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1504.03735	i	plasma ions are generally assumed to be stationary in the theory of ultra - relativistic non - linear plasma electron waves excited as wakefields of a laser or particle beam @xcite-@xcite . important exceptions to this occur when the drive beam ( or a witness beam being accelerated ) in a plasma wakefield accelerator becomes denser than the background plasma density by a factor larger than the ion to electron mass ratio @xcite@xcite . such is the case for the parameters of ultra - low emittance future collider designs at the tev energy scale . ion motion also becomes important in the wake train behind the initial wake oscillation or bubble . understanding the long - term ion behavior @xcite@xcite is important to determine the state of the plasma for succeeding pulses in a future plasma collider of high repetition rate @xcite@xcite . we also show that the resulting ion - wake channel formed is of interest for positron wakefield acceleration . driven by a matched laser pulse ( vector potential @xmath0 and frequency @xmath1 ) with @xmath2 . ( b ) non - linear ion - wake in the form of a cylindrical ion - soliton of radius @xmath3 excited behind the bubble electron wake in a proton plasma . ( c ) transverse ion - density profile at @xmath4 . notice that the ion density perturbation in this excitation phase is still building up and is a fraction of the background ion density , @xmath5 . ] in this paper , we model the excitation of a nonlinear ion - wake in the trail of an electron plasma wake in the bubble regime , driven by either relativistically intense laser or particle beam energy sources . the ion - wake is shown to be a non - linear ion - acoustic wave in the form of a cylindrical ion - acoustic soliton . its characteristics are similar to the solutions of the cylindrical korteweg - de vries equation ( ckdv ) @xcite-@xcite . however , the ion - wake shown here is different from a cylindrical - kdv soliton due to several reasons : the bubble wake electron oscillations do not thermalize into an isothermal plasma ; the ion - wake soliton breaks up into n - solitons as it evolves and there is an ion - density spike on the axis . the soliton propagates radially outwards leaving behind a flat residue resulting in a partially filled ion - wake channel . the dynamics of the ion wake is shown to have two distinct phases . the excitation phase where the time asymmetry of the radial electric fields of the bubble excite the ions into a soliton - like structure . at later times , the propagation phase where the soliton is driven outwards by the pressure of thermalized electrons after the electron oscillations undergo phase mixing @xcite . representative pic simulation results in fig.[fig1:ion - wake - laser ] and fig.[fig2:ion - wake - beam ] illustrate the salient features of the non - linear ion - wake . figure[fig1:ion - wake - laser ] shows the excitation phase at an early time when the bubble wake train is executing ordered oscillations and its fields have begun to excite the ion - wake structure seen in fig.[fig1:ion - wake - laser](b),(c ) . the radial oscillations later phase mix and the electrons thermalize , their thermal pressure then drives the ion - soliton outwards as shown in fig.[fig2:ion - wake - beam ] . as we show below , it is the longitudinal or time asymmetry of the radial electron wakefields that excites the ion soliton which propagates leaving behind a partially - filled channel shown in the pic simulations in fig.[fig1:ion - wake - laser ] and fig.[fig2:ion - wake - beam ] . , @xmath6 , @xmath7 , @xmath8 , these beam - plasma parameters are quite similar to @xcite . ( b ) corresponding ion density in cylindrical coordinates ( fixed - box ) . note the n - soliton formation in the ion - density . this is seen as the ion - wake evolves further , for instance at @xmath9 . ( c ) radial electron and ion density profile at @xmath10 . ] in section [ ion - wake - model - considerations ] we present considerations and assumptions made to derive the ion - wake model . in section [ radial - ion - wave ] using the fluid equations for ion dynamics we model the non - linear ion - acoustic waves as a driven cylindrical ion soliton . the driven wave models are shown to have two distinct phases : the excitation phase and the propagation phase . we present a model for the excitation of the ion - soliton by the electron bubble radial fields in section [ ion - soliton - excitation - phase ] and verify it using simulation results . in section [ ion - soliton - propagation - phase ] we present simulation results showing the dynamics of propagation of the ion - soliton driven by a radial temperature gradient . finally , in section [ ion - soliton - positron - wake ] we analyze the properties of a positron beam driven wakefield in an ion - wake channel .	the excitation of a non - linear ion - wake by a train of ultra - relativistic electron bubble wake- is modeled . the ion - wake is shown to be a driven non - linear ion - acoustic wave in the form of a cylindrical ion - soliton- . the phases of the oscillating radial electric fields of the slowly - propagating electron bubble is asymmetric in time and excites time - averaged inertial ion motion radially . once formed , the channel - edge density - spike is driven radially outwards by the thermal pressure of the wake energy . its channel - like structure due to the flat - residue left behind by the propagating ion - soliton , is independent of the energy - source driving the bubble electron wake .	the excitation of a non - linear ion - wake by a train of ultra - relativistic electron bubble wake- is modeled . the ion - wake is shown to be a driven non - linear ion - acoustic wave in the form of a cylindrical ion - soliton- . the phases of the oscillating radial electric fields of the slowly - propagating electron bubble is asymmetric in time and excites time - averaged inertial ion motion radially . the electron compression in the back of the bubble sucks - in the ions and the space - charge within the bubble cavity expels them , driving a cylindrical ion - soliton structure with on - axis and bubble - edge density - spikes . once formed , the channel - edge density - spike is driven radially outwards by the thermal pressure of the wake energy . its channel - like structure due to the flat - residue left behind by the propagating ion - soliton , is independent of the energy - source driving the bubble electron wake . we explore the use of the partially - filled channel formed by the cylindrical ion - soliton for a novel regime of positron acceleration . osiris pic simulations are used to study the ion - wake soliton structure , its driven propagation and its use for positron acceleration .
1305.6155	i	new physics operating during the big bang nucleosynthesis ( bbn ) can be probed by observed light element abundances . possible indications of new physics come from discrepancies between primordial abundances of @xmath4li and @xmath1li predicted in standard bbn ( sbbn ) model and those inferred from observations of metal - poor stars ( mpss ) . these mpss exhibit a plateau - like abundance ratio , @xmath1li / h @xmath5 at low metallicities of [ fe / h]@xmath6 @xcite , and much lower at extremely low metallicities of [ fe / h]@xmath7 @xcite.@xmath8 , where @xmath9 is the number density of @xmath10 and the subscript @xmath11 indicates the solar value , for elements a and b. ] the plateau abundance is a factor of 24 lower than the sbbn prediction for the baryon - to - photon ratio determined from the observation of the cosmic microwave background radiation with _ wilkinson microwave anisotropy probe _ ( wmap ) ( e.g. , @xmath1li / h=@xmath12 @xcite ) . this discrepancy indicates a need of some mechanism to decrease the @xmath1li abundance . although astrophysical processes such as the combination of atomic and turbulent diffusion in stellar atmospheres @xcite may be a cause of the observed abundances , this is not yet established @xcite . in recent spectroscopic observations of mpss , the lithium isotopic ratio of @xmath4li/@xmath1li is also measured . a possible plateau abundance of @xmath4li / h@xmath13 has been suggested @xcite , which is about 1000 times higher than the sbbn prediction . since an effect of convective motions in stellar atmospheres could cause asymmetries in atomic line profiles and consequently leads to an erroneous estimation of @xmath4li abundance @xcite , the effect should be estimated . even including this effect , high @xmath4li abundances have been evidently detected in at most several mpss @xcite . such a high abundance level at the low - metallicity requires processes other than standard galactic cosmic - ray ( cr ) nucleosynthesis models @xcite . to investigate the @xmath14li problems , in this work , we focus on a model to resolve the lithium problems assuming the presence of negatively charged massive particles @xmath0 @xcite with a mass much larger than the nucleon mass , i.e. , @xmath15 gev , during the bbn epoch @xcite . one of candidates for the @xmath0 particle is stau , the supersymmetric partner of tau @xcite . the @xmath0 particles become electromagnetically bound to positively charged nuclides with binding energies of @xmath16 mev . the bound state of a nuclide @xmath17 and an @xmath0 particle is denoted by @xmath18 . because of these low binding energies the bound states can not form until late in the bbn epoch , when nuclear reactions are no longer efficient . hence , the effect of the @xmath0 particles is rather small @xcite . depending upon their abundance and lifetime , however , the @xmath0 particles can affect lithium abundances through the following processes : 1 ) @xmath4li production via the recombination of @xmath19he with @xmath0 followed by the catalyzed @xmath20 transfer reaction @xmath19he@xmath2(@xmath21,@xmath0)@xmath4li @xcite , 2 ) @xmath1be destruction via the recombination of @xmath1be with @xmath0 followed by the radiative proton capture reaction @xmath1be@xmath2(@xmath22,@xmath23)@xmath24b@xmath2 . in the latter process the destruction of @xmath1be occurs through both the first atomic excited state of @xmath24b@xmath2 @xcite with excitation energy of 0.819 mev in the limit of infinite @xmath0 mass @xcite or the atomic ground state ( gs ) of @xmath24b@xmath25(@xmath26,0.770 mev)@xmath2 composed of the @xmath26 nuclear excited state of @xmath24b and an @xmath0 @xcite li is produced mostly as @xmath1be during the bbn epoch , which transforms into @xmath1li by electron capture in late universe . ] . in all previous investigations , all processes are assumed to start from radiative recombination of fully ionized nuclides @xmath17 and @xmath0 as suggested in ref . @xcite . however , we found a possibility that nonradiative charge exchange reactions between hydrogen - like ions and @xmath0 can contribute to change nuclear abundances in the bbn model including an @xmath0 particle . we focus on the @xmath1be nuclide since the effect on its abundance is expected to be important . we introduce a simple model for estimating the significance of the new process in sec . [ sec2 ] , and show the result of @xmath1be@xmath2 formation rate and time evolution of nuclear abundances in example cases in sec . [ sec3 ] . finally we summarize this work in sec . we adopt natural units , @xmath27 , where @xmath28 is the reduced planck constant , @xmath29 is the speed of light , and @xmath30 is the boltzmann constant .	especially , the final abundance ofli , mainly originating from the electron capture ofbe , has been suggested to reduce by thebe destruction via the radiative capture ofbe followed by the radiative proton capture of the bound state ofbe and (be ) . quantum physical model calculations for related reactions are needed to precisely estimate the efficiency of this pathway in future .	the existence of an exotic long - lived negatively charged massive particle , i.e. , , during big bang nucleosynthesis can affect primordial light element abundances . especially , the final abundance ofli , mainly originating from the electron capture ofbe , has been suggested to reduce by thebe destruction via the radiative capture ofbe followed by the radiative proton capture of the bound state ofbe and (be ) . we suggest a new route ofbe formation , that is thebe charge exchange at the reaction of ion and . the formation rate depends on the number fraction of ion , the charge exchange cross section of and the probability that produced excited statesbe are converted to the ground state . we estimate respective quantities affecting thebe formation rate , and find that this reaction pathway can be more important than ordinary radiative recombination ofbe and . the effect of the charge exchange reaction is then shown in a latest nuclear reaction network calculation . quantum physical model calculations for related reactions are needed to precisely estimate the efficiency of this pathway in future .
1305.6155	i	we studied effects of a long - lived negatively charged massive particle , i.e. , @xmath0 on bbn . in this bbn model including the @xmath0 , @xmath1be destruction can occur , and the @xmath1be abundance can reduce from the abundance predicted in sbbn model . resultingly the final abundance of @xmath1li can explain the abundances observed in mpss . the @xmath1be destruction proceeds through formation of @xmath1be@xmath2 followed by its radiative proton capture reaction . in this work we suggest a new route of @xmath1be@xmath2 formation , i.e. , the @xmath1be charge exchange between ion and @xmath0 . 1 . the rate for the @xmath1be@xmath2 formation through depends on the number fraction of ion , the charge exchange cross section of and the probability that produced excited states @xmath1be@xmath3 are converted to the gs ( sec . [ sec21 ] ) . 2 . in the @xmath1be exchange reaction , i.e. , @xmath1be@xmath38(@xmath0 , @xmath66)@xmath1be@xmath3 , the gs is converted to highly excited states of @xmath1be@xmath3 with main quantum numbers of @xmath276 . the gs and the excited states @xmath1be@xmath3 have almost equal sizes of binding energies and atomic radii ( sec . [ sec22 ] ) . 3 . in the epoch of @xmath1be destruction in the bbn model including the @xmath0 , the ion can be regarded as an isolated system which is separated from particles in thermal bath in the universe ( sec . [ sec23 ] ) . 4 . in the epoch , the rate for the recombination , @xmath1be@xmath277 @xmath74 , is large enough , and the equilibrium abundance ratio of the fully ionized @xmath1be@xmath37 and the partially ionized had been realized ( sec . [ sec24 ] ) . the cross section of the charge exchange reaction @xmath1be@xmath38(@xmath0 , @xmath66)@xmath1be@xmath3 is estimated from an analogy of the protonium ( @xmath62 ) formation . the rate for to form @xmath1be@xmath3 through this reaction is then calculated . the rate is proportional to the @xmath0 abundance @xmath278 , and can be much larger than the cosmic expansion rate in the epoch of the @xmath1be destruction ( sec . [ sec25 ] ) . 6 . the bound - bound transition rate of @xmath1be@xmath3 produced via this charge exchange reaction to the gs @xmath1be@xmath2 is estimated by applying the electric dipole transition rate to the exotic atomic system of @xmath1be@xmath3 ( sec . [ sec26 ] ) . 7 . the cross section of the @xmath1be@xmath3 destruction via @xmath36 collisional ionization is estimated from an analogy of the destruction of muonic hydrogen , @xmath279 , at a collision with @xmath66 . the rate for @xmath1be@xmath3 destruction through this reaction is then calculated . the rate is smaller than that for the transition to the gs only for excited states @xmath1be@xmath3 with main quantum number @xmath187 . such excited states are produced via the @xmath1be exchange of the gs . the gs is , therefore , the only effective path of the gs @xmath1be@xmath2 formation ( sec . [ sec27 ] ) . the @xmath1be charge exchange rate of @xmath1be@xmath3 via the @xmath66 collision is estimated with the detailed balance relation . the rate is smaller than the destruction rate via the @xmath36 collisional ionization at @xmath188 , while it is smaller than rates of spontaneous and stimulated emissions at @xmath223 . the charge exchange reaction , therefore , does not work as an effective reaction for @xmath1be@xmath3 destruction ( sec . [ sec29 ] ) . 9 . the photoionization rate of @xmath1be@xmath3 is estimated with a classical cross section . differently from the rate for the destruction in electronic collisional ionization , the photoionization rate is always much smaller than the spontaneous emission rate . the photoionization is , therefore , not an important reaction of @xmath1be@xmath3 destruction ( sec . [ sec28 ] ) . 10 . using physical quantities relevant to the @xmath1be@xmath2 formation through estimated in this work , effective recombination rates are derived as a function of cosmic temperature for several example cases . our primary rate for the @xmath1be@xmath2 formation through is larger than the rate for the direct formation via the radiative recombination of @xmath1be and @xmath0 . uncertainties in cross sections of the charge exchange @xmath1be@xmath38(@xmath0 , @xmath66)@xmath1be@xmath3 and the destruction @xmath1be@xmath3(@xmath36 , @xmath36 @xmath1be)@xmath0 affect the @xmath1be@xmath2 formation rate . the importance of this reaction is shown in bbn calculations with a latest nonequilibrium reaction network code ( sec [ sec3 ] ) . we are grateful to professor masayasu kamimura for discussion on the reaction cross sections . this work was supported by the national research foundation of korea ( grant nos . 2012r1a1a2041974 , 2011 - 0015467 , 2012m7a1a2055605 ) , and in part by grants - in - aid for scientific research of jsps ( 24340060 ) , and scientific research on innovative area of mext ( 20105004 ) . 99 f. spite and m. spite , astron . astrophys . * 115 * , 357 ( 1982 ) . s. g. ryan , t. c. beers , k. a. olive , b. d. fields and j. e. norris , astrophys . j. * 530 * , l57 ( 2000 ) . j. melendez and i. ramirez , astrophys . j. * 615 * , l33 ( 2004 ) . m. asplund , d. l. lambert , p. e. nissen , f. primas and v. v. smith , astrophys . j. * 644 * , 229 ( 2006 ) . p. bonifacio _ et al . _ , astrophys . * 462 * , 851 ( 2007 ) . w. aoki , p. s. barklem , t. c. beers , n. christlieb , s. inoue , a. e. g. perez , j. e. norris and d. carollo , astrophys . j. * 698 * , 1803 ( 2009 ) . j. i. g. hernandez , p. bonifacio , e. caffau , m. steffen , h. -g . ludwig , n. t. behara , l. sbordone and r. cayrel _ et al . _ , astron . astrophys . * 505 * , l13 ( 2009 ) . l. sbordone , p. bonifacio , e. caffau , h. -g . ludwig , n. t. behara , j. i. g. hernandez , m. steffen and r. cayrel _ et al . _ , astron . astrophys . * 522 * , a26 ( 2010 ) . l. monaco , p. bonifacio , l. sbordone , s. villanova and e. pancino , astron . astrophys . * 519 * , l3 ( 2010 ) . l. monaco , s. villanova , p. bonifacio , e. caffau , d. geisler , g. marconi , y. momany and h. -g . ludwig , astron . astrophys . * 539 * , a157 ( 2012 ) . a. mucciarelli , m. salaris and p. bonifacio , mon . not . . soc . * 419 * , 2195 ( 2012 ) . w. aoki , h. ito and a. tajitsu , astrophys . j. * 751 * , l6 ( 2012 ) . w. aoki , memorie della societa astronomica italiana supplementi * 22 * , 35 ( 2012 ) . a. frebel , w. aoki , n. christlieb , h. ando , m. asplund , p. s. barklem , t. c. beers and k. eriksson _ et al . _ , nature * 434 * , 871 ( 2005 ) . w. aoki , a. frebel , n. christlieb , j. e. norris , t. c. beers , t. minezaki , p. s. barklem and s. honda _ et al . _ , astrophys . j. * 639 * , 897 ( 2006 ) . r. h. cyburt , b. d. fields and k. a. olive , jcap * 0811 * , 012 ( 2008 ) . o. richard , g. michaud and j. richer , astrophys . j. * 619 * , 538 ( 2005 ) . a. j. korn _ et al . _ , astrophys . j. * 671 * , 402 ( 2007 ) . k. lind , f. primas , c. charbonnel , f. grundahl and m. asplund , astron . astrophys . * 503 * , 545 ( 2009 ) . r. cayrel _ et al . _ , astron . astrophys . * 473 * , l37 ( 2007 ) . m. asplund and j. melndez , aip conf . proc . * 990 * , 342 ( 2008 ) . m. steffen , r. cayrel , p. bonifacio , h. g. ludwig and e. caffau , in iau symp . 265 , chemical abundances in the universe : connecting first stars to planets , edited by k. cunha , m. spite and b. barbuy ( cambridge univ . press , cambridge , 2010 ) , p. 23 . m. pospelov , phys . lett . * 98 * , 231301 ( 2007 ) . k. kohri and f. takayama , phys . d * 76 * , 063507 ( 2007 ) . r. h. cyburt , j. r. ellis , b. d. fields , k. a. olive and v. c. spanos , jcap * 0611 * , 014 ( 2006 ) . m. kaplinghat and a. rajaraman , phys . d * 74 * , 103004 ( 2006 ) . k. hamaguchi , t. hatsuda , m. kamimura , y. kino and t. t. yanagida , phys . b * 650 * , 268 ( 2007 ) . c. bird , k. koopmans and m. pospelov , phys . d * 78 * , 083010 ( 2008 ) . m. kusakabe , t. kajino , r. n. boyd , t. yoshida and g. j. mathews , phys . d * 76 * , 121302 ( 2007 ) . m. kusakabe , t. kajino , r. n. boyd , t. yoshida and g. j. mathews , astrophys . j. * 680 * , 846 ( 2008 ) . k. jedamzik , phys . d * 77 * , 063524 ( 2008 ) ; 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hep-ph9511403	i	dynamical chiral symmetry breaking ( dcsb ) plays a very important role in the research of fundamental interactions . up to now , most investigations are focussed on dcsb with mass generation for the fermions . in such a scenario , the bilinear fermion condensate is taken as the order parameter of chiral symmetry breaking and it is known that it can receive a nonzero value when the coupling of the system exceeds some critical value . for a review on dynamical chiral symmetry breaking , see e.g. @xcite . but this is not the complete story for dcsb , since the order parameter may not be the bilinear fermion condensate : in principle , higher @xmath0-point functions which break chiral symmetry might become nonzero , without dynamical mass generation for the fermions @xcite . in a massless @xmath1 gauge theory for example , four - fermion green s functions which break chiral symmetry might become nonzero at values of the coupling below the critical value for dynamical mass generation . such a breaking of the chiral symmetry by the four - fermion condensates , without mass generation for the fermions , was discussed recently by holdom and triantaphyllou @xcite , who have calculated these four - point functions numerically and found a critical coupling constant which is almost the same as that responsible for dynamical mass generation . one could also think of theories where some other symmetry prevents the dynamical generation of a bilinear condensate and a dynamical fermion mass , but where a nonzero condensate of a higher @xmath0-point function is not restricted by this symmetry . in a chiral gauge theory , the gauge symmetry will be broken by the generation of a fermion mass , but a chirality - changing four - fermion condensate does not break the gauge symmetry , and might therefore be generated dynamically . in such a scenario , the chiral symmetry can be realized in more delicate way which may be useful for model building @xcite : it allows for a hierarchy of chiral symmetry breaking , first by the four - fermion condensate at relatively small values of the coupling , and eventually a second phase transition , at higher values of the coupling , leading to mass generation for the fermions , due to the four - fermion condensates . for these purposes one should study this phenomenon in a chiral gauge theory , as suggested in @xcite , but for simplicity and to see whether such a symmetry breaking patterns is possible , we restrict ourselves to a @xmath1 gauge theory . in our paper we confirm analytically the numerical results obtained by holdom and triantaphyllou @xcite , using a slightly different method to calculate the nonperturbative four - fermion functions . we find that there is a critical coupling for dynamical chiral symmetry breaking via the four - fermion condensates , below which there are no nontrivial solutions for the four - fermion functions which break chiral symmetry , but preserve parity , lorentz symmetry , and the flavor symmetry . this critical coupling is ( in our truncation scheme ) exactly the same as the critical coupling for fermion mass generation . this result is obtained by calculating the loop expansion of the effective action to leading order for the nonperturbative four - point functions . our result is also in agreement with an intuitive argument comparing the condensation of two fermions to the condensation of four fermions : for the four - fermion condensate we need at least the same binding force as for the bilinear fermion condensate . our paper is organized as follows . in the next section , we discuss some general features about dynamical symmetry breaking , and we show how in principle the chiral symmetry can be broken without mass generation for the fermions . in sec . [ seceffact ] , we derive a linear integral equation for the four - fermion function , using the loop expansion of the effective action . next , we analyze this equation for the nonperturbative chirality - changing four - fermion functions , using some expansions in order to perform the angular integrations analytically ; more details can be found in the appendix . we find that there is a critical coupling for these functions ; this critical coupling turns out to be the same as the critical coupling for dynamical mass generation . finally we give some concluding remarks in sec . [ secconc ] .	it is shown that in leading order of the loop expansion of the effective action , there is a critical coupling for the nonperturbative parity - invariant chirality - changing four - fermion functions ; this critical coupling however is the same as that for dynamical mass generation . therefore there is no breaking of chiral symmetry through the condensation of four - fermion functions below the critical coupling for dynamical mass generation for the fermions .	the fermion four - point functions and condensates as the chiral symmetry order parameters are calculated analytically in u(1 ) gauge theory in the massless phase . it is shown that in leading order of the loop expansion of the effective action , there is a critical coupling for the nonperturbative parity - invariant chirality - changing four - fermion functions ; this critical coupling however is the same as that for dynamical mass generation . therefore there is no breaking of chiral symmetry through the condensation of four - fermion functions below the critical coupling for dynamical mass generation for the fermions .
1310.2512	r	figure 1 shows a simulation of grain - surface chemistry using the method described above . the simulation uses a gas density of @xmath43 @xmath2 , and dust and gas temperatures of 10 k. the images show accurately the positions of each simulated particle ; however , the size and appearance of each particle in the image is chosen purely for ease of visual identification . as described above , every atom and molecule in the present model is treated as a uniform sphere of radius 1.6 ; no inference as to the polar orientation of molecules should be drawn . the images are constructed using the free - ware ray - tracing software _ pov - ray_. panel ( b ) shows an instance wherein 2 oxygen atoms and 1 hydrogen atom have been accreted from the gas phase . all are free to diffuse , but the hydrogen atom is significantly more mobile than the oxygen atoms . following several thermal hops , the hydrogen atom meets one of the oxygen atoms , with which it reacts to form oh . the further accretion of an oxygen and a hydrogen atom from the gas phase results in the formation of o@xmath0 and h@xmath0o . a video of this sequence may be found in the online version of the journal . figure 3 shows another simulation with a gas density of @xmath43 @xmath2 , extended for a much longer period ; 1000 water molecules are formed over 350 yr . ( an identical simulation is shown in figs.[f_surface]d and [ f_cross]d , extended to 200,000 water molecules , or 8,471 yr ) . the resultant ice mantle is composed primarily of water molecules , as expected . some molecular oxygen ( o@xmath0 ) and molecular hydrogen ( h@xmath0 ) are also present ; panel ( b ) shows an h@xmath0 molecule a little below the center of the image . to the left of this may be seen both an o@xmath0 molecule and a hydrogen peroxide molecule ( h@xmath0o@xmath0 ) . h@xmath0 and h@xmath0o are in fact formed in approximately equal quantities , but the molecular hydrogen evaporates rapidly unless trapped in a strong binding site , typically one with @xmath444 binding partners . panel ( c ) shows that the h@xmath0 indicated in panel ( b ) has left that binding site . in rate equation - based models , the formation of any significant quantity of h@xmath0o@xmath0 by the direct addition of two oh radicals at low temperature would be unlikely , due to the low diffusion rate of oh . such methods treat only the direct diffusion of each stated reactant . however , because the model presented here considers the explicit positions of all particles at all times , h@xmath0o@xmath0 may instead be formed by the diffusion of an o atom to a position that is in contact with an oh radical , followed by the surface diffusion of an h atom onto the oxygen atom . this results in an immediate two - stage reaction : h + o + oh @xmath45 oh + oh @xmath45 h@xmath0o@xmath0 . the occurrence of this process is dependent only on the relatively fast diffusion of hydrogen and oxygen , and not oh . such effects , which are essentially three - body surface reactions , are not generally taken into account in rate - based models . however , a similar process for the surface reaction of h + o + co was considered by garrod & pauly ( 2011 ) , who found this mechanism to be the primary formation route for co@xmath0 ice at low temperatures , due to the immobility of co and oh . because the new model takes explicit account of physical positions and structure , all such multi - stage processes are included by default . the formation of the ice mantle shown in fig . 3 is not uniform ; panels ( b ) and ( c ) in particular show the formation of a `` hole '' in the ice , corresponding to a region on the grain whose geometry results in weaker surface potential minima . in the center of the hole shown in panel ( c ) is a single dust - grain atom , around which six other dust - grain atoms reside . this arrangement produces six contiguous potential minima that allow bonding to only 3 dust - grain atoms , rather than the typical 4 . moderately mobile species that are momentarily bound in these weak sites rapidly diffuse out again . thus , the geometry of the dust grain alone may be seen to influence the consequent ice - mantle structure . there exist 8 such regions on the grain used in these models , where similar behavior is found . in this particular model , these holes eventually close over , as molecules build up at the edges of the holes , presenting positions of stronger binding within . under other conditions , such holes may progress to form pores within the ice structure ( see section 3.1.1 ) . in order to investigate the formation of structure in the ices , simulations have been run to produce ice mantles several times thicker than the diameter of the underlying grain . four sets of models have been produced , corresponding to gas densities in the range @xmath46 @xmath47 @xmath2 . for each density , the model has been run three times , adopting a different initial random number seed . this is done to demonstrate that the behavior of the models is a general feature and not dependent on the specific random numbers used in each run . all the simulations are run until 200,000 water molecules have been formed on the grain . as before , dust and gas temperatures are held at 10 k and the gas - phase fractional abundances of h and o atoms are fixed at @xmath24 . in addition , a single model has been run in which water molecules are accreted directly from the gas phase , with no accretion of h and o atoms . an arbitrary gas density of @xmath47 @xmath2 is used ; however , for the consideration of ice structure , the precise rate of accretion is unimportant , due to the lack of surface chemistry and the neglible rate of water diffusion caused by the low temperature . figure 4 shows the final state of each density model ( run 1 is shown in each case ) , including pure accretion ( panel a ) . hydrogen molecules ( h@xmath0 ) are highlighted in blue to aid the eye . a number of features are immediately apparent ; firstly , the large- and small - scale structure of the ice is strongly dependent on the gas density . the most irregular structure results from the higher - density simulations , culminating in the accretion - only model in this case , water molecules remain wherever they land as the result of accretion . in the simulations with active chemistry , higher densities result in more rapid hydrogenation of surface oxygen atoms , before they have the opportunity to find alternative , stronger binding sites . the higher - density ice mantles exhibit a highly porous , or `` creviced '' structure . panels ( b ) and ( c ) in particular show a `` cauliflower - like '' structure , wherein the crevices act to isolate large - scale nodules of ice . in the lower density simulations , the nodules become broader and the crevices less deep . the lowest - density model indeed shows a fairly smooth ice structure with no deep crevices or voids . in the accretion - only simulation , the ice appears irregular on all scales . the small - scale porous structure is largely the result of the lack of surface diffusion , such that new species are unable to move even a short distance into the stronger binding sites that are provided by areas of extreme small - scale curvature of the ice surface . however , the large - scale irregularity of the ice is caused by the combination of fully - randomized trajectories with a three - dimensional grain ; the growth of randomly - produced surface irregularities , or `` bulges '' , is amplified by their protrusion into the accretion field , picking up more material from a greater solid angle , while blocking out those trajectories for other regions of the grain / ice surface . such effects are still prevalent in the active - chemistry models panel ( c ) shows an ice mantle whose underlying dust grain is centered in the image ; a large protrusion may be seen on the right . while a moderate degree of surface diffusion may act to close over the small - scale pores or crevices in the ice , atoms of oxygen are required to diffuse a significant distance over the ice surface to counteract the large - scale irregularities . consequently , while smooth on the small scale , the lowest - density simulation ( panel e ) nevertheless shows an overall irregular shape . figure 5 shows cross sections of the same final ice mantles . each cross section passes through the dust - grain center at an arbitrary angle , showing molecules that sit within a `` slice '' @xmath48 deep this allows space for up to two molecules along a line of sight . videos of panels ( a ) , ( b ) and ( e ) are available in the online version of the journal , showing cross sections over 360 degrees . the detail of the porosity within the ice mantles is clearly visible in figure 5 . panel ( a ) shows significant and fairly uniform porosity , with pores or crevices that pass deep within the mantle almost down to the dust grain itself . the highest - density simulation with active chemistry is not as extreme , but also shows very deep pores / crevices in places , and exhibits some closed pores . the degree of porosity falls away at lower gas densities , until , for @xmath49 @xmath2 , there are essentially no open pores and the ice is extremely compact . one of the most striking features of fig . 5 is the arrangement of hydrogen molecules ( h@xmath0 ) . shown in blue in figs . 4 and 5 for ease of identification , h@xmath0 is almost completely segregated from the water molecules , especially in the higher - density simulations . furthermore , the h@xmath0 molecules are arranged in `` veins '' that are similar in appearance to the empty porous structures . as may be seen three - dimensionally in fig . 4 , the h@xmath0 indeed fills in crevices between larger structures . the veins of h@xmath0 are typically no more than around 5 molecules across ( commensurate micro - porous structure ) , while many of the unfilled pores are significantly larger . following its formation on the grains , an h@xmath0 molecule may diffuse around the surface . if it finds a weak binding site , it may evaporate entirely , but if it finds a strong binding site such as may be found in a pore , where multiple binding potentials converge then it may remain bound in place . the addition of further hydrogen molecules could then contain it , and allow a pore to fill up with hydrogen . the presence of larger , unfilled pores in the higher - density simulations suggests that these pores have an insufficient degree of inward curvature to produce binding potentials great enough to retain h@xmath0 for long enough before the deposition of new material can lock it into place . figure [ bar_coord ] shows a bar chart of the number of surface bonds of each molecule ( of any species ) within the ice mantle , for each of the simulations shown in figs . 4 and 5 . the accretion - only model shows a very different distribution from the active - chemistry models . approximately 35% of all molecules in this simulation experience only 3 5 bonds , making them ( typically ) surface molecules . conversely , only around 6% of molecules in even the highest - density active - chemistry simulation are so weakly bound , and the number of species with only 3 bonds is negligible . however , this does not imply that potential minima that would allow only 3 bonds do not exist only that they are unoccupied . pores , and the associated h@xmath0 veins , may begin to form in such positions , with ice structure building up around them . the porosity visible in figs . 4 and 5 is reflected in the bonding distributions of fig . 6 , with the most compact ice ( produced by the lowest - density model ) showing the greatest bias toward 10 12 bonds , which are necessarily bulk ice molecules . such distributions may therefore be useful as a measure of porosity in these simulations . figure 7 shows the fraction of bonds shared with an h@xmath0 molecule , averaged over all h@xmath0 molecules . the highest density model shows the greatest degree of clustering of h@xmath0 molecules . based on a purely statistical comparison of abundances , the expected value would be around 13 14% for this density ( based on values in table 3 ) . for the lowest density model , the statistical expectation would be @xmath58% . in each case , the actual fractional bonding of h@xmath0 to h@xmath0 is close to 3 times higher than the statistical expectation . it should also be borne in mind that the binding potentials used for h@xmath0 ( table 2 ) are the same for all binding partners . the h@xmath0 clustering is thus the result of the structural arrangement of the ice mantle to produce pores or concentrations of strong binding sites in which h@xmath0 molecules may become trapped , rather than a preference for h@xmath0 molecules to bind to each other , per se . figure 8 shows time - dependent grain - surface chemical abundances for each of the stable molecules included in the model , for all four gas - density values . results for all three runs at each density are plotted in the same panel . the end - time of each model corresponds to the time at which 200,000 water molecules have been formed ; the precise value varies according to the gas density and , to some degree , according to random variation between runs at the same density . for o@xmath0 and h@xmath0o@xmath0 , which have generally low abundances , there is some random fluctuation apparent at early times , and there are small systematic differences between runs of the same density . however , as a proportion of the total quantities , these variations fall away as the ice mantles grow . table 3 shows the final values for each model run , as well as the total amount of h@xmath0 formed , much of which evaporates back into the gas phase . h@xmath0o@xmath0 shows the largest variation between same - density runs , of around 7 - 8% , but variations for the other species are typically 1 - 2% . the elevated value for h@xmath0o@xmath0 may be due to its more intricate formation mechanism in this model ( see section 3 ) . for reference , table 3 also indicates end - times of the models , @xmath50 , and the greatest radial distance of any ice - mantle particle from the centroid of the grain , @xmath51 , achieved by the end of each run . abundances of species other than h@xmath0o are seen to be somewhat lower for the lower density models , including h@xmath0 . however , the total amount of h@xmath0 formed ( see table 3 ) is much less affected than the quantity that is stored on the grain at each gas density . accreted atomic hydrogen is typically able to remain on the grain for long enough for another reactive species to accrete and react with it , for all density models . in the case where the product is h@xmath0 , it is more likely to evaporate for the lower density models , which have a more regular surface that provides fewer strong - binding positions or pores . in each of the simulations , the amount of h@xmath0 formed is only a small amount larger than the total water formed . the running of the new model over various density conditions allows an assessment of the computational efficiency to be made . each simulation was run with an _ intel xeon x5482 _ cpu , using a single thread . the run - time for all of the three higher - density simulations ( @xmath52 , @xmath53 , and @xmath47 @xmath2 ) is approximately 90 95 hours , depending on which random - number seed run is considered . only the lowest - density simulations show an apparent density dependence , taking @xmath5180 hours to run . the majority of cpu - time is used up on the calculation of diffusion pathways and on the assignment of position and pairing information associated with each surface hop . because the model keeps diffusion paths in memory , the most intensive calculations are typically done only once per particle , providing the positions of surface potential minima for an individual , mobile particle for large numbers of subsequent , identical hops , prior to reaction , desorption or trapping in a strong binding site . it appears that the larger drain on cpu - time in the low - density case is caused by the relative smoothness of the ice surface . in this case , a diffusing particle ( typically atomic hydrogen ) on the grain has a smaller probability of becoming trapped in a strong binding site ( thus ceasing its diffusion ) , while the probability of another particle being accreted onto the grain , and subsequently reacting with the first particle , is smaller ( due to lower gas density ) . this results in a longer sequence of diffusion before a reaction occurs . it is to be expected that the use of larger grains would ameliorate this effect , as the current model dust grain is extremely small , providing low overall rates of accretion . conversely , higher temperatures would most likely make it worse , due to the resulting faster diffusion , although desorption rates would also increase . the inclusion of a broader network of surface species is expected to make the surface more heterogeneous , such that the smoothness of the surface potential would be reduced , minimizing the possibility that surface species may spend long periods of cpu - time without being trapped in a strong binding site .	hydrogen and oxygen atoms accrete onto the grain , to produce ho , h , o and ho . the off - lattice method allows the ice structure to evolve freely ; ice mantle porosity is found to be dependent on the gas density , which controls the accretion rate . collect within the crevices that divide nodules of ice , and within micropores ( whose extreme inward curvature produces strong local potential minima ) .	the first off - lattice monte carlo kinetics model of interstellar dust - grain surface chemistry is presented . the positions of all surface particles are determined explicitly , according to the local potential minima resulting from the pair - wise interactions of contiguous atoms and molecules , rather than by a pre - defined lattice structure . the model is capable of simulating chemical kinetics on any arbitrary dust - grain morphology , as determined by the user - defined positions of each individual dust - grain atom . a simple method is devised for the determination of the most likely diffusion pathways and their associated energy barriers for surface species . the model is applied to a small , idealized dust grain , adopting various gas densities and using a small chemical network . hydrogen and oxygen atoms accrete onto the grain , to produce ho , h , o and ho . the off - lattice method allows the ice structure to evolve freely ; ice mantle porosity is found to be dependent on the gas density , which controls the accretion rate . a gas density of , appropriate to dark interstellar clouds , is found to produce a fairly smooth and non - porous ice mantle . at all densities , h molecules formed on the grains collect within the crevices that divide nodules of ice , and within micropores ( whose extreme inward curvature produces strong local potential minima ) . the larger pores produced in the high - density models are not typically filled with h . direct deposition of water molecules onto the grain indicates that amorphous ices formed in this way may be significantly more porous than interstellar ices that are formed by surface chemistry .
1310.2512	c	this model allows porous structures within the ice mantle to form naturally , as the result of chemical and physical conditions . however , the consideration of porosity in simulations of interstellar dust - grain chemistry is not new ; perets & biham ( 2006 ) used a rate - based model to study the effects of porosity within the dust - grain structure itself . the models indicated that porosity could increase the efficiency of h@xmath0 formation over a wider range of temperatures than would otherwise be possible . taquet et al . ( 2012 ) extended the treatment of perets et al . to a full gas - grain chemical model that included the formation of a porous ice mantle , using pre - defined values for the number and sizes of pores . they found only moderate increases in the production of certain key ice - mantle species . cuppen & herbst ( 2007 ) used a monte carlo technique to treat the formation of ice on a surface with periodic boundary conditions , using a fixed lattice for the positions of particles on the grain or within the ice mantle . depending on the physical conditions , ice structures of varying compactness and porosity were produced , including some with tower - like structures of apparently single - molecule thickness . the models that show the most extreme porosity , however , were obtained assuming temperatures rather higher than the 10 k used here . in the present model , only a limited reaction set is considered , which does not include any activation barrier - mediated reactions . nevertheless , the basic reactions that allow the formation of the most important species , such as h@xmath0 and h@xmath0o , are indeed present . the use of an off - lattice approach in this model requires that the binding of atoms or molecules to the surface involve at least 3 other binding partners . thus , the `` sky - scraper '' structures produced by the models of cuppen & herbst are not found here , both because binding to a single partner can not occur and because the direction of the binding is not pre - determined , but depends on the arrangement of the binding partners . perhaps most importantly , the off - lattice approach of the present model allows the effects of the curvature of the surface to be automatically taken into account . inward curvature , such as may be found within the pores , produces stronger binding conditions resulting from the ability to bind with a greater number of partners ; likewise , the outward curvature found on the bare grain , and on the `` nodules '' or `` bulges '' that form on the ice , tend to minimize the number of binding partners . these curvature effects drive mobile particles into the pores as the pores are forming , so that they become filled with h@xmath0 , producing veins . larger pores which are formed in the higher - density models , and which experience less extreme curvature tend not to fill up in this way . the kind of micro - pores investigated by taquet et al . ( 2012 ) , which appear to be comparable in size to the h@xmath0 veins that form here , may not therefore be long - lived enough to affect the chemistry significantly . the present model indicates that such pores would be filled up , although others may develop in their place . in general , however , the low density model ( which perhaps provides the most appropriate comparison ) tends to predict a compact , albeit segregated , ice structure . the gas - phase chemical abundances used in the model presented here represent dense - cloud conditions , under which most hydrogen takes the form of h@xmath0 , resulting in similar h and o gas - phase abundances . however , higher values for h are entirely plausible , which would result in greater h fluxes onto the grains , and therefore a shorter time period before surface oxygen atoms could find alternative binding sites . it is therefore likely that a cloud with large quantities of h not yet converted to h@xmath0 should produce more porous dust - grain ices . it is also probable that , other model quantities being equal , the smallest of these pores would rapidly fill up . the consideration here of a model that involves the direct accretion of water onto the grain allows a basic comparison with laboratory amorphous solid water ( asw ) ices , which are also formed by the deposition of water molecules directly onto a cold surface . it is well known that the angle of deposition has a strong influence on the degree of porosity in the ice ( e.g. kimmel et al . 2001 ; raut et al . the present model does not investigate the effect of deposition angle directly , but uses a completely randomized field of accreting particles . the result is an extremely porous ice , which is qualitatively different from the forms produced by active grain - surface chemistry , because of the minimal diffusion of the water molecules following accretion . in the active - chemistry models , the slow formation of the ice from its constituent atoms allows voids and strong binding sites to be filled more effectively , so that the lowest - density simulations show an absence of pores , and a relatively small quantity of h@xmath0 veins as compared with higher gas - density ( i.e. faster - accretion ) models . it therefore seems appropriate to suggest that interstellar ice analogs formed in the laboratory may be significantly more porous than actual interstellar ices . this would imply that effects observed in laboratory ices , relating to the absorption of other molecules into pores and their subsequent release at higher temperatures ( e.g. collings et al . 2004 ) , may be of less importance in interstellar ice mantles . in mitigation , the present model does not include any mechanism for super - thermal surface diffusion of the accreted particle , or indeed of newly - formed surface molecules . the acceleration of the accreting particle into a surface potential well , or the release of chemical energy from the surface formation of a molecule , could provide sufficient energy for diffusion . this could allow an otherwise immobile particle to find a nearby binding site with stronger binding properties . however , in view of the experimental evidence for significant porosities in laboratory asw ice ( e.g. westley et al . 1998 , and references therein ) , the importance of this effect may be small . as shown in table 3 , for decreasing density the h@xmath0:h@xmath0o production ratio approaches 1:1 . this may be explained through a simple analysis : taking the 1:1 gas - phase abundance ratio for h : o used in the present model , the ratio of accretion rates is 4:1 , due to the 16 times higher mass of oxygen , as entered into eq . ( 1 ) . under conditions where atomic - hydrogen mobility dominates all surface processes , and accretion dominates evaporation , this rate should indeed produce a 1:1 formation rate for h@xmath0:h@xmath0o . ( for every 1 oxygen that accretes , 4 h - atoms will accrete ; 2 are used up , as they rapidly find the o / oh on the surface , to form water . the other two will on average meet each other and form h@xmath0 . ) this analysis ignores o@xmath0 and h@xmath0o@xmath0 formation , each of which would otherwise remove 4 and 2 more hydrogen atoms , respectively , if their oxygen atoms had instead formed surface water . this difference accounts for around 40% of the h@xmath0 excess over h@xmath0o in the low - density models . it may be seen , therefore , that for the lowest density simulations in particular , the production of h@xmath0 is very close to what may be called a `` smooth - grain '' limit , in which hydrogen - atom mobility is not significantly affected by the presence of strong binding sites . with increasing density , there are more strong binding sites ( due to the more irregular ice structure ) , while the waiting period for the accretion of a new particle is also shorter . these effects heighten the probability that an accreted hydrogen atom will wait for another h to react with it , rather than to diffuse to find a free oxygen atom elsewhere on the dust / ice surface , thus producing a greater proportion of molecular hydrogen . for gas densities less than @xmath5@xmath46 @xmath2 , one should expect that the ice surface would be similarly smooth , and perhaps yet more spherical , while the waiting period for accretion would be greater , all of which should produce h@xmath0:h@xmath0o ratios even closer to unity . under such circumstances , the use of rate - based models that employ generalized binding and diffusion characteristics should not produce strongly divergent results for h@xmath0 production from those obtained here , providing appropriate characteristic values were chosen . such an approach would also require that the stochastic behavior of the chemistry be treated adequately ( e.g. the use of the modified rate equations of garrod 2008 and garrod et al . 2009 ) , as the scenario described clearly falls into the case where standard rate equations should fail . it is unclear , however , whether such an approach could accurately reproduce the quantity of the resultant h@xmath0 that is retained on the grain surface , which is still determined by heterogeneous structural considerations . the choice of physical conditions investigated in the present study has been limited to the gas density , which controls the rate of accretion onto the grain . the gas density demonstrates a clear effect on the resultant ice structure , and thence on the retention of h@xmath0 molecules on the grain . the relative formation rates of o@xmath0 and h@xmath0o@xmath0 are also seen to be affected by the density variation , due to the competition between chemical reactions whose rates are dependent on surface diffusion . each of the effects mentioned above concern the interplay between accretion , diffusion and desorption . the gas density is thus not the only parameter which may affect the chemistry and structure of the ice formed on the grain . future work will address the importance of dust temperature ; however , one may predict that temperatures higher than the 10 k used here would produce more diffusion of oxygen atoms , meaning more compact ices . likewise , lower temperatures would result in more porosity , and greater retention of h@xmath0 within those structures . the present , preliminary model uses a very small grain , of radius 16 , as compared to a canonical value of 0.1 @xmath54 m ( = 1000 ) . however , the final ice - mantle radii are significantly larger , at around 150 190 . future models will investigate chemistry on larger grains . the application of the model to a porous dust grain , of explicitly defined structure , would also be quite possible .	a gas density of , appropriate to dark interstellar clouds , is found to produce a fairly smooth and non - porous ice mantle . at all densities , h molecules formed on the grains the larger pores produced in the high - density models are not typically filled with h .	the first off - lattice monte carlo kinetics model of interstellar dust - grain surface chemistry is presented . the positions of all surface particles are determined explicitly , according to the local potential minima resulting from the pair - wise interactions of contiguous atoms and molecules , rather than by a pre - defined lattice structure . the model is capable of simulating chemical kinetics on any arbitrary dust - grain morphology , as determined by the user - defined positions of each individual dust - grain atom . a simple method is devised for the determination of the most likely diffusion pathways and their associated energy barriers for surface species . the model is applied to a small , idealized dust grain , adopting various gas densities and using a small chemical network . hydrogen and oxygen atoms accrete onto the grain , to produce ho , h , o and ho . the off - lattice method allows the ice structure to evolve freely ; ice mantle porosity is found to be dependent on the gas density , which controls the accretion rate . a gas density of , appropriate to dark interstellar clouds , is found to produce a fairly smooth and non - porous ice mantle . at all densities , h molecules formed on the grains collect within the crevices that divide nodules of ice , and within micropores ( whose extreme inward curvature produces strong local potential minima ) . the larger pores produced in the high - density models are not typically filled with h . direct deposition of water molecules onto the grain indicates that amorphous ices formed in this way may be significantly more porous than interstellar ices that are formed by surface chemistry .
1310.2512	c	the model presented in this paper is the first off - lattice monte carlo kinetic model of interstellar dust - grain chemistry . the model allows the full three - dimensional simulation of chemical kinetics and ice structure on a grain surface defined by the positions of its constituent atoms . the use of an off - lattice technique allows the precise positions , binding strengths and diffusion probabilities of grain - surface particles to be determined according to the interaction potentials with binding partners ; particles are not fixed in a pre - determined lattice structure . the model also allows arbitrary morphologies and structures to be used for the underlying dust grain . this includes not only the local surface roughness of a particle , but the degree of grain porosity , as well as the choice of a spherical , spheroidal , irregular , or any other grain shape . the model opens up a large new parameter space that will be investigated in future , in conjunction with a more extensive chemical network . 1 . the shape of the ice mantle is irregular , even for low gas - density models . the porosity of the ice is strongly dependent on the gas density , with higher densities producing greater porosity . 3 . the small - scale curvature of local regions of the ice / grain surface has a strong effect on the chemistry and structure of the ice formed on top . such considerations can only be treated using an off - lattice approach . 4 . inward curvature on small scales as found with micropores allows binding with a greater number of binding partners than on a relatively flat surface . this increases desorption and diffusion barriers , encouraging the trapping of mobile species in micropores and strong surface binding sites . micropores are formed in the ices , but are rapidly filled with h@xmath0 molecules , forming veins of h@xmath0 . thus , h@xmath0 shows significant segregation from water molecules in all models . larger pores remain unfilled , as they do not provide sufficient small - scale curvature of the surface to significantly increase binding potentials . 7 . for gas densities appropriate to dark interstellar clouds ( @xmath46 @xmath2 ) , the ice mantle is fairly smooth and non - porous , albeit with veins of h@xmath0 throughout . . direct deposition of water molecules , such as is used to produce laboratory amorphous water ice , results in far greater porosity than is achieved when the ice is formed by surface reactions between accreted atoms . , then another hydrogen atom has landed , to react with oh , forming h@xmath0o . _ a video of this sequence is availble in the online version of the journal , showing one thermal hop per frame._,title="fig:",scaledwidth=49.0% ] , then another hydrogen atom has landed , to react with oh , forming h@xmath0o . _ a video of this sequence is availble in the online version of the journal , showing one thermal hop per frame._,title="fig:",scaledwidth=49.0% ] , then another hydrogen atom has landed , to react with oh , forming h@xmath0o . _ a video of this sequence is availble in the online version of the journal , showing one thermal hop per frame._,title="fig:",scaledwidth=49.0% ] , then another hydrogen atom has landed , to react with oh , forming h@xmath0o . _ a video of this sequence is availble in the online version of the journal , showing one thermal hop per frame._,title="fig:",scaledwidth=49.0% ] @xmath2 . the `` hole '' in the ice structure is caused by the comparatively weak surface potential of the underlying grain surface in that region , resulting from its geometry . _ a video of this simulation is availble in the online version of the journal , showing the formation of 1 water molecule per frame._,title="fig:",scaledwidth=32.0% ] @xmath2 . the `` hole '' in the ice structure is caused by the comparatively weak surface potential of the underlying grain surface in that region , resulting from its geometry . _ a video of this simulation is availble in the online version of the journal , showing the formation of 1 water molecule per frame._,title="fig:",scaledwidth=32.0% ] @xmath2 . the `` hole '' in the ice structure is caused by the comparatively weak surface potential of the underlying grain surface in that region , resulting from its geometry . _ a video of this simulation is availble in the online version of the journal , showing the formation of 1 water molecule per frame._,title="fig:",scaledwidth=32.0% ] lrrrrrrrr h & 100 & 100 & 50 & 100 & 100 & 100 & 100 & 100 + h@xmath0 & 50 & 50 & 50 & 50 & 50 & 50 & 50 & 50 + o & 200 & 100 & 50 & 200 & 200 & 200 & 200 & 200 + o@xmath0 & 300 & 100 & 50 & 200 & 300 & 300 & 300 & 300 + oh & 400 & 100 & 50 & 200 & 300 & 400 & 500 & 600 + h@xmath0o & 500 & 100 & 50 & 200 & 300 & 500 & 1000 & 1000 + h@xmath0o@xmath0 & 600 & 100 & 50 & 200 & 300 & 600 & 1000 & 1200 + rcccccccccccc @xmath46 & 1 & & @xmath55 & 147.1 & & 3 & 1 & 3 & 1,238 & 240 & 18,284 & 207,313 + & 2 & & @xmath56 & 152.6 & & 6 & 3 & 3 & 1,241 & 261 & 18,399 & 206,096 + & 3 & & @xmath57 & 149.1 & & 1 & 4 & 0 & 1,260 & 257 & 18,407 & 208,248 + + @xmath52 & 1 & & @xmath58 & 153.9 & & 6 & 7 & 8 & 1,599 & 304 & 23,011 & 209,973 + & 2 & & @xmath59 & 148.3 & & 9 & 4 & 5 & 1,547 & 301 & 22,998 & 206,612 + & 3 & & @xmath60 & 160.0 & & 7 & 6 & 8 & 1,523 & 325 & 23,494 & 208,044 + + @xmath53 & 1 & & @xmath61 & 164.9 & & 37 & 30 & 19 & 3,073 & 620 & 28,872 & 217,227 + & 2 & & @xmath62 & 176.0 & & 27 & 23 & 19 & 2,974 & 618 & 29,216 & 217,463 + & 3 & & @xmath63 & 178.3 & & 27 & 20 & 18 & 3,031 & 596 & 29,620 & 216,183 + + @xmath47 & 1 & & @xmath64 & 191.9 & & 72 & 42 & 52 & 5,308 & 1,321 & 32,824 & 225,258 + & 2 & & @xmath65 & 177.3 & & 60 & 53 & 45 & 5,385 & 1,233 & 31,484 & 228,142 + & 3 & & @xmath66 & 183.6 & & 81 & 42 & 42 & 5,381 & 1,281 & 33,319 & 227,244 + gibb , e. l. , whittet , d. c. b. , schutte , w. a. , boogert , a. c. a. , chiar , j. e. , ehrenfreund , p. , gerakines , p. a. , keane , j. v. , tielens , a. g. g. m. , van dishoeck , e. f. , & kerkhof , o. 2000 , , 536 , 347	the first off - lattice monte carlo kinetics model of interstellar dust - grain surface chemistry is presented . the positions of all surface particles are determined explicitly , according to the local potential minima resulting from the pair - wise interactions of contiguous atoms and molecules , rather than by a pre - defined lattice structure . direct deposition of water molecules onto the grain indicates that amorphous ices formed in this way may be significantly more porous than interstellar ices that are formed by surface chemistry .	the first off - lattice monte carlo kinetics model of interstellar dust - grain surface chemistry is presented . the positions of all surface particles are determined explicitly , according to the local potential minima resulting from the pair - wise interactions of contiguous atoms and molecules , rather than by a pre - defined lattice structure . the model is capable of simulating chemical kinetics on any arbitrary dust - grain morphology , as determined by the user - defined positions of each individual dust - grain atom . a simple method is devised for the determination of the most likely diffusion pathways and their associated energy barriers for surface species . the model is applied to a small , idealized dust grain , adopting various gas densities and using a small chemical network . hydrogen and oxygen atoms accrete onto the grain , to produce ho , h , o and ho . the off - lattice method allows the ice structure to evolve freely ; ice mantle porosity is found to be dependent on the gas density , which controls the accretion rate . a gas density of , appropriate to dark interstellar clouds , is found to produce a fairly smooth and non - porous ice mantle . at all densities , h molecules formed on the grains collect within the crevices that divide nodules of ice , and within micropores ( whose extreme inward curvature produces strong local potential minima ) . the larger pores produced in the high - density models are not typically filled with h . direct deposition of water molecules onto the grain indicates that amorphous ices formed in this way may be significantly more porous than interstellar ices that are formed by surface chemistry .
0906.2242	i	we assume that a large sparse matrix @xmath1 has full column rank and let @xmath2 be its singular value decomposition ( svd ) @xcite , where @xmath3 and @xmath4 are @xmath5 and @xmath6 orthogonal matrices , @xmath7 and @xmath8 is diagonal . @xmath9 , are called the singular values of @xmath0 , @xmath10 s and @xmath11 s are the associated left and right singular vectors , respectively , and @xmath12 s are called singular triplets . in this paper , slightly different from the convention , the singular values are labeled as @xmath13 . we are concerned with the following problem . * problem 1. _ compute numerically the @xmath14 smallest singular triplets @xmath12 of @xmath0 , @xmath15 , where @xmath16 . _ there are many applications of problem 1 , including determination of numerical rank and of spectral condition number , least squares problems , total least squares problems , regression analysis , image and signal processing , pattern recognition and information retrieval , to name a few . consider the @xmath17 augmented matrix @xmath18 then , the eigenvalues of @xmath19 are just @xmath20 and @xmath21 zeros , the associated eigenvectors of @xmath22 and @xmath23 are @xmath24 and @xmath25 , respectively , and the eigenvectors associated with zero eigenvalues have the form @xmath26 , where @xmath27 s are orthogonal to all @xmath28 . therefore , we obtain the following formulation of problem 1 . problem 2*. _ compute numerically the @xmath14 smallest positive eigenvalues and the associated eigenvectors of @xmath29 . _ for the @xmath14 smallest eigenpairs of @xmath19 , problem 2 is a symmetric interior eigenvalue problem . since @xmath30 and @xmath31 are assumed to be large , we can only resort to projection methods . a typical method is the symmetric lanczos method @xcite . it and other standard projection methods usually favor the extreme eigenvalues and the associated eigenvectors but are generally very inefficient for computing interior eigenpairs @xcite . another drawback is that in finite precision the computed eigenvalues do not come in plus - and - minus pairs and the computed eigenvectors do not respect the special structures that the true eigenvectors have . because of the mentioned drawbacks , we should not work on @xmath19 explicitly for computing the smallest singular triplets of @xmath0 . instead we attempt to solve problem 1 directly by working on @xmath29 implicitly . it appears that lanczos bidiagonalization type methods @xcite and jacobi - davidson svd type methods @xcite can solve the mentioned problems elegantly . the lanczos bidiagonalization type methods available have in common that they are all based on the lanczos bidiagonalization process to build up orthonormal bases of certain krylov subspaces . however , their mathematical backgrounds can be fundamentally different . basically , there are three kinds of projection principles that extract different approximate singular triplets with respect to the subspaces . some methods use the standard projection principle @xcite to extract ritz approximations @xcite , some methods use the harmonic projection principle @xcite to extract harmonic ritz approximations @xcite and some methods use the refined projection principle @xcite to extract refined singular vector approximations @xcite . jacobi - davidson type svd methods for problem 1 have several versions that are based on the three projection principles as well as their generalizations , respectively . as observed and claimed in @xcite , the refined extraction version appears to give the best accuracy in general . for problem 1 , due to the storage requirement and computational cost , all the lanczos bidiagonalization type methods as well as jacobi - davidson type methods have to be restarted generally in order to make them converge . that is , for given projection subspaces , if the methods do not converge , then one repeatedly chooses new better starting vectors , constructs better subspaces and computes new approximate singular triplets until they converge . the implicit restarting technique due to sorensen @xcite is a powerful tool for restarting krylov subspace algorithms in various contexts including large svd problems @xcite . the success of an implicitly restarted algorithm heavily depends on both the underlying method itself and a proper selection of the shifts involved ; see , e.g. , @xcite . based on the lanczos bidiagonalization method and one of its harmonic versions , jia and niu @xcite and larsen @xcite have developed an implicitly restarted lanczos bidiagonalization algorithm ( irlb ) , and kokiopoulou _ et al . _ @xcite have proposed an implicitly restarted harmonic lanczos bidiagonalization algorithm ( irlanb ) for computing the smallest singular triplets . irlb uses the unwanted ritz values and irlanb uses the unwanted ritz or harmonic ritz values as shifts , respectively . these shifts are called exact shifts and harmonic shifts . baglama and reichel @xcite propose a thick restarting technique that explicitly augments small subspaces with certain ritz or harmonic ritz vectors , leading to augmented restarted lanczos bidiagonalization algorithms ( irlba ) . @xcite analyze a parallel implementation of this algorithm . based on stewart s work for large eigenproblems @xcite , stoll @xcite presents a krylov - schur type algorithm that is restarted explicitly and is easily implemented . it is shown in @xcite that the lanczos bidiagonalization method may fail to compute singular vectors though it converges for computing singular values for sufficiently good subspaces . to correct this deficiency , applying the refined projection principle proposed by the first author @xcite ( see also @xcite ) , we have proposed a refined lanczos bidiagonalization method , analyzed its convergence and developed an implicitly restarted refined lanczos bidiagonalization algorithm ( irrlb ) @xcite . based on the refined approximations to singular vectors , we have proposed refined shifts that are theoretically better than the exact shifts used within irlb . numerical experiments have demonstrated that irrlb often outperforms irlb @xcite considerably and is more efficient than several other available schemes : propack @xcite , lanso @xcite , the matlab internal function svds and some others when computing the largest and smallest singular triplets . hochstenbach @xcite shows that for nested subspaces ritz values approach the largest singular values monotonically but approach the smallest ones irregularly . so the lanczos bidiagonalization method is more suitable for computing the largest singular triplets and may exhibit irregular convergence behavior when computing the smallest singular triplets . in contrast , the smallest harmonic ritz values converge to the smallest singular values monotonically from above and may be better approximations . we continue to study how to compute the smallest singular triplets more efficiently in this paper . based on the lanczos bidiagonalization process , we propose a harmonic lanczos bidiagonalization method by combining it with the harmonic projection principle . our derivation is different from that in @xcite . the method is the same as that in @xcite but different from the one in @xcite . we prove that for good enough projection subspaces harmonic ritz values converge if the columns of @xmath0 are strongly linearly independent . on the other hand , harmonic ritz values may miss some desired singular values when the columns of @xmath0 are almost linearly dependent . so harmonic ritz values may not be reliable . furthermore , harmonic ritz vectors may converge irregularly and even may fail to converge . these results imply that either implicitly or explicitly restarted algorithms may converge very slowly , converge irregularly or fail to converge . to circumvent these drawbacks , combining the harmonic projection principle with the harmonic projection principle , we propose a refined harmonic lanczos bidiagonalization method that takes the rayleigh quotients of harmonic ritz vectors as more accurate and reliable approximate singular values and extracts the best approximations to the desired singular vectors from the given subspaces that minimize the residuals formed with the rayleigh quotients . we prove that refined harmonic ritz approximations converge once the krylov subspaces are good enough and the rayleigh quotients converge . we then develop an implicitly restarted refined harmonic lanczos bidiagonalization algorithm ( irrhlb ) . based on the refined harmonic ritz approximations to the desired singular vectors , in the spirit of jia s work @xcite , we propose a new shifts scheme , called the refined harmonic shifts , that we show to be theoretically better than the harmonic shifts used within the implicitly restarted harmonic lanczos bidiagonalization algorithm ( irhlb ) and irlanb . motivated by @xcite , we propose an efficient procedure to compute the refined harmonic shifts accurately . it is worth noting that kokiopoulou _ _ @xcite also use the refined projection principle to compute the refined harmonic ritz approximations . they exploit the lower lanczos bidiagonalization process , use the ritz or harmonic ritz values as shifts in the algorithm and compute the smallest singular triplets one by one by exploiting deflation . they only use the refined projection principle as refinement postprocessing at the end of each restart . the authors demonstrate that computing refined ( harmonic ) ritz vectors and thus refined ritz values benefits the overall convergence process . in particular , they show that while convergence is not apparent in terms of harmonic residual norms , monitoring refined residuals predicts convergence more accurately and safely . in contrast , based on the upper lanczos bidiagonalization process and the refined projection principle , we propose a truly new method the refined harmonic lanczos bidiagonalization method that computes refined harmonic ritz vectors as new approximations . we then develop irrhlb with use of the new better shifts , called refined harmonic shifts , based on refined harmonic ritz approximations . irrhlb computes all the desired smallest singular triplets simultaneously . the paper is organized as follows . in 2 , based on the lanczos bidiagonalization process , we derive the harmonic lanczos bidiagonalization method and then present some basic and important properties of approximate singular vectors to be used later . exploiting jia s results in @xcite , we then make a convergence analysis . in 3 we propose the refined harmonic lanczos bidiagonalization method . we prove that the refined harmonic ritz approximations converge for good enough subspaces once the rayleigh quotients converge . in 4 , we consider selection of the shifts involved . for irhlb , similar to what is done in @xcite , we use the harmonic ritz values . for irrhlb , by exploiting the available refined harmonic ritz approximations , we propose the refined harmonic shifts that are proved to be theoretically better than the harmonic shifts . we then present an efficient procedure to compute them . we show that in finite precision the refined harmonic shifts can be computed accurately . meanwhile , we extend the adaptive shifting strategy proposed by larsen @xcite and modified by jia and niu @xcite to irhlb and irrhlb . in 5 , we report numerical results and compare irrhlb with the five other state of art algorithms : irhlb , irrlb , irlb , irlanb and irlba , indicating that irrhlb is at least competitive with the five other algorithms and can be considerably more efficient when computing the smallest singular triplets . finally , we conclude the paper with some remarks in 6 . we introduce some notations to be used . denote by @xmath32 the spectral norm of a matrix and the vector 2-norm , by @xmath33 , by @xmath34 the @xmath35-dimensional krylov subspace generated by the matrix @xmath36 and the starting @xmath37 , by the superscript ` t ' the transpose of a matrix or vector , by @xmath38 the identity matrix with the order clear from the context and by @xmath39 the @xmath35-th coordinate vector of dimension @xmath35 .	we prove that for good enough projection subspaces harmonic ritz values converge if the columns of are strongly linearly independent . on the other hand , harmonic ritz values may miss some desired singular values when the columns of almost linearly dependent . furthermore , harmonic ritz vectors may converge irregularly and even may fail to converge . based on the refined projection principle for large matrix eigenproblems due to the first author , we propose a refined harmonic lanczos bidiagonalization method that takes the rayleigh quotients of the harmonic ritz vectors as approximate singular values and extracts the best approximate singular vectors , called the refined harmonic ritz approximations , from the given subspaces in the sense of residual minimizations . the refined approximations are shown to converge to the desired singular vectors once the subspaces are sufficiently good and the rayleigh quotients converge . an implicitly restarted refined harmonic lanczos bidiagonalization algorithm ( irrhlb ) is developed . we study how to select the best possible shifts , and suggest refined harmonic shifts that are theoretically better than the harmonic shifts used within the implicitly restarted lanczos bidiagonalization algorithm ( irhlb ) . numerical experiments are reported that compare irrhlb with five other algorithms based on the lanczos bidiagonalization process . it appears that irrhlb is at least competitive with them and can be considerably more efficient when computing the smallest singular triplets . singular values , singular vectors , svd , lanczos bidiagonalization , refined projection , harmonic , refined harmonic , implicit restart , harmonic shifts , refined harmonic shifts . 65f15 , 15a18	the harmonic lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix . we prove that for good enough projection subspaces harmonic ritz values converge if the columns of are strongly linearly independent . on the other hand , harmonic ritz values may miss some desired singular values when the columns of almost linearly dependent . furthermore , harmonic ritz vectors may converge irregularly and even may fail to converge . based on the refined projection principle for large matrix eigenproblems due to the first author , we propose a refined harmonic lanczos bidiagonalization method that takes the rayleigh quotients of the harmonic ritz vectors as approximate singular values and extracts the best approximate singular vectors , called the refined harmonic ritz approximations , from the given subspaces in the sense of residual minimizations . the refined approximations are shown to converge to the desired singular vectors once the subspaces are sufficiently good and the rayleigh quotients converge . an implicitly restarted refined harmonic lanczos bidiagonalization algorithm ( irrhlb ) is developed . we study how to select the best possible shifts , and suggest refined harmonic shifts that are theoretically better than the harmonic shifts used within the implicitly restarted lanczos bidiagonalization algorithm ( irhlb ) . we propose a novel procedure that can numerically compute the refined harmonic shifts efficiently and accurately . numerical experiments are reported that compare irrhlb with five other algorithms based on the lanczos bidiagonalization process . it appears that irrhlb is at least competitive with them and can be considerably more efficient when computing the smallest singular triplets . singular values , singular vectors , svd , lanczos bidiagonalization , refined projection , harmonic , refined harmonic , implicit restart , harmonic shifts , refined harmonic shifts . 65f15 , 15a18
1103.0162	i	the hole - doped antiferromagnetic spin-@xmath0 two - leg ladder is used as a model system , theoretically as well as experimentally , for the two - dimensional cuprate superconductors . because the spin ladder is quasi one - dimensional it can more easily be treated by numerical and analytical approaches than the full two - dimensional model . for this reason the spin ladder was subject to many theoretical investigations in recent years @xcite . from a strong coupling perspective it is reasonable to describe the doped spin ladder by a @xmath2-@xmath3-model @xcite . in this paper , our aim is to derive an effective hamiltonian which describes not only the motion of the magnetic degrees of freedom , i.e. , the triplons @xcite , but also of the charges , i.e. , of the doped holes . this task is more challenging than the description of the triplons alone because the two kinds of excitations interact strongly and their energy ranges are not separated but they strongly overlap . hence the excitations are not infinitely long - lived but they decay , at least in certain regions of the brillouin zone . the technique employed here is the approach of self - similar continuous unitary transformations ( scut ) . in this approach the mapping of the true ground state to a vacuum of elementary excitations is constructed systematically , details will be explained in sect . [ chap : scut ] . the basic idea is to implement a transformation that adjusts itself during the procedure of the diagonalisation depending on the current form of the hamiltonian at this instant of the continuous transformation . the change of the hamiltonian induced by the transformation is determined by the current magnitude of the non - diagonal elements . the flowing hamiltonian is given in second quantization , i.e. , it has a certain structure in terms of elementary creation and annihilation operators @xcite . this formulation incorporates the linked cluster property @xcite automatically . the scut systematically defines a set of differential equations for the prefactors of the monomials of the creation and annihilation operators . the key issue is to construct the flow to the effective hamiltonian in a robust way . due to the energetically overlapping states this goal required modifications @xcite with respect to the previously performed unitary transformations . thereby we achieved the successful calculation of the dispersion of a single hole . in sects . [ chap : hole disp without ring exc ] and [ chap : hole disp with ring exc ] we investigate the dispersions of single hole excitations obtained from the effective hamiltonians , which are results of the scut . we also compare our results to the results of other methods . sects . [ chap : summ ] and [ chap : outlook ] conclude this article with a summary and perspectives for future work .	the hole - doped antiferromagnetic spin- two - leg ladder is an important model system for the high- superconductors based on cuprates . using the technique of self - similar continuous unitary transformations we derive effective hamiltonians for the charge motion in these ladders . the key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit .	the hole - doped antiferromagnetic spin- two - leg ladder is an important model system for the high- superconductors based on cuprates . using the technique of self - similar continuous unitary transformations we derive effective hamiltonians for the charge motion in these ladders . the key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit . a real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space . from the effective hamiltonians we calculate the dispersions for single holes . further calculations will enable the calculation of the interaction of two holes so that a handle of cooper pair formation is within reach .
0811.4734	i	nowadays microresonators ( disk- , ring- , and spherical - shaped ) evoke considerable interest because new possibilities have recently opened up to develop these types of resonators in the optical frequency range and to utilize them as oscillation systems for optical lasers @xcite . when used in lasers , such oscillation systems offer a number of serious advantages , among which are low - threshold currents , a high quality of the radiation spectrum , etc . microresonators manufactured as a dielectric disk whose diameter is large as compared to the wave length of the radiation are nothing else but the open quasi - optical dielectric disk resonators which have long been known in the resonator technology for their potential to effectively sustain the electromagnetic ( em ) field inside the resonator volume . the retention of the field is provided due to the total internal reflection ( tir ) from the resonator side boundaries of waves making up resonance oscillations . as a result , em oscillations of whispering gallery ( wg ) type arise . as far as their excitation is not accompanied by the additional dissipative loss , superhigh quality factors are achieved in the ddrs . specifically , in laser systems , in spite of ddr s microscopic dimensions ( the disk diameter is normally about a few @xmath0 m large ) , the quality factors can reach the order of @xmath1 and even more @xcite . the high quality factors of the ddrs , that are often prepared from doped silicon , are generally provided not only due to extremely small loss attainable in this material but also governed by resonator geometry and the perfection of the crystal it is made of . with a certain number of inhomogeneities ( local and/or non - local , random and/or regular ) in the resonator material , the ray picture of em fields in the resonator changes dramatically as against its perfectly homogeneous counterpart . the inhomogeneities give rise to local violation of tir conditions and in this way result in additional energy loss which is evident in the quality factor drop . from the above said there arises the problem of studying the effect produced by random inhomogeneities in the ddrs on their spectral characteristics . in the theoretic analysis of the radiation loss of the ddr two types of inhomogeneities are normally distinguished . to the first type the inhomogeneities of volume nature belong , which are related to regular or random spatial variations of the permittivity in the bulk of the material the ddr is made of . the other class of inhomogeneities includes the so called `` surface '' imperfections normally related to the deviation of the ddr shape from the ideal cylindrical one . the influence of bulk random inhomogeneities on the resonance spectrum was previously studied by the present authors in the particular case of cavity resonators filled with randomly distributed dielectric particles @xcite . it was found that the physical mechanism through which inhomogeneities affect resonator spectrum is basically the intermode scattering . in the case of quasi - optical cavity resonator the peculiar feature of this type of scattering is the selective impact of inhomogeneities on different resonance lines . the most affected lines appear to be those which are the least separated on the frequency axis , whereas solitary lines are subjected to much lesser influence . owing to such a selective effect of random inhomogeneities , the originally dense spectrum of the quasi - optical cavity resonator is considerably rarefied . in refs . @xcite , the investigations were undertaken into the impact of _ surface _ inhomogeneities on spectral properties of open dielectric resonators of cylindrical and spherical shape . the influence of boundary roughness upon the resonance lines was described by means of the simplified quasi - geometric approach where em oscillations scattering due to edge inhomogeneities is taken into account by incorporating into the wave equation the fictitious polarization currents ( pc ) randomly distributed in space @xcite . in particular , within the framework of the model adopted in ref . @xcite the electromagnetic fields close to the resonator side surface were considered as being excited by randomly distributed near - surface current sources whose physical parameters were phenomenologically expressed through statistical characteristics of boundary asperities . it was precisely the radiation produced by these sources that led to the radiation loss of the resonator and , consequently , to the quality factor reduction . such an essentially phenomenological approach to the description of the effect produced by the roughness of open resonator boundaries on its spectral properties can not be reckoned as satisfactory . the volume current method suggested in ref . @xcite , which formed the basis for the pc concept , is , to a large extent , rough and approximate . in this method , the radiation loss is most frequently calculated using green function of the helmholtz equation . the particular form of this function is normally chosen proceeding from the prospective solution of wave equation in the far wave zone . meanwhile , the very notion of the far zone is poorly defined for multiple sources located around the periphery of the quasi - optical ddr we deal with in this particular work . specifically , when deriving characteristic equations for open ddr eigen - frequencies , one needs to join em field components exactly at the boundaries of the system under consideration . at this point a significant uncertainty can arise because the actual external fields subject to _ local _ joining with the internal ones in the presence of surface roughness can deviate considerably from the fields approximated into the boundary vicinity from large distances , i.e. from the far wave zone . to correctly determine the em fields near the random - inhomogeneous resonator surface the theories specially adapted for the description of classic and/or quantum wave scattering by rough interfaces should be applied ( see , e.g. , refs . these theories are generally applicable to the cases where wave scattering by random rough surfaces is in a sense weak . typically , this implies fluctuations of system boundaries to be relatively small in height and sufficiently smooth , so that the applicability of rayleigh hypothesis @xcite was not violated . however , for confined systems like the ddr considered in this work the issues pertinent to wave scattering by surface inhomogeneities appear to be much more complicated . firstly , in practice the inhomogeneities are not always small enough , as well as sufficiently smooth , therefore the conditions for scattering weakness are easily violated . moreover , as the resonance ray trajectories in high-_q _ resonators are periodic , the effect of oscillation scattering caused by the boundary roughness is `` path''-accumulated . scattering can become strong even though the asperities are small - in - height and smooth . this makes the applicability of the above - mentioned theories of rough - surface scattering in the case of high - quality resonators highly questionable . in refs . @xcite , the novel transport theory was developed for waveguide - shaped systems with random rough boundaries . in the framework of this theory it was revealed that the wave scattering resulting from fluctuations of inter - media surfaces can be efficiently described in terms of two physical mechanisms , namely , the _ amplitude _ and the _ gradient _ ones . for the first mechanism it is just the mean - square height of the asperities that serves as a main guiding parameter , whereas for the second one the mean slope of the asperities or , in other words , their sharpness , plays the decisive role . both of these mechanisms contribute additively to the scattering amplitude , but partial probabilities pertaining to them may differ essentially . it was shown in @xcite that , in most cases , the role of the gradient scattering appears to be prevalent . yet there have been no experimental confirmations of this fact in the literature so far . apart from peculiar problems associated with surface nature of scattering in edge - disordered resonators , some more questions arise which need to be resolved when studying the spectra of ddrs subject to surface inhomogeneities . among these questions , particularly , are those related to the vector nature of fields which are excited in these essentially non - integrable systems . it is known that even for ideal cylindrical ddrs the electrical- and magnetic - type oscillations can not be separated in the strict sense . they always remain to the certain extent intermixed @xcite . this fact renders theoretic analysis of such systems spectra rather sophisticated . spectral properties of ddrs without random inhomogeneities were examined in a number of theoretical papers ( see , e.g. , refs . @xcite ) . yet , in deriving characteristic equations some inexact _ a priori _ assumptions where used , which still require both theoretical grounding and experimental corroboration . in our present study , one of the goals is to investigate theoretically the physical mechanisms responsible for widening resonance lines of dielectric microresonators with random surface inhomogeneities . in view of such systems being non - integrable , it is necessary to elaborate an appropriate theoretical model allowing for sufficiently accurate determination of both the frequency spectrum and the quality factors of resonance lines . yet another goal of this study is to corroborate experimentally which of the physical mechanisms does play a dominant role in the scattering of em oscillations excited in microresonators with random rough side boundaries . from the theoretical viewpoint , the spectrum analysis in our study is carried out in terms of scalar potentials , specifically , electrical and magnetic hertz functions @xcite . we formulate the conditions wherein these potentials make independent contributions to em fields in the resonator , which is equivalent to decoupling the oscillations of te and tm polarization . the helmholtz equation for hertz potentials in an irregular - shaped open resonator is equivalent to schrdinger equation for electrons moving in the piecewise continuous space subject to random potential . owing to this one can extend the results obtained in the present study to quantum systems as well , in particular , to open quantum dots having random rough boundaries . to solve wave equations in the rough - bounded resonator , the eigen - mode separation method is used , previously developed with reference to waveguide - like systems subject to arbitrary static potential @xcite ) . using this method , the originally posed statistical problem of determining the fields in three - dimensional ddr with complex , randomly rough , side boundary is rigorously reduced to the set of one - dimensional dynamic equations that contain some _ effective _ random potentials . we show that under the conditions where gradient scattering mechanism is dominant , the boundary roughness effect on the resonator spectrum can be described through certain renormalization of mode wave numbers and azimuth indices of the bessel functions in the characteristic equation . the values of renormalized wave numbers and mode indices decrease as the asperities get sharpened , which is consistent with a decrease in the resonator _ q_-factor . we are thus led to the conclusion that the observed reduction of resonant line quality factors results not from the extra dissipative loss but rather from em field intermode rayleigh scattering induced by random surface inhomogeneities . the imperfection of the resonator shape results in the local violation of the tir conditions . this leads to additional radiation loss of em energy and , hence , to a decrease in the level of localization of em fields inside the resonator . since characteristic dimensions of surface inhomogeneities in actual microresonators are always quite small ( of the order of nanometers ) , to verify our theoretical findings experimentally we have decided upon the method of simulation with macroscopic devices . as a model system we have employed a millimeter wave quasi - optical resonator made of a circular teflon disk . wg oscillations of te and tm types were excited in the disk using a special waveguide antenna . the inhomogeneities of the resonator side boundary were made in the form of teflon bracket - bars randomly attached to the outside cylindrical surface . our experimental results have demonstrated excellent qualitative agreement with the developed theory as regards spectral lines widening caused by the resonator side boundary roughness . furthermore , the relatively simple model of the ddr field distribution , which was adopted in our study , enabled us to calculate both the _ q_-factors and the frequencies of the resonance lines with quite satisfactory accuracy . the calculations appeared to be in fair conformity with our experimental data .	is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential . we prove theoretically that it is the gradient mechanism of wave - surface scattering which is the highly responsible for non - dissipative loss in the resonator . the influence of side - boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation . to study experimentally the effect of inhomogeneities on the resonator spectrum , the method of modeling in the millimeter wave range is applied . as a model object our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen - frequencies and the _ q_-factors of resonance spectral lines to fairly good accuracy .	the influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally . to solve the equations governing the dynamics of electromagnetic fields the method of eigen - mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential . we prove theoretically that it is the gradient mechanism of wave - surface scattering which is the highly responsible for non - dissipative loss in the resonator . the influence of side - boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation . to study experimentally the effect of inhomogeneities on the resonator spectrum , the method of modeling in the millimeter wave range is applied . as a model object we use dielectric disc resonator ( ddr ) fitted with external inhomogeneities randomly arranged at its side boundary . experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism . it is shown theoretically and confirmed in the experiment that tm oscillations in the ddr are less affected by surface inhomogeneities than te oscillations with the same azimuth indices . the ddr model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen - frequencies and the _ q_-factors of resonance spectral lines to fairly good accuracy . the results of calculations agree well with obtained experimental data .
0811.4734	r	the main goal of experimental studies in this work was to validate our theory as regards microresonator spectra and the effect of random surface inhomogeneities on them . the point is that essential assumption adopted in the theory is that it virtually does not consider electromagnetic fields radiated from the resonator external edges into the corner regions labeled by numbers 4 and 4@xmath125 in fig . [ fig5 ] ( see appendix [ unperturbed_spectrum ] ) . at the same time , without making quite complex calculations one can not make _ a priori _ statements about these fields being small enough to neglect them in calculating the resonator spectrum . yet another goal of the experiment was to examine our theoretical findings concerning the physical mechanism that adequately describes the influence of random surface inhomogeneities on microresonator spectral properties . the studies of the microresonator spectrum were performed through modeling these quite small systems in the millimeter wave band . for this purpose we used a quasioptic dielectric disk resonator . physically , oscillation properties of this macroscopic system are identical with properties of silicon microresonators used as oscillation systems in real optical lasers . our resonator was made of teflon whose permittivity is not significantly far from unity ( @xmath126 ) and whose dielectric loss in the millimeter range are fairly small ( @xmath127 ) . in the model ddr , whispering gallery oscillations were excited with the em field concentrated at the periphery of the disk , in the narrow region close to its side boundary . this enabled us to use the disk core to fix it in the level position without introducing additional dissipative losses to the experiment . the source of wg modes was positioned close to the resonator side boundary . its role was played by the waveguide antenna powered by the microwave generator . the antenna was fabricated as a waveguide tapered along the short wall , whose butt end was positioned near the resonator side surface . the receiving antenna was made identical to the source antenna and was placed at the diametrically opposite point off the disk . thin dielectric bracket - bars were used as the inhomogeneities of the resonator side boundary . they were attached to the ddr side surface . the basic requirement imposed on the inhomogeneities was for them not to cause noticeable additional dissipative losses . to this end , the bracket - bars [ .75 ] the gap between the antenna and the ddr s side surface , which is used to tune the coupling of antenna with the resonator . the diameter of the ddr is 102 mm , the thickness is 7.6 mm . the inhomogeneities dimensions are : the length , the width , and the thickness 7.6 mm , 3 mm , and 2 mm , respectively . [ fig2],title="fig : " ] were made of the same teflon as the resonator body . the inhomogeneities distribution on the resonator side surface was random and varied for each different realization . in fig . [ fig2 ] , the general view of the resonator is shown along with the exciting and the receiving antennas as well as with the attached teflon bracket - bars . in order to excite te or tm oscillations in the resonator , two different configurations of antenna - versus - resonator were used . for te oscillations the antenna magnetic field was directed along the resonator axis , @xmath3 . to achieve this , the wide plate of the waveguide was aligned parallel to this axis . in the case of tm oscillations , along the axis @xmath3 the electric field was directed . for this purpose the wide side of the antenna was oriented transversely . by changing the distance between the exciting waveguide butt end and the resonator side boundary , as well as the angle between them , we were able to adjust the coupling between the antenna and the resonator to optimize it . as the optimal coupling we accepted the one whereby the additional loss caused by the antenna was much less than the eigen - loss in the resonator . at the same time , it was necessary to keep the level of the coupling sufficient for spectral lines to be traceable . the pattern of whispering gallery em fields in the ddr in known to be very sensitive to the frequency variation . therefore the resonator - to - waveguide coupling is different for each of the modes . based upon this , we established the optimal coupling for each of the spectral lines separately while carrying out the measurements in a wide frequency range . spectral measurements with the model resonator were made in the on - pass regime using millimeter waveband standing - wave ratio meter . since the experiments were conducted over a wide range of frequencies and for large number of realizations of surface inhomogeneities , all spectral measurements were rendered automatic . the signal from the ratio meter was sent to the computer and processed by means of the especially designed program to find both the frequencies and the quality factors of resonance lines . the accuracy of the measurements was 0.01% and 5% for the resonance frequencies and the quality factors , respectively . to identify the spectral lines , it was necessary to determine the value of azimuth index for each of the lines in the absence of inhomogeneities . to this end , the miniature rotating probe made of a thin metal plate was used , which we inserted into the region at the resonator disk where the electric field antinode was positioned . in so doing , the source was tuned to the frequency of the particular spectral line . when the probe rotated about the resonator axis , the signal registered by the receiver varied in time at the rate the probe passed across the regions with electric field loops . this enabled us to determine the desired mode index through the measurements of the signal modulation frequency . in fig . [ fig3 ] , the results of numerical calculations of the resonator spectrum are shown along with spectral measurements data . as seen from fig . [ fig3]a , the measured spectra of te and tm modes correlate well with the calculated spectra . the difference between spectral line frequencies found from eq . , including intrinsic . for @xmath128 mode : 1 calculation , 2 experiment ; for @xmath129 mode : 3 calculation , 4 experiment . [ fig3],title="fig : " ] . for @xmath128 mode : 1 calculation , 2 experiment ; for @xmath129 mode : 3 calculation , 4 experiment . [ fig3],title="fig : " ] dissipation loss in the dielectric , and experimentally measured frequencies is no more than 1% . the quality factors obtained in the experiment ( as shown in fig . [ fig3]b ) are smaller than those calculated theoretically . we attribute this to the fact that the measured @xmath130-factor includes not only eigen - loss in the resonator material but also is affected by the loss resulting from coupling with the antenna . from the diagrams in fig . [ fig3 ] one can observe the nearly equidistant character of the spectrum ( the frequency interval @xmath131 ghz ) , which is typical for open resonators with wg - type oscillations @xcite , as well as the exponential dependence on the mode index @xmath54 of the calculated and the measured @xmath130-factors . our calculations suggested , and that was experimentally confirmed , that for tm oscillations the resonator quality factor is significantly larger than that for te oscillations , both of them being taken with the same azimuth index . this suggests that in the case of tm oscillations the ddr has the property to more efficiently retain electromagnetic field in its volume than the resonator with te oscillations does . we have thus established that both the theoretical model of the resonator we have chosen for our calculations and the characteristic equations obtained thereupon have found impressive experimental confirmations . according to the findings of our theory , the main physical mechanism for em field scattering by random inhomogeneities of the resonator side boundaries is the gradient mechanism . the scattering arisen due to fluctuations in the asperity slope can be allowed for by way of modification of the cylindrical functions indices along with the wave numbers in the characteristic equation eq . . the modification reduces to multiplying the parameters @xmath54 , @xmath119 , @xmath123 and @xmath122 by factor of @xmath132 . in order to identify the main scattering mechanism experimentally and thus to check the developed theory it was necessary to estimate the value of the parameter @xmath39 starting from the parameters relevant to a particular experiment . we were governed by the following considerations . setting the correlation length equal to an average distance between the centers of the attached dielectric bracket - bars , i.e. , @xmath133 , where @xmath134 is the total number of the bracket - bars , with gaussian distributed inhomogeneities we obtain @xmath135^{-1/2}\ .\ ] ] it can be easily seen that the parameter @xmath136 tends to decrease with an increasing number of bracket - bars , which leads to a decrease in the effective wave number @xmath137 and the effective mode index @xmath138 . since the dependence of the quality factor on the mode index is nearly exponential , @xmath139 , the availability of surface inhomogeneities should result in the decrease in the resonator quality factor , whose origin is not an additional dissipative loss . according to our theory , with a small number of inhomogeneities the effect of slope - controlled scattering must be fairly slight ( the parameter @xmath39 decreases with lowering @xmath134 ) . therefore the value of quality factor must be weakly dependent on @xmath134 as well . such was indeed the case in our experiments whose results are depicted in fig . [ fig4 ] . [ .58]-factor curves versus the number of inhomogeneities on the resonator side surface . @xmath140 oscillations : 1 theory , 2 experiment ; @xmath141 oscillations ; 3 theory , 4 experiment . calculations were carried out at @xmath142 mm and @xmath143 mm . [ fig4],title="fig : " ] in the same figure , the curves @xmath144 are plotted for comparison , which are calculated from characteristic equation including modification factor @xmath136 and the dissipation loss in the resonator material . the loss was taken into consideration phenomenologically , by adding the imaginary part to permittivity @xmath145 , see eq . . with the statistical nature of our measurements ( the averaging is done over a large number of realizations of the bracket - bar set ) , the agreement between theoretical and experimental results appears to be quite satisfactory . this suggests that , since both in our theory and in the numerical calculations based upon it the slope scattering mechanism alone is taken into account , the qualitative agreement between theory and experiment unambiguously corroborates the dominant role of this particular type of wave - surface scattering . as is also seen from fig . [ fig4 ] , the influence of surface inhomogeneities on the ddr spectrum differs significantly for te- and tm - type oscillations . the quality factors of te oscillations are to a far larger extent subjected to the resonator boundary roughness as against the factors of tm oscillations . with a given number of inhomogeneities , the @xmath130-factor of te oscillations is noticeably smaller than that of tm oscillations . this fact , which is quite important for practical applications of microresonators in laser oscillation systems , was given certain attention in ref . yet in the present work it has been comprehensively substantiated .	the influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally . to solve the equations governing the dynamics of electromagnetic fields the method of eigen - mode separation we use dielectric disc resonator ( ddr ) fitted with external inhomogeneities randomly arranged at its side boundary . the results of calculations agree well with obtained experimental data .	the influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally . to solve the equations governing the dynamics of electromagnetic fields the method of eigen - mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential . we prove theoretically that it is the gradient mechanism of wave - surface scattering which is the highly responsible for non - dissipative loss in the resonator . the influence of side - boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation . to study experimentally the effect of inhomogeneities on the resonator spectrum , the method of modeling in the millimeter wave range is applied . as a model object we use dielectric disc resonator ( ddr ) fitted with external inhomogeneities randomly arranged at its side boundary . experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism . it is shown theoretically and confirmed in the experiment that tm oscillations in the ddr are less affected by surface inhomogeneities than te oscillations with the same azimuth indices . the ddr model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen - frequencies and the _ q_-factors of resonance spectral lines to fairly good accuracy . the results of calculations agree well with obtained experimental data .
1507.06168	i	due to the local nature of the problem - , we recall the notion of _ smooth germs _ around a base point . two maps are considered as _ germ - equivalent _ when both maps are locally identical ; more precisely , when there exists a neighborhood of the base point so that both maps are equal on the neighborhood . a _ germ _ is a _ germ - equivalence _ class of a smooth map . we denote @xmath9 for the set of all scalar smooth germs whose base point is the origin . from now on we merely work with elements of @xmath9 rather than a scalar smooth map ; see @xcite . following ( * ? ? ? * chapter 7 ) and @xcite , we study the local zeros of maps when there is only one distinguished parameter denoted by @xmath10 , i.e. , [ eq1 ] g : , g(x,)=0,g(0,0)=g_x(0,0)=0 , m:=1 . the effect of additional parameters may be treated by study of their small perturbations . the main goal of this theory is to classify _ qualitative _ types of equation and its arbitrary small perturbations . in order to achieve this goal , we first define a _ qualitative property _ as a property that is invariant under an appropriate equivalence relation . here , we use _ contact - equivalence _ relation : * we say that the germs @xmath11 and @xmath12 are contact - equivalent when there exist a smooth germ @xmath13 and diffeomorphic germs @xmath14 and @xmath15 such that [ conteqvl ] g(x,)= s(x,)h(x(x , ) , ( ) ) , where @xmath16 @xmath17 and @xmath18 other alternative equivalences have also been reported in the literature based on their applications ; e.g. , see @xcite where _ right - left _ and _ strategy equivalences _ have been used . _ right equivalence _ is also used to study the isolated hypersurface of geometric singularities and to study the bifurcation analysis in _ catastrophe theory _ ; see @xcite . the contact - equivalence is here used , since it is the most natural equivalence relation preserving the zero structures . now we briefly describe the approach in singularity theory and how the computational algebraic tools may help to implement them . to study the local zeros of , we choose a representative ( say @xmath5 ) from contact - equivalent class of @xmath11 that is considered to be the _ simplest _ for the analysis and call it a _ normal from_. in order to compute the normal form of a singular germ , we need to compute certain ideals in the _ local ring of smooth germs_. this signifies the importance of the well - known ideal membership problem in algebraic geometry , that is , deciding what kinds of germs belong to an ideal generated by a given set . one may study the zero structures of the normal forms and then , conclude about the solution behavior of equation . for instance , let [ exmp1 ] g(x , ) : = ( x^2)+2(x)-3+().using the command @xmath19 in singularity , we obtain its normal form by @xmath20 the bifurcation diagrams of @xmath5 and @xmath11 are depicted in figure [ a ] and [ b ] . here , @xmath21 provides an approximation @xmath22 modulo degree 5 for @xmath23 which transforms @xmath11 into @xmath5 via equation . the locally invertible transformation @xmath24 sends the bifurcation diagram of @xmath5 into that of @xmath11 . real life problems can not be perfectly modeled by a system of equations and _ imperfections _ are always inevitable . furthermore , the singularity of a germ @xmath11 implies that the zeros of a small perturbation of @xmath25 say [ unfold ] h(x , , ) = 0 , h(x , , 0)=g ( x , ) , may behave substantially different than what the zero structure associated with @xmath26 does . the parameterized germ @xmath12 in is called an _ unfolding _ of @xmath27 hence , _ modeling imperfections _ and the possible existence of additional parameters in a model are the main obstacles of simply using normal forms of a singular germ for the qualitative understanding of a real life problem . thus , the approach needs to be refined through the notion of _ universal unfolding_. in fact , we are interested to find a parameterized family like [ eq4 ] g(x , , ) = 0 , ^p , such that for any small perturbation @xmath28 , the germ @xmath29 would be contact - equivalent to @xmath30 for some germ @xmath31 we call such germ @xmath32 a _ versal unfolding _ of @xmath27 a versal unfolding with the minimum possible number of parameters is called a _ universal unfolding _ for @xmath11 ; see ( * ? ? ? * definitions 6.4.2 and 6.4.3 , page 176 ) and ( * ? ? ? * definitions 1.1 and 1.3 , pages 120121 ) . the number of parameters in a universal unfolding is named the _ codimension _ of @xmath27 the universal unfolding accommodates any possible modeling imperfections , any arbitrary small perturbation and also the existence of any possible number of parameters ( in addition to the distinguished parameter @xmath33 in order to derive the universal unfolding of a given singularity , the computation of a vector space called _ tangent space _ or instead a basis for its complement is required . using singularity s command @xmath34 for @xmath11 in gives rise to [ univexmp ] g(x , , _ 1 , _ 2):= x^4++_1x+_2x^2 . _ bifurcation diagram classification _ of the universal unfolding gives an insight to the zero structure of a germ and any of its perturbations . this is studied by the notion of _ persistence _ in the bifurcation diagrams . in fact a bifurcation diagram is called _ persistent _ when all its small perturbations remain self contact - equivalent , and otherwise it is called _ nonpersistent_. finding nonpersistent systems and their associated subset of the parameter space ( the so - called _ transition set _ @xmath35 ) play a central role in this classification . more precisely , all parametric germs associated with parameters in a connected component of @xmath36 complement of @xmath37 are contact - equivalent . therefore by choosing a parameter from each connected component of @xmath36 a complete list of persistent bifurcation diagrams modulo contact - equivalent is obtained . the non - persistence may either originate from a local nature or be caused by the singular boundary conditions . local nonpersistent bifurcation diagrams are determined with families of germs associated with three semi - algebraic parameter spaces of codimension one ; i.e. , _ bifurcation _ @xmath38 , _ hysteresis _ @xmath39 and _ double limit point _ @xmath40 ; see ( * ? ? ? * page 140 ) for details . nonpersistent germs associated with boundary conditions add extra complications into the solution dynamics , when bifurcation diagrams cross the boundary ; see ( * ? ? ? * pages 154165 ) . given our description for any finite codimension singularity , the connected components of the complement set of the transition set , i.e. , @xmath41 provide the qualitative classification of persistent bifurcation diagrams . the command @xmath42)$ ] for @xmath32 in gives @xmath43 and @xmath44 the transition set @xmath35 is plotted in figure [ c ] . @xmath45 plots a complete list of all contact - inequivalent types of persistent bifurcation diagrams for @xmath32 ; see the second row in figure [ fig1 ] .	the local zero structure of a smooth map may _ qualitatively _ change , when the map is subjected to small perturbations . the changes may include births and/or deaths of zeros . singularity_. the local bifurcation analysis of singularities has been extensively studied in _ singularity theory _ and many powerful algebraic tools have been developed for their study . we provide some required criteria along with rigorous proofs for efficient and cognitive computer - implementation . we have accordingly developed a maple end - user friendly library , named `` ` singularity ` '' , for an efficient and complete local bifurcation analysis of real zeros of scalar smooth maps . we have further constructed a built - in help for ` singularity ` and provided a comprehensive user - guide . recent progresses in maple have been used so that ` singularity ` generates the list of inequivalent persistent bifurcation diagrams for parametric singularities . the approach is independent of the _ singularity s codimension _ ( _ a measure of its complexity _ ) . the main features of ` singularity ` are briefly illustrated along with a few examples . phone : ( 98 - 31 ) 33913634 ; fax : ( 98 - 31 ) 33912602 ; email : [email protected] . ] and mahsa kazemi _ keywords _ : singularity and bifurcation theory ; ideal membership problem ; standard and grbner bases . hence , we may assume that the base point is the origin and . we say that is _ singular_. equation may appear by direct mathematical modeling of a singular engineering problem or indirect , through reduction methods such as _ liapunov - schmidt reduction _ ; e.g. , see , ( * ? ? ? * pages 156162 ) and ( * ? ? ? * chapter vii ) . in fact , the theory described here is known as a `` natural framework '' for _ equilibrium bifurcation theory _ ; see thus in this paper , we assume that [ m00 ] n=1 ( 0,0)=0.we will deal with the case of multi - state dimensional problems in a future project . when is a singular map and the parameters vary , the number of solutions for equation may change and any of such changes is called a _ bifurcation diagram_. singularities ( including those different from here ) and the theories to deal with them have appeared in several mathematical disciplines with the same or similar keywords . arnold in late 1960s . depending on the context , space and equivalence relation , they are faced with essentially different tools , algebraic and geometric structures , applications and/or objectives ; e.g. , see . for an instance a _ geometric singularity _ refers to a variety whose tangent space is not regularly defined ; e.g. , a self intersecting curve or a cusp ; see . - _ and _ right_-equivalences for his normal form classification of smooth functions . _ strategy equivalence _ is used for the analysis of _ strategy functions _ in . _ right - left _ equivalence is applied in to treat bifurcations of hamiltonian systems . the other instance is _ catastrophe theory _ and usually uses almost identical keywords as ours . catastrophe theory addresses basically different qualitative properties using _ right equivalence _ than the qualitative properties we pursue here using _ we only refer to the methodologies in dealing with the local bifurcation analysis of real zeros of smooth maps as singularity theory ; see for our main references of this subject . many powerful algebraic tools have been developed for local bifurcation analysis of zeros in equation . armbruster proposed a cognitive use of basis and encouraged a systematic implementations of the existing results in a computer . yet to the best of our knowledge , there does not exist any end - user symbolic library available ( neither free nor paid ) to everyone for the _ local bifurcation analysis of zeros of smooth maps_. this is a long overdue contribution despite its importance and wide applications . in the last two decades , there has been a considerable progress in development of computer algebra systems so that an efficient _ symbolic _ implementation of the results in singularity theory is now feasible ; see for numeric approaches . singularity theory uses two fundamental notions of _ intermediate order terms _ and _ high order terms _ for _ normal form computation_. recall that theory of normal forms here is to simplify singular maps and qualitative study of their zeros . a contribution here is to generalize some existing techniques and concepts from algebraic geometry to the context of ( locally ) smooth maps ( germs ) for a correct implementation . due to the infinite nature of taylor series of smooth maps , singularity ` is adopted accordingly . we accordingly provide guidelines for efficient symbolic implementation of the existing results from singularity theory ; see ( * ? ? ? * chapters 67 ) , ( * ? ? ? * sections 6.2 and 6.3 ) , ( * ? ? ? * chapters 14 ) and . this simply illustrates an interesting and realistic application of computational algebraic geometry to the equilibrium bifurcation analysis of real world problems . ` singularity ` has benefited from an efficient use of these capacities of maple . besides and their integration with ` singularity ` shall lead to a toolbox for local bifurcation control and analysis of singularities . ` we use identical notations and terminologies from as far as it is feasible . ` ` singularity ` efficiently simplifies _ intermediate _ and _ high order terms_. it , further , generates _ persistent bifurcation diagrams ( plot or animation ) , _ and estimates the _ transformations _ transforming _ contact - equivalent scalar maps to each other_. finally , ` singularity ` solves _ the recognition problem for normal forms and universal unfoldings_. an interesting capability of ` singularity ` is the classification of persistent bifurcation diagrams by generating an automatic list . in order to develop ` singularity ` , we have discussed some modified concepts ( suitable in our context ) from computational algebraic geometry including _ division remainders , _ _ standard bases , _ _ elimination ideals , _ _ ideal membership problem _ and _ colon ideals _ for the local rings of fractional ( germ ) maps , formal power series and smooth maps . we further explain how singularity theory is related to _ ideal membership problem _ in algebraic geometry . these implementations include high order term ideals , tangent spaces , transition sets , persistent bifurcation diagram classifications , normal forms and the universal unfolding . the capabilities of the main features of ` singularity ` along with a few examples are sketched in section [ secfeatures ] .	the local zero structure of a smooth map may _ qualitatively _ change , when the map is subjected to small perturbations . the changes may include births and/or deaths of zeros . the _ qualitative properties _ are defined as the invariances of an appropriate _ equivalence relation_. the occurrence of a _ qualitative change _ in the zero structures is called a _ bifurcation _ and the map is named a _ singularity_. the local bifurcation analysis of singularities has been extensively studied in _ singularity theory _ and many powerful algebraic tools have been developed for their study . however , there does not exist any available symbolic computer - library for this purpose . we suitably generalize some powerful tools from algebraic geometry for correct implementation of the results from singularity theory . we provide some required criteria along with rigorous proofs for efficient and cognitive computer - implementation . we have accordingly developed a maple end - user friendly library , named `` ` singularity ` '' , for an efficient and complete local bifurcation analysis of real zeros of scalar smooth maps . we have further constructed a built - in help for ` singularity ` and provided a comprehensive user - guide . recent progresses in maple have been used so that ` singularity ` generates the list of inequivalent persistent bifurcation diagrams for parametric singularities . the approach is independent of the _ singularity s codimension _ ( _ a measure of its complexity _ ) . the main features of ` singularity ` are briefly illustrated along with a few examples . our maple library is not only useful for research goals and engineering applications involving singularities but also for pedagogical purposes . + [ 0.1 in ] majid gazorcorresponding author . phone : ( 98 - 31 ) 33913634 ; fax : ( 98 - 31 ) 33912602 ; email : [email protected] . ] and mahsa kazemi _ keywords _ : singularity and bifurcation theory ; ideal membership problem ; standard and grbner bases . _ 2010 mathematics subject classification _ : 37g10 ; 13p10 ; 58k50 ; 58k60 . _ public access _ : ` singularity ` will be released for public access once this draft paper is peer - reviewed in a refereed journal . ' '' '' many real life problems may result in the analysis of local zeros ( around a zero solution , named a _ base point _ ) of a smooth map [ m0 ] f:^n^m^n , f(x,)=0 , x^n , ^m . we refer to by state variables , by state dimension and by parameters . note that locating singular base points of a smooth map is related to finding roots of nonlinear systems and is not the purpose of our work here ; see . hence , we may assume that the base point is the origin and . equation may demonstrate a surprising change on the solution set when the parameters vary . this occurs when the jacobian matrix of does not have a full rank . in this case we say that is _ singular_. equation may appear by direct mathematical modeling of a singular engineering problem or indirect , through reduction methods such as _ liapunov - schmidt reduction _ ; e.g. , see , ( * ? ? ? * pages 156162 ) and ( * ? ? ? * chapter vii ) . for example , equation appears in the study of equilibria and limit cycles of dynamical systems or steady - state solutions of partial differential equations . in fact , the theory described here is known as a `` natural framework '' for _ equilibrium bifurcation theory _ ; see . using liapunov - schmidt reduction , we can reduce the state dimension so that the jacobian matrix at the origin is the zero matrix . thus in this paper , we assume that [ m00 ] n=1 ( 0,0)=0.we will deal with the case of multi - state dimensional problems in a future project . when is a singular map and the parameters vary , the number of solutions for equation may change and any of such changes is called a _ bifurcation_. the equation is called a _ bifurcation problem _ and the set ( x,):f(x,)=0is called a _ bifurcation diagram_. singularities ( including those different from here ) and the theories to deal with them have appeared in several mathematical disciplines with the same or similar keywords . these theories have a long history dating back to the original works of hassler whitney , and then john mather , rene thom and v.i . arnold in late 1960s . depending on the context , space and equivalence relation , they are faced with essentially different tools , algebraic and geometric structures , applications and/or objectives ; e.g. , see . for an instance a _ geometric singularity _ refers to a variety whose tangent space is not regularly defined ; e.g. , a self intersecting curve or a cusp ; see . this leads to a theory of its own and it is named _ singularity theory_. arnold in uses _ - _ and _ right_-equivalences for his normal form classification of smooth functions . _ strategy equivalence _ is used for the analysis of _ strategy functions _ in . _ right - left _ equivalence is applied in to treat bifurcations of hamiltonian systems . the other instance is _ catastrophe theory _ and usually uses almost identical keywords as ours . catastrophe theory addresses basically different qualitative properties using _ right equivalence _ than the qualitative properties we pursue here using _ contact equivalence_. all of these mentioned subject areas follow different objectives and goals than what ours do . in this paper we only refer to the methodologies in dealing with the local bifurcation analysis of real zeros of smooth maps as singularity theory ; see for our main references of this subject . many powerful algebraic tools have been developed for local bifurcation analysis of zeros in equation . armbruster proposed a cognitive use of basis and encouraged a systematic implementations of the existing results in a computer . yet to the best of our knowledge , there does not exist any end - user symbolic library available ( neither free nor paid ) to everyone for the _ local bifurcation analysis of zeros of smooth maps_. this is a long overdue contribution despite its importance and wide applications . in the last two decades , there has been a considerable progress in development of computer algebra systems so that an efficient _ symbolic _ implementation of the results in singularity theory is now feasible ; see for numeric approaches . singularity theory uses two fundamental notions of _ intermediate order terms _ and _ high order terms _ for _ normal form computation_. recall that theory of normal forms here is to simplify singular maps and qualitative study of their zeros . intermediate order terms have a complicated structure and do not seem to hold a convenient algebraic structure . therefore , basis type of tools ( i.e. , its local versions ) alone are not sufficient to simplify removable intermediate order terms in a singular germ . furthermore as far as our information is concerned , there does not yet exist a complete algebraic characterization for _ high order terms _ in many cases of multi - state variables . this does not mean that high and intermediate order terms are computationally inaccessible but it does mean crude uses of basis type of tools fail to address _ normal form computations_. ( note that the basic and principal ideas in singularity theory start with normal form computation . ) indeed , the approach needs to be refined along with nonlinear normalization techniques . our approach efficiently simplifies removable intermediate order terms and is adoptable for simplification of high order terms even for the generalization of our results to multi - state variable cases . our main contributions here are some natural generalizations of known tools from algebraic geometry for correct symbolic implementation and providing certain criteria along with rigorous proofs for alternative and efficient symbolic implementation , an efficient symbolic implementation of the results of singularity theory ( one dimensional state variable ) in maple , developing an end - user friendly maple library named ` singularity ` , writing a user guide and constructing a comprehensive built - in maple help for ` singularity ` . a contribution here is to generalize some existing techniques and concepts from algebraic geometry to the context of ( locally ) smooth maps ( germs ) for a correct implementation . due to the infinite nature of taylor series of smooth maps , the computations are performed modulo a given degree . we provide a sufficient condition for a given degree whose truncation does not lead to error . the default work of ` singularity ` tests the condition and do the computations modulo an optimal degree . however , this approach adds a computational cost . further , smooth maps involve flat functions ( functions with zero taylor series ) and this may cause unnecessarily complicated formulas . thereby , it is fundamentally helpful to use a ring smaller than the ring of smooth maps when it is feasible . unlike the ring of formal power series , the associated computations in the ring of polynomials or fractional maps are exact and no truncation is required . we provide conditions along with rigorous proofs for the possible efficient implementations using ideals generated in either the rings of polynomials , fractional maps or formal power series . ` singularity ` is adopted accordingly . we accordingly provide guidelines for efficient symbolic implementation of the existing results from singularity theory ; see ( * ? ? ? * chapters 67 ) , ( * ? ? ? * sections 6.2 and 6.3 ) , ( * ? ? ? * chapters 14 ) and . this simply illustrates an interesting and realistic application of computational algebraic geometry to the equilibrium bifurcation analysis of real world problems . maple is one of the two major ( along with mathematica ) symbolic computer algebra systems . besides , maple is user - friendly and is widely used for mathematics and engineering research as well as educational purposes . thus , maple is a good choice for end - user libraries in general , and in particular for ` singularity ` due to various applications of singularity theory in different engineering disciplines . further , many useful and advanced techniques from computational algebraic geometry such as basis , elimination ideals for polynomial ring , regular chains and triangular decomposition method have already been developed and are now available in built - in packages of maple 18 . so far , the most efficient basis computation is due to maple algorithm implemented by jean - charles faugre ( see ) while regular chains and triangular decomposition method are only available in maple . ` singularity ` has benefited from an efficient use of these capacities of maple . besides , we have already developed some maple programs for ( parametric and orbital ) normal form computation of _ singular differential equations _ and their integration with ` singularity ` shall lead to a toolbox for local bifurcation control and analysis of singularities . ` singularity ` has been tested by all scalar examples ( nonsymmetric and without modal parameters ) and classifications given in and a few ( differences , error or not already reported data due to computational burden ) are verified in our favor . we use identical notations and terminologies from as far as it is feasible . ` singularity ` computes a variety of algebraic structures associated with singular scalar maps including _ tangent _ and _ restricted tangent spaces , _ _ high order term ideals , _ and the _ intrinsic ideals _ associated with ideals of both _ finite _ and _ infinite codimension . _ our maple library derives _ low and intermediate order terms , _ _ normal forms , universal unfolding , _ and _ transition sets . _ ` singularity ` efficiently simplifies _ intermediate _ and _ high order terms_. it , further , generates _ persistent bifurcation diagrams ( plot or animation ) , _ and estimates the _ transformations _ transforming _ contact - equivalent scalar maps to each other_. finally , ` singularity ` solves _ the recognition problem for normal forms and universal unfoldings_. an interesting capability of ` singularity ` is the classification of persistent bifurcation diagrams by generating an automatic list . this latter capability is in fact enabled by using a powerful built - in maple 18 package called regularchains . in order to develop ` singularity ` , we have discussed some modified concepts ( suitable in our context ) from computational algebraic geometry including _ division remainders , _ _ standard bases , _ _ elimination ideals , _ _ ideal membership problem _ and _ colon ideals _ for the local rings of fractional ( germ ) maps , formal power series and smooth maps . these are accordingly implemented in ` singularity ` . the rest of this paper is organized as follows . singularity theory and bifurcation analysis of equation - is discussed in section [ sec1int ] . we further explain how singularity theory is related to _ ideal membership problem _ in algebraic geometry . section [ sec2 ] describes how to treat the ideal membership problem . in this direction , computational algebraic tools such as standard and bases for ideals in three different rings , and the concept of _ finite codimension ideals are introduced . _ intrinsic ideals _ and their associated ideal representations are discussed in section [ sec3 ] . we further explain a procedure for computing the intrinsic part of an ideal . section [ sec4 ] gives our suggestions on how to implement some objects and results from singularity theory . these implementations include high order term ideals , tangent spaces , transition sets , persistent bifurcation diagram classifications , normal forms and the universal unfolding . the capabilities of the main features of ` singularity ` along with a few examples are sketched in section [ secfeatures ] . finally , our future and in - progress projects are outlined in section [ secfuture ] .
1607.08084	i	the development of technologies to trap and cool neutral atoms has led to the emergence of cold atom physics as a new subfield of atomic physics . the atoms can be cooled to temperatures that are orders of magnitude smaller than the tiny differences between the hyperfine energy levels of the atoms . many of the most important loss processes for ultracold atoms involve deeply inelastic reactions , which produce atoms with kinetic energies much larger than those of the cold trapped atoms . one such process is three - body recombination , in which a collision of three low - energy atoms results in the binding of two of the atoms into a diatomic molecule . if the binding energy of the molecule is large compared to the energy scale of the cold atoms , the momenta of the molecule and the recoiling atom are often large enough for them to escape from the trapping potential for the atoms . ultracold atoms can be described by a local nonrelativistic effective field theory for which the coupling constant is the scattering length @xcite . local effective field theories can be applied most rigorously to a system in which there is an energy gap separating the low - energy particles described explicitly by the effective field theory from the higher - momentum particles @xcite . in a system consisting of low - energy atoms , conservation of energy ensures that a high - momentum atom can only appear through a virtual state that , by the time - energy uncertainty principle , has a short lifetime . during that short lifetime , the high - momentum atom can propagate only over a short distance . its effects on low - energy atoms are therefore restricted to short distances . these effects can be reproduced by local hermitian operators in the hamiltonian for the effective field theory . local effective field theories have also been applied to systems with deeply inelastic reactions that produce particles with momenta too large to be described accurately within the effective field theory . for example , a deeply inelastic three - body recombination event produces a molecule and an atom whose momenta may be outside the domain of validity of the effective theory . the large energy release from the inelastic reaction comes from the conversion of rest energy into kinetic energy . the standard argument for the locality of the effective field theory does not apply . the particles with large momenta produced by the inelastic reaction can propagate over arbitrarily long distances , so their effects on low - energy particles are not obviously restricted to short distances . nevertheless , there are general arguments based on the uncertainty principle that indicate that their effects can be taken into account systematically through local anti - hermitian operators in the effective hamiltonian @xcite . the effective hamiltonian can be expressed as @xmath0 , where @xmath1 and @xmath2 are hermitian . the dynamics of a multi - atom system with deeply inelastic reactions is conveniently described by a density matrix . a system that starts as a pure quantum state with @xmath3 low - energy atoms evolves into a mixed quantum state that is a superposition of a state with @xmath3 low - energy atoms and states with fewer low - energy atoms , as the inelastic reactions shift probability from the low - energy atoms into the high - momentum atoms . an effective density matrix @xmath4 can be defined by tracing the density matrix over states containing high - momentum atoms . naively we might expect the time evolution equation for @xmath4 to be @xmath5 - i \left\{k,\rho\right\}. \label{eq : drhodt - naive}\end{aligned}\ ] ] as we will demonstrate in this paper , the correct evolution equation for the effective density matrix is the _ lindblad equation _ @xcite , which has an additional term . the lindblad equation arises in the quantum information theory of _ open quantum systems_. an open quantum system consists of all the degrees of freedom of both the subsystem of interest and the environment . under special circumstances , the density matrix for the subsystem evolves in time according to the lindblad equation . in the lindblad equation for the density matrix of an effective field theory obtained by integrating out deeply inelastic reactions , the additional lindblad term is local , and it can be deduced from the local anti - hermitian terms in the effective hamiltonian . an open quantum system in which the subsystem of interest is a field theory is called an _ open effective field theory _ @xcite . grozdanov and polonyi have proposed that an open effective field theory for the hydrodynamic modes of a quantum field theory can be used as a framework for deriving dissipative hydrodynamics @xcite . burgess , holman , tasinato , and williams have applied open effective field theory to the super - hubble modes of primordial quantum fluctuations in the early universe @xcite . in the stochastic inflation framework , the master equation is the lindblad equation . since the density matrix for an effective field theory in which deeply inelastic reaction products have been integrated out satisfies the lindblad equation , this system can also be regarded as an open effective field theory @xcite . in this case , the environment consists of the high - momentum particles produced by the deeply inelastic reactions . the paper is organized as follows . in section [ sec : densitymatrix ] , we summarize the basic properties of the density matrix and we introduce the lindblad equation . in section [ sec : effective theory ] , we explain how integrating out deeply inelastic reaction products results in local operators in the effective lagrangian density . we also explain why the effective density matrix obtained by tracing over states that include deeply inelastic reaction products must satisfy the lindblad equation . in section [ sec : atomloss ] , we apply the lindblad equation to the mean number of low - energy atoms . we derive the universal relation for the two - atom inelastic loss rate for fermions with two spin states and the universal relation for the three - atom inelastic loss rate for identical bosons . our results are summarized briefly in section [ sec : summary ] . in an appendix , we demonstrate how the lindblad equation for the density matrix emerges from the diagrammatic analysis of a simple field theory model with a deeply inelastic two - atom scattering reaction .	the loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low - energy atoms by adding local anti - hermitian terms to the effective hamiltonian . here we show that it satisfies a lindblad equation , with local lindblad operators determined by the local anti - hermitian terms in the effective hamiltonian . we use the lindblad equation to derive the universal relation for the two - atom inelastic loss rate for fermions with two spin states and the universal relation for the three - atom inelastic loss rate for identical bosons .	the loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low - energy atoms by adding local anti - hermitian terms to the effective hamiltonian . here we show that when multi - atom systems are considered , an additional modification is required in the equation governing the density matrix . we define an effective density matrix by tracing over the states containing high - momentum atoms produced by deeply inelastic reactions . we show that it satisfies a lindblad equation , with local lindblad operators determined by the local anti - hermitian terms in the effective hamiltonian . we use the lindblad equation to derive the universal relation for the two - atom inelastic loss rate for fermions with two spin states and the universal relation for the three - atom inelastic loss rate for identical bosons .
astro-ph0307180	i	in the present work we have used the magnitude - limited ssrs2 to identify galaxies with active galactic nuclei , and to investigate how the properties of agn host galaxies relate to general population of galaxies in the parent sample . the main results of this work are summarized below . * we find that 162/5339 ( 3% ) of the galaxies in the ssrs2 are seyfert galaxies . this number is comparable to other works studying the local universe ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as with the number of agns detected in a high redshift sample ( e.g. , * ? ? ? the ratio of seyfert 2s to 1s is about 3:1 . * the majority of the agn host galaxies in the ssrs2 are in systems classified morphologically betwen s0a and sb , which are galaxies containing significant bulge components . this result is consistent with findings of @xcite . we find that @xmath2 10% of the seyfert galaxies are found in hosts with indication of an ongoing merger event . there is no significant difference between the morphological distributions of seyfert 1 relative to seyfert 2 hosts . * the agns are preferentially detected in high luminosity hosts ( @xmath86 ) . this result is similar to previous findings ( e.g. , * ? ? ? * ) , though in conflict with that found by @xcite using the sdss database . this discrepancy can be explained by the fact that the present sample does not allow separating the contribution to the total luminosity due to the agn from that of the host galaxy . * seyfert galaxies are twice as frequent in barred hosts than in galaxies without nuclear activity . * using a percolation algorithm we find that seyfert galaxies are more commonly found in binary systems than in groups with higher multiplicities or as `` isolated '' galaxies , when compared to galaxies in the parent sample . * we do not find strong correlation between the presence of an agn with indicators of the strength of gravitational perturbation by companions , such as the projected local density , the group velocity dispersion , the nearest neighbor distance and the maximum tidal influence . * we find marginal evidence that seyfert 1 galaxies have closer companions and are more susceptible to tidal effects than seyfert 2 galaxies are . * the results above suggest that the large - scale environment does not seem to play an important role in enhancing the agn activity . on the other hand , internal characteristics such as morphology , luminosities , existence of bars and other asymmetries are more strongly correlated with the presence of the agn . the authors thank the referee , dr . john huchra , whose suggestions allowed us to improve the text . we also thank alberto rodrguez - ardilla and lei hao for useful discussions and caryl gronwall , vicki sarajedini and john salzer for providing the kiss non - parametric luminosity function . this research has made use of nasa / ipac extragalactic database ( ned ) . rsm acknowledges financial support from pibic - cnpq scholarship , magm to cnpq grant 301366/86 - 1 and faperj e-26/171.619/2001 , and cnaw to nsf ast 95 - 29028 and ast 00 - 71198 . da costa , l.n . , willmer , c.n.a , pellegrini , p.s . , chaves , o.l . , rite , c. , maia , m.a.g . , geller , m.j . , latham , d.w . , kurtz , m.j . , huchra , j.p . , ramella , m. , fairall , a.p . , smith , c. , & lipari , s. 1998 , aj 116 , 1 gronwall , c. , sarajedini , v.l . , & salzer , j.j . 2001 , in `` agn surveys '' , i.a.u . colloquium 184 , eds . green , e.ye . khachikian , & d.b . sanders asp conference series ( san francisco : asp ) , astro - ph/0111519 kauffmann , g. , heckman , t.m . , tremonti , c. , brinchmann , j. , charlot , s. , white , s.d.m . , ridgway , s. , brinkmann , j. , fukugita , m. , hall , p. , ivezic , z. , richards , g. , & schneider , d. 2003 , astro - ph/0304239 sarajedini , v.l . 2002 , in `` agn surveys , asp conference proceedings , vol . 284 . edited by r.f . green , e.ye . khachikian , and d.b . sanders . '' , ( san francisco : astronomical society of the pacific , in press ) lllrrrcrr 00 03 32.1 & -10 44 41 & ngc 7808 & 14.47 & 8922 & -2 & n & 1.00 & s1 + 00 53 29.8 & -08 46 04 & ngc 0291 & 14.64 & 5695 & 2 & y & 0.45 & s2 + 00 10 01.0 & -04 42 38 & mrk 0937 & 14.70 & 8851 & 3 & n & 1.00 & s1 + 00 10 54.3 & -21 04 03 & eso 538- g 025 & 15.02 & 7782 & 2 & n & 0.22 & s2 + 00 18 35.9 & -07 02 56 & gsc 4670 00946 & 14.36 & 5620 & 0 & n & 1.00 & s2 + 00 19 44.0 & -14 07 18 & ic 0009 & 15.42 & 12622 & 0 & n & 0.75 & s2 + 00 26 00.0 & -02 55 07 & mcg -01 - 02 - 013 & 15.49 & 20282 & 15 & n & 0.72 & s2 + 00 30 53.8 & -09 12 07 & mcg -02 - 02 - 035 & 15.28 & 5939 & -2 & n & 0.50 & s2 + 00 34 13.8 & -21 26 21 & eso 540- g 001 & 13.96 & 8030 & 4 & y & 0.69 & s1 + 00 35 48.8 & -13 36 38 & ngc 0166 & 15.18 & 6020 & 0 & n & 0.33 & s2 + 00 38 18.4 & -14 50 07 & mcg -03 - 02 - 027 & 15.40 & 10971 & 3 & n & 0.67 & s2 + 00 41 11.7 & -21 07 54 & eso 540- g 014 & 15.38 & 1653 & -5 & n & 0.50 & s2 + 00 42 52.8 & -23 32 29 & ngc 0235a & 14.18 & 6589 & 15 & n & 0.44 & s2 + 00 54 54.5 & -32 01 54 & eso 411- g 029 & 15.04 & 9622 & 0 & n & 0.38 & s2 + 00 55 02.6 & -19 00 18 & eso 541- g 001 & 13.61 & 6366 & 3 & y & 0.62 & s2 + 00 58 22.2 & -36 39 37 & eso 351- g 025 & 15.12 & 10415 & 2 & n & 0.58 & s2 + 01 02 17.4 & -19 40 09 & eso 541-ig 012 ned01 & 15.22 & 16905 & 15 & n & 0.85 & s2 + 01 08 47.6 & -15 50 34 & ic 0078 & 14.46 & 12066 & 1 & n & 0.41 & s2 + 01 11 27.5 & -38 05 01 & ngc 0424 & 13.90 & 3496 & 0 & n & 0.50 & s1 + 01 12 19.2 & -32 03 43 & ngc 0427 & 14.87 & 10011 & -2 & y & 0.62 & s1 + 01 14 07.0 & -32 39 03 & ic 1657 & 13.12 & 3564 & 3 & n & 0.25 & s2 + 01 19 25.0 & -15 41 07 & mcg -03 - 04 - 046 & 15.26 & 15234 & 4 & y & 1.00 & s2 + 01 23 54.4 & -35 03 56 & ngc 0526a & 14.66 & 5725 & 15 & n & 0.53 & s2 + 01 31 50.4 & -33 08 10 & eso 353- g 009 & 14.07 & 4970 & 2 & y & 1.00 & s2 + 01 39 24.8 & -09 24 04 & ngc 0640 & 15.45 & 7490 & 2 & n & 0.67 & s2 + 01 43 37.6 & -33 42 20 & eso 353- g 038 & 14.85 & 8884 & 5 & n & 0.36 & s2 + 01 51 41.7 & -36 11 16 & eso 354- g 004 & 15.08 & 10045 & 3 & n & 0.93 & s1 + 01 59 51.3 & -06 50 25 & ic 0184 & 14.87 & 5382 & 1 & n & 0.50 & s2 + 02 01 06.5 & -06 48 56 & ngc 0788 & 13.50 & 4078 & -5 & n & 0.77 & s2 + 02 06 53.1 & -36 27 08 & ngc 0824 & 14.05 & 5836 & 2 & y & 0.95 & s2 + 02 09 20.9 & -10 08 00 & ngc 0833 & 13.64 & 3867 & 3 & n & 0.47 & s2 + 02 10 11.4 & -09 03 36 & gsc 5281 00378 & 15.23 & 12491 & 3 & n & 0.50 & s2 + 02 24 40.6 & -19 08 30 & eso 545- g 013 & 13.59 & 10253 & 3 & n & 0.73 & s1 + 02 30 05.5 & -08 59 53 & mcg -02 - 07 - 024 & 15.25 & 4859 & -2 & n & 0.86 & s1 + 02 31 51.0 & -36 40 16 & ic 1816 & 13.66 & 5215 & 3 & n & 0.93 & s2 + 02 34 37.8 & -08 47 15 & ngc 0985 & 15.00 & 19150 & 15 & n & 1.00 & s1 + 02 35 13.5 & -29 36 17 & eso 416- g 002 & 15.06 & 17700 & 1 & n & 0.50 & s2 + 02 38 45.2 & -30 48 24 & eso 416- g 005 & 15.34 & 18587 & 5 & n & 0.80 & s1 + 02 41 04.8 & -08 15 21 & ngc 1052 & 12.08 & 1519 & -3 & n & 0.70 & s2 + 02 41 38.7 & -28 10 17 & ic 1833 & 14.28 & 4952 & -2 & n & 0.58 & s2 + 02 43 07.8 & -08 46 26 & ngc 1071 & 15.41 & 11302 & 3 & n & 0.45 & s2 + 02 44 02.9 & -26 11 11 & eso 479- g 030 & 15.29 & 10504 & 2 & n & 0.24 & s2 + 02 46 19.0 & -30 16 29 & ngc 1097 & 10.23 & 1195 & 3 & n & 0.62 & s1 + 02 49 33.8 & -38 46 12 & eso 299- g 020 & 13.96 & 5008 & 1 & n & 0.45 & s2 + 02 51 40.3 & -16 39 04 & ngc 1125 & 13.87 & 3303 & 0 & y & 0.50 & s2 + 02 56 09.8 & -13 41 07 & mcg -02 - 08 - 031 & 15.38 & 6935 & 3 & n & 0.50 & s2 + 02 56 21.5 & -32 11 06 & eso 417- g 006 & 14.34 & 4947 & -2 & n & 0.83 & s2 + 02 57 49.6 & -10 10 07 & mcg -02 - 08 - 033 & 14.02 & 4516 & 3 & n & 0.30 & s2 + 03 00 04.3 & -10 49 28 & mcg -02 - 08 - 038 & 15.27 & 9770 & 0 & y & 0.50 & s1 + 03 00 30.7 & -11 24 07 & mcg -02 - 08 - 039 & 14.57 & 8989 & 3 & y & 0.69 & s2 + 03 02 13.2 & -23 35 20 & gsc 6438 00439 & 14.93 & 10514 & -2 & n & 0.39 & s1 + 03 08 10.8 & -22 57 39 & ngc 1229 & 14.82 & 10676 & 1 & n & 0.69 & s2 + 03 11 14.7 & -08 55 20 & ngc 1241 & 13.26 & 4036 & 3 & y & 0.61 & s2 + 03 24 48.7 & -03 02 32 & ngc 1320 & 13.67 & 2698 & 2 & n & 0.32 & s2 + 03 25 04.9 & -12 18 07 & mcg -02 - 09 - 040 & 14.93 & 4400 & -2 & n & 0.33 & s2 + 03 25 25.3 & -06 08 39 & mrk 0609 & 15.06 & 10236 & -5 & n & 0.75 & s2 + 03 30 40.9 & -03 08 16 & mrk 0612 & 15.10 & 6195 & 3 & y & 0.62 & s2 + 03 33 39.7 & -05 05 22 & ngc 1358 & 13.30 & 4013 & 0 & y & 0.77 & s2 + 03 33 36.4 & -36 08 25 & ngc 1365 & 10.34 & 1659 & 3 & y & 0.71 & s1 + 03 36 46.4 & -35 59 58 & ngc 1386 & 12.64 & 924 & -2 & n & 0.38 & s2 + 03 37 03.2 & -25 14 57 & eso 482- g 014 & 15.39 & 12889 & 1 & n & 0.40 & s2 + 03 42 03.2 & -21 14 50 & eso 548- g 081 & 12.92 & 4341 & 1 & n & 0.87 & s1 + 03 43 26.5 & -31 44 38 & gsc 7028 00092 & 14.90 & 9574 & 3 & n & 0.64 & s2 + 03 45 12.5 & -39 34 30 & gsc 7569 01468 & 15.48 & 12884 & -5 & n & 0.96 & s1 + 03 55 09.3 & -17 28 10 & eso 549- g 036 & 14.64 & 8501 & 4 & y & 0.75 & s2 + 03 57 38.2 & -19 12 59 & ngc 1489 & 14.36 & 11421 & 3 & y & 0.44 & s2 + 04 02 25.7 & -18 02 51 & eso 549- g 049 & 14.36 & 7872 & 3 & n & 0.75 & s2 + 04 02 46.1 & -21 07 09 & eso 549- g 050 & 14.17 & 7532 & 3 & n & 0.67 & s2 + 04 04 27.5 & -10 10 07 & mcg -02 - 11 - 014 & 15.41 & 9267 & 2 & y & 0.62 & s2 + 04 13 49.7 & -32 00 25 & eso 420- g 013 & 13.52 & 3594 & 0 & n & 0.90 & s2 + 04 39 37.3 & -37 05 08 & gsc 7045 01444 & 15.22 & 12292 & 3 & n & 0.48 & s2 + 04 40 59.6 & -37 34 11 & eso 304- g 011 & 15.34 & 12392 & 3 & y & 0.45 & s2 + 09 42 33.3 & -03 41 55 & ngc 2974 & 12.30 & 1908 & 1 & n & 0.57 & s2 + 09 50 56.5 & -04 59 07 & mcg -01 - 25 - 049 & 14.46 & 6628 & 1 & y & 0.42 & s2 + 10 02 00.1 & -08 09 42 & gsc 5476 01170 & 15.22 & 4569 & 15 & n & 0.90 & s1 + 10 18 03.3 & -03 47 41 & gsc 4907 01728 & 15.36 & 11947 & 2 & n & 1.00 & s2 + 10 20 57.8 & -04 57 03 & gsc 4908 01685 & 15.25 & 11889 & 1 & y & 1.00 & s2 + 10 25 50.2 & -11 26 07 & mcg -02 - 27 - 003 & 15.00 & 11858 & 0 & n & 1.00 & s2 + 10 26 51.9 & -03 27 52 & ic 0614 & 15.39 & 10194 & 0 & n & 0.71 & s2 + 10 35 27.3 & -14 07 07 & mcg -02 - 27 - 009 & 14.33 & 4577 & 2 & n & 0.26 & s2 + 10 38 20.6 & -10 07 04 & gsc 5495 00478 & 15.41 & 8710 & 2 & y & 0.50 & s1 + 10 39 46.3 & -05 29 00 & mcg -01 - 27 - 031 & 14.07 & 6194 & 1 & y & 0.75 & s1 + 10 42 18.7 & -17 38 07 & mcg -03 - 27 - 026 & 14.80 & 6191 & -2 & n & 0.29 & s2 + 10 57 53.6 & -04 54 18 & ic 0657 & 15.44 & 9697 & 1 & y & 0.42 & s2 + 11 00 45.4 & -06 34 43 & gsc 4927 01023 & 15.36 & 8997 & 3 & n & 0.24 & s2 + 11 23 32.2 & -08 39 30 & ngc 3660 & 13.06 & 3678 & 4 & y & 0.87 & s2 + 11 24 56.3 & -03 48 41 & gsc 4926 01061 & 15.04 & 6788 & 2 & n & 0.40 & s2 + 11 25 02.1 & -05 04 07 & mcg -01 - 29 - 018 & 14.53 & 8518 & 2 & n & 0.90 & s2 + 11 34 23.3 & -09 40 07 & mcg -01 - 30 - 005 & 15.12 & 6419 & -3 & n & 1.00 & s2 + 11 43 18.6 & -12 52 42 & ngc 3831 & 13.60 & 5254 & 1 & n & 0.22 & s2 + 11 45 11.6 & -09 18 51 & ngc 3858 & 13.94 & 5729 & 0 & y & 0.67 & s2 + 11 45 40.5 & -18 27 16 & gsc 6096 00769 & 14.70 & 9877 & 2 & n & 0.55 & s1 + 11 52 38.2 & -05 12 07 & mcg -01 - 30 - 041 & 14.70 & 5749 & 0 & y & 0.50 & s2 + 12 00 43.3 & -20 50 01 & gsc 6100 00370 & 15.46 & 18639 & 15 & n & 0.76 & s1 + 12 16 60.0 & -26 12 36 & eso 505-ig 031 & 15.49 & 11840 & 15 & y & 0.88 & s2 + 12 39 39.4 & -05 20 39 & ngc 4593 & 12.21 & 2698 & 2 & y & 0.83 & s1 + 12 39 59.4 & -11 37 23 & ngc 4594 & 9.50 & 994 & 0 & n & 0.62 & s2 + 12 42 25.3 & -06 58 16 & ngc 4628 & 14.50 & 2828 & 1 & n & 0.23 & s2 + 12 51 32.4 & -14 13 17 & mcg -02 - 33 - 030 & 14.23 & 4298 & 1 & n & 0.43 & s1 + 12 52 12.4 & -13 24 54 & ngc 4748 & 14.27 & 4426 & 15 & n & 0.86 & s1 + 12 52 36.4 & -21 54 39 & eso 575-ig 016 ned02 & 14.87 & 6865 & 15 & n & 0.70 & s2 + 12 56 36.3 & -06 49 03 & ngc 4813 & 14.15 & 1373 & 1 & n & 0.40 & s2 + 13 00 52.9 & -13 26 59 & ngc 4897 & 13.23 & 2546 & 3 & y & 0.80 & s2 + 13 04 14.3 & -10 20 23 & ngc 4939 & 11.99 & 3117 & 3 & n & 0.38 & s2 + 13 04 13.1 & -05 33 06 & ngc 4941 & 12.43 & 1108 & 1 & n & 0.48 & s2 + 13 06 56.5 & -23 55 01 & ic 4180 & 13.88 & 2972 & 0 & y & 0.77 & s2 + 13 07 05.9 & -23 40 39 & ngc 4968 & 13.92 & 2930 & 0 & n & 0.47 & s2 + 13 10 17.3 & -07 27 07 & mcg -01 - 34 - 008 & 14.54 & 6713 & 3 & n & 0.86 & s2 + 13 17 03.4 & -02 15 41 & ic 4218 & 14.90 & 5808 & 1 & n & 0.27 & s1 + 13 19 31.7 & -12 39 26 & ngc 5077 & 12.41 & 2817 & -5 & n & 0.50 & s2 + 13 20 06.4 & -17 07 06 & mcg -03 - 34 - 049 & 15.14 & 6713 & 0 & n & 0.83 & s1 + 13 22 24.5 & -16 43 07 & mcg -03 - 34 - 064 & 14.64 & 6393 & -2 & n & 0.80 & s2 + 13 24 35.2 & -19 45 11 & gsc 6128 00106 & 14.97 & 5284 & 3 & n & 0.77 & s2 + 13 27 12.7 & -24 51 41 & gsc 6717 00254 & 15.42 & 12131 & 2 & n & 0.79 & s1 + 13 30 41.7 & -21 39 47 & gsc 6133 00078 & 15.49 & 7292 & 0 & y & 0.73 & s2 + 13 31 13.9 & -25 24 10 & eso 509- g 038 & 14.74 & 7786 & 15 & n & 0.42 & s1 + 13 32 39.1 & -10 28 53 & mcg -02 - 35 - 001 & 14.82 & 6638 & 2 & y & 0.67 & s1 + 13 33 08.3 & -23 32 37 & gsc 6714 00714 & 14.50 & 10342 & 3 & n & 0.81 & s2 + 13 34 39.6 & -23 26 48 & eso 509-ig 066 & 14.70 & 10031 & 15 & n & 0.77 & s2 + 13 37 35.1 & -21 12 58 & gsc 6134 00646 & 15.26 & 15703 & 3 & n & 0.49 & s2 + 13 37 50.0 & -23 59 41 & eso 509-ig 083 ned01 & 14.70 & 9044 & 15 & n & 0.63 & s2 + 13 40 19.7 & -23 51 29 & ngc 5260 & 13.42 & 6539 & 2 & y & 0.88 & s2 + 13 46 20.1 & -03 25 42 & mcg + 00 - 35 - 020 ned02 & 15.02 & 6948 & 2 & n & 0.38 & s2 + 13 58 59.7 & -20 02 44 & gsc 6144 00913 & 15.50 & 11797 & -5 & n & 1.00 & s2 + 14 03 26.1 & -06 01 51 & ngc 5427 & 12.50 & 2618 & 3 & n & 1.00 & s2 + 14 13 14.9 & -03 12 27 & ngc 5506 & 13.37 & 1753 & 3 & n & 0.57 & s2 + 14 26 12.3 & -11 54 07 & mcg -02 - 37 - 004 & 15.48 & 12480 & 3 & y & 0.80 & s2 + 14 33 43.5 & -14 37 11 & ngc 5664 & 14.52 & 4537 & 2 & n & 0.42 & s2 + 14 42 23.9 & -17 15 10 & ngc 5728 & 12.81 & 2793 & 4 & y & 0.58 & s2 + 14 59 24.8 & -16 41 36 & ngc 5793 & 14.17 & 3522 & 2 & n & 0.35 & s2 + 15 33 20.7 & -08 42 07 & mcg -01 - 40 - 001 & 14.64 & 6888 & 4 & y & 0.38 & s2 + 21 07 59.9 & -29 50 10 & gsc 6936 00748 & 15.10 & 5750 & 1 & n & 0.90 & s2 + 21 27 02.8 & -22 59 32 & eso 530- g 047 & 14.51 & 9761 & 2 & n & 0.59 & s2 + 21 48 19.5 & -34 57 06 & ngc 7130 & 13.33 & 4829 & 15 & n & 0.94 & s2 + 21 56 56.6 & -11 39 31 & gsc 5797 01005 & 15.37 & 17650 & 1 & n & 0.54 & s1 + 22 00 21.6 & -13 08 49 & ic 1417 & 14.36 & 5446 & 3 & n & 0.29 & s2 + 22 01 17.0 & -37 46 07 & mcg -06 - 48 - 013 & 14.82 & 10005 & -2 & n & 0.75 & s2 + 22 02 01.7 & -31 52 18 & ngc 7172 & 12.95 & 2593 & 1 & n & 0.52 & s2 + 22 08 28.3 & -34 06 23 & eso 404- g 032 & 14.33 & 4431 & 4 & n & 0.20 & s2 + 22 09 07.7 & -27 48 34 & ngc 7214 & 13.05 & 6832 & 4 & n & 0.74 & s1 + 22 14 42.0 & -38 48 23 & eso 344- g 016 & 15.08 & 11906 & 2 & y & 1.00 & s1 + 22 34 49.8 & -25 40 37 & eso 533- g 050 & 14.40 & 7928 & 0 & y & 0.89 & s2 + 22 35 45.9 & -26 03 01 & ngc 7314 & 11.88 & 1430 & 4 & n & 0.42 & s2 + 22 36 46.5 & -12 32 43 & mcg -02 - 57 - 023 & 14.82 & 7169 & 4 & n & 0.30 & s1 + 22 36 55.9 & -22 13 15 & eso 602- g 031 & 14.88 & 10101 & 3 & n & 0.50 & s1 + 22 47 47.6 & -11 48 59 & ngc 7378 & 13.64 & 2580 & 2 & y & 0.64 & s2 + 22 49 37.1 & -19 16 07 & mcg -03 - 58 - 007 & 14.84 & 9488 & 3 & y & 0.80 & s2 + 22 54 15.7 & -37 04 59 & eso 406- g 018 & 15.29 & 17215 & 15 & n & 0.54 & s2 + 22 55 01.0 & -39 39 41 & ngc 7410 & 11.61 & 1751 & 1 & y & 0.29 & s2 + 22 59 01.4 & -25 31 42 & eso 535- g 001 & 13.84 & 9015 & 2 & n & 0.94 & s2 + 23 00 47.8 & -12 55 07 & ngc 7450 & 14.00 & 3134 & 1 & y & 1.00 & s1 + 23 03 11.1 & -08 59 21 & ic 1464 & 14.90 & 7247 & 15 & n & 0.67 & s2 + 23 04 43.5 & -08 41 09 & mcg -02 - 58 - 022 & 15.00 & 14185 & 1 & n & 1.00 & s1 + 23 16 37.4 & -02 19 50 & ngc 7566 & 14.27 & 7972 & 1 & y & 0.54 & s2 + 23 18 22.5 & -04 24 59 & ngc 7592 & 14.50 & 7328 & 15 & n & 0.80 & s2 + 23 25 24.2 & -38 26 51 & gsc 8013 01279 & 14.89 & 10761 & 5 & n & 1.00 & s1 + 23 30 32.3 & -02 27 45 & mcg -01 - 59 - 027 & 15.14 & 10006 & 0 & y & 0.68 & s1 + 23 30 47.7 & -13 29 08 & ic 1495 & 14.14 & 6391 & 2 & y & 0.77 & s2 + 23 42 05.2 & -39 13 00 & gsc 8014 00236 & 15.42 & 12828 & 3 & n & 0.71 & s1 + 23 53 19.8 & -30 09 03 & eso 471-ig 037 ned02 & 15.24 & 14660 & 15 & n & 0.65 & s2 + 23 57 28.0 & -30 27 41 & mcg -05 - 01 - 013 & 14.97 & 9080 & 3 & n & 0.56 & s1 + 23 59 10.7 & -04 07 37 & ic 1524 & 13.94 & 5662 & 2 & y & 0.62 & s1 +	seyfert galaxies in this sample are twice as common in barred hosts than the non - seyferts . by assigning galaxies to groups using a percolation algorithm we find that the seyfert galaxies in the ssrs2 are more likely to be found in binary systems , when compared to galaxies in the ssrs2 parent sample . however , there is no statistically significant difference between the seyfert and ssrs2 parent sample when systems with more than 2 galaxies are considered . the analysis of the present sample suggests that there is a stronger correlation between the presence of the agn phenomenon with internal properties of galaxies ( morphology , presence of bar , luminosity ) than with environmental effects ( local galaxy density , group velocity dispersion , nearest neighbor distance ) .	the magnitude - limited catalog of the southern sky redshift survey ( ssrs2 ) , is used to characterize the properties of galaxies hosting active galactic nuclei . using emission - line ratios , we identify a total of 162 ( 3% ) seyfert galaxies out of the parent sample with 5399 galaxies . the sample contains 121 seyfert 2 galaxies and 41 seyfert 1 . the ssrs2 seyfert galaxies are predominantly in spirals of types sb and earlier , or in galaxies with perturbed appearance as the result of strong interactions or mergers . seyfert galaxies in this sample are twice as common in barred hosts than the non - seyferts . by assigning galaxies to groups using a percolation algorithm we find that the seyfert galaxies in the ssrs2 are more likely to be found in binary systems , when compared to galaxies in the ssrs2 parent sample . however , there is no statistically significant difference between the seyfert and ssrs2 parent sample when systems with more than 2 galaxies are considered . the analysis of the present sample suggests that there is a stronger correlation between the presence of the agn phenomenon with internal properties of galaxies ( morphology , presence of bar , luminosity ) than with environmental effects ( local galaxy density , group velocity dispersion , nearest neighbor distance ) .
1101.3459	r	the observing results are separately presented in two sections . in section [ chap_geometry ] , we focus on discussions of the warm and dense molecular gas , mainly traced by the nh@xmath0 and the ch@xmath0oh emissions . in section [ chap_dynamics ] , we examine the dynamics of the more extended components , based on the observations of the cs ( 10 ) transition . cross comparisons of the molecular lines have been omitted , when there are no additional significant physical implications . figure [ fig_mnt0 ] shows the velocity integrated maps of the ch@xmath0oh 5(0,5)4(0,4 ) a+ transition , the blended ch@xmath0oh 5(-2,4)4(-2,3 ) e and ch@xmath0oh 5(2,3)4(2,2 ) e transitions , and the ch@xmath0oh 5(-3,3)4(-3,2 ) e transition . in figure [ fig_nh3 ] , we present these three images in rgb colors , and an overlay with the velocity integrated map of the nh@xmath0 ( 3,3 ) main hyperfine line . in the projected area of the uc hii region , the nh@xmath0 ( 3,3 ) main hyperfine line is detected in strong absorption ( see keto , ho & haschick 1987 ; keto , ho , & haschick 1988 ; sollins et al . 2005 ; liu et al . 2010 for more descriptions ) and is presented with much larger contour intervals . we see that : * the highest excitation ch@xmath0oh transition ( blue ) exclusively traces a compact ( @xmath80.1 pc ) flattened hot toroid in the center ( @xmath8300k , klaassen et al . 2009 ; @xmath887 k , beltrn et al . the lower excitation ch@xmath0oh transitions trace the warm ( @xmath850 k ; keto , ho & haschick 1987 ) and dense molecular gas to an extended ( @xmath80.5 pc ) region . the ratio of the velocity integrated flux of the ch@xmath0oh 5(0,5)4(0,4 ) a+ transition to that of the ch@xmath0oh 5(-3,3)4(-3,2 ) e transitions in the hot toroid region is about 0.56 . in the optically thin limit , this line ratio reflects an averaged excitation temperature of @xmath8500 k. if the lower excitation line is saturated owing to high optical depth , the excitation temperature would be overestimated . * we see the complicated structures from the extended ch@xmath0oh emissions . the majority of the ch@xmath0oh emission has a southeast northwest distribution . two low column density cavities are clearly seen northeast and southwest of the hot toroid . we note that the size scale of the region where we detect significant emissions is small as compared with the angular size scale of the sma primary beam ( @xmath81@xmath15 ) and that of the vla primary beam ( @xmath82@xmath15 ) . since the detected structures are well centered within the primary beams , they are not affected by the primary beam attenuation . we therefore do not perform primary beam corrections to the maps . the shortest baselines of the ch@xmath0oh and the nh@xmath0 data sets ( table [ table_molecule_list2 ] ) correspond to the maximum angular size scale of @xmath835@xmath7 and @xmath890@xmath7 , respectively . hence the absence of structures with angular size scales @xmath520@xmath7 suggests that the compact appearance of the emissions is physical in nature , and is not caused by sampling defects . from figure [ fig_nh3 ] , we see that most structures traced by the ch@xmath0oh emissions have their nh@xmath0 counterparts ; however , the nh@xmath0 emission shows more significantly detected structures than the ch@xmath0oh emissions . a similar effect appears in the velocity domain . figure [ fig_ch3ohpv ] shows the position - velocity ( pv ) diagrams of the nh@xmath0 ( 3,3 ) main hyperfine line and all selected ch@xmath0oh j=5 transitions . the pv cut is centered on the brightest free - free continuum source at the coordinates of r.a . = 18@[email protected]@xmath18 and decl = -19@[email protected]@xmath7 with a position angle pa = 140@xmath14 ( the positive angle is defined in the usual counterclockwise fashion ) . from these pv diagrams , we see that : * the ch@xmath0oh 5(-3,3)4(-3,2 ) e transition has the highest upper level energy e@xmath12 of 96.9 k. the pv diagram of this transition reveals the fast rotating hot toroid . * the ch@xmath0oh transitions with lower upper level energies trace the molecular gas in a more extended region . a significant velocity gradient is also seen in the extended emission . * from the left most panel of figure [ fig_ch3ohpv ] , we see that the dominant emission of the nh@xmath0 ( 3,3 ) main hyperfine inversion line shows a good agreement with the ch@xmath0oh emissions . the nh@xmath0 ( 3,3 ) absorption line consistently traces the fast rotating hot toroid as seen in the pv diagram of the ch@xmath0oh 5(-3,3)4(-3,2 ) e transition . additionally , the nh@xmath0 ( 3,3 ) emission shows significant detections of broad line emission features ( e.g. at 7@xmath7 and 11@xmath7 ) and some diffuse broad line emission ( e.g. around -3@xmath7 -11@xmath7 ) . the nh@xmath0 molecule has a stable abundance over a large range of densities and temperature without depletion onto grains . hence its emission lines can be used to trace the dynamics in the bulk of the dense molecular accretion flow . the detected velocity gradients can be explained by the marginally centrifugally supported motion of the molecular gas , in response to the gravity of the enclosed molecular and the stellar mass ( see liu et al . 2010 for more discussions ) . the projected area and the rotational motions traced by the ch@xmath0oh are highly consistent with those which are traced by the nh@xmath0 emissions . this suggests that these two molecules are tracing dense gas in the same region . nevertheless , there are differences in their detailed brightness distributions which suggest that in this particular source , the ch@xmath0oh emissions are tracing different excitation / chemical conditions ( e.g. temperature ) , in the same flow traced by nh@xmath0 ( see also the discussions for the ch@xmath0oh emissions in liu , ho & zhang 2010 ) . in addition , the abundance of the ch@xmath0oh molecule may also be affected by outflow . the nh@xmath0 ( 3,3 ) main hyperfine inversion transition has comparable upper level energy ( e@xmath12/k = 124.5 k ) with the highest excitation ch@xmath0oh 5(-3,3)4(-3,2 ) e transition ( e@xmath12/k = 96.9 k ) , but in contrast it shows an extended distribution . one explanation is that the nh@xmath0 molecule has a higher abundance ( [ nh@xmath0]/[h@xmath9 ] = 10@xmath21 ; keto , ho & haschick 1987 ) than the ch@xmath0oh molecule ( [ ch@xmath0oh]/[h@xmath9 ] = 2@xmath2210@xmath23 ; takakuwa , ohashi , & hirano 2003 ) , and thus becomes optically thick and shows strong emission . the excellent match between the nh@xmath0 emission and the lowest excitation ch@xmath0oh emission suggests that the emissions of both molecules trace the real physical structures . we know that for the dense gas with temperature around 50 k , the statistical weight compensates the boltzmann factor , and therefore the population of nh@xmath0 at the ( 3,3 ) level can be comparable to the population at the lowest excitation ( 1,1 ) level . the ch@xmath0oh emissions and the nh@xmath0 ( 3,3 ) main hyperfine emission may both trace a population of molecular gas which is significantly warmer and denser than the ambient molecular gas . _ we call this warm ( @xmath2430 k ) and dense ( @xmath510@xmath10 @xmath11 ) region the massive envelope hereafter . _ the previous observations on c@xmath6o ( 21 ) unveiled a parsec scale filamentary structure in the south of the massive envelope ( ho , terebey , & turner 1994 ) . the distribution of the molecular mass on an even larger scale has to be further examined by sensitive single dish maps . the selected ch@xmath0oh transitions have higher einstein a coefficients than the nh@xmath0 ( 3,3 ) main hyperfine inversion transition , and potentially only trace the denser components . the observations in the clearest example of photon - dominated regions ( pdr ) , the orion bar , further suggest that the ch@xmath0oh emissions trace the clumpy materials , which have an h@xmath9 volume density higher than 10@xmath25 @xmath11 , and are self - shielded from photo ionization ( leurini et al . 2010 ) . the abundance of the ch@xmath0oh molecule can be greatly enhanced if the molecular gas is shocked by high velocity outflows with velocities greater than @xmath820 kms@xmath26 ( see discussions in takakuwa , ohashi , & hirano 2003 ) . we therefore can not rule out the possibilities that zones with locally enhanced ch@xmath0oh abundance / emission are distributed over the entire region . part of those extended nh@xmath0 emissions can also be attributed to the externally heated lower density surfaces of the extended structures . other possibilities will have to be investigated by higher resolution observations which define the detailed temperature and density profiles of individual local structures . in figure [ fig_ionout ] , we compare the distribution of the molecular gas traced by the ch@xmath0oh transitions with the distribution of the ionized gas traced by the 3.6 cm free free continuum emission . by comparing the left panel of figure [ fig_nh3 ] with this figure , we find that the 3.6 cm free - free continuum emissions peak at the hot toroid . the distribution of the extended free - free continuum emission fits into the projected area of the low column density cavities seen in the ch@xmath0oh rgb map . these observed features suggest an overall geometry of a core envelope cavity system . this overall geometry resembles the standard disk envelope system in the low mass ( @xmath31 m@xmath4 ) star forming region with bipolar outflow and outflow cavity , except on a larger and more massive scale . this overall geometry remains even after the embedded ob cluster starts the nuclear burning , and other physical processes start to affect the dynamical evolution ( section [ chap_introduction ] ) . we emphasize that the subject under consideration is the formation and accretion of a cluster of ob star . by comparing the flux of the ionizing photons and the bolometric luminosity , ho and haschick ( 1981 ) suggested that a few massive stars ( from 06.5 to b0 ) have already been formed and are embedded in the central 0.1 pc region ( see also the discussions in keto 2002 , sollins & ho 2005 , and keto & wood 2006 ) . this cluster of ob stars contains @xmath8200 m@xmath4 of stellar mass in total . as pointed out by sollins and ho ( 2005 ) , the source g10.6 - 0.4 stands distinct from the cases where a single massive star dominates at the center ( e.g. iras 20126 , iras 18089 , g192.16 , etc . zhang et al . 1998 ; beuther et al . 2004 ; shepherd et al . 2001 ) , which might have formed in a process similar to low mass stars ( keto & zhang 2010 ) . in g10.6 - 0.4 , a parsec scale massive envelope ( @xmath242500 m@xmath4 over the central 30@xmath7 region ; ho , terebey & turner 1994 ) appears to be undergoing a coherent motion in response to the gravity of the enclosed mass and the specific angular momentum . in this case , the mass of the embedded ob stars is a less significant fraction ( @xmath110% ) as compared to the molecular mass in the envelope . the fact that a concentration of ob stars formed in the small central 0.1 pc region suggests that the global contraction of the massive envelope may have been efficient . we note that in another ob cluster forming region g20.08 - 0.14n ( [email protected]@xmath2210@xmath10 l@xmath4 , [email protected] kpc ) , the emissions of the nh@xmath0 molecules and various hot core tracers also show a similar geometry and kinematic profile with those in g10.6 - 0.4 ( galvn - madrid et al . 2009 ) . figures [ fig_cs ] and [ fig_csx ] show the velocity integrated ( moment 0 ) map of the cs ( 10 ) emission , the 1.3 mm continuum image , and the 3.6 cm continuum image . in the 3.6 cm continuum image ( figure [ fig_csx ] ) , we see three isolated uc hii regions ( from east to west , uc hii region a , b , c hereafter ) , of which we also detect their free - free continuum emission at 1.3 mm ( figure [ fig_cs ] , right panel ) . the visibilities of the cs ( 10 ) data cover a range of uv distances of 4245 @xmath27 , which correspond to @xmath852@[email protected] in angular scale . the 1@xmath28 rms in the cs velocity integrated map is @xmath877 mjy / beam@xmath22kms@xmath26 ( 24 k@xmath22kms@xmath26 ) . the achieved brightness sensitivity is comparable to the theoretical rms noise ( also achieved in the channel maps ) . with the presence of the bright uc hii regions , the detection of cs ( 10 ) is locally biased by the continuum subtraction . structures distributed in front of the uc hii regions will be detected in emission line only if they emit brighter cs ( 1 - 0 ) emission than the local free - free continuum background ; otherwise , they will be detected in absorption line . we omit plotting the negative flux due to absorption to enhance the contrast of emission features in the gray scale . structures behind the uc hii region are not affected by the continuum subtraction and are always detected in emission line , unless the 49 ghz continuum emission is optically thick . in regions where the brightness temperature of the free - free continuum emission is comparable with the excitation temperature of the molecular gas , the absolute values of the flux density of the emission line and the absorption line are comparable . smoothed by the finite synthesized beam , the emission line and the absorption line signatures may cancel each other , and reduce the signal to noise ratio . from figures [ fig_cs ] and [ fig_csx ] we see : * the brightest regions of the cs ( 10 ) emission agrees well with the 1.3 mm continuum emission . ( the significant deficit of cs ( 10 ) emission in the middle of the maps is due to the subtraction of the bright free - free continuum in the uc hii region . ) * we see an extended dense flattened structure with a size scale of @xmath80.5 pc . the orientation is indicated by the red dashed line , which has a position angle of 135@xmath14 , and is consistent with the orientation of the central 0.1 pc hot toroid ( liu et al . * northeastern to the dense flattened structure , the extended cs emission shows filamentary structures . the size scale of those filamentary structures is a few times of 0.1 pc . southwestern to the dense flattened structure , we see an upside down * v * shaped cavity wall signature . the 1.3 mm continuum emission arises predominantly from the free - free continuum emission in the central 2@xmath73@xmath7 uc hii region ; in the extended region , the 1.3 mm continuum emission traces the thermal dust emission ( liu et al . 2010 ; liu , ho & zhang 2010 ) . the thermal dust emission is usually regarded as a reliable tracer of the molecular hydrogen . the general agreement between the cs ( 10 ) image and the 1.3 mm continuum image indicates that cs ( 10 ) also traces the molecular hydrogen . however , in the optically thick case , the velocity integrated flux of cs ( 10 ) can be biased by saturation and/or foreground absorption , and also by the non uniform excitation temperature . these explain some inconsistency between the cs ( 10 ) velocity integrated image and the 1.3 mm continuum image . by inspecting the position velocity diagrams ( section [ chap_pv ] ) , we do not see a gap of emission line , and therefore we argue that the self absorption does not severely affect the overall picture of geometry . the excitation temperature only changes the relative strength of emissions , and should not greatly alter the overall picture either , as long as the excitation does not change by a very large factor . the distribution of the cs ( 10 ) emissions is consistent with the overall geometry suggested by our observations of the ch@xmath0oh j=5 transitions . however , instead of seeing a clean biconical feature as in the ch@xmath0oh maps , we detect significant cs ( 1 - 0 ) emission in the projected area of the biconical cavity . this can be due to the fact that the cs ( 10 ) transition has a much lower upper level energy ( e@xmath12 = 2.35 k ) , and a factor of @xmath850 lower einstein a coefficient . these two factors make cs easily excited in the outer layer of the cavity wall with lower temperature ( and molecular gas density ) . this property allows us to robustly detect the dynamics of the cavity wall , and explicitly measure the expansional velocity . our cs ( 10 ) maps additionally unveil an unprecedentedly detailed morphology in the massive cluster forming clump . the velocity integrated map apparently shows abundant structures with a size scale of a few arcseconds ( 0.03 pc ) . in figures [ fig_chm78 ] , we present an example channel image at @xmath29@xmath30= -7.8 kms@xmath26 . in this channel , we do not detect compact ( 2@xmath73@xmath7 ) absorption features towards the brightest uc hii region a , which alleviates the potential confusion from the sidelobes of a strong source . we see that the arcsecond scale structures have a high contrast with respect to the background diffuse emission . we note that it is unlikely that our images can achieve the theoretical rms noise level if the extended diffuse emission has dominant contributions to the total flux . the small scale emissions may come from compact dense molecular cores , or from local structures with high temperature or high cs abundance owing to the interactions with the ( proto)stellar activities and shocks . the compact dense molecular cores are potentially the future or current sites of star formation . in figure [ fig_chm78 ] , we see that two significant local maxima of cs ( 10 ) emission are spatially associated with water maser sources ( water maser e , and the cluster of water maser sources around the uc hii region a ; hofner & churchwell 1996 ) . figure [ fig_pvwater ] shows the pv diagrams of three cuts through the water maser sources n , e , and w. from this figure we see detections of bright components near ( @xmath31@xmath7 ) the water maser sources e and w. the water maser source e may be associated with the local maxima of cs ( 10 ) emission at -7.8 kms@xmath26 , or -5.4 kms@xmath26 . we do not find bright local cs ( 10 ) emission peak around the water maser source n , which may be due to the fact that its parent molecular core is already dispersed by the outflows . recalling the small high opacity clumps detected in the nh@xmath0 ( 3,3 ) hyperfine inversion line absorption ( sollins and ho 2005 ) , it is not surprising that more of them are detected in emission line . however , our current data are insufficient to robustly distinguish the dense cores from the local shock and outflow signatures , which leads to the difficulties in a quantitative analysis of the core mass function . in the other paper on high velocity molecular outflows in this region , we will discuss the feedback from those local sites of star formation and the implications of clustering of stars ( liu , ho & zhang 2010 ) . we show the mean velocity map ( moment one ) and the velocity dispersion map ( moment two ) of the cs ( 10 ) emission in figure [ fig_mnt12 ] . from figure [ fig_mnt12 ] , we see that the entire system has a bimodal velocity profile . in addition to the general rotation with velocity gradient from the southeast to the northwest , we see blueshifted gas in the northeast and redshifted gas in the southwest . these additional blueshifted and redshifted gas cover a larger velocity range than the general rotational motion , and the orientation resembles a bipolar expansion with a certain inclination . geometrically , the upside down * v * shaped cavity wall signature in the southwest can also be explained by the bipolar expansion . we note that our 3@xmath28 detection limit is about 18 k , which is only sensitive to structures which are sufficiently warm and have high optical depth . the moment one and moment two maps thus can be biased due to the cutoff of the fainter high velocity line wings , and over interpretations should be omitted . to understand the dynamics of the cavity wall , we make two pv cuts through the southern part of the biconical cavity ( centered at * cut1 : * r.a . = 18@[email protected]@xmath18 , decl = -19@[email protected]@xmath7 , and * cut2 : * r.a . = 18@[email protected]@xmath18 , decl = -19@[email protected]@xmath7 ) with a position angle 140@xmath14 ( consistent with the rotational plane of the central compact hot core pa=140@xmath14@xmath315@xmath14 ; liu et al . 2010 ) ; and we make one pv cut through the uc hii regions b , c , and the northern part of the biconical cavity ( centered at * cutn : * r.a . = 18@[email protected]@xmath18 , decl = -19@[email protected]@xmath7 , with position angle 70@xmath14 ) . features we identify from these three pv cuts are described as follows . owing to the complexity of the observed region and the limited signal to noise ratio of the observations , there could be other dynamical features not revealed in the current maps . [ [ cutn ] ] cutn + + + + from the pv diagram of the cutn ( figure [ fig_pv2 ] ) , we identify the expansional signature in the northern part of the biconical cavity . around the uc hii region b , we marginally see the arc shaped signatures which have broad velocity width , and may also be explained as expansional signatures around the uc hii region b. the expansional velocities in these two regions are about 3 kms@xmath26 . in these two regions , the expansional signatures are confused with the global rotation / contraction of the dense gas , and therefore the size and the expansional velocities are not robustly constrained . the detection of the expansional signature in the uc hii region c is marginal , with a suggested expansional velocity of 3.8 kms@xmath26 . [ [ cut1-and - cut2 ] ] cut1 and cut2 + + + + + + + + + + + + + both the cut1 and cut2 are located south to the dense flattened structure ; the center of cut2 is south of the center of cut1 . we argue that pv cuts in the position angle of 140@xmath14 is less confused by the dynamics of the fast rotating ( @xmath834 kms@xmath26 rotational velocity ) dense gas in the mid - plane of the envelope , and provides the clean information of the dynamics of the molecular cavity wall . the top and bottom panels of figure [ fig_pv ] show the pv diagram of cut1 and cut2 , respectively . the cs ( 10 ) emission in both panels clearly show arc shaped expansional signatures centered at v@xmath30@xmath8 - 3 kms@xmath26 , with an averaged brightness temperature of 2030 k , and the peak brightness temperature of 45 k. supposedly cs ( 10 ) is optically thick at the peak , then the brightness temperature represents the excitation temperature of the molecular gas . the maximum excitation temperature of 45 k in the projected area of the biconical cavity explains why the ch@xmath0oh transitions are difficult to be excited and have low optical depth . the projected linear scale of the expansional signature is about 10@xmath7 ( 0.3 pc ) , which is consistent with the scale of the visually identified biconical features in the cs ( 1 - 0 ) maps ( figures [ fig_cs ] , [ fig_csx ] ) , and the ch@xmath0oh maps ( figures [ fig_nh3 ] , [ fig_ionout ] ) . the arc shaped signatures in the pv diagrams have a different physical size scale and geometry from the typical outflow signatures ( liu , ho , & zhang 2010 ) . the arc shaped feature shown by the cut1 may be explained as the redshifted expansional motion of the cavity wall . since the center of cut1 is closer to the free - free continuum peak , its blueshifted counter part may be affected by the free - free continuum subtraction , and therefore we can not obtain significant detections ; or , it can be explained by the non - uniformity of excitation temperature and density distribution ( the 1@xmath28 detection limit is 5.9 k ) . the arc shaped feature shown by cut2 can be explained as the blueshifted expansional motion . the lack of the redshifted counter part of the expansional motion can either be explained by the asymmetry of molecular gas density , or asymmetrical stellar ionization . the line of sight expansional velocity of both features is about 2.55 kms@xmath26 . this interpretation can be constrained by observing the lower density tracers ( e.g. @xmath32co ( 2 - 1 ) or c@xmath6o ( 2 - 1 ) ) , to sample the lower density / temperature part of the cavity wall . the emissions of those lower density tracers are extended , and the single dish observations will be needed in order to robustly interpret the data .	free continuum emissions in this region . the comparisons of the molecular line emissions with the free free continuum emissions reveal a 0.5 pc scale massive molecular envelope which is being partially dispersed by the dynamically expanding bipolar ionized cavity . lies a compact (.1 pc ) hot ( k ) toroid , in which a cluster of o type stars has formed . this overall geometry is analogous to the standard core collapse picture in the low mass star forming region , with a central ( proto)stellar object , a disk , an envelope , and a bipolar outflow and outflow cavity .	the massive clump g10.6 - 0.4 is an ob cluster forming region , in which multiple uc hii regions have been identified . in the present study , we report arcsecond resolution observations of the cs ( 10 ) transition , the nh ( 3,3 ) main hyperfine inversion transition , the choh j=5 transitions , and the centimeter free free continuum emissions in this region . the comparisons of the molecular line emissions with the free free continuum emissions reveal a 0.5 pc scale massive molecular envelope which is being partially dispersed by the dynamically expanding bipolar ionized cavity . the massive envelope is rotationally flattened and has an enhanced molecular density in the mid plane . in the center of this massive clump lies a compact (.1 pc ) hot ( k ) toroid , in which a cluster of o type stars has formed . this overall geometry is analogous to the standard core collapse picture in the low mass star forming region , with a central ( proto)stellar object , a disk , an envelope , and a bipolar outflow and outflow cavity . however , g10.6 - 0.4 has a much larger physical size scale (.1 pc for typical low mass star forming core ) . based on the observations , we propose a schematic picture of the ob cluster forming region , which incorporates the various physical mechanisms . this model will be tested with the observations of other embedded ob clusters , and with numerical simulations .
0807.4074	i	there are several definitions of orthogonal designs ( ods ) in the literature @xcite the well known being as given in @xcite : [ cod ] a complex orthogonal design ( cod ) @xmath11 ( in short @xmath12 ) for @xmath0 transmit antennas is defined as a @xmath13 matrix such that ( i ) the nonzero entries of @xmath12 are the complex variables @xmath14 and their conjugates and ( ii ) @xmath15 where @xmath16 stands for the complex conjugate transpose and @xmath17 is the @xmath18 identity matrix . the matrix @xmath12 is also said to be a @xmath19 $ ] cod and its rate in complex symbols per channel use is @xmath20 when @xmath21 are real variables , the designs are called real orthogonal design ( rod ) . space - time block codes ( stbcs ) from cods have been widely studied for square designs , i.e. , @xmath22 since they correspond to minimum decoding delay codes for co - located multiple - antenna coherent communication systems . however , non - square designs naturally appear and important in the following situations . 1 . in coherent co - located mimo systems , for a specified number of transmit antennas , non - square designs can give much higher rate than the square designs @xcite . 2 . in non - coherent mimo systems with non - differential detection , non - square designs with @xmath23 lead to low decoding complexity stbcs @xcite . space - time - frequency codes can be viewed as non - square designs @xcite . 4 . in distributed space - time coding for relay channels , rectangular designs naturally appear @xcite . rate @xmath3 non - square cods have been proposed for use in analog transmission with application to channel feedback @xcite . the rate of the square cods falls exponentially with increase in the number of transmit antennas . the following theorem relates the rate of a square od , real / complex , with the number of transmit antennas . for an integer @xmath24 where @xmath25 and @xmath26 and @xmath27 being integers with @xmath28 the hurwitz - radon number @xmath29 is defined as @xmath30 [ thm1 ] the maximal rate of a square rod for @xmath0 transmit antennas is given by @xmath31 where @xmath32 is the hurwitz - radon number of @xmath0 , while that of a square cod is given by @xmath33 where @xmath34 is the exponent of @xmath35 in the prime factorization of @xmath4 several authors have constructed square cods achieving maximal rate @xcite . in @xcite , the following induction method is used to construct square cods for @xmath36 antennas , @xmath37 , starting from @xmath38,~ g_a= \left[\begin{array}{rr } g_{a-1 } & -x_{a}^i_{2^{a-1 } } \\ x_{a}i_{2^{a-1 } } & g_{a-1}^\mathcal{h } \end{array}\right],\ ] ] where @xmath39 is a @xmath40 complex matrix . note that @xmath39 is a square cod in @xmath41 complex variables @xmath42 . it is clear from theorem [ thm1 ] as well as the construction given by that the square ods , real and complex are not bandwidth efficient and naturally one is led to study non - square ods in order to obtain codes with higher rate . it is known that @xcite there always exists a rate-1 rod for any number of transmit antennas . in fact , the existence of rate-1 @xmath43 $ ] rod is equivalent to that of a @xmath44 $ ] square rod . for a rate-1 rod , the minimum value of decoding delay @xmath45 as a function of @xmath0 , denoted by @xmath46 , is given by @xmath47 it is known @xcite that the maximal rate of a non - square cod is equal to @xmath48 when the number of transmit antennas is @xmath49 or @xmath50 . liang in @xcite has given an explicit construction of non - square cods achieving this maximal rate for any number of antennas . there is also another construction of these codes given by lu et al @xcite . the former construction is algorithmic in nature while the latter one is based on _ patch - up _ of several matrices . the minimum decoding delay for the maximal rate non - square cods is , in general , not known . the following theorem states what is known about the minimum delay of these code . for details , see @xcite . [ delaycod ] a tight lower bound on the decoding delay of maximum rate non - square cods for @xmath0 antennas is @xmath51 for @xmath52 or @xmath53 . moreover , if @xmath0 is congruent to @xmath54 or @xmath8 modulo @xmath6 , then this lower bound is achievable . if @xmath0 is congruent to @xmath35 modulo @xmath6 , the minimum decoding delay is upper bounded by @xmath55 . as the rate of these maximal rate codes is close to @xmath10 for large number of antennas , it is sufficient to focus on rate @xmath10 codes when large number of antennas is under consideration . then , a natural problem to study is construction of rate @xmath10 non - square cods with the decoding delay as small as possible . tarokh et al @xcite have given a class of rate @xmath10 codes obtained from rate-1 rods , which has lower delays than those of maximal - rate codes constructed in @xcite for number of transmit antennas more than 5 . for example , for four transmit antennas , the rate @xmath10 code is @xmath56.\ ] ] notice that , contrary to the definition in @xcite of a cod , in this code , the variables appear in a column more than once and each entry of all the columns of the design matrix is scaled by @xmath57 in order to satisfy the condition @xmath58 of a cod . we call such designs _ scaled _ cod which is not a cod in the conventional sense as in @xcite ( definition [ cod ] ) . we define the class of scaled cods as follows : [ scod ] a _ @xmath59-scaled complex orthogonal design _ , for a positive integer @xmath60 ( @xmath59-scaled cod ) @xmath12 is a @xmath61 matrix in @xmath62 complex variables @xmath63 such that a non - zero entry of the matrix is a variable or its complex conjugate , or the negative of these and all the entries of any subset of columns of the matrix is scaled by @xmath64 satisfying the condition : @xmath65 the matrix @xmath12 is also said to be a @xmath19 $ ] @xmath66scaled cod . notice that a @xmath59-scaled cod with with no column scaled by @xmath64 is a cod . in columns with scaling by @xmath64 all the variables appear exactly @xmath59 times . in this paper we consider only the case @xmath67 and call these codes simply scaled - cod . _ contributions of this paper : _ the contributions of this paper may be summarized as follows : for the rate @xmath10 scaled cods of @xcite , all the columns are scaled by the factor @xmath68 which led to the reduced delay compared to the codes of liang and a main result of this paper is that by having only a subset of the columns scaled by @xmath57 further reduction in delay by 50% is possible . we use following notations to refer to the rate 1/2 cods given by tarokh et al @xcite , the maximal rate codes given in lu et al @xcite and the codes of this paper . * * @xmath69 is the maximal rate cod for @xmath0 transmit antennas with the decoding delay as specified in the theorem [ delaycod ] . * * @xmath70 is the rate @xmath10 scaled cods for @xmath0 transmit antennas constructed by tarokh et al @xcite . * * @xmath71 is the rate @xmath10 scaled cods for @xmath0 transmit antennas constructed in this paper . + note that as @xmath0 increases , the maximal rate of @xmath69 approaches @xmath10 , thus two codes @xmath69 and @xmath70 can be compared for large value of @xmath72 based on their delays . it is not difficult to see that the decoding delay of @xmath70 is less than that of @xmath69 for large @xmath0 . we provide an explicit construction of rate @xmath10 scaled cods for any number of transmit antennas such that the decoding delay of these codes is @xmath46 when @xmath0 is the number of transmit antennas , whereas the delay for the codes @xmath70 is @xmath73 the table [ recparameters ] at the top of the next page shows that for large values of @xmath72 but for a marginal decrease in the rate with respect to @xmath74 the codes of this paper are the best codes . * for the case of 9 transmit antennas our rate-@xmath3 code is shown to be of minimal - delay . + c\|\|rrrrrrrrrrrrrrrr @xmath0 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 + decoding delay of @xmath71 & 8 & 8 & 8 & 8 & 16 & 32 & 64 & 64 & 128 & 128 & 128 & 128 + decoding delay of @xmath70 & 16 & 16 & 16 & 16 & 32 & 64 & 128 & 128 & 256 & 256 & 256 & 256 + @xmath69 & 15 & 30 & 56 & 56 & 210 & 420 & 792 & 792 & 3003 & 6006 & 11440 & 11440 + @xmath75 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 + @xmath76 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 & 1/2 + @xmath77 & 2/3 & 2/3 & 5/8 & 5/8 & 3/5 & 3/5 & 7/12 & 7/12 & 4/7 & 4/7 & 9/16 & 9/16 + * as a byproduct of the above mentioned construction , a general construction of square real orthogonal designs ( rods ) is presented which includes as special cases well known constructions of adams , lax and phillips @xcite and geramita and pullman @xcite . * even though scaling only a subset of columns allowed us to decrease the delay , it is shown that such a scaling limits the rate of the design strictly to @xmath78 in other words , the maximal rate of the scaled - cods is @xmath3 when scaling is present in atleast one column . * zero entries in a design increase the peak - to - average power ratio ( papr ) in the transmitted signal and it is preferred not to have any zero entries in the design . this problem has been addressed for square designs in @xcite . all the known maximal rate non - square designs have zero entries . our initial construction of rate-@xmath3 scaled cods have zero entries in the design matrix which will lead to higher peak - to - average power ratio ( papr ) in contrast to the designs @xmath79 however , we show that by post - multiplication of appropriate matrices , our construction leads to designs with no zero entries without change in the parameters of the design . the remaining part of the paper is organized as follows : in section [ sec2 ] , we present the main result of the paper given by theorem [ rate12cod ] . before this , construction of a new set of maximal - rate square rods is given in subsection [ subsec2 - 1 ] . in subsection [ subsec2 - 2 ] , construction of two new sets of rate-1 rods from the maximal - rate square rods of subsection [ subsec2 - 1 ] is presented and in subsection [ subsec2 - 3 ] , construction of the low - delay rate-1/2 scaled - cods is achieved using rate-1 rods of the previous subsection . in subsection [ subsec2 - 4 ] , it is shown that the maximal rate for scaled - cods is @xmath78 for the special case of 9 transmit antennas , in section [ sec3 ] , it is shown that our construction is of minimal delay . in section [ sec4 ] , we show that the codes discussed so far can be made to have no zero entries in by appropriate preprocessing without affecting the parameters of the design . concluding remarks constitute section [ sec5 ] . in appendix [ appendixii ] , it is shown that the well known constructions of square rods by adams - lax - phillips and geramita - pullman are special cases of our construction .	the maximal rate for non - square complex orthogonal designs ( cods ) with transmit antennas is if is even and if is odd , which are close to for large values of a class of maximal rate non - square cods have been constructed by liang ( ieee trans . theory , 2003 ) and lu et . al . theory , 2005 ) have shown that the decoding delay of the codes given by liang , can be reduced by when number of transmit antennas is a multiple of . al . are of minimal delay when is a multiple of however , these minimal delays are large compared to the delays of the rate non - square cods constructed by tarokh et al ( ieee trans . theory , 1999 ) from rate- real orthogonal designs ( rods ) . in this paper this is achieved by giving first a general construction of rate-1 square real orthogonal designs ( rods ) which includes as special cases the well known constructions of adams , lax and phillips and geramita and pullman , and then making use of it to obtain the desired rate- non - square cod . for the case of 9 transmit antennas , our rate- cod is shown to be of minimal - delay . the proposed construction results in designs with zero entries which may have high peak - to - average power ratio ( papr ) and it is shown that by appropriate postmultiplication , a design with no zero entries can be obtained with no change in the code parameters .	the maximal rate for non - square complex orthogonal designs ( cods ) with transmit antennas is if is even and if is odd , which are close to for large values of a class of maximal rate non - square cods have been constructed by liang ( ieee trans . inform . theory , 2003 ) and lu et . al . ( ieee trans . inform . theory , 2005 ) have shown that the decoding delay of the codes given by liang , can be reduced by when number of transmit antennas is a multiple of . adams et . al . ( ieee trans . inform . theory , 2007 ) have shown that the designs of liang are of minimal - delay for equal to and modulo 4 and that of lu et.al . are of minimal delay when is a multiple of however , these minimal delays are large compared to the delays of the rate non - square cods constructed by tarokh et al ( ieee trans . inform . theory , 1999 ) from rate- real orthogonal designs ( rods ) . in this paper , we construct a class of rate- non - square cods for any with the decoding delay equal to of that of the delay of the rate-1/2 codes given by tarokh et al . this is achieved by giving first a general construction of rate-1 square real orthogonal designs ( rods ) which includes as special cases the well known constructions of adams , lax and phillips and geramita and pullman , and then making use of it to obtain the desired rate- non - square cod . for the case of 9 transmit antennas , our rate- cod is shown to be of minimal - delay . the proposed construction results in designs with zero entries which may have high peak - to - average power ratio ( papr ) and it is shown that by appropriate postmultiplication , a design with no zero entries can be obtained with no change in the code parameters .
0706.1004	i	it is an obvious fact that the asymptotic behavior of an oscillatory integral of the form @xmath0 does not change under a smooth change of variables @xmath1 this observation is employed already in the proof of van der corput s lemma ( see , e.g. , @xcite ) , according to which the asymptotic behavior of a one - dimensional oscillatory integral is determined by the maximal order of vanishing at the critical points of the phase function @xmath2 in higher dimensions , the problem of determining the exact asymptotic behavior of an oscillatory integral is substantially more difficult . v.i . arnold conjectured in @xcite that the asymptotic behavior of the oscillatory integral @xmath3 is determined by the newton polyhedron associated to the phase function @xmath4 in a so - called `` adapted '' coordinate system . for some special cases this conjecture was then indeed verified by means of arnold s classification of singularities ( see @xcite ) . later , however , a.n . varchenko @xcite disproved arnold s conjecture in dimensions three and higher . moreover , in the same paper he was able to verify arnold s conjecture for two - dimensional oscillatory integrals . in particular , he proved in dimension two the existence of adapted coordinate systems , and showed that the leading term of the asymptotic expansion of @xmath3 can be constructed from the newton polyhedron associated to the phase function @xmath4 in such an adapted coordinate system . the purpose of this article is to present a new , elementary and concrete approach to the latter results in two dimensions , which is based on the puiseux series expansion of roots of the given function @xmath2 our method applies to arbitrary real analytic functions , and even extends to arbitrary smooth functions of finite type . moreover , by avoiding hironaka s theorem , we can give necessary and sufficient conditions for the adaptedness of a given coordinate system in the smooth , finite type setting .	arnold , plays an important role in the study of asymptotic expansions of oscillatory integrals . in two dimensions , a. n. varchenko gave sufficient conditions for the adaptness of a given coordinate system and proved the existence of an adapted coordinate system for a class of analytic functions without multiple components . varchenko s proof is based on hironaka s theorem on the resolution of singularities . in this article , we present a new , elementary and concrete approach to these results , which is based on the puiseux series expansion of roots of the given function . our method applies to arbitrary real analytic functions , and even extends to arbitrary smooth functions of finite type . moreover , by avoiding hironaka s theorem , we can give necessary and sufficient conditions for the adaptedness of a given coordinate system in the smooth , finite type setting .	the notion of an adapted coordinate system , introduced by v .i . arnold , plays an important role in the study of asymptotic expansions of oscillatory integrals . in two dimensions , a. n. varchenko gave sufficient conditions for the adaptness of a given coordinate system and proved the existence of an adapted coordinate system for a class of analytic functions without multiple components . varchenko s proof is based on hironaka s theorem on the resolution of singularities . in this article , we present a new , elementary and concrete approach to these results , which is based on the puiseux series expansion of roots of the given function . our method applies to arbitrary real analytic functions , and even extends to arbitrary smooth functions of finite type . moreover , by avoiding hironaka s theorem , we can give necessary and sufficient conditions for the adaptedness of a given coordinate system in the smooth , finite type setting .
1606.06016	i	long - range interactions between highly excited rydberg atoms are of interest for quantum information processing with single neutral atoms [ 1,2 ] . resonant dipole - dipole interaction between atoms in an identical _ nl _ rydberg state can be implemented via stark - tuned frster resonances [ 3,4 ] . a rydberg state should be exactly midway between two other rydberg states of the opposite parity [ fig . 1(a ) ] to induce a frster resonance . the electric field corresponding to the frster resonance has certain values defined by the polarizabilities and energy spacing of rydberg states in a zero field . upon appropriate experimental conditions ( highly stable and homogeneous electric field , absence of stray electric fields , weak dipole - dipole interaction ) , stark - tuned frster resonances can be as narrow as a few millivolts per centimeter [ 5 ] . in our earlier papers [ 6 - 8 ] we studied the line shape of the frster resonance @xmath2 in cold rb rydberg atoms excited by a broadband pulsed laser radiation via a three - photon transition . the resonance was recorded by slowly scanning a weak electric field near the resonant value of 1.79 v / cm [ fig . when the field was scanned by @xmath00.2 v / cm , the frequency of the optical transition @xmath3 on the third excitation step changed by tens of megahertz due to the stark effect . this frequency change was unimportant for broadband pulsed radiation as the radiation line width was much broader ( @xmath010 ghz ) . however , an electric - field pulse was applied at the moment of laser excitation to pull out the cold rb photoions formed due to photoionization by the intense pulsed laser radiation ; otherwise , the frster resonance became asymmetrical due to inhomogeneous electric fields from the photoions [ 8 ] . in our recent experiments [ 2,9,10 ] we have switched to three - photon excitation by narrowband cw lasers . this prevents the appearance of photoions , since the laser intensities used are much lower than those for pulsed excitation , and the pulling electric - field pulse is not required . however , scanning the electric field by just 50 mv / cm shifts the rydberg level out of resonance with the laser radiation , as the cw lasers have line widths below 1 mhz [ 9 ] . in order to avoid this problem , one needs to apply a stark - switching technique [ 11 - 14 ] to excite the atoms first in a fixed electric field and then to induce the interactions in a lower electric field , which is scanned across the frster resonance [ 10,13 ] , as shown in fig . we have found that the transients at the edges of the controlling electric pulses strongly affect the line shapes of the frster resonances , since the population transfer at the resonances occurs on a time scale of @xmath0100 ns , which is comparable with the duration of the transients . for example , a short - term ringing at a certain frequency causes additional radio - frequency ( rf)-assisted frster resonances , while non - sharp edges lead to asymmetry ( see fig . 3 ) . the short - time scale of the rydberg interactions between cold atoms was also observed in refs . [ 15,16 ] . ( color online ) ( a ) frster resonance rb(_np_)+rb(_np_)@xmath4rb(_ns_)+rb([__n__+1]_s _ ) for two rb rydberg atoms . dipole - dipole interaction induces transitions from the initial @xmath5 state to the final @xmath6 and @xmath7 states in both atoms . ( b ) timing diagram of the laser and electric - field pulses . ( c ) collective states of the frster resonance rb(37__p__)+rb(37__p__)@xmath4rb(37_s_)+rb(38_s _ ) in the dc electric field . intersection at 1.79 v / cm corresponds to a stark - tuned frster resonance . ( d ) collective states of the frster resonance rb(39__p__)+rb(39__p__)@xmath4rb(39_s_)+rb(40_s _ ) in the dc electric field . a dc stark - tuned frster resonance is impossible , but it can be induced by adding a @xmath0100-mhz radio - frequency field ( green arrow ) that binds the collective states [ 10 ] . ] in this paper , we present a detailed experimental and theoretical analysis of the frster resonance line shapes and time dynamics in a time - varying electric field used for the stark switching . the resonance under study is the frster resonant energy transfer @xmath1s_{1/2 } ) $ ] due to dipole - dipole interaction of two rb rydberg atoms [ fig . 1(a ) ] in a small single laser excitation volume of a frozen rydberg gas . the energy detuning of this resonance , @xmath8s_{1/2 } ) -2e(np_{3/2 } ) $ ] , is controlled by a weak dc electric field @xmath9 . the energy shift of a rydberg level @xmath10 with nonzero quantum defect is quadratic and is defined by its polarizability , @xmath11 . the detuning is then given by @xmath12s } ) f^{2}.\ ] ] here , @xmath13 is the detuning in a zero electric field ( for example , @xmath14103 mhz for _ _ n__=37 and + 74 mhz for _ _ the detuning can be tuned to zero for rydberg states with @xmath15 , as shown in fig . 1(c ) for the @xmath16 state , while for states with @xmath17 , the dc electric field only increases @xmath18 , as shown in fig . 1(d ) for the @xmath19 state . for the latter , a frster resonance can be obtained by adding a @xmath0100 mhz rf field that induces rf transitions between collective states and compensates for the frster energy defect , as demonstrated in our recent paper [ 10 ] . an experimental and theoretical line - shape analysis of the stark - tuned frster resonances was performed in ref . [ 17 ] for the case of potassium rydberg atoms colliding in a thermal atomic beam . it was found that averaging over atomic velocities leads to a cusped line shape , while resonant collisions in a velocity - selected atomic beam have nearly lorentzian line shape . this finding agrees with what we have observed in a similar experiment on resonant rydberg collisions in a sodium thermal atomic beam [ 18 ] . it is quite surprising that cusp - shaped frster resonances are also observed in cold rydberg atom gases , where the atoms are nearly frozen [ 19,20 ] . line - shape analysis was performed in several papers . in ref . [ 21 ] , it was found theoretically that the rare pair fluctuation at small spatial separation is the dominant factor contributing to the broadening of the frster resonances . our numerical monte carlo simulations using the schrdinger s equation [ 7,22 ] and our experimental data [ 7,10 ] have shown that spatial averaging over the random positions of @xmath20 rydberg atoms interacting in a single laser excitation volume results in cusp - shaped frster resonances as soon as the resonances saturate and the interaction time is long enough . cusp - shaped frster resonances were also observed recently at high rb rydberg atom density in ref . [ 23 ] and an analytical model has been proposed . another recent paper [ 24 ] reports on the broadening and overlapping of the frster resonances in rb rydberg atoms at high density . quasi - forbidden frster resonances in cs rydberg atoms were observed in ref . [ 25 ] . finally , in ref . [ 26 ] , microwave pump - probe experiments also demonstrated cusped line shapes observed in the spectra of dipole - dipole broadened microwave transitions in rb rydberg atoms . the line - shape analysis of the resonant dipole - dipole interaction thus remains a hot topic in the study of cold rydberg atom samples .	the observation of the stark - tuned frster resonances between rydberg atoms excited by narrowband cw laser radiation requires usage of a stark - switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field , which is scanned across the frster resonance . in our experiments with a few cold rb rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the frster resonances , since the population transfer at the resonances occurs on a time scale of ns , which is comparable with the duration of the transients . for example , a short - term ringing at a certain frequency causes additional radio - frequency - assisted frster resonances , while non - sharp edges lead to asymmetry .	the observation of the stark - tuned frster resonances between rydberg atoms excited by narrowband cw laser radiation requires usage of a stark - switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field , which is scanned across the frster resonance . in our experiments with a few cold rb rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the frster resonances , since the population transfer at the resonances occurs on a time scale of ns , which is comparable with the duration of the transients . for example , a short - term ringing at a certain frequency causes additional radio - frequency - assisted frster resonances , while non - sharp edges lead to asymmetry . the intentional application of the radio - frequency field induces transitions between collective states , whose line shape depends on the interaction strengths and time . spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the frster resonance . we present a detailed experimental and theoretical analysis of the line shape and time dynamics of the stark - tuned frster resonancess_{1/2 } ) $ ] for two rb rydberg atoms interacting in a time - varying electric field .
1606.06016	c	in this paper , we have performed a detailed experimental and theoretical analysis of the line shape and time dynamics of the stark - tuned frster resonances @xmath1s_{1/2 } ) $ ] for two rb rydberg atoms interacting in a time - varying electric field . in the theoretical analysis , we used an effective two - level density - matrix model that allowed us to account for the additional broadenings of the frster resonances due to the unresolved hyperfine structure and parasitic ac electric fields . the analytical formulas have been obtained for the amplitude and line shape of the frster resonances that correctly describe the time dynamics and dephasing of the rabi - like population oscillations . averaging over the random spatial positions of two rydberg atoms in the interaction volume leads to the formation of a cusped line shape if the interaction time exceeds 1 @xmath134s and the dipole - dipole interaction is strong enough to broaden the resonance . for the strong resonance , the line shape and width are shown to depend on the interaction time . at short interaction time , the resonance width is limited by the fourier transform of the interaction pulse . these theoretical considerations agree well with our experimental results for two rb rydberg atoms interacting in a single small laser - excitation volume . we have observed both the cusp - shaped frster resonances at the long interaction time and fourier broadened resonances at the short interaction time . the time dependences of their amplitude and width are well reproduced by the numerical simulations . good agreement between experiment and theory confirms that any unresolved ( hyperfine or zeeman ) structure or parasitic ac stark broadening of the frster resonances can be accounted for theoretically by a single parameter @xmath70 . this significantly reduces the number of equations and simplifies the calculations of the line shapes and time dynamics of the frster resonances . the time dynamics itself is represented either by the smooth exponential saturation in disordered atom ensembles , as observed in our present experiment , or by the damped rabi - like oscillations for two frozen rydberg atoms , as in refs . [ 31,32 ] . in our experiments , we have also found that the transients at the edges of the controlling electric pulses strongly affect the line shapes of the frster resonances , since the population transfer at the resonances occurs on a time scale of @xmath0100 ns , which is comparable with the duration of the transients . a short - term ringing at certain frequency causes additional radio - frequency - assisted frster resonances , while non - sharp edges lead to an asymmetry . an intentional application of the radio - frequency field induces transitions between collective states of two rydberg atoms whose line shape depends on the interaction strengths and time . these resonances are the rf transitions between collective floquet rydberg states formed by the rf field due to the stark effect . in the presence of the dc electric field , they can be induced both for frster resonances which can be tuned by the dc field alone and for those which can not be tuned . the van der waals interaction of arbitrary rydberg states can thus be efficiently tuned to resonant dipole - dipole interaction using the rf field . this work was supported by the rfbr grants no . 14 - 02 - 00680 and no . 16 - 02 - 00383 , the russian science foundation grant no . 16 - 12 - 00028 ( for laser excitation of rydberg states ) , the siberian branch of the russian academy of sciences , the eu fp7-people-2009-irses project colima , and the novosibirsk state university .	the intentional application of the radio - frequency field induces transitions between collective states , whose line shape depends on the interaction strengths and time . spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the frster resonance . we present a detailed experimental and theoretical analysis of the line shape and time dynamics of the stark - tuned frster resonancess_{1/2 } ) $ ] for two rb rydberg atoms interacting in a time - varying electric field .	the observation of the stark - tuned frster resonances between rydberg atoms excited by narrowband cw laser radiation requires usage of a stark - switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field , which is scanned across the frster resonance . in our experiments with a few cold rb rydberg atoms we have found that the transients at the edges of the electric pulses strongly affect the line shapes of the frster resonances , since the population transfer at the resonances occurs on a time scale of ns , which is comparable with the duration of the transients . for example , a short - term ringing at a certain frequency causes additional radio - frequency - assisted frster resonances , while non - sharp edges lead to asymmetry . the intentional application of the radio - frequency field induces transitions between collective states , whose line shape depends on the interaction strengths and time . spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the frster resonance . we present a detailed experimental and theoretical analysis of the line shape and time dynamics of the stark - tuned frster resonancess_{1/2 } ) $ ] for two rb rydberg atoms interacting in a time - varying electric field .
1306.3577	i	studies on partial differential equations , or pdes for brevity , are mostly focused on finding properties of pdes within a specific discipline and on developing a technique specialized to them . however , finding a common structure over different disciplines and unifying theories from different subjects into a generalized theory is the direction that mathematics should go in . the purpose of this paper is to develop geometric arguments to combine oleinik or aronson - benilan type one - sided estimates that arise from various disciplines from hyperbolic to parabolic problems . this unification of existing theories from different disciplines will provide a true generalization of such theories to a wider class of pdes . it is clear that algebraic or analytic formulas and estimates that depend on the specific pde can not provide such a unified theory and we need a different approach . in this paper we will see that a geometric structure of solutions may provide an excellent alternative in doing such a unification . the main example of this paper is the entropy solution of an initial value problem of a scalar conservation law , @xmath7 dafermos @xcite and hoff @xcite showed that , if the flux @xmath8 is convex , the entropy solution satisfies the oleinik inequality , @xmath9 in a weak sense . this is a sharp version of a one - sided inequality obtained by oleinik @xcite for a uniformly convex flux case . this inequality provides a uniqueness criterion and the sharp regularity for the admissible weak solution . however , if the flux is not convex , then the oleinik estimate fails . one may find a similar theory from a different discipline of pdes , nonlinear diffusion equations , @xmath10 this equation is called the porous medium equation ( pme ) if @xmath11 with @xmath12 , the fast diffusion equation ( fde ) with @xmath13 , and the heat equation if @xmath14 . aronson and bnilan @xcite showed that , for @xmath15 , its solution satisfies a one - sided inequality @xmath16 this inequality played a key role in the development of nonlinear diffusion theory that the oleinik inequality did . the equation ( [ nonlineardiffusion ] ) is called the @xmath17-laplacian equation ( ple ) if @xmath18 with @xmath19 and its solution satisfies a similar one - sided inequality . however , these inequalities depend on the homogeneity of the function @xmath20 . the oleinik inequality for hyperbolic conservation laws and the aronson - benilan type inequalities for porous medium or p - laplacian equations are one - sided inequalities that provide key features of solutions such as the uniqueness and sharp regularity . even though these key inequalities are from different disciplines of pdes , they reflect the very same phenomenon . however , this kind of one - sided estimates do not hold without convexity or homogeneity assumption of the problem . such a key estimate for a general situation has been the missing ingredient to obtain theoretical progress for a long time in related disciplines . the purpose of this paper is to present a unified and generalized version of such one - sided inequalities for a general first or second order differential equation in the form of @xmath21 where the sub - indices stand for partial derivatives and the initial value @xmath22 is nonnegative and bounded . the main hypothesis on @xmath23 is the parabolicity , @xmath24 which is not necessarily uniformly parabolic . here , we denote @xmath25 and @xmath26 by @xmath27 and @xmath28 , respectively . the solution of ( [ eqn ] ) is not unique in general . for example , the conservation law ( [ c law ] ) is in this form with @xmath29 and its weak solution is not unique . however , it is well known that the zero viscosity limit of a conservation law is the entropy solution . for the wide class of problems in ( [ eqn ] ) , one can still consider zero - viscosity limits as follows . let @xmath30 be small and @xmath31 be the solution to a perturbed problem @xmath32 where @xmath33 and @xmath34 are smooth perturbations of @xmath22 and @xmath23 , respectively , and @xmath34 satisfies @xmath35 if @xmath23 is smooth , one may simply put @xmath36 . in fact @xmath34 is required to be @xmath37 with respect to @xmath28 , @xmath38 with respect to @xmath17 , and @xmath39 with respect to @xmath40 . for a conservation law case , @xmath41 is already smooth enough and such a perturbation is standard . the convergence of the perturbed problem is known for many cases including pme and ple . the focus of this paper is the structure of the limit of @xmath42 as @xmath43 and hence we assume such a convergence . let @xmath5 be a nonnegative fundamental solution of ( [ eqn ] ) with mass @xmath6 , i.e. , @xmath44 the idea for the unification of the one - sided inequalities comes from the observation that they are actually comparisons with fundamental solutions , where a fundamental solution satisfies the equality . for example , the oleinik inequality can be written as @xmath45 for all @xmath46 . similarly , the aronson - bnilan inequality becomes @xmath47 for all @xmath46 . this observation indicates that the unified version of such one - sided inequalities should be a comparison with fundamental solutions . the unification process is to find the basic common feature , which will be given in terms of geometric concept of connectedness of a level set . first we introduce the connectedness of the zero level set in a modified way . [ def.connectedness ] the zero level set @xmath48 is connectable by adding zeros , or simply connectable , if there exists a connected set @xmath49 such that @xmath50 . in other words , if we can connect the zero level set @xmath48 by adding a part of zeros of the function @xmath51 , we call it connectable or simply connected . for example , if the graph of @xmath52 is as given in figure [ fig0 ] , its zero level set is connectable by adding zeros . in other words we are actually interested in sign changes . in this paper the connectedness the level set is always in this sense . notice that , for a uniformly parabolic case that @xmath53 , the usual connectedness is just enough . however , to include the case @xmath54 , we need to generalize the connectedness as in the definition . of the function @xmath51 in the figure is not connected . the set @xmath55 is not connected neither . however , the set @xmath56 is connectable by adding zeros in the sense of definition [ def.connectedness].,width=264 ] finally , we are ready to present the unified version of the one - sided inequalities . [ thm.generalization ] let @xmath57 be the nonnegative zero - viscosity solution of ( [ eqn])-([positivity ] ) , @xmath58 be the fundamental solution with mass @xmath6 , and @xmath59 . then , the zero level set @xmath60 is connectable for all @xmath61 and @xmath4 . the proof of theorem [ thm.generalization ] is given in section [ sect.proofofmaintheorem ] using the zero set theory ( see @xcite ) . main parts of this paper come after the proof . it is shown that the connectedness of the level set is equivalent to the oleinik inequality for a conservation law with a convex flux , theorem [ thm.equi1 ] , and the aronson - benilan inequality for the porous medium and the fast diffusion equation , theorem [ thm.equi2 ] . in this way we may see that the connectedness of the level set is a true unification of the one - sided inequalities from different disciplines . the estimates for solutions of pdes are usually obtained by using analytical relations , but not geometrical ones . however , the geometric approach in this paper will show that they are equally useful and convenient . in fact , in certain situations , geometric relations provide simple and intuitive way to estimate solutions . one of the purposes of this paper is to develop geometric approaches to estimate solutions of pdes . in section [ sect.steepness ] , the connectivity of the zero level set in theorem [ thm.generalization ] is developed to obtain geometric steepness estimates of the solution . a bounded solution is compared to fundamental solutions in theorem [ thm.steepness ] . the steepness comparison can be considered as an estimate of solution gradients . however , in a delicate situation as in the theorem , geometric arguments may provide a relatively simple and intuitive way to estimate of solutions which is not possible by usual analytical approaches . the steepness comparison is used as a key to show the uniqueness of the solution to a conservation law without convexity in theorem [ thm.uniquenessclaw ] . it is shown in the theorem that , if the zero level set in theorem [ thm.generalization ] is connected for all fundamental solutions , it is the unique entropy solution even without the convexity assumption . this steepness comparison also shows that the total variation of the solution is uniformly bounded for any given time and bounded domain in theorem [ thm.tvb ] . such an estimate is well known for a convex flux case , where the oleinik inequality is the key for the estimate . hence it is not surprising that the geometric generalization of the oleinik inequality gives a similar tv estimation without the convexity assumption . the challenge of the geometric approach of this paper is to extend it to multi - dimensions . the main difficulty is that there is no multi - dimensional version of a lap number theory nor a zero set theory . in fact , the number of connected components of zero level set has no monotonicity property , which is the reason why there is no multi - dimensional version of such theories . however , our interest is a special case of comparing a general bounded solution @xmath57 to a fundamental solution @xmath58 . such connectedness will provide the steepness comparison for multi - dimensions . in fact , it is proved in theorem [ thm.heateqn ] that the level set is convex for the heat equation . a brief discussion for an extension of theory to multi - dimensions is given in section [ sect.rn ] .	the oleinik inequality for conservation laws and aronson - benilan type inequalities for porous medium or p - laplacian equations are one - sided inequalities that provide the fundamental features of the solution such as the uniqueness and sharp regularity . in this paper such one - sided inequalities are unified and generalized for a wide class of first and second order equations in the form of where the non - strict parabolicity is assumed . the generalization or unification of one - sided inequalities is given in a geometric statement that the zero level set is connected for all and , where is the fundamental solution with mass . this geometric statement is shown to be equivalent to the previously mentioned one - sided inequalities and used to obtain uniqueness and tv boundedness of conservation laws without convexity assumption . multi - dimensional extension for the heat equation is also given .	the oleinik inequality for conservation laws and aronson - benilan type inequalities for porous medium or p - laplacian equations are one - sided inequalities that provide the fundamental features of the solution such as the uniqueness and sharp regularity . in this paper such one - sided inequalities are unified and generalized for a wide class of first and second order equations in the form of where the non - strict parabolicity is assumed . the generalization or unification of one - sided inequalities is given in a geometric statement that the zero level set is connected for all and , where is the fundamental solution with mass . this geometric statement is shown to be equivalent to the previously mentioned one - sided inequalities and used to obtain uniqueness and tv boundedness of conservation laws without convexity assumption . multi - dimensional extension for the heat equation is also given .
1107.5440	i	we studied the nature of the multiple-@xmath3 ordered states realized in the @xmath0-@xmath1 pyrochlore - lattice heisenberg model by means of a mean - field analysis and a monte carlo simulation . performing a mean - field analysis beyond the previous analysis by reimers _ et al._@xcite , we could explicitly determine the possible multiple-@xmath3 spin structures of the model , which include a cubic - symmetric sextuple-@xmath3 state , a non - cubic quadruple-@xmath3 state and a non - cubic double-@xmath3 state . we have found that these multiple-@xmath3 states have considerably lower free energy than that of the single-@xmath3 spiral , while the free energy difference between these different multiple-@xmath3 states are rather small . with reference to the mean - field results , we also performed an extensive mc simulations of the model , mainly for the case of @xmath98 , to determine which state is really stabilized as an ordered phase . as expected from the mean - field analysis , we found that the system exhibited a phase transition from the paramagnetic phase to the multiple-@xmath3 ordered state characterized by the multiple peaks in the spin structure factor . recent studies have revealed that such multiple-@xmath3 states are also stabilized in other frustrated heisenberg magnets , _ e.g. _ the triangular lattice heisenberg antiferromagnet with the next - nearest or the third neighbor interactions under magnetic fields @xcite . with the help of the mixed - phase method , we found that the cubic - symmetric sextuple-@xmath3 state is stabilized just blow the transition temperature @xmath141 down to at least @xmath185 , while , at sufficiently low temperatures , the non - cubic quadruple-@xmath3 state becomes stable . hence , another phase transition from the sextuple-@xmath3 state to the quadruple-@xmath3 state should occur at a temperature @xmath186 . the nature of each transition was also examined . the transition at @xmath187 is first order , as was already indicated by previous studies . note that , at this transition the cubic symmetry of the lattice is still fully preserved . it is remarkable that , in spite of the incommensurate and rather complex nature of the spin order , the cubic symmetry of the lattice is fully respected in the ordered state . the second transition at @xmath188 is weakly first order , and it accompanies a spontaneous breaking of the cubic symmetry of the lattice . it should be noticed that the phase transition between the sextuple-@xmath3 and the quadruple-@xmath3 states analyzed in the present paper is distinct from the transition between the paramagnetic state and the nematic state ( or the one between the nematic state and the multiple-@xmath3 state ) as discussed by chern _ et al._@xcite . we also performed mc simulations for several smaller values of @xmath189 where chern _ et al . _ observed the nematic phase . in such smaller-@xmath94 region , we found as metastable states both the sextuple-@xmath3 and the quadruple-@xmath3 states in the parameter region where chern _ et al . _ reported the multiple-@xmath3 state ( chern _ et al . _ did not specify the type of the multiple-@xmath3 state ) . thus , there remains a possibility that , even for smaller @xmath94-values where the nematic phase appears at higher temperature region , another phase transition from the sextuple-@xmath3 state to the quadruple-@xmath3 state occurs at a lower temperature . we also determined the explicit spin configuration of the multiple-@xmath3 ordered state . the sextuple-@xmath3 state is a superposition of six sdws running along the wavevector @xmath190 and its cubic - symmetry counterparts . in this sextuple-@xmath3 state , the system fully retains a cubic symmetry of the lattice . by contrast , the quadruple-@xmath3 state is a superposition of two helices and two sdws . this state spontaneously breaks the cubic symmetry of the lattice as one can easily see from the fact that two out of six critical wavevectors should vanish in this state . both the sextuple-@xmath3 and the quadruple-@xmath3 spin configurations are consistent with the ones obtained in our mean - field analysis . in both cases of the sextuple-@xmath3 and the quadruple-@xmath3 states , a broad distribution of internal fields was observed . such broad distributions reflect the distribution of frozen spin moments which arises from the multiple-@xmath3 nature of the ordering . hence , if the pyrochlore magnets are in the multiple-@xmath3 ordered phase we proposed , one should observe two apparently conflicting features , _ i.e. _ , the coexistence of sharp bragg peaks measured by neutron diffraction and of enhanced spin fluctuations measured by local probes such as nmr . experimental observation of the multiple-@xmath3 states as revealed here remains most interesting . the authors are thankful to z. hiroi , s. maegawa and t. arima for useful discussion . this work is supported by grand - in - aid for scientific research on priority areas `` novel state of matter induced by frustration '' ( 19052006 ) . we thank the supercomputer center , institute for solid state physics , university of tokyo , and the cyber media center , osaka university for providing us with the cpu time .	the ordering of the classical heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest - neighbor interaction and the ferromagnetic next - nearest - neighbour interaction is investigated by means of a mean - field analysis and a monte carlo simulation . for a moderate-value , the model exhibits a first - order transition into an incommensurate multiple- ordered state where multiple bragg peaks coexist in the spin structure factor . we show that there are two types of metastable multiple- states , a cubic symmetric sextuple- state and a non - cubic symmetric quadruple- state . based on a monte carlo simulation , we find that the cubic sextuple- state appears just below the first - order transition temperature , while another transition from the cubic sextuple- state to the non - cubic quadruple- state occurs at a lower temperature .	the ordering of the classical heisenberg model on the pyrochlore lattice with the antiferromagnetic nearest - neighbor interaction and the ferromagnetic next - nearest - neighbour interaction is investigated by means of a mean - field analysis and a monte carlo simulation . for a moderate-value , the model exhibits a first - order transition into an incommensurate multiple- ordered state where multiple bragg peaks coexist in the spin structure factor . we show that there are two types of metastable multiple- states , a cubic symmetric sextuple- state and a non - cubic symmetric quadruple- state . based on a monte carlo simulation , we find that the cubic sextuple- state appears just below the first - order transition temperature , while another transition from the cubic sextuple- state to the non - cubic quadruple- state occurs at a lower temperature .
math0612224	i	we consider closed queueing networks containing a server station and @xmath0 client stations . the server station is an infinite server queueing system with identical servers . client stations are single - server queueing systems with an autonomous service mechanism , where customers ( units ) are served only at random instants generated by a strictly stationary and ergodic sequence of random variables . queueing systems with an autonomous service mechanism were introduced and originally studied by borovkov @xcite , @xcite . the formal definition of these systems in the simplest case of single arrivals and departures is as follows . let @xmath6 denote an arrival point process , let @xmath7 denote a departure point process , and let @xmath8 be a queue - length process , and all of these processes are started at zero ( @xmath9 ) . then the autonomous service mechanism is defined by the equation : @xmath10 the queueing systems with an autonomous service mechanism have been studied in many papers ( e.g. abramov @xcite , @xcite , @xcite , fricker @xcite , @xcite , gelenbe and iasnogorodski @xcite ) . the structure of queueing systems or networks with autonomous service and their analysis is much easier than those structure and analysis of usual " systems with generally distributed service times . queueing systems and networks with autonomous service , because of their simple construction , are studied under general settings on dependent inter - arrival and inter - departure times , and their analysis is often based on methods of stochastic calculus and the theory of martingales . the corresponding results for usual markovian queueing systems or networks follow as a particular case of the corresponding results for queueing systems or networks with poisson input and autonomous service . for different applications of queueing systems ( networks ) with autonomous service see e.g. @xcite , @xcite , @xcite and @xcite . the assumption that the queueing mechanism is autonomous substantially simplify the analysis . however , according to sample - path results of @xcite this assumption can be removed . so , all of the main results remain valid for quite general client / server networks without the special assumption that the service mechanism is autonomous . in the present paper we study client / server networks in a semi - markov environment . there has been an increasing attention to queueing systems in a random environment in the literature ( e.g. @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and others ) . however , most of these papers mainly develop the theory and remain far from real - world applications . the aim of the present paper is twofold . first , we establish new theoretical results for client / server networks in semi - markov environment describing the behavior of queue - length processes of this network . second , we show how these theoretical results can be applied to solve real - world problems . some of these problems are solved in the present paper . other ones will be solved in the future . the model of the network , which is considered in this paper , is very close to the models considered in @xcite and @xcite ( see figure 1 ) . for a more general construction of network with two types of node and multiple customer classes see @xcite . the description of the present model is based on that of the model of @xcite . for other papers studying the models of client / server networks see also @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and other papers . the previous assumptions of @xcite , that are also used in the present paper , are repeated below . the departure instants in the @xmath3th client station ( @xmath11 ) are denoted by @xmath12 , @xmath13 , @xmath14 , , and @xmath15 each sequence @xmath16 forms a strictly stationary and ergodic sequence of random variables . the corresponding point process associated with departures from the client station @xmath3 is denoted @xmath17 the total number of units in the network is @xmath1 . the number @xmath1 is a large parameter , and we assume that @xmath1 increases indefinitely . this means that we assume that @xmath1 is a series parameter , and the series of models ( with different @xmath1 ) are considered on the same probability space . it was assumed in @xcite that the service time of each unit in the server station is an exponentially distributed random variable with a _ given _ parameter @xmath18 . in the present paper , the assumption is another . under the assumption that an environment is random ( markov or semi - markov ) , the parameter @xmath18 is not longer a _ constant value_. it is a random variable , taking values in dependence of environment states . ( by environment states we mean the states of the corresponding markov chain , which is described later . ) the same is noted regarding the routing probability matrix . there were the standard assumptions in @xcite that after a service completion at the server station , a unit was transmitted to the client station @xmath3 with probability @xmath4 , @xmath19 , and @xmath20=1 . these assumptions are not longer valid in the case of the system considered in this paper . the routing probabilities are assumed to be random , taking the values in dependence of the environment states as well . let us first describe _ markov states _ of semi - markov environment , and then latter we describe the notion of semi - markov environment as well . the network is assumed to be complete in the following sense . the server station and @xmath0 client stations communicate by links . the number of links is @xmath0 . therefore , the markov chain of the environment states is defined as follows . the number of possible environment states is assumed to be finite or countable infinite . these states are denoted by @xmath21 , @xmath22 . for the markov or semi - markov environment considered later we shall also use the notation @xmath23 . the meaning of this notation is the state of markov chain in time @xmath24 . the initial state is denoted by @xmath25 or @xmath26 . the completeness of the network means that @xmath15 for any @xmath3=1,2 , , @xmath0 there exists @xmath27 , such that @xmath28 . this assumption is not used in our proofs explicitly . nevertheless , it must be mentioned . if @xmath29 for all @xmath27 , then the station @xmath3 becomes isolated and therefore not representative . in the above assumption by @xmath30 we mean the value of probability @xmath31 when the network is in state @xmath21 . it is assumed additionally that for any @xmath22 , the sum of probabilities @xmath32 = 1 . the notation with similar meaning is used for parameter @xmath18 . namely , @xmath33 is assumed to be strictly positive for any state @xmath21 , however @xmath34 = @xmath35 can be equal to 0 ( because @xmath30 need not be strictly positive in general ) . the results of @xcite are associated with the asymptotic analysis of a closed client / server network with a bottleneck station as @xmath1 increases indefinitely . one of the main results of @xcite was then developed in @xcite for networks containing two types of node and multiple customer classes , where one of client stations was bottleneck . the results obtained in @xcite , @xcite , @xcite as well as in preceding paper @xcite all are a theoretical contribution to the theory of client / server computer networks with bottlenecks . the aim of the present paper is another . we follow towards performance analysis , and are aimed to use the known theoretical results of @xcite and @xcite . however , the known theoretical results obtained in these papers are scanty for their immediate application to real telecommunication systems , whose parameters can change in time . therefore , for the purpose of performance analysis , a substantial development of the earlier results related to this model is required . therefore , before studying the behaviour of queueing networks in semi - markov environment , we first study the behaviour of this network in its special case of piece - wise deterministic environment . then the results are extended to the more general situation of semi - markov environment . the paper is organized as follows . in section [ motivation ] , the paper is motivated by formulating the concrete real - world problems , where the results of the present paper can be applied . in section [ definitions ] , necessary notions of piece - wise deterministic , markov and semi - markov environments as well as classification of bottleneck stations are defined . in section [ semi - martingale ] , the semi - martingale decomposition for the queue - length process in semi - markov environment is derived . then in section [ piece - wise deterministic ] , the queue - length processes in piece - wise deterministic environment are studied . in fact we study usual " closed client / server networks under general assumptions . in section [ semi - markov ] , the results are extended to the case of semi - markov environment . in section [ application ] , an example of an application of the main theorems of the present paper to client / server computer network with failing client stations is considered . in section [ discussion ] , new problems and monotonicity conditions associated with these problems for the case of markov environment are discussed . in section [ numerical example ] , the example of numerical study for the simplest network is considered . the results of the paper are concluded in section [ concluding remarks ] .	the paper studies closed queueing networks containing a server station and client stations . the server station is an infinite server queueing system , and client stations are single - server queueing systems with autonomous service , i.e. every client station serves customers ( units ) only at random instants generated by a strictly stationary and ergodic sequence of random variables . the total number of units in the network is . the expected times between departures in client stations are . after a service completion in the server station , a unit is transmitted to theth client station with probability , and being processed in theth client station , the unit returns to the server station . then the routing probabilities and transmission rates ( which are expressed via parameters of the network ) depend on a markov state of the environment . the questions risen in this paper have immediate relation to quality control of complex telecommunication networks , and the obtained results are expected to lead to the solutions to many practical problems of this area of research .	the paper studies closed queueing networks containing a server station and client stations . the server station is an infinite server queueing system , and client stations are single - server queueing systems with autonomous service , i.e. every client station serves customers ( units ) only at random instants generated by a strictly stationary and ergodic sequence of random variables . the total number of units in the network is . the expected times between departures in client stations are . after a service completion in the server station , a unit is transmitted to theth client station with probability , and being processed in theth client station , the unit returns to the server station . the network is assumed to be in a semi - markov environment . a semi - markov environment is defined by a finite or countable infinite markov chain and by sequences of independent and identically distributed random variables . then the routing probabilities and transmission rates ( which are expressed via parameters of the network ) depend on a markov state of the environment . the paper studies the queue - length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network . the questions risen in this paper have immediate relation to quality control of complex telecommunication networks , and the obtained results are expected to lead to the solutions to many practical problems of this area of research .
1502.03137	i	it is now well known that luminous red giants are variable and that the periods of the observed variability lie on discrete sequences in period luminosity diagrams . @xcite and @xcite used data from macho observations of stars in the large magellanic cloud ( lmc ) to define five sequences a , b , c , d and e in the ( @xmath3 , @xmath4 ) and ( @xmath5 , @xmath4 ) planes , respectively ( where @xmath3 is a reddening - free weisenheit index defined as @xmath61.38(@xmath7@xmath6 ) ) . the sequences a , b and c were identified as containing pulsating stars , while sequence e was found to consist of binary stars and sequence d was the sequence formed by the long secondary periods ( lsps ) that occur in 3050% of luminous pulsating red giants . in this paper , the pulsating stars will be discussed . these stars lie on sequences a , b and c and two other sequences a@xmath1 and c@xmath1 which are described below . further examination of the ellipsoidal variables on sequence e can be found in @xcite , @xcite , @xcite and @xcite while studies of the origins of the lsps can be found in @xcite , @xcite , @xcite , @xcite , @xcite and @xcite . following the discovery of sequences a , b and c , @xcite used extensive @xmath5 band photometry combined with macho periods to show that sequence b was in fact two sequences which were renamed b and c@xmath1 . the next refinement to the luminous sequences was by @xcite who used ogle data to show the existence of a new sequence on the short period side of sequence a. @xcite labelled this sequence a@xmath8 but in this paper the designation a@xmath1 will be used ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? @xcite also made the important discovery that sequence a consisted of three closely - spaced parallel sequences . @xcite claimed that sequences b and a@xmath1 also consisted of three closely - spaced parallel sequences ( hereinafter referred to as sub - sequences ) . more recently , @xcite have drawn attention to a probable faint sequence designated f between sequences c@xmath1 and c. @xcite assumed that all the variable luminous red giants found by the macho observations were asymptotic giant branch ( agb ) stars . however , @xcite and @xcite showed that both agb and red giant branch ( rgb ) stars were variable and that there was a slight offset in period between the sequences of rgb and agb stars . @xcite also noted this offset but they did not find evidence for two slightly offset sequences for sequence a@xmath1 which they suggested consisted of agb stars only . however , this result was challenged by @xcite who showed that an rgb component of sequence a@xmath1 does exist . various attempts have been made to identify the pulsation modes associated with the pulsation sequences c , c@xmath1 , b , a and a@xmath1 and the sub - sequences of b , a and a@xmath1 . @xcite ( see also @xcite ) showed that the radial fundamental mode could fit sequence c with reasonable assumptions about the mass of the star and that the first few radial overtone modes had periods similar to those of sequences b ( which now includes c@xmath1 ) and a , although the data available at the time was not extensive enough for a detailed matching of these latter sequences with modes . they also noted that the large - amplitude mira variables fell on sequence c , making them fundamental mode pulsators . additional evidence in favour of this modal assignment is provided by the fact that nonlinear fundamental mode radial pulsation models reproduce the light and velocity curves of local mira variables quite well ( e.g. * ? ? ? * ; * ? ? ? recently , using extensive observational data from ogle , @xcite showed that the period ratios in stars of sequences c and c@xmath1 were consistent with those expected for fundamental mode pulsation of sequence c and first overtone pulsation on sequence c@xmath1 . @xcite compared period ratios for ogle variables near the tip of the rgb with models and concluded that sequences c@xmath1 , b and a corresponded to the radial first , second and third overtones , consistent with the assignments by @xcite and @xcite . in contrast to the above results , @xcite concluded that the sequences a , b and c@xmath1 corresponded to the radial 2nd overtone , first overtone and fundamental modes , respectively , when they used used radial pulsation models to try fit the sequences in the period luminosity ( pl ) plane at rgb luminosities ( see also @xcite ) . this means that the longer period sequence c containing the miras has no explanation in terms of radial pulsation . this study was extended by @xcite who matched the a and b sequences at rgb luminosities to sequences of kepler radial mode pulsators in a pl plane where frequency data was used as a proxy for luminosity . this result produces a close match between sequences b and a and the radial first and second overtones , respectively , in agreement with @xcite but not with @xcite , @xcite and @xcite . there thus exists two extant assignments of the radial modes to the pl sequences a , b , c@xmath1 and c that differ by one radial order . in another study using kepler data , @xcite showed that in the luminous kepler red giants , triplets of modes with periods corresponding to spherical degrees @xmath2=0 , 2 and 1 ( in increasing order of period ) are excited for a given radial order . the mode with @xmath2=1 has the largest amplitude for radial orders @xmath9=3 or more ( the second or higher radial overtones ) . this suggests the ogle sequences b , a and a@xmath1 may be dominated by @xmath2=1 modes . in this paper , the period and luminosity data given in the ogle iii catalogue of long - period variables ( lpvs ) in the lmc @xcite is analysed in detail . purely empirical results related to the modes , masses and evolution of the stars on the sequences are derived . then the data are compared to pulsation models in order to throw further light on the modes of pulsation involved .	the period luminosity sequences and the multiple periods of luminous red giant stars are examined using the ogle iii catalogue of long - period variables in the large magellanic cloud . shows that the radial pulsation modes associated with sequences a , a , b , c and c are the 4th , 3rd , 2nd and 1st overtones and the fundamental mode , respectively .	the period luminosity sequences and the multiple periods of luminous red giant stars are examined using the ogle iii catalogue of long - period variables in the large magellanic cloud . it is shown that the period ratios in individual multimode stars are systematically different from the ratios of the periods at a given luminosity of different period luminosity sequences . this leads to the conclusion that the masses of stars at the same luminosity on the different period luminosity sequences are different . an evolutionary scenario is used to show that the masses of stars on adjacent sequences differ by% at a given luminosity , with the shorter period sequence being more massive . the mass is also shown to vary across each sequence by a similar percentage , with the mass increasing to shorter periods . on one sequence , sequence b , the mass distribution is shown to be bimodal . it is shown that the small amplitude variables on sequences a , a and b pulsate in radial and nonradial modes of angular degree=0 , 1 and 2 , with the=1 mode being the most common . the stars on sequences c and c are predominantly radial pulsators (=0 ) . matching period ratios to pulsation models shows that the radial pulsation modes associated with sequences a , a , b , c and c are the 4th , 3rd , 2nd and 1st overtones and the fundamental mode , respectively . [ firstpage ] stars : agb and post - agb stars : oscillations stars : variables : general .
1502.03137	i	multiple pulsation modes in stars in the ogle iii catalogue of lpvs in the lmc have been examined . it has been shown that the ratios of the multiple periods in individual stars do not agree with the ratios of the periods of the sequences of lpvs in the pl diagram . this leads to the conclusion that the average masses of stars on the different sequences vary , with the shorter period sequences containing more massive stars . an examation of the evolution of stars in the pl diagram shows that the mass variation between sequences is the same as the mass variation across individual sequences . as an example , it is shown that the average mass of a star on sequence a is @xmath026% higher than the average mass of a star on sequence b and that the mass variation across sequence a is of a similar magnitude , with the more massive stars on the shorter period side of the sequence . in general , the masses of stars at a fixed luminosity on adjacent sequences are found to increase by @xmath01626% towards the shorter period sequence . fitting pulsation models to the period ratios in multimode pulsators shows that the sequences c , c@xmath1 , b , a and a@xmath1 correspond to pulsation in radial orders 1 to 5 , respectively ( with radial order 1 corresponding to the fundamental mode ) . closely - spaced modes revealed by the period ratios in individual stars show the presence of nonradial modes . the observed period ratios indicate the presence of the @xmath30 , 1 and 2 modes on sequence a ( radial order 4 ) and the @xmath30 and 1 modes on sequence b ( radial order 3 ) . the relative populations and amplitudes of the modes of different @xmath2 show that the @xmath31 mode is the most common and of the largest amplitude in both sequences . the positions of secondary mode sequences relative to primary mode sequences in the pl diagram also suggest that the @xmath31 mode is the most prominent primary and secondary mode on sequences a@xmath1 , a and b and that the @xmath30 mode is the most prominent primary and secondary mode on sequences c@xmath1 and c. this result is supported by the good fit of the period ratios in radial pulsation models to the observed period ratios .	it is shown that the period ratios in individual multimode stars are systematically different from the ratios of the periods at a given luminosity of different period luminosity sequences . this leads to the conclusion that the masses of stars at the same luminosity on the different period an evolutionary scenario is used to show that the masses of stars on adjacent sequences differ by% at a given luminosity , with the shorter period sequence being more massive . the mass is also shown to vary across each sequence by a similar percentage , with the mass increasing to shorter periods . on one sequence , sequence b , the mass distribution is shown to be bimodal .	the period luminosity sequences and the multiple periods of luminous red giant stars are examined using the ogle iii catalogue of long - period variables in the large magellanic cloud . it is shown that the period ratios in individual multimode stars are systematically different from the ratios of the periods at a given luminosity of different period luminosity sequences . this leads to the conclusion that the masses of stars at the same luminosity on the different period luminosity sequences are different . an evolutionary scenario is used to show that the masses of stars on adjacent sequences differ by% at a given luminosity , with the shorter period sequence being more massive . the mass is also shown to vary across each sequence by a similar percentage , with the mass increasing to shorter periods . on one sequence , sequence b , the mass distribution is shown to be bimodal . it is shown that the small amplitude variables on sequences a , a and b pulsate in radial and nonradial modes of angular degree=0 , 1 and 2 , with the=1 mode being the most common . the stars on sequences c and c are predominantly radial pulsators (=0 ) . matching period ratios to pulsation models shows that the radial pulsation modes associated with sequences a , a , b , c and c are the 4th , 3rd , 2nd and 1st overtones and the fundamental mode , respectively . [ firstpage ] stars : agb and post - agb stars : oscillations stars : variables : general .
nucl-ex0201021	r	the experiments were performed at the vivitron tandem facility of the ires strasbourg laboratory using 112 mev and 180 mev @xmath1si beams which were incident on @xmath2c targets ( 160 and 180 @xmath18g/@xmath19 thick , respectively ) mounted in the icare scattering chamber @xcite . the effective thicknesses of the @xmath2c targets were accurately determined using rutherford back scattering ( rbs ) techniques with @xmath20h and @xmath21he beams provided by the strasbourg 4 mv van de graaff accelerator @xcite . the carbon buildup corrections were found to be less than 2@xmath22 of the total of c atoms in the targets . both the heavy fragments ( a @xmath3 10 ) and their associated lcp s ( protons and @xmath4 particles ) were detected in coincidence using the icare charged - particle multidetector array @xcite which consists of nearly 40 telescopes . inclusive data have also been collected for heavy fragments and lcp s and presented in sec . iii.a . for the measurement at e@xmath10(@xmath1si ) = 112 mev , the heavy fragments consisting of er as well as quasi - elastic , deep - inelastic , and fusion - fision fragments , were detected in 8 gas - silicon hybrid telescopes ( ic ) , each composed of a 4.8 cm thick ionization chamber , with a thin mylar entrance window , followed by a 500 @xmath18 m thick si(sb ) detector . the ic s were located at @xmath23 = @xmath2415@xmath25 , -20@xmath25 , @xmath2425@xmath25 , -30@xmath25 , -35@xmath25 , and -40@xmath25 in two distinct reaction planes ( for each plane , the positive and negative angles are defined in a consistent manner as for the lcp detectors described below ) . the in - plane detection of coincident lcp s was done using 4 three - element telescopes ( tl3 ) ( 40 @xmath18 m si , 300 @xmath18 m si , and 2 cm csi(tl ) ) placed at forward angles ( @xmath23 = + 15@xmath25 , + 25 @xmath25 , + 35@xmath25 , and + 45@xmath25 ) , 16 two - element telescopes ( tl2 ) ( 40 @xmath18 m si , 2 cm csi(tl ) ) placed at forward and backward angles ( + 40@xmath25 @xmath9 @xmath23 @xmath9 + 115@xmath25 ) and , finally , two other ic telescopes located at the most backward angles @xmath23 = + 130@xmath25 and + 150@xmath25 . the csi(tl ) scintillators were coupled to photodiode readouts . the ic s were filled with isobutane at a pressure of 30 torr for the backward angle telescopes and of 60 torr for the forward angle detectors , thus allowing for the simultaneous measurement of both light and heavy fragments . for the measurement at e@xmath10(@xmath1si ) = 180 mev , three distinct reaction planes were defined . two for in - plane correlations and a third one , perpendicular to the lcp detection plane , for out - of - plane correlation measurements . the heavy fragments were detected in 10 ic s located at @xmath23 = @xmath2410@xmath25 , @xmath2415@xmath25 , @xmath2420@xmath25 , and @xmath2425@xmath25 ( @xmath26 = 0@xmath25 ) for the in - plane coincidences , and at @xmath23 = + 10@xmath25 and + 20@xmath25 ( @xmath26 = 90@xmath25 ) for the out - of - plane coincidences . both the in - plane and out - of - plane coincident lcp s were detected using 3 tl3 s placed at forward angles ( 2 at @xmath23 = + 30@xmath25 and one at @xmath23 = + 35@xmath25 ) and 24 tl2 s placed at forward and backward angles ( + 40@xmath25 @xmath9 @xmath23 @xmath9 + 95@xmath25 ) . the ic s were filled with isobutane at a pressure of 60 torr . the acceptance of each telescope was defined by thick aluminium collimators . the distances of these telescopes from the target ranged from 10.0 to 30.0 cm , and the solid angles varied from 1.0 msr at the most forward angles to 5.0 msr at the backward angles , according to the expected counting rates . the energy calibrations of the different telescopes of the icare multidetector array were done using radioactive @xmath27th and @xmath28am @xmath4-particle sources in the 5 - 9 mev energy range , a precision pulser , and elastic scatterings of 112 mev and 180 mev @xmath1si from @xmath29au , @xmath1si , and @xmath2c targets in a standard manner . in addition , the @xmath2c(@xmath14o,@xmath4)@xmath13mg@xmath30 reaction at e@xmath10 = 53 mev @xcite was used to provide known energies of @xmath4 particles feeding the @xmath13 mg excited states , thus allowing for calibration of the backward angle detectors . the proton calibration was achieved using scattered protons from formvar targets bombarded in reverse kinematics reactions with both @xmath1si and @xmath14o beams . on an event - by - event basis , corrections were applied for energy loss of heavy fragments ( a @xmath3 10 ) in the targets and in the entrance window mylar foils of the ic s and thin al - mylar foils of the si diodes , and for the pulse height defect in the si detectors . the ic energy thresholds and energy resolution for heavy fragments are better than 1.5 mev / nucleon and 0.7@xmath22 , respectively , as shown in fig . 2 for the c and o exit fragments for the @xmath1si(112 mev ) + @xmath2c reaction at @xmath23 = 15@xmath31 . the total energy resolution of 8.78 mev @xmath4 particles from thorium sources has been found to be better than 2.2@xmath22 for both the three - element and two - element light - ion csi(tl ) telescopes . absolute cross sections of inclusive measurements could be obtained within 10 - 12@xmath22 error bars as due to 3 - 5@xmath22 uncertainties in the target thickness and to 8 - 10@xmath22 uncertainties in the electronic deadtime corrections . more details on the experimental setup of icare and on the analysis procedures can be found in refs . @xcite and references therein .	both inclusive and exclusive measurements of the heavy fragments ( a 10 ) and their associated light charged particles ( protons and particles ) have been made at the ires strasbourg vivitron tandem facility at bombarding energies of(si ) = 112 mev and 180 mev by using the icare charged particle multidetector array . pacs number(s ) : 25.70.gh , 25.70.jj , 25.70.mn , 24.60.dr	the possible occurence of highly deformed configurations in theca di - nuclear system formed in thesi +c reaction is investigated by analyzing the spectra of emitted light charged particles . both inclusive and exclusive measurements of the heavy fragments ( a 10 ) and their associated light charged particles ( protons and particles ) have been made at the ires strasbourg vivitron tandem facility at bombarding energies of(si ) = 112 mev and 180 mev by using the icare charged particle multidetector array . the energy spectra , velocity distributions , in - plane and out - of - plane angular correlations of light charged particles are compared to statistical - model calculations using a consistent set of parameters with spin - dependent level densities . this spin dependence approach suggests the onset of large nuclear deformation inca at high spin . this conclusion might be connected with the recent observation of superdeformed bands in theca nucleus . the analysis of particles in coincidence withs fragments suggests a surprisingly strongbe cluster emission of a binary nature . pacs number(s ) : 25.70.gh , 25.70.jj , 25.70.mn , 24.60.dr
nucl-ex0201021	c	the possible occurence of highly deformed configurations in the @xmath0ca dinuclear system has been investigated by using the icare charged - particle multidetector array at the vivitron tandem facility of the ires strasbourg . the properties of the emitted lcp s in the @xmath1si + @xmath2c reaction , have been analysed at two bombarding energies e@xmath10 = 112 mev and 180 mev , and compared with a statistical model that was adopted to calculate evaporation spectra and angular distributions for deformed nuclei . a monte carlo technique has been employed in the framework of the well documented hauser - feshbach code cacarizo . the measured observables such as velocity distributions , energy spectra , in - plane and out - of - plane angular correlations are all reasonably well described by the monte carlo calculations when they include spin - dependent level densities , and indicate that effects due to differences in nuclear shapes are large enough to be observed . the magnitude of the adjustements in the yrast line suggests significant deformation effects at high spin for the @xmath0ca dinuclear system comparable to recent @xmath76-ray spectroscopy data for the @xmath0ca nucleus at much lower spins @xcite . the extent to which the resonant behaviour @xcite is responsible to the observed nuclear deformation is still an open question . a non - statistical binary component is found in the @xmath4-particle energy spectra measured in coincidence with s residues that is attributed to the cluster decay of unbound @xmath96be nuclei , produced through the @xmath4-cluster - transfer reaction @xmath1si + @xmath2c @xmath42 @xmath6s + @xmath7be @xcite . this new type of `` transferlike '' mechanism , which does not appear at lower bombarding energies @xcite below threshold , allows to populate some n = z nuclei with a well defined excitation energy . therefore , sophisticated particle-@xmath76 experiments ( see refs . @xcite for instance ) using sc euroball iv and/or sc gammasphere should be performed in the very near future in order to well define and understand what are the best types of reaction which can populate significantly the superdeformed bands discovered and/or predicted in this mass region @xcite . this paper is based upon the ph.d . thesis of m. rousseau , universit louis pasteur , strasbourg , 2000 . the authors would like to thank the staff of the vivitron for providing us with good stable beams , m.a . saettel for preparing the targets , and j. devin and c. fuchs for their excellent support in carrying out these experiments . particular appreciation to m.a . saettel for preparing the targets , and to j.p . stockert and a. pape for assistance during their rbs measurements . we also whish to thank n. rowley and w. catford for useful discussions and for a careful reading of the manuscript . one of us ( m.r . ) would like to acknowledge the conseil rgional dalsace for the financial support of his ph.d . thesis work . parts of this work has also been done in collaboration with c.e . during his summer stay at the ires with a janus grant of in2p3 . this work was sponsored by the french cnrs / in2p3 , and partially by the cnrs / nsf and cnrs / cnpq collaboration programs . d. shapira , r. novotny , y. c. chan , k. a. erb , j. l. c. ford jr . , j. c. peng , and j. d. moses , phys . lett . * 114b , 111(1982 ) ; d. shapira , d. schull , j. l .c . ford , jr . , b. shivakumar , r. l. parks , r. a. cecil , and s. t. thornton , phys . * 53 , 1634 ( 1984 ) . * * b. fornal , f. gramegna , g. prete , r. burch , g. derasmo , e. m. fiore , l. fiore , a. pantaleo , v. paticchio , g. viesti , p. blasi , n. gelli , f. lucarelli , m. anghinolfi , p. corvisiero , m. taiuti , a. zucchiatti , p. f. bortignon , j. ruiz , g. nebbia , m. gonin , and j. b. natowitz , + phys . b * 255 * , 325 ( 1991 ) . c. bhattacharya , m. rousseau , c. beck , v. rauch , r.m . freeman , d. mahboub , r. nouicer , p. papka , o. stezowski , a. hachem , e. martin , a.k . dummer , s.j . sanders , and a. szanto de toledo , phys . rev . c * 65 * , 014611 ( 2002 ) . m. rousseau _ et al . _ , in proceedings of the 7@xmath97 international conference on clustering aspects of nuclear structure and dynamics , eds . m. korolija , z. basrak and r. caplar ( world scientific publishing co. , singapore , 2000 ) , p.189 . et al . _ , in proceedings of the 9@xmath97 international conference on nuclear reactions , varenna , italy , 2000 , edited by e. gadioli [ ricerca scientifica ed educatione permanente , suppl . * 115 , ( 2000 ) p. 407 ] . * m. rousseau _ et al . _ , in proceedings of the xxxix international winter meeting on nuclear physics , bormio , italy , 2001 , edited by i. iori [ ricerca scientifica ed educatione permanente , suppl . * 117 , ( 2001 ) p. 370 . ] . * g. viesti , v. rizzi , d. fabris , m. lunardon , g. nebbia , m. cinausero , b , e. fioretto , g. prete , a. brondi , g. la rana , r. moro , e. vardaci , m. aiche , m. m. aleonard , g. barreau , d. boivin , j. n. scheurer , j. f. chemin , k. hagel , j. b. natowitz , r. wada , s. courtin , f. haas , n. rowley , b. m. nyako , j. gal and j. molnar , phys . lett . * 521b , 165 ( 2001 ) . * r. nouicer , c. beck , r .m . freeman , f. haas , n. aissaoui , t. bellot , g. de france , d. disdier , g. duchne , a. elanique , a. hachem , f. hoellinger , d. mahboub , v. rauch , s. j. sanders , a. dummer , f. w. prosser , a. szanto de toledo , sl . cavallaro , e. uegaki , and y. abe , phys . c * 60 , 41303 ( 1999 ) . * c. beck , r. nouicer , d. disdier , d. duchne , g. de france , r. m. freeman , f. haas , a. hachem , d. mahboub , v. rauch , m. rousseau , s. j. sanders , and a. szanto de toledo , phys . rev . c * 63 , 014607 ( 2001 ) . * figure 1 : experimental c ( solid squares ) , n ( solid triangles ) , and o ( solid circles ) cross sections measured in the @xmath1si + @xmath2c reaction @xcite as compared to the calculations ( dotted curves ) performed with the equilibrium model of orbiting @xcite . the solid curves are the predictions of the transition - state model @xcite . the open squares , triangles and circles are the present data of the c , n , and o fully - damped yields with error bars smaller than the size of the symbols . the full diamonds correspond to er cross sections quoted in refs . @xcite . figure 3 : angular distributions ( open symbols ) of heavy fragments ( c , n , o , and ne ) measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 112 mev . the full symbols are the c , n and o data taken from ref . @xcite at e@xmath10 = 115 mev . the ne angular distribution has been scaled down by a factor 10 for the sake of clarity . the curves correspond to 1/sin@xmath32 functions . figure 4 : angular distributions of heavy fragments ( z = 5 to 11 ) measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the n and na angular distributions have been scaled down by a factor 10 for the sake of clarity . the curves correspond to 1/sin@xmath32 functions . figure 5 : inclusive energy spectra of @xmath4 particles measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev between @xmath44 = 30@xmath25 and 55@xmath25 . the experimental data are shown by the solid points with error bars visible when greater than the size of the points . the solid and dashed lines are statistical - model calculations discussed in the text . figure 6 : two - dimensional scatter plots of galilean - invariant cross sections ( d@xmath37/d@xmath38de)p@xmath39c@xmath39 of inclusive @xmath4 particles ( left side ) and protons ( right side ) measured in the ( v@xmath41,v@xmath40 ) plane for the @xmath1si + @xmath2c reaction at e@xmath10 = 112 mev ( up ) and 180 mev ( down ) . the experimental detector thresholds are drawn along the laboratory angles of each telescope . the circular arcs are centered on the velocity of the center of mass . figure 7 : exclusive energy spectra of @xmath4 particles emitted at the angles + 40@xmath98 + 65@xmath31 , in coincidence with individual p and s er s detected at -15@xmath25 in the @xmath1si + @xmath2c reaction at e@xmath10 = 112 mev . the experimental data are given by the solid points with error bars visible when greater than the size of the points . the solid lines are statistical - model calculations discussed in the text . figure 8 : exclusive energy spectra of @xmath4 particles emitted at the angles + 40@xmath98 + 95@xmath31 , in coincidence with individual p and s er s detected at -10@xmath25 in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the experimental data are given by the solid points with error bars visible when greater than the size of the points . the solid lines are statistical - model calculations discussed in the text . figure 9 : exclusive energy spectra of protons emitted at the angles + 40@xmath99 + 70@xmath31 , in coincidence with individual p and s er s detected at -10@xmath25 , at the indicated laboratory angles , in the @xmath1si(180 mev ) + @xmath2c reaction . the solid lines are statistical - model calculations discussed in the text . figure 10 : in - plane angular correlations of coincident @xmath4 particles ( circles ) and protons ( triangles ) measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 112 mev . the proton correlations have been multiplied by a factor 10@xmath100 for the sake of clarity . the arrow indicates the position of the ic detector at @xmath23= -15@xmath25 . on the abscissa , the positive angle refer to the opposite side of the beam from the direction of the er detected in ic . the solid lines correspond to statistical - model calculations discussed in the text . figure 11 : in - plane angular correlations of coincident @xmath4 particles ( circles ) and protons ( triangles ) measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the proton correlations have been multiplied by a factor 10@xmath101 for the sake of clarity . the arrow indicates the position of the ic detector at @xmath23= -10@xmath25 . on the abscissa , the positive angle refer to the opposite side of the beam from the direction of the er detected in ic . the solid lines correspond to statistical - model calculations discussed in the text . figure 12 : out - of - plane angular correlations of coincident @xmath4 particles ( circles ) and protons ( triangles ) measured in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the proton correlations have been multiplied by a factor 10@xmath101 for the sake of clarity . the er s are detected at @xmath23 = -10@xmath25 . the solid lines correspond to statistical - model calculations discussed in the text . figure 13 : energy - correlation plots between coincident @xmath4 particles and s er s produced in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the heavy fragment is detected at @xmath82 = -10@xmath25 and the @xmath4-particle angle settings are given in the figure . the dashed lines correspond to different contours with their associated labellings discussed in the text . figure 14 : experimental ( left side ) and calculated ( right side ) energy - correlation plots between coincident @xmath4 particles and s er s produced in the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev . the s is identified at @xmath82 = -10@xmath25 and the @xmath4 particles are detected at @xmath83 = + 40@xmath25 , and + 70@xmath25 , respectively . cacarizo calculations are discussed in the text . figure 15 : excitation - energy spectra calculated for the @xmath1si + @xmath2c reaction at e@xmath10 = 180 mev for @xmath7be ( left side ) and @xmath6s ( right side ) in coincidence with the g.s . ( above ) and first excited level ( below ) of @xmath7be . the solid line corresponds to the energy of the first excited state of @xmath7be ( 3.08 mev ) . the dashed lines correspond to an excitation energy in @xmath6s expected for an @xmath4-transfer process .	the possible occurence of highly deformed configurations in theca di - nuclear system formed in thesi +c reaction is investigated by analyzing the spectra of emitted light charged particles . the energy spectra , velocity distributions , in - plane and out - of - plane angular correlations of light charged particles are compared to statistical - model calculations using a consistent set of parameters with spin - dependent level densities .	the possible occurence of highly deformed configurations in theca di - nuclear system formed in thesi +c reaction is investigated by analyzing the spectra of emitted light charged particles . both inclusive and exclusive measurements of the heavy fragments ( a 10 ) and their associated light charged particles ( protons and particles ) have been made at the ires strasbourg vivitron tandem facility at bombarding energies of(si ) = 112 mev and 180 mev by using the icare charged particle multidetector array . the energy spectra , velocity distributions , in - plane and out - of - plane angular correlations of light charged particles are compared to statistical - model calculations using a consistent set of parameters with spin - dependent level densities . this spin dependence approach suggests the onset of large nuclear deformation inca at high spin . this conclusion might be connected with the recent observation of superdeformed bands in theca nucleus . the analysis of particles in coincidence withs fragments suggests a surprisingly strongbe cluster emission of a binary nature . pacs number(s ) : 25.70.gh , 25.70.jj , 25.70.mn , 24.60.dr
1701.00426	i	the use of processors based on multi- and many - core architectures is a common option in high performance computing ( hpc ) . several variants of these processors exist , differing mainly in the number and architecture of the cores integrated in a single silicon die . conventional cpus integrate tens of fat cores sharing a large on - chip cache . fat cores include several levels of caches and complex control structures , able to perform hardware optimization techniques ( branch - speculation , instruction scheduling , register renaming , etc ) . vector instructions are also supported by these cores , with a moderate level of data parallelism : 2 to 4 vector elements are processed by one vector instruction . this architecture is reasonably efficient for many type of regular and non - regular applications and delivers a level of performance of the order of hundreds of gigaflops per processor . on the other side of the spectrum we have graphics processor units ( gpu ) , available as accelerator boards attached to conventional cpus . gpus integrate thousands of slim cores able to efficiently support regular streams of computation , and deliver performances of the order of several teraflops . gpus are extremely aggressive in terms of data - parallelism , implementing vector units with large vector sizes ( 16 and 32 words are presently available options ) . midway between these two architectures , we have the intel _ many integrated cores _ ( mic ) architecture based on several tens of slim cores . in this case , cores are similar to their fat counterparts , but their design has been simplified removing many hardware control structures ( instruction scheduler , register renaming , etc ) and adopting wider vector units , able to process up to 4 or 8 vector elements in parallel . large scale computing centers today have not reached a common consensus on the `` best '' processor option for hpc systems , also because system choices are driven not only by application performances , but also by cost of ownership and energy aspects which are becoming increasingly critical parameters@xcite . several computing centers do adopt machines based on gpus , but other ones prefer to stay on more traditional cpus , offering a lower peak performance , but better computing efficiency for a wider range of applications . in this scenario , the development of applications would greatly benefit from the availability of a unique code version , written in an appropriate programming framework , able to offer portability , in terms of code and performance , across several present and possibly future state - of - the - art processor architectures . a single code version , portable across several architectures , is of great convenience in particular for scientific applications , where code changes and development iterations are very frequent , so keeping several architecture - specific code versions up - to - date is a tedious and error prone effort@xcite . directives based programming models are going exactly in this direction , abstracting parallel programming to a descriptive level as opposite to a prescriptive level , where programmers must specify how the code should be mapped onto the target machine . openmp@xcite and openacc@xcite are among the most common such programming models , already used by a wide scientific community . both are based on directives : openmp was introduced to manage parallelism on traditional multi - core cpus , while openacc is mainly used to target gpus ( although designed to be architecture agnostic)@xcite . these two frameworks are in fact converging and extending their scope to cover a large subset of hpc applications and architectures : openmp version 4 has been designed to support also accelerators , while compilers supporting openacc ( such as the pgi@xcite ) are starting to use directives also to target multi - core cpus . in this work we describe the implementation of a lattice qcd ( lqcd ) monte carlo code designed to be portable and efficient across several architectures . lqcd simulations represent a typical and well known hpc grand challenge , with physics results strongly limited by available computational resources@xcite ; over the years , several generations of parallel machines , optimized for lqcd , have been developed@xcite , while the development of lqcd codes running on many core architectures , in particular gpus , has seen large efforts in the last 10 years@xcite . our goal is to have just one code able to run on several processors without any major code changes , and possibly to have roughly the same level of efficiency , looking for an acceptable trade - off between portability and efficiency@xcite . as a programming model we have selected openacc , as it currently has a wider compiler support , in particular targeting nvidia gpus , which are widely used in hpc clusters and commonly used for scientific computations . openacc has been successfully used to port and run other scientific codes , such as lattice boltzmann applications@xcite in computational fluid - dynamics , showing a good level of code and performance portability on several architectures . the migration of our code to openmp4 , if needed , as soon as compiler support becomes more mature , is expected to be a simple additional effort . we have developed a code with all key features for a state - of - the - art simulations of qcd with dynamical fermions . using this code as a user test case , we assess : i ) if it is possible to write the code in such a way that the most computationally critical kernels can be executed on accelerators , as in previous cuda implementations@xcite ; ii ) how many of the presently available multi and many - core architectures can be really used ; iii ) how efficient are these codes , and in particular what is the price to pay in terms of performance with respect to a code written and optimized for a specific architecture ( e.g. , using cuda for gpus ) . we believe that our work is a non trivial step forward in the development of a fully portable production - grade lqcd monte carlo code , using the openacc programming model . an earlier paper@xcite presented tests of selected portions of an openacc lqcd implementation on fermi and k20 nvidia gpus , comparing performances with an openmp implementation for cpus . similarly , in a preliminary study@xcite , we compared the performance of selected kernels of a full simulation , written in openacc , with an equivalent cuda implementation , on a k20 nvidia gpu . in this work , we extend the use of openacc in several new directions : i ) we show the portability of a complete implementation across several architectures ; ii ) we show performance figures for the same openacc code on a variety of multi and many - core processors , including the most recent gpus like the k80 and the recently released p100 ; iii ) we compare results with a previous implementation of the same full application written in cuda@xcite . the remainder of the paper is organized as follows : in section [ simalg ] we give a brief introduction to lqcd and to the main computational aspects of our application ; in section [ hpctrend ] we highlight recent developments in hpc hardware and programming tools ; in section [ implementation ] we describe the openacc implementation of our code ; in section [ results ] we analyze our results ; finally , section [ conclusions ] , contains our concluding remarks .	the present panorama of hpc architectures is extremely heterogeneous , ranging from traditional multi - core cpu processors , supporting a wide class of applications but delivering moderate computing performance , to many - core gpus , exploiting aggressive data - parallelism and delivering higher performances for streaming computing applications . in this scenario , code portability ( and performance portability ) become necessary for easy maintainability of applications ; this is very relevant in scientific computing where code changes are very frequent , making it tedious and prone to error to keep different code versions aligned . in this work we present the design and optimization of a state - of - the - art production - level lqcd monte carlo application , using the directive - based openacc programming model . openacc abstracts parallel programming to a descriptive level , relieving programmers from specifying how codes should be mapped onto the target architecture . we describe the implementation of a code fully written in openacc , and show that we are able to target several different architectures , including state - of - the - art traditional cpus and gpus , with the same code . we also measure performance , evaluating the computing efficiency of our openacc code on several architectures , comparing with gpu - specific implementations and showing that a good level of performance - portability can be reached .	the present panorama of hpc architectures is extremely heterogeneous , ranging from traditional multi - core cpu processors , supporting a wide class of applications but delivering moderate computing performance , to many - core gpus , exploiting aggressive data - parallelism and delivering higher performances for streaming computing applications . in this scenario , code portability ( and performance portability ) become necessary for easy maintainability of applications ; this is very relevant in scientific computing where code changes are very frequent , making it tedious and prone to error to keep different code versions aligned . in this work we present the design and optimization of a state - of - the - art production - level lqcd monte carlo application , using the directive - based openacc programming model . openacc abstracts parallel programming to a descriptive level , relieving programmers from specifying how codes should be mapped onto the target architecture . we describe the implementation of a code fully written in openacc , and show that we are able to target several different architectures , including state - of - the - art traditional cpus and gpus , with the same code . we also measure performance , evaluating the computing efficiency of our openacc code on several architectures , comparing with gpu - specific implementations and showing that a good level of performance - portability can be reached .
1402.4130	i	we have investigated how the recently discovered dsph galaxy perseus i and the ngc 3109 association extended with the recently discovered dwarf galaxy leo p are related to , and might fit in with , the dwarf galaxy structures present in the lg . our work has shown that the ngc 3109 association can not necessarily be interpreted as an independent group of galaxies , but might be related to the lg dwarf galaxy population and as such might provide important constraints on attempts to model the whole lg . the main results of our analysis are : 1 . perseus i is consistent with being part of the lgp1@xmath5 , the dominant plane of non - satellite galaxies in the lg , at least if andromeda xvi is associated with the gpoa . 2 . in the context of mond , we have predicted perseus i s velocity dispersion to be @xmath120 . the corresponding prediction for cetus ( @xmath121 ) is in much better agreement with the more recent observational value ( @xmath122 : * ? ? ? * ) than with the previous measurement ( @xmath123 : * ? ? ? the prediction for tucana ( @xmath124 ) is in conflict with the available measurement . we note that the observations of lack the spectral resolution to resolve the predicted velocity dispersion . unfortunately , no similar predictions are possible in a @xmath1cdm context . the orientation of the ngc 3109 association consisting of the dwarf galaxies ngc 3109 , antlia , sextans a , sextans b and leo p has been determined in the same coordinate system used to review the planes of co - orbiting satellite galaxies around the mw and m31 and the symmetric larger - scale dwarf galaxy structure in the lg @xcite . the association aligns with the supergalactic plane , is almost perpendicular to our line - of - sight and parallel but offset by 300 - 500kpc to lgp1@xmath5 . 4 . the members of the ngc 3109 association have large receding velocities which indicate that they have been close to the mw in the past , possibly at the same time about 79gyr ago . this is consistent with their orbits passing within @xmath90kpc of the mw suggested by @xcite and the identification as likely backsplash galaxies by @xcite . together with the association s extremely narrow extent and perpendicular orientation this argues against the association tracing a thin and cold cosmological filament . the timing is consistent with independent timing estimates for several suggested major galaxy encounter scenarios in the lg , during which phase - space correlated populations of tdgs could have formed that would today give rise to the observed dwarf galaxy structures . the association aligns with the other three distant ( @xmath125kpc ) lg galaxies in the northern hemisphere of the mw in a narrow plane ( rms height of @xmath126kpc and axis ratios of @xmath127 and @xmath128 ) . this `` great northern plane '' passes through the center of the lg , is inclined to lgp1@xmath5 by only @xmath6 and to the gpoa by @xmath101 and is consistent with being aligned with the preferred orbital plane of the mw satellites in the vpos . five out of seven ( 6 of 8 if the later discovered leo p would be included ) of the galaxies in the great northern plane have been identified as likely backsplash objects by @xcite , and most of the remaining five backsplash candidates in the southern galactic hemisphere are also situated close to the same plane . as only a small fraction of sub - haloes in simulations are identified as backsplash objects the finding of a majority of such galaxies in one hemisphere is extremely unlikely ( @xmath2 per cent ) and might constitute an `` overabundant backsplash problem '' for @xmath1cdm . it would mean that more galaxies are receding in one direction from the mw than are being accreted onto the mw from that direction . a natural explanation for this would be the local formation of galaxies as tdgs , which , if expelled to large distances , have very similar orbital properties like cosmological backsplash galaxies . that the backsplash candidates preferentially lie in a common plane is also consistent with an interpretation as phase - space correlated tdgs . lg galaxies are found to be preferentially infalling in the galactic south and receding in the galactic north , which possibly indicates that the mw is moving through a stream of dwarf galaxies . this would be in qualitative agreement with the m31-merger scenario by @xcite , in which our galaxy passes through the tidal debris expelled in a past merger forming m31 ( see also * ? ? ? * ; * ? ? ? . however , the tdg origin would be in m31 , such that the galaxies move away from m31 sufficiently fast which would imply that they have a tangential velocity component relative to the mw , rendering the timing estimate of sect . [ sect : timing ] somewhat useless . the scenario should however be testable on lg scales if proper motion measurements of the distant dwarf galaxies could be obtained .	the recently discovered dwarf galaxy perseus i appears to be associated with the dominant plane of non - satellite galaxies in the local group ( lg ) . the ngc 3109 association , including the recently discovered dwarf galaxy leo p , aligns with the dwarf galaxy structures in the lg such that all known nearby non - satellite galaxies in the northern galactic hemisphere lie in a common thin plane ( rms height 53 kpc ; diameter 1.2 mpc ) . this plane has an orientation similar to the preferred orbital plane of the milky way ( mw ) satellites in the vast polar structure . the ngc 3109 association supports the notion that material preferentially falls towards the mw from the galactic south and recedes towards the north , as if the mw were moving through a stream of dwarf galaxies .	the recently discovered dwarf galaxy perseus i appears to be associated with the dominant plane of non - satellite galaxies in the local group ( lg ) . we predict its velocity dispersion and those of the other isolated dsphs cetus and tucana to be 6.5 , 8.2 , and , respectively . the ngc 3109 association , including the recently discovered dwarf galaxy leo p , aligns with the dwarf galaxy structures in the lg such that all known nearby non - satellite galaxies in the northern galactic hemisphere lie in a common thin plane ( rms height 53 kpc ; diameter 1.2 mpc ) . this plane has an orientation similar to the preferred orbital plane of the milky way ( mw ) satellites in the vast polar structure . five of seven of these northern galaxies were identified as possible backsplash objects , even though only about one is expected from cosmological simulations . this may pose a problem , or instead the search for local backsplash galaxies might be identifying ancient tidal dwarf galaxies expelled in a past major galaxy encounter . the ngc 3109 association supports the notion that material preferentially falls towards the mw from the galactic south and recedes towards the north , as if the mw were moving through a stream of dwarf galaxies . [ firstpage ] galaxies : dwarf galaxies : individual : perseus i galaxies : kinematics and dynamics local group dark matter
hep-ph0202054	i	in the standard model ( sm ) , lepton number is exactly preserved in contradiction with the observed neutrino oscillations @xcite . several extension of the sm include patterns of neutrino masses and mixings which can provide a satisfactory explanation for these flavor oscillations . the consequences of the individual violation of the lepton numbers @xmath0 for charged lepton will be manifest in processes such as @xmath3 , @xmath7 , @xmath8 conversion in heavy nuclei , @xmath9 and @xmath10 @xcite . the experimental upper bound for these processes is quite restrictive , which imposes a significant constraint for the explanation of flavor in models beyond the sm . however , the mechanisms used to explain the origin of the tiny neutrino masses required to explain solar and atmospheric neutrino oscillations , typically imply that these processes may occur at small rates , motivating an increasing experimental interest in exploring further charged lepton flavor violating processes . the rates for charged lepton flavor violation ( lfv ) are extremely small in the sm with right handed neutrinos ( @xmath11 @xcite ) . in r parity conserving supersymmetric ( susy ) models , like the minimal supersymmetric standard model ( mssm ) , the presence of lfv processes is associated with vertices involving leptons and their superpartners @xcite . these processes are sensitive to the scalar mass matrices structure , a non diagonality of the latter in a basis in which fermions are diagonal , leads to a hard violation of flavor . the structure of the scalar mass matrices is very sensitive to the susy breaking , in particular in models where susy is softly broken , lfv imposes a severe constraint in the flavor dependence of the soft terms as they are generated in gut s and string inspired models @xcite . the inclusion of a `` see saw '' mechanism in the mssm provides a very attractive scenario to understand neutrino oscillations with very small neutrino masses , and at the same time gives rates for lfv processes accessible in projected experiments @xcite . the waiving of the r - parity symmetry in the mssm provides an alternative scenario to explain the generation of small neutrino masses . in this case the r - parity violating operators can be constrained by rare processes @xcite . the simplest extension of the mssm with bilinear r parity violation ( brpv ) @xcite ( allowing b conserving but l - violating interactions ) can explain neutrino masses and mixings which can account for the observed neutrino oscillations @xcite . the brpv model has been extensively discussed in the literature @xcite . it is motivated by the fact that it provides an effective truncation of models where r parity breaks _ spontaneously _ by singlet sneutrino vev s around the weak scale @xcite . moreover , they allow for the radiative breaking of r - parity , opening also new ways to unify gauge and yukawa couplings @xcite and with a potentially slightly lower prediction for @xmath12 @xcite . for recent papers on phenomenological implications of these models see ref . @xcite . as the parameters involved in the r parity violating operator are constrained in order to predict neutrino masses in the sub - ev range , we address in this paper the question of whether this operator will induce rates for charged lfv processes of experimental interest . some of them occur at tree level such as double @xmath13 decay @xcite and @xmath8 conversion in nuclei @xcite . one loop lfv decays as @xmath14 become interesting on this framework due to the experimental interest in improving the current limits @xcite : @xmath15 as we will show , the predictions for the last two processes are much lower than the above limits and will not constrain the brpv model . for @xmath5 the predictions are compatible with the current limit but could begin to constrain the model for the bounds that will be reached in current @xcite or planned experiments @xcite , if only the atmospheric neutrino data were taken in account . however the requirement that the one loop induced @xmath4 is in agreement with the solar neutrino data will imply that the predicted rates for @xmath5 will not be visible , even in those new experiments . this paper is organized as follows . in sections [ sec : themodel ] , [ sec : thepot ] and [ sec : massmatrices ] we describe the model , the scalar potential and the fermion mass matrices , respectively . in section [ sec : expressions ] we derive the expressions for the lfv processes . the results are presented in section [ sec : results ] and in section [ sec : conclusions ] we give our conclusions . the more technical questions regarding the mass matrices , couplings and the explicit formulas for the amplitudes are given in the appendices .	the simplest unified extension of the minimal supersymmetric standard model with bi - linear r parity violation naturally predicts a hierarchical neutrino mass spectrum , suitable to explain atmospheric and solar neutrino fluxes . we study whether the individual violation of the lepton numbers in the charged sector can lead to measurable rates for and . we find that some of the r parity violating terms that are compatible with the observed atmospheric neutrino oscillations could lead to rates for measurable in projected experiments . hep - ph/0202054 + fisist/022002/cfif + * charged lepton flavor violation in supersymmetry with bilinear r	the simplest unified extension of the minimal supersymmetric standard model with bi - linear r parity violation naturally predicts a hierarchical neutrino mass spectrum , suitable to explain atmospheric and solar neutrino fluxes . we study whether the individual violation of the lepton numbers in the charged sector can lead to measurable rates for and . we find that some of the r parity violating terms that are compatible with the observed atmospheric neutrino oscillations could lead to rates for measurable in projected experiments . however , the obtained for those parameters is too high to be compatible with the solar neutrino data , excluding therefore the possibility of having measurable rates for in the model . hep - ph/0202054 + fisist/022002/cfif + * charged lepton flavor violation in supersymmetry with bilinear r parity violation * d. f. carvalho , m. e. gmez and j. c. romo + _ departamento de fsica , instituto superior tcnico _ + _ av . rovisco pais 1 , 1049 - 001 lisboa , portugal _ + ( 1,0)140 email addresses : [email protected] , [email protected] , [email protected]
1101.4219	i	following the epoch of recombination at z @xmath61000 , the next major event in the history of the universe was its reionization by an early generation of massive stars and/or black holes . one of the major goals of modern cosmology is to understand this process : what sources were responsible and when did it occur ? observations of the cosmic microwave background with wmap show that reionization occurred at a mean redshift of [email protected] ( dunkley et al . 2009 ) , while observations of absorption due to the lyman @xmath1 forest in quasars show that reionization was not quite complete until a redshift of about six ( e.g. fan et al . 2006 ) . based on the observed luminosity functions of active galactic nuclei and star - forming galaxies at the relevant redshifts , the latter appear to be the more energetically plausible source for reionization ( e.g. bouwens et al . 2010 ) . however , a major uncertainty in the contribution of star forming galaxies is the poorly constrained fraction of ionizing photons that are able to leak out of such galaxies into the intergalactic medium . bouwens et al . ( 2010 ) estimate that an escape fraction of 20% ( 60% ) is required for consistency with the wmap results at the 2@xmath8 ( 1 @xmath8 ) level . many attempts have been made to measure this escape - fraction in star - forming galaxies at low - redshift ( leitherer et al . 1995 ; hurwitz et al . 1997 ; deharveng et al . 2001 ; heckman et al . 2001 - hereafter h01 ; bergvall et al . 2006 ; grimes et al . 2009 - hereafter g09 ) , intermediate redshift ( malkan et al . 2003 , siana et al . 2007,2010 ; cowie et al . 2009 ) and high- redshift ( steidel et al . 2001 ; giallongo et al . 2002 ; fernandez - soto et al . 2003 ; inoue et al . 2005 ; vanzella et al . 2010 ) . for the most part , these measurements have only yielded upper limits , although significant escaping lyman continuum emission has been detected in 17 out of a sample of 198 lyman break and lyman @xmath1 galaxies at @xmath9 ( iwata et al . 2009 ) , consistent with earlier results for a smaller sample of lyman break galaxies ( shapley et al . in contrast , vanzella et al . ( 2010 ) found evidence for escaping lyman continuum in only 1 of 100 lyman break galaxies at z @xmath6 4 . why do only a minority of the high - z galaxies and none of the low - z galaxies show a significant leakage of ionizing radiation ? in this regard , it is instructive to note that an hi column density of only 1.6 @xmath10 @xmath11 is required to produce unit optical depth at the lyman edge . the area - averaged column densities of cold gas in star - forming galaxies are much larger , ranging from @xmath12 @xmath11 in ordinary low - redshift galactic disks to as high as @xmath13 @xmath11 in local starbursts and high - z star - forming galaxies ( kennicutt 1998 ; genzel et al . the escape of ionizing radiation must then be determined by the topology of the interstellar medium , which will in turn be strongly influenced by feedback from massive stars . it may be that rather exceptional circumstances are required to produce the required channels of very low column - density neutral gas . such processes have been extensively studied from a theoretical perspective ovre the past decade ( e.g. dove et al . 2000 ; clarke & oey 2002 ; fujita et al . 2003 ; gnedin & kravtsov 2008 ; wise & cen 2009 ; razoumov & somer - larson 2010 ; yajima et al . 2010 ) . these considerations provide the motivation of the present paper : to find local examples of galaxies in which a potentially significant fraction of the ionizing radiation may be escaping , and to then exploit the relative ease of observing such bright local objects to gain insight into the physical processes that facilitate this escape . to be able to assess the cosmological implications of the results of such an approach , it is important to observe local galaxies that most closely resemble the type of uv - bright high - redshift galaxies that are candidates for the reionization of the universe . we began such an investigation in overzier et al . ( 2009 - hereafter o09 ) , where we reported on spitzer photometry , hst imaging , and sloan digital sky survey ( sdss ) optical spectroscopy of a sample of 31 lyman break analogs ( lbas ) . these lbas are a very rare population of local galaxies that strongly resemble the high - z lyman break galaxies ( heckman et al . 2005 ; hoopes et al . 2007 ; overzier at al . 2008;2010 ; basu- zych et al . 2007;2009 ) . they are defined to have a range in far - uv luminosity ( @xmath14 l@xmath4 ) and far - uv effective surface brightness ( @xmath15 l@xmath4 kpc@xmath16 ) that are similar to typical lyman break galaxies . we showed in o09 that the morphologies of lbas as revealed in multi - band hst images fall into two distinct categories . the first class ( 25 objects ) consists of galaxies in which multiple bright complexes of clumps and knots reside in a galaxy whose disturbed morphology is suggestive of a major merger or strong tidal interaction . the second class ( six objects ) consists of galaxies whose uv image is dominated by a single extremely massive ( @xmath17 one - to - several billion @xmath18 ) and compact ( radius of - order 100 pc ) central object ( a dominant central object , or dco ) . we pointed out that the star - formation rates derived for these six galaxies based on the extinction- corrected h@xmath1 luminosities were systematically smaller than those derived from the spitzer mid - ir luminosity ( by factors of @xmath6 2 to 5 ) , and speculated that a possible explanation was that these galaxies were leaking ionizing radiation into the intergalactic medium . in this paper we test this idea using new hubble space telescope ( hst ) far - uv observations with the cosmic origins spectrograph ( cos ) of a sample of eight lbas from o09 . we will combine these new data with archival far ultraviolet spectroscopic explorer ( fuse ) data for three other lbas and for fifteen more typical uv - bright local starbursts . we will describe the sample selection in section 2 and the observations and data analysis in section 3 . we will present our results and consider their interpretation in section 4 , and summarize these results and their implications in section 5 .	the source responsible for reionizing the universe at remains uncertain . while an energetically adequate population of star - forming galaxies may be in place , it is unknown whether a large enough fraction of their ionizing radiation can escape into the intergalactic medium . attempts to measure this escape - fraction in intensely star - forming galaxies at lower redshifts have largely yielded upper limits . in this paper we present new hst cos and archival fuse far - uv spectroscopy of a sample of eleven lyman break analogs ( lbas ) , a rare population of local galaxies that strongly resemble the high - z lyman break galaxies . we combine these data with sdss optical spectra and spitzer photometry . we also analyse archival fuse observations of fifteen typical uv - bright local starbursts . these objects represent three of the four lbas that contain a young , very compact ( pc ) , and highly massive ( m ) dominant central object ( dco ) . these three objects also differ from the other galaxies in showing a significant amount of blueshifted ly emission , which may be related to the low covering factor of neutral gas .	the source responsible for reionizing the universe at remains uncertain . while an energetically adequate population of star - forming galaxies may be in place , it is unknown whether a large enough fraction of their ionizing radiation can escape into the intergalactic medium . attempts to measure this escape - fraction in intensely star - forming galaxies at lower redshifts have largely yielded upper limits . in this paper we present new hst cos and archival fuse far - uv spectroscopy of a sample of eleven lyman break analogs ( lbas ) , a rare population of local galaxies that strongly resemble the high - z lyman break galaxies . we combine these data with sdss optical spectra and spitzer photometry . we also analyse archival fuse observations of fifteen typical uv - bright local starbursts . we find evidence of small covering factors for optically - thick neutral gas in three cases . this is based on two independent pieces of evidence : a significant residual intensity in the cores of the strongest interstellar absorption - lines tracing neutral gas and a small ratio of extinction - corrected h to uv plus far - ir luminosities . these objects represent three of the four lbas that contain a young , very compact ( pc ) , and highly massive ( m ) dominant central object ( dco ) . these three objects also differ from the other galaxies in showing a significant amount of blueshifted ly emission , which may be related to the low covering factor of neutral gas . all four lbas with dcos in our sample show extremely high velocity outflows of interstellar gas , with line centroids blueshifted by about 700 km s and maximum outflow velocities reaching at least 1500 km s . we show that these properties are consistent with an outflow driven by a powerful starburst that is exceptionally compact . we speculate that such extreme feedback may be required to enable the escape of ionizing radiation from star forming galaxies .
1101.4219	r	before considering constraints on the escape of ionizing radiation , it is important to establish that an ionizing population of massive stars ( o stars ) is in fact present in our targets . the strongest spectroscopic signature of these stars is provided by the broad p - cygni profiles in the resonance transitions of highly ionized species that arise in the stellar winds ( e.g. robert et al . 1993 ; 2003 ) . the strongest such feature that is present in all our cos spectra is nv@xmath231240 . in figure 3 we show the nv profile for our eight targets and overplot the generic examples of starburst99 model spectra described above . we defer to a future paper a detailed discussion of the properties of the stellar populations in the lbas . here we merely point out that the far - uv spectra of the lbas are all consistent with a normal population of ionizing stars expected for a strong starburst . in figure 4 we show the [email protected] absorption - line profiles for our cos data on eight lbas . the corresponding profiles for the [email protected] line from the fuse data can be found in h01 and g09 . a striking result is that there is a significant residual intensity in the absorption - line profiles in four lbas ( lba0213 + 12 , lba0808 + 39 , lba0921 + 45 , and lba0926 + 45 ) . the first three objects all contain a dco . these results contrast strongly with the results in h01 and g09 in which the [email protected] absorption - line in the fuse data is black or nearly black at line center in all cases . to understand our approach in using the cii line as a probe of the lyman continuum , let us consider two limiting idealized cases . in the first , we assume a picket - fence model in which the far - uv source is surrounded by a population of clouds that are optically thick in both the absorption line and the lyman continuum and that cover a fraction @xmath25 of the sky as seen by the source . in this case the residual relative intensity at the core of the line ( @xmath26 ) is just @xmath27 . thus , a significant residual intensity in the line core implies a significant escape of lyman continuum radiation . in the second case we assume that the far - uv source is surrounded by a uniform shell with unit covering factor . as discussed in h01 , in this case the optical depth in the ism just below the lyman edge is related to the optical depth at the core of the absorption - line by : + 1 ) @xmath28 km s@xmath29 + where @xmath30 is the gas - phase carbon abundance scaled to the solar value of @xmath31 ( asplund et al . 2009 ) , we assume that cii is the dominant ionization state in the neutral gas , @xmath32 is the velocity dispersion in the neutral gas , and @xmath33 17 and 12 for the 1036.3 and 1334.5 lines respectively ( morton 2003 ) . since the optical depth at the lyman edge is over an order- of - magnitude larger than in the line core , in this idealized case a significant residual intensity in the core of the absorption lines is a necessary but not sufficient condition for the escape of ionizing radiation . to test these two models , we have used the set of siii absorption - lines available in the cos data . like cii , siii is the dominant ion of silicon in the neutral ism . by using lines that all arise in the same ionic species , but which span a range in oscillator strengths , a comparison of the absorption profiles among these lines allows us to estimate the optical depth and covering factor of the gas ( e.g. heckman et al . 2000 ; rupke et al . 2002 ; quider et al . 2009 ; erb et al . 2010 ) . in the case of optically - thick clouds that do not fully cover the far - uv source , the line profiles of the different transitions should look the same . in the case of a uniform shell , the residual intensity will increase with decreasing oscillator strength @xmath34 ( since @xmath35@xmath36@xmath34 ) . we will use the following transitions ( with the respective values of @xmath37@xmath34 from morton 2003 ) : [email protected] ( -1.32 ) , 1193.3 ( -1.65 ) , and 1190.4 ( -1.95).1301.2,1303.3 stellar photospheric features ( walborn et al . 1995 ; massa 1989 ) and the adjacent [email protected] interstellar line ) . ] for each galaxy we simultaneously fit a single gaussian profile to the three different siii lines , forcing the three lines to share a common centroid and width but allowing the normalization ( depth ) of each line to vary freely . in all four galaxies the results strongly favor the picket fence model with an implied covering factor of optically - thick clouds of about 40% for lba0213 + 12 and lba0926 + 45 , 50% for lba0808 + 39 , and 60% for lba0921 + 45 . we show these fits for the case of lba0921 + 45 in figure 5 . in principle , the sightlines that avoid the clouds could be optically - thin to the metal lines but still be optically - thick to the lyman continuum ( equation 1 ) . thus , confirmation that there is significant escaping ionizing radiation will require direct observations below the lyman edge in these cases . in the mean time we can consider whether there is other evidence for the escape of ionizing radiation in these four lbas . in o09 we highlighted the relative weakness of the extinction - corrected h@xmath1 emission - line in most of the lbas with dcos , and speculated that a significant fraction of the ionizing radiation might be escaping . this information is listed in table 2 where we compare the star - formation rates derived from the extinction - corrected h@xmath1 emission - line ( @xmath38 ) to that obtained from the sum of the total - ir and far- uv luminosity ( @xmath39 ) . it is noteworthy that three of the four objects above in which we have inferred an incomplete covering of the far - uv source by neutral clouds have the highest ratios of @xmath40 : lba0213 + 12 ( a ratio of 8.2 ) , lba0808 + 39 ( 3.0 ) , and lba0921 + 45 ( 3.2 ) . all three of these contain a dco . in contrast , the mean ratio of @xmath40 for the other five galaxies is 1.4 . _ thus , based on two independent lines of evidence , we suggest that there is a significant leakage of ionizing radiation from three of the eight lbas in our sample . _ how do these results compare to what is seen at high redshift ? there are four gravitationally - lensed high - z galaxies that have been observed with spectral resolution and signal - to - noise similar to our sample . ) , so that the line profiles are not well - resolved in individual objects ( and could miss gas with a high covering factor but low velocity dispersion ) . the stacking process itself could also smear out black , narrow components found in the spectra of individual galaxies . ] of these , the residual relative intensities of [email protected] , oi @xmath231302.2 , and siii @xmath23 1260.4 ( the strongest metal lines tracing the neutral ism ) are very small in ms 1512-cb58 ( pettini et al . 2002 ) , the cosmic eye ( quider et al . 2010 ) , and the 8 oclock arc ( dessauges - zavadsky et al . 2010 ) , but large ( @xmath640% ) in the cosmic horseshoe ( quider et al . in fact , the last object appears to a good example of the type of picket fence situation seen in the dcos in our sample . as discussed above , dust can also be a significant source of opacity to ionizing radiation in galaxies . following shapley et al . ( 2006 ) and g09 , we can distinguish between the absolute and relative escape fractions . the former is the actual fraction of ionizing photons that escape the galaxy , including the effect of dust . the latter neglects the effect of dust and is defined as the ratio of the fraction of escaping ionizing photons to escaping non - ionizing far - uv photons ( e.g. it measures only the effect of the photoelectric opacity of the gas ) . our measurements discussed above provide information about the relative escape fraction . given that the ratio of far - ir to far - uv fluxes for the galaxies with dcos are of - order ten , the implied absolute escape fractions will be proportionately smaller . we list our estimates for both the relative and absolute escape fractions in tables 1 ( fuse ) and 2 ( cos ) . as can be seen in figure 4 , the [email protected] absorption - line profiles in all the lbas are blueshifted with respect to the galaxy systemic velocity , implying a large - scale outflow of gas . further evidence for outflows is provided by the broad blue - asymmetric wings seen on the optical emission - line profiles ( o09 ) . the absorption - line profiles in figure 4 show evidence for exceptionally high outflow speeds in the dcos . to further investigate this , we turn to the si iii @xmath231206.5 feature . this is the strongest metal line that is accessed in all four dco spectra , and arises in the ionized gas . as shown in figure 6 , outflowing gas is detected at extraordinarily high velocities in all four galaxies with dcos . the flux - weighted line centroid is blueshifted by about 700 km s@xmath5 in these objects ( table 2 ) . it is difficult to determine the maximum outflow velocity because of blending with the ni@xmath231200 triplet , which lies @xmath61600 km s@xmath5 blueward of the siiii line . conservatively , the maximum outflow speed seen in the dcos reaches at least 1500 km s@xmath5 . these velocities are much higher than in the local starburst sample and in the lbas without a dco . this is shown in figure 7 where we plot the outflow speeds in the ionized gas in local starburst and lba samples _ vs. _ the star formation rate and galaxy mass ( see tables 1 and 2 ) . for galaxies with fuse data we use the [email protected] and/or [email protected] and/or [email protected] lines . the outflow velocities in the dcos are also significantly larger than those typically seen in high - z galaxies . steidel et al . ( 2010 ) find line centroids that are blueshifed on - average by 164 km s@xmath5 and maximum outflow speeds that are typically @xmath6 800 km s@xmath5 for galaxies with star formation rates of @xmath41 to @xmath42 year@xmath5 . outflows from intensely star - forming galaxies are believed to be produced as gas clouds are accelerated by the ram pressure of a hot and fast wind driven by the collective thermal / kinetic energy supplied by supernovae and massive stellar winds ( e.g. heckman et al . 2000 ; veilleux et al . 2005 ; marcolini et al . 2005 ; strickland & heckman 2010 ) , and/or by radiation pressure acting on dust ( murray et al . 2005 ; 2010 ) . can the unusually high velocities seen in the dcos be explained in this way ? we consider a simple idealized model of a cloud with a column density @xmath43 accelerated outward from an initial radius @xmath44 by the ram pressure of a wind that carries momentum at a rate @xmath45 into a solid angle @xmath46 . then the terminal velocity of this cloud will be : + 2 ) @xmath47 km s@xmath5 + here the momentum flux is in units of @xmath48 dynes , the initial radius is in units of 100 pc and the cloud column density is in units of @xmath12 @xmath11 . the dco star formation rates imply momentum fluxes of this order ( leitherer & heckman 1995 ) , while the hst images yield typical dco radii of 100 pc ( o9 ) . as discussed below in section 4.6 , a column density of @xmath12 @xmath11 is a reasonable estimate for the ionized gas in these objects . the above neglects gravitational forces ( cf . wang 1995 ; martin 2005 ; murray et al . 2010 ; strickland & heckman 2010 ) . this is justified here because the typical sizes and radii of the dcos imply virial velocities of only about 200 km s@xmath5 ( much smaller than the maximal outflow speeds we observe ) . note that murray et al . ( 2010 ) conclude that outflows driven out of massive star clusters by radiation pressure will only have outflow speeds of - order the local escape velocity . this is not the case in the dcos . these considerations imply that a galactic wind driven by an extreme starburst can in principle accelerate clouds to the high velocities that we see in the dcos . the significantly higher velocities in these galaxies compared to typical starbursts can be naturally explained by the combination of a large number of massive stars confined within an unusually small radius . this leads to a very large wind ram pressure and/or radiation pressure at the launch point of the clouds . an alternative form of extreme feedback could be provided by an agn . as discussed in overzier et al . ( 2009 ) the optical spectra of the lbas with dcos may imply a composite of both an intense starburst and an obscured ( type 2 ) agn . the cos data show that the far - uv radiation in these objects is dominated by light produced by hot massive stars ( figures 2 and 3 ) , which does not rule out the presence of a type 2 agn . recent observations with xmm - newton ( jia et al . 2010 ) show that lbas with such apparently composite optical spectra are also over - luminous in the 2 - 10 kev x - ray band by factors of roughly three to thirty compared to pure starbursts of the same far - ir luminosity . they conclude that it is likely that at least some of these objects do harbor an agn , but that the overall bolometric luminosity of the galaxy is primarily due to an intense starburst . could a type 2 agn be responsible for the unusually high outflow speeds and/or the apparently low covering factor of neutral gas due to a highly ionized state of the interstellar medium ? very high outflow speeds ( many thousands of km s@xmath5 ) are commonly observed in _ unobscured _ ( type 1 ) agn ( e.g. rupke et al . 2005 ; krug et al . however these same authors show that outflows similar to those we see in the dcos ( maximium outflow speeds of at least 1500 km s@xmath5 ) are extremely rare in composite obscured - agn / starburst systems and not seen at all in `` pure '' obscured agn . they conclude that the agn can drive very high - speed outflows , but these flows are confined to a small region very near the black hole ( and are hence undetectable in type 2 agn ) . they also conclude that the agn plays little or no role in driving the large - scale outflows seen in the composite systems . it therefore seems unlikely that the high velocity outflows in the dcos are driven by an obscured agn . tremonti et al . ( 2007 ) have detected outflows at velocities ranging from 500 to 2000 km s@xmath5 in massive post - starburst galaxies at z @xmath6 0.6 . they speculate that such high velocities may require an agn - driven outflow . it is also possible that the these objects are more massive versions of the dcos in this paper . this could be confirmed by hst imaging of their galaxies . the properties of the ly@xmath1 profile are highly sensitive to the kinematics and distribution of the outflowing gas and dust in star - forming galaxies ( e.g. steidel et al . 2010 ; hansen & oh 2006 ; verhamme et al . 2006 , 2008 ; kornei et al . in figure 8 we plot the ly@xmath1 profiles for the eight lbas with cos data , and highlight one very suggestive trend . in the five cases in which the inferred relative escape fraction is small , there is very little ( if any ) ly@xmath1 emission blueward of the systemic velocity . instead , the profiles show ly@xmath1 emission redward of the systemic velocity and either pure absorption or a mix of absorption and weak emission to the blue . such profiles are typical of high - z star forming galaxies ( e.g. shapley et al . 2003 ; steidel et al . in contrast , for the three objects in which we infer a high relative escape fraction ( lba0213 + 12 , 0808 + 39 , and 0921 + 45 ) a significant fraction of the ly@xmath1 emission is blueshifted with respect to the systemic velocity . to quantify this , we have measured the net equivalent widths ( emission - absorption ) blueward and redward of the systemic velocity in these eight lbas . we define net emission ( absorption ) to have a positive ( negative ) equivalent width . we then take the ratio of the red and blue equivalent widths ( @xmath49 ) . we list the results in table 2 . for the five galaxies with low inferred escape fractions @xmath49 is either negative ( redshifted emission and blueshifted absorption ) or small and positive ( strong redshifted emission and weak blueshifted net emission ) : lba0055- 00 ( @xmath50 -0.21 ) , 0150 + 13 ( -0.78 ) , 0926 + 45 ( 0.14 ) , 0938 + 54 ( -0.17 ) , and 2103 - 07 ( 0.04 ) . for the three galaxies with high inferred escape fractions @xmath49 is of - order one and positive ( similar amounts of red- and blue - shifted emission ) : 0213 + 12 ( @xmath50 0.36 ) , 0808 + 39 ( 0.27 ) , and 0921 + 45 ( 0.75 ) . profiles with significant blueshifted emission are uncommon but not unknown in star- forming galaxies at @xmath19 2 - 3 . verhamme et al . ( 2008 ) discuss two such cases and interpret them as arising due to radiative transfer effects in a static medium . this model can not be correct for the three dcos in figure 8 because the metal lines demonstrate that the gas is rapidly outflowing ( figures 4 and 6 ) . erb et al . ( 2010 ) discuss the case of a high - z galaxy with both an outflow detected in the metal lines and a significant amount of blueshifted ly@xmath1 emission . they argue that in this case the optical depth to ly@xmath1 photons is unusually low in the foreground outflowing material and that this is naturally related to the low covering factor of neutral gas they infer in this object ( precisely the situation we see in our three galaxies ) . it is important to note that the observed uv spectral energy distributions ( seds ) of the dcos are significantly redder than the intrinsic sed of a starburst ( overzier et al . 2011 , and see table 2 ) . for a normal starburst or smc dust attenuation law ( calzetti 2001 ; leitherer et al , 2002 ) these seds imply roughly two magnitudes of dust extinction along the line - of- sight to the dco in the far - uv . this then raises a very interesting question . how can there be this much dust when the observations of interstellar absorption - lines from the neutral gas imply that such gas only covers a fraction of the far - uv source ? the answer must be that this dust is associated with _ ionized _ gas that covers most or all of the dco . this picture requires that the cores of the strongest absorption - lines due to the ionized gas should be nearly black ( unlike the case of lines from the neutral phase ) . examination of the profiles in figure 6 shows that this is the case in lba0808 + 39 ( a relative residual intensity in the [email protected] line of 10% ) , lba0921 + 45 ( 7% ) , and lba2103- 07 ( @xmath243% ) . in the case of lba0213 + 12 , the relative residual intensity in this line is high ( @xmath640% ) . however , the redshift of this galaxy is large enough to shift the [email protected] line into the cos g130l spectrum . this should be the strongest interstellar line due to ionized gas , and as such provides the most sensitive probe . although the data are noisy , the relative residual intensity in this line is small ( 10% or less ) . thus , in this galaxy the siiii line is optically thin , while the ciii line is optically thick . we therefore conclude that the ionized gas has a near - unit covering factor in the dcos . one plausible physical model would be that the neutral gas represents the denser cores of clouds being accelerated by the wind , while the ionized gas represents a lower density halo of gas and dust surrounding the cloud core and which is being ablated by the wind and photoionized by the intense radiation field ( e.g. marcolini et al . 2005 ) . can the dco photoionize a column of gas with the required amount of dust ? elementary considerations of photoionization equilibrium imply that a source of radiation can photoionize a stromgren slab with a column density given by : + 3 ) @xmath51 @xmath11 + where @xmath52 is the dimensionless ionization parameter defined as the ratio of the density of ionizing photons to electrons in the slab . in order for a significant fraction of ionizing photons to escape , the actual gas column must be less than this value ( to provide matter - bounded conditions ) . the optical depth due to dust in the far - uv ( 1500 ) is related to the gas column density by : + 4 ) @xmath53 @xmath11 + where the coefficients refer to an smc ( starburst ) dust attenuation law ( leitherer et al . 2002 ) and we assume that the dust - to - gas ratio is proportional to the metallicity . the lbas with dcos all have gas - phase oxygen abubdances close to solar ( o09 ) and the line - of - sight reddening implies @xmath54 2 . thus , to explain the line - of - sight reddening towards the dcos in a matter - bounded situation we need @xmath55 . alternatively , the optical depth at the lyman edge due to neutral hydrogen in ( mostly ) ionized gas with a column density @xmath56 is given by : + 5 ) @xmath57 + for @xmath58 @xmath11 , we require @xmath59 for @xmath35@xmath60 . is this plausible ? heckman , armus , & miley ( 1990 ) and lehnert & heckman ( 1996 ) showed that the observed radial gas density profiles seen in the optical emission - line nebulae in starburst winds are consistent with theoretical expectations for photoionized clouds exposed to the ram - pressure of the hot wind fluid ( chevalier & clegg 1985 ) . it is straightforward to show that in this case the ionization parameter in the clouds is given by : + 6 ) @xmath61 + where @xmath62 is the wind momentum flux in units of 10@xmath63 dynes and @xmath64 is the starburst ionizing photon production rate ( in units of 10@xmath65 sec@xmath66 ) . the ionizing photons are produced by the most massive stars with lifetimes @xmath24 4 myr , while the momentum in the starburst wind derives primarily from supernovae ( whose progenitors have lifetimes of @xmath24 40 myr ) . in equilibrium ( e.g. a constant rate of star formation for longer than 40 myr ) , @xmath67 0.5 and so @xmath68 . more generally , this ratio will be time dependent . for example , values of @xmath69 are associated with constant star formation for a duration less than 20 myr and for an age @xmath24 4 myr in an instantaneous burst . these ages are consistent with current constraints on the dcos ( o09 and see figure 3 ) . we therefore conclude that it is feasible for the dcos to photoionize a matter - bounded column of gas that is sufficient to contain enough dust to produce the observed reddening and the inferred attenuation of the far - uv continuum and yet have a photoelectric opacity at the lyman edge that is less than one .	we find evidence of small covering factors for optically - thick neutral gas in three cases . this is based on two independent pieces of evidence : a significant residual intensity in the cores of the strongest interstellar absorption - lines tracing neutral gas and a small ratio of extinction - corrected h to uv plus far - ir luminosities .	the source responsible for reionizing the universe at remains uncertain . while an energetically adequate population of star - forming galaxies may be in place , it is unknown whether a large enough fraction of their ionizing radiation can escape into the intergalactic medium . attempts to measure this escape - fraction in intensely star - forming galaxies at lower redshifts have largely yielded upper limits . in this paper we present new hst cos and archival fuse far - uv spectroscopy of a sample of eleven lyman break analogs ( lbas ) , a rare population of local galaxies that strongly resemble the high - z lyman break galaxies . we combine these data with sdss optical spectra and spitzer photometry . we also analyse archival fuse observations of fifteen typical uv - bright local starbursts . we find evidence of small covering factors for optically - thick neutral gas in three cases . this is based on two independent pieces of evidence : a significant residual intensity in the cores of the strongest interstellar absorption - lines tracing neutral gas and a small ratio of extinction - corrected h to uv plus far - ir luminosities . these objects represent three of the four lbas that contain a young , very compact ( pc ) , and highly massive ( m ) dominant central object ( dco ) . these three objects also differ from the other galaxies in showing a significant amount of blueshifted ly emission , which may be related to the low covering factor of neutral gas . all four lbas with dcos in our sample show extremely high velocity outflows of interstellar gas , with line centroids blueshifted by about 700 km s and maximum outflow velocities reaching at least 1500 km s . we show that these properties are consistent with an outflow driven by a powerful starburst that is exceptionally compact . we speculate that such extreme feedback may be required to enable the escape of ionizing radiation from star forming galaxies .
0909.0552	i	bridgeland introduced the notion of a stability condition on a triangulated category @xmath5 in @xcite and proved that the set of locally - finite stability conditions forms a complex manifold @xmath6 . this space provides a geometric picture of many aspects of the category and carries a natural action of its automorphisms . each stability condition determines an abelian heart in the triangulated category . if we denote the subset of locally - finite stability conditions with heart @xmath1 by @xmath0 then the @xmath0 partition @xmath6 . if the heart @xmath1 has finite length and @xmath2 simple objects then @xmath7 where @xmath8 in this case @xmath9 is non - empty and of codimension one when @xmath3 is a simple left tilt of @xmath1 ( * ? ? * lemma 5.5 ) , i.e. when @xmath3 is obtained from @xmath1 by tilting in the sense of @xcite at a torsion theory generated by a simple object . we generalise this result as follows . fix a heart @xmath1 and assume that any heart obtained from it by a finite sequence of simple tilts has finite length and finitely many indecomposable objects . in particular each of these hearts therefore has finitely many simple objects and finitely many torsion theories . in this case we show that @xmath10 if and only if @xmath3 is the left tilt of @xmath1 at some torsion theory . the codimension of the intersection is governed by the size of the torsion theory , lower codimension corresponding to a smaller torsion theory ( see corollary [ intersection corollary ] for a precise statement ) . proposition [ constraints ] says that points in the boundary of @xmath11 correspond to limiting central charges of stability conditions in @xmath0 for which the central charge of no semi - stable object vanishes . furthermore , the union of subsets of stability conditions with hearts obtained from @xmath1 by sequences of simple tilts forms a connected component of @xmath6 ( theorem [ component thm ] ) . together these results yield a description of a component of @xmath6 in terms of the combinatorics of tilting in @xmath5 . in brief , [ torsion theories ] , [ tilting ] and [ tilting at simples ] provide the necessary background on the relation between @xmath12-structures , torsion theories and tilting in triangulated categories . [ stability conditions ] recalls the definition and basic properties of stability conditions . this material is standard and is included for expository purposes only . the main results , outlined above , are in [ main results ] . they are illustrated in [ constructible ] in which we compute ( a component of ) the space of stability conditions on the constructible derived category of @xmath13 stratified by a point and its complement . ( algebraists may prefer to view this example as the derived category of representations of the bound quiver @xmath14_c & \cdot \ar@/{}_{.5pc}/[l]_v } \qquad vc=0\ ] ] and symplectic geometers as the subcategory of the derived asymptotic fukaya category of @xmath15 generated by the zero section and a cotangent fibre . ) this example is sufficiently simple to allow explicit computation and yet complicated enough to exhibit all the interesting features of the results . finally [ coherent ] discusses the contrasting case of coherent sheaves on @xmath13 , following the detailed treatment in @xcite . in this example the hearts do not have finitely many indecomposables and we no longer obtain an entire component of the space of stability conditions by iterating simple tilts . i m grateful to ivan smith and michael butler for several helpful conversations and to tom bridgeland for his comments and for pointing me towards the example of coherent sheaves on @xmath13 as a useful counterpoint . i am indebted to the referee who spotted several gaps and errors in the original version .	the space of stability conditions on a triangulated category is naturally partitioned into subsets of stability conditions with a given heart . if has finite length and simple objects then has a simple geometry , depending only on . furthermore , bridgeland has shown that if is obtained from by a simple tilt , i.e. by tilting at a torsion theory generated by one simple object , then the intersection of the closures of and has codimension one . suppose that , and any heart obtained from it by a finite sequence of ( left or right ) tilts at simple objects , has finite length and finitely many indecomposable objects . then we show that the closures of and intersect if and only if and are related by a tilt , and that the dimension of the intersection can be determined from the torsion theory . in this situation the union of subsets , where is obtained from by a finite sequence of simple tilts , forms a component of the space of stability conditions . we illustrate this by computing ( a component of ) the space of stability conditions on the constructible derived category of the complex projective line stratified by a point and its complement .	the space of stability conditions on a triangulated category is naturally partitioned into subsets of stability conditions with a given heart . if has finite length and simple objects then has a simple geometry , depending only on . furthermore , bridgeland has shown that if is obtained from by a simple tilt , i.e. by tilting at a torsion theory generated by one simple object , then the intersection of the closures of and has codimension one . suppose that , and any heart obtained from it by a finite sequence of ( left or right ) tilts at simple objects , has finite length and finitely many indecomposable objects . then we show that the closures of and intersect if and only if and are related by a tilt , and that the dimension of the intersection can be determined from the torsion theory . in this situation the union of subsets , where is obtained from by a finite sequence of simple tilts , forms a component of the space of stability conditions . we illustrate this by computing ( a component of ) the space of stability conditions on the constructible derived category of the complex projective line stratified by a point and its complement .
0908.2263	c	the bright stellar content of the nearby ( d @xmath127 mpc ) s0 galaxy ngc 5102 has been surveyed with the wircam and megacam imagers on the cfht . with the exception of the crowded central regions of the galaxy , the megacam data cover all of ngc 5102 , while the wircam data are spatially complete out to r@xmath128 kpc . this is the first published study of the stellar content of ngc 5102 at near - infrared wavelengths , and the data have been used to probe the spatial distribution of stars , with particular emphasis on the outer regions of the galaxy . structural information of this nature will provide insights into the past evolution of ngc 5102 , and may identify the trigger of the elevated star - forming activity that occured within the past 1 gyr . there is a large body of literature that deals with the properties of gas - poor disks , and most of the papers focus on the higher mass kindred of ngc 5102 . given that the current paper deals with only a single galaxy , no attempt is made to present a comprehensive review of the literature on s0 galaxies . rather , we simply note here that it is broadly accepted that the progenitors of s0 galaxies are spiral galaxies that have experienced gas depletion . there is an environmental dependence ( e.g. butcher & oemler 1984 ) , and the mechanism causing gas removal has been the subject of much debate , focusing on galaxy - galaxy interactions ( e.g. lavery & henry 1988 ) , or infall from the field into an area with a dense intergalactic medium ( e.g. van dokkum et al . 1998 ) . an active nucleus may also drive gas from a galaxy ( e.g. silk 2005 ; silk & norman 2009 ) , although this is expected to be restricted to disk systems that have massive spheroids . of course , it is possible that not all s0s were subjected to the same gas - removal mechanism . low surface brightness structures such as those found here in the vicinity of ngc 5102 may prove challenging to detect in more distant s0 galaxies , and so ngc 5102 may play an important role for investigating the formation and evolution of gas - depleted disks . this being said , the reader is reminded that some characteristics of ngc 5102 are not typical of s0 galaxies . these include its intrinsic faintness ( m@xmath129 ; karachentsev et al . 2002 ) , the blue central colors and deep balmer absorption lines ( gallagher et al . 1975 ) , the modest total dust mass ( van woerden et al . 1993 ) , the low number of x - ray binaries , and the low globular cluster specific frequency ( kraft et al . 2005 ) . in regards to the modest intrinsic brightness and blue central colors of ngc 5102 , bedregal et al . ( 2008 ) investigate the spectroscopic properties of fornax cluster s0 galaxies that span a range of masses , and find a trend between luminosity - weighted central age and galaxy mass , in the sense that lower mass s0 s have younger central ages . the blue central colors of ngc 5102 may thus be tied to its modest mass . [ [ tracing - star - formation - in - ngc-5102-the - recent - past - and - the - immediate - future ] ] tracing star formation in ngc 5102 : the recent past and the immediate future ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ there is only a modest number of resolved bright ms stars and rsgs throughout the disk of ngc 5102 , demonstrating the low sfr during the past @xmath130 myr . the majority of young stars are in the southern half of the galaxy , which is where the only hii regions are located . this is also where the hi density is highest and there are hi clumps ; for comparison , hi in the northern part of the ngc 5102 disk is more uniformly distributed , with a lower mean density ( van woerden et al . 1993 ) . the hi distribution strongly suggests that barring some external influence the part of the disk that is presently south of the galaxy center will continue to be the dominant area of star formation for time scales of at least a few disk crossing times . rsgs and agb stars span a much wider range of ages than the brightest ms stars , and these objects are more uniformly distributed throughout the disk of ngc 5102 than bright ms stars . this indicates that star formation within the past @xmath131 gyr was not restricted to selected locations in the disk . indeed , the number densities of frsg / bagb stars at intermediate radii along the northern and southern arms of the major axis are similar , indicating that the northern and southern parts of the galaxy had similar time - averaged sfrs @xmath131 gyr in the past . the number counts of objects that are classified as frsg / bagb stars suggest that the light profile of the ngc 5102 disk does not follow a single power law , but breaks to a shallower profile near r@xmath132 kpc ( 5.5 6.7 disk scale lengths ) . the error bars in the frsg / bagb counts are significant at large radii , and background galaxies that at an angular resolution of roughly an arcsec are unresolved introduce a considerable source of uncertainty . still , the majority of early - type disk galaxies have light profiles that become shallower at large radii ( pohlen & trujillo 2006 ) . the spatial distribution of oagb stars , selected from the wircam data , is more compact than that of the frsg / bagb stars . given that the oagb stars tend to be older than those in the frsg / bagb sample , then this suggests that the outer disk of ngc 5102 has a younger mean age than the inner disk . this is similar to what is seen in m81 , where the structural properties of the outer disk have almost certainly been affected by interactions with m82 ( davidge 2009 ) . stars along the major axis of ngc 5102 , which presumably belong to the disk , can be traced out to r@xmath133 kpc , or @xmath134 disk scale lengths , in the southern half of the galaxy . this indicates that the disk may extend to a greater distance than was estimated by davidge ( 2008a ) , who used rgb star counts along the minor axis to trace the disk out to a de - projected radius of @xmath16 kpc . clumpiness in the outer disk of ngc 5102 may explain why the disk radius estimated made by davidge ( 2008a ) along the minor axis differs from that found here . the distribution of frsg / bagb stars in figure 8 indicates that there is structure in the outer disk of ngc 5102 , with a marked concentration of objects along the south west semi - major axis ( 4.3 ) . the disk of ngc 5102 is also markedly warped at large radii in the northern portion of the galaxy . this is evident in the hi map of van woerden et al . ( 1993 ) , where the hi distribution veers to the north west of the northern arm of the major axis as extrapolated from smaller r@xmath33 . oagb stars follow the hi warp . a cluster of background galaxies could masquerade as the southern extension of the ngc 5102 disk , although such a cluster would have to be positioned fortuitously along the major axis of ngc 5102 . deep images with angular resolutions of the order 0.1 arcsec or better will provide the data needed to confirm the nature of the objects that define the low surface brightness structures along the major axis of ngc 5102 . if , as suggested here , the structures are made up of stars that belong to the disk of ngc 5102 , as opposed to background galaxies , then the projected density of extended objects in these structures will be comparable to that in other parts of the area around ngc 5102 . on the other hand , if high angular resolution observations detect an excess population of galaxies then the frsg / bagb counts will need to be re - visited . [ [ the - nature - of - the - agb - concentration - near - the - center - of - ngc-5102-star - cluster - or - satellite ] ] the nature of the agb concentration near the center of ngc 5102 : star cluster or satellite ? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ the kpc - sized concentration of agb stars immediately to the west of the galaxy center is the most prominent structure found in the vicinity of ngc 5102 , and the nature of this feature is of considerable importance for understanding the recent evolution of ngc 5102 . the relatively blue @xmath30 colors of the majority of agb stars in this area ( 5 ) suggest that this was probably an area of localized star formation in the not - to - distant past . the physical coincidence with a probable superbubble ( mcmillan et al . 1994 ) suggests that star formation may have continued in this stellar concentration up to within the past few tens of myr , and hi is concentrated in this area ( van woerden et al . deeper images should reveal a population of intermediate age ms stars in the agb concentration with a spatial density that is roughly twice that on the eastern side of the disk . the age measured from the main sequence turn off of this stellar concentration will provide a means of timing star burst activity in ngc 5102 . two possible origins for the agb concentration are considered here . one is that the agb concentration is a large cluster in the disk of ngc 5102 . an awkward aspect of this interpretation is that much of the most recent star - forming activity during intermediate epochs in ngc 5102 would have been concentrated in a single region of the disk that is offset from the center of the galaxy . this is not typical for starburst systems , where star formation tends to be centered on the nucleus ( e.g. kewley , geller , & barton 2006 , and references therein ) . still , if the star cluster interpretation is correct then it can not be older than @xmath11 gyr . the crossing time of the ngc 5102 disk is on the order of a few hundred myr , and coherent structures might be expected to dissipate after a few crossing times , due to kinematic heating by interactions with large gas clouds and other star clusters . the difference in colors between the brightest m giants in the disk to the east of the galaxy center and the agb concentration ( figure 6 ) is qualitatively consistent with a relatively ` young ' age for the agb concentration , although it is difficult to assign a reliable absolute age from these data alone . the second interpretation is that the stellar concentration is a satellite galaxy seen in projection against ( or behind ) the disk . kraft et al . ( 2005 ) hypothesize that a gas - rich dwarf galaxy triggered the large episode of star formation in ngc 5102 during intermediate epochs . a long - recognized difficulty with this hypothesis is that ngc 5102 is in an isolated environment . using distances measured by karachentsev et al . ( 2007 ) , the nearest known neighbor of ngc 5102 is the barred spiral galaxy eso383-g087 , which is at a distance of @xmath135 mpc . the satellite interpretation of the agb concentration is thus attractive as it provides a trigger for the burst of star formation in ngc 5102 . comparatively easy tests of the satellite hypothesis are that ( 1 ) a satellite would have left a trail of material as it was disrupted , and this trail might still be visible , and ( 2 ) ngc 5102 should show signs of having experienced a recent interaction . while ambiguous stellar streams have not been detected near ngc 5102 , there are two _ possible _ tidal remnants . the grouping of stars along the minor axis could be the remnant of an interaction involving a satellite with an orbit that was perpendicular to the disk plane . the integrated brightness of the three minor axis pixels in figure 8 that breech the @xmath118 threshold is v @xmath136 , such that m@xmath137 , which is @xmath138 of the integrated brightness of ngc 5102 . mori & rich ( 2007 ) model interactions in which satellites with masses that are no more than a few percent of the total mass of m31 pass through the central regions of m31 . while caution should of course be exercised when extending these results to ngc 5102 , some broad conclusions are worth noting . the satellite is significantly disrupted , and its stars are distributed throughout the extraplanar environment , forming distinct streams and shells during the first @xmath11 gyr . the disk of m31 is not affected significantly as long as the satellite has a mass that is less than @xmath138 of that of the galaxy . a few gyr after the first interaction the extraplanar region is dominated by a diffuse component , with little evidence of streams and shells . the clumpy structures found in the outer disk of ngc 5102 are reminiscent of the extended outer disk of m31 ( ibata et al . 2005 ) . based on its disk - like stellar content , faria et al . ( 2007 ) argue that the m31 ` cluster ' g1 , which falls along the major axis of m31 , might actually be a fragment of the m31 disk that was pulled from the disk during a past interaction . richardson et al . ( 2008 ) find that the stellar content throughout the outer disk of m31 is highly uniform , and argue that the extended disk may be the consequence of the heating and disruption of the thin disk of m31 by a satellite . an extended disk formed in this manner may stay in place for many gyr given the long mixing times in the outer regions of galaxies ( e.g. johnston , hernquist , & bolte 1996 ) . it is further worth noting that the ring - like hi distribution in ngc 5102 is reminiscent of the distribution of gas and dust in m31 , which simulations suggest may be the result of a smaller companion ( presumably m32 ) passing through the disk ( e.g. block et al . the warping of the ngc 5102 disk , which is seen in both the hi and stellar distributions , may also be the consequence of a tidal encounter . there are other tests of the satellite hypothesis , but they will prove challenging to implement . a satellite galaxy would probably contain a substantial old population , with a metallicity that may be distinct from that of ngc 5102 . however , such a population would prove difficult to detect given that the proposed satellite is viewed against / through the crowded inner regions of ngc 5102 . another test is that the radial velocities of stars in the cluster and the disk may differ . an obvious difficulty is that an investigation of the velocities of even the most luminous stars will require larger telescopes than those currently available . this being said , the agb concentration is coincident with a localized peak in the hi distribution , and this feature is not kinematically distinct in hi channel maps ( van woerden et al . 1993 ) . a large velocity difference between ngc 5102 and the supposed satellite may not be present today , as dynamical friction will act to harmonize the kinematic properties of stars in the satellite with those in ngc 5102 , although this may require very long time scales depending on the orbital geometry and relative system masses ( e.g. colpi , mayer , & governato 1999 ) . in 6.3 the collection of stars at a projected galactocentric distance of @xmath114 kpc on the south east minor axis of ngc 5102 was discussed in the context of it being a possible tidal remnant . in this section we consider another possible origin for this structure . galaxies with elevated sfrs may experience outflows , and this can have an impact on their surroundings . the outflow from m82 may trigger star formation in its extraplanar regions ( e.g. davidge 2008c , d ) , as the wind interacts with circumgalactic clouds that presumably were tugged from m82 and/or m81 as they interacted , or condensed from material that was ejected from m82 by winds . the features identified as the ` cap ' ( devine & bally 1999 ) and m82 south ( davidge 2008d ) are perhaps the most obvious signatures of the interplay between the m82 outflow and surrounding material . the ism of ngc 5102 shows only marginal evidence for an outflow at the present day ( shwartz et al . 2006 ) , although kraft et al . ( 2005 ) find diffuse x - ray emission in the central 1 kpc of ngc 5102 , which they attribute to a superbubble that is powered by sne associated with the most recent burst of star - forming activity . however , the sfr in ngc 5102 during intermediate epochs was probably sufficient to power a galaxy wind ( 7.3 of davidge 2008a ) . could the diffuse stellar component along the south east minor axis of ngc 5102 have formed in such an outflow ? an outflow origin for these stars provides a natural explanation for their location along the minor axis of ngc 5102 . however , such structures will probably not be long - lived , and will probably be disrupted over a few orbital timescales around ngc 5102 ( i.e. within @xmath11 gyr ) . there would also have to be a large diffuse gas component surrounding ngc 5102 , and no evidence for this has been found . finally , with m@xmath139 ( 6.3 ) the minor axis structure would be much larger than the largest outflow cluster in m82 ( davidge 2008d ) . thus , while an outflow origin for these stars can not be ruled out , this possibility appears to be unlikely .	the spatial distribution of stars in the nearby s0 galaxy ngc 5102 is investigated using images obtained with wircam and megacam on the canada - france - hawaii telescope . with the exception of gaps between detector elements , the entire galaxy is surveyed in and , while the and data extend out to r kpc , which corresponds to almost 7 disk scale lengths . rsgs and bright agb stars are traced out to a radius of 14 kpc ( 15.6 scale lengths ) along the southern portion of the major axis , while a tentative detection is also made of bright agb stars at a projected distance of kpc along the south east minor axis .	the spatial distribution of stars in the nearby s0 galaxy ngc 5102 is investigated using images obtained with wircam and megacam on the canada - france - hawaii telescope . with the exception of gaps between detector elements , the entire galaxy is surveyed in and , while the and data extend out to r kpc , which corresponds to almost 7 disk scale lengths . a modest population of main sequence ( ms ) stars with m and ages myr are detected throughout the disk , with the majority located in the southern half of the galaxy . the stellar disk in the northern half of the galaxy is warped , following structure that is also seen in hi . objects with photometric properties that are consistent with those of bright agb stars are seen throughout the disk , and the ratio of c stars to bright m giants is consistent with an overall increase in the star formation rate within the past 1 gyr . star - forming activity during the interval gyr was more centrally concentrated than during the past myr . the structure of the disk changes near r kpc ( 5.5 disk scale lengths ) , in the sense that the radial surface density profile defined by red supergiants ( rsgs ) and bright agb stars levels off at larger radii . rsgs and bright agb stars are traced out to a radius of 14 kpc ( 15.6 scale lengths ) along the southern portion of the major axis , while a tentative detection is also made of bright agb stars at a projected distance of kpc along the south east minor axis . a large clump of agb stars that subtends arcmin is identified to the west of the galaxy center . it is argued that this is the remnant of a companion galaxy that triggered past episodes of elevated star - forming activity . = 1.0 cm
1510.02622	i	the current knowledge and main ideas of the structure , formation , evolution of the milky way bulge are under debate and in rapid development , mainly due to the recent large amount of new observations of kinematics , photometry , and abundances of bulge stars , as well as sophisticated modelling and interpretation . the milky way bulge or bulge / bar can nowadays be seen upon as the inner structure of the bar @xcite and is certainly a complex environment . it might be a composite system with a mixture of different populations , similarly to many bulges at low redshift @xcite . for recent reviews of the milky way bulge , see @xcite , @xcite , and @xcite . originally , it was thought that the milky way bulge was a classical bulge formed by an initial collapse , with an early , rapid , and intense star formation , in an inside - out formation scenario ( e.g. * ? ? ? * ) , or through accretion of substructures and/or large violent merger events in the @xmath8cdm scenario ( e.g. * ? ? ? * ; * ? ? ? however , the observational evidence for a classical bulge has weakened and the classical contribution seems to be small @xcite , see however the discussions in @xcite and @xcite . at present , a range of observations points toward a complex situation which may be consistent with multiple components / populations or gradients within populations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? on the one hand , kinematic surveys , e.g. @xcite and @xcite are strongly consistent with the bar / x - structure being the predominant population by mass ( see also * ? ? ? * ) . however , there are strong correlations observed between abundances and kinematics , which pose challenges to any unified picture ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? according to the chemical evolution models of @xcite , the modelled spheroidal component formed rapidly on a short timescale via an intense burst of star formation in a classical gravitational gas collapse , and the component created by bar evolution formed later on a longer time scale . note , however , that much of the metal - rich component has elevated alphas ( * ? ? ? * ; * ? ? ? * see also this work ) . the nature of these components are not certain ( see e.g. * ? ? ? * ) and associating them with specific formation scenarios should be done with caution @xcite . important diagnostics for discriminating between models of bulge formation and evolution are _ ( i ) _ @xmath0-abundance trends with metallicity , and _ ( ii ) _ spatial abundance - gradients in the bulge : _ ( i ) _ abundance trends can set constraints on the formation time - scales of the different components @xcite . the dynamics and abundance trends of bulge stars from the metal - poor component ( even though there are differences , see e.g. * ? ? ? * ) point to similarities especially with the ( local ) thick disk ( e.g. * ? ? ? * ; * ? ? ? @xcite show that from a chemical point of view , an inside - out formation , modelled with a initial collapse , be it a due to an early star burst in a disk , a classical bulge , or a thick disk , fits the chemical data . large samples with chemistry and dynamics are needed in order to constrain the formation in detail . _ ( ii ) _ abundance gradients are important outcomes of formation models . there is observational evidence that there is a metallicity gradient from @xmath9 to @xmath10 latitude ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but the origin of this is debated . it could either reflect varying relative proportions of the different components @xcite or it could reflect an intrinsic metallicity gradient produced by the bar due to an original disk gradient @xcite . within @xmath11 , only a few investigations of the metallicity distribution based on stellar spectra at medium- and high resolutions exist . the galactic centre ( gc ) and the region defined by the inner few hundred parsecs have escaped detailed study of stellar abundances and abundance gradients from giants , due to the extreme optical obscuration , resulting in only a handful studies in the literature . @xcite provide evidence for a break in the gradient , being absent with a narrow metallicity distribution at [ fe / h]@xmath12 between @xmath13 and @xmath14 to the south of the galactic centre . these studies are based on @xmath15 spectroscopy of 50 giants observed in the h band . recently , @xcite found a double - peaked distribution with peaks at slightly sub - solar and super - solar metallicities at a northern latitude of @xmath16 , based on medium - resolution spectra of 112 stars in the field . @xcite and @xcite obtained k - band spectra of the supergiant population in the galactic center , finding [ fe / h]@xmath17 , with a narrow dispersion . recently , @xcite also find a metallicity peak in the galactic centre at [ fe / h]@xmath18 , but with a slightly larger spread , also from k - band spectra . all these galactic centre studies are based on approximately 10 stars each , so caution should be exercised when drawing conclusions . recently , @xcite determined metallicities of 83 giants within the inner 1 pc of the galactic center , based on low - resolution ifu spectra ( @xmath19 ) , and found an surprisingly large dispersion ( @xmath20[fe / h]@xmath21 ) . high - resolution spectra are needed to validate these results . in this paper , we will discuss these issues for the inner bulge , within a projected distance of 300 pc ( @xmath22 ) from the center of the galaxy . to overcome the extreme optical extinction in these regions , we observe all our stars at @xmath23@xmath2 . the extinction in the k band is a factor of 10 lower that in the v band @xcite . the large crowding of stars can be dealt with thanks to adaptive optics . to ensure a detailed abundance analysis , we record our spectra with high spectral resolution . we will be able to link the galactic center and the bulge by analysing similar stars and using the same analysis techniques including the same spectral region and high spectral resolution , which to our knowledge has not really been done before . the luminosity and temperature ranges of our stars in the galactic center and the other two fields is similar as well . as presented in @xcite , we also argue that this population is at least 1 gyr old , with no substantial membership from the youngest 10 myr stars .	the structure , formation , and evolution of the milky way bulge is a matter of debate . important diagnostics for discriminating between models of bulge formation and evolution include-abundance trends with metallicity , and spatial abundance and metallicity gradients . due to the severe optical extinction in the inner bulge region , only a few detailed investigations have been performed of this region . here we aim at investigating the inner 2 degrees of the bulge ( projected galactocentric distance of approximately 300 pc ) , rarely investigated before , by observing the [/fe ] element trends versus metallicity , and by trying to derive the metallicity gradient in the region . we could interpret this as a continuation of the metallicity gradient established further out in the bulge , but due to the low number of stars and possible selection effects , more data of the same sort as presented here is necessary to conclude on the inner metallicity gradient from our data alone .	the structure , formation , and evolution of the milky way bulge is a matter of debate . important diagnostics for discriminating between models of bulge formation and evolution include-abundance trends with metallicity , and spatial abundance and metallicity gradients . due to the severe optical extinction in the inner bulge region , only a few detailed investigations have been performed of this region . here we aim at investigating the inner 2 degrees of the bulge ( projected galactocentric distance of approximately 300 pc ) , rarely investigated before , by observing the [/fe ] element trends versus metallicity , and by trying to derive the metallicity gradient in the region . [/fe ] and metallicities have been determined by spectral synthesis of 2 spectra of 28 m - giants in the bulge , lying along the southern minor axis at , , and . these were observed with the crires spectrometer at the _ very large telescope , vlt _ at high spectral resolution . low - resolution k - band spectra , observed with the isaac spectrometer at the _ vlt _ , are used to determine the effective temperature of the stars . we present the first connection between the galactic center and the bulge using similar stars , high spectral resolution , and analysis techniques . the [/fe ] trends in all our three fields show a large similarity among each other and with trends further out in the bulge . all point to a rapid star - formation episode in the bulge . we find that there is a lack of an [/fe ] gradient in the bulge all the way into the centre , suggesting a homogeneous bulge when it comes to the enrichment process and star - formation history . we find a large range of metallicities from}<+0.3 $ ] , with a lower dispersion in the galactic center :}<+0.3 $ ] . the derived metallicities of the stars in the three fields get , in the mean , progressively higher the closer to the galactic plane they lie . we could interpret this as a continuation of the metallicity gradient established further out in the bulge , but due to the low number of stars and possible selection effects , more data of the same sort as presented here is necessary to conclude on the inner metallicity gradient from our data alone . our results firmly argues for the center being in the context of the bulge rather than very distinct .
1510.02622	r	in table [ abund ] we present our abundances : metallicities , [ fe / h ] , and the @xmath0-element abundances of [ mg / fe ] and [ si / fe ] . we have normalised our derived abundances to the solar abundances of @xcite : @xmath95 , @xmath96 , and @xmath97 . we have redetermined the abundances for the galactic center stars of @xcite , in order to be homogenous with the other fields . they only change slightly , in most cases by much less than 0.1 dex , but in a few cases by more than that , which demonstrates that systematic uncertainties can be of that order for stars of low signal - to - noise , or heavy line density in the spectrum . lccc gc1 & 0.19 & & 1.72 + gc20 & 0.00 & & 0.96 + gc22 & 0.12 & & 1.49 + gc25 & 0.34 & & 1.71 + gc27 & 0.16 & & 1.58 + gc28 & 0.06 & & 1.29 + gc29 & 0.14 & & 1.55 + gc37 & 0.15 & & 1.41 + gc44 & 0.08 & & 1.57 + bm1 - 06 & 0.04 & & 1.53 + bm1 - 07 & @xmath250.45 & & 1.06 + bm1 - 08 & @xmath250.06 & & 0.96 + bm1 - 10 & 0.01 & & 1.18 + bm1 - 11 & @xmath250.01 & & 1.20 + bm1 - 13 & 0.00 & & 0.71 + bm1 - 17 & 0.21 & & 1.27 + bm1 - 18 & @xmath250.00 & & 1.29 + bm1 - 19 & 0.09 & & 0.90 + bm2 - 01 & 0.06 & & 1.03 + bm2 - 02 & @xmath250.03 & & 1.02 + bm2 - 03 & 0.17 & & 1.48 + bm2 - 05 & 0.11 & & 1.67 + bm2 - 06 & @xmath250.30 & & 0.49 + bm2 - 11 & @xmath250.10 & & 0.85 + bm2 - 12 & 0.06 & & 1.22 + bm2 - 13 & 0.05 & & 1.17 + bm2 - 15 & 0.04 & & 1.31 + bm2 - 16 & 0.25 & & 1.58 + bd-012971 & @xmath250.03 & & 0.95 + 142173 & 0.02 & & 0.99 + 171877 & 0.05 & & 0.97 + 225245 & 0.08 & & 1.02 + 313132 & 0.38 & & 1.52 + 343555 & @xmath250.01 & & 0.96 + hd 787 & @xmath250.08 & & 0.82 + we have not determined the c and n - abundances for our stars since we do not have any co lines in our wavelength range . however , we have numerous cn lines that we need to fit in the spectral synthesis in order to take blends into account properly . we have therefore determined the c and n abundances such that these are synthesised properly . since the c and n abundances are degenerate , we have determined one of them for a given typical abundance of the other . this means that our carbon or nitrogen abundances are not necessarily the stellar abundances , but rather merely the values we need in combination with the given n or c abundances , respectively , to fit the cn lines . in the second column in table [ cn ] we thus provide the [ c / fe ] abundance that is required to fit the cn lines for a given typical n enhancement for heavily cn - cycled red giants , [ n / fe]@xmath84 @xcite . we see that the carbon abundances , in this case , are more than scaled solar , which is not expected for these type of giants @xcite . in the third column in the table , conversely , the [ n / fe ] abundance that is required to fit the cn lines for a given typical c depletion , [ c / fe]@xmath85 @xcite , are provided . in order to fit the cn lines , in this case , unexpectedly high intrinsic nitrogen abundances are needed . there thus seems to be an indication that we need a high [ c+n / fe ] abundance in these bulge stars , but also our thick disk stars . we note that @xcite measure the c , n , and o abundances in m giants in the inner bulge and find typical red giant values . in @xcite the c , n , and o abundances are also measured from co , cn , and oh lines , which we can not do in the present spectra , and they find only slightly enhanced [ c+n / fe ] for k giants . we find a more extreme change of the c and n abundances , more resembling arp4203 in @xcite , which is a star more resembling those in this paper . we find no correlation with @xmath98 magnitude , but there is a clear correlation with @xmath30 , in the sense that the lower the temperature , the higher the c or n enhancement . in table [ errors ] we show that this large discrepancy can not be explained by an uncertainty in , e.g. , @xmath30 . we do not discuss this further , since we have not measured these abundances , but merely infer them from forcing the cn lines to fit the observations . determining the c , n , and o abundances of these stars or more inner bulge stars would be rewarding . we plot the [ mg / fe ] and [ si / fe ] trends as a function of the metallicity , [ fe / h ] , in figure [ afe1 ] separately for each field : the galactic center , the @xmath99 , and for the @xmath100 fields . in figure [ afe2 ] , we show the trends for all our observed stars in the entire region ( within a projected distance of 300 pc ) together . in this figure , we also include the mean abundance ratios of the two populations of terzan 5 at @xmath101,@xmath102 from @xcite . from the figures we see that the @xmath0-abundance trends , here represented by the [ mg / fe ] and the [ si / fe ] versus [ fe / h ] trends , are very similar in the three inner bulge fields . plotting the trend for all our stars in the inner 300 pc region strengthens this finding . in the figures showing the inner bulge trends , we have also included the trends outlined by the abundances derived from micro - lensed dwarfs from the ` outer ' bulge @xmath103 ) as derived by @xcite . the [ mg / fe ] and [ si / fe ] trends in all three inner regions , from the galactic center to a latitude of @xmath37 , follow the outer bulge trends , within uncertainties , with low values of [ @xmath0/fe ] at [ fe / h]@xmath104 . from these plots it is evident that we can not claim that our [ @xmath0/fe ] trend in the inner 300 pc is particular compared to the ` outer ' bulge , @xmath105 . our thick disk trend also follow the micro - lensed dwarf trend , which gives confidence in the analysis method and shows that we are on the same scale , with room for only small systematic uncertainties . the metallicity of the @xmath37 , @xmath36 , and galactic center fields ranges from @xmath6}<+0.3 $ ] , @xmath106}<+0.3 $ ] , and @xmath7}<+0.3 $ ] , respectively . the two southern fields start picking up some metal - poorer stars , some at very low metallicities ( even below [ fe / h]@xmath107 ) . the spread in metallicities we find are larger than what has been found earlier : @xcite find a dispersion of approximately 0.1 dex around [ fe / h]=@xmath108 to @xmath109 and @xcite find a total spread of @xmath110 dex around [ fe / h]=@xmath111 for the luminous giants and supergiants in the central cluster located within 2.2 pc of the galactic center . the metallicity distributions for the different fields we find in this investigation , are presented in figure [ mdf ] , with the upper three panels showing the three inner fields , and the lowest panel showing the combined metallicity - distribution histogram . the global mean - metallicities of all the observed stars in each of the inner bulge regions are , from the galactic center and outwards , @xmath112 > = + 0.06 $ ] , @xmath113 , and @xmath114 , respectively . for comparison , we can compare our mean metallicities with @xcite who find a mean metallicity of approximately @xmath115[fe / h@xmath116@xmath117 for their fields at @xmath118 and @xmath119 ) , i.e. at slightly lower latitudes . our mean metallicities within the inner @xmath11 gives a formal gradient of @xmath120 or @xmath121dex / degree . this number should be handled with caution due to the very low number of stars . also , there might be undetermined selection effects , which prevents us from selecting metal - poor stars , due to the large and variable extinction in the galactic center field . more stars analysed in the same maner as done here are needed to determine the metallicity distributions in these fields , in order to derive a gradient in the inner bulge .	the [/fe ] trends in all our three fields show a large similarity among each other and with trends further out in the bulge . all point to a rapid star - formation episode in the bulge . we find a large range of metallicities from}<+0.3 $ ] , with a lower dispersion in the galactic center :}<+0.3 $ ] .	the structure , formation , and evolution of the milky way bulge is a matter of debate . important diagnostics for discriminating between models of bulge formation and evolution include-abundance trends with metallicity , and spatial abundance and metallicity gradients . due to the severe optical extinction in the inner bulge region , only a few detailed investigations have been performed of this region . here we aim at investigating the inner 2 degrees of the bulge ( projected galactocentric distance of approximately 300 pc ) , rarely investigated before , by observing the [/fe ] element trends versus metallicity , and by trying to derive the metallicity gradient in the region . [/fe ] and metallicities have been determined by spectral synthesis of 2 spectra of 28 m - giants in the bulge , lying along the southern minor axis at , , and . these were observed with the crires spectrometer at the _ very large telescope , vlt _ at high spectral resolution . low - resolution k - band spectra , observed with the isaac spectrometer at the _ vlt _ , are used to determine the effective temperature of the stars . we present the first connection between the galactic center and the bulge using similar stars , high spectral resolution , and analysis techniques . the [/fe ] trends in all our three fields show a large similarity among each other and with trends further out in the bulge . all point to a rapid star - formation episode in the bulge . we find that there is a lack of an [/fe ] gradient in the bulge all the way into the centre , suggesting a homogeneous bulge when it comes to the enrichment process and star - formation history . we find a large range of metallicities from}<+0.3 $ ] , with a lower dispersion in the galactic center :}<+0.3 $ ] . the derived metallicities of the stars in the three fields get , in the mean , progressively higher the closer to the galactic plane they lie . we could interpret this as a continuation of the metallicity gradient established further out in the bulge , but due to the low number of stars and possible selection effects , more data of the same sort as presented here is necessary to conclude on the inner metallicity gradient from our data alone . our results firmly argues for the center being in the context of the bulge rather than very distinct .
1510.02622	c	how large spiral galaxies and their various structures are formed is not know today ( see e.g. * ? ? ? . an important step on the way to the clarifying this issue , is to study the milky way bulge , which is a major component of our galaxy , a galaxy which we can study in detail . important observables in this context are the [ @xmath0/fe ] trends as a function of metallicity and the latitudinal metallicity - gradients . in this paper , we have presented new abundances and gradients of 28 m - giants located in the inner 300 pc of the milky way bulge . we observed the giants at high spectral resolution in the k band , in order to avoid the extreme visual extinction . our [ mg / fe ] and [ si / fe ] abundances as a function of metallicity show similar behaviour in all three fields , from the galactic centre out to a latitude of @xmath37 . the abundance trends also follow the trends of stars at lower latitudes , in the ` outer ' bulge : the abundance ratios are constant up to [ fe / h]@xmath160 , after which they turn down reaching close to solar - values at [ fe / h]=0 . the ratios then level off at values slightly above scaled - solar values , up to a metallicity of [ fe / h]@xmath161 . we thus find a lack of an [ @xmath0/fe]-gradient in the inner bulge region , similarly to what has been found for the rest of the bulge . we thus conclude that the lack of an [ @xmath0/fe ] gradient further out extends all the way into the galactic centre , which means a rapid formation scenario and a homogeneity of the enrichment process @xcite . our galactic chemical evolution modelling of the inner 300 pc of the bulge shows that our observed abundance ratios and the metallicity distributions , are compatible with this region having experienced a main early , rapid ( @xmath162 gyr ) , strong burst of star formation , with a high star - formation efficiency . also , it indicates a need for an imf skewed to relatively more massive stars compared to the solar vicinity . the inner 300 pc includes the central molecular zone ( cmz ) , with a recent ( second burst of ) intense star formation . this second burst can not have been trigged by more than a modest episode of gas infall or accretion of gas induced by the bar @xcite . this episode does not affect the abundance patterns , however . our data shows a trend where the fraction of metal - poor stars increases the further away from to the galactic centre one looks . in the light of the fact that @xcite find no metal - poor stars in the inner @xmath163 , and since we only have very few stars yet observed in every region , and since there might be selection effects in the galacitc center field due to extreme and variable extinction , often not precisely known , we can not conclude anything about the inner metallicity gradient . more stars in every field is thus needed to draw firm conclusions , which we retrain from doing yet . a metallicity gradient is well established in the bulge at @xmath142 from several different studies . whether this gradient continues all the way into the galactic centre or not , our data can not tell for certain . what we do find is a quite a large range of metallicities in the inner bulge . to summarise , we have presented the first study to connect old stars in the galactic center with the bulge , using high - resolution spectroscopy , stars of similar luminosities , temperatures , and gravities , and using the same analysis methods , including the same spectral region . it firmly argues for the center being in the context of the bulge rather than very distinct . one may tentatively conclude that the very center was not built by the infall of halo or even bulge - like globular clusters , based on metallicity . the @xmath0-element trends with metallicity are very similar for the different regions . only the metallicity distribution seems to change with latitude . this could be expected if the metal - rich component is defined by the boxy / peanut bulge , which increases its fractional importance toward the centre . the boxy / peanut bulge is the inner structure of the bar , originating from vertical instabilities in the disk . this stellar population is , therefore , expected to be similar to the inner disk @xcite . however , as mentioned earlier , a distinct metal - poor population should have presented itself clearly in the brava survey @xcite , which it did not . we would like to thank livia origlia for very fruitful and insightful discussions . acknowledges support from the swedish research council , vr ( project number 621 - 2014 - 5640 ) , funds from kungl . fysiografiska sllskapet i lund . ( stiftelsen walter gyllenbergs fond and mrta och erik holmbergs donation ) . f.m . and v.g . acknowledge financial support from prin miur 2010 - 2011 , project the chemical and dynamical evolution of the milky way and local group galaxies , prot . 2010ly5n2 t . rmr acknowledges support from grant ast-1413755 from the national science foundation , nsf . this work is based on observations collected at the european southern observatory , chile , program number 089.b-0312(a)/vm / crires and 089.b-0312(b)/vm / isaac . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . _ facilities : _ , . , h .- u . , ballester , p. , biereichel , p. , et al . 2004 , in presented at the society of photo - optical instrumentation engineers ( spie ) conference , vol . 5492 , society of photo - optical instrumentation engineers ( spie ) conference series , ed . a. f. m. moorwood & m. iye , 12181227 , w. , & wallace , l. 1991 , an atlas of the solar spectrum in the infrared from 1850 to 9000 cm-1 ( 1.1 to 5.4 micrometer ) ( nso technical report , tucson : national solar observatory , national optical astronomy observatory , 1991 )	we present the first connection between the galactic center and the bulge using similar stars , high spectral resolution , and analysis techniques . we find that there is a lack of an [/fe ] gradient in the bulge all the way into the centre , suggesting a homogeneous bulge when it comes to the enrichment process and star - formation history . our results firmly argues for the center being in the context of the bulge rather than very distinct .	the structure , formation , and evolution of the milky way bulge is a matter of debate . important diagnostics for discriminating between models of bulge formation and evolution include-abundance trends with metallicity , and spatial abundance and metallicity gradients . due to the severe optical extinction in the inner bulge region , only a few detailed investigations have been performed of this region . here we aim at investigating the inner 2 degrees of the bulge ( projected galactocentric distance of approximately 300 pc ) , rarely investigated before , by observing the [/fe ] element trends versus metallicity , and by trying to derive the metallicity gradient in the region . [/fe ] and metallicities have been determined by spectral synthesis of 2 spectra of 28 m - giants in the bulge , lying along the southern minor axis at , , and . these were observed with the crires spectrometer at the _ very large telescope , vlt _ at high spectral resolution . low - resolution k - band spectra , observed with the isaac spectrometer at the _ vlt _ , are used to determine the effective temperature of the stars . we present the first connection between the galactic center and the bulge using similar stars , high spectral resolution , and analysis techniques . the [/fe ] trends in all our three fields show a large similarity among each other and with trends further out in the bulge . all point to a rapid star - formation episode in the bulge . we find that there is a lack of an [/fe ] gradient in the bulge all the way into the centre , suggesting a homogeneous bulge when it comes to the enrichment process and star - formation history . we find a large range of metallicities from}<+0.3 $ ] , with a lower dispersion in the galactic center :}<+0.3 $ ] . the derived metallicities of the stars in the three fields get , in the mean , progressively higher the closer to the galactic plane they lie . we could interpret this as a continuation of the metallicity gradient established further out in the bulge , but due to the low number of stars and possible selection effects , more data of the same sort as presented here is necessary to conclude on the inner metallicity gradient from our data alone . our results firmly argues for the center being in the context of the bulge rather than very distinct .
cond-mat9601131	i	the two - dimensional xy - model with random phase - shift , defined in eq . ( [ h ] ) below , captures the physics of a variety of physical systems . among them are xy - magnets with non - magnetic impurities , which are coupled to the xy - spins via the dzyaloshinskii - moriya interaction,@xcite josephson - junction arrays with geometric disorder,@xcite and crystals with quenched impurities.@xcite disordered xy - models are related to even more physical systems , like impure superconductors . it is in particular the interest in vortex - glass phases in type - ii superconductors , which motivates an analysis of possible glassy features in the paradigmatic two - dimensional bond - disordered system . the most fundamental question is , whether this model has an ordered phase . in the absence of disorder , there exists at low temperatures a phase with quasi long - range order . the famous kosterlitz - thouless transition separates it from the high - temperature phase with short - ranged order.@xcite the analysis by cardy and ostlund@xcite and more explicitly by rubinstein , shraiman and nelson@xcite predicted that the phase transition should be reentrant in the presence of disorder . later korshunov suggested,@xcite that the ordered phase might be completely destroyed by disorder . ozeki and nishimori@xcite showed for models with gauge - invariant disorder distributions , that the phase transition can not be reentrant , leaving open whether the ordered phase does exist or not . experiments@xcite on josephson junction arrays and simulations@xcite were in favor of the existence of an ordered phase without reentrance . in this controversial situation nattermann , scheidl , korshunov , and li@xcite as well as cha and fertig@xcite reconsidered only recently the problem and found that the ordered phase _ does _ exist and its boundary _ does not _ have reentrant shape . the earlier observation of reentrance was attributed to an overestimation of vortex fluctuations at low temperatures . the present study extends refs . and , which focused on the absence of reentrance . the purpose of this article is to examine in more detail the ordered phase , which is shown to be composed of different _ regions_. they are distinguished by the behavior of vortex correlation functions on large length scales , which are calculated _ quantitatively_. a low - temperature regime is found to exhibit glassy behavior in its correlations . in addition to the previous studies we find that the strength of disorder is increased under renormalization . this effect does not destroy the ordered phase but it is crucial for the universality type of the transition at low temperatures . in the following a generalized self - consistent screening approach is applied to the replicated system . the main improvement compared to earlier approaches@xcite on the same basis is achieved by including all relevant fluctuations and by taking special care when the number of replicas is sent to zero . we use the replica formalism mainly for two reasons : i ) the calculation of correlations becomes very convenient : one may use an expansion technique ( small fugacity and density of vortices ) which fails@xcite in the unreplicated system . ii ) we show that in the present model there is _ no _ need for replica symmetry breaking , even at lowest temperatures . in particular , the reentrance disappears and the glassiness occurs without a breaking of replica symmetry . this might astonish , since for various disordered systems reentrance has been explained as an artifact of a replica - symmetric ( exact mean - field or approximate variational ) approach , which has been overcome by breaking the replica symmetry.@xcite the paper is organized as follows : in sec . ii we set up our model and map it onto an effective coulomb gas . we recapitulate the breakdown of fugacity expansion in the presence of disorder . in sec . iii we set up the renormalization group within a self - consistent formulation of screening . the consistency of this approach in the original and replicated system is demonstrated . iv is devoted to the evaluation of the self - consistency and the proper performance of the replica limit . the results of the renormalization group treatment are worked out in sec . v , which are discussed and compared to the results of previous work in sec .	the analysis is based on a renormalization group for the replicated system . the transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature . in contrast to previous approaches the disorder strength is found to be renormalized to larger values . the renormalization group approach yields the glassy features without a breaking of replica symmetry . 2	the two - dimensional xy - model with random phase - shifts on bonds is studied . the analysis is based on a renormalization group for the replicated system . the model is shown to have an ordered phase with quasi long - range order . this ordered phase consists of a glass - like region at lower temperatures and of a non - glassy region at higher temperatures . the transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature . in contrast to previous approaches the disorder strength is found to be renormalized to larger values . several correlation functions are calculated for the ordered phase . they allow to identify not only the transition into the glassy phase but also an additional crossover line , where the disconnected vortex correlation changes its behavior on large scales non - analytically . the renormalization group approach yields the glassy features without a breaking of replica symmetry . 2
cond-mat9601131	r	in the previous sections the technical part of deriving the flow equations has been achieved . the most important flow equations are eqs . ( [ flow.compact]a-c ) . originally , the two - component parameters @xmath164 , @xmath165 , and @xmath166 have been functions of @xmath26 and @xmath88 . in the asymptotic approximation @xmath26 and @xmath88 have been eliminated , the two - component parameters are given by eq . ( [ def.fpq ] ) as simple functions of @xmath192 , and the fugacity flows according to eq . ( [ flow.y.asy ] ) . these flow equations can be summarized by [ flow.sum ] @xmath193 thus we are in position to discuss the physical implications of these flow equations . to start with , we address qualitative aspects and show that the flow equations satisfy some fundamental physical criteria . according to eqs . ( [ def.y.eff ] ) and ( [ undo.yeff ] ) all correlations @xmath194 are negative , since all fugacities are positive @xmath195 . this is consistent with a screening that weakens the attractive interaction between vortices of the same sign and weakens the repulsive interaction between vortices of the same sign . as a consequence , the two - component parameters are also non - negative . our asymptotic expressions show , that the fraction of polarizable dipoles @xmath196 vanishes linearly at small temperature , whereas the fraction of frozen dipoles @xmath197 becomes unity . screening reduces the coupling @xmath198 since @xmath199 , and it increases the strength of disorder , @xmath200 . in comparison to the pure case the screening of @xmath201 is reduced by the factor @xmath202 , the fraction of polarizable dipoles . whereas previous theoretical approaches did not yield a renormalization of @xmath61 , eq . ( [ flow.sum]c ) manifests that our renormalization scheme leads to an _ increase _ of @xmath61 . the free energy density is reduced by screening , see eq . ( [ flow.sum]d ) . due to disorder the contribution of dipoles is modified by a factor @xmath203 . the increase of @xmath61 seems to contradict the tendency of thermal vortices @xmath7 to _ neutralize _ quenched vortices @xmath40 . this neutralization is expected from eq . ( [ h.eff ] ) . however , the screened @xmath61 is _ not _ defined by the fluctuations of @xmath204 . rather , it was introduced via the fluctuation of the screened disorder potential @xmath205 . the fluctuations of @xmath205 are proportional to @xmath206 . the expected neutralization shows up as @xmath207 . this holds even though @xmath208 since the reduction of @xmath24 dominates the increase of @xmath61 , which follows from @xmath209 that is easily proven with the asymptotic expressions . the most important quantity to analyze is the flow of entropy . from spin - glass models one knows , that a replica - symmetric theory might lead to a negative entropy . this unphysical feature then indicates that the symmetric approach is insufficient and one has to allow for a breaking of replica symmetry . we now show that the present replica - symmetric theory does not suffer from this problem . therefore we believe that a _ breaking of replica symmetry is not necessary_. when the entropy @xmath210 is derived from the reduced free energy , the unrenormalized values of @xmath201 and @xmath61 have to be kept fixed . according to the flow equation for @xmath139 , a non - negative entropy is guaranteed by @xmath211 . the demonstration of this inequality is complicated by the temperature dependence , which is implicit to the screened @xmath201 and @xmath61 for @xmath212 . if one ignores this implicit dependence , one easily verifies @xmath213 , since @xmath214 and @xmath215 hold for @xmath189 and @xmath216 separately . the implicit temperature dependencies can be taken into account by showing @xmath217 . this is verified in the leading order , where one has @xmath218 for @xmath219 . if one would use the same expression for @xmath216 , one would obtain a negative entropy flow . however , for @xmath216 we find @xmath220 . therefore the entropy flow is non - negative even at very low temperatures . a numerical integration of the flow equations ( even without asymptotic approximations ) shows , that below some transition line @xmath221 in the @xmath222-plane the renormalization flow indeed does converge for @xmath223 to fixed points with @xmath224 , @xmath225 , and @xmath226 . this is true not only in the limit of large @xmath22 ( small fugacity ) , but also for arbitrarily small @xmath22 . only the extent of the ordered phase shrinks with increasing @xmath22 . this implies in particular , that the original xy - model described by @xmath23 has an ordered phase . above @xmath227 all quantities diverge under renormalization and the present renormalization group leaves its range of validity , which is limited to small fugacities already due to the independent dipole approximation . the properties of the ordered phase are evident in terms of the renormalized parameters @xmath228 and @xmath229 . due to screening they are related to the bare parameters by @xmath230 and @xmath231 , where the inequalities become equalities for vanishing fugacity within the ordered phase . in the ordered phase , the irrelevance of vortices requires that the fugacities vanish on large scales . therefore the flow equation ( [ flow.sum]a ) of fugacity must have a negative eigenvalue . this is true at temperatures and disorder strength below @xmath221 , which is located at @xmath232 in terms of the renormalized parameters . it is depicted in fig . [ fig_pdg0 ] as function of the renormalized parameters and of the unrenormalized parameters for @xmath233 . the most striking feature of the phase boundary is the absence of reentrance . reentrance was predicted by earlier approaches.@xcite absence of reentrance without a loss of the ordered phase was found only recently in improved approaches.@xcite as a function of the renormalized parameters , the phase boundary @xmath234 has a horizontal part at large @xmath228 , i.e. at low temperatures . in terms of bare parameters , the line @xmath221 can be parametrized by a function @xmath235 or @xmath236 . due to the renormalization of disorder strength , @xmath237 and due to the reduction of the coupling @xmath238 the end points are found at @xmath239 and @xmath240 and @xmath241 has no longer a horizontal part for finite fugacity . concerning the asymptotic behavior of the vortex correlation functions , one can distinguish three regions within the ordered phase . they are separated by a line @xmath242 , fixed by @xmath243 ( equivalent to @xmath244 ) , and a line @xmath245 , fixed by @xmath246 ( equivalent to @xmath247 ) , see fig . [ fig_pdg0 ] . in the @xmath248-diagram these lines emerge from the origin . they are straight lines in the limit of zero fugacity and bent upwards for finite fugacity . the correlations are retrieved from the fugacities , eq . ( [ y.asy ] ) , by omitting rescaling and inserting @xmath249 . thereby we find ( @xmath250 ) [ cs ] @xmath251 for @xmath252 and @xmath253 for @xmath254 . the limiting values for the fraction of polarizable and frozen dipoles are related to the correlations by [ pqf.inf ] @xmath255 naturally the question arises , whether these regimes are separated by a true thermodynamic transition at @xmath242 and @xmath245 . as we have observed , that asymptotic form of the flow equations and of the correlations changes its dependence on @xmath61 and @xmath24 non - analytically at @xmath179 and @xmath180 . however , a phase transition in the strict sense requires a non - analytic dependence of the integrated free energy on the unrenormalized parameters @xmath61 and @xmath24 . we were not able to prove such a singularity at @xmath242 and @xmath245 , which we therefore consider as crossover lines only . however , a true transition is expected at @xmath221 just as in the pure case . region ii can be distinguished _ qualitatively _ from the other regions . one can consider @xmath256 as order parameter for the low - temperature regime ii . it measures the relative strength of the disconnected vortex density correlation to the usual correlation on large scales . in the definition of this order parameter the normalization of the disconnected correlation by the usual correlation is necessary , since true long - range order is absent . the glassy order reflected by the edwards - anderson like correlation can therefore be only quasi long - ranged , too . nevertheless one may compare @xmath256 to the edwards - anderson order parameter in spin - glasses and we interpret it as order parameter for the _ glassiness _ of in the vortex system . the regions ia and ib differ only by the analytic dependence of the connected correlation on @xmath228 and @xmath229 . the correlation under consideration do not provide an order parameter comparabe to @xmath166 for the line @xmath245 . the universality class of the pure xy - model is defined by the behavior of the critical exponents @xmath257 and @xmath258 at the transition and the exponential divergence of the correlation length when the transition is approached from above.@xcite in the presence of disorder , the spin correlation decays with exponent@xcite @xmath259 along the line @xmath221 the exponent takes the value @xmath260 for @xmath261,@xcite which decreases with temperature until it reaches the value @xmath262 for @xmath34.@xcite in the disordered phase , where correlations decay exponentially , @xmath263 formally . thus the value of @xmath264 at the transition becomes non - universal , i.e. it is disorder dependent . only for @xmath265 or @xmath34 the jump of @xmath264 is universal ( from 1/4 or 1/16 to @xmath266 respectively ) in the sense that it does not depend on the bare coupling @xmath201 or bare fugacity @xmath163 . for @xmath188 or @xmath267 the jump lies inbetween and will depend on microscopic details . in the present work we have not included a magnetic field . therefore we can not determine @xmath268 in the presence of disorder . we now attempt to analyze how the correlation length @xmath269 diverges when the transition line is approached from above . even though the flow equations become invalid for large fugacity , kosterlitz@xcite has argued that @xmath269 is given by the length scale where the fugacity becomes of order unity . in the pure case , where the flow equations reduce to @xmath270 and @xmath271 he found @xmath272 with a non - universal constant @xmath273 . in the zero - temperature limit the flow equations read @xmath274 and @xmath275 . by a replacement @xmath276 they can be mapped onto the flow equations of the pure case . therefore we conclude , that the zero temperature transition has @xmath277 with some other non - universal @xmath273 . for finite temperature _ and _ finite disorder , our flow equations are too complicated for being integrated up analytically . however , we naturally expect that the functional form of the divergence is preserved and that only the argument of the square - root has to be replaced by the distance to the transition line , say @xmath278^{1/2}$ ] .	this ordered phase consists of a glass - like region at lower temperatures and of a non - glassy region at higher temperatures . they allow to identify not only the transition into the glassy phase but also an additional crossover line , where the disconnected vortex correlation changes its behavior on large scales non - analytically .	the two - dimensional xy - model with random phase - shifts on bonds is studied . the analysis is based on a renormalization group for the replicated system . the model is shown to have an ordered phase with quasi long - range order . this ordered phase consists of a glass - like region at lower temperatures and of a non - glassy region at higher temperatures . the transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature . in contrast to previous approaches the disorder strength is found to be renormalized to larger values . several correlation functions are calculated for the ordered phase . they allow to identify not only the transition into the glassy phase but also an additional crossover line , where the disconnected vortex correlation changes its behavior on large scales non - analytically . the renormalization group approach yields the glassy features without a breaking of replica symmetry . 2
1503.01654	r	previous work by feldberg@xcite and henstridge _ _ et . al.__@xcite showed that in the marcus - hush model of electron transfer kinetics , steady state currents can be kinetically rather than diffusionally limited for small values of the reorganisation energy , @xmath8 . in feldberg s study , an approximate equation of oldham and zoski@xcite describing steady state voltammetry at a microdisc was invoked and modified to use marcus - hush , rather than butler - volmer kinetics . henstridge used numerical simulation to generate marcus - hush steady state responses at a conductive nanosphere resting on an electrochemically inert but conductive surface . in this study , we simulate steady state voltammetry numerically using the symmetric marcus - hush formalism of electron transfer , and compare the circumstances in which a kinetically limited current is observed at a microdisc to those at a nanosphere . we also extend previous work showing the equivalence of microdiscs and spheres - on - surfaces under the butler - volmer formalism ( subject to a mass transport correction factor)@xcite , and show that the approximate equivalence is retained when marcus - hush kinetics are used . steady state voltammetry at a microdisc electrode was simulated using the model outlined above . various values of dimensionless reorganisation energy , @xmath45 , and dimensionless heterogeneous rate constant , @xmath102 , were simulated , and the results are shown in fig . [ vary k disc ] . part ( a ) shows results for @xmath103 , ( b ) shows @xmath104 and ( c ) shows @xmath105 . also shown in each case is the steady state voltammetry simulated using butler - volmer kinetics with the same values of @xmath102 , and @xmath106 , and marcus - hush results are shown relative to this butler - volmer result . for all three values of @xmath102 , it is seen that large @xmath45 values produce the same limiting current as the butler - volmer model . as @xmath45 becomes smaller , the limiting current becomes less than predicted by the butler - volmer model as kinetic control takes over . this effect is more extreme for the smallest values of @xmath102 , where even a @xmath45 value of 200 has not reached the butler - volmer limit at all points on the wave . for @xmath107 , unfeasibly small @xmath45 values would be required to show significant deviation form the butler - volmer result . this is in qualitative agreement with the previous studies of this nature@xcite . the definition of @xmath102 in our dimensionless model is : @xmath108 lowering @xmath102 will therefore mean that either @xmath3 or @xmath17 is lowered , or @xmath109 is raised . lowering @xmath3 trivially means the electrochemical kinetics become more likely to be the limiting factor in the steady state current as opposed to diffusion . either lower @xmath17 or increasing @xmath109 also both lower @xmath102 and lead to a more kinetically limited current . this is due to the fact that either of these changes will increase mass transport efficiency to the electrode surface , thus making electrochemical kinetics the more limiting factor . therefore , in order to see a kinetically limited current , it is desirable to have a small @xmath3 , a small @xmath17 and a large @xmath109 . recent work by molina _ _ et . al.__@xcite shows that steady state voltammetry at an isolated spherical electrodes alone in solution , a spherical electrode supported on a conductive but inert surface and a microdisc electrode ( all shown schematically in fig . [ 3 geometries ] ) may all be approximately described ( under the butler - volmer formalism ) by a single equation : @xmath110 } \label{steady state equation}\ ] ] where @xmath111 is a dimensionless heterogeneous rate constant scaled by a geometry dependent mass transport factor . these parameters are defined for isolated spheres ( is ) spheres supported on surfaces ( sos ) and microdiscs ( md ) as : @xmath112 therefore , steady state voltammetry at a microdisc of electrochemical rate constant @xmath113 produces approximately the same result as steady state voltammetry at a sphere on a surface of heterogeneous rate constant @xmath114 , as was shown . we now investigate if this relation holds under the marcus hush formalism over a wide range of @xmath102 and @xmath45 values . to do so , steady state voltammetry was simulated using the marcus - hush model described above for both a microdisc and a sphere on a surface . for each microdisc heterogeneous rate constant ( @xmath113 ) that was used , a corresponding sphere on a surface simulation was run with @xmath114 , with @xmath45 the same in each case . [ compare ] shows simulated steady state voltammograms at a microdisc electrode ( solid line ) and a sphere on a surface electrode ( circles ) at varying values of @xmath45 ( 20 , 24 , 30 , 40 , 60 , 100 and 200 ) . @xmath102 is equal to @xmath115 for the microdisc and @xmath116 for the sphere . qualitatively , the best agreement between the two geometries is seen at the smallest values of @xmath45 where an almost exact fit is observed . less good fits are seen at intermediate values of @xmath45 . [ error ] ( a ) shows the percentage error between the fits in fig . [ compare ] , as well as for three other values of @xmath113 : @xmath117 ( b ) , @xmath118 ( c ) , and @xmath119 ( d ) . to obtain the corresponding values of @xmath120 , @xmath113 is multiplied by @xmath121 . the percentage error is defined as : @xmath122 it is seen that as @xmath102 increases , the error becomes less and less dependent on the values of @xmath45 . this is because at high @xmath102 the marcus - hush model of electron transfer approaches the butler - volmer limit , and becomes independent of @xmath45 . over the whole range of @xmath102 and @xmath45 values here studied , the error in the equivalence between a microdisc and a sphere on a surface never exceeds 2.55% in regions of appreciable current . it is thus reasonable to say that the correspondence between the two geometries holds within the marcus - hush model of electron transfer , as well as within the butler - volmer model . we now apply our butler - volmer and marcus - hush models for voltammetry at a microdisc to the reduction of oxygen in two ionic liquids , and compare the effectiveness of the models in simulating experimental data .	the developed butler - volmer and symmetric marcus - hush programs are also used to theoretically study the possibility of kinetically limited steady state currents , and to establish an approximate equivalence relationship between microdisc electrodes and spherical electrodes resting on a surface for steady state voltammetry for both butler - volmer and symmetric marcus - hush theory .	the voltammetry for the reduction of oxygen at a microdisc electrode is reported in two room temperature ionic liquids : 1-butyl-1-methylpyrrolidinium _ bis_(trifluoromethylsulfonyl)imide + ( [ bmpyrr][ntf ) and trihexyltetradecylphosphonium _ bis_(trifluoromethylsulfonyl)imide + ( [ p[ntf ) at 298 k. simulated voltammograms using butler - volmer theory and symmetric marcus - hush ( smh ) theory were compared with experimental data . butler - volmer theory consistently provided experimental parameters with a higher level of certainty than smh theory . a value of solvent reorganisation energy for oxygen reduction in ionic liquids was inferred for the first time as 0.4 - 0.5 ev , which is attributable to inner - sphere reorganisation with a negligible contribution from solvent reorganisation . the developed butler - volmer and symmetric marcus - hush programs are also used to theoretically study the possibility of kinetically limited steady state currents , and to establish an approximate equivalence relationship between microdisc electrodes and spherical electrodes resting on a surface for steady state voltammetry for both butler - volmer and symmetric marcus - hush theory .
1503.01654	r	this section reports the comparative outcome of the use of bv theory and smh theory to model experimental cyclic voltammetry of the reduction of oxygen in the ionic liquids [ bmpyrr][ntf@xmath0 and [ p@xmath1[ntf@xmath0 : @xmath132 this is followed by the inference of physical implications from the application of smh and the determination of a value for solvent reorganisation energy , @xmath8 , for both rtils . the first system under study is the reduction of oxygen in [ bmpyrr][ntf@xmath0 . this ionic liquid was chosen for its relatively low viscosity ( 70 cp at 298 k)@xcite and previously observed well characterised voltammetry for oxygen reduction.@xcite cyclic voltammetry ( cv ) was performed on saturated solutions of oxygen in [ bmpyrr][ntf@xmath0 over a range of scan rates ( 100 - 400 mv s@xmath26 ) . a blank cv , from -3 v - 2 v vs ag , was recorded prior to the introduction of oxygen to ensure the ionic liquid was free from impurities , and to estimate solution capacitance for each scan rate . the capacitative current was subtracted from the experimental current to generate corrected voltammograms prior to further analysis . in all further experimental cases , the potential was swept from 0.00 v ( vs ag ) , a voltage at which _ ca . _ zero faradaic current flows , to a potential cathodic of the reduction of oxygen ( -1.50 v vs ag ) , then back to 0.00 v ( vs ag ) . at a scan rate of 200 mv s@xmath26 , the oxidative peak current at -0.8 v was 1.7 na , the limiting current was -4.4 na , and the half peak potential was -0.9 v vs ag wire . the peak corresponding to the reduction of oxygen appeared on the forward scan at _ ca . _ -1.3 v vs ag , whilst the oxidative peak appeared on the reverse scan at _ ca . _ -0.8 v vs ag . the resultant voltammograms ( fig . [ bmpyrrntf2 ] , a - c ) show more steady - state - like behaviour in the forward wave , which corresponds to the reduction of oxygen to superoxide , than in the back wave , corresponding to the reoxidation of superoxide to oxygen . the disparity in diffusion coefficients of the reactant and product in the ionic solvent results in different types of diffusion being observed at the electrode surface . in the case of oxygen , we see convergent fickian diffusion of oxygen , whereas for the more slowly diffusing superoxide we observe planar fickian diffusion.@xcite cvs were modelled using a previously reported program@xcite that utilises butler - volmer kinetics , as outlined above . as this is a well - reported system,@xcite the starting point for the diffusion coefficient and the concentration of oxygen were taken from literature . optimised values for @xmath3 , @xmath5 , @xmath133 , @xmath134 , @xmath135 , and @xmath136 ( tabulated in table [ bmpyrr parameters ] ) were obtained to give the `` best fit '' , which was quantified with the calculation of a mean scaled absolute deviation ( msad , as described in section [ msad ] ) . these values were used across the scan rates with all values remaining constant , with the exception of @xmath136 , which was allowed to deviate slightly ( @xmath137 v ) to account for the use of a quasi - reference electrode.@xcite the optimised values and the mean msads across the scan rates are reported in table [ bmpyrr parameters ] . the value of @xmath135 , the diffusion coefficient of the superoxide ion , is an order of magnitude smaller than that of the diffusion coefficient for oxygen , @xmath134 . this is due to the charged superoxide ion s increased interaction with the ionic solvent , which reduces its movement through the solution . this behaviour has been reported in other ionic liquids by buzzeo _ et al_,@xcite evans _ et al_,@xcite and huang _ et al_.@xcite the value for the transfer coefficient , @xmath5 , of 0.29 , suggests an early , reactant - like transition state.@xcite another notable outcome is the value for @xmath3 , of @xmath138 cm s@xmath26 , which is comparable to @xmath3 for oxygen reduction in other ionic solvents , as seen in table [ lit values ] , which details transfer coefficients and rate constants for oxygen reduction in a range of ionic liquids . symmetric marcus - hush ( smh ) theory was next used to model the electrode kinetics , and the same procedure as outlined above was followed to establish independent , optimal values for the parameters of concern . in this case , the transfer coefficient , @xmath5 , is no longer a parameter that is taken into consideration . instead , the reorganisation energy , @xmath8 , is used . the standard electrochemical rate constant , @xmath3 , also takes on different values in this model . the best fit values and the mean msad values are outlined in table [ bmpyrr parameters ] . the experimental value for @xmath8 was determined to be 0.4 @xmath139 0.1 ev in this solvent . this was determined by establishing best - fit parameters for the smh model with experimental data . the bv program reproduces experimental data with a greater level of accuracy that the smh program , as evidenced by lower msad values and a better fit , as seen in table [ bmpyrr parameters ] and fig . [ bmpyrrntf2 ] . this suggests bv kinetics parameterise the data better than the smh model . a similar conclusion has been reached with respect to the modelling of redox processes in molecular solvents@xcite . the second system under consideration is the chemically irreversible reduction of oxygen in [ p@xmath1[ntf@xmath0 . this ionic liquid has high hydrophobicity@xcite and previously reported well defined voltammetry.@xcite cyclic voltammetry ( cv ) was performed on saturated solutions of oxygen in [ p@xmath1[ntf@xmath0 over a range of scan rates ( 100 - 400 mv s@xmath26 ) ( see fig . [ p14666ntf2 ] , a - c ) . a blank cv was recorded prior to the introduction of oxygen to ensure the ionic liquid was free from impurities . the baselines of the raw experimental cvs were adjusted to generate corrected voltammograms prior to further analysis . in all cases , the potential was swept from 0.00 v vs ag , to a potential cathodic of the reduction of oxygen ( -2.3 v vs ag ) . at a scan rate of 200 mv s@xmath26 , the limiting current was -6.5 na , and the half peak potential was -1.6 v vs ag . the reduction of oxygen occurred on the forward scan at -2.20 v vs ag , whilst an oxidative feature appeared on the reverse scan at -0.86 v vs ag . unlike the case discussed in section [ o2 in bmpyrr ] , in this situation the highly reactive superoxide that is generated by the initial reduction encounters a proton source in the form of the cation of the solvent . evans _ _ et . al__@xcite detailed the mechanism of this process ( shown in scheme 1 ) and suggested that the observed back peak in the experimental voltammetry could be an oxygen - derived species created in follow - up reactions , most likely ho@xmath140 . given the documented chemical irreversibility of this system , only the forward wave was considered for further analysis . both the butler - volmer and marcus - hush programs were modified to account for a homogeneous chemical step in the mass transport equations , as detailed in the theory section . for the purposes of determining a starting point for @xmath134 and concentration , potential step chronoamperometry was performed on this system by stepping from a potential at which no current flows , 0.0 v , to -2.0 v for 2s ( see fig . [ chrono ] ) . this data was then analysed with respect to the shoup and szabo@xcite equation ( as detailed in the section 2.4 ) , to simultaneously determine the concentration and diffusion coefficient of oxygen ( see table [ p14666 parameters ] ) . optimised values for @xmath3 , @xmath5 , @xmath133 , @xmath134 , and @xmath136 were obtained to give the `` best fit '' using the modified butler - volmer program described above , which was quantified with the calculation of a mean scaled absolute deviation ( msad , as described in the section [ msad ] ) . these values were used across the scan rates with all values remaining constant , with the exception of @xmath136 , which was allowed to deviate slightly ( @xmath139 0.02 v ) to account for the use of a quasi - reference electrode . the optimised values and the mean msads across the scan rates are reported in table [ p14666 parameters ] . the values obtained for @xmath134 and @xmath133 are consistent with previous literature reports and are in agreement with reported diffusion coefficients and saturated concentrations of oxygen in a range of ionic liquids ( table [ lit values ] ) . the value for the transfer coefficient , @xmath5 , of 0.31 , suggests an early , reactant - like transition state . this is congruent with the result found in section [ o2 in bmpyrr ] , and a similar @xmath3 of @xmath141 cm s@xmath26 is reported , which is again in agreement with the literature values reported in table [ lit values ] . smh theory was used independently to generate the same set of parameters as generated in the bv theory with the transfer coefficient , @xmath5 , once again being replaced by a representation for reorganisation energy , @xmath8 . the experimental value for @xmath8 was determined to be 0.5 @xmath139 0.1 ev in this solvent . once again , the bv program provides parameters with a significantly greater level of certainty that the smh program . and , although the smh theory gives greater physical insight compared with the phenomenological bv theory , this greater uncertainty leaves bv as the preferred theory , in terms of attaining more reliable parameterisation . both systems under study , oxygen reduction in either a pyrrolidinium or phosphonium based il , display similarly low diffusion coefficients ( @xmath134 = 2.05 and 3.95 @xmath142 m@xmath127 s@xmath26 respectively ) and solubilities of oxygen ( @xmath133 = 10 and 7.3 mm ) . in addition to this , both the transfer coefficients ( @xmath5 = 0.29 @xmath139 0.01 , and 0.31 @xmath139 0.01 respectively ) and the reorganisation energies ( @xmath8 = 0.4 @xmath139 0.1 , and 0.5 @xmath139 0.1 respectively ) are similar . as outlined in the introduction , @xmath8 encompasses contributions from both inner - sphere reorganisation of the molecule itself , and outer - sphere solvent reorganisation about the electroactive species . the inner - sphere reorganisation is due to the change in bond length on going from o@xmath124 to o@xmath143 ( 0.12 )@xcite , with outer - sphere solvent reorganisation dominating in aqueous systems . literature reports suggest the overall reorganisation energy for the oxygen self - exchange reaction in water is 1.26 - 4.51 ev.@xcite the inner - sphere contribution was estimated to be 0.4 - 0.6 ev.@xcite given the close agreement with previously reported values for inner sphere reorganisation@xcite , the experimental values for @xmath8 in both of the systems considered in this work are consistent with a process dominated by an inner sphere contribution . previous reports have indicated that oxygen itself had weak interactions with an ionic liquid,@xcite and the result reported in the present work suggests that the ionic liquid does not undergo any significant reorganisation on moving from oxygen to superoxide . this may be related to the very small size of the o@xmath124/o@xmath143 species compared to the component ions of the rtil . the reported best fit values for the rate constant given by smh theory are similar to those established by bv theory , however there is less agreement with the experimental data than is seen when the bv program is used . this is reflected both in the larger mean msad values , and qualitatively observing the fit as seen in figs . [ bmpyrrntf2 ] and [ p14666ntf2 ] . further studies may involve consideration of asymmetric mh theory , which relaxes the requirement that the potential energy parabola are of equal curvature , and introduces a new parameter to describe the disparity in curvature between the reactant and product . this has been considered in a number of molecular systems,@xcite and has been determined to fit experimental data more accurately than smh .	butler - volmer theory consistently provided experimental parameters with a higher level of certainty than smh theory . a value of solvent reorganisation energy for oxygen reduction in ionic liquids was inferred for the first time as 0.4 - 0.5 ev , which is attributable to inner - sphere reorganisation with a negligible contribution from solvent reorganisation .	the voltammetry for the reduction of oxygen at a microdisc electrode is reported in two room temperature ionic liquids : 1-butyl-1-methylpyrrolidinium _ bis_(trifluoromethylsulfonyl)imide + ( [ bmpyrr][ntf ) and trihexyltetradecylphosphonium _ bis_(trifluoromethylsulfonyl)imide + ( [ p[ntf ) at 298 k. simulated voltammograms using butler - volmer theory and symmetric marcus - hush ( smh ) theory were compared with experimental data . butler - volmer theory consistently provided experimental parameters with a higher level of certainty than smh theory . a value of solvent reorganisation energy for oxygen reduction in ionic liquids was inferred for the first time as 0.4 - 0.5 ev , which is attributable to inner - sphere reorganisation with a negligible contribution from solvent reorganisation . the developed butler - volmer and symmetric marcus - hush programs are also used to theoretically study the possibility of kinetically limited steady state currents , and to establish an approximate equivalence relationship between microdisc electrodes and spherical electrodes resting on a surface for steady state voltammetry for both butler - volmer and symmetric marcus - hush theory .