , dgp models that involve gravitons leaking through large extra dimensions @xcite , @xmath26 gravity @xcite etc . these models are well motivated as complete geometric physical theories , but they have more degrees of freedom than and they also require significant fine - tuning in order to be consistent with both the observed cosmic accelerating expansion and the gravitational solar system constraints that prevent large local departures from general relativity . * * inhomogeneous and isotropic lemaitre - tolman - bondi void models @xcite : * within this framework , an additional dark energy component is not needed to secure consistency with the cosmological data that indicate accelerating expansion . the basic idea that lies behind them is to consider that the increased expansion rate occurs locally in space rather than at recent cosmological times , a fact that can be achieved by assuming a locally - reduced matter energy density @xcite . thus , the observer is placed close to the center of a giant void with dimensions of a few gpc @xcite . even though this approach is free of dark energy , it is by no means free of fine tuning . apart from the unnatural assumption of giant - size gpc voids , which are very unlikely to be produced in any cosmology , these models require the observer to be placed within a very small volume at the center of the void ( about @xmath27 of the total volume of the void ) . a slightly off - center observer , however , will naturally experience a preferred cosmological direction ( towards the center of the void ) , which may help to resolve some of the observational puzzles of discussed above . in the present study we consider yet an alternative approach for the generalization of . instead of breaking the time translation invariance of dark energy , as in the class of quintessence models , we break its space translation invariance ( homogeneity ) . we thus consider a spherically symmetric overdensity of dark energy with typical scale of a few gpc : _ inhomogeneous dark energy ( ide)_. this class of models adds degrees of freedom to in a manner that is generically different from the other three classes considered above . thus , it also has specific advantages as compared to them . in particular : * * physical mechanism : * there is a well - defined _ physical mechanism _ that can produce this type of spherically symmetric , hubble - scale ide . it is based on applying the principles of _ topological inflation _ @xcite to the case of late - time acceleration . according to the idea of topological inflation , the false vacuum energy of the core of a topological defect can give rise to accelerating expansion if the core size reaches the hubble scale when gravity starts dominating the dynamics . thus , for example , a recently formed global monopole with appropriate scale of symmetry breaking and coupling could naturally produce a hubble - scale , spherically symmetric , isocurvature dark energy overdensity . by analogy with topological inflation , this mechanism may be called _ topological quintessence_. * * naturally large scale : * whereas matter inhomogeneities ( voids ) of a few gpc are very unlikely to be formed through large scale structure mechanisms , ide on hubble scales is more natural and easy to construct . in the ide case ( also in contrast to inhomogeneous matter models ) , the homogeneous limit ( ) is consistent with observations and one interesting question is _ ` what is the smallest scale of inhomogeneity for which this consistency remains?'_. * * more natural off - center observers ( less fine tuning ) : * due to the arbitrarily large scale of ide ( supported by observations , as we will see ) , there is less fine tuning for the location of the observer with respect to the center of the spherical inhomogeneity . in fact , as the inhomogeneity scale approaches the horizon the model becomes indistinguishable from and there is no observational constraint for the location of the observer . * * natural generation of a preferred cosmological axis : * as we have seen , most of the observational challenges of hint towards the existence of a preferred cosmological direction . such a direction is naturally provided for an off - center observer in an inhomogeneous matter or dark energy model : _ the direction that connects the location of the observer with the center of the inhomogeneity_. the displacement of the observer naturally leads to an alignment of low cmb multipole moments and bulk velocity flows . the additional degrees of freedom ( with respect to ) introduced in this class of models are similar to the corresponding ones in models that break the time translation invariance of dark energy . we also need a scalar field , but now with spatial rather than temporal dependence . compared to matter void models , however , the ide setup requires more ( and less natural ) degrees of freedom . this is the price to pay for the reduction in the amount of fine tuning . the goal of the present study is to investigate some of the observational consequences and constraints of ide models . we focus on the constraints coming from snia data and the cmb low multipole moments . we also discuss the physical mechanism that could give rise to ide ( _ topological quintessence _ ) , although we postpone a complete analysis of this mechanism for a future study @xcite . the structure of this paper is the following : in the next section we derive the cosmological equations , light - like geodesics and luminosity distance for on and off - center observers in the presence of ide . we also discuss the basics of topological quintessence as a mechanism for producing inhomogeneous dark energy and derive the angular dependence of the cmb temperature fluctuations induced by the shift of the observer from the center of the inhomogeneity . in section 3 we use the predicted luminosity distance to constrain the model parameters using the union2 snia data @xcite . in the same section we compare the values of the low multipole moments ( dipole , quadrupole ) of cmb perturbations induced by the displacement of the observer from the center to the corresponding observed values and derive constraints on the parameters of the model . finally , in section 4 we conclude and discuss the implications and possible extensions of our results . in what follows we fix the present age of the universe to @xmath28gyr . in the best fit model , this would correspond to fixing @xmath29km/(smpc ) . we also refer to a comoving radial distance simply as ` distance ' .

we consider on - center and off - center observers in an inhomogeneous , spherically symmetric , isocurvature ( flat ) concentration of dark energy with typical size of a few gpc . such a concentration could be produced e.g. by a recently formed global monopole with core size that approaches the hubble scale . in this case we would have what may be called ` topological quintessence ' in analogy with the well - known _ as expected , the best - fit fractional dark energy density at the center , , approaches the corresponding value for large enough values of the inhomogeneity radius ( ) . using the union2 data , the model naturally predicts the existence of a preferred axis and alignment of the low cmb multipoles . however , the constraints on coming from the magnitude of the cmb dipole remain a severe challenge to the copernican principle and lead to even for an inhomogeneity radius as large as .

we consider on - center and off - center observers in an inhomogeneous , spherically symmetric , isocurvature ( flat ) concentration of dark energy with typical size of a few gpc . such a concentration could be produced e.g. by a recently formed global monopole with core size that approaches the hubble scale . in this case we would have what may be called ` topological quintessence ' in analogy with the well - known _ topological inflation_. we show that the minimum comoving radius of such a dark energy inhomogeneity that is consistent with the union2 type ia supernovae ( snia ) data at the level is . as expected , the best - fit fractional dark energy density at the center , , approaches the corresponding value for large enough values of the inhomogeneity radius ( ) . using the union2 data , we show that the maximum allowed shift of the observer from the center of the inhomogeneity is about which respects the copernican principle . the model naturally predicts the existence of a preferred axis and alignment of the low cmb multipoles . however , the constraints on coming from the magnitude of the cmb dipole remain a severe challenge to the copernican principle and lead to even for an inhomogeneity radius as large as .

1203.6206

i

we consider in this work a cauchy problem for the following reaction - diffusion equation in one space dimension : @xmath0 supplemented with the initial condition @xmath1 here the function @xmath2 satisfies the periodicity condition @xmath3 for some @xmath4 . we will assume , throughout this paper , that there exists a positive and @xmath5-periodic stationary solution @xmath6 of : @xmath7 the function @xmath8 is also a stationary solution of the following auxiliary equation , the @xmath5-periodic counterpart of : @xmath9 it is obvious that any solution of is also a solution of . equation will later play an important auxiliary role in the analysis of . + our aim is to investigate the profile of solutions of connecting the two stationary states @xmath10 and @xmath8 . in particular , we will study the long time behavior of solutions with heaviside - type initial data . roughly speaking , our main results state that the solution will converge to what we call a propagating terrace , the meaning of which will be specified later . this result , in particular , implies the existence of pulsating traveling waves ( or a set of traveling waves ) under rather mild assumptions . + we now state our main assumptions . the first one is concerned with the attractiveness of @xmath8 with respect to at least one compactly supported initial data . our main theorems ( theorems [ heavip2 ] and [ heavip2-cv ] ) will only need this assumption : [ assumption - p1 ] there exists a solution @xmath11 of - with compactly supported initial data @xmath12 that converges locally uniformly to @xmath8 as @xmath13 . this assumption covers a wide variety of nonlinearities that include not only such standard ones as monostable , bistable or combustion nonlinearities , but also much more general and complex ones . for instance , it even allows an infinite number of stationary solutions between 0 and @xmath8 . in this paper , we will show that this rather weak condition is in fact sufficient for deriving our main results on the convergence to a propagating terrace . the next assumption guarantees that our propagating terrace consists of a single ( pulsating ) traveling wave . thus , under this additional assumption , our main results imply the existence of a pulsating traveling wave , as well as the convergence of solutions to this traveling wave ( theorem [ heavip1 ] ) : [ assumption - p2 ] there exists no @xmath5-periodic stationary solution @xmath14 with @xmath15 that is both isolated from below and stable from below with respect to . let us clarify the notions introduced in this assumption . a stationary solution @xmath14 of is said to be * isolated from below * ( resp . * above * ) if there exists no sequence of other stationary solutions converging to @xmath14 from below ( resp . above ) . a stationary solution @xmath14 is said to be * stable from below * ( resp . * above * ) with respect to equation if it is stable in the @xmath16 topology under nonpositive ( resp . nonnegative ) perturbations . otherwise , @xmath14 is called * unstable from below * ( resp . * above * ) . it is known that , if @xmath14 is isolated from below , then it is stable from below if and only if there exists a solution @xmath17 converging to @xmath14 as @xmath18 , and unstable from below if and only if there exists an ancient solution ( that is , a solution defined for all sufficiently negative @xmath19 ) @xmath17 converging to @xmath14 as @xmath20 ( see theorem 8 in @xcite ) . note that this additional assumption holds for a large class of standard nonlinearities including the following : there exists no @xmath5-periodic stationary solution @xmath14 satisfying @xmath21 for all @xmath22 . furthermore , @xmath10 is unstable from above . the stationary solution @xmath10 is stable from above with respect to , and @xmath8 is stable from below with respect to . furthermore , all other stationary solutions between 0 and @xmath8 are unstable . there exists a family of @xmath5-periodic stationary solutions @xmath23}$ ] that forms a continuum in @xmath24 and satisfies @xmath25 . furthermore , there exists no stationary solution @xmath14 satisfying @xmath26 for all @xmath27 . a classical example of the bistable nonlinearity is the allen - cahn nonlinearity @xmath28 , where @xmath29 , @xmath30 . an important subclass of the monostable nonlinearity is the kpp type nonlinearity , in which @xmath10 is assumed to be linearly unstable and @xmath31 is sublinear with respect to @xmath11 ; a typical example being @xmath32 , with @xmath33 . kpp type equations have been widely studied , even in the periodic setting , by numerous authors including @xcite . while most of those studies rely heavily on the linear instability of @xmath10 , our approach in the present paper largely avoid the need for linear analysis , allowing our results to be applicable even to strongly degenerate situations that have not been treated before . we now introduce some notions which will play a fundamental role in this paper . we begin with the following : [ def : steep ] let @xmath34 be two entire solutions of . we say that @xmath35 is * steeper than * @xmath36 if for any @xmath37 , @xmath38 and @xmath39 in @xmath40 such that @xmath41 , we have either @xmath42 here , by an entire solution " we mean a solution that is defined for all @xmath43 . the above property implies that the graph of the solution @xmath35 ( at any chosen time moment @xmath37 ) and that of the solution @xmath36 ( at any chosen time moment @xmath38 ) can intersect at most once unless they are identical , and that if they intersect at a single point , then @xmath44 is positive on the left - hand side of the intersection point , while negative on the right - hand side . note that , according to this definition , if the ranges of @xmath35 and @xmath36 are disjoint , then @xmath35 and @xmath36 are steeper than each other , since their graphs never intersect . [ def : puls ] given two distinct periodic stationary states @xmath45 and @xmath46 , by a * pulsating traveling wave solution * ( or * pulsating traveling front * ) of connecting @xmath45 to @xmath46 , we mean any entire solution @xmath11 satisfying , for some @xmath47 , @xmath48 for any @xmath22 and @xmath49 , along with the asymptotics @xmath50 where the convergence is understood to hold locally uniformly in the space variable . the ratio @xmath51 is called the * average speed * ( or simply the * speed * ) of this pulsating traveling wave . one can easily check that , for any @xmath52 , @xmath53 is a pulsating traveling wave connecting @xmath45 to @xmath46 with speed @xmath54 if and only if it can be written in the form @xmath55 , where @xmath56 satisfies @xmath57 along with the following equation that is equivalent to : @xmath58 let us recall some known results on traveling waves from the literature . in the case of spatially homogeneous problems , existence of traveling waves is well studied ( see for instance @xcite for a review of the area ) . more precisely , in the kpp case , there exists a continuum of admissible speeds @xmath59 , while in the bistable or combustion cases , the admissible speed is unique . stability and convergence to those traveling waves are also studied extensively . among other things , in the one - dimensional kpp case ( or , more generally , the monostable case ) , uchiyama @xcite , bramson @xcite and lau @xcite proved that solutions of the cauchy problem with compactly supported initial data converge to the traveling front with minimal speed as @xmath60 . in this case , the solution does not converge to the traveling wave with an asymptotic phase , but a phase drift of order @xmath61 occurs @xcite . similar results hold for multi - dimensional problems as long as the parameters of the equation are invariant in the direction of propagation @xcite . in the case of spatially periodic problems , the state of research is slightly behind , for obvious technical difficulties . nonetheless , in the kpp case , the existence of a continuum of admissible speeds is well established , as in the case of spatially homogeneous problems . it is also known that there is a close relation between the speed of a traveling wave @xmath62 and its decay rate as @xmath63 , at least under some assumptions on the linearized problem around @xmath10 ; the smaller the speed @xmath54 , the faster the decay ; hence steeper the front profile . convergence to those traveling waves was studied in @xcite in a periodic framework . more precisely , it has been shown that if the initial data has the same exponential decay as a given traveling wave as @xmath64 , then the solution of the cauchy problem converges to this traveling wave as @xmath18 . however , the case of very fast decaying initial data ( for instance , a heaviside or a compactly supported function ) has been left open up to now in the periodic framework , although the appearance of some phase drift of order @xmath61 has also been highlighted in @xcite . let us now come back to the main theme of the present paper a propagating terrace . as we mentioned earlier , a traveling wave is a special case of a propagating terrace , but the latter is a more suitable notion for describing typical frontal behaviors in equations of multistable nature . the aim of the present paper is to study properties of propagating terraces in a spatially periodic setting , thereby generalizing ( and improving ) some of the aforementioned results on pulsating traveling waves . [ def : terrace ] a * propagating terrace * connecting @xmath10 to @xmath8 is a pair of finite sequences @xmath65 and @xmath66 such that : * each @xmath67 is an @xmath5-periodic stationary solution of satisfying @xmath68 * for each @xmath69 , @xmath70 is a pulsating traveling wave solution of connecting @xmath67 to @xmath71 . * the speed @xmath72 of each @xmath70 satisfies @xmath73 . furthermore , a propagating terrace @xmath74 connecting @xmath10 to @xmath8 is said to be * minimal * if it also satisfies the following : * for any propagating terrace @xmath75 connecting @xmath10 to @xmath8 , one has that @xmath76 * for each @xmath77 , the traveling wave @xmath70 is steeper than any other traveling wave connecting @xmath67 to @xmath71 . roughly speaking , a propagating terrace can be pictured as a layer of several traveling fronts going at various speeds , the lower the faster ( figure [ fig : terrace ] ) . the aim of the present paper is to show that the solution of with heaviside - type initial data will converge to a minimal propagating terrace , as illustrated in figure [ fig : terrace - like ] . in some standard problems such as the kpp and the bistable equations , the terrace actually consists of a single front ( that is , @xmath78 ) , which means that the solution will eventually look like a single traveling wave ; see theorem [ heavip1 ] . however , in more general equations , one can not expect such simple dynamics , and this is where the notion of terrace plays a fundamental role . the existence of a multi - step terrace has been known in the spatially homogeneous case ( where @xmath79 ) . let us give a simple example . consider @xmath31 as in figure [ fig : f_terrace ] ( left ) , which is kpp on @xmath80 $ ] , and bistable on @xmath81 $ ] . the speed of the upper part of the solution is bounded from above by the speed , say @xmath54 , of the traveling wave for the bistable nonlinearity @xmath82}$ ] . on the other hand , the lower part of the solution is pushed from behind by a spreading front for the kpp nonlinearity @xmath83}$ ] , whose speed is known to approach @xmath84 . therefore , if @xmath85 , the upper and lower parts of the solution necessarily move at two distinct speeds . [ fig : fterrace ] that produce a multi - step terrace , title="fig:",scaledwidth=90.0% ] another example was exhibited by fife and mcleod in @xcite , where they considered a specific case of a non - degenerate tristable nonlinearity , that is , when @xmath86}$ ] and @xmath87}$ ] are both bistable for some @xmath88 , and that @xmath89 , @xmath90 and @xmath91 are all strictly negative ; see figure [ fig : f_terrace ] ( right ) . they showed that if the speed of the upper bistable part is smaller than the speed of the lower bistable part , then there does not exist any single front connecting @xmath10 to @xmath92 . furthermore , some solutions of the cauchy problem , in particular for heaviside type initial data , converge to a combination of those two fronts . this may be seen as an early study of a propagating terrace for some very specific examples . although the method in @xcite was expected to hold for homogeneous nonlinearities composed of a finite number of bistable parts , it relied strongly on the particular shape of @xmath31 , and on the non - degeneracy of the equilibria . this means that they needed some important a priori knowledge on the shape of the nonlinearity , which we do not need in the present paper . more importantly , what makes our work different from those early observations is that we are not simply giving examples of propagating terraces but are establishing the ubiquity of such terraces for large classes of reaction nonlinearities , thus showing that the notion of propagating terrace is fundamental for studying the dynamics of fronts in general reaction - diffusion equations . we consider solutions of - whose initial data are given in the form @xmath93 where @xmath94 is any constant , and @xmath95 denotes the heaviside function , which is defined by @xmath96 hereafter , for each @xmath97 , we denote by @xmath98 such solutions . we will prove that @xmath99 converges in some sense to a minimal propagating terrace as @xmath60 . [ heavip2 ] let assumption [ assumption - p1 ] hold . then there exists a propagating terrace @xmath100 that is minimal in the sense of definition [ def : terrace ] . such a minimal propagating terrace is unique , in the sense that any minimal propagating terrace shares the same @xmath101 and that @xmath70 is unique up to time - shift for each @xmath102 . moreover , it satisfies : a. for any @xmath103 , the @xmath5-periodic stationary solution @xmath67 is isolated and stable from below with respect to . b. all the @xmath67 and @xmath70 are steeper than any other entire solution of . the existence of a minimal terrace as stated in the above theorem gives various useful information about the qualitative properties of the equation . for example , statement @xmath104 implies , in particular , that there exists no traveling wave that intersects any of the @xmath67 . note that , in the spatially homogeneous case ( namely , @xmath79 ) , the stability of @xmath67 in statement @xmath105 implies that each @xmath67 is a constant ; hence the terrace consists of flat steps . we now state our convergence result : [ heavip2-cv ] let assumption [ assumption - p1 ] hold . then for any @xmath106 , the solution @xmath107 converges as @xmath18 to the minimal propagating terrace @xmath100 in the following sense : a. there exist functions @xmath108 with @xmath109 as @xmath18 such that @xmath110 locally uniformly on @xmath40 , @xmath72 being the speed of @xmath70 . b. for any @xmath111 , there exists @xmath112 such that , for any @xmath113 , @xmath114 ) } \leq \delta \ \ \hbox{as}\ t\to + \infty , \ ] ] together with @xmath115 ) } \leq \delta \ \ \hbox{as}\ t\to + \infty , \ ] ] @xmath116 roughly speaking , statements @xmath105 and @xmath104 of the above theorem describe , respectively , the ascending part and the stationary part of the terrace , the latter being flat if @xmath79 , as mentioned above . it should be noted that , under assumption [ assumption - p1 ] , there may exist an infinite number of isolated stationary solutions between @xmath10 and @xmath8 , but our theorem [ heavip2 ] states that only a finite number of layers appear in the limiting terrace . the solution seems to ignore excessive complexity of such nonlinearities . the proofs of theorems [ heavip2 ] and [ heavip2-cv ] are , in a sense , one and the same . in fact , by first showing that the steepness of the heaviside type initial data implies that the limiting profile of the solution is steeper than any other entire solution , we will then use this fact to prove the convergence of the solution to a minimal terrace without assuming the existence of a terrace . hence it automatically implies the existence of a minimal terrace . in the special case where assumption [ assumption - p2 ] also holds , the above two theorems reduce to the following result on pulsating traveling waves . thus it gives a new and highly original proof for the existence of pulsating traveling waves . [ heavip1 ] let assumptions [ assumption - p1 ] and [ assumption - p2 ] hold . then there exists a pulsating traveling wave @xmath117 connecting @xmath10 to @xmath8 with speed @xmath118 that is steeper than any other entire solution between @xmath10 and @xmath8 . furthermore , for any @xmath106 , there exists a function @xmath119 with @xmath120 as @xmath121 such that @xmath122 let us make some comments on theorem [ heavip1 ] , which is a special case of the previous two theorems . as regards the existence part , there have been earlier studies of the existence of pulsating traveling waves for monostable ( possibly degenerate ) and combustion cases @xcite , as well as for some periodic bistable case @xcite . in contrast to those earlier results , which are derived by various different methods depending on the type of nonlinearities , our theorem relies on a new , unified and rather straightforward proof , thus avoiding to deal directly with the particular features and difficulties of each case . as mentioned earlier , the convergence result for fast decaying initial data such as our heaviside type ones was previously known only in the homogeneous setting . indeed , even in the standard kpp case with spatially periodic coefficients , almost all the convergence results in the literature are concerned with solutions whose initial data have roughly the same decay rate as one of the traveling waves near @xmath123 . only very recently , there are some works in progress that are trying to deal with some fast decaying initial data @xcite . note that , though our results cover a large class of equations , they are concerned only with a specific type of inital data . however , by analogy with the homogeneous case ( see for instance the proofs in @xcite ) , we expect that similar convergence results hold for more general initial data , such as compactly supported ones . this is a topic of particular relevance from an applied point of view , and we will give a partial answer to this question in a forthcoming paper @xcite . [ [ plan - of - the - paper ] ] plan of the paper + + + + + + + + + + + + + + + + + our paper is organized as follows . in section [ sec : preliminaries ] , we will present some preliminaries . as our proofs largely rely on the so - called intersection number ( or the zero number ) argument , we will first give its precise definition and basic properties . we will then use this method to prove our fundamental lemma ( lemma [ lem : omega - steep ] ) , which roughly states the following : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ * fundamental lemma : * any function that appears in the @xmath124-limit set of @xmath99 is steeper than any other entire solution , where @xmath125 is the solution of for the initial data _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ one immediate consequence of the above fundamental lemma is that any two elements of the @xmath124-limit set are steeper than each other . this means that they are either identical ( up to time shift ) or strictly ordered , that is , one is above or below the other . this observation is important both for establishing convergence results and for the construction of a multi - step terrace . here we note that the definition of the @xmath124-limit set in this paper is slightly different from the standard one , in that we consider arbitrary spatial translations while taking the limit as @xmath126 ; see definition [ def : omegalimit ] . the reason for adopting this slightly non - standard defintion is that , since each step of the terrace moves at a different speed , we can not capture the asymptotic profile of the solution in a single frame . a multi - speed observation is unavoidable in the case of a multi - step terrace . in the last part of section [ sec : preliminaries ] , we will prove a lemma on the spreading speed of @xmath99 , which will be used repeatedly in later sections but is also of independent interest in its own right . in section [ sec : lemmas ] , we will use our fundamental lemma to prove the convergence of solutions with heaviside type initial data to a unique limit around any level set . the entire solution thereby constructed possesses , in some sense , some qualitative properties of traveling fronts , such as monotonicity in time . the same result could in fact be shown with a similar argument in a more general setting without the periodicity assumption . we will then show in section [ sec : periodic ] that this limit is a pulsating traveling wave connecting some pair of @xmath5-periodic stationary solutions @xmath127 that lie between @xmath10 and @xmath8 . once again the above - mentioned fundamental lemma plays a key role in deriving this result . this leads to construction of a multi - step minimal terrace inductively , as described in theorems [ heavip2 ] and [ heavip2-cv ] . in the special case where assumtion [ assumption - p2 ] holds , we have @xmath128 , thus the terrace is a single traveling wave . as the existence of any traveling wave is not a priori assumed , this leads to both the existence and the convergence results in theorem [ heavip1 ] .

we consider one - dimensional reaction - diffusion equations for a large class of spatially periodic nonlinearities including multistable ones and study the asymptotic behavior of solutions with heaviside type initial data . our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front , but by a layer of several fronts which we call a terrace . hence , on top of the peculiar phenomenon of propagation that our work highlights , several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before . * key words*. multistable reaction - diffusion equation , periodic environment , long time behavior , propagating terrace , zero - number argument . * 2010 mathematical subject classification*.35k55 , 35c07 , 35b08 , 35b40

we consider one - dimensional reaction - diffusion equations for a large class of spatially periodic nonlinearities including multistable ones and study the asymptotic behavior of solutions with heaviside type initial data . our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front , but by a layer of several fronts which we call a terrace . existence and convergence to such a terrace is proven by using an intersection number argument , without much relying on standard linear analysis . hence , on top of the peculiar phenomenon of propagation that our work highlights , several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before . * key words*. multistable reaction - diffusion equation , periodic environment , long time behavior , propagating terrace , zero - number argument . * 2010 mathematical subject classification*.35k55 , 35c07 , 35b08 , 35b40

0912.1233

i

the focusing nonlinear schrdinger equation ( nls ) @xmath2 where @xmath3 , and @xmath4 is the laplacian , has been the subject of intense study , due to its role in various areas of physics , such as nonlinear optics and bose - einstein condensates ( bec ) . it is well - known that the nls possesses solutions that become singular in a finite time @xcite . of special interest is the critical ( @xmath5 ) nls @xmath6 which models the collapse of intense laser beams that propagate in a bulk kerr medium . in this study , we consider the focusing biharmonic nonlinear schrdinger equation ( bnls ) @xmath7 where @xmath8 is the biharmonic operator . equation admits waveguide ( standing - wave ) solutions of the form @xmath9 , where @xmath10 satisfies the `` standing - wave '' equation @xmath11 the bnls is called `` _ @xmath0-critical _ '' , or simply `` critical '' if @xmath12 . in this case , the @xmath0 norm ( `` _ power _ '' ) is conserved under the bnls dilation symmetry @xmath13 . the critical bnls can be rewritten as @xmath14 correspondingly , the bnls with @xmath15 is called subcritical , and the bnls with @xmath16 is called supercritical . this is analogous to the nls , where the critical case is @xmath17 . in @xcite , ben - artzi , koch and saut proved that the bnls is locally well - posed in @xmath18 , when @xmath19 is in the _ @xmath18-subcritical _ regime @xmath20 global existence and scattering of bnls solutions in the @xmath18-critical case @xmath21 were studied by miao , xu and zhao @xcite and by pausader @xcite . the latter work also showed well - posedness for small data . the @xmath18-critical defocusing bnls was studied by miao , xu and zhao @xcite and by pausader @xcite . the above studies focused on non - singular solutions . in this work , we study singular solutions of the bnls in @xmath18 , i.e. , solutions that exist in @xmath22 over some finite time interval @xmath23 , but for which @xmath24 the first study of singular bnls solutions was done by fibich , ilan and papanicolau @xcite , who proved the following results : [ thrm : ge_subcritical ] solutions of the subcritical ( @xmath15 ) focusing bnls exist globally . [ thrm : ge_critical ] let @xmath25 , where @xmath26 , and @xmath10 is the ground state of with @xmath27 . then , the solution of the critical focusing bnls exists globally . the simulations in @xcite suggested that there exist singular solutions for @xmath12 and @xmath16 , and that these singularities are of the blowup type , namely , the solution becomes infinitely localized . however , in contradistinction with nls theory , there is currently no rigorous proof that solutions of the bnls can become singular in either the critical or the supercritical case . to the best of our knowledge , the only work , apart from @xcite , which considered singular solutions of the bnls is by chae , hong and lee @xcite , who proved that if singular solutions of the critical bnls exist , then they have a power - concentration property . see section [ ssec : power_conc ] for more details . in this work , we consider singular solutions of the focusing bnls in the @xmath18-subcritical regime . our purpose is to characterize these singular solutions : their profile , blowup rate , power concentration , et cetera . in some cases , we assume radial symmetry , i.e. , that @xmath28 where @xmath29 in these cases , equation reduces to @xmath30 where @xmath31 is the radial biharmonic operator . specifically , the critical bnls reduces to @xmath32 the paper is organized as follows : in section [ sec : invariance ] , we use noether theorem to derive conservation laws for the bnls . we recall that in the critical nls , the conservation law which follows from invariance of the action integral under dilation leads to the nls `` variance identity '' , which can be used to prove the existence of singular solutions . in section [ ssec : varid ] we use a similar procedure to derive the `` variance identity '' for the critical bnls , and then generalize it to the supercritical bnls . however , since it is not clear that the `` bnls variance '' is positive definite , this identity does not lead to a proof of the existence of singular solutions . the ground states of the bnls standing - wave equation were previously computed only in the one - dimensional case @xcite , since they were computed using a shooting method , which can not be easily generalized to multi - dimensions . in section [ sec : stationary ] we use the spectral renormalization method to compute the ground - states of the critical bnls for one , two and three dimensions . the calculated ground - states provide the first numerical estimate of the critical power for collapse @xmath33 in the two - dimensional and three - dimensional cases , see section [ sec : critical_power ] . direct simulations of the critical bnls suggest that the constant @xmath34 in theorem [ thrm : ge_critical ] is optimal . in section [ sec : rigorous ] we use rigorous analysis to study the critical bnls . the blowup rate is shown to be lower - bounded by a quartic root , i.e. , @xmath35 the corresponding bound for the critical nls is a square root , i.e. , @xmath36 we then prove that singular solutions converge to a self - similar profile strongly in @xmath37 , for any @xmath19 in the @xmath18-subcritical regime . this implies that the singular solutions have the power - concentration property , whereby the amount of power that enters the singularity point is at least @xmath34 . these rigorous results mirror those of the critical nls . let us denote the location of the maximal amplitude of a radially - symmetric solution by @xmath38 singular solutions are called `` _ peak - type _ '' when @xmath39 for @xmath40 , and `` _ ring - type _ '' when @xmath41 for @xmath42 . in this work , we use asymptotic analysis and numerics to find and characterize peak - type singular solutions of the bnls equation . ring - type singular solutions of the bnls will be studied elsewhere @xcite . in section [ sec : crit_peak ] we use asymptotics and numerics to show that peak - type singular solutions of the critical bnls collapse with the quasi self - similar profile @xmath43 where the self - similar profile is the ground state @xmath44 . the blowup rate is shown to be slightly faster than the quartic - root bound . this is analogous to the critical nls , where the blowup rate of peak - type solutions is slightly faster than the square - root bound , due to the loglog correction ( the `` loglog law '' ) . it is an open question whether the correction to the bnls blowup rate is also a loglog term . in section [ sec : supercrit_peak ] we consider peak - type singular solutions of the supercritical bnls . in this case , asymptotics and numerics show that singular solutions are of the quasi self - similar form @xmath45 the blowup rate of @xmath46 is exactly a quartic - root , and the self - similar profile @xmath47 is different from the ground - state . rather , as in the supercritical nls , the self - similar profile @xmath48 is the zero - hamiltonian solution of a nonlinear eigenvalue problem . although @xmath47 is not in @xmath0 , it can be the self - similar profile of a collapsing @xmath18 solution , since the collapsing solution is `` only '' quasi self - similar . section [ sec : num_meth ] presents the numerical methods . the computations of singular bnls solutions that focus by factors of @xmath1 and more , necessitated the usage of adaptive grids . we develop a modified version of the static grid redistribution method @xcite , which is more convenient for the biharmonic problem . calculating the bnls standing waves in multi - dimensions is done using the spectral renormalization method . in this study , we use rigorous theory , asymptotic theory and numerics to analyze singular solutions of the bnls . all the results presented in this work mirror those of the nls , `` up to a change by a factor of @xmath49 '' in the blowup rate ( @xmath50 ) , in the critical value of @xmath19 ( @xmath51 ) , et cetera . however , several key features of nls theory are still missing from bnls theory . first , the `` variance identity '' for the bnls can not be used to prove that singular solutions exist . second , the critical nls is invariant under the pseudo - conformal ( `` lens - transformation '' ) symmetry which can also be used to construct explicit singular solutions . at this time , it is unknown whether an analogous identity for the critical bnls exists . third , in critical nls theory , the self - similar profile is known to possess a quadratic radial phase term , i.e. , @xmath52 this term represents the focusing of the solution towards @xmath53 , and plays a key role in the rigorous and asymptotic theory of the critical nls . at this time , we do not know the analogous radial phase term for the critical bnls . finally , we note that a similar `` up to a factor of @xmath49 '' connection exists between singular solutions of the nonlinear heat equation , see @xcite , and the biharmonic nonlinear heat equation , see @xcite . for example , the @xmath54 norm of singular solutions blows up as @xmath55 for the nonlinear heat equation , and as @xmath56 for the biharmonic heat equation . the `` similarity up to a factor of @xmath49 '' , however , is not perfect . for example , the self - similar spatial variable is @xmath57 for the nonlinear heat equation , and @xmath58 { { { t_{\rm c}}}-t } $ ] for the biharmonic nonlinear heat equation . another difference between the equations is that singular solutions are _ asymptotically _ self - similar for the nonlinear heat equation , and truly self - similar for the biharmonic heat equation . in contrast , the nls possesses self - similar singular solutions , whereas for the bnls it is unknown whether singular solutions are truly , or only asymptotically , self - similar .

we consider singular solutions of the biharmonic nls . in the-critical case , the blowup rate is bounded by a quartic - root power law , the solution approaches a self - similar profile , and a finite amount of-norm , which is no less than the critical power , concentrates into the singularity ( `` strong collapse '' ) . in the-critical and supercritical cases , we use asymptotic analysis and numerical simulations to characterize singular solutions with a peak - type self - similar collapsing core . in the critical case , the blowup rate is slightly faster than a quartic - root , and the self - similar profile is given by the standing - wave ground - state . in the supercritical case , the blowup rate is exactly a quartic - root , and the self - similar profile is a zero - hamiltonian solution of a nonlinear eigenvalue problem . we also calculate the ground states of the standing - wave equations and the critical power for collapse in two and three dimensions .

we consider singular solutions of the biharmonic nls . in the-critical case , the blowup rate is bounded by a quartic - root power law , the solution approaches a self - similar profile , and a finite amount of-norm , which is no less than the critical power , concentrates into the singularity ( `` strong collapse '' ) . in the-critical and supercritical cases , we use asymptotic analysis and numerical simulations to characterize singular solutions with a peak - type self - similar collapsing core . in the critical case , the blowup rate is slightly faster than a quartic - root , and the self - similar profile is given by the standing - wave ground - state . in the supercritical case , the blowup rate is exactly a quartic - root , and the self - similar profile is a zero - hamiltonian solution of a nonlinear eigenvalue problem . these findings are verified numerically ( up to focusing levels of ) using an adaptive grid method . we also calculate the ground states of the standing - wave equations and the critical power for collapse in two and three dimensions .

0905.0048

i

closed 2-manifolds embedded locally flatly in the euclidean 4-space @xmath1 or the 4-sphere @xmath2 are called _ surface links_. it is known that any oriented surface link can be described in a form of the closure of a simple surface braid , i.e. in a braid form over the standard 2-sphere ( cf . @xcite ) . as surface knots of genus one which can be made from classical knots , there are _ spun @xmath0-knots , turned spun @xmath0-knots , symmetry - spun tori _ and _ torus @xmath0-knots_. consider @xmath1 as obtained by rotating @xmath3 around the boundary @xmath4 . then a _ spun @xmath0-knot _ is obtained by rotating a classical knot ( cf . @xcite ) , a _ turned spun @xmath0-knot _ by turning a classical knot once while rotating it ( cf . @xcite ) , a _ symmetry - spun torus _ by turning a classical knot with periodicity rationally while rotating ( cf . @xcite ) , and a _ torus @xmath0-knot _ is a surface knot on the boundary of a neighborhood of a solid torus in @xmath1 ( cf . symmetry - spun tori include spun @xmath0-knots , turned spun @xmath0-knots and torus @xmath0-knots . we call the link version of a symmetry - spun torus , a spun @xmath0-knot , and a turned spun @xmath0-knot a _ symmetry - spun @xmath0-link _ , a _ spun @xmath0-link _ and a _ turned spun @xmath0-link _ respectively . we enumerate several properties of symmetry - spun @xmath0-links . 1 . a symmetry - spun @xmath0-link is equivalent to a spun @xmath0-link or a turned spun @xmath0-link ( cf . 2 . a spun @xmath0-link is ribbon and the turned spun @xmath0-link of a non - trivial classical link is not ribbon ( cf . 3 . a symmetry - spun @xmath0-link is pseudo - ribbon and has the triple point number zero ( cf . 4 . a symmetry - spun @xmath0-link has a classical link group ( cf . @xcite ) . now we consider oriented surface links which can be described in braid forms over the standard torus , which we will define as _ torus - covering - links _ ( see definition [ def2 - 1 ] ) . by definition , a torus - covering - link is associated with a _ torus - covering - chart _ , which is a chart on the standard torus . torus - covering - links include symmetry - spun @xmath0-links ( and spun @xmath0-links , turned spun @xmath0-links , and torus @xmath0-links ) . a torus - covering - link has no 2-knot component . each component of a torus - covering - link is of genus at least one . there is a natural question . + ( q ) what difference from symmetry - spun @xmath0-links do torus - covering - links have ? in section [ t - c - knot ] , we consider torus - covering - links in @xmath2 , and from section [ knotgroup ] throughout this paper we consider torus - covering @xmath0-links in @xmath1 , i.e. torus - covering - links in @xmath1 whose each component is of genus one . torus - covering @xmath0-links are associated with torus - covering - charts without black vertices . in section [ t - c - knot ] we define torus - covering - links ( definition [ def2 - 1 ] ) , and _ turned torus - covering - links _ ( definition [ def2 - 4 ] ) . in section [ knotgroup ] we study link groups of torus - covering @xmath0-links . we show that `` ( theorem [ thm4 - 6 ] ) . we show its knot version as well : '' ( theorem [ thm4 - 9 ] ) . this means that torus - covering @xmath0-links are not always symmetry - spun @xmath0-links . concerning theorem [ thm4 - 6 ] , we have a corollary : " ( corollary [ cor4 - 6 ] ) . in section [ ribbon ] we show that the torus - covering - links given in theorems [ thm4 - 6 ] and [ thm4 - 9 ] are ribbon , i.e. " ( theorem [ thmr ] ) . symmetry - spun @xmath0-links are pseudo - ribbon and by theorem [ thmr ] the torus - covering @xmath0-links given in theorems [ thm4 - 6 ] and [ thm4 - 9 ] are ribbon . both of them have the triple point number zero . in section [ triplepoint ] we show that `` ( theorem [ thm2 - 11 ] ) . moreover we have '' ( corollary [ cor2 - 12 ] ) . the author would like to thank professors takashi tsuboi and elmar vogt for suggesting this problem , and professor akio kawauchi for advising this title .

we consider surface links in the 4-space or the 4-sphere which can be described in braid forms over the standard torus , which we call torus - covering - links . torus - covering - links include spun-knots , turned spun-knots , symmetry - spun tori and torus-knots . in this paper

we consider surface links in the 4-space or the 4-sphere which can be described in braid forms over the standard torus , which we call torus - covering - links . torus - covering - links include spun-knots , turned spun-knots , symmetry - spun tori and torus-knots . in this paper we give examples of interesting torus - covering - links , namely , torus - covering-links which are ribbon but not symmetry - spun-links , and a torus - covering-knot whose triple point number is positive .

astro-ph0003028

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the existence of disks around young stars was spectacularly confirmed by direct images from the _ hubble space telescope _ ( _ hst _ ) ( mccaughrean & odell 1996 ; burrows et al . observations suggest that young stars are usually found in binary systems and that young binaries typically interact strongly with the disks that surround the stars ( ghez , neugebauer , & matthews 1993 ; mathieu 1994 ; osterloh & beckwith 1995 ; jensen , mathieu , & fuller 1996 ) . there is growing evidence that disks within a binary are sometimes inclined with respect to the binary orbital plane . such a case may have been seen in _ hst _ and keck images of a disk in the young binary hk tau ( stapelfeldt et al . 1998 ; koresko 1998 ) . suppose that a protostellar disk surrounds a star in a circular - orbit binary system , and that the disk is tilted with respect to the binary orbital plane . the evolution of the disk is affected by the tidal field of the companion star , as has been considered by papaloizou & terquem ( 1995 ) . some features of their analysis were confirmed in three - dimensional numerical simulations by larwood et al . the basic physics involved may be summarized as follows ( see also bate et al . 2000 ) . in a non - rotating frame of reference centered on the star about which the disk orbits , the companion star orbits at the binary frequency @xmath2 and exerts a time - dependent tidal torque on the disk . this torque may be decomposed into a steady component and an oscillatory component with a frequency of @xmath3 , and their effects may be considered separately . consider first the steady torque . if the disk were composed of non - interacting circular rings , the steady torque would cause each ring to precess , about an axis perpendicular to the binary plane , at a rate that depends on the radius of the ring , resulting in a rapid twisting of the disk . if the disk is able to maintain efficient radial communication , whether by wave propagation , viscosity , or self - gravitation , it may be able to resist this differential precession by establishing an internal torque in the disk . this can be arranged so that the net torque on each ring is such as to produce a single , uniform precession rate . however , to establish this internal torque , the disk must become warped . the concomitant dissipation changes the total angular momentum of the disk , tending to bring it into alignment with the binary plane in addition to causing accretion . consider now the oscillatory torque . applied to a single ring , this would cause a modulation of the precession rate and also a nutation ( katz et al . however , in the presence of radial communication , the oscillatory torque drives a bending wave ( with azimuthal wavenumber @xmath4 ) in the disk . papaloizou & terquem ( 1995 ) showed that , if the wave is subject to dissipation , it too may change the total angular momentum of the disk and tend to increase its inclination . the net effect of the steady and oscillatory torques determines whether an initially coplanar disk will acquire a tilt over time or whether an initially inclined disk will evolve towards coplanarity . the purpose of this paper is to determine this outcome , which could provide clues to the origin of misaligned disks in systems such as hk tau . the basic mechanism suggested by papaloizou & terquem for generating a tilt by the oscillatory torque can be related to earlier work by lubow ( 1992 ) , who showed that an aligned , keplerian disk in a circular binary may be linearly unstable to tilting if it contains a local resonance at which the orbital angular velocity @xmath5 satisfies @xmath6 here @xmath7 is the azimuthal wavenumber of the component of the tidal potential that is involved in the instability cycle . the cycle works through a mode - coupling process as follows : given a perturbation with @xmath4 ( a tilt ) , the tidal potential interacts with it to a drive a wave with @xmath8 at the resonant radius . this in turn interacts with the tidal potential to produce a stress with @xmath4 , which can influence the tilt . the role of dissipation is subtle , since some dissipation is required to provide a change in the angular momentum of the disk if instability is to occur , yet the associated damping can compete with the intrinsic growth rate of the instability . in particular , if the disk extends to the @xmath9 resonance ( @xmath10 ) it may be unstable to tilting through the @xmath11 component of the tidal potential . this resonance has the smallest @xmath7 for which equation ( [ resonance ] ) can be satisfied ( for a prograde disk ) and is the closest resonance to the central star . it is difficult for disks to extend even as far as the @xmath9 resonance , because of the effects of tidal truncation ( paczyski 1977 ; papaloizou & pringle 1977 ) . superhump binary disks might extend to the @xmath9 resonance because of their extreme binary mass ratios , the secondary companion having less than @xmath12 the mass of the primary about which the disk orbits ( see the review by osaki 1996 ) . this instability is related to , and occurs at the same position as , the eccentric instability that is believed to be responsible for superhumps in cataclysmic variable disks ( lubow 1991 ) . however , the growth rate is invariably much smaller for tilting than for eccentricity , and the weak tilt instability may be suppressed by the effects of viscous damping and accretion ( murray & armitage 1998 ) . the same instabilities had been previously identified in the context of planetary rings for higher @xmath7 ( goldreich & tremaine 1981 ; borderies , goldreich , & tremaine 1984 ) . more fundamentally , free - particle orbits undergo even stronger , parametric instabilities at these resonant locations ( paczyski 1977 ) , although free particles fail to model properly the behavior of a fluid disk at resonances . we relate this theory to the suggestion of papaloizou & terquem ( 1995 ) by noticing in equation ( [ resonance ] ) that , for @xmath13 , a near resonance is obtained in the inner part of the disk where @xmath14 . indeed , papaloizou & terquem rely on the @xmath1 component of the tidal potential to drive an @xmath4 bending wave in the tilted disk . the resulting response is a slowly rotating @xmath4 bending wave , with frequency @xmath3 in the inertial frame . such a wave is close to resonance in the inner part of a nearly keplerian disk because of the near coincidence of the effective wave driving frequency @xmath15 and the frequency of vertical oscillations @xmath16 ; this is indeed the origin of equation ( [ resonance ] ) with @xmath13 . an additional resonant effect occurs owing to the near coincidence of the driving frequency and the epicyclic frequency of horizontal oscillations @xmath17 . we describe the instability cycle associated with the oscillatory torque as a mode - coupling process in fig . 1 . however , because the resonance is not exact , and because of the importance of resonantly induced horizontal motions , a proper treatment requires a distinct analysis from that of lubow ( 1992 ) . in this paper , we therefore examine whether a flat , aligned disk in a binary is linearly unstable to tilting even if it does not extend to the @xmath9 resonance . this problem is most conveniently analyzed in the binary frame where the tidal potential is static , since the disk can then be considered to be steady and to admit normal modes . these modes do not have a pure azimuthal wavenumber because the disk is non - axisymmetric as a result of tidal distortions . however , the tilting instability , if present , may be expected to appear as a modification of the rigid - tilt mode , which is trivial in the absence of the companion star . this mode may be followed continuously as the mass of the companion is increased , in order to determine whether it acquires a net rate of growth or decay . in general , the analysis of a normal mode of a tidally distorted disk is very difficult owing to the non - axisymmetric distortions of the disk . we therefore adopt the following simple approach , which is appropriate when only @xmath4 bending waves are involved . we start by writing down the reduced equations for linear bending waves in a protostellar disk subject to an axisymmetric external potential ( section 2 ) . these can be derived formally without great effort ( see the appendix ) . we then give a physical interpretation of these equations and use this insight to see how to modify them in the presence of a non - axisymmetric potential ( sections 3 and 4 ) . we present a simple disk model ( section 5 ) and describe the results of numerical calculations of normal modes ( section 6 ) . some further analysis illuminates the underlying physics and helps to explain the numerical results ( section 7 ) . finally , we summarize our findings ( section 8) .

our aim is to determine whether , if the disk is initially tilted with respect to the plane of the binary orbit , the inclination of the system will increase or decrease with time . the problem is conveniently formulated in the binary frame in which the tidal potential of the companion star is static . we may then consider a steady , flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations . the dynamics is controlled by the competing effects of the and azimuthal fourier components of the tidal potential . in the presence of dissipation , the disk can be unstable to tilting and acquire a warped shape , even in the absence of dissipation .

we consider the dynamics of a protostellar disk surrounding a star in a circular - orbit binary system . our aim is to determine whether , if the disk is initially tilted with respect to the plane of the binary orbit , the inclination of the system will increase or decrease with time . the problem is conveniently formulated in the binary frame in which the tidal potential of the companion star is static . we may then consider a steady , flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations . the dynamics is controlled by the competing effects of the and azimuthal fourier components of the tidal potential . in the presence of dissipation , the component causes alignment of the system , while the component has the opposite tendency . we find that disks that are sufficiently large , in particular those that extend to their tidal truncation radii , are generally stable and will therefore tend to alignment with the binary plane on a time - scale comparable to that found in previous studies . however , the effect of the component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency . under such circumstances , the disk can be unstable to tilting and acquire a warped shape , even in the absence of dissipation . the outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius . for disks smaller than the primary resonance , the component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center . we discuss these results in the light of recent observations of protostellar disks in binary systems .

astro-ph0003028

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equations ( [ ell_x])([g_y ] ) are solved numerically using the complex variables defined in equations ( [ tilde_ell_x])([tilde_g_y ] ) . when solving the odes for a normal mode , it is advisable to integrate away from the singular points at the edges of the disk . we apply the arbitrary normalization condition @xmath168 and guess the values of the four complex parameters @xmath82 , @xmath169 , @xmath170 , and @xmath171 . we then integrate separately into @xmath172 and @xmath173 , meeting at the midpoint , where @xmath174 , @xmath175 , @xmath176 , and @xmath177 should all be continuous . these four conditions are solved by newton - raphson iteration , using derivative information obtained by simultaneously integrating the odes differentiated with respect to the four parameters . we first identify a ` reference model ' with parameters that we consider appropriate for a protostellar disk that is tidally truncated by the companion star ( table 1 ) . the orbit of the companion is taken to be prograde . before considering the reference model as such , we examine the same disk but with no viscosity ( @xmath178 ) and with a companion of zero mass ( @xmath179 ) . an infinite set of discrete bending modes is obtained , which are characterized by the number of nodes in the eigenfunction @xmath174 ( say ) . the basic frequencies of these modes in the inertial frame are @xmath180 , @xmath181 , @xmath182 , @xmath183 , @xmath184 , etc . we refer to these modes as modes @xmath125 , @xmath116 , @xmath185 , @xmath186 , @xmath187 , etc . mode @xmath125 is the ( trivial ) rigid - tilt mode and has no nodes . in the binary frame , the full set of frequencies appears much more complicated , as shown in table 2 . the modes in the left - hand column consist purely of @xmath188 and @xmath189 , having @xmath190 and @xmath191 . for such a mode , the frequency in the binary frame is less than the frequency in the inertial frame by an amount @xmath2 ( cf . eq . [ [ hatl ] ] ) . since , in the inertial frame , we may have a prograde or retrograde mode @xmath98 with frequency @xmath192 , we obtain frequencies @xmath193 in the binary frame . these are labeled @xmath194 . the modes in the right - hand column are physically equivalent . the eigenfunctions and eigenvalues are obtained from those in the left - hand column by complex conjugation and a change of sign . such modes consist purely of @xmath195 and @xmath196 , having @xmath197 and @xmath198 . thus the frequencies in the binary frame are @xmath199 . these modes are labeled @xmath200 . we consider next the effect of a small viscosity on the modes by increasing @xmath27 from @xmath125 to its reference value @xmath118 , but still with a companion of zero mass ( @xmath179 ) . the results are shown in table 3 . we omit the complex - conjugate modes from now on , but their existence should not be forgotten . evidently the real part of the frequency changes very little in the presence of a small viscosity , but , with the exception of the rigid - tilt mode , the frequency acquires a positive imaginary part , which signifies a damping rate . the damping rate depends relatively little on the order of the mode . it can be seen from the governing equations that the effect of viscosity is simply to damp the horizontal motions locally at a rate @xmath201 ( cf . eq . [ [ dgvecdt ] ] ) . since the horizontal motions are an essential part of each proper bending mode , this leads to a damping rate for each mode of order @xmath201 ( evaluated in the outer parts of the disk ) . the exception is the rigid - tilt mode , for which the horizontal motions are exactly zero . finally , we reach the reference model by increasing the binary mass ratio @xmath202 from @xmath125 to its reference value @xmath116 . we start with mode @xmath125 , which corresponds to a rigid tilt and consists purely of @xmath188 . the frequency of the mode ( now the ` modified ' rigid - tilt mode ) changes continuously from @xmath203 to @xmath204 . the mode also acquires a @xmath195 component . viewed in the inertial frame , the mode changes from a pure @xmath188 mode with zero frequency to a combination of @xmath188 and @xmath195 contributions having frequencies of @xmath205 and @xmath206 , respectively ( see eq . [ [ hatl ] ] ) . the first frequency corresponds to a retrograde precession of the tilted disk , forced by the @xmath0 component of the tidal potential . the second corresponds to the forcing of a bending wave ( @xmath195 ) by the @xmath1 component of the potential . the two potential components provide the ` steady ' and ` oscillatory ' torques , respectively . since the imaginary part of the frequency is positive , the whole pattern decays at a rate @xmath207 . the other modes of the disk are of course damped much more rapidly , and we conclude that the reference model disk is linearly stable to tilting . we now search the parameter space around the reference model for any regions of instability . in particular , we try varying the outer radius @xmath111 of the disk . in fig . 2 we plot the dimensionless growth rate @xmath208 against @xmath120 for a number of different values of @xmath27 it is clear that the net growth rate is a combination of two parts . one part is a damping ( @xmath209 ) that is proportional to @xmath27 and increases rapidly with increasing @xmath111 . the second part is a growth ( @xmath210 ) with an entirely different behavior . the growth is localized in a sequence of peaks which become higher and narrower as @xmath27 decreases . in fig . 3 we show an expanded view of the primary peak for the cases @xmath178 and @xmath211 . to verify the origin of the two parts , we repeated the calculation using equations that retain only the @xmath0 component of the tidal potential , or only the @xmath1 component . it is obvious from this that the damping is due entirely to the @xmath0 component , while the growth is due entirely to the @xmath1 component . there is a slight shift in the positions of the peaks when the @xmath0 component of the tidal potential is neglected . it is evident that the growth ( that is , the instability ) is associated with a series of resonances that occur when the outer radius of the disk is in the vicinity of certain discrete values . in the absence of viscosity , the resonances come about as follows . as @xmath120 is varied , the frequency eigenvalues of all bending modes migrate along the real axis in the @xmath82-plane . with the exception of mode @xmath125 , all modes are very sensitive to the position of the outer boundary , which reflects the waves . as a result , collisions occur on the real axis . in particular , when @xmath120 is increased from @xmath117 towards the primary resonance , mode @xmath125 undergoes a collision with mode @xmath130 ( a bending mode with one node ) . the modes move briefly off the real axis , producing a complex - conjugate pair , and then return to the real axis to continue their original migration . the other resonances occur when mode @xmath125 undergoes collisions with modes @xmath138 , @xmath146 , etc . during a collision , the two modes exchange characteristics , and the eigenfunctions are hybrids of the two original ones . in particular , mode @xmath125 no longer resembles a rigid tilt during a collision with a proper bending mode . this means that a disk made unstable by this means would develop a warped shape ( see section 6.4 below ) . in the presence of a very small viscosity , the proper bending modes are damped and their eigenvalues are displaced somewhat above the real axis . the collisions are no longer exact and each mode can be followed continuously as @xmath120 is varied . for @xmath211 , say , the modes pass sufficiently close that a strong interaction occurs . the tracks of the eigenvalues are deflected to avoid a collision , and , in so doing , mode @xmath125 acquires a positive growth rate that appears as a resonance . during the interaction , the eigenfunction of mode @xmath125 is distorted significantly from a rigid tilt , but not so strongly as in the inviscid case ( see section 6.4 below ) . when the viscosity is increased , the resonances become broader and weaker . a positive growth rate is not achieved if the height of the resonance is less than the damping rate arising from the @xmath0 potential . therefore the regions of instability are suppressed as @xmath27 is increased . it appears that , as long as the primary resonance survives , the net growth rate ( for @xmath212 ) is always positive for disks smaller than the size of the primary resonance , although the growth rate may be minuscule . this may be considered as a long tail of the primary resonance . however , the primary peak is dramatically reduced in height as @xmath27 is increased , and it also shifts to smaller radius . in the cases investigated here , all traces of instability are eliminated when @xmath213 . to elucidate further the condition for resonance , we examined the bending modes at their points of collision with mode @xmath125 and evaluated their natural frequencies ( i.e. in the absence of the tidal potential , and evaluated in the inertial frame ) . in each case the natural frequency is close to @xmath3 at the point of collision . the resonances therefore occur when the oscillatory torque due to the @xmath1 potential resonates with a free bending mode of the disk . we remark that the global resonant excitation of bending waves has been identified by terquem ( 1998 ) when calculating the tidal torque exerted on a protostellar disk by a companion in an inclined circular orbit . however , the consequences for the evolution of the relative inclination of the system were not investigated . the results for a companion in a retrograde orbit are not significantly different . the heights of the resonant peaks are very similar , but they are shifted slightly in radius . the shift of the resonances ( also observed , as noted above , when the @xmath0 component of the tidal potential is omitted ) is related to the precession of the disk , which changes the effective frequency of the oscillatory torque and , therefore , the condition for resonance . the precession is always retrograde in the inertial frame , irrespective of the sense of the companion s orbit . therefore the effective driving frequency depends on the sense of the orbit , but the shift is generally small . in fig . 4 we plot the precession rate of the modified rigid - tilt mode against the outer radius of the disk , for the reference model . the precession is always retrograde and the rate increases rapidly with increasing @xmath111 . excellent agreement is found with the simple analytic approximation given by bate et al . ( 2000 ; eq . [ 22 ] ) . ( we have set the dimensionless parameter @xmath214 , since this represents fairly accurately the disk models we have adopted . ) for much smaller values of @xmath27 , a noticeable deviation from this curve occurs in the vicinity of resonances , since the path of the eigenvalue in the @xmath82-plane is temporarily diverted . in fig . 5 we plot the decay rate of the modified rigid - tilt mode , for the reference model . when only the @xmath0 component of the tidal potential is included , the decay rate is always positive and increases rapidly with increasing @xmath111 . when the full potential is used , the behavior is modified in the vicinity of resonances . also shown is the simple estimate @xmath215 given by bate et al . ( 2000 ; eq . [ 35 ] ) . apart from the resonances , the simple estimate captures the correct dependence on @xmath111 . it should be borne in mind that the estimate of bate et al . ( 2000 ) was based on an order - of - magnitude analysis , and can be expected to be accurate only within a factor of order unity . for comparison with observations , it is of interest to examine the shape adopted by the disk while executing the modified rigid - tilt mode . information on the shape of the disk is contained in four real functions of radius , namely the real and imaginary parts of the eigenfunctions @xmath216 and @xmath217 . we display this information in figs 6 and 7 by showing cross - sections through the disk in the @xmath56- and @xmath218-planes at two instants , corresponding to phase @xmath125 and phase @xmath219 of the period seen in the binary frame . 6 is for a disk with @xmath220 , in the middle of the primary resonance . three different viscosities , @xmath178 , @xmath211 , and @xmath221 , are considered . in each case the mode has a positive growth rate . in the absence of viscosity , the resonance is strong and the disk becomes distinctly warped in a smooth and global manner . as already noted , when viscosity is included , the resonance is much weaker and the disk appears tilted with less noticeable warping . 7 is for a disk with the reference value @xmath222 representative of a tidally truncated disk . we fix @xmath221 and consider disks of varying thickness , @xmath223 , @xmath224 , and @xmath225 . in each case the mode is damped . for @xmath223 , the disk appears tilted without noticeable warping . for thinner disks , the deviation from a rigid tilt is noticeable in the outer part of the disk where the tidal forcing is strongest . recall that the derivation of equations ( [ dldt ] ) and ( [ dgvecdt ] ) requires that the warp vary on a length - scale long compared to the thickness of the disk ( see the appendix ) . this condition is indeed satisfied in the solutions we present here .

however , the effect of the component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency . under such circumstances , the outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius . for disks smaller than the primary resonance

we consider the dynamics of a protostellar disk surrounding a star in a circular - orbit binary system . our aim is to determine whether , if the disk is initially tilted with respect to the plane of the binary orbit , the inclination of the system will increase or decrease with time . the problem is conveniently formulated in the binary frame in which the tidal potential of the companion star is static . we may then consider a steady , flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations . the dynamics is controlled by the competing effects of the and azimuthal fourier components of the tidal potential . in the presence of dissipation , the component causes alignment of the system , while the component has the opposite tendency . we find that disks that are sufficiently large , in particular those that extend to their tidal truncation radii , are generally stable and will therefore tend to alignment with the binary plane on a time - scale comparable to that found in previous studies . however , the effect of the component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency . under such circumstances , the disk can be unstable to tilting and acquire a warped shape , even in the absence of dissipation . the outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius . for disks smaller than the primary resonance , the component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center . we discuss these results in the light of recent observations of protostellar disks in binary systems .

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in this paper , we have considered the linear stability of a coplanar protostellar disk that surrounds a star in a circular - orbit binary system . we have determined whether a slight tilt introduced into the disk would grow or decay in time . the outcome depends on the size of the disk . for disks that are truncated by standard tidal torques , typically resulting in an outer disk radius of about @xmath121 times the binary separation , we find that the disk tilt generally decays in time . for smaller disks , tilt growth is possible . as seen in fig . 2 , a disk undergoes a strong , ` primary ' resonance with the tidal field when its outer radius is a certain fraction of the binary separation . this characteristic radius , which we denote by @xmath270 , is approximately @xmath281 times the binary separation for the parameters we have considered ( see table 1 ) , but would be smaller still for thinner disks with @xmath282 . in such a resonance , the disk experiences a growing tilt and becomes significantly warped ( see fig . this resonance occurs when the frequency of the lowest - order global bending mode in the disk matches the tidal forcing frequency , which is here twice the binary orbital frequency . weaker resonances occur at a series of discrete resonances corresponding to radii greater than @xmath270 . there is also a near resonance that occurs close to the disk center . for disks smaller than radius @xmath270 , this resonance causes a very slight tilt growth if @xmath27 is sufficiently small ( but non - zero ) , and any initial tilt would be retained . for disks with radii larger than @xmath270 , including disks truncated by standard tidal torques , the tilt will decay on approximately the viscous time - scale of the disk , or roughly @xmath283 binary orbits for @xmath221 ( see fig . 5 ) . for disks with large tilts , nonlinear effects may shorten the time - scale to reach small tilts , perhaps to the precessional time - scale of the disk , or about @xmath284 binary orbits ( bate et al . 2000 ) . the net outcome of growth or decay of the disk tilt is determined by the competition of two torques . as seen in the inertial frame , the tidal torque acting on a tilted disk may be decomposed into a steady component and an oscillatory component with twice the binary orbital frequency . the steady torque , resulting from the @xmath0 component of the tidal field , causes the disk to become aligned with the binary orbit in the presence of dissipation , while the oscillatory torque , resulting from the @xmath1 component of the tidal field , causes misalignment . the steady torque produces an intuitively simple result because it causes the disk to settle to a state of coplanarity , where it experiences a minimum tidal potential energy , as a result of dissipation . the effect of the oscillatory torque is somewhat counterintuitive , but can be understood in terms of a mode - coupling model ( see fig . 1 ) . provided that @xmath27 is sufficiently small , the oscillatory torque slightly dominates for smaller disks because material in such disks is generally closer to the near resonance that occurs in the vicinity of the disk center ( see eq . [ [ resonance ] ] ) . a major issue is the origin of the tilt in observed protostellar disks . in the case of hk tau , the disk surrounds the secondary star , but the two stars are similar in spectral type ( monin , mnard , & duchne 1998 ) . although there are considerable uncertainties in the system parameters , the disk could extend to its standard tidal truncation radius , as suggested by stapelfeldt et al . ( 1998 ) . in that case , the results of this paper imply that tidal effects may cause decay of the primordial tilt , but in any case would not cause tilt growth . on the other hand , the existence of the tilt means that the decay time - scale can not be much shorter than the binary age , estimated as @xmath285 yr . this places some constraints on both the theory and the binary parameters , although there are considerable uncertainties . for example , consider the case that the binary separation is close to its projected value of 340 au . for @xmath221 , the linear tilt decay time - scale ( based on figure 2 ) would be several times longer than the estimated system age . on the other hand , the nonlinear decay time - scale estimate of bate et al ( 2000 ) suggests a decay time - scale substantially shorter than the estimated age . the nonlinear time - scale estimate would be more compatible with a somewhat larger binary separation . the predicted shape of a tilted , tidally truncated disk with @xmath286 is not strongly warped ( see fig . 7 ) , in accord with the observations ( stapelfeldt et al . 1998 ; koresko 1998 ) . the lack of an observed warp can not be used as evidence against binarity . on the other hand , a slight warp does occur for thinner disks such as in fig . 7 case b , which could be observed as a small asymmetry . note that the decay time - scale of proper bending modes of this disk ( based on table 3 ) is of order @xmath287 yr if @xmath221 , much shorter than the linear tilt decay time - scale . if the disk were tilted and warped in an arbitrary way as a result of its formation process , we would expect it to evolve rapidly to a tilted but essentially unwarped shape , then the tilt itself would decay on a longer time - scale . however , the nonlinear effects discussed by bate et al . ( 2000 ) are likely to speed up both stages considerably . similar considerations apply to a recent observational test of coplanarity among a sample of t tauri binaries by donar , jensen , & mathieu ( 2000 ) . the data show some evidence for approximate coplanarity on a statistical basis . it is possible that some tidal evolution of the tilt towards coplanarity may be have occurred , if the tilt decays as rapidly as a disk precessional time - scale . it is important to understand whether disk truncation could occur close to the resonant radius @xmath270 , so that the disk would be unstable to tilting . for disks with a substantial tilt , terquem ( 1998 ) has shown that a disk of radius close to @xmath270 is sometimes subject to a strong resonant torque that is parallel to its spin axis . this resonant torque can exceed the viscous torque in the disk for sufficiently small values of @xmath27 , @xmath288 . if this torque could truncate an initially tilted disk at radius @xmath270 , the disk might become strongly warped ( as seen in fig . 6 ) and tilted further . the disk radius would be less than half of the standard tidal truncation radius . however , it is unclear that this torque would lead to disk truncation at @xmath270 because it is smoothly distributed over the disk rather than being concentrated near @xmath270 . this is because the resonance is global rather than local . the lack of a strong warp in hk tau argues against this process in that system . disks in cataclysmic binaries are expected to be much colder than protostellar disks , having a smaller value of @xmath257 . consequently , such disks are even less likely to be unstable to tilting as a result of the @xmath1 component of the tidal field ( see eq . [ [ stab ] ] ) . in several x - ray binaries , most notably her x-1 , there is evidence for a tilted , precessing disk ( see wijers & pringle 1999 and references therein ) . the tilting mechanism we have described is very unlikely to operate in such disks , which are expected to be tidally truncated and to have @xmath289 . therefore , it appears that tidal torques are not responsible for the tilting of disks in x - ray binaries ( cf . larwood 1998 ) . possible mechanisms for tilting these disks include wind torques ( schandl & meyer 1994 ) and radiation torques ( wijers & pringle 1999 ) . another possible application of this work is to nearly keplerian disks that surround black holes in active galactic nuclei . if the disk is subject to a bar potential from the galaxy and the disk radius is sufficiently smaller than the corotation radius of the bar , then the disk will be subject to this tilt instability . the results in this paper have implications to protostellar disks perturbed by inclined planets . a secular resonance occurs where the precession frequency of a planet matches the local precession frequency of an orbiting particle . the resonant radius changes as the nebula disperses and the resonance sweeps across a major portion of the solar nebula ( ward 1981 ) . however , the current results suggest that the effects of such resonances on the gaseous nebula are mild and are distributed over the disk . further analysis can be carried out through the methods described in this paper . we thank jim pringle for encouraging this investigation and for providing useful discussions . we acknowledge support from nasa grant nag5 - 4310 and from the stsci visitor program . gio was supported by the european commission through the tmr network ` accretion on to black holes , compact stars and protostars ' ( contract number erbfmrx - ct98 - 0195 ) . bate , m. r. , bonnell , i. a. , clarke , c. j. , lubow , s. h. , ogilvie , g. i. , pringle , j. e. , & tout , c. a. 2000 , , submitted borderies , n. , goldreich , p. , & tremaine , s. 1984 , , 284 , 429 burrows , c. j. et al . 1996 , , 473 , 437 demianski , m. , & ivanov , p. 1997 , , 324 , 829 donar , a. , jensen , e. l. n. jensen , & mathieu , r. d. 2000 , baas , in press gammie , c. f. , goodman , j. , & ogilvie , g. i. 2000 , , submitted ghez , a. m. , neugebauer , g. , & matthews , k. 1993 , , 106 , 2005 goldreich , p. , & tremaine , s. 1981 , , 243 , 1062 jensen , e. l. n. , mathieu , r. d. , & fuller , g. a. 1996 , , 458 , 312 katz , j. i. , anderson , s. f. , grandi , s. a. , & margon , b. 1982 , , 260 , 780 koresko , c. d. 1998 , , 507 , l145 larwood , j. d. 1998 , , 299 , l32 larwood , j. d. , nelson , r. p. , papaloizou , j. c. b. , & terquem , c. 1996 , , 282 , 597 lubow , s. h. 1991 , , 381 , 259 lubow , s. h. 1992 , , 398 , 525 mccaughrean , m. j. , & odell , c. r. 1996 , , 111 , 1977 mathieu , r. d. 1994 , , 32 , 465 monin , j .- l . , mnard , f. , & duchne , g. 1998 , , 339 , 113 murray , j. r. , & armitage , p. j. 1998 , , 300 , 561 ogilvie , g. i. 1999 , , 304 , 557 ogilvie , g. i. 2000 , , submitted osaki , y. 1996 , , 108 , 39 osterloh , m. , & beckwith , s. v. w. 1995 , , 439 , 288 paczyski , b. 1977 , , 216 , 822 papaloizou , j. c. b. , & lin , d. n. c. 1995 , , 438 , 841 papaloizou , j. c. b. , & pringle , j. e. 1977 , , 181 , 441 papaloizou , j. c. b. , & pringle , j. e. 1983 , , 202 , 1181 papaloizou , j. c. b. , & terquem , c. 1995 , , 274 , 987 pringle , j. e. 1992 , , 258 , 811 schandl , s. , meyer , f. 1994 , , 289 , 149 stapelfeldt , k. r. , krist , j. e. , mnard , f. , bouvier , j. , padgett , d. l. , & burrows , c. j. 1998 , , 502 , l65 terquem , c. e. j. m. l. j. 1998 , , 509 , 819 wijers , r. a. m. j. , pringle , j. e. 1999 , , 308 , 207

we consider the dynamics of a protostellar disk surrounding a star in a circular - orbit binary system . the component causes alignment of the system , while the component has the opposite tendency . we discuss these results in the light of recent observations of protostellar disks in binary systems .

we consider the dynamics of a protostellar disk surrounding a star in a circular - orbit binary system . our aim is to determine whether , if the disk is initially tilted with respect to the plane of the binary orbit , the inclination of the system will increase or decrease with time . the problem is conveniently formulated in the binary frame in which the tidal potential of the companion star is static . we may then consider a steady , flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations . the dynamics is controlled by the competing effects of the and azimuthal fourier components of the tidal potential . in the presence of dissipation , the component causes alignment of the system , while the component has the opposite tendency . we find that disks that are sufficiently large , in particular those that extend to their tidal truncation radii , are generally stable and will therefore tend to alignment with the binary plane on a time - scale comparable to that found in previous studies . however , the effect of the component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency . under such circumstances , the disk can be unstable to tilting and acquire a warped shape , even in the absence of dissipation . the outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius . for disks smaller than the primary resonance , the component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center . we discuss these results in the light of recent observations of protostellar disks in binary systems .

1005.1862

c

we have shown theoretically and via simulation studies that : * the _ limiting spectral distribution _ ( lsd ) of rcv matrix depends not only on that of the icv matrix , but also on the time - variability of covolatility process ; * in particular , even with the same targeting icv matrix , the _ empirical spectral distribution _ ( esd ) of rcv matrix can vary a lot , depending on how the underlying covolatility process evolves over time ; * for a class @xmath69 of processes , our proposed estimator , the _ time - variation adjusted realized covariance _ ( tvarcv ) matrix , possesses the following desirable properties as an estimator of the icv matrix : as long as the targeting icv matrix is the same , the esds of tvarcv matrices estimated from processes with different covolatility paths will be close to each other , sharing a unique limit ; moreover , the lsd of tvarcv matrix is related to that of the targeting icv matrix through the same marcenko pastur equation as in the sample covariance matrix case . furthermore , we establish a marcenko pastur type theorem for weighted sample covariance matrices . for a class @xmath69 of processes , we also establish a marcenko pastur type theorem for rcv matrices , which explicitly demonstrates how the time - variability of the covolatility process affects the lsd of rcv matrix . in practice , for given @xmath0 and @xmath1 , based on the ( observable ) esd of tvarcv matrix , one can use existing algorithms to obtain an estimate of the esd of icv matrix , which can then be applied to further applications such as portfolio allocation , risk management , etc .

we consider the estimation of integrated covariance ( icv ) matrices of high dimensional diffusion processes based on high frequency observations . we start by studying the most commonly used estimator , the _ realized covariance _ ( rcv ) matrix . we show that in the high dimensional case when the dimension and the observation frequency grow in the same rate , the limiting spectral distribution ( lsd ) of rcv depends on the covolatility process _ not only through the targeting icv _ , _ but also on how the covolatility process varies in time_. we establish a marenko pastur type theorem for weighted sample covariance matrices , based on which we obtain a marenko pastur type theorem for rcv for a class of diffusion processes . we show that for processes in class , the tvarcv possesses the desirable property that its lsd depends solely on that of the targeting icv through the marenko pastur equation , and hence , in particular , the tvarcv can be used to recover the empirical spectral distribution of the icv by using existing algorithms . . .

we consider the estimation of integrated covariance ( icv ) matrices of high dimensional diffusion processes based on high frequency observations . we start by studying the most commonly used estimator , the _ realized covariance _ ( rcv ) matrix . we show that in the high dimensional case when the dimension and the observation frequency grow in the same rate , the limiting spectral distribution ( lsd ) of rcv depends on the covolatility process _ not only through the targeting icv _ , _ but also on how the covolatility process varies in time_. we establish a marenko pastur type theorem for weighted sample covariance matrices , based on which we obtain a marenko pastur type theorem for rcv for a class of diffusion processes . the results explicitly demonstrate how the time variability of the covolatility process affects the lsd of rcv . we further propose an alternative estimator , the _ time - variation adjusted realized covariance _ ( tvarcv ) matrix . we show that for processes in class , the tvarcv possesses the desirable property that its lsd depends solely on that of the targeting icv through the marenko pastur equation , and hence , in particular , the tvarcv can be used to recover the empirical spectral distribution of the icv by using existing algorithms . . .

1303.3776

i

we consider the problem of factorization of permutations . we begin with a discussion of some simple mathematical ideas behind a matching game known as amidakuji concerning the assignment of @xmath0 jobs to @xmath0 people . it is shown that the ideas are related to the study of other topics including sorting algorithms in computer science , permutations in abstract algebra , and research in genomics . in section 2 , we extend the ideas to obtain new results and discuss new problems on factorization of permutations into special type of transpositions . amidakuji , also known as ghost leg drawing , is a matching game ( with a certain degree of randomness ) for creating a one - one correspondence between @xmath0 people and @xmath0 jobs , or between @xmath0 boys and @xmath0 girls . this game is quite popular in asian regions ( japan , korea , hong kong , taiwan ) , and has even been created into an iphone app . @xcite . to do the matching , one draws @xmath0 vertical lines connecting persons @xmath1 to jobs @xmath2 , which yields the natural assignment that @xmath3 corresponds to @xmath4 for @xmath5 . one then randomly adds some horizontal line segments between any pair of adjacent vertical lines so that no two horizontal line segments meet . now , @xmath3 will find their job assignment by going down the @xmath6th vertical line and making a turn ( to left , right , or going down ) whenever an intersection of a horizontal and vertical line segments is encountered . this will set up a one - one correspondence between @xmath1 and @xmath2 . one can see the example in figure 1 ( from @xcite ) below . first time players are often amazed by the fact that the procedure always leads to a one - one correspondence between @xmath0 people and @xmath0 jobs . that is , at the end of the game , no two people will be assigned the same job . also , it is natural to ask whether one can get all possible job assignments , and how to draw the horizontal lines to arrange the specific job assignment . we list several natural questions in the following . 1 . why do we always get a one - one correspondence ? is it possible to get every possible job assignments ? 3 . what is the minimum number of horizontal lines one has to add to achieve a certain specific job assignment ? 4 . what is the job assignment so that the minimum number of horizontal lines needed for the assignment is maximum ? the answer of question 1 is easy if one approaches it in the `` right '' way . one can interpret the procedure as follows . the people @xmath1 sit in a row of chairs labeled by @xmath2 . adding a line segment corresponds to switching an adjacent pair of people . of course , no matter how many horizontal line segments are added , @xmath0 people will still occupy the @xmath0 seats without any conflicts . formally , one can prove the result by induction on the number of horizontal line segments . if there is no horizontal line segment , clearly one has a one - one correspondence between the people and jobs . suppose @xmath7 horizontal line segments will give rise to a one - one correspondence . then adding one more line segment will only add an additional switch of the job assignment of an adjacent pair of people . using the above interpretation , one can readily answer questions 2 4 . we can represent the original sitting arrangement by @xmath8 $ ] and the final sitting arrangement by @xmath9 $ ] , which is referred to as a _ permutation _ of @xmath10 we can always restore the order of @xmath9 $ ] by doing the following . survey the list from left to right , whenever we encounter two consecutive number so that the left one is larger than the right one , we switch the two numbers . we * claim * that after a number of such switches , one will not see any pair of consecutive terms such that the left number is larger than the right one . then the permutation must be @xmath10 $ ] at that stage . reversing the above switching steps , we will generate the permutation @xmath9 $ ] from @xmath11 $ ] . hence , we can generate any permutation if we can prove our * claim*. to this end , we define the number of inversions of a permutation @xmath9 $ ] as the sum of the numbers inv@xmath12 , where inv@xmath12 is the numbers of integers smaller than @xmath6 lying on the right side of @xmath6 in @xmath9 $ ] . for example , the number of inversions in @xmath13 $ ] is @xmath14 . note that if we exchange two consecutive numbers we either increase or decrease the inversion numbers by @xmath15 or @xmath16 depending on whether the left number is smaller or larger . thus , each step of our proposed scheme will reduce the number of inversions by 1 . as a result , after a number of steps ( equal to the number of inversions ) , we will have no more inversions . * figure 1 * the above analysis does not only show that one can get all permutations of @xmath17 $ ] . it also tells us the minimum number of switches needed to get to a special permutation @xmath9 $ ] , namely , the number of inversions in the permutation . now , it is clear that the permutation with the maximum number of inversions is @xmath18 $ ] requiring @xmath19 switches . so , we have the answers for questions 2 4 . * sorting algorithm * it is easy to see that the mathematical idea behind the amidakuji game can be used to determine the number of steps required to restore the order of a permutation @xmath9 $ ] under the restriction that one can only switch two consecutive numbers in each step . in fact , this is the well known bubble sort algorithm in computer science study ; see @xcite and its references . the basic idea is : to restore a permutation @xmath9 $ ] to the identity permutation @xmath17 $ ] by exchanging a consecutive pair of numbers in each step , the minimum number of steps needed is the number of inversions in @xmath9 $ ] . as long as one exchanges a pair of numbers @xmath20 for @xmath21 in each step to reduce the total number of inversions in the permutation , the procedure will bring @xmath9 $ ] to @xmath17 $ ] in the minimum number of steps . there are many other efficient sorting algorithms . we refer the readers to the excellent reference @xcite for more details . * genome rearrangements * it turns out that the study is related to the study of genome rearrangement . in nature , some species have similar genetic make up and differ only in the order of their genes . finding the shortest rearrangement path between two related bacteria or viruses is useful in drug discovery and vaccine development . the study is also useful in the study of mutations . in fact , a slight change of the genetic sequence may have significant effect , and it is more likely to see a change ( permutation ) of the positions of the nucleotides close to each other in the genetic sequences . that is why there are keen interest in studying such permutations in genetic sequences ; for example , see @xcite and their references . * group theory and cayley graph * the problem is clearly related to the study of group theory and cayley graph in abstract algebra . denote by @xmath22 the set of permutations of @xmath10 $ ] , i.e. , symmetric group of degree @xmath0 , and regard every permutation as a vertex . we connect two vertices @xmath23 and @xmath24 if @xmath25 for a permutation @xmath26 which exchanges two consecutive numbers at the @xmath27th and @xmath28st positions for some @xmath29 . then the bubble sort algorithm amounts to moving a permutation @xmath9 $ ] to @xmath17 $ ] in the cayley graph most efficiently ( using the minimum number of steps ) . moreover , @xmath30 is the maximum distance from @xmath17 $ ] to another permutation @xmath9 $ ] , which is @xmath31 $ ] . one easily shows that the value @xmath30 is actually the maximum distance between any two vertices , and is known as the diameter of the cayley graph . it also indicates that a permutation is a product of no more than @xmath30 transpositions of the form @xmath32 . a more general version of the above problem is how to represent a permutation as a product of a minimal number of permutations selected from a certain set . the study has a long history , and attracted many authors ; see @xcite and their references . we will consider this type of problem in the next section . the study of this problem has a long history . d@xmath33nes @xcite determined that the minimum number is @xmath34 , where @xmath35 is the number of disjoint cycles in the given permutation on @xmath0 letters . other approaches have been used to get the minimum number in @xcite . later on , people found it natural and interesting to determine the number of minimal factorization of a permutation and the minimal product with factors from a given set of transpositions @xcite . * graph algorithms * graph algorithms concern the study of efficient computational methods in solving pure and applied problems which can be modeled using graph theory ; see @xcite and their references . formulating our problem in terms of the permutation group and cayley graph naturally lead to the use of graph algorithms to search the shortest path from a given permutation @xmath36 $ ] to the identity @xmath17 $ ] , and the search of the diameter of the cayley graph . in our study , we also develop some computer programs in our study ; see section 2.3 .

we consider the problem of factorization of permutations . we begin with a discussion of some simple mathematical ideas behind a matching game known as amidakuji concerning the assignment of jobs to people . it is shown that the ideas are related to the study of other topics including sorting algorithms in computer science , permutations in abstract algebra , and research in genomics . we then extend the ideas to obtain new results and discuss new problems on factorization of permutations into special type of transpositions . .85 * keywords . * amidakuji , bubble sort , genomics , permutation , symmetric groups , cayley graphs .

we consider the problem of factorization of permutations . we begin with a discussion of some simple mathematical ideas behind a matching game known as amidakuji concerning the assignment of jobs to people . it is shown that the ideas are related to the study of other topics including sorting algorithms in computer science , permutations in abstract algebra , and research in genomics . we then extend the ideas to obtain new results and discuss new problems on factorization of permutations into special type of transpositions . .85 * keywords . * amidakuji , bubble sort , genomics , permutation , symmetric groups , cayley graphs .

1512.06552

i

coupled cluster ( cc ) theory @xcite is perhaps the most powerful method for describing dynamical electron correlation effects within the realm of modern quantum chemistry . the cc singles and doubles ( ccsd ) model @xcite , in which the cluster operator is truncated at the level of double excitations , is a robust and useful model , but it is well - known that the effects of triple ( and higher - level ) excitations need to be taken into account in order to obtain highly accurate results that may compete with the accuracy of experiments @xcite . however , the steep scaling of the cc singles , doubles , and triples @xcite ( ccsdt ) and cc singles , doubles , triples , and quadruples @xcite ( ccsdtq ) models limits their use to rather modest molecular systems . for this reason , a computationally tractable alternative to the expensive iterative ccsdt and ccsdtq models is to develop approximate models , for which the important triples and/or quadruples contributions are determined from a perturbation analysis , and hence included in a cheap and non - iterative fashion . a plethora of different models for the approximate treatment of triples and/or quadruples effects have been suggested , and we refer to ref . for a recent theoretical overview of approximate non - iterative triples and quadruples models and refs . and for a numerical comparison of many of these . in the present work , we focus on perturbation theory within a cc framework , where a mller - plesset ( mp ) partitioning of the hamiltonian is performed @xcite , and the energy difference between a zeroth - order ( parent ) cc model and a higher - level ( target ) cc model is expanded in orders of the perturbation ( the fluctuation potential ) . in particular , we will base the perturbation analysis on a bivariational cc lagrangian obtained by adding to the cc target energy the cc amplitude equations with associated lagrange multipliers . we note that the linearly parametrized state formally spanned by the lagrange multipliers is often referred to as the cc @xmath3-state @xcite , and that this is in general different from the exponentially parametrized cc state . as pointed out by arponen @xcite , extensively exploited in the cc lagrangian formulation@xcite , and recently discussed by kvaal @xcite , the cc energy may be interpreted as a cc functional in both the cc amplitudes and the @xmath3-state parameters . we will show that the fastest convergence is obtained when these two sets of state parameters are treated on an equal footing in the perturbative expansion of the energy difference between a parent and a target cc model . thus , we will distinguish between a perturbation expansion of the cc energy , for which only parent amplitudes are used at the expansion point , and a perturbation expansion of the cc lagrangian , for which both parent amplitudes _ and _ parent multipliers are used at the expansion point . at first sight , the bivariational lagrangian formulation might seem like an unnecessary complication , since , for the target model , the lagrangian formally equals the energy . the purpose of this work is , however , to highlight and exemplify that not only is the lagrangian formulation a convenient mathematical tool that may simplify the derivation of various perturbation expansions ; in many cases , the lagrangian formulation will actually lead to different perturbation series than the corresponding energy formulation . to exemplify this difference , we consider two perturbation series which both expand the difference between the energies of the ccsd and ccsdt models . we initially introduce the @xmath0 series , in which the ccsd amplitude equations are satisfied at the expansion point , and next compare it to the recently developed @xmath1 series @xcite , in which not only the ccsd amplitude equations are satisfied at the expansion point , but also the ccsd multiplier equations . despite depending on the fluctuation potential to infinite order in the space of all single and double excitations , the ccsd amplitudes are formally considered as zeroth - order parameters in both the @xmath0 and @xmath1 series , since the ccsd model represents the expansion point . similarly , the ccsd multipliers , which too depend on the fluctuation potential , are considered as zeroth - order parameters for the @xmath1 series , but not so for the @xmath0 series . the path from the ccsd expansion point towards the ccsdt target energy , as defined by a perturbation expansion , is thus different within the @xmath0 and @xmath1 series , and , as will be shown in the present work , the @xmath1 series is the more rapidly converging of the two , since more information is utilized at the expansion point . we finally reiterate that the lowest - order contribution of the @xmath1 series ( that of the @xmath4 model ) is identical to the triples - only part of the ccsd(2 ) model of gwaltney and head - gordon @xcite and the second - order model of the cc(@xmath5)pt(@xmath6 ) series of hirata _ et al . _ @xcite , the @xmath7 model is identical to the triples - only part of the third - order cc(@xmath5)pt(@xmath6 ) model , while for fourth and higher orders , the @xmath1 and cc(@xmath5)pt(@xmath8 ) series are different @xcite . the @xmath0 series , however , differs from the aforementioned perturbation series for all corrections . + the present study is outlined as follows . in [ sec : theory ] , we derive the @xmath0 series and compare it to the @xmath1 series in order to illustrate the importance of treating parent amplitudes and multipliers on an equal footing . in [ sec : results ] , we present numerical results for the @xmath0 and @xmath1 energies , while some concluding remarks are given in [ sec : conclusion ] .

we consider two distinct coupled cluster ( cc ) perturbation series that both expand the difference between the energies of the ccsd ( cc with single and double excitations ) and ccsdt ( cc with single , double , and triple excitations ) models in orders of the mller - plesset fluctuation potential . we initially introduce the series , in which the ccsd amplitude equations are satisfied at the expansion point , and compare it to the recently developed series [ j. chem . , 064108 ( 2014 ) ] , in which not only the ccsd amplitude , but also the ccsd multiplier equations are satisfied at the expansion point . . the present analysis can be generalized to any perturbation expansion representing the difference between a parent cc model and a higher - level target cc model . in general , we demonstrate that , whenever the parent parameters depend upon the perturbation operator , a perturbation expansion of the cc energy ( where only parent amplitudes are used ) differs from a perturbation expansion of the cc lagrangian ( where both parent amplitudes _ and _ parent multipliers are used ) . for the latter case , the bivariational lagrangian formulation becomes more than a convenient mathematical tool , since it facilitates a different and faster convergent perturbation series than the simpler energy - based expansion .

we consider two distinct coupled cluster ( cc ) perturbation series that both expand the difference between the energies of the ccsd ( cc with single and double excitations ) and ccsdt ( cc with single , double , and triple excitations ) models in orders of the mller - plesset fluctuation potential . we initially introduce the series , in which the ccsd amplitude equations are satisfied at the expansion point , and compare it to the recently developed series [ j. chem . phys . , 064108 ( 2014 ) ] , in which not only the ccsd amplitude , but also the ccsd multiplier equations are satisfied at the expansion point . the computational scaling is similar for the two series , and both are term - wise size extensive with a formal convergence towards the ccsdt target energy . however , the two series are different , and the series is found to exhibit a more rapid convergence up through the series , which we trace back to the fact that more information at the expansion point is utilized than for the series . the present analysis can be generalized to any perturbation expansion representing the difference between a parent cc model and a higher - level target cc model . in general , we demonstrate that , whenever the parent parameters depend upon the perturbation operator , a perturbation expansion of the cc energy ( where only parent amplitudes are used ) differs from a perturbation expansion of the cc lagrangian ( where both parent amplitudes _ and _ parent multipliers are used ) . for the latter case , the bivariational lagrangian formulation becomes more than a convenient mathematical tool , since it facilitates a different and faster convergent perturbation series than the simpler energy - based expansion .

1103.2484

i

for every map @xmath0 of connected reductive groups over @xmath1 we may regard the representations of @xmath2 as representations of @xmath3 via its action through @xmath4 for any irreducible representation @xmath5 of @xmath2 there is a direct sum decomposition into irreducible @xmath3 representations . @xmath6 the vector spaces @xmath7 determine the restriction functor @xmath8 on the categories of finite dimensional representations of @xmath3 and @xmath9 and a calculation of the dimensions of these spaces is called a branching rule associated to @xmath4 recall that equivalence classes of irreducible representations of @xmath2 are in bijection with the lattice points of convex rational cone @xmath10 a weyl chamber of @xmath11 solving the branching problem can be seen as assigning non - negative integers , the dimensions of the above spaces , to the dominant weights in @xmath12 this leads naturally to questions about the nature of the sets of points where these numbers are non - zero . one general approach to this problem is to bring in techniques from commutative algebra by integrating the spaces @xmath7 into a commutative algebra , @xmath13 this algebra is constructed from the algebra of invariants by a maximal unipotent @xmath14 in the coordinate ring @xmath15.$ ] as a representation of @xmath9 this algebra is the multiplicity free sum of the irreducible representations of @xmath11 @xmath16^u = \bigoplus_{\lambda \in \delta_g } v(\lambda)\\\ ] ] this algebra is finitely generated by the representations associated to the fundamental weights in @xmath17 multiplication can be computed component - wise by the cartan product , which is projection onto the highest weight component of the tensor product . @xmath18 for @xmath0 a map of reductive groups , the branching algebra for @xmath19 is defined as the invariant ring of @xmath20 by @xmath21 or equivalently as the @xmath22invariants of @xmath23 where @xmath24 is a maximal unipotent subgroup . @xmath25^h = r_g^{u_h}\\\ ] ] it is worth mentioning two special cases of this construction . for @xmath26 the algebra @xmath27 is the subalgebra of highest weight vectors in @xmath23 in other words it is the toric algebra attached to the semigroup of dominant weights of @xmath9 @xmath28.$ ] for the unity morphism @xmath29 the algebra is just @xmath30 for all @xmath31 @xmath32 is finitely generated and graded by the monoid of dominant weights @xmath33 and the non - zero branching numbers for @xmath0 correspond to the non - zero graded components of @xmath34 we call this submonoid @xmath35 since @xmath32 is finitely generated , the monoid @xmath36 is finitely generated as well , this implies that its non - negative real saturation is a convex rational cone in @xmath37 the cone @xmath36 itself can be difficult to understand so in order to get more information about the polyhedral and algebraic properties of @xmath36 it helps to find a cone @xmath38 which can be understood more easily , and a surjection @xmath39 conceptually , the cone @xmath38 `` enriches '' the branching structure described by @xmath40 and meaningful @xmath38 correspond to combinatorial rules which solve or simplify the branching problem , such as the littlewood - richardson rule or the pieri rule in type @xmath41 throughout this paper we will describe two ways a cone like @xmath38 can be constructed , how to combine these constructions , and some of the resulting algebraic and geometric implications for @xmath32 . the principle driving our constructions is that different meaningful @xmath42 arising from different combinatorial rules for understanding branching problems , correspond to flat degenerations of @xmath34 and that these degenerations fit together into a polyhedral structure that is described by elements of tropical geometry . the connection with tropical geometry comes from our use of valuations to construct the degenerations of @xmath13 it is a theorem from tropical geometry ( see @xcite and section [ trop ] ) that the tropical variety @xmath43 of any ideal @xmath44 from a presentation of @xmath32 can be constructed as an image of @xmath45 the set of all valuations on @xmath32 into the tropical real line @xmath46 which are trivial on @xmath47 we define a complex of rational , pointed cones @xmath48 for each morphism @xmath19 in the category of reductive groups which is informed by the factorizations of @xmath31 and we show that points in this complex define valuations on the branching algebra @xmath13 these valuations do not always have toric associated graded algebras , so we explain how they can be enhanced to toric degenerations of @xmath32 in the special cases when @xmath19 is a diagonal embedding @xmath49 or an inclusion of a levi subgroup @xmath50 . for any branching problem @xmath51 it is possible to enrich @xmath36 by studying factorizations of @xmath4 @xmath52 @xmath53 by the semisimplicity of the categories @xmath54 the space @xmath55 decomposes into a direct sum . @xmath56 we think of elements of these spaces as diagrams of intertwiners . @xmath57 we abbreviate the summands on the right above as @xmath58 and @xmath32 has a direct sum decomposition into these spaces as a vector space . forgetting all but the dominant weight data results in a fiber product cone @xmath59 with a natural map to @xmath60 on the level of commutative algebra the above direct sum decomposition is a filtration of the multiplication operation on @xmath32 . the following will be discussed in section [ branch ] . [ branchfiltration ] for any factorization of a morphism of reductive groups @xmath61 there is a filtration of @xmath32 defined on the spaces @xmath62 by the ordering on the dominant weight labels . @xmath63 the associated graded algebra is isomorphic to @xmath64^{t_1 \times \ldots \times t_{n-1 } } \subset \otimes_{i = 1}^n r(\phi_i).$ ] furthermore , @xmath64^{t_1 \times \ldots \times t_{n-1}}$ ] is a flat degeneration of @xmath13 the torus @xmath65 is a product of the maximal tori in the groups @xmath66 a general summand of @xmath67 is of the form @xmath68 and this algebra has an action of @xmath69 where @xmath70 acts with weight @xmath71 we take invariants by the action by the anti - diagonal subtorus @xmath72 so the components in the invariant algebra satisfy @xmath73 to each such factorization we will then associate a rational polyhedral cone @xmath74 we take the product @xmath75 of the dual weyl - chambers of the groups , in other words the weyl chambers of their respective langlands dual groups . these elements can be realized as linear functionals on the weyl chambers @xmath76 so we define @xmath77 as the quotient of @xmath75 by the relation which identifies two elements having the same values on @xmath78 the following will be proved in section [ branch ] . [ valcon ] there is a map @xmath79 we construct a complex out of the cones @xmath77 as @xmath80 runs over all factorizations of @xmath19 in the category of reductive groups . let @xmath81 be the simplicial set defined as follows . the @xmath82-simplices are defined as length-@xmath82 factorizations @xmath83 of the morphism @xmath4 the face and degeneracy maps are defined by the following operations on chains of morphisms . @xmath84 @xmath85 to make this well - defined , we can take some small category in the category of reductive groups which contains all such factorizations up to equivalence . the cones @xmath77 carry maps which correspond to the degeneracy maps in the above simplicial set by setting the appropriate coordinate to be @xmath86 and the face maps are realized by adding the two adjacent coordinates which come from the same group . @xmath87 @xmath88 @xmath89 @xmath90 we can glue the @xmath77 together along these maps by taking a colimit to obtain a polyhedral model of @xmath91 which we call @xmath92 these gluing maps will be shown to be compatible with the maps @xmath93 [ valcom ] there is a map @xmath94 in particular , every tropical variety @xmath43 associated to a presentation of the ring @xmath32 has a subset which is the image of the polyhedral complex @xmath92 in this way , the structure of the category of reductive groups informs the tropical geometry of branching algebras . we now describe special factorizations of two types of morphisms , a diagonal @xmath49 and the inclusion of a levi subgroup @xmath95 the degenerations defined by these special factorizations can be completed to toric degenerations . as a vector space , the branching algebra @xmath96 is a direct sum of the invariants in all @xmath97-fold tensor products of representations of @xmath9 for this reason we call it the full tensor algebra of @xmath11 @xmath98^g\\\ ] ] we make a special application of the branching construction described above to reduce the study of @xmath96 to @xmath99 for any @xmath100 define an oriented @xmath101-tree to be a @xmath102 with @xmath97 leaves labeled @xmath103 where each edge is directed in such a way that each non - leaf vertex has exactly one in - edge , the @xmath104 leaf is a source , and all other leaves are sinks . note that the orientation is entirely defined by the labeling @xmath105 to each oriented @xmath101-tree we define a factorization of @xmath106 by assigning each vertex @xmath107 the morphism @xmath108 where @xmath109 is the valence of @xmath110 . ( -15 , 4)*g ; ( 12 , 10)*g ; ( 35 , -2)*g ; ( 35 , -14)*g ; ( 12 , -1)*g ; ( 0,4)*_2 ; ( 25 , -3 ) * _ 2 ; ( 0,0 ) * = `` aa '' ; ( 30,15 ) * = `` bb '' ; ( 45,-5 ) * = `` cc '' ; ( 40,-25 ) * = `` dd '' ; ( -30,0 ) * = `` ee '' ; ( 25,-7 ) * = `` ff '' ; `` bb '' ; `` aa '' ; * * ? > * ; `` aa '' ; `` ee '' ; * * ? > * ; `` ff '' ; `` aa '' ; * * ? > * ; `` dd '' ; `` ff '' ; * * ? > * ; `` cc '' ; `` ff '' ; * * ? > * ; the branchings defined by this tree construction define a connected subcomplex of @xmath111 which we call @xmath112 the factorization diagrams corresponding to @xmath102 are labellings of the edges @xmath113 of @xmath102 by dominant @xmath2-weights , and the vertices @xmath114 of @xmath102 by @xmath2-tensors . by theorem [ branchfiltration ] above , this results in a filtration on @xmath96 with associated graded algebra a subalgebra of torus invariants in @xmath115 if @xmath102 is trivalent , we obtain a subalgebra of of @xmath116^{\otimes n-2}.$ ] the complex @xmath117 can be recognized as the space of phylogenetic trees defined by billera , holmes and vogtman in @xcite to give a geometric context to phylogenetic algorithms from mathematical biology . there is a distinguished class of factorizations we can use on the map defined by the inclusion of a levi subgroup @xmath118 as well , namely factorizations by other levi subgroups . for any chain of levi subgroups @xmath119 we obtain a cone of valuations @xmath120 with a flat degeneration of @xmath121 to @xmath122^{t_1 \times \ldots \times t_m}.$ ] each such cone can be represented combinatorially by a nesting of the dynkin diagrams defining the @xmath123 ( 100 , 0)*sl_6 ( ) ; ( 100 , -10)*sl_4()^ * sl_2 ( ) ; ( 100 , -20)*sl_3()(^*)^2 sl_2 ( ) ; ( 100 , -30)*^*sl_2 ( ) ( ^*)^2 sl_2 ( ) ; ( 100 , -40)*(^*)^4sl_2 ( ) ; ( 100 , -5 ) * ; ( 100 , -15 ) * ; ( 100 , -25 ) * ; ( 100 , -35 ) * ; ( 0,0 ) * = `` a '' ; ( 10,0 ) * = `` b '' ; ( 20,0 ) * = `` c '' ; ( 30,0 ) * = `` d '' ; ( 40,0 ) * = `` e '' ; `` a '' ; `` b '' ; * * ? > * ; `` b '' ; `` c '' ; * * ? > * ; `` c '' ; `` d '' ; * * ? > * ; `` d '' ; `` e '' ; * * ? > * ; ( 0,-10 ) * = `` a1 '' ; ( 10,-10 ) * = `` b1 '' ; ( 20,-10 ) * = `` c1 '' ; ( 40,-10 ) * = `` e1 '' ; `` a1 '' ; `` b1 '' ; * * ? > * ; `` b1 '' ; `` c1 '' ; * * ? > * ; ( 0,-20 ) * = `` a2 '' ; ( 10,-20 ) * = `` b2 '' ; ( 40,-20 ) * = `` e2 '' ; `` a2 '' ; `` b2 '' ; * * ? > * ; ( 10,-30 ) * = `` b3 '' ; ( 40,-30 ) * = `` e3 '' ; ( 40,-40 ) * = `` e4 '' ; we define @xmath124 to be the connected subcomplex defined by all chains of levi subgroups which begin with @xmath125 for a fixed choice of maximal torus . just as exploring @xmath126 for @xmath127 has lead to some interesting combinatorics ( see @xcite , @xcite ) , we anticipate that the study of @xmath128 for various @xmath125 and @xmath2 to yield interesting combinatorial structures as well . factorization diagrams provide a convenient combinatorial filtration of general branching algebras , but the associated graded algebras of these filtrations are not always monoidal . now we describe how to use the dual canonical basis ( crystal basis ) of lusztig to complete the branching degenerations associated to the valuations in @xmath126 and @xmath128 to toric degenerations . a full solution to a branching problem would be a cone @xmath129 where each element of a basis of branching maps @xmath130 is assigned a unique element of @xmath38 . ideally , one wants 1 . a finitely generated monoid @xmath131 + 2 . a map @xmath132 which recovers @xmath36 , such that the number of points in the fiber over @xmath133 is @xmath134.$ ] + 3 . an algebraic relationship between @xmath131 and @xmath13 we will use the convex polyhedral descriptions of branching for inclusion of levi subgroup @xmath135 and the diagonal map @xmath136 given by berenstein and zelevinsky in @xcite , @xcite to give a variety of solutions to @xmath137 , @xmath138 , and @xmath139 above in these cases . the dual canonical basis @xmath140 has a parametrization by @xmath141tuples of non - negative integers for each reduced decomposition @xmath142 of the longest word of the weyl group @xmath143 of @xmath2 . @xmath144 this defines an injective map @xmath145 and a partial ordering on @xmath146 where @xmath147 if @xmath148 as dominant weights , or @xmath149 and @xmath150 lexicographically . the image of this map is the set of integer points in a convex cone @xmath151 multiplication in @xmath152 with respect to the basis @xmath153 was shown to be lower - triangular by caldero @xcite , see also @xcite . @xmath154 this is similar to the filtration defined by factorization diagrams . we will employ an observation we believe to be essentially due to zhelobenko @xcite to realize the branching algebras @xmath99 and @xmath155 as subalgebras of @xmath156 $ ] and @xmath152 respectively in order to show the following . [ basisinherit ] the algebras @xmath99 and @xmath155 inherit the dual canonical basis along with its lower triangular multiplication property from @xmath30 using the work of berenstein and zelevinsky @xcite , we observe that the the bases of @xmath99 and @xmath155 both come with natural labelings by the integer points in convex rational cones @xmath157 and @xmath158 respectively , one for each choice of string parameter @xmath159 the algebras @xmath99 and @xmath155 carry flat degenerations @xmath160 $ ] and @xmath161 $ ] respectively . in the examples we explain a particular nice instance of a cone @xmath157 in type @xmath41 these degenerations allow us to complete the branching degenerations of @xmath96 and @xmath155 defined above to toric degenerations . [ diagtoric ] the full tensor algebra @xmath96 has a toric degeneration for each choice of the following objects . 1 . a trivalent , oriented @xmath101-tree , @xmath102 . an ordering of the internal vertices @xmath107 + 3 . an assignment @xmath162 of strings to internal vertices of @xmath163 the resulting rational cone @xmath164 is a fiber product of cones @xmath165 over copies of @xmath166 according to the topology of @xmath163 an element of this cone is a labeling of @xmath102 by dominant weights on the edges of @xmath102 and compatible dual canonical basis elements on the trinodes . the map which forgets all data except the labels on the leaves is a map on cones @xmath167 which enriches the tensor branching cone . ( -15 , 4)*_0 ; ( 12 , 10)*_1 ; ( 38 , -2)*_2 ; ( 35 , -14)*_3 ; ( 12 , -1 ) * ; ( 0,5)*b__0 , _ 1 , , ; ( 25 , -3 ) * b _ , _ 2 , _ 3 , ; ( 0,0 ) * = `` aa '' ; ( 30,15 ) * = `` bb '' ; ( 50,-5 ) * = `` cc '' ; ( 40,-25 ) * = `` dd '' ; ( -30,0 ) * = `` ee '' ; ( 25,-7 ) * = `` ff '' ; `` bb '' ; `` aa '' ; * * ? > * ; `` aa '' ; `` ee '' ; * * ? > * ; `` ff '' ; `` aa '' ; * * ? > * ; `` dd '' ; `` ff '' ; * * ? > * ; `` cc '' ; `` ff '' ; * * ? > * ; these degenerations are all @xmath168 invariant with respect to the action which grades @xmath96 by the tuple of dominant weights in each tensor product , so we also get toric degenerations of every subalgebra @xmath169 given as the sum of the graded pieces for a submonoid @xmath170 @xmath171 in particular , we get a degeneration of the algebra corresponding to the monoid of non - negative integer multiples of a particular tuple of weights , @xmath172 this algebra , @xmath173 is the projective coordinate ring associated to a line bundle @xmath174 on a configuration space of @xmath9 defined as the following git quotient . @xmath175\\\ ] ] here @xmath176 is the parabolic subgroup of @xmath2 corresponding to the face of @xmath166 which contains @xmath177 let @xmath178 be the polytope obtained from @xmath164 by fixing the leaf edge values at the weights @xmath179 the lattice points in @xmath178 are in bijection with a basis of the space of global sections @xmath180 these spaces have been studied in detail for @xmath181 where @xmath182 is always the projective line , see @xcite , @xcite , @xcite . we also have a similar statement for the branching algebra @xmath183 [ levitoric ] for any choices of the following information we construct a toric degeneration of @xmath183 1 . a chain of levi subgroups @xmath184 + 2 . a choice of string @xmath185 for each levi @xmath186 + the result is easiest to describe when the strings @xmath185 are all compatible in the sense that they concatenate to a string @xmath187 of @xmath11 for choices of these `` adapted '' strings , @xmath155 degenerates to the toric algebra @xmath188.$ ] here @xmath189 is the fiber product @xmath190 where @xmath191 is the cone for the inclusion of @xmath192 into @xmath193 there is also a map @xmath194 which enriches the levi branching cone . in section [ examples ] we discuss a particular realization of @xmath196 $ ] for @xmath197 using berenstein - zelevinsky triangles @xcite . the result is a description of a particular @xmath164 as the non - negative integer points in the intersection of a collection of linear spaces . in certain cases the two constructions presented here apply to the same algebras . as with @xmath198 any subalgebra @xmath199 corresponding to a submonoid @xmath200 inherits the degenerations defined by a chain of levi subgroups @xmath201 with selected strings @xmath202 an example of such a submonoid is given by the multiplies of the @xmath203 dominant weight @xmath204 of @xmath205 the subalgebra @xmath206 is the projective coordinate ring of the grassmannian @xmath207 this algebra can also be realized as a subalgebra @xmath208 for @xmath209 it would interesting to see how the different degenerations constructed here for @xmath152 and @xmath96 are related under these dualities . valuations have been used to connect the combinatorics of branching problems to the commutative algebra of branching algebras before . howe , tan and willenbring @xcite arrive at a sagbi ( sub - algebra analogue of grbner basis for ideals ) , interpretation of the littlewood - richardson rule , this is in the same spirit as this paper , as sagbi degenerations arise from the higher rank valuations implicit in the lexicographic ordering on the dual canonical basis . also in a similar spirit , kaveh and anderson@xcite , @xcite , have been connecting the dual canonical basis to a special type of valuation built from a full flag of subspaces in a flag variety or schubert variety of @xmath11 this allows them to realize meaningful polytopes from representation theory as the so - called okounkov bodies of these valuations . it would be interesting to see a similar interpretation the polytope @xmath210 as an okounkov body for some flag of subspaces in the projective variety @xmath211

we construct polyhedral families of valuations on the branching algebra of a morphism of reductive groups . this establishes a connection between the combinatorial rules for studying a branching problem and the tropical geometry of the branching algebra . in the special case when the branching problem comes from the inclusion of a levi subgroup or a diagonal subgroup , we use the dual canonical basis of lusztig and kashiwara to build toric deformations of the branching algebra . keywords : branching problem , reductive group , tropical geometry , toric variety , valuation .

we construct polyhedral families of valuations on the branching algebra of a morphism of reductive groups . this establishes a connection between the combinatorial rules for studying a branching problem and the tropical geometry of the branching algebra . in the special case when the branching problem comes from the inclusion of a levi subgroup or a diagonal subgroup , we use the dual canonical basis of lusztig and kashiwara to build toric deformations of the branching algebra . keywords : branching problem , reductive group , tropical geometry , toric variety , valuation .

hep-ph0005281

i

the parity - violating ( pv ) nucleon - nucleon interaction has been a subject of interest in nuclear and particle physics for some time . to date , pv observables generated by this interaction remain the only experimental windows on the @xmath11 , nonleptonic weak interaction . since the 1970 s , the pv nn interaction has been studied in a variety of processes , including @xmath12 and @xmath13nucleus scattering , @xmath14-decays of light nuclei , the scattering of epithermal neutrons from heavy nuclei , and atomic pv ( for a review , see refs . the on - going interest in the subject has spawned new pv experiments in few - body systems , including high - energy @xmath12 scattering at cosy , @xmath15 at lansce@xcite , @xmath16 at jlab@xcite , and the rotation of polarized neutrons in helium at nist . the theoretical analysis of these pv observables is complicated by the short range of the low - energy weak interaction . the compton wavelength of the weak gauge bosons ( @xmath17 fm ) implies that direct @xmath18 and @xmath19 exchange between nucleons is highly suppressed by the short - range repulsive core of the strong nn interaction . in the conventional framework , longer range pv effects arise from the exchange of light mesons between nucleons . one requires the exchange of the @xmath20 , @xmath21 and @xmath22 in order to saturate the seven spin - isospin channels associated with the quantum numbers of the underlying four - quark strangeness - conserving pv interaction , @xmath23 ( henceforth , the @xmath11 will be understood ) . these exchanges are parameterized by pv meson - nucleon couplings , @xmath24 , whose values may be extracted from experiment . at present , there appear to be discrepancies between the values extracted from different experiments . in particular , the values of the isovector @xmath25 coupling , @xmath5 , and the isoscalar @xmath26 coupling , @xmath27 as extracted from @xmath28 scattering and the @xmath14-decay of @xmath29f , do not appear to agree with the corresponding values implied by the anapole moment of @xmath30cs as measured in atomic pv @xcite . the origin of this discrepancy is not understood . one possibility is that the use of @xmath21 and @xmath22 exchange to describe the short - range part of the pv nn interaction is inadequate . an alternate approach , using effective field theory ( eft ) , involves an expansion of the short - range pv nn interaction in a series of four - nucleon contact interactions whose coefficients are _ a priori _ unknown but in principle could be determined from experiment . the use of @xmath21 and @xmath22 exchange amounts to adoption of a model rather than the use of experiment to determine the coefficients of the higher - derivative operators in this expansion . whether or not the application of eft to nuclear pv can yield a more self - consistent set of pv low - energy constants than the meson - exchange approach remains to be seen . a comprehensive analysis of nuclear pv observables using eft has yet to be performed . the least ambiguous element shared by both approaches involves the long - range @xmath20-exchange interaction . at leading order in the derivative expansion , the pv @xmath25 interaction is a purely isovector , yukawa interaction . the strength of this interaction is characterized by the same constant @xmath5 in both the eft and meson - exchange approaches . at the level of the standard model ( sm ) , @xmath5 is particularly sensitive to the neutral current component of @xmath31 . in this respect , the result of @xmath29f pv @xmath14-decay measurement is puzzling : @xmath32 where @xmath33 gives the scale of the @xmath24 in the absence of neutral currents@xcite . this result is especially significant , since the relevant two - body nuclear parity - mixing matrix element can be obtained by isospin symmetry from the @xmath34-decay of @xmath29ne @xcite . the result in eq . ( [ eq : flourine ] ) is , thus , relatively insensitive to the nuclear model . theoretical calculations of @xmath5 starting from @xmath31 have been performed using su(6)@xmath35 symmetry and the quark model @xcite , the skyrme model @xcite , and qcd sum rules @xcite . as a benchmark for comparison with experiment , we refer the su(6)@xmath35/quark model analysis of refs . hereafter referred to as ddh , fcdh . in order to connect weak vector meson and pion couplings the predictions relating pion couplings alone to hyperon decay data rely only su(3 ) . ] these authors quote a best value `` and reasonable range '' for the @xmath24 : @xmath36 where here the best value `` is more aptly described as an educated guess , while the reasonable range '' indicates a set of numbers such that theory would be very hard - pressed to explain were the experimental value not found to be within this band . neverthess , the difference between the best value " of eq . ( [ eq : fcdhbest ] ) and the @xmath29f result would appear to call for an explanation , and in the following note we comment on a possible source of the discrepancy . in general , the problem of relating the fundamental weak quark - quark interaction to the low - energy constants which parameterize hadronic matrix elements of that interaction is non - trivial . in the framework of eft , one may define these constants at tree - level in the hadronic effective theory . the quantities extracted from experiment in the conventional analysis , however , are not the tree - level parameters , but rather renormalized couplings . denoting the latter as @xmath37 , one has @xmath38 where @xmath39 is the coefficient of the leading - order , pv yukawa interaction in the effective theory , @xmath40 and @xmath41 denotes chiral loop renormalizations of the nucleon and pion wavefunctions , respectively , and @xmath42 denotes contributions from chiral loops and higher - dimension operators to the yukawa interactions ( only the finite parts of these couplings are implied ; loop divergences are cancelled by the corresponding pole terms in @xmath39 and the @xmath43 ) . at leading order in @xmath44 , one has @xmath45 , @xmath46 , and @xmath47 . the renormalized coupling appears as the coefficient in the one - pion - exchange ( ope ) pv nn potential @xmath48 \ \ \ , \ ] ] where @xmath49 is the strong @xmath25 coupling and @xmath50 . neglecting the effects of three - body pv forces and @xmath51-exchange interactions , it is @xmath37 to which the result in eq . ( [ eq : flourine ] ) corresponds . the relationship between @xmath37 and the coupling obtained by computing @xmath52 in a microscopic model is not immediately transparent . in what follows , we make several observations about this relationship . we first show that @xmath53 and @xmath42 are substantial , so that @xmath37 differs significantly from @xmath39 . to that end , we compute all of the chiral corrections to the pv yukawa interaction through @xmath54 , where @xmath55 . we work to leading order in @xmath56 in heavy baryon chiral perturbation theory ( hbchpt ) . of particular significance is the dependence of @xmath42 on other low - energy constants parameterizing pv @xmath51 production and the pv @xmath57 transition . we subsequently reexamine the su(6)@xmath35/quark model calculation of refs . @xcite and argue that most if not all of the chiral loop effects which renormalize @xmath5 are not included in the microscopic calculation . thus , the relationship between @xmath37 and microscopic calculations remains ambiguous at best . this ambiguity is unlikely to be resolved until an unquenched lattice qcd calculation of @xmath5 using light quarks becomes tenable . in the meantime , one should not necessarily view a discrepancy between the experimental value of @xmath37 and microscopic model calculations as disturbing . our discussion of these observations is organized as follows . in section 2 we summarize our conventions and notation , including the pv chiral lagrangians relevant to @xmath5 renormalization . section 3 gives a discussion of the loop calculations . in section 4 we comment on the scale of the loop corrections and provide simple estimates of some of the new pv low - energy constants appearing in the analysis . section 5 gives our discussion of the relationship between @xmath37 and the calculation of refs . section 6 summarizes our conclusions . some technical details are relegated to the appendices .

we construct the complete parity - violating ( pv ) interaction lagrangian with one derivative , and calculate the chiral corrections to the pv yukawa coupling constant through in the leading order of heavy baryon expansion . we discuss the relationship between the renormalized , the measured value of , and the corresponding quantity calculated microscopically from the standard model four - quark pv interaction . 0.5 true cm pacs indices : 21.30.+y , 13.40.ks , 13.88.+e , 11.30.er = -1 cm = -0.7 cm = -0.7 cm # 1#1 # 1#1 # 1#2 # 1 # 1 # 1#1 # 1^#1 # 1#1 # 1#1 # 1#1 # 1_phys . holstein , m. j. ramsey - musolf department of physics , university of connecticut , storrs , ct 06269 usa + theory group , thomas jefferson national accelerator facility , newport news , va 23606 usa + department of physics and astronomy , university of massachusetts , amherst , ma 01003 usa

we construct the complete parity - violating ( pv ) interaction lagrangian with one derivative , and calculate the chiral corrections to the pv yukawa coupling constant through in the leading order of heavy baryon expansion . we discuss the relationship between the renormalized , the measured value of , and the corresponding quantity calculated microscopically from the standard model four - quark pv interaction . 0.5 true cm pacs indices : 21.30.+y , 13.40.ks , 13.88.+e , 11.30.er = -1 cm = -0.7 cm = -0.7 cm # 1#1 # 1#1 # 1#2 # 1 # 1 # 1#1 # 1^#1 # 1#1 # 1#1 # 1#1 # 1_phys . rev . _ * # 1 * # 1_phys . rev . _ * c#1 * # 1_phys . rev . _ * d#1 * # 1_phys . rev . lett . _ * # 1 * # 1_nucl . phys . _ * a#1 * # 1_nucl . phys . _ * b#1 * # 1_ann . of phys . _ * # 1 * # 1_phys . reports _ * # 1 * # 1_phys . lett . _ * b#1 * # 1_z . fr phys . _ * a#1 * # 1_z . fr phys . _ * c#1 * 0q_^0 shi - lin zhu , s.j . puglia , b.r . holstein , m. j. ramsey - musolf department of physics , university of connecticut , storrs , ct 06269 usa + theory group , thomas jefferson national accelerator facility , newport news , va 23606 usa + department of physics and astronomy , university of massachusetts , amherst , ma 01003 usa

1212.2077

i

the solidification of a liquid or the melting of a solid lead to complex free boundary problems involving many different physical effects . for example , latent heat is set free at the interface and a competition between surface energy and diffusion leads to instabilities like the mullins sekerka instability . the resulting model is a stefan problem with boundary conditions taking surface energy effects and kinetic effects at the interface into account , see e.g. @xcite . crystals forming in an undercooled melt lead to very complex patterns and , in particular , dendritic growth can be observed since the growth is typically diffusion limited , see @xcite . the numerical simulation of time - dependent stefan problems , or variants of it , is a formidable task since the evolving free boundary has to be computed . hence , direct front tracking type numerical methods need to adequately capture the geometry of the interface and to evolve the interface approximation , often with a coupling to other physical fields . this coupling , in particular , represents a significant initial hurdle towards obtaining practical implementations , and thus numerical simulations for the problem at hand . examples of the implementation of such direct methods can be found in e.g. @xcite . a further drawback of direct front tracking methods has been the inability of most direct methods to deal with so - called mesh effects , or to prevent them altogether . when a discrete approximation of an interface , for example a polygonal curve in the plane , evolves in time , then in general it is possible for the approximation to deteriorate or to break down . examples of such pathologies are self - crossings and vertex coalescence . while for simple isotropic problems in the plane these issues can be dealt with , for example by frequent remeshings or by using clever formulations that only allow equidistributed approximations , see e.g. @xcite , until very recently there has been no remedy for fully anisotropic problems in two and three space dimensions . however , building on their work for isotropic problems in @xcite , the present authors recently introduced stable parametric finite element schemes for the direct approximation of anisotropic geometric evolution equations in @xcite , for which good mesh properties can be guaranteed . in particular , even for the simulation of interface evolutions in the presence of strong anisotropies , no remeshing or redistribution of vertices is needed in practice . these schemes , in which only the interface without a coupling to bulk quantities is modelled , have been extended to approximations of the stefan problem with fully anisotropic gibbs thomson law and kinetic undercooling in @xcite . the novel method from @xcite can be shown to be stable and to have good mesh properties . we remark that these approaches extend earlier ideas from @xcite . here we recall the pioneering work of schmidt @xcite , where the full stefan problem in three dimensions was solved within a sharp interface framework for the first time . phase field methods are an alternative approach to solve solidification phenomena in the framework of continuum modelling . in phase field approaches a new non - conserved order parameter @xmath0 is introduced , which in the two phases is close to two different prescribed values and which smoothly changes its value across a small diffuse interfacial region . a parabolic partial differential equation for @xmath0 is then coupled to an energy balance , which results in a diffusion equation for the temperature taking latent heat effects into account . we refer to @xcite and to the five review articles @xcite for further details . in particular , it can be shown that solutions to the phase field equations converge to classical sharp interface problems , see e.g. @xcite and the references therein . the popularity of phase field methods , often also called diffuse interface methods , can be explained by two characteristic features that they share with the level set method , which is another sharp interface computational tool . firstly , phase field methods naturally allow for changes of topology . and secondly , computing simulations for phase field models only requires the solution of partial differential equations on standard cartesian domains . the fact that these can usually be implemented and solved in a relatively straightforward way makes the phase field method particularly appealing . it is the aim of this article to investigate the practical merits of phase field models compared to the recently introduced sharp interface algorithm for the approximation of stefan problems from @xcite ; see also @xcite . of particular interest will be the relative accuracy of the two methods , in situations where a true solution to the sharp interface problem is known . in a phase field simulation the observed error is made up of contributions from * the asymptotic error , * the spatial and temporal discretization errors , * rounding errors and solver tolerances . here the asymptotic error is induced by the choice of interfacial parameter @xmath1 . in general one can formally show that the asymptotic error converges to zero as @xmath2 , see e.g. @xcite . for certain phase field models and under certain conditions it can be rigorously shown that the asymptotic error vanishes as @xmath3 , see e.g. @xcite . in computations for sharp interface approximations , on the other hand , the observed error is made up of the latter two contributions only , i.e. of discretization and rounding errors . a disadvantage of phase field models is that the resulting pdes become stiff for decreasing @xmath4 , leading to a requirement for very fine spatial and temporal discretizations . hence it becomes computationally challenging to produce very accurate phase field simulations . in any case , the available computational resources will often set a limit on the smallest interfacial parameter @xmath4 that one can compute for . hence another aspect that needs to be taken into account in an objective comparison between phase field simulations and sharp interface approximations is the overall cpu time that is needed to obtain the results . while it can often be formally shown that phase field computations can attain an arbitrarily high accuracy , the existing limitations on computer hardware often mean that in practice very fine computations can not be performed . in addition , as discussed in @xcite , the early computational approaches were limited as they could only be used in the presence of interfacial kinetics in the gibbs thomson law . historically these limitations of the phase field model have long been known , and as a result a different underlying interpretation of the model , the so - called `` thin interface limit '' , has been introduced and analyzed by karma and rappel @xcite . their approach made it possible to do efficient computations with a smaller capillary length to interface thickness ratio , and to study the physically relevant case of small or zero kinetic coefficients . later the findings of karma and rappel were reinterpreted as second order convergence with respect to the interfacial thickness , see @xcite . the first successful phase field computations of dendritic growth were performed by kobayashi @xcite , and his computations demonstrated the importance of anisotropy for dendritic growth . since then many successful improvements with respect to numerical simulations have appeared in the literature . we refer to @xcite and the references therein . finally , we would like to mention work on the numerical analysis of phase field and sharp interface approaches . numerical analysis of discretizations of phase field models can be found in e.g.@xcite . numerical analysis of discretizations of sharp interface models can be found in @xcite . we also remark that level set methods are another possible way to solve stefan problems and related free boundary problems . we refer to @xcite for more details on how the level set method can be used to solve free boundary problems . the remainder of the paper is organized as follows . in section [ sec:2 ] we state the sharp interface formulation of the two phase stefan problem with kinetic undercooling and an anisotropic gibbs thomson law . in section [ sec:3 ] we state the corresponding phase field model and recall the finite element algorithms from @xcite . in section [ sec:4 ] we numerically compare the sharp interface method from @xcite with the phase field algorithms from section [ sec:3 ] for some isotropic benchmark problems with known true solutions . computations for a phase field model with a correction term , for which a second order convergence property can formally be shown , are presented in section [ sec:43 ] . finally , we compare the sharp interface and phase field methods for a variety of anisotropic model problems in section [ sec:5 ] .

= 1 phase field models , parametric sharp interface methods , stefan problem , anisotropy , solidification , crystal growth , numerical simulations , benchmark problems 35k55 , 35r35 , 35r37 , 53c44 , 65m12 , 65m50 , 65m60 , 74e10 , 74e15 , 74n20 , 80a22 , 82c26

we critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification . particular emphasis is put on stefan problems , and their quasi - static variants , with applications to crystal growth . new approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem . = 1 phase field models , parametric sharp interface methods , stefan problem , anisotropy , solidification , crystal growth , numerical simulations , benchmark problems 35k55 , 35r35 , 35r37 , 53c44 , 65m12 , 65m50 , 65m60 , 74e10 , 74e15 , 74n20 , 80a22 , 82c26

1210.6292

i

a _ clustering method _ is an algorithm that takes as input a finite space with a distance function ( typically , a finite metric space ) @xmath3 and gives as output a partition of @xmath4 . kleinberg discussed in @xcite the problem of clustering in an axiomatic way and proposed a few basic properties that a clustering scheme should hold . then , he proved that no standard clustering scheme satisfying this conditions simultaneously can exist . this does not imply the impossibility of defining a consistent standard clustering algorithm . kleinberg s impossibility only holds when the unique input in the algorithm is the space and the set of distances . it can be avoided including , for example , the number of clusters to be obtained as part of the input . see @xcite and @xcite . also , ackerman and ben - david , see @xcite , showed that these axioms are consistent in the setting of clustering quality measures . carlsson and mmoli , see @xcite , studied the analogous problem for clustering schemes that yield hierarchical decompositions instead of a certain partition of the space . see also @xcite and @xcite . hierarchical clustering methods also take as input a finite metric space but the output is a hierarchical family of partitions of @xmath4 . they approach the subject focusing on a theoretical basis for the study of hierarchical clustering ( @xmath5 ) . in the spirit of kleinberg s result , they define a few reasonable conditions that a @xmath5 method should hold . they prove that the unique @xmath5 method satisfying three basic conditions is ( the well - known ) single linkage hierarchical clustering , @xmath6 @xmath5 . ackerman and ben - david , see @xcite , proved also a characterization of the class of linkage - based algorithms , including @xmath6 . see also @xcite . in the setting of partitional ( standard ) clustering see @xcite . carlsson and mmoli also study the theoretical properties of @xmath6 @xmath5 obtaining some interesting results . the main advantage seems to be that this method enjoys some sort of stability which is defined by means of the gromov - hausdorff distance . however , the main weakness of @xmath6 @xmath5 is the so called _ chaining effect _ which may merge clusters that , in practice , _ should be detected _ by the algorithm and kept separated . one way to address this difficulty is to take into account the density . in a preprint entitled _ multiparameter hierarchical clustering methods _ the same authors do this by including in the input of the algorithm a function that provides that information . our aim is to define a @xmath5 method which offers some solution to this particular weakness without including any extra information . the first challenge is that the concept of _ clusters that should be detected _ by the algorithm depends on the characteristics of the problem under study . the same happens with what we may consider the _ undesired _ chaining effect . the definition from lance and williams , @xcite , makes reference to the higher tendency of the points to add to a pre - existing group rather than defining the nucleus of a new group or joining to another single point . our algorithm is oriented to another aspect of the chaining effect which is the tendency to merge two clusters when the minimal distance between them is small ( even though they may have dense cores which are clearly distant apart ) . this is typically the problem of @xmath6 @xmath5 . also , we include as an undesired chaining effect the case of two big clusters joined by a chain of points or small clusters . these isolated points or small clusters may be interpreted as noise in the sample and we might want to distinguish the big picture and ignore their effect . this idea is closer to the type of chaining effect considered by wishart in @xcite . there exist other linkage - based methods that enjoy some sort of sensitivity to density and offer some resistance to these chaining effects as average linkage , @xmath7 , or complete linkage , @xmath8 . these methods are extensively used in practice . however , although the main problem of the chaining effect of @xmath6 @xmath5 is reduced , there appears another effect that might be unwanted too . in these methods the distance between a point and a cluster is greater than the minimal distance . therefore , they have a tendency to merge isolated points before joining them to pre - existing big clusters . also , these methods are proved to be extremely unstable in the sense that small perturbations on the data yield very different dendrograms . herein , we define a new @xmath5 method on the basis of @xmath6 : _ @xmath0-unchaining single linkage _ or @xmath1 . the definition of @xmath1 is based in the dimension of the rips complexes defined by the points of @xmath4 . these complexes contain some information about the density distribution of the sample . this allows us to define a density sensitive algorithm such that the input is just the set of distances between the points and a fixed parameter @xmath9 . the parameter determines how sensitive the method will be to the chaining effect . to treat the chaining through single points or smaller blocks , we define another version of the method , @xmath2 , by adding an extra condition on @xmath1 . it is worth mentioning that ester , kriegel , sander and xu , see @xcite , defined a standard clustering method called dbscan . dbscan is also a density - sensitive algorithm where the input is just the data set and some parameters . although this is not hierarchical clustering algorithm we include a short discussion comparing the type of clusterings detected by this method with the clusterings that @xmath1 and @xmath2 may detect in the levels of the dendrogram this paper intends to give a theoretical basis to the study of the problem . so , instead of checking the algorithm on examples of real data we rather try to find general properties characterizing what would be an undesired chaining of two blocks and how good is the algorithm detecting and unchaining them . however , we include several examples where the unchaining properties can be explicitly seen in the resulting dendrogram . to the study the chaining effect we define the concepts of _ chained subsets _ and _ subsets chained by smaller blocks _ as situations of minimal chaining so that they contain what we consider the problematic examples . nevertheless , there may be many examples of chained subsets which should be clearly merged and there is margin to be more restrictive . in such context , a @xmath5 method is _ strongly chaining _ if every pair of chained subsets are always merged before they appear contained in different clusters . a @xmath5 method is _ completely chaining _ if , in addition , every pair of subsets chained through smaller blocks are merged before they appear contained in different clusters . thus , strongly chaining methods and completely chaining methods are extremely sensitive to these effects . this is the case , for example , of @xmath6 @xmath5 . see theorem [ th : complete chaining ] . we define also precise conditions to define what we consider two blocks that should necessarily appear as independent blocks at some point . the definition considers two blocks that have dense cores and such that the minimal distance between them is small only because of a single pair of points . in particular , this pair of points creates a chaining between their dense cores . see figure [ ejp chained edge ] . this is a particular , more restrictive , example of chained subsets . we say that a @xmath5 method is _ weakly unchaining _ if , at least , it distinguishes that pair of blocks . then , we prove that @xmath1 satisfies this condition while other methods which are not strongly chaining as @xmath7 and @xmath8 @xmath5 fail to be weakly unchaining . see theorem [ th : weakly ] , corollary [ cor : weakly ] and example [ ejp : al - cl ] . we also define a minimal condition of two subsets chained by single points that should be detected . we say that a @xmath5 method is _ @xmath0-bridge - unchaining _ if it is able to separate two blocks in that situation . @xmath2 is proved to be more sensitive than that . it also detects some classes of chaining through smaller blocks as it is proved in proposition [ prop : moderate_2 ] . in particular , @xmath2 is @xmath0-bridge - unchaining . see corollary [ cor : unchaining ] . the structure of the paper is the following : section [ section : background ] contains the basic definitions and notation involved . it may be skipped by the experts . in section [ section : hc ] we recall some well known hierachical clustering methods and include some different ways to formulate them . in section [ section : modified sl ] we first introduce the idea of what are we considering undesired chaining effect . formal definitions are left to the last sections to enhance readability . in this section we are just trying to give the reader some notion of what is @xmath1 trying to detect . then , we present @xmath1 . we include a short explanation of the role of each step of the method and check it on a few examples . section [ section : sl^ * ] deals with the problem of chaining through smaller blocks . again , we leave formal definitions for the last sections and we only discuss the intuitive idea . then , we introduce a further step in the algorithm to define @xmath2 and check it on some examples . section [ section : unchaining properties ] studies the unchaining properties of @xmath1 . first we fix the theoretical background to study the chaining effect . we define the concepts of _ chained subsets _ and subsets _ chained by a single edge_. we define the property of being _ strongly chaining _ for @xmath5 methods which are extremely sensitive to the chaining effect . we prove that @xmath6 is strongly chaining while @xmath7 and @xmath8 @xmath5 are not . then , we say that a @xmath5 method is _ weakly unchaining _ if it is at least capable of detecting a certain clustering when the subsets are chained by a single edge . we prove that @xmath1 is weakly unchaining while other methods , partially sensitive to the chaining effect as @xmath7 and @xmath8 , are not . we also compare the results obtained by our method and the results offered by the standard clustering algorithm dbscan . section [ section : unchaining properties 2 ] studies the unchaining properties of @xmath2 . we define the concept of subsets _ chained through smaller blocks_. we say that a @xmath5 method is _ completely chaining _ if it is strongly chaining and also unable to detect clusters if they are chained through smaller blocks . we prove that @xmath6 is completely chaining . then , we define the property of being _ @xmath0-bridge - unchaining _ for algorithms which are able to detect , at least , some type of subsets chained through single points . we prove that @xmath2 is @xmath0-bridge - unchaining . we compare this case , also , with the treatment of the same input by dbscan . section [ section : conclusions ] includes a short discussion about the main advantages of the methods defined and some comments about future research .

we define a hierarchical clustering method :-unchaining single linkage or . the input of this algorithm is a finite metric space and a certain parameter . this method is sensitive to the density of the distribution and offers some solution to the so called chaining effect . we also define a modified version , , to treat the chaining through points or small blocks . msc : 62h30 , 68t10 .

we define a hierarchical clustering method :-unchaining single linkage or . the input of this algorithm is a finite metric space and a certain parameter . this method is sensitive to the density of the distribution and offers some solution to the so called chaining effect . we also define a modified version , , to treat the chaining through points or small blocks . we study the theoretical properties of these methods and offer some theoretical background for the treatment of chaining effects . keywords : hierarchical clustering , single linkage , chaining effect , weakly unchaining ,-bridge - unchaining . msc : 62h30 , 68t10 .

1508.04694

i

microscale and nanoscale solid state heat transfer as mediated by phonon transport has received considerable attention in connection with a number of diverse practical applications , such as heat management in microelectronic devices , passive cooling and thermoelectric energy conversion @xcite , but also due to the number of scientific challenges it poses . particularly notable is the wide range of scales present in these problems , typically starting from the atomistic ( including quantum ) and extending to the macroscopic ( device ) . kinetic - theory approaches based on the boltzmann transport equation ( bte ) @xcite , especially if informed by ab - initio information on the material properties @xcite , can be quite effective in bridging this range of scales . one limitation of such approaches appears in the small mean free path limit , @xmath0 , where kinetic descriptions become stiff . here , @xmath1 denotes the knudsen number defined as the ratio of the mean free path to the characteristic system lengthscale ; a more precise definition will be given in section [ background ] . as is well known , in the limit @xmath2 , the stiff boltzmann description need not be used because it can be replaced by the heat conduction equation ; derivation of the bulk thermal conductivity from the boltzmann equation in the relaxation approximation via a chapman - enskog type of expansion @xcite is well established , thus providing a `` pathway '' for recording the effect of molecular structure on the constitutive behavior in that limit . however , the chapman - enskog expansion is only applicable in the bulk and provides no information on the boundary conditions that need to supplement the heat conduction description in order to obtain solutions that are consistent with the ( more fundamental ) boltzmann solution . moreover , a rather large gap exists between lengthscales that truly satisfy @xmath3 and the regime where boltzmann equation solution is no longer problematic ( @xmath4 ) . in this paper , we use an asymptotic expansion procedure using @xmath1 as a small parameter to derive , from the bte , the `` continuum '' equations governing phonon - mediated heat transfer in the small mean free path limit . this procedure recovers the classic heat conduction equation ( including fourier s law as a constitutive relation ) as the equation governing the temperature field that is consistent with solution of the boltzmann equation to order @xmath5 , as expected . however , in contrast to chapman - enskog - type procedures , this procedure , also _ derives _ the boundary conditions that the heat equation is to be solved subject to . specifically , for fixed temperature boundaries , the fourier boundary conditions are found to be of the dirichlet type at the boundary temperature ; for diffusely specular walls , the fourier boundary conditions are shown to be the neumann no - flux boundary condition . although these results have been _ empirically _ established centuries ago , this is the first time they are shown to arise , rigorously , from a solution of the boltzmann equation . more importantly , by extending the asymptotic expansion to first and second order in @xmath1 , we derive the governing `` continuum - level '' equation _ and boundary conditions _ for finite but small values of the knudsen number ( @xmath0 ) . specifically , for steady problems , the governing equation is shown to be the steady heat conduction equation up to order @xmath6 , while the corresponding boundary conditions are shown to be of the temperature - jump type , with jump coefficients that , in general , depend on the material and boundary properties . for unsteady problems , we show that the governing equation is the unsteady heat conduction equation up to first order in @xmath1 with boundary conditions remaining the same as in the steady case up to that order for the case of prescribed - temperature boundaries . jump boundary conditions have been observed before in solutions of the boltzmann equation @xcite and attempts were made @xcite to explain these invoking differences in local equilibrium conditions across interfaces . the present work shows how temperature jumps arise as a result of the incompatibility between the isotropic distributions associated with boundary conditions and the anisotropic distribution associated with non - equilibrium resulting from transport ( temperature gradients ) . a well - known manifestation of this physical behavior are the temperature jumps associated with the kapitza interface problem . in section [ kapitza ] we show how our asymptotic approach can be used to calculate the interface conductance ( and associated temperature jump ) from first principles ( at the kinetic level , that is , given the interface transmission and reflection coefficient ) . the temperature jump relations derived in this work are manifestations of what is known in the kinetic theory community as `` slip '' , which gives its name to the slip regime , @xmath7 . it is generally known @xcite that in this regime the material constitutive law may still be used _ unmodified _ and kinetic effects are accounted for by modified boundary conditions . in the field of rarefied gas dynamics , cercignani @xcite and sone with co - workers @xcite were the first to provide systematic asymptotic solutions up to second order in @xmath1 , demonstrating the possibility of using the traditional `` continuum '' fluid dynamics , albeit with modified boundary conditions , beyond the slip regime and into the early transition regime . the transition regime is typically defined by @xmath8 and represents the regime in which transport transitions from diffusive ( @xmath0 ) to ballistic ( @xmath9 ) . discussions of the use of asymptotic solutions of the boltzmann equation in rarefied gas dynamics can be found in @xcite . the practical implications of the present work are twofold : first , solution of the heat equation is significantly easier ( analytically or numerically ) compared to the boltzmann equation , especially in the regime @xmath0 where the latter becomes stiff . in addition to ease of solution , centuries of investment in continumm formulations such as the heat equation , either in the form of education , mathematical solution techniques or numerical solution software , make this by far the preferred approach . this can be easily seen from the considerable efforts expended in developing approximate `` effective thermal conductivity '' concepts that enable the use of fourier s law in the transition regime . the present work provides _ rigorous _ methods for obtaining solutions _ consistent with the boltzmann equation _ in the slip and early transition regime . studies in rarefied gas dynamics show that , depending on the problem and the amount of error that can be tolerated , slip / jump formulations could be used up to @xmath10 and sometimes beyond @xcite . second , by using the asymptotic solution as a control in deviational monte carlo schemes , one can overcome the stiffness associated with the @xmath0 regime . this happens because @xcite the asymptotic solution becomes increasingly more accurate as @xmath3 , thus requiring increasingly less computational resources to describe the deviation therefrom as this limit is approached . this yields computational methods that are able to efficiently simulate problems characterized by @xmath11 locally or globally , in contrast to traditional boltzmann solution methods . the present paper is organized as follows : in section [ background ] we introduce the governing ( boltzmann ) equation and the notation used in this paper ; in section [ asymptotic_analysis ] , we present the asymptotic analysis leading to derivation of the governing equation in the bulk up to second order in the knudsen number . associated boundary conditions and boundary layer corrections up to first order in the knudsen number are derived in section [ order1bl ] . in section [ order2bl ] we present results obtained from extending the boundary layer analysis to second order in knudsen number . in section [ summary ] we summarize and discuss our results and provide example applications to one - dimensional and two - dimensional problems . in section [ time - dep ] we discuss the applicability of the asymptotic theory and its results ( governing equations , boundary conditions and corrective boundary layers ) to time - dependent problems . in section [ kapitza ] we show how the asymptotic theory can be used to calculate the kapitza conductance ( and temperature jump ) associated with the interface between two materials . we conclude with some final remarks in section [ final ] .

we derive the continuum equations and boundary conditions governing phonon - mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized boltzmann equation in the relaxation time approximation . our approach uses the ratio of the mean free path to the characteristic system lengthscale , also known as the knudsen number , as the expansion parameter to study the effects of boundaries on the breakdown of the fourier descrition . we illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the kapitza resistance ( and temperature jump ) associated with an interface between two materials .

we derive the continuum equations and boundary conditions governing phonon - mediated heat transfer in the limit of small but finite mean free path from asymptotic solution of the linearized boltzmann equation in the relaxation time approximation . our approach uses the ratio of the mean free path to the characteristic system lengthscale , also known as the knudsen number , as the expansion parameter to study the effects of boundaries on the breakdown of the fourier descrition . we show that , in the bulk , the traditional heat conduction equation using fourier s law as a constitutive relation is valid at least up to second order in the knudsen number for steady problems and first order for time - dependent problems . however , this description does not hold within distances on the order of a few mean free paths from the boundary ; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a boltzmann boundary - layer problem to be determined . matching the inner , boundary layer , solution to the outer , bulk , solution yields boundary conditions for the fourier description as well as additive corrections in the form of _ universal _ kinetic boundary layers ; both are found to be proportional to the bulk - solution gradients at the boundary and parametrized by the material model and the phonon - boundary interaction model ( boltzmann boundary condition ) . our derivation shows that the traditional no - jump boundary condition for prescribed temperature boundaries and no - flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the knudsen number ; at higher order , boundary conditions are of the jump type . we illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the kapitza resistance ( and temperature jump ) associated with an interface between two materials . all results are validated via comparisons with low - variance deviational monte carlo simulations .

1505.04247

i

there are many methods for determining an asteroid position during observations with a ccd camera . for example , the full width at half magnitude ( fwhm ) approach @xcite , which is based on the analytical description of the object images on the ccd frame , as well as other methods , in which the position of an object s maximum brightness on a ccd image is taken as its coordinates ( @xcite ) . most of these methods have a common feature . they use psf - fitting ( point - spread function ) to approximate the object image and get the information about regularities in the distribution of the registered photons on ccd frame(see , for detail , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) , among the models of photons distribution , which are used more often , we note the two - dimensional gaussian model ( @xcite , @xcite , @xcite ) , moffat model ( @xcite , @xcite ) or lorentz model ( @xcite , @xcite ) . these models are usually described by the continuous functions , while the ccd images are discrete ones . such an approach was criticised reasonably by @xcite . the principal disadvantage is that these models work well only with a large amount of the data . it leads to the fact that , firstly , the computation process becomes much more complicated , and , secondly , the problem related with the adequacy of the used estimations of psf parameters can not be solved . as a result , the error of the coordinate determination of the observed celestial objects has to be increasing . in addition to the aforementioned disadvantage , the existing methods do not pay sufficient attention for taking the noise component of the object image into account . it is assumed that its registration and compensation are performed during the preliminary stage of image processing ( @xcite ) or that the object image is exempted from noise according to the accepted signal - to - noise model ( @xcite , @xcite ) . at the same time , the error introduced by the operation of removing the noise component from the object image is not considered in the subsequent procedure of coordinate determination . the errors of ccd astrometry are traditionally divided into the instrument , reduction , reference catalogue and measurement errors . the first ones traditionally include errors of instrumental parameters as shutter delay and clock correction , which result in incorrect timing . the second error category ( reduction ) is associated with the method related to the standard and measured coordinates and depends on the choice of the algorithm relation between these coordinates . for example , being not sufficient for the wide - angle astrographs such an error depends strongly on the choice of the type and degree of the polynomial approximation in turner method . it is important to note that a systematic error of timing is not shared with the coordinate error along the tracking an object in the sky , so it must be caught clearly with a reliable shutter sync . the reference catalogue errors are divided into three main classes : zonal errors ( systematic errors of the reference catalogue ) ; coordinate errors of reference stars in the catalogue epoch ; proper motion errors of reference stars . therefore , a choice of the reference catalogue is very important . for example , hipparcos or tycho catalogues had no errors in the epoch of 1990.0 , because an intrinsic accuracy was at the level of millisecond of arc , but for the present epoch there is a necessity to take into account the proper motion errors of reference stars . the solution of this problem , i.e. , creation of new huge database of proper motions of stars , is one of the task of the gaia mission . it is worth noting that the choice of reference catalogue is not so important , when monitoring observations of sky are conducted with the aim of discovery of new solar system small bodies , because an intrinsic accuracy of a catalogue should not be necessarily maximised as compared with those for the following tracking the discovered object . the measurement error is related , first of all , to the determination of coordinates of the image centre or the accuracy of a digital approximation of the ccd image ( fitting ) . the attempt to improve the fitting may not lead to expected results if the reference catalogue errors and timing are not taken attentively into account . each of the aforementioned factors could be the source of both systematic and random errors . any attempt to reduce one of these errors is impossible without control of other factors . therefore , the task of the observers is to be responsible for monitoring all the possible sources of errors . the aim of this paper is to help the observers to refine the coordinate measurements of the object image on the ccd frame and to control the errors of the measured coordinates . with this aim , we developed a new method for accurately estimating asteroid coordinates on a set of ccd frames , which is based on the subpixel gaussian model of the discrete image of an object . in this model , a kind of the coordinate distribution of the photons hitting a pixel on the ccd frame is known a priori , while its parameters can be determined from the real digital image of the object . our method has low computational complexity due to the use of equations of maximum likelihood , as well as the proposed model is more flexible , adapting to any form of the real image of the object . for example , in fact psf is a super - pixel function because it describes the changes in the brightness of a pixels of celestial object image . we propose to use the density function of coordinates of hitting photons from celestial object instead of the psf . this function is sub - pixel one . to get the point - spread function from this function , it should be integrated over the area of determination of each image pixel of object or compact group of objects . it turns out that sub - pixel models are more flexible and may describe the real image more adequately . this effect does not occur in case of bright objects . but applying a more flexible model for the faint objects , we are able to improve the accuracy of the measurements ( for example , as comparing with astrometrica ) by 30 - 50% ( more details are given in the discussion ) . our method also takes into account the principal peculiarities of the object image formation on the ccd frame along with the possible irregular distribution of the residual noise component both on the object image and in its vicinity . some generalisations of the proposed method are presented in our previous works ( @xcite , @xcite , @xcite , @xcite @xcite , @xcite , @xcite , @xcite , @xcite ) . since 2010 , due to its application with the colitec ( collection light technology ) software , which was installed at several observatories of the world , four comets ( c/2010 x1 ( elenin ) , p/2011 no1(elenin ) , c/2012 s1 ( ison ) , and p/2013 v3 ( nevski ) ) and more than 1500 small solar system bodies ( including five neos , 21 trojan asteroids of jupiter , and one centaur object ) were discovered . these results confirm the efficiency of the proposed method . the main stages of image processing with the colitec software are presented in fig . [ fig : colitec ] . the structure of this article is as follows : we describe a problem statement and the method in chapters 2 - 3 , respectively . the results based on the testing of this method with the colitec software are presented in chapter 4 . we compare and discuss the accuracy and other parameters for determining the position of the faint celestial object on the ccd frame obtained by the proposed method and others in chapter 5 . conclusive remarks are given in chapter 6 .

we describe a new iteration method to estimate asteroid coordinates , which is based on the subpixel gaussian model of a discrete object image . is known a priori , while the associated parameters are determined from a real digital object image . since 2010 , the method was tested as the basis of our colitec ( collection light technology ) software , which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of ccd frames . as the result , four comets ( c/2010 x1 ( elenin ) , p/2011 no1(elenin ) , c/2012 s1 ( ison ) , and p/2013 v3 ( nevski ) ) as well as more than 1500 small solar system bodies ( including five neos , 21 trojan asteroids of jupiter , and one centaur object ) were discovered . we discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency . in 2014 [ firstpage ] methods : data analysis ; minor planets , asteroids , comets ; techniques : image processing .

we describe a new iteration method to estimate asteroid coordinates , which is based on the subpixel gaussian model of a discrete object image . the method operates by continuous parameters ( asteroid coordinates ) in a discrete observational space ( the set of pixels potential ) of the ccd frame . in this model , a kind of the coordinate distribution of the photons hitting a pixel of the ccd frame is known a priori , while the associated parameters are determined from a real digital object image . the developed method , being more flexible in adapting to any form of the object image , has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure , which is implemented to obtain the best fit instead of a least - squares method and levenberg - marquardt algorithm for the minimisation of the quadratic form . since 2010 , the method was tested as the basis of our colitec ( collection light technology ) software , which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of ccd frames . as the result , four comets ( c/2010 x1 ( elenin ) , p/2011 no1(elenin ) , c/2012 s1 ( ison ) , and p/2013 v3 ( nevski ) ) as well as more than 1500 small solar system bodies ( including five neos , 21 trojan asteroids of jupiter , and one centaur object ) were discovered . we discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency . in 2014 , the colitec software was recommended to all members of the gaia - fun - sso network for analysing observations as a tool to detect faint moving objects in frames . [ firstpage ] methods : data analysis ; minor planets , asteroids , comets ; techniques : image processing .

1505.04247

c

a new iteration method of asteroid coordinate estimation on the digital image has been developed . the method operates by continuous parameters ( asteroid coordinates ) in a discrete observation space ( the set of pixels potential of the ccd matrix ) . high rates of the colitec program during 2011 - 2012 as concerns with the accuracy of measurements have been obtained due to the use of the subpixel gaussian model . this model of the object image takes into account a prior form of the object image and consequently it is adapted more easily to any forms of real image . in other words , nevertheless that a real coordinate distribution of photons hitting the pixels on the ccd frame is not known , the form of this distribution is known a priori and its parameters can be estimated according to the real object image . at that time many other methods mentioned in introduction consider by default that the density of hit photons inside the pixel is uniform . the advantages of subpixel gaussian model become more obvious for the fainter celestial objects . moreover , the developed method has a high measurement accuracy as well as a low calculating complexity because the maximum likelihood procedure is implemented to obtain the best fit instead of the least - squares method and levenberg - marquardt algorithm for the minimisation of the quadratic form . the efficiency of the proposed method , including its advantages for accurately estimating asteroids coordinates , was confirmed during observations as the part of the colitec ( collection light technology ) program for automatic discoveries of asteroids and comets on a set of the ccd frames . efficiency is a crucial factor in the discovery of near - earth asteroids ( nea ) and potentially - hazardous asteroids . current asteroid surveys yield many images per night . it is no longer possible for the observer to quickly view these images in the blinking mode . it causes a serious difficulty for large - aperture wide - field telescopes , capturing up to several tens of asteroids in one image . the colitec software solves the problem of the frame processing for asteroid surveys in a real - time mode . we compared also our software and astrometrica , which is widely used for detecting the newly objects . limits of measurements of colitec software are wider than of astrometrica , but that the most valuable , this expansion comes into area of extremely small snr allowing to search the fainter solar system small bodies ( measurements with the astrometrica at a low snr have an rms of 30 - 50% larger than that of the colitec ) . as for the area of snr@xmath1297 , the results of colitec and astrometrica are approximately identical . however , exactly the area of extremely small snr is more promising for the discovery of new celestial objects . the automatically detected small solar system bodies are subject to follow - up visual confirmation . the colitec software is in use for the automated detection of asteroids at the andrushivka astronomical observatory , ukraine ( since 2010 ) , at the russian remote observatory ison - nm ( mayhill , new mexico , usa ) since 2010 , at the observatory ison - kislovodsk since 2012 , and at the ison - ussuriysk observatory since 2013 ( see tables 1 - 3 ) . as the result , four comets ( c/2010 x1 ( elenin ) ( @xcite ) , p/2011 no1(elenin ) ( @xcite , @xcite ) , c/2012 s1 ( ison ) ( @xcite ) , and p/2013 v3 ( nevski ) ( @xcite ) as well as more than 1500 small solar system bodies ( including five neos , 21 trojans of jupiter , and one centaur object ) have been discovered . in 2014 the colitec software was recommended to all members of the gaia - fun - sso network ( a network for solar system transient objects ) for analysing observations as a tool to detect faint moving objects in frames . information about colitec with link to web - site has been posted on the gaia - fun - sso wiki ( https://www.imcce.fr/gaia-fun-sso/ ) . the authors thank dr . f. velichko for his useful comments . we are grateful to the reviewer for his helpful remarks that improved this work . we express our gratitude to mr . w. thuillot , coordinator of the gaia - fun - sso network , for the approval of colitec as a well - adapted software to the gaia - fun - sso conditions of observation . we also thank dr . ya . yatskiv for his support of this work in frames of the target program of space science research of the national academy of science of ukraine ( 2012 - 2016 ) and the ukrainian virtual observatory ( http://www.ukr-vo.org ) . the colitec program is available through http://colitec.neoastrosoft.com/en ( one can access to the download package http://www.neoastrosoft.com/download_en and some instructions http://www.neoastrosoft.com/documentation_en ) . abreu , d. , kuusela , j. ( 2013 ) upgraded camera for esa optical space surveillance system . in : 35 european space surveillance conference 7 - 9 june 2011 , inta hq , madrid , spain . bauer , t. ( 2009 ) . improving the accuracy of position detection of point light sources on digital images . in : _ proceedings of the iadis multiconference , computer graphics , visualization , computer vision and image processing , algarve _ , portugal , june 20 - 22 , 2009 , p. 3 burden , r.l . , faires , j.d . ( 2010 ) _ numerical analysis 9th ad . broocs / cole _ , 877 . david , g. , et al . ( 2013 ) . a new image acquisition system for the kitt peak national observatory mosaic-1 imager . http://www.noao.edu/kpno/mosaic/ news / spie7735 - 117.pdf[http://www.noao.edu / kpno / mosaic/ news / spie7735 - 117.pdf ] dell@xmath130oro , a. , cellino , a. ( 2012 ) . _ planetary and space science _ , * 73 * , 10 . elenin , l. , et al . ( 2010 ) . _ central bureau electronic telegrams _ , * 2384 * , 1 . elenin , l. , et al . 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( 2006 ) . image subtraction procedure for observing faint asteroids . _ bulletin of the minor planets section of the association of lunar and planetary observers _ , * 33 * , 16 . gural , p.s . , larsen , j.a . , gleason , a.e . ( 2005 ) . _ the astronomical journal _ , * 30 * , 1951 . harris , w.e . _ publications of the astronomical society of the pacific _ , * 102 * , 949 . honscheid , k. , et al . ( 2008 ) . the dark energy camera ( decam ) . 34th international conference on high energy physics . horizons system . http://ssd.jpl.nasa.gov/?horizons ivashchenko , yu . , kyrylenko , d. ( 2011 ) . minor planet observations [ a50 andrushivka astronomical observatory ] . _ mpc _ , * 77269 * , 7 . ivashchenko , yu . , kyrylenko , d. , gerashchenko , o. ( 2012 ) . minor planet observations [ a50 andrushivka astronomical observatory ] . _ mpc _ , * 81732 * , 6 . ivashchenko , yu . , kyrylenko , d. , gerashchenko , o. 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( 1999 ) . determination of coordinates of the statistically dependent objects on a discrete image . _ radio electronics and informatics _ , issue 1 , 4 . savanevych , v.e . models and the data processing techniques for detection and estimation of parameters of the trajectories of a compact group of space small objects . manuscript for dr . thesis , kharkiv : kharkiv national university for radio electronics , 446 p. 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the method operates by continuous parameters ( asteroid coordinates ) in a discrete observational space ( the set of pixels potential ) of the ccd frame . in this model , a kind of the coordinate distribution of the photons hitting a pixel of the ccd frame the developed method , being more flexible in adapting to any form of the object image , has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure , which is implemented to obtain the best fit instead of a least - squares method and levenberg - marquardt algorithm for the minimisation of the quadratic form . , the colitec software was recommended to all members of the gaia - fun - sso network for analysing observations as a tool to detect faint moving objects in frames .

we describe a new iteration method to estimate asteroid coordinates , which is based on the subpixel gaussian model of a discrete object image . the method operates by continuous parameters ( asteroid coordinates ) in a discrete observational space ( the set of pixels potential ) of the ccd frame . in this model , a kind of the coordinate distribution of the photons hitting a pixel of the ccd frame is known a priori , while the associated parameters are determined from a real digital object image . the developed method , being more flexible in adapting to any form of the object image , has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure , which is implemented to obtain the best fit instead of a least - squares method and levenberg - marquardt algorithm for the minimisation of the quadratic form . since 2010 , the method was tested as the basis of our colitec ( collection light technology ) software , which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of ccd frames . as the result , four comets ( c/2010 x1 ( elenin ) , p/2011 no1(elenin ) , c/2012 s1 ( ison ) , and p/2013 v3 ( nevski ) ) as well as more than 1500 small solar system bodies ( including five neos , 21 trojan asteroids of jupiter , and one centaur object ) were discovered . we discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency . in 2014 , the colitec software was recommended to all members of the gaia - fun - sso network for analysing observations as a tool to detect faint moving objects in frames . [ firstpage ] methods : data analysis ; minor planets , asteroids , comets ; techniques : image processing .

math0701591

i

this paper deals with various notions originating from the theory of tight closure , which we now review briefly . let @xmath0 be a commutative ring of prime characteristic @xmath1 ; for each ideal @xmath2 we define the _ @xmath3 frobenius power _ of @xmath4 , denoted @xmath5}$ ] , to be the ideal of @xmath0 generated by @xmath6 . for any ideal @xmath2 we can then define its _ tight closure , _ denoted @xmath7 , to be the set of all @xmath8 such that for some @xmath9 not in a minimal prime of @xmath0 we have @xmath10}$ ] for all @xmath11 . tight closure is indeed a closure operation , in the sense that @xmath12 and @xmath13 ; we refer the reader to the seminal paper @xcite and to @xcite for a description of tight closure and its properties . tight closure has played an important role in many recent advances in commutative algebra . a short sample of its useful applications could include short proofs to some of the homological conjectures , the study of singularities , positive - characteristic analogues of multiplier ideals and many more . among the most interesting and useful results obtained early in the development of the theory of tight closure is the existence of _ test - elements _ ( cf . chapter 2 in @xcite ) . notice that the element @xmath9 occurring in the definition of tight closure could depend on the ideal @xmath4 and the element @xmath14 . test - elements are elements @xmath9 not in any minimal prime such that for _ all _ ideals @xmath2 and _ all _ @xmath8 , @xmath15 if and only if @xmath10}$ ] for all @xmath16 . notice , for example , that @xmath17 for all ideals @xmath2 if and only if @xmath18 is a test - element ( in this case we refer to tight closure as being a _ trivial operation _ ) . test - elements exist in many rings of interest ( e.g. , reduced algebras of finite type over excellent local rings ) and they play a vital role . one also defines the _ test - ideal _ of @xmath0 to be the ideal generated by all test - elements . in many applications one restricts one s attention to local rings and to the tight - closure of ideals generated by systems of parameters . one then naturally considers the notion of _ parameter - test - ideals _ : these are elements @xmath9 not in any minimal prime such that for all ideals @xmath2 _ generated by a system of parameters _ and all @xmath8 , @xmath15 if and only if @xmath10}$ ] for all @xmath16 . it is worth noting that when @xmath0 is a gorenstein ring , the notions of parameter - test - ideals and test - ideals coincide ( cf . chapter 2 in @xcite ) . the calculation of tight closure is notoriously hard no general algorithm is known and specific calculations are carried out with technical ad - hoc methods ( for example , see @xcite for such a calculation of a seemingly simple example which settled a major conjecture ) . there is not even an algorithm for deciding whether the tight closure operation in a given ring is trivial . the main aim of this paper is to provide a description of parameter test ideals of local cohen - macaulay rings of prime characteristic @xmath1 . the nature of this description will be such that it will allow us to give an algorithm for producing these ideals . as a result one also obtains an algorithm for deciding whether a ring is _ @xmath19-rational , _ i.e. , whether the tight closure of ideals generated by systems of parameters is trivial ; in the gorenstein case this property is equivalent to the tight closure of _ all _ ideals being trivial . the results in this paper will follow from an analysis of frobenius maps on injective hulls of the residue fields @xmath20 of the ring @xmath0 under consideration , i.e. , of additive maps @xmath21 which satisfy @xmath22 for all @xmath23 and @xmath24 . this analysis is inspired by gennady lyubeznik s work on @xmath19-modules and indeed , a crucial tool used here , namely , the functors @xmath25 defined in section [ section : a duality ] below , are nothing but `` the first step '' in the construction of lyubeznik s @xmath26 functors in section 4 of @xcite . the study of @xmath0-modules with frobenius maps can be elucidated by treating them as left modules over a certain skew polynomial ring @xmath27 $ ] . a crucial ingredient in this paper is rodney sharp s recent study of these modules in general , and of the @xmath27$]-module structure of the top local cohomology module in particular . in @xcite the parameter test ideal of @xmath0 was described in terms of certain @xmath27$]-submodules of the top local cohomology of @xmath0 , and it is this description on which our explicit description and algorithm is based on . along the way we gain new insights into the @xmath27$]-module structure of injective hulls of residue fields which translate into new results . one such result is an algorithm for computing the index of nilpotency ( in the sense of section 4 of @xcite ) of top local cohomology modules , which , together with the results in @xcite translate into an algorithm for computing the frobenius closure of parameter ideals in cohen - macaulay local rings and in view of @xcite provide an important ingredient for the corresponding computation in generalized cohen - macaulay rings as well . another spinoff is a very simple proof of a crucial ingredient in @xcite which together with corollary 3.6 there gives an alternative proof of the fact that for a power series ring @xmath28 of prime characteristic , for all nonzero @xmath29 , @xmath30 generates @xmath31 as a @xmath32-module .

we describe an algorithm for computing parameter - test - ideals in certain local cohen - macaulay rings . the algorithm is based on the study of a frobenius map on the injective hull of the residue field of the ring and on the application of rodney sharp s notion of `` special ideals '' . our techniques also provide an algorithm for computing indices of nilpotency of frobenius actions on top local cohomology modules of the ring and on the injective hull of its residue field . the study of nilpotent elements on injective hulls of residue fields also yields a great simplification of the proof of the celebrated result in .

we describe an algorithm for computing parameter - test - ideals in certain local cohen - macaulay rings . the algorithm is based on the study of a frobenius map on the injective hull of the residue field of the ring and on the application of rodney sharp s notion of `` special ideals '' . our techniques also provide an algorithm for computing indices of nilpotency of frobenius actions on top local cohomology modules of the ring and on the injective hull of its residue field . the study of nilpotent elements on injective hulls of residue fields also yields a great simplification of the proof of the celebrated result in .

1201.0783

i

understanding the evolution of galaxies and large scale structure remains a fundamental challenge in astrophysics . many ambitious galaxy surveys have been carried out to address this problem , but limited time on large telescopes results in a classic problem : sky coverage , depth , and spectral resolution choose two . for example , the very - wide - area sloan digital sky survey ( sdss ) provides a wealth of spectral information for galaxies over a cosmologically significant volume , but its modest depth limits the sdss to the relatively local , ` modern ' universe . conversely , the hubble ultra - deep field photometric survey probes deep into cosmic time to the epoch of reionization , but only over a tiny volume whose small population of galaxies leads to large uncertainties on their physical properties . while the union of such surveys has begun to paint a coherent picture of galaxy growth , significant patches of blank canvas limit our ability to fully describe how environmental processes , the infall of gas that fuels star formation , galaxy mergers and acquisitions , and feedback , all shape the evolution of galaxies over cosmic time . the carnegie - spitzer - imacs survey ( csi ) has been designed to address one of the most dramatic and least understood features of galaxy evolution the remarkably rapid decline in cosmic star formation since @xmath1 . it is during this extended epoch of galaxy maturation that galaxy groups and clusters have also emerged as a conspicuous feature of the landscape . the csi survey is uniquely able to link together the evolution of individual galaxies with these features of large - scale structure growth . in our ambitious spectrophotometric redshift survey of distant galaxies , we strike a balance between the aforementioned three factors : ( 1 ) high completeness to moderate redshift ( @xmath9 ) , ( 2 ) spectral resolution intermediate between conventional photometric and spectroscopic surveys ( combining the efficiency of imaging surveys with a spectral resolution high enough to resolve large - scale structure and prominent emission - lines ) ; and ( 3 ) an unprecedented area of 15 deg@xmath2 for a @xmath10 survey . this gives the csi survey a volume comparable to the sdss , with a selection method that efficiently traces stellar mass over 2/3 the age of the universe ( @xmath11 ) spanning the critical redshift range where cosmic star formation precipitously drops , and groups and clusters become prominent . as the redshift survey with the largest unbiased volume at @xmath12 , csi will allow us to comprehensively address the interplay between environment , galaxy mass buildup , and star formation at these redshifts . in this , the first paper of the csi survey , we describe the design of the project , with particular focus on the flux limits of the selection , the data processing and the spectral energy distribution ( sed ) fitting with its attendant determination of redshifts and redshift errors . we apply our methodologies to the first batch of data in 5 degs@xmath2 of the swire xmm - lss field , and provide an overview of some basic properties of galaxies over the past 9 gyr , with an emphasis on the gains made by selecting galaxies by stellar mass instead of by their rest - frame uv light .

we describe the carnegie - spitzer - imacs ( csi ) survey , a wide - field , near - ir selected spectrophotometric redshift survey with the inamori magellan areal camera and spectrograph ( imacs ) on magellan - baade . by defining a flux - limited sample of galaxies in spitzer _ irac _ m imaging of swire fields , the csi survey efficiently traces the stellar mass of average galaxies to . this first paper provides an overview of the survey selection , observations , processing of the photometry and spectrophotometry . we also describe the processing of the data : new methods of fitting synthetic templates of spectral energy distributions are used to derive redshifts , stellar masses , emission line luminosities , and coarse information on recent star - formation . our unique methodology for analyzing low - dispersion spectra taken with multilayer prisms in _ imacs

we describe the carnegie - spitzer - imacs ( csi ) survey , a wide - field , near - ir selected spectrophotometric redshift survey with the inamori magellan areal camera and spectrograph ( imacs ) on magellan - baade . by defining a flux - limited sample of galaxies in spitzer _ irac _ m imaging of swire fields , the csi survey efficiently traces the stellar mass of average galaxies to . this first paper provides an overview of the survey selection , observations , processing of the photometry and spectrophotometry . we also describe the processing of the data : new methods of fitting synthetic templates of spectral energy distributions are used to derive redshifts , stellar masses , emission line luminosities , and coarse information on recent star - formation . our unique methodology for analyzing low - dispersion spectra taken with multilayer prisms in _ imacs _ , combined with panchromatic photometry from the ultraviolet to the ir , has yielded 37,000 high quality redshifts in our first 5.3 degs of the swire xmm - lss field . we use three different approaches to estimate our redshift errors and find robust agreement . over the full range of m fluxes of our selection , we find typical uncertainties of . in comparisons with previously published vvds redshifts , for example , we find a scatter of for galaxies at . for galaxies brighter and fainter than mag , we find and , respectively . notably , our low - dispersion spectroscopy and analysis yields comparable redshift uncertainties and success rates for both red and blue galaxies , largely eliminating color - based systematics that can seriously bias observed dependencies of galaxy evolution on environment .

astro-ph0605355

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in recent years , great advances in our understanding of the nature and evolution of high redshift galaxies have been made , thanks to the availability of large samples . the techniques that have been developed rely either on colour selection criteria ( e.g. steidel et al . 2003 , 2004 , franx et al . 2003 , daddi et al . 2004 ) or detection in the submillimeter through blank field surveys using the submillimeter common user bolometer array ( scuba ) on the james clerk maxwell telescope ( jcmt , e.g. , hughes et al . , 1998 ) or the max - planck millimeter bolometer array ( mambo , e.g. bertoldi et al 2000 , eales et al . 2000 ) . all these surveys have unveiled large numbers of @xmath5 galaxies but the overlap between the various populations is by no means easy to investigate . among the various methods the lyman break dropout technique ( steidel & hamilton 1993 ) , sensitive to the presence of the 912@xmath6 break , is designed to select @xmath7 galaxies . the typical star formation rate ( sfr ) deduced from the uv continuum emission of lyman break galaxies ( lbgs ) is estimated to be moderate , around 2050 m@xmath8yr ( assuming h@xmath9=70 km s@xmath10mpc@xmath10 and q@xmath9=0.5 ) . the sfr value quoted is the `` mean '' sfr which is derived from the entire lbg sample which ranges from 10 to 1000 m@xmath8yr ( for the most massive lbgs ) . there is clear evidence , however , for the presence of significant amounts of dust in lbgs ( e.g. sawicki & yee 1998 , calzetti 2001 , takeuchi & ishii 2004 ) . when corrected for the presence of dust then this `` mean '' sfr values increase to @xmath0 100 m@xmath8yr . the high sfrs and co - moving density of lbgs , together with the results of the clustering analyses ( e.g. adelberger et al . 2004 ) makes them plausible candidates for the long - sought progenitors of present day elliptical galaxies ( e.g pettini et al . the nature of the relationship between lbgs and submm - luminous galaxies ( hereafter smgs ) has , however , remained unclear . one possible scenario is the one where lbgs and smgs form a continuum of objects with the submm galaxies representing the `` reddest '' dustier lbgs . central to such a hypothesis is of course the issue of dust in lbgs . a number of techniques have been used to deduce the dust content of lbgs ranging from studies of the optical line ratios ( pettini et al . 2001 ) to formal fits of the overall sed of lbgs based on various star forming scenaria ( e.g. shapley et al . 2001 , 2003 ) . both methods agree that the most intrinsically luminous lbgs , which have higher sfrs , contain more dust ( e.g. adelberger & steidel 2000 , reddy et al . more recently , x - ray stacking studies have shown that intrinsically more luminous lbgs also contain more dust ( e.g. nandra 2002 , reddy & steidel 2004 ) . another important issue in understanding lbg evolution and their connection to smgs is the study of their stellar mass content . the co - moving stellar mass density at any given redshift is the integral of past star - forming activity . thus , stellar mass is a robust tool to probe galaxy evolution and is subject to fewer uncertainties than the star formation rate ( sfr ) . until recently , stellar mass estimates for z@xmath03 lbgs have been based on ground based photometry which only samples out to rest frame optical band . the observed luminosity at these wavelengths is dominated by recent star - formation activity rather than the stellar population that has accumulated over the galaxy s lifetime . with the advent of the spitzer space telescope ( hereafter spitzer , werner et al . 2004 ) we now have access to longer wavelengths . in particular the availability of the irac instrument ( fazio et al . 2004 ) with imaging capabilities out to 8 microns allow us to probe rest frame k band ( for z@xmath03 galaxies ) where the light is sensitive to the bulk of the stellar content . preliminary results of adding irac photometry to stellar mass estimates have been presented in e.g. barmby et al . ( 2004 ) for z@xmath03 lbgs and shapley et al . ( 2005 ) for bx@xmath11bm objects . in this paper , we present sensitive mid infrared photometry for a sample of spectroscopically confirmed z@xmath03 lbgs detected as part of the irac guaranteed time observations ( gto ) program on the extended groth strip ( egs ) . we focus on the broad band spectral energy distributions ( seds ) of luminous lbgs detected with irac channel 4 ( 8 @xmath1 m corresponding to rest frame k band ) . the sample benefits from deep ground based optical photometry and spectroscopy ( steidel et al . our aim is to explore the range of stellar masses and assess the benefits of adding longer wavelength observations . we examine the correlation between mass and absolute luminosity ( magnitude ) from optical to the k band . the paper is organised as follows : in section 2 we present a brief account of the observations and data reduction while in section 3 we review the sample properties followed by a discussion of the detailed seds ( section 4 ) . we discuss the detailed models used to estimate stellar masses in section 5 while in section 6 we present the actual masses . we focus on the properties of massive lbgs in section 7 and we discuss their possible evolution and connection to submm - luminous galaxies . we estimate the number density of these massive lbgs in section 8 and summarize our conclusions in section 9 .

we describe the spectral energy distributions ( seds ) of lyman break galaxies ( lbgs ) at z using deep mid - infrared and optical observations of the extended groth strip , obtained with irac and mips on board spitzer and from the ground , respectively . we focus on lbgs with detections at all four irac bands , in particular the 26 galaxies with irac 8 m band ( rest frame k - band ) detections . we discuss the link between these lbgs and submm - luminous galaxies .

we describe the spectral energy distributions ( seds ) of lyman break galaxies ( lbgs ) at z using deep mid - infrared and optical observations of the extended groth strip , obtained with irac and mips on board spitzer and from the ground , respectively . we focus on lbgs with detections at all four irac bands , in particular the 26 galaxies with irac 8 m band ( rest frame k - band ) detections . we use stellar population synthesis models and probe the stellar content of these galaxies . based on best fit continuous star - formation models we derive estimates of the stellar mass for these lbgs . as in previous studies , we find that a fraction of lbgs have very red colors and large estimated stellar masses ( m 10 m ) : the present spitzer data allow us , for the first time , to study these massive lbgs in detail . we discuss the link between these lbgs and submm - luminous galaxies . we find that the number density of these massive lbgs at high redshift is higher than predicted by current semi - analytic models of galaxy evolution .

1102.4355

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the goal of this paper is to describe composition - closed equational classes of boolean functions not necessarily containing projections , thereby generalizing post s description of boolean clones . first we recall the definition of a clone , and then we give an informal overview of the problem that we consider . for formal definitions and more background see section [ sect preliminaries ] and @xcite . we define the _ composition _ of an @xmath0-ary function @xmath1 by the @xmath2-ary functions @xmath3 as the @xmath2-ary function @xmath4 given by@xmath5 we say that @xmath6 is the _ outer function _ of the composition , and @xmath7 are the _ inner functions_. a _ clone _ on the set @xmath8 is a class @xmath9 of finitary functions that is closed under composition and contains the _ _ projections__@xmath10 ( here , and in the rest of the paper , @xmath11 , i.e. , we exclude @xmath12 from the set of natural numbers . ) although the above definition of composition is restrictive in the sense that the inner functions must have the same arity , by making use of projections one can see that clones are closed under compositions without restrictions on the arities . for example , let us suppose that @xmath6 is a ternary function in a clone @xmath13 , and @xmath14 are unary , binary , ternary functions in @xmath13 , respectively . if we would like to build the composite function @xmath15 using only compositions of the form ( [ eq comp ] ) , then we could proceed as follows : first construct ternary functions @xmath16 with the help of the projections:@xmath17 and then form the composition @xmath18 . as we can see from the above example , composing a function with projections allows us to add dummy variables to the function ( see @xmath19 ) , to permute the variables of the function ( see @xmath20 ) and to identify variables of the function ( see @xmath21 ) . function classes closed under the latter three operations are called _ equational classes _ , since they can be defined by functional equations ( see subsection [ subsect equational classes ] ) . the above discussion shows that every clone is an equational class , but , as we shall see in subsection [ subsect equational classes ] , there are equational classes that are not clones . all clones on a given finite base set @xmath8 form an algebraic lattice . this _ clone lattice _ has continuum cardinality if @xmath22 ( see @xcite ) , and it seems to be a very hard problem to describe its structure . the case @xmath23 , i.e. , the case of boolean functions was settled by e. l. post , who described all clones of boolean functions in @xcite . there are countably many such clones , and their lattice is known as the post lattice ( see figure [ fig post ] ) . we will generalize the notion of a clone by considering function classes that are closed under composition ( in the sense of ( [ eq comp ] ) ) but do not necessarily contain the projections . however , we would like to be able to identify and permute variables and introduce dummy variables , therefore we only consider composition - closed equational classes . these classes form a complete lattice that contains the clone lattice as the principal filter generated by the clone of projections ( see figure [ fig biglattice ] ) . the main result of this paper is a description of this lattice over a two - element base set . although the clone lattice is countable in this case , we will see that the lattice of composition - closed equational classes of boolean functions is uncountable . composition - closed equational classes subsume iterative algebras as well . a function class @xmath24 is an _ iterative algebra _ if @xmath25 , whenever @xmath26 and @xmath27for @xmath28 . clearly , every iterative algebra is a composition - closed equational class , and an iterative algebra is a clone iff it contains the projections . the difference between composition - closed equational classes and iterative algebras can be best understood by visualizing compositions as trees . as an example , let us consider the following two compositions : if @xmath24 is an iterative algebra and @xmath29 , then both @xmath8 and @xmath30 must belong to @xmath24 . however , if @xmath24 is only assumed to be a composition - closed equational class , then @xmath8 does not necessarily belong to @xmath24 , as it involves the composition @xmath31 , where one inner function is a projection . this problem does not arise with @xmath30 , hence @xmath32 is guaranteed , whenever @xmath24 is a composition - closed equational class . in general , we can say that composition - closed equational classes are closed under compositions whose tree satisfies the following condition : for any internal node , either all or none of its children are leaves . as an exercise in handling such compositions , we invite the reader to verify the following fact : the clone generated by the addition operation of a field ( or , more generally , of any additive commutative semigroup ) consists of functions of the form @xmath33 the iterative algebra generated by addition contains only those such functions where @xmath35 , while the composition - closed equational class generated by addition contains only those where @xmath36 is even . the paper is organized as follows : in section [ sect preliminaries ] we present the necessary background on equational classes , boolean clones , and galois connections between functions and relations . in section [ sect idempotents vs clones ] we make some basic observations about composition - closed equational classes of boolean functions , and we outline a strategy for constructing all of them . in section [ sect easy ] we carry out this strategy for the easy cases , and then we deal with the harder cases in sections [ sect w_infty ] and [ sect w_k ] . finally , in section [ sect concluding ] we put together all the information we found to get a picture about the lattice of composition - closed equational classes of boolean functions .

we determine all composition - closed equational classes of boolean functions . these classes provide a natural generalization of clones and iterative algebras : they are closed under composition , permutation and identification ( diagonalization ) of variables and under introduction of inessential variables ( cylindrification ) , but they do not necessarily contain projections . thus the lattice formed by these classes is an extension of the post lattice . the cardinality of this lattice is continuum , yet it is possible to describe its structure to some extent .

we determine all composition - closed equational classes of boolean functions . these classes provide a natural generalization of clones and iterative algebras : they are closed under composition , permutation and identification ( diagonalization ) of variables and under introduction of inessential variables ( cylindrification ) , but they do not necessarily contain projections . thus the lattice formed by these classes is an extension of the post lattice . the cardinality of this lattice is continuum , yet it is possible to describe its structure to some extent .

math0306189

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a problem of considerable interest in both mathematics and physics is to determine the asymptotics of the distribution functions @xmath0 of an orthonormal basis @xmath1 of eigenfunctions of a laplacian ( or similar hamiltonian ) on a compact manifold ( see @xcite ) . in general , it is hopelessly difficult to obtain more than crude bounds on such distribution functions , which of course control the @xmath2-norms of the eigenfunctions . numerical analyses and heuristics from quantum chaos and disordered systems suggest however a rich picture in which the asymptotics of @xmath3 is related to the classical dynamics underlying the eigenvalue problem . ( some references will be discussed at the end of the introduction . ) the purpose of this paper is to give a rather complete analysis of the limit distribution of eigenfunctions in one of the few settings where such a detailed analysis is possible , namely where the phase space is a toric khler variety @xmath4 . let us recall the definitions ( see 1 for details ) . toric varieties are complex manifolds on which the complex torus @xmath5 acts with an open dense orbit . by a toric khler variety we mean a toric variety equipped with a khler form @xmath6 that is invariant under the underlying real torus @xmath7 . the action of @xmath8 is hamiltonian with respect to @xmath9 , and thus toric varieties are models of completely integrable systems . they are of a very special type because integrable systems usually generate an @xmath10 action rather than a @xmath8 action . although there are rigidity theorems limiting the class of such examples in the world of real riemannian manifolds @xcite , toric varieties provide a plentiful collection in the world of complex manifolds . the torus action can be ` quantized ' or linearized on the hilbert space completion of the coordinate ring @xmath11 where @xmath12 is a holomorphic line bundle with @xmath13 and where @xmath14 denotes the space of holomorphic sections of its @xmath15-th tensor power . this quantization is generally known as the holomorphic ( bargmann - fock ) representation in the physics literature . the space @xmath16 is spanned by joint eigenfunctions of the linearized @xmath5 action , which we refer to as ` monomials . ' in the fundamental case of @xmath17 , the joint eigenfunctions are the monomials given in an affine chart by @xmath18 the monomials lift ( by homogenization ) to homogeneous monomials on @xmath19 . we consider the case where @xmath20 is a smooth projective toric variety ; i.e. , @xmath21 , @xmath22 , where @xmath23 is an integral delzant polytope ( see [ background ] ) . then the linearized @xmath7 action is generated by @xmath24 commuting operators @xmath25 , @xmath26 on @xmath27 which preserve @xmath28 , and the joint spectrum of the eigenvalue problem @xmath29 consists of lattice points @xmath30 . our main results concern the asymptotics of their distribution functions @xmath31 with @xmath32 as @xmath33 . the function @xmath34 of @xmath35 is the pull - back of the fubini - study norm under a monomial embedding of the form @xmath36 : ( { { \mathbb c}}^*)^m \to { { { \mathbb c}}{{\mathbb p}}}^{d}\;,\qquad p\cap{{\mathbb z}}^m=\{{\alpha}(1),\dots,{\alpha}(d+1)\}\;,\ ] ] for a choice of constants @xmath37 . the volume in @xmath27 and the hermitian norm @xmath38 on @xmath39 are by definition the pull - backs of the fubini - study metric and form under this monomial embedding , and the @xmath40 norm on the space @xmath41 is in turn induced from the volume form and the hermitian pointwise norm of @xmath38 . ( see [ background ] for details . ) as figure [ monfig ] illustrates , the monomial @xmath42 is something like a gaussian bump centered on the real torus @xmath43 , where @xmath44 is the moment map for the classical hamiltonian @xmath8-action on @xmath27 ( see 1 ) . [ monfig ] times the monomial @xmath45 for @xmath46 ( left ) and @xmath47 ( right ) for @xmath48 and @xmath49 , where @xmath50 is the standard simplex . the variable @xmath51 is chosen as @xmath52 . see proposition [ localp ] in section [ massasym ] . , title="fig : " ] times the monomial @xmath45 for @xmath46 ( left ) and @xmath47 ( right ) for @xmath48 and @xmath49 , where @xmath50 is the standard simplex . the variable @xmath51 is chosen as @xmath52 . see proposition [ localp ] in section [ massasym ] . , title="fig : " ] since we would like to determine the properties of eigenfunctions @xmath53 when @xmath54 is large , but not necessarily a multiple of a lattice point in @xmath23 , we shall consider a sequence of approximate multiples , as in the following definition : let @xmath55 be a sequence of lattice points , and let @xmath56 . we say that @xmath57 is a sequence of approximate multiples of @xmath58 if @xmath59 our first result gives the pointwise behavior of the eigenfunctions : let @xmath58 be a point in the interior @xmath60 of the polytope @xmath23 , which is not necessarily a lattice point . then there exists a non - negative function @xmath61 such that @xmath62 if and only if @xmath63 , and for every sequence @xmath64 of approximate multiples of @xmath58 , we have @xmath65\ ] ] uniformly on @xmath66 , where @xmath67 . [ pointww ] the constant @xmath68 is defined in and ( and also appears in theorems [ unrescal ] and [ mldist ] ) . when we consider a sequence of the lattice points of the form @xmath69 with a lattice point @xmath70 , the assumption that @xmath71 is not necessary . in fact , we will give the pointwise asymptotics for @xmath69 with any lattice point @xmath72 in section [ massasym ] ( see propositions [ localss ] and [ localv ] ) . in the above theorem , the function @xmath73 ( @xmath74 ) on @xmath66 is defined by @xmath75 where @xmath76 is the vector given by the equation @xmath77 here @xmath78 is the moment map for the @xmath79 action on @xmath80 ( see for the definition ) , and we write @xmath81 we can express ( as in ( * ? ? ? * ( 17)(18 ) ) ) the function @xmath82 in the more intuitive form as follows : we introduce the real power ` monomials ' @xmath83 and define @xmath84 where ( cf . ) @xmath85 ( the normalized monomial @xmath86 has sup - norm @xmath87 , attained on the torus @xmath88 . ) then is equivalent to : @xmath89 since the sequence of monomials flattens out exponentially quickly away from the peak set @xmath88 , the distribution function is clearly tending to zero . the rate of decay of the distribution function is given by the following result : * let @xmath55 be a sequence of lattice points which are approximate multiples of @xmath74 ( see ) . then , for @xmath90 , we have @xmath91 * let @xmath92 . then , for @xmath90 , we have @xmath93 where @xmath94 , @xmath95 being the face of @xmath23 containing @xmath54 . [ unrescal ] here @xmath96 means the ratio of the left and right hand sides tends to @xmath87 , and the constants @xmath97 are given by and . we recall that if @xmath58 is a point in a face @xmath98 of codimension @xmath99 , then @xmath100 . hence @xmath101 . the exponentially localized behavior of the monomials suggests studying the distribution function on various length scales . first , we show that the @xmath102 have a universal scaling limit on a small length scale : [ mldist ] * let @xmath64 be a sequence of lattice points satisfying the condition with some point @xmath74 . then , for @xmath103 , we have @xmath104 * let @xmath105 . then @xmath106 for @xmath107 , where @xmath108 . a sample graph of the scaling limit distribution function for @xmath109 is given in figure [ limitd ] . with @xmath48 , @xmath110 , @xmath111 as in theorem [ mldist ] , the limit of the rescaled distributions has a universal form , _ i.e. _ it does not depend on the geometry of the manifold @xmath80 , and is given by a logarithmic power of the form @xmath112 with some constant @xmath113 . the logarithmic power appears because the @xmath114-normalized monomials are close to gaussian around the peak set @xmath115 on a vector space of dimension @xmath116 ( or dimension @xmath117 for the boundary lattice cases ) . more precisely , theorem [ pointww ] ( and propositions [ localss ] and [ localv ] ) shows that the function @xmath82 has a positive definite hessian at the peak point . we then observe that the distribution of a gaussian function on @xmath118 , @xmath119 ( where @xmath120 is a real positive @xmath121-matrix ) is given by the logarithmic power law @xmath122 c=\frac{1}{\sqrt{\det a}},\quad 0 < t \leq c,\end{gathered}\ ] ] relative to the normalized lebesgue measure @xmath123 thus , the rescaled distribution of an @xmath114-normalized monomial at the ` center ' of its localized bump has a universal gaussian form . to analyze the ` tails ' of the eigenfunctions , we next use an exponential rescaling of the distribution function so that the global distribution law has a non - zero limit as @xmath33 . as may be expected , it is no longer universal but depends on the geometry of @xmath124 . let @xmath64 satisfy the condition with a point @xmath74 . then @xmath125 where @xmath126 is the hessian matrix of @xmath127 a more general scaling limit law is given in theorem [ tnonrescaled ] . in the above theorem , the assumption that @xmath128 is not necessary . in fact , we will give similar result for @xmath69 with any lattice point @xmath129 ( theorem [ thnonrescaled ] ) in section [ invmprob ] . our strategy for proving theorems [ unrescal ] and [ tnonrescaledintro ] on the distribution functions of monomials is based on their pointwise asymptotics ( theorem [ pointww ] , and also propositions [ localss ] and [ localv ] in section [ massasym ] ) . pointwise asymptotics of monomials are more or less equivalent to asymptotics of their @xmath130 norms . since the latter are of independent interest , we state these asymptotics explicitly in : [ ml2knorm ] * let @xmath64 satisfy the condition for a point @xmath74 . let @xmath131 denote the @xmath132-norm of the @xmath114-normalized monomial @xmath133 with the weight @xmath134 . then we have @xmath135 where @xmath136 depends on @xmath137 . * let @xmath72 with @xmath108 . then we have @xmath138 we close the introduction with some general remarks and references . as mentioned above , our results pertain to phase space distribution of eigenfunctions ( husimi distributions ) rather than to their configuration space distribution . to our knowledge , the only prior example in dimension @xmath139 for which the limit distribution of eigenfunctions has been determined is the case of certain ( so - called ) hecke eigenfunctions of discrete quantum cat maps , due to kurlberg - rudnick @xcite . they work in a simpler discrete model rather than the holomorphic model . the main result of kurlberg - rudnick @xcite is that the distribution functions of ( un - scaled ) eigenfunctions tend to the semi - circle law . their method was to relate the eigenfunctions to exponential sums studied by katz @xcite and to apply the value distribution of exponential sums . since value distribution depends on the representation , it is not clear that the same semi - circle law would hold for hecke eigenfunctions in the holomorphic ( bargmann - fock ) representation , and this appears to be a challenging and interesting problem . part of the motivation for this paper was to set a baseline for eigenfunction distribution problems by studying a class of explicitly solvable examples . it would also be interesting to study the limit distribution of real eigenfunctions in the schrdinger representation , i.e. on the configuration space rather than the phase space . to our knowledge , the physics results mainly pertain to these configuration space results . the cases most studied and speculated about are those of chaotic or disordered systems . when eigenfunctions are delocalized , their spatial distribution is conjectured to be gaussian ( see e.g. @xcite ) . in the opposite regime where the eigenfunctions of disordered systems are exponentially localized , the expected distribution in the low amplitude ( tail ) region is given by a power of a logarithm @xcite , precisely the one we obtained in the high amplitude ( center ) region . the reason is that the distribution law is universal and gaussian in the tail region for exponentially localized eigenfunctions of disordered systems @xcite , while it is universal and gaussian in the center for our problem ( theorem [ pointww ] ) . the only studies we have located which are related to distribution laws of integrable eigenfunctions are those of one of the authors with j. a. toth ( cf . @xcite ) and that of berry - hannay - ozorio de almeida @xcite , which describes the asymptotic expansions of @xmath140 norms ( moment intensities ) of real oscillatory integrals of several stable types . such oscillatory integrals define quasimodes for a quantum integrable system , and in generic cases one can express eigenfunctions as oscillatory integrals of various kinds @xcite . in general , many possible kinds of oscillatory integrals could arise , including ones associated to singular lagrangean tori . hence , one can only expect complete results in special cases . to take the simplest example , our methods could be adapted to find the scaling limit distributions of squares of the standard spherical harmonics @xmath141 on @xmath142 ( or @xmath143 ) . these eigenfunctions are also joint eigenfunctions of commuting operators which generate a quantum torus action . to our knowledge , the distribution laws of even such simple eigenfunctions are unknown at this time . * acknowledgments : * this paper was written during a stay of the second author at johns hopkins university on a jsps fellowship . he would like to express his special thanks to the faculty in the department of mathematics of johns hopkins university .

we determine the asymptotics of the joint eigenfunctions of the torus action on a toric khler variety . such varieties are models of completely integrable systems in complex geometry . we first determine the pointwise asymptotics of the eigenfunctions , which show that they behave like gaussians centered at the corresponding classical torus . we then show that there is a universal gaussian scaling limit of the distribution function near its center . we also determine the limit distribution for the tails of the eigenfunctions on large length scales . these are not universal but depend on the global geometry of the toric variety and in particular on the details of the exponential decay of the eigenfunctions away from the classically allowed set .

we determine the asymptotics of the joint eigenfunctions of the torus action on a toric khler variety . such varieties are models of completely integrable systems in complex geometry . we first determine the pointwise asymptotics of the eigenfunctions , which show that they behave like gaussians centered at the corresponding classical torus . we then show that there is a universal gaussian scaling limit of the distribution function near its center . we also determine the limit distribution for the tails of the eigenfunctions on large length scales . these are not universal but depend on the global geometry of the toric variety and in particular on the details of the exponential decay of the eigenfunctions away from the classically allowed set .

0904.1416

i

fermion masses are one of the least understood parts of the standard model ( sm ) . even the charged fermion masses span over five orders of magnitude from the top quark to the electron , begging for a theoretical explanation . the majority of these masses and mixing angles are precisely constrained by experiment . still , this wealth of data does not conclusively single out any theory of flavor . in the near future , this may change dramatically with the discovery of new particles at the weak scale . new particles may only deepen the mystery , as would be the case if a fourth generation were discovered . on the other hand , the masses and mixings of the new particles may be governed by the same principles that determine the sm fermion masses . in this case , rather than extending the fermion sector , the new particles will shed light on the existing fermion spectrum . weak - scale supersymmetry provides examples of both possibilities . in pure gauge - mediated models , for example , squark and slepton masses are set by flavor - blind contributions , with no connection to the sm fermion masses . however , in gravity - mediated models and hybrid models with both gauge- and gravity - mediated contributions , squark and slepton masses may receive contributions that are governed by flavor symmetries that also determine the sm fermion masses @xcite . the latter possibility leads to non - trivial flavor effects in high - energy experiments @xcite , opening the possibility for real progress on the sm flavor problem at the large hadron collider , as has been emphasized recently by many authors ( see , for example , refs . @xcite ) . here we study the implications of flavor violation for the three - body decays of charged sleptons . such processes are most relevant for colliders in models with a gravitino lightest supersymmetric particle ( lsp ) and a slepton next - to - lightest supersymmetric particle ( nlsp ) , a generic possibility in models with both gauge - mediated supersymmetry breaking @xcite and gravity - mediated supersymmetry breaking @xcite . we consider a situation where the lightest particles are a gravitino lsp , several light sleptons , and the lightest neutralino , with the masses of each light slepton less than the mass of the lightest neutralino . this results in the typical two - body decays of these light sleptons being highly suppressed or kinematically inaccessible , leaving the three - body decays as the dominant decay modes . in these cases , the three - body decays are also often the last visible step in cascade decays of squarks and gluinos , and so they impact nearly all supersymmetry searches and studies . three - body slepton decays have been studied previously in an important , flavor - conserving case , where the authors considered @xmath1 and @xmath2 , with the @xmath3 a mixture of left- and right - handed staus @xcite . these decays are characterised by two distinct channels : a `` charge - preserving '' channel @xmath4 with opposite - sign leptons and a `` charge - flipping '' channel @xmath5 with same - sign leptons . flavor - conserving three - body decays of squarks have also been considered @xcite , as have flavor - conserving three - body decays with sneutrinos as parent or daughter particles @xcite . our work generalizes the charged slepton analysis to the case of arbitrary lepton flavor violation ( lfv ) and arbitrary left - right mixing . in the presence of general lfv , any three - body decay of @xmath6 has up to 9 possible charge - preserving modes @xmath7 and 6 possible charge - flipping modes @xmath8 , where @xmath9 . in addition , lfv and left - right mixing bring additional complications that are absent in the flavor - conserving case , including new processes mediated by higgs and @xmath10 bosons , new final states with neutrinos and quarks , and new interference effects in charge - flipping processes . these complications are well worth confronting , however , as there is a wealth of information in these branching ratios , which may shed light on the sm flavor problem . these decays , if present , are also relevant more broadly , for example , for supersymmetric searches and precision mass measurements . for example , in the flavor - conserving examples studied previously @xcite , the final states necessarily contain @xmath11 leptons . since these decay with missing energy , they degrade searches based on energetic leptons , and they greatly reduce the prospects for precision mass measurements . with lfv , however , even if the lightest slepton is a stau , there may also be decay modes with two electrons , two muons , or an electron and a muon . even if these branching ratios are suppressed , they may be the more obvious signals at colliders , and they may also provide better opportunities for precision mass measurements . it is therefore of interest to know the size of these branching ratios , and what determines them . in the following three sections , we begin with a general discussion of three - body decays and move gradually to more specific scenarios and concrete calculations . in sec . [ sec : diagrams ] we present the new final states and new feynman diagrams that are relevant to three - body decays once general flavor and left - right mixing are introduced . in sec . [ sec : widths ] we discuss these results in more detail and explain the relative phenomenological importance of the various contributing diagrams in particular scenarios . in sec . [ sec : plots ] we then show concrete results in two toy models with two - generation slepton mixing to illustrate our results . finally , in sec . [ sec : conclusion ] , we present our conclusions and explain how our results have been incorporated into spice , a publicly available computation package for generating supersymmetric spectra and branching ratios in scenarios with arbitrary slepton mixing . we stress that , although we strive to give readers a intuitive feel for our results by considering concrete cases in the body of the paper , our analysis is valid for fully general lfv and left - right mixing . the complete , model - independent calculation is lengthy , but the full expressions for all three - body decay modes are given in a series of appendices . our conventions and notations are defined in appendix [ app : lagrangian ] . these are consistent with those of ref . @xcite , where full details may be found .

these decays are important in scenarios in which the lightest supersymmetric particle is the gravitino , a generic possibility in models with gauge- and gravity - mediated supersymmetry breaking . three - body decays have been discussed previously assuming flavor conservation and left - right mixing in only the stau sector . flavor violation and general left - right mixing open up many new decay channels , which provide new avenues for precision mass measurements and may play an essential role in solving the standard model flavor problem . we present results for toy models with two - generation mixing , and discuss the implementation of these results in spice , a program that simplifies collider event simulations of flavor - violating supersymmetric models .

we determine the widths of three - body decays of sleptons , , in the presence of arbitrary slepton flavor violation and left - right mixing . these decays are important in scenarios in which the lightest supersymmetric particle is the gravitino , a generic possibility in models with gauge- and gravity - mediated supersymmetry breaking . three - body decays have been discussed previously assuming flavor conservation and left - right mixing in only the stau sector . flavor violation and general left - right mixing open up many new decay channels , which provide new avenues for precision mass measurements and may play an essential role in solving the standard model flavor problem . we present results for toy models with two - generation mixing , and discuss the implementation of these results in spice , a program that simplifies collider event simulations of flavor - violating supersymmetric models .

1701.01847

c

to conclude , we have developed a theory for the relaxation of optically pumped two - level systems coupled to a bosonic bath using the nonequilibrium keldysh technique and the diagrammatic perturbation theory . to elucidate the effects of bath phase transition , we have considered the cases when the bosonic bath is in the normal state and in the bose - condensed state . we then apply our theory to study the scenario of an illuminated quantum dot coupled to a dipolar exciton gas . the condensate and non - condensate fractions of the bath particles contribute to the relaxation rate by variable proportions depending on the value of pump field amplitude . when the pump field is weak , both fractions contribute by about the same order of magnitude ; while for strong pump field , the non - condensate fraction becomes the dominant contribution . our findings also show that the phase transition of the dipolar exciton gas to the bec regime results in a strong dependence of the relaxation rate on the optical pump field . the relaxation rate then exhibits a strong non - monotonic behavior , reaching a maximum and then becoming exponentially suppressed as a function of both the pump field s frequency and amplitude . such a non - monotonic dependence could in principle serve as a smoking gun for detecting bec phase transition of the coupled dipolar exciton gas . finally , we point out that despite our focus on dipolar exciton gas in this work , the theory we have developed is also applicable to other types of bose gas , such as 2d exciton - polaritons @xcite , magnons @xcite and cold atoms @xcite .

we develop a microscopic theory for the relaxation dynamics of an optically pumped two - level system ( tls ) coupled to a bath of weakly interacting bose gas . using keldysh formalism and diagrammatic perturbation theory , expressions for the relaxation times of the tls rabi oscillations are derived when the boson bath is in the normal state and the bose - einstein condensate ( bec ) state . we apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two - dimensional dipolar exciton gas . our theory also shows that a phase transition of the bath from the normal to the bec state strongly influences the relaxation rate of the tls rabi oscillations . phase transition of the dipolar exciton gas leads to a non - monotonic dependence of the tls relaxation rate on both the pump field frequency and field strength , providing a characteristic signature for the detection of bec phase transition of the coupled dipolar exciton gas .

we develop a microscopic theory for the relaxation dynamics of an optically pumped two - level system ( tls ) coupled to a bath of weakly interacting bose gas . using keldysh formalism and diagrammatic perturbation theory , expressions for the relaxation times of the tls rabi oscillations are derived when the boson bath is in the normal state and the bose - einstein condensate ( bec ) state . we apply our general theory to consider an irradiated quantum dot coupled with a boson bath consisting of a two - dimensional dipolar exciton gas . when the bath is in the bec regime , relaxation of the rabi oscillations is due to both condensate and non - condensate fractions of the bath bosons for weak tls - light coupling and dominantly due to the non - condensate fraction for strong tls - light coupling . our theory also shows that a phase transition of the bath from the normal to the bec state strongly influences the relaxation rate of the tls rabi oscillations . the tls relaxation rate is approximately independent of the pump field frequency and monotonically dependent on the field strength when the bath is in the low - temperature regime of the normal phase . phase transition of the dipolar exciton gas leads to a non - monotonic dependence of the tls relaxation rate on both the pump field frequency and field strength , providing a characteristic signature for the detection of bec phase transition of the coupled dipolar exciton gas .

nucl-th0302040

i

the lowest order in the interaction mean - field treatments of the nuclear pairing in bulk nuclear matter and in finite nuclei are conceptually simple and have been reasonably consistent with the phenomenology of these systems . the hartree - fock - bogolyubov ( hfb ) theory with zero- or finite - range ( e.g. , the skyrme and the gogny ) phenomenological forces has been the standard tool in the studies of the nuclear structure to describe the bulk of the experimental data @xcite . at the same time , the calculations of the pairing gaps in bulk nuclear matter based on the bardeen - cooper - schrieffer ( bcs ) theory with interactions modeled by the bare ( realistic ) nucleon - nucleon forces and quasiparticle spectra in the effective mass approximation are not inconsistent with the cooling simulations of neutron stars or the phenomenology of their rotation dynamics . although there is no direct evidence for higher order correlations in the phenomenology of nuclear systems , these can not be discarded on the basis of purely phenomenological arguments . the effective forces used in the hfb calculations are fitted to the pairing properties of ( some ) nuclei , consequently the contributions beyond mean field are built - in automatically ( e.g. , the effective skyrme or gogny forces include the contributions from the ladder diagrams ) . the values of the pairing gaps deduced from the phenomenology of neutron stars depend sensitively on the physical input , such as the equation of state , the matter composition , and its dynamical properties . provided the uncertainties in these ingredients the phenomenological values of the gap can be off by an order of magnitude . from the theory point of view the higher order correlations might not be manifest due to large cancellation between the vertex and propagator renormalization . the on - mass - shell properties of the pairing gaps are well understood at the mean - field level . upon ignoring the renormalization effects , the on - mass - shell gaps can be directly computed from the nucleon - nucleon scattering phase shifts . since the pairing is a low - temperature phenomenon , a well - defined fermi sea implies that the on - shell self - energies of weakly excited quasiparticles can be expanded around their fermi momentum . the magnitude of the gap is then controlled by the renormalization of density of states at the fermi surface . since the ratio of the momentum - dependent effective mass to the bare mass is less than unity the reduction of the density of states causes a reduction of the pairing gap . the early work to construct renormalization schemes for strongly interacting fermions introduced wave - function renormalization factors in the kernel of the gap equation and modeled the pairing interaction in terms of particle - hole irreducible vertices @xcite . these were related to the phenomenological landau fermi liquid parameters which can ( in principle ) be fixed by comparison with experiments . the landau parameters can be obtained from _ ab initio _ microscopic calculations as well , which are needed , for example , to describe isospin asymmetric nuclear systems that are not directly accessible in laboratories @xcite . various aspects of the pairing in the infinite nuclear matter beyond the mean - field ( bcs ) approximation were addressed during the past two decades by employing either more advanced schemes to calculated the self - energy and vertex corrections and/or modern ( phase - shift equivalent ) interactions . this work includes the microscopic calculations of the effective interactions and landau parameters using variants of the babu - brown @xcite or related ( e.g. , polarization potential ) schemes of summing the polarization graphs in neutron matter @xcite . the polarization effects were found to suppress the on - shell pairing gaps by large factors . earlier , similar reduction was found from the correlated basis variational calculations based on the jastrow ansatz for fermionic wave functions @xcite . more recent work concentrated on the calculations of the wave - function renormalizations and their implementations in gap equations employing self - energies derived within brueckner theory at first @xcite and second @xcite order in the hole - line expansion . while again a suppression was found due to the wave function renormalizations , supplementing these self - energy corrections with appropriate vertex corrections largely compensates for the latter effect @xcite . the finite temperature @xmath0 matrix was utilized to deduce the pairing correlations that include full spectral information on the system by using the thouless criterion @xcite , wave - function renormalizations in the gap equations , or the @xmath0 matrix in the superfluid phase @xcite . the reduction of the critical temperature of superfluid phase transition found in these approaches is due to dressing of propagators in the particle - particle channel , i.e. , the analog effect of the self - energy renormalizations in the brueckner scheme @xcite . ( it is unrelated to the reduction mentioned above caused by the polarization of the interaction that follows from the resummations in the particle - hole channels . ) renormalization group approach has been used to resume the particle - hole channels and deduce the pairing gap from the matrix elements defined on the fermi surface @xcite ; the overall magnitude of the reduction of the gap is consistent with the results mentioned above . the pairing gaps computed from the renormalization group motivated interactions are in good agreement with the calculations based on the original bare interactions @xcite or the effective gogny interactions @xcite below the renormalization scale . the off - mass - shell physics of the nuclear pairing is much less understood . contributions to the ( complex ) pairing gap can be generated by time nonlocal interactions . the simplest example is the fermionic fock - exchange diagram in a boson - exchange interaction model . the generic theory of the boson - exchange superconductors is known in the form first developed by eliashberg @xcite to describe the superconductivity in materials where the electron - phonon coupling is of the order of unity ( see also the general references @xcite ) . because the theory contains another small parameter - the ratio of the phonon debye energy to the fermi energy of electrons - the vertex corrections ( according to the migdal theorem ) can be neglected . for the same reason , the quasiclassical approximation can be used where the on - shell energy of the original green s functions are integrated out . in our context the coupling of the pionic modes to baryons is not small and the characteristic energies of the off - shell excitations are not small compared to the fermi energy . below , we shall partially overcome these difficulties , first , by including a vertex renormalization by the short - range correlations in the pion - nucleon vertex and , second , by applying an improved version of the quasiclassical approximation . pairing in nuclear systems , induced by retarded interactions , was discussed previously in refs . @xcite . in the context of laboratory nuclei the retarded pairing interaction is driven by an exchange of virtual phonons - low - lying collective bosonic excitation @xcite . in the astrophysical context of neutron star crusts the attractive pairing interaction is mediated by an exchange of _ real _ phonons of the nuclear coulomb lattice of the crusts @xcite . the approach taken here differs from the models above in the nature of the bosonic modes that mediate the pairing interactions . while the density fluctuations are responsible for the pairing interaction in the models above , we concentrate here at the modes that have the quantum numbers of pions . in what follows , we construct a model of pairing in neutron matter that is based on the meson - exchange picture of the nuclear interactions . specific to our model is the explicit treatment of the mesonic degrees of freedom including retardation . unlike the potential models , the interaction incorporates medium modifications of the dispersion relation of the mesons ( pions ) and they are treated dynamically , i.e. , only in the static limit the retarded interaction reduces to a meson ( pion)-exchange potential . we note that the meson - exchange picture of pairing is known from applications of the walecka mean - field model to the pairing problem @xcite . these approaches , however , do not include the pion dynamics or retardation . in computing the renormalization of the pionic propagator and the pion - nucleon vertex , we shall use a simplified version of the resummation of the particle - hole diagrams by modeling the residual interaction in terms of a contact approximation to the @xmath1 landau parameter . this corresponds to the random phase approximation ( rpa ) renormalizations of pion propagators in migdal s theory of finite fermi systems @xcite . the retardation effects are included by evaluating the fock ( exchange ) self - energies of neutrons which are coupled to dynamical ( off - mass - shell ) pions . we determine numerically the resulting off - mass - shell gap function and wave - function renormalization self - consistently by solving the coupled integral equations for these two complex functions . to elucidate our model , we start with the @xmath2-exchange interaction among neutrons in a low -density neutron matter relevant for the physics of neutron star crusts . in the density regime @xmath3 , where @xmath4 @xmath5 is the nuclear saturation density , the matter in neutron stars is an admixture of unbound neutron liquid and a coulomb lattice of nuclei with a charge - neutralizing background of relativistic electrons @xcite . we shall assume that the neutrons form a homogenous fermi liquid which is characterized by an isotropic fermi surface . the remainder of the paper is organized as follows . ii is devoted to the formulation of the model in the framework of the real time green s functions formalism . iii describes a method of solution of the coupled , nonlinear integral eliashberg equations . the results are discussed for the case under study the pairing in the low - density neutron matter where the retarded pairing interaction is mediated by an exchange of neutral pions . iv contains our conclusions . in the appendix we discuss the quasiclassical approximation to the propagators and its improved version , which is used in our numerical work .

the model is applied to the low - density neutron matter in neutron star crusts by separating the interaction into a long - range one - pion - exchange component and a short - range component parametrized in terms of landau fermi liquid parameters . the resulting eliashberg - type coupled nonlinear integral equations are solved by an iterative procedure . the damping of the neutron pair correlations due to the coupling to the pionic modes is small , but becomes increasingly important as the energy is increased . we discuss an improved quasiclassical approximation under which the numerical solutions are obtained .

we develop a model of off - mass - shell pairing correlations in nuclear systems , which is based on the meson - exchange picture of nuclear interactions . the temporal retardations in the model are generated by the fock exchange diagrams . the kernel of the complex gap equation for baryons is related to the in - medium spectral function of mesons , which is evaluated nonperturbatively in the random phase approximation . the model is applied to the low - density neutron matter in neutron star crusts by separating the interaction into a long - range one - pion - exchange component and a short - range component parametrized in terms of landau fermi liquid parameters . the resulting eliashberg - type coupled nonlinear integral equations are solved by an iterative procedure . we find that the self - energies extend to off - shell energies of the order of several tens of mev . at low energies the damping of the neutron pair correlations due to the coupling to the pionic modes is small , but becomes increasingly important as the energy is increased . we discuss an improved quasiclassical approximation under which the numerical solutions are obtained .

1508.04664

i

up until fairly recently , most authors working with steady water waves have made the assumption that the vorticity @xmath0 of the velocity field @xmath1 vanishes identically . such waves are known as irrotational , as opposed to rotational waves where @xmath2 is allowed to be nonzero . rotational waves can exhibit more exotic behavior than irrotational ones , including interior stagnation points and critical layers of closed streamlines @xcite . stagnation points correspond to fluid particles that are stationary with respect to the wave , and for irrotational flows this can only occur at a sharp crest @xcite . irrotational waves are mathematically simpler to work with than rotational ones , due to the availability of the velocity potential . the velocity potential is the harmonic conjugate of the stream function , thus enabling the use of tools such as complex analysis , which are not available with nonzero vorticity . the survey @xcite treats the theory of stokes waves an important class of irrotational waves and the results on the so - called stokes conjecture for such waves . this conjecture was not fully settled until the appearance of the paper @xcite . the first , and still the only known , explicit nontrivial traveling wave solution to the euler equations was given in @xcite and is rotational ( which was only later pointed out by stokes ) . much later came the first existence result for small - amplitude waves with general vorticity distributions @xcite . it was not , however , before the pioneering article @xcite that large - amplitude waves were constructed using an extension of the global bifurcation theory of rabinowitz @xcite , leading to renewed interest in rotational waves . due to the methods used , neither the waves in @xcite nor those in @xcite exhibit stagnation . the first waves with a critical layer were constructed in @xcite , having constant vorticity . a different approach was used in @xcite , allowing for wave profiles with overhang ( for which existence is still an open question , with some numerical evidence in the affirmative @xcite ) . the method of proof for the existence of nontrivial rotational waves is typically bifurcation from parallel flows with a prescribed vorticity distribution , which are described in @xcite . other authors have looked at waves with density stratification @xcite , waves with compactly supported vorticity @xcite and waves with a general vorticity distribution and stagnation @xcite . of particular interest to us are @xcite , which cover small - amplitudes waves with an affine vorticity distribution . this is the natural step up from the constant vorticity considered in @xcite , and the resulting waves can have an arbitrary number of critical layers @xcite . in this paper , which builds upon @xcite , we consider the same setting as in @xcite . small - amplitude solutions with an affine vorticity distribution are found by bifurcating from trivial solutions that depend naturally on three parameters . by using other choices for the bifurcation parameters in our argument , we obtain waves that , in general , are different from those found in @xcite . in order to show that these are new waves , we are led to examine the asymptotic behavior of the bifurcation curves ; in particular for carefully chosen special cases . a complicating factor for our choice of bifurcation parameters is that they require an additional condition on the parameters . this condition can be interpreted as a nondegeneracy condition for the equation governing the dimension of the linearized problem . another novel aspect of this work is a fairly complete description of the nontrivial solutions near any trivial solution where the linear problem is one - dimensional , and for a class of trivial solutions with a two - dimensional linearized problem . we also show , by explicit construction , that the dimension of the linear problem can become arbitrary large for certain wavenumbers . this opens up the possibility for waves with arbitrarily many modes . the outline of the paper is as follows : in we formulate the problem and describe the setting in which we will work . contains the bifurcation result for a one - dimensional kernel and gives the properties of the resulting bifurcation curves , while the final section , , covers two - dimensional bifurcation . some useful derivatives are listed in .

we establish the existence of small - amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution . an important part of the analysis is a fairly complete description of the small - amplitude solutions . finally , we investigate the asymptotic behavior of solutions on the local bifurcation set .

we establish the existence of small - amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution . the solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period . our bifurcation argument differs slightly from earlier theory , and under certain conditions we prove that the waves found are different from the ones in previous investigations . an important part of the analysis is a fairly complete description of the small - amplitude solutions . finally , we investigate the asymptotic behavior of solutions on the local bifurcation set .