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0901.1050

c

the hidden charge model ( shortly : the model ) is introduced by two concepts : @xcite conceptual separation of mass and energy behind @xmath204 , and @xcite a new entity for an initial cosmological liquid . the model remains in four dimensions , has a clearly arranged particle spectrum confined by the tev scale , and is supplied with a rich thermodynamics . this allows a serious prosy representation and a heuristic approach which two are suited to the early stage of the conventional new standard cosmology . the model is much simpler and more robust than highly sophisticated approaches , e.g. string theory . a hadronic inflation emerges because cold baryons can first be realized in the length scale of @xmath292fermi . for @xmath5 , the filter elements for culminating - point baryons with @xmath9 tangent objects are too small for quantum mechanics in a cold reality . dense dark - matter liquids , however could be realized for @xmath5 because their tangent objects are @xmath149 euclidean allowing points smaller than @xmath4 . the sudden occurrence of baryons ( and hadron pairs ) at @xmath293 generates a large ( hadronic ) amount of negative pressure and therefore a violent pulse for inflationary expansion . during its cosmic time scale the first small black holes emerge that allow a cold hawking unification of the four interactions . the new entities in the liquid are called glarum levy defects ( @xmath0 defects ) . it is finally the shaping power of the levy distribution that forms the galaxies of the universe and allows a relation between their number @xmath81 and the tilt ( @xmath22 ) in the density fluctuation . @xmath239 would mean no tilt and no gravitation . the decrease of the filter element size during forming the culminating points corresponds to a map of the universe in the @xmath9 tangent objects near culminating point particles . in this dollhouse universe are , in accordance with mach s principle , the galaxies mapped to small spots that are used to construct gravitons as charges from four hidden @xmath121 segments randomly connected by the spots . this defines gravitation , in the vacuum as a shadow metric over flat @xmath9 tangent objects as basis . the underlying flatness is based on electromagnetism , much stronger than the weakness of the shadow metric from gravitation ( factor 10@xmath126 ) . this allows a purely geometric interpretation of the cosmological parameter @xmath256 ( that was called dark energy before ) as a consequence of this flatness since the primordial stage of the universe , @xmath294 . not all reality objects are quantized so as usually assumed . the electroweak interaction remains quantized in the form that follows from feynman path integrals . dark matter , if not isolated in the vacuum of minkowski space , is not conventionally quantized ( e.g. in dense liquids ) . somewhere between these limiting cases is the quantization of strong interaction for hadrons , in particular for baryons where @xmath149 tangent objects are inside from prebaryons , and also the gravitation . although gravitons are constructed as charges , the possibility of a further general quantization of the einstein riemann metric manifold must seriously be questioned . dark energy as geometrical flatness does not allow any quantization . some conventional priors important for cosmology are substituted by the model as follows : there are no higgs particles because corresponding eigensolutions are missing ; the filter elements are not independent fields and can not be quantized because they do not fluctuate due to their huge numbers . a hot big bang is not necessary , because cold dark matter particles remain points also at large densities in the initial liquid for they can not be quantized in the euclidean @xmath149 tangent objects there . the cosmological parameter @xmath176 needs not to be an dark energy , because it can be reduced to spatial flatness . @xmath7 in the frame of our hidden charge model , a search for higgs particles or independent dark energy is not useful .

the defects are formed by the shaping power of levy distribution ( preponderant component , hierarchy , damping factor ) . a relation between the number of galaxies , the tilt in the density fluctuation , and the temperature amplitude of the cmb this allows a geometric interpretation of the stony dark energy as flatness on the golden side of the einstein equation , .

a new thermodynamics for liquids related to von laue s approach ( 1917 ) substitutes some particle priors of gibb s rational thermodynamics . this allows the definition of a new dynamic entity ( defect ) whose diffusion properties also claim a largest causal region ( speckle ) . in the frame of the hidden charge model it is discussed , whether this new thermodynamics can be applied to an initial liquid for cosmology , where the defects lead to the later galaxies and the speckles to a finite expanding universe of diameter . far below a hadronic compton wave length of order 1 fermi , , there is no room left for too small filter elements , that would , however , be necessary for a filter convergence to an isolated cold quantum mechanical point particle . when the expansion of the universe comes to , i.e. for , then many hadrons are created . the related negative pressure gets large amounts and leads to an intense hadronic cosmological inflation . the defects are formed by the shaping power of levy distribution ( preponderant component , hierarchy , damping factor ) . a relation between the number of galaxies , the tilt in the density fluctuation , and the temperature amplitude of the cmb is obtained . for ( much vacuum ) , the electromagnetic tangent objects are large and flat . this allows a geometric interpretation of the stony dark energy as flatness on the golden side of the einstein equation , . * keywords : * 1 . inflation 2 . power spectrum 3 . dark energy theory 4 . gravity

1107.0468

i

a conventional approach to nonlinear electromagnetic scattering problems is based on the power series expansion in a nonlinear susceptibility @xmath0 . for example , for the 2nd order susceptibility , the physical parameter that determines nonlinear effects is @xmath1 where @xmath2 is the electric field at the scattering structure . the smallness of @xmath3 justifies the use of perturbation theory and the solution is analytic in @xmath0 . the situation is different if the scattering structure has resonances . planar periodic structures ( e.g. , gratings ) are known to exhibit sharp scattering resonances when illuminated by electromagnetic waves ( for a review see , e.g. , @xcite ) . furthermore , it is known ( see , e.g. , @xcite ) that in such structures a local electromagnetic field @xmath2 is amplified if the structure has narrow resonances : @xmath4 , where @xmath5 is the amplitude of the incident wave and @xmath6 is the width of the resonance . consequently , optical nonlinear effects are amplified if the system has a sufficiently narrow resonance . for example , an amplification of the second harmonics generation by a single periodic array of dielectric cylinders @xcite and by other single - array periodic systems @xcite have been reported , but no significant flux conversion rate , comparable to that in conventional methods of second harmonic generation , has been found . owing to the smallness of @xmath0 and a _ finite _ @xmath7 , the condition @xmath8 still holds for the studied structures . if two identical planar periodic structures are aligned parallel and separated by a distance @xmath9 , then it can be shown that for each resonance associated with the single structure , the combined structure has two close resonances whose width depends continuously on @xmath10 so that the width of one of the resonances vanishes , i.e. , @xmath11 as @xmath12 for some discrete set of distances @xmath13 , for sufficiently large @xmath10 @xcite . this means that the system has _ bound states in the radiation continuum_. their existence was first predicted in quantum mechanics by von neumann and wigner @xcite in 1929 and later they were discovered in some atomic systems @xcite ( see also @xcite for more theoretical studies ) . their analog in maxwell s theory has only attracted attention recently @xcite . in particular , for a system of two parallel arrays of periodically positioned subwavelength dielectric cylinders ( depicted in panel ( a ) of fig . [ fig:1 ] ) , the existence of bound states in the radiation continuum has been first established in numerical studies of the system @xcite . a complete classification of bound states as well as their analytic form for this system is given in @xcite for tm polarization . it is also shown @xcite that bound states exist in the spectral range in which more than one diffraction channel are open . from the physical point of view , bound states in the radiation continuum are localized solutions of maxwell s equations like waveguide modes , but in contrast to the latter their spectrum lies in the spectrum of scattering radiation ( diffraction ) modes . the perturbation theory parameter @xmath14 , as defined above , can no longer be considered small if bound states in the radiation continuum are present . this qualitative assessment should be taken with a precaution . in the present study , a rigorous analysis of the nonlinear scattering problem by means of the formalism of siegert states ( appropriately extended to periodic structures @xcite ) shows that no divergence of a local field occurs as @xmath12 . however , the conventional perturbative approach fails because the solution is not analytic in @xmath0 . the situation can be compared with a simple mechanical analog . consider a scattering problem for a particle on a line in a hard core repulsive potential @xmath15 , @xmath16 . no matter how small @xmath17 is , the particle never crosses the origin @xmath18 and a full reflection occurs , but it does so when @xmath19 ( a full transmission ) . so , the scattering amplitude is not analytic in @xmath17 . other , more sophisticated , examples of quantum systems with such properties are studied in @xcite . the purpose of the present study is twofold . first , the nonlinear scattering problem is studied in _ the presence of bound states in the radiation continuum_. a non - perturbative approach is developed to solve the problem . second , as an application of the developed formalism , the problem of the second harmonic generation is analyzed with an example of the system depicted in fig . [ fig:1 ] ( panel ( a ) ) . in section [ sec:1 ] , the nonlinear resonant scattering problem with bound states in the radiation continuum is transformed into a system of integral equations . a non - perturbative method is proposed to solve these equations in the approximation that takes into account two nonlinear effects : a second harmonic generation in the leading order of @xmath0 , and the fundamental harmonic generation by mixing the second and fundamental harmonics in the leading order in @xmath20 . this is the second order effect in @xmath0 known in the theory as the _ optical rectification_. the latter is shown to be necessary to ensure the energy flux conservation . the formalism is illustrated with an example of two parallel periodic arrays of dielectric cylinders shown in panel ( a ) of fig . [ fig:1 ] . the analysis is based on the subwavelength approximation ( section [ sec:2 ] ) when the incident wave length is larger than the radius @xmath21 of the cylinders . if @xmath22 is the magnitude of the wave vector , then the theory has three small parameters : @xmath23 where all the distances are measured in units of the structure period , in particular @xmath24 . @xmath25 is the scattering phase for a single cylinder , @xmath26 is the linear dielectric susceptibility , and the amplitude of the incident wave is set to one , @xmath27 . with this choice of units , all three parameters are dimensionless . the scattering amplitudes of the fundamental and second harmonics are explicitly found in section [ sec:3 ] . in section [ sec:4 ] , it is shown that the ratio of the flux of the second harmonic along the normal direction and the incident flux is @xmath28 where @xmath29 is the fundamental field on the cylinders , and @xmath30 is some function . the function @xmath2 is _ non - analytic _ in the vicinity of zero values of its arguments . the non - perturbative approach of section [ sec:1 ] is used to prove that the generated flux of the second harmonic attains its maximal value when the small parameters satisfy the condition @xmath31 where @xmath32 is a numerical constant , and @xmath33 is the magnitude of the wave vector of the bound state that occurs at @xmath34 . under this condition , @xmath35 becomes analytic in the scattering phase @xmath36 so that in the leading order , @xmath37 an interesting feature to note is the independence of the conversion efficiency on the nonlinear susceptibility @xmath0 ( in the leading order in the scattering phase @xmath36 ) . in other words , given a nonlinear susceptibility @xmath0 , by a fine tuning of the distance between the arrays one can always reach the maximal value which is only determined by the scattering phase at the wave length of a bound state . the lowest value of @xmath33 for the system considered occurs just below the first diffraction threshold ( the wavelength is slightly larger than the structure period ) @xcite , i.e. , @xmath38 . taking , for example , @xmath39 and @xmath40 ( so that @xmath41 ) , the conversion rate reads @xmath42 , that is , about @xmath43 of the incident flux is converted into the second harmonic flux , which is comparable with the conversion rate achieved in slabs ( crystals ) of optical nonlinear materials @xcite . from the physical point of view , the scattering structure plays the role of a resonator with the quality factor inversely proportional to @xmath6 . the field in the resonator is not uniform and has periodic peaks of the amplitude @xmath4 due to a constructive interference of the scattered fundamental harmonic . the second harmonic is produced by the induced dipole radiation of point scatters located at these peaks . the induced dipole strength is proportional to @xmath44 . the dipoles are excited by the incident wave and , due to their periodic arrangement , they radiate in phase producing a plane wave in the asymptotic region ( just like a phased array antenna ) . if the system has a resonance whose width @xmath6 can be continuously driven to zero by changing a physical parameter of the system , i.e. , the system has a bound state in the radiation continuum , then the strength of the induced dipoles radiating the second harmonics can be magnified as desired , but the resonator can not be excited by the incident radiation if @xmath45 ( a bound state is decoupled from the radiation continuum ) . so , the optimal width @xmath6 at which the second harmonic amplitude is maximal occurs for some @xmath46 , which explains the existence of conditions like ( [ condition ] ) . since the second harmonic is generated by point scatterers , the phase matching condition , needed for optically nonlinear crystals , is not required . the energy flux of the incident radiation is automatically redistributed and focused on the scatterers owing to the constructive interference . thanks to these physical features , an active length at which the conversion rate is maximal is close to @xmath47 whose smallest value for the system studied is roughly a half of the wave length of the incident light @xcite ( i.e. for an infrared incident radiation it is about a few hundreds nanometers ) .

a nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum . it is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory fails . a non - perturbative approach is proposed and applied to the system of two parallel periodic arrays of dielectric cylinders with a second order nonlinear susceptibility . this scattering system is known to have bound states in the radiation continuum . in particular , it is demonstrated that , for a wide range of values of the nonlinear susceptibility , the conversion rate of the incident fundamental harmonic into the second one can be as high as 40% when the distance between the arrays is as low as a half of the incident radiation wavelength . the effect is solely attributed to the presence of bound states in the radiation continuum .

a nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum . it is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory fails . a non - perturbative approach is proposed and applied to the system of two parallel periodic arrays of dielectric cylinders with a second order nonlinear susceptibility . this scattering system is known to have bound states in the radiation continuum . in particular , it is demonstrated that , for a wide range of values of the nonlinear susceptibility , the conversion rate of the incident fundamental harmonic into the second one can be as high as 40% when the distance between the arrays is as low as a half of the incident radiation wavelength . the effect is solely attributed to the presence of bound states in the radiation continuum .

1507.00406

i

inspiralling compact binaries containing spinning neutron stars and ( or ) black holes ( bhs ) are key sources for the network of second generation interferometric gravitational wave ( gw ) detectors @xcite . these instruments include the two advanced ligo ( aligo ) observatories @xcite , the advanced virgo @xcite , the kagra @xcite , the geo - hf @xcite and the planned ligo - india @xcite . in contrast , massive spinning bh binaries are one of the most exciting sources for the space - based gw observatory like the planned elisa @xcite . gws from such inspiralling compact binaries , whose components are specified by their masses and spins , can be accurately modeled using perturbative approaches to tackle the underlying einstein field equations @xcite . therefore , the optimal detection technique of _ matched filtering _ can be employed to detect and characterize inspiral gws from such binaries @xcite . this involves cross correlating the interferometric output data with a bank of templates that theoretically model inspiral gws from spinning compact binaries . a successful detection demands that at least one template should remain in phase as much as possible with the buried weak gw signals in the frequency windows of various gw observatories @xcite . during the gw emission induced inspiral , dynamics and associated gws from compact binaries can be accurately described using the post - newtonian ( pn ) approximation to general relativity @xcite . the pn description provides interesting quantities , required for various template constructions , as an asymptotic series in terms of certain dimensionless parameter . for binaries in quasi - circular orbits , it is usual to use @xmath3 as the pn expansion parameter while constructing inspiral templates , where @xmath4 and @xmath5 stand for the total mass and orbital ( angular ) frequency of the binary @xcite . currently , gw frequency and associated phase evolution , crucial inputs to construct various inspiral template families , are known to 3.5pn order for non - spinning compact binaries @xcite . in other words , pn corrections to the above two quantities are computed to the @xmath6 order beyond the leading quadrupolar ( newtonian ) order for such binaries . moreover , the amplitudes of the two gw polarization states , @xmath7 and @xmath8 , for non - spinning binaries are available to 3pn order @xcite . very recently , detailed computations led to the determination of the dynamics of such binaries to the 4pn order @xcite . binaries that contain compact objects with intrinsic rotations , the spin effects enter the dynamics and gw emission via spin - orbit and spin - spin interactions @xcite . in binaries containing maximally spinning bhs , the spin - orbit coupling ( linear in the spins ) first appears at the 1.5pn order , while the spin - spin interaction ( which is quadratic in spins ) first occurs at the 2pn order @xcite . additionally , @xmath9 , @xmath10 and @xmath1 , the two spin and orbital angular momenta , for generic spinning compact binaries precess around the total angular momentum @xmath11 due to spin - orbit and spin - spin interactions . this forces substantial modulations of the emitted gws from inspiralling generic spinning compact binaries compared to their non - spinning counterparts @xcite . therefore , it is important to incorporate various effects due to the intrinsic rotations of compact objects while constructing inspiral gw templates for spinning compact binaries . at present , gw frequency evolution and amplitudes of @xmath7 and @xmath8 for bh binaries having maximally spinning components are fully determined to 2.5pn and 2pn orders , respectively , while incorporating all the relevant spin induced effects @xcite . moreover , the on - going detailed computations are providing various higher pn order spin - orbit and spin - spin contributions to the dynamics of spinning compact binaries in general orbits and to the orbital frequency evolution for quasi - circular inspiral . at present , the spin - orbit contributions to binary dynamics and gw frequency evolution are available up to the next - to - next - to - leading order ( 2pn order ) beyond the leading order @xcite while adapting the mpm ( multipolar post - minkowskian ) approach @xcite . in contrast , the higher order spin - spin contributions to the binary dynamics are usually tackled in the arnowitt - deser - misner canonical formalism @xcite and in the effective field theory formalism @xcite ( note that the spin - orbit effects in the effective field theory formalism are computed , for example , in @xcite ) . these approaches provide various spin(1)-spin(2 ) and spin - squared contributions to the orbital dynamics @xcite . moreover , various source multipole moments needed to obtain the spin contributions to gw luminosity at the 3pn order and gw polarization states to the 2.5pn order were computed in @xcite . the construction of time - domain @xmath7 and @xmath12 associated with inspiralling generic spinning compact binaries requires us to numerically solve a set of pn accurate differential equations for @xmath13 and the orbital phase @xcite , where @xmath0 is the newtonian orbital angular momentum . the numerical integration provides temporal evolutions for the orbital phase , the associated angular frequency and the two angles that specify the orientation of the orbital plane in an inertial frame associated with the direction of @xmath14 at the initial epoch . these variations are incorporated into the pn accurate expressions for @xmath7 and @xmath8 to obtain pn accurate time - domain inspiral waveforms from such binaries @xcite . in this approach , the differential equation for the orbital phase explicitly depends on the precessional motion of the orbital plane @xcite . therefore , it is not possible to express the orbital phase as an integral of the orbital frequency as usually done in the case of non - spinning compact binaries @xcite . a decade ago , buonanno , chen and vallisneri proposed an approach , referred to as the precessing convention , that factorizes the generic spinning binary waveform into a _ carrier signal _ and a _ modulated amplitude _ term @xcite . in this approach , the phase of the carrier signal ( @xmath15 ) essentially coincides with the accumulated orbital phase such that @xmath16 . moreover , the precessional dynamics of the orbital plane only influences the modulated amplitude part of inspiral waveform even for generic compact binaries . therefore , the precessing convention disentangles the precessional effects from its non - precessional counterparts while modeling both the amplitude and the phase evolutions of inspiral gws from such astrophysical systems . this convention was employed to model inspiral gw signals from compact binaries containing misaligned single - spin and to probe its data analysis benefits @xcite . very recently , inspiral - merger - ringdown waveforms for generic spinning bh binaries , invoking the effective - one - body approach @xcite , also adapted the precessing convention to model gws from the inspiral part @xcite . we note that this convention requires a _ precessing source frame _ which is usually based on the newtonian orbital angular momentum @xmath0 . however , @xcite employed both @xmath17 and @xmath0 to model gws during the late part of the binary inspiral just prior to the plunge . in this paper , we develop a prescription to compute pn accurate inspiral waveforms for generic spinning compact binaries while using the pn accurate orbital angular momentum @xmath17 to construct the precessing source frame . this is influenced by the usual practice of employing precessional equation appropriate for @xmath1 to evolve @xmath0 and the associated precessing source frame while constructing inspiral waveforms via the precessing convention of @xcite . we show that the use of such an adiabatic approximation , namely employing an orbital averaged differential equation for @xmath0 , can lead to pn corrections to @xmath18 . these observations motivated us to provide a set of pn accurate equations to obtain temporally evolving quadrupolar order inspiral gw polarization states for generic spinning compact binaries in the @xmath17-based precessing convention . in our approach , the spin precession induced modulations enter the differential equation for the orbital phase only at the 3pn order . moreover , the @xmath17-based convention requires us to include additional 3pn order terms in the differential equation for @xmath19 , compared to the usual @xmath0-based approach . we explore the practical implications of these additional terms with the help of _ match _ computations , detailed in @xcite . the match computations involve two inspiral families where one is constructed via our @xmath1-based precessing convention and therefore incorporate the above mentioned 3pn order terms . the other family is based on the lalsuite spintaylort4 code , developed by the ligo scientific collaboration ( lsc ) @xcite , that implemented the @xmath0-based precessing convention of @xcite . in this code , the precessional dynamics is fully 2pn accurate while the differential equation for @xmath19 incorporates spin - orbit contributions to 3.5pn order . for match computations , we employ pn accurate relation connecting @xmath0 and @xmath1 to construct two waveform families with physically identical initial orbital and spin orientations . we terminate the two inspiral waveform families when their respective @xmath19 parameter reaches @xmath20 which roughly corresponds to orbital separations @xmath21 . these considerations allow us to attribute the reported match estimates to the above mentioned additional 3pn order terms present in our differential equations for the orbital phase and frequency . we find that the match estimates are less than the optimal 0.97 value for a non - negligible fraction of unequal mass spinning compact binaries . it may be recalled that such an optimal match value roughly corresponds to a @xmath22 loss in the ideal event rate . in what follows , we briefly summarize the usual implementation of the @xmath0-based precessing convention and explore the consequence of employing an orbital averaged precessional equation for @xmath0 . in section [ sec_l ] , we detail the construction of quadrupolar order gw polarization states in our @xmath1-based precessing convention . the match estimates involving these two inspiral families with physically equivalent initial configurations and associated discussions are listed in section [ result ] while section [ sec_dis ] provides a brief summary .

a precessing source frame , constructed using the newtonian orbital angular momentum , can be invoked to model inspiral gravitational waves from generic spinning compact binaries . however , this convention usually employs a post - newtonian ( pn ) accurate precessional equation , appropriate for the pn accurate orbital angular momentum , to evolve the-based precessing source frame . the match estimates are found to be smaller than the optimal value , namely , for a non - negligible fraction of unequal mass spinning compact binaries .

a precessing source frame , constructed using the newtonian orbital angular momentum , can be invoked to model inspiral gravitational waves from generic spinning compact binaries . an attractive feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution . however , this convention usually employs a post - newtonian ( pn ) accurate precessional equation , appropriate for the pn accurate orbital angular momentum , to evolve the-based precessing source frame . this influenced us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly employ to describe the binary orbits . our approach introduces certain additional 3pn order terms in the evolution equations for the orbital phase and frequency with respect to the usual-based implementation of the precessing convention . we examine the practical implications of these additional terms by computing the match between inspiral waveforms that employ and-based precessing conventions . the match estimates are found to be smaller than the optimal value , namely , for a non - negligible fraction of unequal mass spinning compact binaries .

1410.0721

i

lateral motion of membrane components is required for proper physiological functioning in cellular biology @xcite and serves as fertile grounds for biophysical studies involving lipid bilayer model systems @xcite . a key aspect of dynamics taking place at the membrane surface is hydrodynamic flow , both within the membrane itself and in the fluids surrounding the membrane . the membrane environment is thus distinct from traditional three dimensional ( 3d ) or two dimensional ( 2d ) hydrodynamic systems , incorporating aspects of both 2d and 3d flow ; the membrane components move in a two dimensional space defined by the membrane surface , but are coupled to fluid motions in a full 3d space . for this reason , it has been suggested that membrane hydrodynamics might best be described as quasi-2d " @xcite . saffman and delbrck @xcite ( sd ) introduced the standard hydrodynamic model for lipid bilayer membranes . in the sd model , the membrane is treated as a flat thin incompressible fluid sheet with surface viscosity @xmath0 , surrounded by an infinite incompressible aqueous bulk of viscosity @xmath1 . this model can be solved in the creeping flow limit to yield analytical predictions for the diffusion coefficient of cylindrical bodies embedded within the membrane via no - slip boundary conditions @xcite , which are in good agreement with experiments recording the diffusion of membrane proteins and lipid domains @xcite . ( however , some experimental studies claim deficiencies in the sd model for membrane protein diffusion @xcite . ) the sd model also correctly predicts the dynamics of lipid domain boundary fluctuations @xcite and the dynamics of phase separation in ternary model membrane systems @xcite . perhaps the most concise way to express the physics contained within the sd model is through the green s function formulation of the hydrodynamic problem . the membrane s velocity response to in - plane forcing is given by @xmath2 here , @xmath3 is the @xmath4 velocity of the membrane at position @xmath5 . ( we assume the membrane plane is coincident with the @xmath4 plane of our coordinate system . ) @xmath6 is an in - plane force / area applied to the membrane and the green s function tensor @xmath7 captures the hydrodynamic response to forcing in the sd model . explicitly @xcite , @xmath8 \right .\delta_{ij } \nonumber \\ & & \left . - \left [ h_0 ( \tilde{r } ) - \frac{2 h_1 ( \tilde{r})}{\tilde{r } } + y_2(\tilde{r } ) + \frac{4}{\pi \tilde{r}^2 } \right ] \frac{\tilde{r}_i \tilde{r}_j}{\tilde{r}^2 } \right \}\end{aligned}\ ] ] where @xmath9 and @xmath10 are bessel functions of the second kind and struve functions , respectively . the dimensionless distance @xmath11 , where @xmath12 is the saffman - delbruck length . @xmath13 defines a crossover between 2d and 3d - like hydrodynamics in the quasi-2d sd model ; for separations well below @xmath13 the green s function is that of a 2d fluid with surface viscosity @xmath0 , whereas at separations larger than @xmath13 the green s function is similar to that of a 3d system of viscosity @xmath1 @xcite . for typical lipid bilayer systems @xmath13 is on the order of a micron @xcite . in principle , eq . [ eq : v - field ] is restricted to fluid regions and would not immediately seem to be of use in solving problems involving particles suspended within the fluid ( e.g. prediction of diffusion coefficients ) . however , within creeping flow , there is no physical or mathematical distinction between a solid particle embedded within the fluid via no - slip boundary conditions and a fluid " region that occupies the same physical space as the embedded particle with the supplemental restriction to undergo only rigid body motions . computational strategies that supplement eq . [ eq : v - field ] ( typically the 3d version of it ) with the constraint of rigid - body motion over particle associated regions within the fluid have the capability to predict particulate dynamics . well known schemes that take advantage of this strategy to calculate diffusion coefficients and related properties associated with particulate flows include the kirkwood approximation @xcite , shell method @xcite and related techniques @xcite . ( see ref . and the references within for a review of these approaches . ) though the majority of work in this direction has been aimed at studying various solid bodies immersed in homogeneous 3d hydrodynamic environments , the quasi-2d membrane case has previously been considered with a method similar to the kirkwood approximation by levine liverpool and mackintosh @xcite . ( it should also be mentioned that the green s function approach naturally leads to diffusion coefficients for circular fluid domains in the membrane geometry @xcite . ) though the kirkwood approximation is simple to implement and often gives rise to qualitatively correct predictions , the method is known to be inexact and , in extreme cases , can yield unphysical results @xcite . in 3d geometries , the shell method @xcite resolves these shortcomings , however this method is not easily applied to the sd problem as it requires use of the rotne - prager tensor @xcite ; a quasi-2d analog to the rotne - prager tensor has not been derived . an appealing alternative to the shell method is the method of regularized stokeslets ( rs ) @xcite . ( section [ sec : rs - method ] provides an introduction of the rs method . ) this technique is known to reproduce the correct velocity fields and particle diffusion coefficients for model problems in 3d @xcite and is immediately extended to the sd hydrodynamic geometry without difficulty . in recent work @xcite , two of us presented this extension and verified that rs calculations quantitatively reproduce the known analytical results for single - particle mobility problems ( i.e. prediction of diffusion coefficients ) in the quasi-2d environment . while single - particle mobility / diffusion problems present a convenient test of computational methodologies , the methods discussed above ( rs included ) are applicable to a broader class of problems involving the motions of multiple embedded bodies and the hydrodynamic interactions between them . the study of many body dynamics in fluid environments has received considerable theoretical / numerical attention @xcite , but primarily in the context of 3d systems . the few prior studies in the membrane geometry are restricted to limiting regimes and circular particles @xcite , due to the focus of these works on analytical calculations . the complicated form of eq . [ eq : mem_green ] hinders analytical progress without invoking some manner of approximation . a versatile numerical tool to quantitatively study the dynamics of multiple membrane - embedded bodies has yet to be developed , despite the growing experimental interest in the dynamics of solid body suspensions in membrane systems and related quasi-2d environments @xcite . in this work , we extend the membrane rs method to consider many - body systems . a general framework is presented , which is applied in detail to the the study of two circular disks within the membrane . we also briefly revisit our earlier calculations @xcite involving the diffusion of diamond shaped lipid domains and tethered protein assemblies , as motivated by recent experiments @xcite . this work is structured as follows : in sec . [ sec : dif - tensor ] we discuss and present the diffusion matrix for a many - body system . in sec . [ sec : rs - method ] we generalize the quasi-2d rs method to calculations involving multiple bodies embedded in the membrane . this allows for the calculation of the full many - body diffusion matrix . though both sections [ sec : dif - tensor ] and [ sec : rs - method ] focus primarily on the two - body case for concreteness , the many - body generalization is straightforward and is discussed as well . in sec . [ sec : res ] we present detailed results for the case of two identical disks embedded within the membrane . in sections [ sec : dimers ] and [ sec : diamonds ] we consider the case of tethered two - disk dimers and correlations between diamond shaped domains , respectively . finally , sec . [ sec : summary ] discusses our results and concludes .

the method is used to validate recent analytical predictions by oppenheimer and diamant [ biophys . j. , 96 , 3041 , 2009 ] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near - field lubrication results as objects closely approach one another , however the present methodology also applies outside of the limiting regimes where analytical results are available .

a recently introduced numerical scheme for calculating self - diffusion coefficients of solid objects embedded in lipid bilayer membranes is extended to enable calculation of hydrodynamic interactions between multiple objects . the method is used to validate recent analytical predictions by oppenheimer and diamant [ biophys . j. , 96 , 3041 , 2009 ] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near - field lubrication results as objects closely approach one another , however the present methodology also applies outside of the limiting regimes where analytical results are available . multiple different examples involving pairs of disk - like objects with various constraints imposed on their relative motions demonstrate the importance of hydrodynamic interactions in the dynamics of proteins and lipid domains on membrane surfaces . it is demonstrated that the relative change in self - diffusion of a membrane embedded object upon perturbation by a similar proximal solid object displays a maximum for object sizes comparable to the saffman - delbrck length of the membrane .

1602.07072

i

a timelike metric space is a hausdorff topological space @xmath1 equipped with a partial order relation @xmath2 and a distance function @xmath3 which plays the role of a metric . this metric is asymmetric in the sense that the distance from @xmath4 to @xmath5 is not necessarily equal to the the distance from @xmath5 to @xmath4 . more drastically , the distance from @xmath4 to @xmath5 may be defined whereas the distance from @xmath5 to @xmath4 is not defined . more precisely , the distance @xmath6 is defined only for pairs @xmath7 satisfying @xmath8 ( that is , either @xmath9 ot @xmath10 ) . this distance function satisfies @xmath11 for every @xmath4 in @xmath1 , @xmath12 for every @xmath4 and @xmath5 such that @xmath10 , and the _ time inequality _ , namely , the reversed triangle inequality @xmath13 for all triples of points @xmath14 satisfying @xmath15 . the distance function @xmath3 and the order relation @xmath2 satisfy a set of axioms including compatibility conditions with respect to each other . for instance , it is required that every neighborhood of a point @xmath16 in @xmath1 contains points @xmath4 and @xmath5 satisfying @xmath17 . this axiom and others are stated precisely in the memoir @xcite by herbert busemann . the theories of timelike metric spaces , timelike @xmath18-spaces , locally timelike metric spaces and locally timelike @xmath18-spaces initiated by busemann generalize the geometric theories of metric spaces and of @xmath18-spaces that he developed in his book @xcite and in other papers and monographs . the motivation for the study of timelike metrics comes from the geometry underlying the theory of relativity . the classical example is the @xmath0-dimensional lorentzian space . as other interesting examples of timelike metric spaces , busemann introduced timelike analogues of the funk and hilbert geometries . in the present paper , we investigate these geometries . we establish several results concerning their geodesics , their convexity properties and their infinitesimal structure . we show in particular that they are finsler metrics in an appropriate sense ( we call them timelike finsler metrics ) . we also give a description of the de sitter space as a special case of a more general timelike hilbert geometry in a spherical geometry setting .

a timelike metric space is a hausdorff topological space equipped with a partial order relation and a distance function satisfying a set of axioms including certain compatibility conditions between these two objects . herbert busemann developed an axiomatic theory of timelike metric spaces and of locally timelike metric spaces . his motivation comes from the geometry underlying the theory of relativity and the classical example he gives is the-dimensional lorentzian spaces . two other interesting classes of examples of timelike metric spaces introduced by busemann are the timelike analogues of the funk and hilbert geometries . in this paper , we investigate these geometries . in particular , the de sitter metric is described as a special case of a timelike spherical hilbert metric . _ keywords. _ _ ams classification. _ 53c70 , 53c22 , 5cc10 , 53c23 , 53c50 , 53c45 .

a timelike metric space is a hausdorff topological space equipped with a partial order relation and a distance function satisfying a set of axioms including certain compatibility conditions between these two objects . the distance function is defined only on a certain subset ( whose definition uses the partial order ) of the product of the space with itself containing the diagonal . distances between triples of points , whenever they are defined , satisfy the so - called _ time inequality _ , which is a reversed triangle inequality . in the 1960s , herbert busemann developed an axiomatic theory of timelike metric spaces and of locally timelike metric spaces . his motivation comes from the geometry underlying the theory of relativity and the classical example he gives is the-dimensional lorentzian spaces . two other interesting classes of examples of timelike metric spaces introduced by busemann are the timelike analogues of the funk and hilbert geometries . in this paper , we investigate these geometries . we shall find new interactions among the euclidean , affine , projective and spherical timelike geometries . in particular , the de sitter metric is described as a special case of a timelike spherical hilbert metric . _ keywords. _ timelike space , timelike hilbert geometry , timelike funk geometry , time inequality , convexity , metric geometry , busemann geometry , lorentzian geometry , relativity . _ ams classification. _ 53c70 , 53c22 , 5cc10 , 53c23 , 53c50 , 53c45 .

0706.0395

i

photonic crystals ( phc ) embedded in planar waveguides , also called phc slabs , are at the heart of current research on photonic crystals@xcite because of the possibility of confining light in all spatial directions combined with the advantage of a lithographic definition of the pattern . the propagation of light in these systems can be controlled by a two - dimensional ( 2d ) photonic lattice in the waveguide plane , and by total internal reflection in the perpendicular direction . waveguides with strong refractive index contrast ( like the suspended membrane , or air bridge ) support truly guided modes lying below the light line dispersion in the cladding materials.@xcite however , most of the photonic modes ( or all of them , in the case of waveguides with weak refractive index contrast ) lie above the light line and are only quasi - guided , as they are subject to intrinsic losses due to out - of - plane diffraction.@xcite the physical properties of phc slabs can be significantly different from those of the corresponding 2d system , for several reasons . first , the 2d photonic modes are subject to confinement in the vertical waveguide and the resulting blue shift is strongly polarization - dependent . second , the presence of second- and higher - order waveguide modes can produce a complicated pattern of photonic bands , especially for higher - lying states . third , diffraction losses of quasi - guided modes are an inherent feature of phc slabs which is absent in the ideal 2d case . for all of these reasons , some basic and well - known properties of 2d photonic crystals can not be easily translated to phc slabs . for example , it is well known that the triangular lattice of circular air holes in 2d supports a complete photonic band gap for all propagation directions and light polarizations at sufficiently large air fractions.@xcite nevertheless , the same lattice realized in a high - index membrane does not possess a complete band gap , as the odd modes with respect to a horizontal mirror plane ( often called quasi - tm modes ) are subject to a strong and non - uniform blue shift which eliminates the gap.@xcite indeed , most applications of phc slabs employ the even modes ( often called quasi - te ) , which do possess a band gap for all propagation directions . it was recently suggested@xcite that the triangular lattice of triangular air holes in a high - index membrane gives rise to a complete photonic gap for both even and odd modes . the physical mechanism is the reduction of symmetry of the basis in the unit cell , as compared to the hexagonal symmetry of the 2d lattice , giving rise to a splitting between the first and the second odd bands at the k point of the brillouin zone : when realized in a high - index membrane , this gap overlaps the usual gap between the first and the second even bands , giving rise to a complete gap for all directions and polarizations . the experimental results reported in ref . support the existence of a complete photonic gap . a main purpose of this paper is to perform a systematic study of the triangular lattice of triangular holes , as compared to the triangular lattice of circular holes , both being realized in a high - index dielectric membrane . we calculate the photonic band dispersion , gap maps , and intrinsic losses of quasi - guided modes for the 2d lattice . we also treat line - defect waveguides obtained by removing a full row of holes , and point cavities consisting of three missing holes . in addition to a determination of photonic gaps for even and odd modes as a function of membrane thickness and air fraction , we compare diffraction losses for the lattices with conventional ( circular ) and reduced symmetry ( triangular ) holes : this comparison is important in order to assess the possible usefulness of the reduced - symmetry lattice . among the results , we find interesting prospects of the triangular lattice of triangular holes for nonlinear optics , as it may allow to achieve doubly - resonant second - harmonic generation ( shg ) with an even ( quasi - te ) fundamental wave and an odd ( quasi - tm ) harmonic wave when line - defect waveguides or photonic cavities are introduced . the calculations reported in this paper are performed with an approach which we name guided - mode expansion ( gme ) method . maxwell equations are treated by expanding the magnetic field into the basis of guided modes of an effective homogeneous waveguide , and by solving the resulting eigenvalue equation numerically . intrinsic losses of quasi - guided modes are obtained by calculating the coupling to leaky modes of the effective waveguide within perturbation theory ( i.e. , the photonic analog of fermi golden rule for quantum - mechanical problems ) . the gme method , although being an approximate one ( since the basis of guided modes is not a complete basis set ) , has been applied to a variety of photonic lattices and has proven to be useful especially for obtaining quasi - guided modes and their diffraction losses.@xcite it has also been successfully employed for the interpretation of optical experiments on phc slabs.@xcite another purpose of this paper is to provide a detailed description of the gme method , together with convergence tests and exemplifying applications . the rest of this work is organized as follows . in section ii we outline the gme method and discuss a few convergence tests . section iii contains the results for the 2d triangular lattice of triangular holes in a high - index membrane , namely photonic dispersion , gap maps and intrinsic losses . in sec . iv we present a few results for line - defect waveguides and point cavities in the triangular lattice of triangular holes . section v contains a discussion of the results and of prospective applications of the investigated lattice . technical details , which are needed by the reader in order to implement the gme method , are given in the appendices .

et al . _ , lett . * 87 * , 061107 ( 2005 ) ] , the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two - dimensional photonic crystal slabs . in this work we present a systematic theoretical study of this photonic lattice in a high - index membrane , and a comparison with the conventional triangular lattice of circular holes , by means of the guided - mode expansion method whose detailed formulation is described here . photonic mode dispersion below and above the light line , gap maps , and intrinsic diffraction losses of quasi - guided modes are calculated for the periodic lattice as well as for line- and point - defects defined therein . the main results are summarized as follows : ( i ) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode , but the useful region is generally limited by the presence of second - order waveguide modes ; ( ii ) the lattice may support the usual photonic band gap for even modes ( quasi - te polarization ) and several band gaps for odd modes ( quasi - tm polarization ) , which could be tuned in order to achieve doubly - resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second - harmonic frequency ; ( iii ) diffraction losses of quasi - guided modes in the triangular lattices with circular and triangular holes , and in line - defect waveguides or point - defect cavities based on these geometries , are comparable . the results point to the interest of the triangular lattice of triangular holes for nonlinear optics , and show the usefulness of the guided - mode expansion method for calculating photonic band dispersion and diffraction losses , especially for higher - lying photonic modes .

according to a recent proposal [ s. takayama _ et al . _ , appl . phys . lett . * 87 * , 061107 ( 2005 ) ] , the triangular lattice of triangular air holes may allow to achieve a complete photonic band gap in two - dimensional photonic crystal slabs . in this work we present a systematic theoretical study of this photonic lattice in a high - index membrane , and a comparison with the conventional triangular lattice of circular holes , by means of the guided - mode expansion method whose detailed formulation is described here . photonic mode dispersion below and above the light line , gap maps , and intrinsic diffraction losses of quasi - guided modes are calculated for the periodic lattice as well as for line- and point - defects defined therein . the main results are summarized as follows : ( i ) the triangular lattice of triangular holes does indeed have a complete photonic band gap for the fundamental guided mode , but the useful region is generally limited by the presence of second - order waveguide modes ; ( ii ) the lattice may support the usual photonic band gap for even modes ( quasi - te polarization ) and several band gaps for odd modes ( quasi - tm polarization ) , which could be tuned in order to achieve doubly - resonant frequency conversion between an even mode at the fundamental frequency and an odd mode at the second - harmonic frequency ; ( iii ) diffraction losses of quasi - guided modes in the triangular lattices with circular and triangular holes , and in line - defect waveguides or point - defect cavities based on these geometries , are comparable . the results point to the interest of the triangular lattice of triangular holes for nonlinear optics , and show the usefulness of the guided - mode expansion method for calculating photonic band dispersion and diffraction losses , especially for higher - lying photonic modes .

1409.8401

i

superstring theory in a flat ten dimensional space time can provide a framework to describe the elementary particles and their interactions including gravity beyond the standard model . the heterotic string theory , with its elegant inclusion of gauge symmetry , can naturally accommodate models with grand unification of the gauge interactions ( see for example @xcite ) , while the structure of yukawa couplings in the standard model can find a natural setting in type iia / iib superstring theory with d - branes ( see for example @xcite ) . both scenarios , however , rest on a six dimensional compact internal space whose volume and shape should be fixed or stabilized ( moduli stabilization ) . aside from the wide arbitrariness in the choice of vacuum , this remains a difficult problem in string theory . in this paper we focus on the moduli stabilization problem in type iib theory , which has been extensively studied only in the low energy effective field theory , the type iib supergravity , introducing three form fluxes from massless modes of the corresponding closed string ( `` flux compactifications '' ) @xcite , while it is generally not accessible with string methods . therefore , it appears important to explore insofar as possible the actual predictions of string theory while keeping within the reach of conventional world sheet theory . a scenario without three form fluxes was already proposed in type i theory @xcite . it rests on the magnetic flux of the d9-brane gauge field in orientifold models @xcite , and the basic idea of this scenario is simple . once the distribution of magnetic fluxes on d9-branes is fixed by supersymmetry conditions , or minimum energy conditions , volume and shape of the compact space can be fixed as a result of quantization conditions of magnetic fluxes . since magnetic fluxes on d - branes can be analyzed within conventional world sheet theory , this type of scenario grants calculability . although it seems difficult to stabilize all moduli by this simple mechanism , it is therefore worth exploring this idea further . we investigate the volume stabilization of orbifold compact spaces with magnetic fluxes on d - branes in more general situations without supersymmetry . the d - branes are not necessarily space time filling , while supersymmetry may be broken , for instance , by `` brane supersymmetry breaking '' @xcite while retaining , for the bulk , supersymmetric compactifications . in addition to the above idea related to magnetic fluxes , we examine volume stabilization ( khler moduli stabilization ) resulting from the balance of attractive and repulsive forces between d - branes in the compact space . we propose a mechanism that can in principle stabilize the volumes of some orbifold spaces with fixed shapes , and thus lacking complex structure moduli , as for example @xmath0 , @xmath1 , @xmath2 ( see fig.[fig : balance ] for a schematic picture ) . orbifold and the three fixed points ( left ) . balance of the forces between three objects located at three different fixed points ( right ) . as a result , the area of the fundamental region is fixed , or stabilized . , width=529 ] in these contexts , mutual attractive forces could result from the simultaneous presence of d - branes and anti - d - branes , while in principle the non - bps - branes of @xcite and the fractional non - bps states of @xcite could provide additional repulsive contributions . a concrete model whose compact space is stabilized by this scenario , even if incomplete , could allow a related discussion of early cosmology , and thus of cosmic inflation , within string theory . in particular , the fields describing brane displacements away from their balanced locations could play the role of inflatons , while the vacuum energy of balanced configurations could be the origin of dark energy . models of this type also possess the attractive feature of linking spontaneous gauge symmetry breaking in string theory to geometrical d - brane displacements , along the lines of @xcite . one might also conceive of turning the constraint that the compact internal space be stabilized , which is unavoidable in a strict sense , into a constructive principle to build realistic models of elementary particles and their interactions . in this paper we concentrate on a compact six dimensional orbifold of @xmath2 , which possesses three volume moduli ( untwisted khler moduli , corresponding to the areas of the three two tori of @xmath3 ) , 81 blow up moduli ( 3 twisted khler moduli for each of the 27 fixed points ) and no complex structure moduli . we investigate the behavior of d@xmath4- , d@xmath5- and d@xmath6-branes in this compact space , where the index identifies the d5-branes whose world volumes _ include _ @xmath7-th torus , and the d7-branes whose world volume _ do not include _ it . since the numbers of dirichlet neumann directions of the open string stretched between d@xmath8- and d@xmath9-branes are not multiples of 4 , the system breaks supersymmetry and has a tachyonic ground state . however , as we shall see the inclusion of appropriate magnetic fluxes on d@xmath6-branes can make the system supersymmetric ( namely the lowest energy state ) while removing the tachyon instability ( see also the related work of @xcite ) . moreover , this configuration fixes the total volume of the first and second tori in the @xmath2 orbifold , the inclusion of a d3-brane pose an additional constraint on the magnetic flux on the d@xmath6-brane , so that finally the radii of the first and second tori are both fixed . the d3-brane should be located far enough from the d@xmath5-brane , in order to exclude tachyonic ground states for d@xmath4-d@xmath5 open strings . the magnetized d@xmath5-d@xmath6 system can be placed at a @xmath2 orbifold fixed point , while satisfying twisted ramond ramond tadpole cancelation conditions for the consistency at the quantum level . the simplest system of this type with overall ramond ramond tadpole cancelation involves a magnetized d@xmath5-d@xmath6 and its anti system placed at two different orbifold singularities . if these are separated in the third torus , its radius is driven to shrink by mutual attractive forces , so that other objects are needed to stabilize the internal volume . in this paper we propose a non trivial treatment of the tadpole problem , ubiquitous for d - branes in compact spaces , which can lead to this physically reasonable result . the paper is organized as follows . in section [ one - loop ] we provide a brief review of one loop vacuum amplitudes for open strings ending on magnetized d - branes . a number of basic facts that are scattered in many articles are collected for later convenience . in section [ stabilization-1 ] the system of magnetized d@xmath5- and d@xmath6-branes is investigated in detail . the vacuum energy determined by tree level closed string exchange is calculated both in the low energy effective theory and in the string world sheet theory . we shall see in detail that the vacuum energy vanishes for a certain configuration of magnetic fluxes , when the system possesses supersymmetry . the resulting configuration of magnetic fluxes stabilizes the overall volume of the first and second tori , while the inclusion of a d3-brane completes the stabilization of their radii . in section [ singularity ] we put the system of magnetized d@xmath5- and d@xmath6-branes at a singularity of the @xmath2 orbifold . the twisted ramond ramond tadpole cancelation is non trivial due to the magnetic fluxes , and supersymmetry is broken . in section [ stabilization-2 ] we discuss the force , or potential energy , between the d@xmath5-d@xmath6 system and its anti system lying at a different singularity separated in third torus , and we also propose a non trivial treatment on the sum of the open string winding modes in the third torus . in section [ conclusion ] we provide a summary of this work and briefly address some future problems . many techniques in this paper are familiar to string theorists , but we take the freedom to show them in detail for the benefit of others who might develop further these ideas in more realistic settings for the purpose of model building .

all the models of elementary particles and their interactions derived from string theory involve a compact six dimensional internal space . its volume and shape should be fixed or stabilized , since otherwise massless scalar fields ( moduli ) reflecting their deformations appear in our four dimensional space time , with sizable effects on known particles and fields . our main motivation and goal is to proceed insofar as possible within conventional string world sheet theory . as we shall see , d - branes with magnetic flux ( `` magnetized d - branes '' ) and the forces between them can be used to this end .

all the models of elementary particles and their interactions derived from string theory involve a compact six dimensional internal space . its volume and shape should be fixed or stabilized , since otherwise massless scalar fields ( moduli ) reflecting their deformations appear in our four dimensional space time , with sizable effects on known particles and fields . we propose a strategy towards stabilizing the compact space without fluxes of three form fields from closed strings . our main motivation and goal is to proceed insofar as possible within conventional string world sheet theory . as we shall see , d - branes with magnetic flux ( `` magnetized d - branes '' ) and the forces between them can be used to this end . we investigate here some necessary ingredients : open string one loop vacuum amplitudes between magnetized d - branes , magnetized d - branes fixed at orbifold singularities , and potential energies among such d - branes in the compact space that result from tree level closed string exchanges . * * 1.2 towards the stabilization of extra dimensions by brane dynamics noriaki kitazawa department of physics , tokyo metropolitan university , + hachioji , tokyo 192 - 0397 , japan + e - mail : [email protected]

astro-ph9808359

c

0.2 in we ran 53 different simulations , varying all possible galaxy parameters and allowed up to 75% of the galaxy s gas to undergo starburst . while we could significantly change the galaxies total color , creating very blue lsb galaxies , it was virtually impossible ( without placing a high threshold criteria for the gas ) to significantly alter the galaxy s central surface brightness . instead the primary effect of large amounts of induced star formation was to produce a centralized core ( bulge ) component . while some lsbs have this component ( e.g. malin 1 ) , most are devoid of any central luminosity excess above the fitted exponential which strongly suggests that such centralized bursts did nt happen in these systems . we also suggest that lsb galaxies evolve through sporadic bursts of star formation and that the colors and noisy morphologies displayed by many detected lsb galaxies can be explained by recent starbursts triggered through distant / weak tidal interaction . since the observed current sfrs are an order of magnitude too low to produce the observed luminosity in lsb disks , it seems clear that some sort of episodic star formation has occurred . our modeling procedure has assumed that @xmath22 in lsb galaxies . de blok & mcgaugh ( 1997 ) have already shown , through analysis of rotation curves , that the low surface light density of these systems does translate into low surface mass density . we believe this to be the basic physical difference between hsb and lsb disks that should directly translate into different star formation histories . of course , one should question this assumption as it potentially leads to the following dilemma : if ( @xmath72 in a continuous manner then how come do the very low @xmath3(0 ) systems have any stars in them at all , provided a molecular cloud medium is a prerequisite for large scale star formation to occur in _ any _ disk galaxy . ? on the other hand if @xmath23 is the similar between high and low surface brightness disks , one is very hard pressed to understand why star formation appears to be so different in the lsbs and/or the lack of dust / heavy elements in lsbs relative to hsbs of the same @xmath6 . we suspect that the actual truth lies somewhere between these two extremes but that truth will be elusive . while this is the subject of a larger investigation ( oneil , bothun & carollo 1998 ) the executive summary is that , in a lsb disk , to obtain the equivalent gas mass which is , say , contained in a gmc in our galaxy , requires a significantly larger length scale . when the disk of our model lsb galaxy is broken up into cells , the net result of this large length scale requirement is that the probability of massive star formation per cell is low . this predicted dearth of massive star formation , of course , is consistent with the low metallicity and dust content observed in lsb disks and would result in a very slowly evolving population but leaves open the question of how such low surface density disks could have formed in the first place . to overcome this dearth of massive star formation we have run a set of models that fixes a threshold column density of h i that remains so even as @xmath44(0 ) decreases . in this case , there is significantly more gas available for star formation and some of the limitations of the previous models are overcome . however , in most cases the threshold models cause an inner r@xmath50 component to develop . thus the lsb disk gains a `` bulge '' in response to the starburst and this is generally not observed . to effect a large increase in @xmath3(0 ) with a localized disk starburst event generally requires an inordinate amount of gas to be converted into stars . moreover , its unclear that the threshold model is able to preserve the observed and important non - correlation between @xmath3(0 ) and disk color or account for the offset in mean log o / h at a given @xmath6 with respect to hsb galaxies . most worrisome about the threshold model is its implication that lsb disks of arbitrarily low @xmath3(0 ) are sitting around with ample amounts of gas . to date , systems like this have not been discovered in blind h i surveys . hence we believe that the slow evolutionary rate of lsb disks is likely controlled by low gas density that accompanies low @xmath3(0 ) which precludes the formation of very many massive stars per star formation event . our primary result from the modeling procedure is that once @xmath3(0 ) is established for lsb systems , it is extremely difficult to alter it . that is , disk systems are quite unlikely to hop back and forth between states of high and low surface brightness due to episodic star formation . we thus conclude that if a galaxy forms as a lsb galaxy , due to low gas density , environmental conditions , etc , it will remain a lsb galaxy barring any major encounter catastrophe . this implies that the large space density of lsb galaxies at z = 0 should hold to substantially higher redshifts . this may have relevance to understanding the nature of qso absorption line systems at these redshifts ( see linder 1998 ) . this also suggests that deep ccd surveys should reveal this population , if those surveys are relatively free of selection effects . this selection effects , of course , will be more severe than those associated with finding z=0 lsb systems due to the significant ( 1+z)@xmath73 dilution factor . alvensleben , f - v . 1998 , preprint + bahcall , j. , hut , p. , & tremaine , s. 1985 , apj , 290 , 15 + becker , s. 1981 , apjs , 45 , 475 + becker , s. & iben , i. 1979 , apj , 232 , 831 + bothun , g.d . & mcgaugh , s 1998 in preparation + bothun , g.d . , impey , c. , & mcgaugh , s. 1997 pasp 109 , 745 + bothun , gregory d. , schombert , james m. , impey , christopher d. , sprayberry , david , & mcgaugh , stacy s. 1993 aj 106 , 530 + bothun , g.d . , et al 1990 apj , 360 , 427 + bothun , gregory d. , mould , jeremy r. , caldwell , nelson , & macgillivray , harvey t. 1986 aj 92 , 1007 + bothun , g.d . , & schommer , r.a . 1982 aj 87 , 1368 + briggs , f.h . 1990 aj , 100 , 999 + bushouse , h. 1986 , aj , 91 , 255 + caldwell , n. , & bothun , g.d . 1987 aj 94 , 1126 + davies , r. l. , bertschinger , e. , & baggley , g. 1993 mnras 262 , 475 + dalcanton , julianne j. , spergel , david n. , gunn , james e. , schmidt , maarten , & schneider , donald p. 1997 aj 114 , 63 + de blok , w. 1997 , ph.d . thesis university of groningen , groningen , netherlands + de blok , w. , & mcgaugh , s. 1997 , mnras 290 , 533 + de blok , w. , bothun , g. , & van der hulst , j. 1995 , mnras , 274 , 23 + de jong , r.s . 1996 a&a , 313 , 377 + downes , & solomon , 1998 apj , in press + garnett , d. r. , et al 1997 apj , 489 , 63 + guiderdoni , b. & rocca - 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dotted line before and dotted line after ) . figure [ fig : finalgas](b ) shows models a3 ( solid line before and dashed line after ) and l3 ( dash - dotted line before and dotted line after ) . finally , figure [ fig : finalgas](c ) shows models i3 ( solid line before and dashed line after ) and l4 ( dash - dotted line before and dotted line after ) . figure [ fig : concent ] . the starburst distribution for four of the models c2 , c5 , f1 , and f2 . the shading is proportional to the total mass involved in the starburst . thus the darkest regions on the plot typically lie at the core of the starburst while the white regions were unaffected by the starburst ( no gas was converted to stars ) . models c2 and c5 show the effects of moving the burst radius from 0.10r@xmath64 to 0.80r@xmath64 , while models f1 and f2 show the effects of altering the concentration parameter c from 1.0 to 5.0 . figure [ fig : stars ] . the distribution of stellar masses for four different models - model e2 ( solid line ) , model e1 ( dashed line ) , model e3 ( dash - dotted line ) , and model j5 ( dotted line ) . model e2 ( solid line ) is representative of the majority of the models . figure [ fig : fig1 ] . the color and surface brightness plots for each of the models . the top plot is the change in total u@xmath10b color , with time , for each of the models . the bottom two plots show the surface brightness profile and u@xmath10b color profile of each model 2 myr after the burst . figure [ fig : gal ] . examples of surface brightness and color profiles of two lsb galaxies p2 - 4 ( @xmath18(0)= 25.14 mag arcsec@xmath5 , figure [ fig : gal](a ) & ( b ) ) , and p3 - 3 ( @xmath18(0)= 23.22 mag arcsec@xmath5 , figure [ fig : gal](c ) & ( d ) ) ( from oneil , et al , 1997a , 1997b ) . table [ tab : paramch ] . results for the one cell models discussed in section 3.1 ( table [ tab : model ] ) . the numbers given are the change in total color and magnitude between t=0 ( before the starburst ) and t=2 myr .

although numerous simulations have been done to understand the effects of intense bursts of star formation on high surface brightness galaxies , few attempts have been made to understand how localized starbursts would affect both the color and surface brightness of low surface brightness ( lsb ) galaxies . to remedy this , we have run 53 simulations involving bursts of star formation activity on lsb galaxies , varying both the underlying galaxy properties and the parameters describing the starbursts . we discovered that although changing the total color of a galaxy was fairly straightforward , it was virtually impossible to alter a galaxy s central surface brightness and thereby remove it from the lsb galaxy classification without placing a high ( and fairly artificial ) threshold for the underlying gas density . the primary effect of large amounts of induced star formation was to produce a centralized core ( bulge ) component which is generally not observed in lsb galaxies . the stability of disk central surface brightness to these periods of star formation argues that the large space density of lsb galaxies at z = 0 should hold to substantially higher redshifts .

although numerous simulations have been done to understand the effects of intense bursts of star formation on high surface brightness galaxies , few attempts have been made to understand how localized starbursts would affect both the color and surface brightness of low surface brightness ( lsb ) galaxies . to remedy this , we have run 53 simulations involving bursts of star formation activity on lsb galaxies , varying both the underlying galaxy properties and the parameters describing the starbursts . we discovered that although changing the total color of a galaxy was fairly straightforward , it was virtually impossible to alter a galaxy s central surface brightness and thereby remove it from the lsb galaxy classification without placing a high ( and fairly artificial ) threshold for the underlying gas density . the primary effect of large amounts of induced star formation was to produce a centralized core ( bulge ) component which is generally not observed in lsb galaxies . the noisy morphological appearance of lsb galaxies as well as their noisy surface brightness profiles can be reproduced by considering small bursts of star formation that are localized within the disk . the trigger mechanism for such bursts is likely distant / weak tidal encounters . the stability of disk central surface brightness to these periods of star formation argues that the large space density of lsb galaxies at z = 0 should hold to substantially higher redshifts . = -0.25 in = -0.25 in = -0.25 in = 6.5 in = 8.5 in 0.2 in

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when the particle systems have the characteristic momenta which are of the same order or even much larger than the masses of the particles involved , it is part of nature that a relativistic treatment is called for in order to describe those systems properly . in particular , relativistic effects are most essential to describe the low - lying hadron systems in terms of strongly interacting quarks / antiquarks and gluons in quantum chromodynamics ( qcd ) . for the study of relativistic particle systems , dirac proposed the three different forms of the relativistic hamiltonian dynamics in 1949 @xcite : i.e. the instant ( @xmath2 ) , front ( @xmath3 ) , and point ( @xmath4 ) forms . while the instant form dynamics ( ifd ) of quantum field theories is based on the usual equal time @xmath5 quantization ( @xmath6 unit is taken here ) , the equal light - front time @xmath7 quantization yields the front form dynamics , more commonly called light - front dynamics ( lfd ) , correspondingly . although the point form dynamics has also been explored @xcite , the most popular choices were thus far the equal-@xmath0 ( instant form ) and equal-@xmath8 ( front form ) quantizations . a crucial difference between the instant form and the front form may be attributed to their energy - momentum dispersion relations . when a particle has the mass @xmath9 and the four - momentum @xmath10 , the relativistic energy - momentum dispersion relation of the particle at equal-@xmath0 is given by @xmath11 where the energy @xmath12 is conjugate to @xmath0 and the three - momentum vector @xmath13 is given by @xmath14 . however , the corresponding energy - momentum dispersion relation at equal-@xmath8 is given by @xmath15 where the light - front energy @xmath16 conjugate to @xmath8 is given by @xmath17 and the light - front momenta @xmath18 and @xmath19 are orthogonal to @xmath16 . while the instant form ( eq.([eq.01 ] ) ) exhibits an irrational energy - momentum relation , the front form ( eq.([eq.02 ] ) ) yields a rational relation and thus the signs of @xmath20 and @xmath16 are correlated , e.g. the momentum @xmath20 is always positive when the system evolve to the future direction ( i.e. positive @xmath8 ) so that the light - front energy @xmath16 is positive . in the instant form , however , no sign correlations for @xmath12 and @xmath13 exist . such a difference in the energy - momentum dispersion relation makes the lfd quite distinct from other forms of the relativistic hamiltonian dynamics . the light - front quantization @xcite has already been applied successfully in the context of current algebra @xcite and the parton model @xcite in the past . with further advances in the hamiltonian renormalization program @xcite , lfd appears to be even more promising for the relativistic treatment of hadrons . in the work of brodsky , hiller and mccartor @xcite , it is demonstrated how to solve the problem of renormalizing light - front hamiltonian theories while maintaining lorentz symmetry and other symmetries . the genesis of the work presented in @xcite may be found in @xcite and additional examples including the use of lfd methods to solve the bound - state problems in field theory can be found in the review of qcd and other field theories on the light cone @xcite . these results are indicative of the great potential of lfd for a fundamental description of non - perturbative effects in strong interactions . this approach may also provide a bridge between the two different pictures of hadronic matter , i.e. the constituent quark model ( cqm ) ( or the quark parton model ) closely related to experimental observations and the qcd based on a covariant non - abelian quantum field theory . again , the key to possible connection between the two pictures is the rational energy - momentum dispersion relation given by eq.([eq.02 ] ) that leads to a relatively simple vacuum structure . there is no spontaneous creation of massive fermions in the lf quantized vacuum . thus , one can immediately obtain a constituent - type picture @xcite in which all partons in a hadronic state are connected directly to the hadron instead of being simply disconnected excitations ( or vacuum fluctuations ) in a complicated medium . a possible realization of chiral symmetry breaking in the lf vacuum has also been discussed in the literature @xcite . moreover , the poincar algebra in the ordinary equal-@xmath0 quantization is drastically changed in the light - front equal-@xmath8 quantization . in lfd , the maximum number ( seven ) of the ten poincare generators are kinematic ( i.e. interaction independent ) and they leave the state at @xmath21 unchanged @xcite . however , the transverse rotation whose direction is perpendicular to the direction of the quantization axis @xmath22 at equal @xmath8 becomes a dynamical problem in lfd because the quantization surface @xmath8 is not invariant under the transverse rotation and the transverse angular momentum operator involves the interaction that changes the particle number @xcite . leutwyler and stern showed that the angular momentum operators can be redefined to satisfy the su(2 ) spin algebra and the commutation relation between mass operator and spin operators @xcite ; @xmath23 = i { \epsilon_{ijk } } { \cal{j}}_k,\ ] ] @xmath24 = 0.\ ] ] nonetheless , in lfd , there are two dynamic equations to solve : @xmath25 and @xmath26 where the total angular momentum ( or spin ) and the mass eigenvalues of the hadron ( @xmath27 ) are given by @xmath28 and @xmath29 . thus , it is not a trivial matter to specify the total angular momentum of a specific hadron state . as a step towards understanding the conversion of the dynamical problem from boost to rotation , we constructed the poincar algebra interpolating between instant and light - front time quantizations @xcite . we used an orthogonal coordinate system which interpolates smoothly between the equal - time and the light - front quantization hypersurface . thus , our interpolating coordinate system had a nice feature of tracing the fate of the poincare algebra at equal time as the hypersurface approaches to the light - front limit . the same method of interpolating hypersurfaces has been used by hornbostel @xcite to analyze various aspects of field theories including the issue of nontrivial vacuum . the same vein of application to study the axial anomaly in the schwinger model has also been presented @xcite , and other related works @xcite can also be found in the literature . in the present work , we introduce the interpolating scattering amplitude that links the corresponding time - ordered amplitudes between the two forms of dynamics . we exemplify the physical meaning of the kinematic transformations in contrast to the dynamic transformations by means of checking the invariance of each individual time - ordered amplitude for an arbitrary interpolation angle . our analysis further clarifies why and how the longitudinal boost is kinematical only in the lfd but not in any other interpolation angle dynamics including ifd . in particular , we show the disappearance of the connected contributions to the current arising from the vacuum when the interpolation angle is taken to yield the lfd . since we do nt need any infinite momentum frame ( imf ) to show this disappearance and our proof is completely independent of reference frames , it resolves the confusion between the lfd and the imf that sometimes appears in the discussion on related topics . the well - known utility of imf usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes . in the next section , section [ sec.02 ] , we introduce the interpolating scattering amplitude that links the corresponding time - ordered amplitudes between the two forms of dynamics and show the disappearance of the connected contributions to the current arising from the vacuum when the interpolation angle is taken to yield the lfd . taking just the simplest possible example ( viz . spin - less scalar particles ) and keeping only the fundamental degrees of freedom , i.e. particle momenta , we focus only on the essential part of the time - ordered scattering amplitude , namely the energy denominators . in section [ sec.03 ] , we discuss the kinematic transformations that allow the invariance of each individual time - ordered amplitude for an arbitrary interpolation angle and present the explicit results of particle momenta under those kinematic transformations . in this section , we also discuss a remarkable difference of the lfd result compared to the result for any other interpolation angle dynamics including ifd and the role of the longitudinal boost that becomes kinematic only in lfd . in section [ sec.04 ] , we explicitly show the invariance of the individual time - ordered amplitude under kinematic transformations plotting the results obtained in section [ sec.03 ] and extend the well - known utility of imf in ifd to an arbitrary interpolation angle dynamics . conclusions follow in section[sec.05 ] .

among the three forms of relativistic hamiltonian dynamics proposed by dirac in 1949 , the instant form and the front form can be interpolated by introducing an interpolation angle between the ordinary time and the light - front time . using this method , we introduce the interpolating scattering amplitude that links the corresponding time - ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time - ordered amplitude for an arbitrary interpolation angle . in particular , it exhibits that the longitudinal boost is kinematical only in the front form dynamics , or the light - front dynamics ( lfd ) , but not in any other interpolation angle dynamics . it also shows that the disappearance of the connected contributions to the current arising from the vacuum occurs when the interpolation angle is taken to yield the lfd . since it does nt require the infinite momentum frame ( imf ) to show this disappearance and the proof is independent of reference frames , it resolves the confusion between the lfd and the imf . the well - known utility of imf usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes . permanent address : instituto de fsica terica - unesp universidade estadual paulista , + rua dr . bento teobaldo ferraz , 271 - bloco ii - 01140 - 070 , so paulo , sp , brazil . ]

among the three forms of relativistic hamiltonian dynamics proposed by dirac in 1949 , the instant form and the front form can be interpolated by introducing an interpolation angle between the ordinary time and the light - front time . using this method , we introduce the interpolating scattering amplitude that links the corresponding time - ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time - ordered amplitude for an arbitrary interpolation angle . in particular , it exhibits that the longitudinal boost is kinematical only in the front form dynamics , or the light - front dynamics ( lfd ) , but not in any other interpolation angle dynamics . it also shows that the disappearance of the connected contributions to the current arising from the vacuum occurs when the interpolation angle is taken to yield the lfd . since it does nt require the infinite momentum frame ( imf ) to show this disappearance and the proof is independent of reference frames , it resolves the confusion between the lfd and the imf . the well - known utility of imf usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes . permanent address : instituto de fsica terica - unesp universidade estadual paulista , + rua dr . bento teobaldo ferraz , 271 - bloco ii - 01140 - 070 , so paulo , sp , brazil . ]

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research in estimating losses for catastrophes have led to the development of a wide variety of earthquake loss models . earthquake loss models can generate loss values before an event occurs or while an event is evolving or after an event occurs . earthquake loss models can be classified as probabilistic , deterministic and real - time models . probabilistic models produce a maximum probable loss value using a stochastic event catalog which represents a sample of possible future earthquakes . models such as capra - central american probabilistic risk assessment @xcite , eqrm - earthquake risk model @xcite and riskscape @xcite are probabilistic models . in deterministic models the losses caused by a specific event that occurred are estimated . lnecloss @xcite , redars - risks from earthquake damage to roadway systems @xcite and nhematis @xcite are deterministic models . real - time models estimate losses soon after ( near real - time ) an earthquake has occurred . examples include eler - earthquake loss estimation routine @xcite , emergeo @xcite and pager - prompt assessment of global earthquakes for response @xcite . a hybrid of the former models are seen in hazus ( combines deterministic , probabilistic and real - time models ) @xcite , koeriloss @xcite and maeviz @xcite . in this paper , a loss estimator which produces loss values in near real - time and can model past earthquake events is presented . models that focus on generating a probable loss value use a catalog of possible future earthquakes . in such models , there is no focus on a specific event and any analysis is done before an earthquake may occur and is called pre - event analysis . examples include air @xcite , dbela - displacement - based earthquake loss assessment @xcite and mdla @xcite . for quick and imminent decision making it is desirable that loss estimates be accurately generated as an event evolves . post - event analysis presents a timely evaluation of losses due to an earthquake in the minutes , hours , days and weeks immediately following an earthquake . examples of post - event models are inlet - internet - based loss estimation tool @xcite , pager @xcite and extremum @xcite . models combining both pre - event and post - event analysis are available in epedat - early post - earthquake damage assessment tool @xcite , hazus - @xcite and selena - seismic loss estimation using a logic tree approach @xcite . the model proposed in this paper focuses on analysing the effects of an earthquake soon after it occurs and modelling the effects of a past earthquake . pre - event models are of limited interest in the context of estimating losses in real - time . in this paper the focus is on post - event analysis since it is different from pre - event analysis in a number of important ways : * the focus is on a single earthquake event which has just occurred rather than a catalog of possible future events , or on a past earthquake event which can be modelled from archived sensory data . * there is an evolving view of the event as it unfolds , and therefore the sensor data related to the event changes hours , days and weeks after the event , * there is a need for rapid estimation of losses to guide early responses @xcite , and * since post - event data is available from multiple sources , there is a need to visualise and integrate hazard , exposure and loss data from these multiple sources . the 2011 tohoku earthquake that struck off the pacific coast of japan at 05:46 utc on friday , 11 march 2011 is a recent example that illustrates the importance of post - event analysis . figure 1 presents the timeline of the earthquake . fifteen alerts @xmath0 were issued by pager / shakemap in time periods ranging from within an hour to six months after the earthquake . the first alert was issued twenty three minutes after the event and reported a magnitude 7.9 earthquake . additional information such as initial peak ground velocity and peak ground acceleration maps of the ground shake was also available with the alert . further , over the course of the first day alone four additional alerts were issued each updating the data available . not only did the earthquake event unfold over time but the data describing the event and our knowledge of the event evolved . the earthquake data alone was not sufficient to produce reliable loss estimates because between 06:15 utc and 07:52 utc a tsunami struck the coastal towns . additional data sources are required for complete loss estimation . estimating loss values of a future earthquake is based on using a static catalog containing data related to historic events and is employed in pre - event analysis . for example , models such as air @xcite , dbela @xcite and eqrm @xcite employ static catalogs . a static catalog therefore is not sufficient to estimate accurate losses as an earthquake evolves over hours and days of its occurrence . there is a need for up - to - date information of an earthquake as it evolves . one possibility is to make use of seismic sensor networks which can provide earthquake information as soon as minutes after it has occurred . shakemaps @xcite , for example , are a representation of earthquake sensory information . models that employ real - time models include emergeo @xcite , inlet @xcite and pager @xcite . a few models incorporate both historic and sensor data such as in hazus @xcite , mdla @xcite and selena @xcite . in this paper , we investigate how sensor data from multiple sources can be used for timely estimation of losses . the use of regional seismic sensor networks can provide a model with only region specific data and thereby restricts loss estimation to regions . this may be due to the nature of the research where the project was undertaken and therefore only a country or a region was considered . models such as openrisk @xcite , tefer - turkish emergency flood and earthquake recovery programme earthquake model @xcite and teles - taiwan earthquake loss estimation system @xcite are examples that analyse earthquakes in a region . to ensure global applicability of the model it needs to rely on global sensor networks . epedat @xcite , radius @xcite and qlarm - earthquake loss assessment for response and mitigation @xcite are a few examples . further , full - fledged global applicability also implies being able to use the model to estimate losses at different geographic levels ( for example , loss estimation at cities , counties , states and countries ) . the model presented in this paper explores how global applicability can be achieved . among the earthquake loss estimation models that have been referenced , eler , emergeo , epedat , extremum , hazus , inlet , pager , qlarm , quake - loss , selena and teles support post - event analysis . among these , models such as , eler , epedat , hazus , inlet and teles are region restricted . while these models may provide close to accurate loss estimates , yet they do not support global earthquakes . this may be due to the reliance of the models on regional seismic networks . the emergeo earthquake model produces maps of mmi and peak ground acceleration ( pga ) and can predict damages . loss estimates are not a focus in the model . both the extremum and quakeloss models rely on multiple data sources but are focused on structural and human losses . financial loss estimates are not considered in both models . pager ( prompt assessment of global earthquakes for response ) provides fatality and economic loss impact estimates . however , pager does not determine region specific loss data . global financial and economic organisations need to know the losses ( estimates ) incurred at different geographical levels . the qlarm model calculates human losses and damage in a given human settlement . however , qlarm does not focus on estimating financial losses . the selena model and the complementing rise ( risk illustrator for selena ) @xcite visualisation software computes real - time loss estimates and presents the losses visually . however , there seems to be less automation along the pipeline from obtaining real - time data to visualising the losses . the real - time data needs to be provided by the user to the selena model . research that is pursued for automated post - event estimation of financial losses globally is sparse at best , though many loss models are available in the public domain @xcite . the research reported in this paper is motivated towards the development of ( a ) a real - time , ( b ) a post - event , ( c ) a multiple sensor data relying and ( d ) a globally applicable loss model . to achieve this there is a need to support rapid data ingestion , rapid loss estimation , rapid visualisation and integration of data from multiple data sources and rapid visualisation at multiple geographic levels . the * * a**utomated * * p**ost-**e**vent * * e**arthquake * * l**oss * * e**stimation and * * v**isualisation ( ape - elev ) system is proposed , which comprises three primary modules , namely the earthquake loss estimator ( ele ) , the earthquake visualiser ( ev ) and the elev database ( elev - db ) . the ele module is built on pager and shakemap for accessing real - time earthquake data and estimating losses at different geographic levels . the ele module computes financial losses . visualisation of the losses is facilitated by the ev module . the elev - db module aids the functioning of the ele and ev modules . the remainder of this paper is organised as follows . section [ centralisedarchitecture ] proposes a centralised architecture for the automated post - event earthquake loss estimator and visualiser ( ape - elev ) . the loss estimation module is presented in section [ estimator ] and the loss visualiser module is presented in section [ visualiser ] . section [ distributedarchitecture ] presents a distributed architecture for the ape - elev and how estimation and visualisation are distributed across the server and the client respectively . section [ experiments ] presents one test case using ape - elev and a validation study of the model using ten global earthquakes . section [ conclusion ] concludes the paper .

an automated , real - time , multiple sensor data source relying and globally applicable earthquake loss model and visualiser is desirable for post - event earthquake analysis . to achieve this there is a need to support rapid data ingestion , loss estimation and integration of data from multiple data sources and rapid visualisation at multiple geographic levels . in this paper , since post - event data is often available immediately from multiple disparate sources , a geo - browser is employed to facilitate the visualisation and integration of earthquake hazard , exposure and loss data .

an automated , real - time , multiple sensor data source relying and globally applicable earthquake loss model and visualiser is desirable for post - event earthquake analysis . to achieve this there is a need to support rapid data ingestion , loss estimation and integration of data from multiple data sources and rapid visualisation at multiple geographic levels . in this paper , the design and development of the automated post - event earthquake loss estimation and visualisation ( ape - elev ) system for real - time estimation and visualisation of insured losses incurred due to earthquakes is presented . a model for estimating ground up and net of facultative losses due to earthquakes in near real - time is implemented . since post - event data is often available immediately from multiple disparate sources , a geo - browser is employed to facilitate the visualisation and integration of earthquake hazard , exposure and loss data . the feasibility of ape - elev is demonstrated using a test case earthquake that occurred in tohoku , japan ( 2011 ) . the ape - elev model is further validated for ten global earthquakes using industry loss data . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

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this section in the first instance considers the experimental platform and the user interface of ape - elev , followed by feasibility and validation studies of the ape - elev model . the feasibility of ape - elev is confirmed using a test case earthquake of magnitude 9.0 that occurred on 11th march 2011 , commonly known as the tohoku earthquake or referred to as near the east coast of honshu , japan with an event i d usc0001xgp in pager . the validation study considers 10 global earthquakes and the expected losses computed by ape - elev is compared against normalised historic loss data . the validation study is also pursued to determine the probability of the expected losses falling within a pre - defined loss threshold . the data related to the earthquake was available on the pager archive @xcite and shakemap archive @xcite . the event data extractor in the ape - elev architecture fetches data related to the event from the pager archive in .xml format and instantiates the ele module . after the ele module is instantiated , the losses are estimated as considered in section [ estimator ] . the ev module is then employed to visualise the estimated losses . geometry data for the geographic levels was obtained from the global administrative areas database @xcite , as shapefiles . the shapefiles obtained were large in size containing accurate boundary specification . since the experiment reported here was a preliminary test , approximate boundary specifications were sufficient , and therefore the shapefile was simplified using the mapshaper tool @xcite . figure 5 is a screenshot of the visualiser . the inline map shown on the screenshot represents the shakemap representation of the earthquake . the earthquake related data is shown on the right - hand side of the map . the four visualisers of the ev module are listed under google earth visualisation as static data , exposure data , hazard data and loss data . the visualisation techniques ( choropleth in the screenshot ) are available in a drop - down box . the shakemap link presents the shakemap on the google earth application . the ground up and net of facultative losses computed by the ele module are displayed under global earthquake loss model . the portfolio loss link presents four pie charts that compares the losses and exposures by line of business such as industrial , personal and commercial . the test case employed in the feasibility study is magnitude 9.0 , which occurred in tohoku , japan on 11 march 2011 that struck off the pacific coast of japan at 05:46 utc on friday , 11 march 2011 . this recent earthquake was a major catastrophe and affected 28 prefectures . it is worthwhile to note that the catastrophe was due to both a tsunami and an earthquake . the ape - elev model does not incorporate any mechanism to differentiate between the tsunami and the earthquake related losses . this differentiation , however , is achieved in the model since the input data from usgs pager and shakecast differentiates the catastrophe by producing earthquake related data . therefore , the model inherently produces loss estimates for the catastrophe data provided and its accuracy is dependent on the input . figures 6 - 10 are a set of screenshots obtained from the visualiser . figure 6 shows the mmi of the affected prefectures using the prism visualisation technique . the gradient scale on the left hand side shows the mmi at the prefectures . the right most pop - up shows gul and nfl for the earthquake . the pop - up in the centre shows the exposure , population and hazard data of shizuoka prefecture . figure 7 shows the mdr of the affected prefectures . the choropleth visualisation technique is employed for representing the mdr . the gradient scale on the left hand side shows the mmi at the prefectures . the pop - up shown on the right side shows information relevant to the earthquake for japan and the pop - up in the centre shows regional information for the fukushima prefecture . figure 8 shows the superimposition of mdr and population of the affected prefectures . choropleth is employed for visualising mdr of the prefectures , prisms are employed for visualising nfl and push - pins are used for visualising populations . the two gradient scales on the left side show the scale of mdr and populations . the pop - up shown on the right side shows information relevant to the earthquake and the pop - up in the centre shows regional information relevant to miyagi prefecture . figure 9 shows the mmi of the affected prefectures using choropleth , the population in the prefectures using human push - pins and the estimated losses using prisms . the two gradient scales on the left side show the scale of mmi and population . the pop - up on the right side shows the estimated loss information for the entire event in the gul and nfl categories . the pie charts indicate the losses for industrial , personal , commercial and other lines of business for the exposure data used . figure 10 shows a different view of information visualised in figure 9 . the mmi of the affected prefectures using choropleth , the population in the prefectures using human push - pins and the estimated losses using prisms . mmi and population are shown on the gradient scale . while the right - most pop up showing the pie charts indicates the loss for the entire event , the pop up in the centre shows the losses specific to the saitama prefecture . the gul and nfl aggregated for the prefecture along with information relevant to the prefecture and the event are presented . figures 11 - 18 are screenshots of different alert versions , @xmath0 of the test - case earthquake which shows the evolving view of the earthquake and how losses can be rapidly estimated . the mmi of the affected prefectures are shown using choropleth visualisation technique and the height of the prisms are indicative of the ground up losses . @xmath66 were received within the first day after the event , @xmath67 within the same week after the event , @xmath68 within the same month after the event and the remaining alerts within six months after the event . figure 11 is based on the first alert , @xmath69 which presented data for an overall magnitude of 7.9 twenty two minutes and fifty eight seconds after the event occurred . in this alert , as shown in the figure fourteen prefectures are affected - six prefectures with mmi vii ( dark yellow ) , six prefectures with mmi vi ( light yellow ) and two prefectures with mmi v ( green ) . the ground up loss for the prefectures are estimated and presented above the prisms indicative of the magnitude of the loss . the estimated losses are highest for the chiba and kanagawa prefectures . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] figure 12 is based on the third alert , @xmath70 which presented data data for an overall magnitude of 8.8 one hour and fifteen minutes after the event occurred . in this alert , more data was available and was used to update the first alert . while there is a difference in the data showing the magnitude of the earthquake , the mmi data and the estimates for the ground up loss remained the same . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] figure 13 is based on the fifth alert , @xmath71 which presented data for an overall magnitude of 8.9 two hours and forty four minutes after the event . the mmi information of the prefectures were updated - six prefectures with mmi vii ( dark yellow ) , eight prefectures with mmi vi ( light yellow ) , five prefectures with mmi v ( light green ) and three prefectures with mmi iv ( light blue ) . the loss estimates for the prefectures have rapidly changed after this alert . for example , for the chiba and kanagawa prefectures the ground up loss estimates have increased by approximately 8 times after the first and third alert . the sensor data in this alert has gathered more information about the prefectures which are land - locked . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] figure 14 is based on the seventh alert , @xmath72 which presented data for an overall magnitude of 9.0 four days and nine hours after the event . again the mmi information of the prefectures are updated with more accurate information gathered by the sensors . one prefecture has an mmi viii and the ground up loss estimates of the prefectures around chiba and kanagawa prefectures have increased . more prefectures to the south of the island have an mmi iv though the losses estimated here are zero . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] figure 15 is based on the ninth alert , @xmath73 which presented data for magnitude similar to the previous alert and was received one week and one day after the event . the data for the next alerts will remain almost similar with minor details updated . while in the previous alerts an evolving view of the hazard , vulnerability and loss were visualised from this alert a constant view is obtained . again loss estimates in the prefectures to the vicinity of the coastal prefectures are updated . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] figure 16 , figure 17 and figure 18 are based on alerts , @xmath74 , @xmath75 and @xmath76 respectively . the overall data visualised in these alerts are more or less the same with minimal updates to the mmi and losses estimated for the prefectures . of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] of magnitude 9.0 , tohoku , japan , 11 march 2011 earthquake , scaledwidth=50.0% ] a study that compares the predicted losses of ten global earthquakes against historic loss data was pursued in order to validate the ape - elev model . table 1 shows the list of earthquakes selected for this study , their date of occurrence ( dd - mm - yyyy ) , magnitude , latitude and longitude , historic losses in millions of usd in the year of occurrence of the earthquake , adjustment multipliers to normalise the historic losses to 2012 usd , predicted losses in millions of usd and percent error between the normalised historic and predicted losses . the earthquakes were selected such that ( a ) they were distributed geographically across different continents , ( b ) their magnitude was over 5.5 , ( c ) and had occurred in the last 30 years . m1.4 cm | m1.4 cm | m1 cm | * region affected * & * country * & * date * & * mag * & * lat * & * long * & * historic losses in millions of usd for year y , @xmath77 * & & * normalised historic losses in millions of 2012 usd , @xmath78 * & * predicted losses in millions of 2012 usd * & * percent error % * + & & & & & & & * * & * * & * * & * * & & & + libertador ohiggins & chile & 11/03/2010 & 6.9 & -34.2592 & -71.9288 & 16.0500 & 1.0558 & 0.9957 & 0.9651 & 1.0318 & 16.8732 & 238.8136 & 1315.33 + wnw of ferndale & usa & 09/01/2010 & 6.5 & 40.6520 & -124.6920 & 25.0000 & 1.0352 & 0.9850 & 0.9683 & 1.0172 & 25.4904 & 16.8655 & -33.84 + california & usa & 28/06/1992 & 7.3 & 34.2012 & -116.4360 & 37.8403 & 1.4926 & 1.1539 & 0.9368 & 1.2316 & 65.1718 & 601.4143 & 822.81 + ne of san simeon & usa & 22/12/2003 & 6.5 & 35.7058 & -121.1010 & 120.7670 & 1.1981 & 1.0003 & 0.9268 & 1.0793 & 144.7416 & 46.4220 & -67.93 + & usa and mexico & & & & & 400.0000 & - & - & - & - & 421.4479 & 488.3228 & 15.87 + & usa & & & & & 250.0000 & 1.0302 & 0.9897 & 0.9729 & 1.0172 & 254.9038 & 370.2505 & - + & mexico & & & & & 150.0000 & 1.0853 & 1.0230 & 0.9893 & 1.0341 & 166.5441 & 118.0722 & - + california & usa & 18/10/1989 & 6.9 & 37.0400 & -121.8800 & 2,510.0000 & 1.6103 & 1.2119 & 0.9525 & 1.2724 & 4,898.6913 & 7,316.6145 & 49.36 + south island of new zealand & new zealand & 13/06/2011 & 6.0 & -43.5800 & 172.7400 & 2,816.4549 & 0.9909 & 1.0165 & 1.0099 & 1.0066 & 2,836.7903 & 3,132.1219 & 10.41 + south island of new zealand & new zealand & 21/02/2011 & 6.1 & -43.6000 & 172.7100 & 13,000.0000 & 1.0025 & 1.0047 & 0.9976 & 1.0070 & 13,093.8628 & 17,660.6445 & 34.88 + california & usa & 17/01/1994 & 6.7 & 34.2130 & -118.5360 & 22,920.0000 & 1.4381 & 1.1106 & 0.9204 & 1.2066 & 36,606.3931 & 4,787.6419 & -86.92 + tohuku & japan & 11/03/2011 & 9.0 & 38.2970 & 142.3730 & 37,200.0000 & 0.9935 & 0.9978 & 0.9873 & 1.0106 & 36,877.4566 & 4,611.4482 & -87.49 + the historic data related to all the earthquakes were collected from multiple sources , namely the national geophysical data centre ( nsdc ) @xcite , united states geological survey ( usgs ) @xcite , pager @xcite , shakemap @xcite , em - dat @xcite and cat - dat @xcite . the information collected includes , event data , exposure data , hazard data and loss data . the collected loss data is denoted as @xmath77 which are in usd of year @xmath79 in which the earthquake occurred . normalisation of loss data is reported by @xcite , @xcite , @xcite and @xcite . in this paper , the historic loss data is normalised to 2012 usd , denoted as @xmath78 using the normalisation method described by @xcite and @xcite . three adjustment multipliers are used for the normalisation . firstly , the inflation multiplier , denoted as @xmath80 , which uses the implicit price deflator ( ipd ) for gross domestic product metric sometimes also referred to as gdfdef . using this metric any output obtained at the current price is converted into constant - dollar gdp by taking inflation into account . how much change in a base year s gdp is dependent on the changes in the price level is captured by the metric . this metric is available from economic research of the federal reserve bank of st . louis @xcite and the us bureau of economic analysis @xcite are employed . secondly , the population multiplier , denoted as @xmath81 , which is the ratio of the population in 2012 and the year of occurrence of the earthquake . the population data is available from the census data published by governmental agencies . thirdly , the wealth multiplier , denoted as @xmath82 is computed as @xmath83 . @xmath84 for year , @xmath79 normalised to 2012 is the inflation - corrected wealth adjustment obtained as @xmath85 . the fixed asset and consumer durable goods ( facdg ) metric in a year is used indicative of the wealth in that given year . the computation of fixed assets capture private and governmental assets and the computation of consumer durable goods take into account non - business goods consumed by households . this metric is obtained from the us bureau of economic analysis ( bea ) . the sole use of the measure of wealth is not indicative of inflation adjustments and therefore the consumer price index ( cpi ) is taken into account . further the wealth multiplier are adjusted for population to a per capita basis . the per capita adjustment is taken into account since increase in wealth is dependent on population and the rate of change of wealth and population are different . the normalisation equation is @xmath86 or can be restated as @xmath87 if the implicit price deflator ( ipd ) index of the gdp is taken into account for computing the inflation - corrected wealth adjustment instead of the consumer price index ( cpi ) , then the normalisation equation is @xmath88 in the research reported in this paper , however , @xmath78 is computed using equation which uses both ipd and cpi . the equation takes into account the effect of population based on the consumption ( definition of cpi ) in normalisation . however , there is no direct dependence on population as seen in equation and equation . there are challenges in considering the population for earthquake losses . for example , consider an area that was affected by a major earthquake 20 years ago and was sparsely populated then which resulted in minimal ground up loss . for normalising the loss of that earthquake in 2012 factors such as how densely populated that area was in 2012 and the ground up loss if the earthquake occurred in 2012 needs to be considered . for such a consideration regional population statistics will need to be incorporated into the equation . consider for example the earthquake that affected wnw of ferndale , usa on 9 january 2010 with a magnitude of 6.5 . the historic loss for this earthquake in 2010 us dollars is 25 million , represented as @xmath89 . the @xmath89 value needs to be normalised for 2012 usd denoted as @xmath78 . the implicit price deflator index in 2010 normalised for 2012 , represented as @xmath90 can be obtained as the ratio of the implicit price deflator in 2012 ( @xmath91 ) to the implicit price deflator in 2010 . in 2012 , @xmath93 and @xmath94 ^ 1^. therefore , @xmath95 . computing the wealth multiplier index for 2010 normalised to 2012 denoted as @xmath96 requires the computation of two indices , namely the inflation corrected wealth multiplier index ( @xmath97 ) and the population multiplier index ( @xmath98 ) . the wealth of usa in 2012 is 51,117.4 billion usd and the wealth in 2010 is 48,758.9 billion usd computed from the fixed assets and consumer durable goods account^2^. therefore , the ratio of wealth of 2012 to 2010 is @xmath99 . the consumer price index ( cpi ) for 2012 is 231.227 and for 2010 is 217.230 ^ 3^. the ratio of the consumer price index of 2012 to 2010 is computed as @xmath100 . @xmath97 is obtained by dividing the ratio of wealth and the ratio of cpis of 2012 to 2010 , which is @xmath101 . the population of us in 2012 was 314,055,800 and the population in 2010 was 308,745,538 . therefore , the population multiplier index , @xmath102 . the wealth multiplier index , @xmath96 can then obtained as @xmath103 . therefore , for the us earthquake in 2010 , normalisation in 2012 us dollars is obtained as @xmath104 pager data ( mmi at city level , affected cities due to an earthquake ) for global earthquakes are only available after 2007 . therefore , for earthquakes prior to 2008 a in - house computer script was developed to extract data from two sources . the first source was a list of cities whose population is greater than one thousand people . this list is provided by geonames @xcite and contains all the cities in the world whose population is more than one thousand . the model assumes population as point values for cities in all its computations . however , in reality population is a gradient , and the loss estimation technique presented can not take into account its continuous nature and underestimates the computation of loss taking into account centres with less than a thousand people . the second source was the shakemap file which is a representation of the affected grid on a map due to an earthquake and comprises a large set of point data ( latitude , longitude and the mmi at that point ) . the script extracts the list of cities that are affected within the grid and their mmis . the cities are mapped onto their respective regions using the latitude and longitude information . the exposure data for the geographic levels are collected from publicly available sources . the above inputs were used to calculate losses using the method in the ape - elev model . as shown in equation , the mmi at the city level is used to compute the mdr at the same level using the jaiswal and wald mdr model , either by direct comparison or by interpolation . the exposure data , which is available for higher geographic levels , is disaggregated onto the city level based on population . the losses for a region are then computed by calculating the sum of the losses for individual cities ( loss for individual cities can be computed by the product of the exposure and mdr at the city ) within that region . a number of obstacles were encountered during the validation study , which are as follows : * exposure data had to be collected from a number of disparate sources and was not easy to obtain . * hazard data is not readily available for events preceding 2008 . to collect data for events prior to 2008 , as presented above , an in - house script had to be developed . * as data obtained from multiple sources which do not follow a standard convention were integrated in the validation study , significant efforts had to be made towards ordering and organising data and eliminating irrelevant information from the sources . despite the above obstacles , ( a ) event data was easily collected , ( b ) population data was publicly available and ( c ) the mmi to mdr was straight forward to calculate based on the vulnerability curves used in pager . two column charts were generated based on increasing historic losses . in figure 19 , the predicted and historic losses are shown in millions of usd for events with historic losses less than 1 billion usd , and in figure 20 , for events with historic losses greater than 1 billion usd . there are multiple sources of error in the validation study and are as follows : 1 . input errors , which refer to the flaws and inaccuracy in the input data to the model . cities with a population of over 1000 were only considered . this data is constructed on the assumption that population is a discrete distribution , while in reality it is continuous ( population outside a city with less than 1000 human inhabitants is not considered ) . the population data obtained from geonames was inaccurate since a large number of cities presented zero population . this was partially overcome by doing manual look - ups with other reliable sources . however , conflicts with the dates of census of the geonames and the source of the manual look - ups persisted . application errors , which refer to the inaccuracies and assumptions that exist within the model . the mmi of a city was converted to a mdr value using country - based mmi - mdr curves . the assumption here is that every city follows the same curve ( values ) as of its country . the losses for a few events are calculated in the currency of its country of origin . the value of the currency is then converted to us dollars based on an average conversion rate for the year in which the event occurred . benchmark errors , which refer to the assumptions that exist in setting a benchmark . a range of values are available for historic insured losses . it is difficult to determine which value needs to be selected as the benchmark for comparison against the predicted loss . for certain events , historic insured losses were not available , and therefore , the total economic losses were used to estimate the insured loss . this was based on a countrywide take - up rate which may not be accurate for certain regions in a country . it is observed that there are two events from the sample which have over 100% error . the first event affected california in 06/28/1992 with a magnitude of 7.3 , have significant error . this is likely because the most recent exposure for california was only available for the validation study , thereby leading to a significant over - prediction . the second event occurred on 03/11/2010 in chile with a magnitude of 6.9 . the over - prediction is in part likely due to the fact that exposure was disaggregated based on population . in this case , the assumption that exposure is proportional to population is less accurate since only one city with a population of over 1000 was affected . the seven events that have less than 100% error indicate the model is feasible . further accuracy can be achieved by calibrating the model . the loss predicted by the ape - elev model is a mean value for an earthquake . to study the probability of a loss threshold @xmath105 the @xmath106 distribution which is the standard normal cumulative distribution function is employed as follows @xcite : @xmath107 - \phi \left [ \frac{ln(a ) - \mu_{ln(l)}}{\zeta}\right]\ ] ] where @xmath108 is the predicted value of the logarithm of loss obtained from the model and is assumed to be a lognormal random variable , and @xmath109 is the normalised standard deviation of the logarithm of loss obtained from @xcite . figure 21 shows the estimate of probability of different loss thresholds ( @xmath110 , @xmath111 , @xmath112 , @xmath113 , @xmath114 , @xmath115 , @xmath116 ) represented in millions of usd for the earthquakes of table 1 . these loss thresholds best represent magnitude losses and are therefore chosen for validating the results in this paper . different thresholds can be used by appropriately setting @xmath117 and @xmath118 values in equation . in this section we have evaluated the performance on ape - elev both in terms of how well its data acquisition and visualisation facilities are able to capture the evolving history of earthquake alerts and the performance of its simplistic loss model . the tohoku earthquake used in evaluating the feasibility demonstrates how data can be rapidly ingested from multiple sources to visualise earthquake alerts as the data related to the event evolves over hours , days and months after its occurrence . evaluation of loss models is tricky at best due to the inherent difficulty in collect consistent exposure and loss data for historic events . in the case of ape - elev is important to remember that the goal is to produce on a global basis a crude loss estimate rapidly , as an event evolves , based on very limited information . in this context , the distribution of expected losses is much more important than the point estimates . our validation demonstrated that the methodology pioneered in pager @xcite for economic loss can be usefully applied in the context of portfolio losses . in 50% of our evaluation events the observed historical losses and the predicted losses fall into the same loss threshold . in 90% of our test events the observed historical losses and the predicted losses fall into the two highest loss thresholds . given the limited data , the loss model gives reasonable order of magnitude estimates , but it is important that users be aware of the inherent limitations of the underlying approach .

the feasibility of ape - elev is demonstrated using a test case earthquake that occurred in tohoku , japan ( 2011 ) . the ape - elev model is further validated for ten global earthquakes using industry loss data . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

an automated , real - time , multiple sensor data source relying and globally applicable earthquake loss model and visualiser is desirable for post - event earthquake analysis . to achieve this there is a need to support rapid data ingestion , loss estimation and integration of data from multiple data sources and rapid visualisation at multiple geographic levels . in this paper , the design and development of the automated post - event earthquake loss estimation and visualisation ( ape - elev ) system for real - time estimation and visualisation of insured losses incurred due to earthquakes is presented . a model for estimating ground up and net of facultative losses due to earthquakes in near real - time is implemented . since post - event data is often available immediately from multiple disparate sources , a geo - browser is employed to facilitate the visualisation and integration of earthquake hazard , exposure and loss data . the feasibility of ape - elev is demonstrated using a test case earthquake that occurred in tohoku , japan ( 2011 ) . the ape - elev model is further validated for ten global earthquakes using industry loss data . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

0803.4186

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a general effective description for nanoparticles was presented , starting from a smoothing procedure in which the real spatial density profile inside the nanoparticles is replaced by a spherically symmetric one . the resulting effective interactions between a nanoparticle and a point particle as well as between two nanoparticles are then given by spherically symmetric potentials , thus greatly simplifying the description over an all - atom model . the main results of this approach are the formulation of the effective potentials in terms of auxiliary potentials , eqs . ( [ auxiliaryi ] ) and ( [ auxiliaryij ] ) , which provide a unified description of overlapping and non - overlapping configurations . the auxiliary potentials are related to the basic interaction potentials through eqs . ( [ aidef ] ) and ( [ aijdef ] ) . furthermore , the effective potentials for hollow particles were found to be related to those for solid nanoparticles by simple differentiation with respect to the radii of the nanoparticles , see eqs . ( [ vhdef ] ) and ( [ urelations ] ) , and as such also allow a formulation in terms of auxiliary potentials , as given in sec . [ sec : solid - hollow ] . as an application of the formalism , explicit effective pair potentials for solid and hollow nanoparticles were obtained for various basic pair potentials . different pair potentials have different applications . for instance , the lennard - jones potential is a general - purpose potential , while the buckingham potential is suited to describe the physics of particles close together such as in high pressure systems . these basic potentials result in effective nanoparticle potentials with hard cores plus a soft potential . they reduce in limiting cases to some of the existing model potentials for colloids , such as hard spheres and the hamaker potential,@xcite but not to more ad hoc models such as the description of a colloid as a single big lennard - jones particle.@xcite in contrast , the morse potential is able to describe bounded systems or penetrable particles , making it possible to model nanoparticles that could passively capture and trap specific types of particles . this could have applications in modeling drug delivery by nanoparticles@xcite and viral capsids.@xcite for the case of a lennard - jones basic potential , a comparison was carried out with an atomic model of a nanocluster . in this model , the atoms making up the nanoparticle were assumed to be arranged in an fcc lattice structure . to find approximate spherical structures , the atoms were restricted to lie within a certain distance from the central atom in the nanocluster . configurations with up to 19,861 atoms were studied . the effective potentials were compared with the orientionally averaged sum of lennard - jones potentials due to the individual atoms . the agreement tends to be very good , provided the radius in the effective description is treated as a fitting parameter . for some configurations , however , the fitting procedure underestimates the depth of the minimum of the potentials . this may be due to surface roughness of these structures , which is caused by the imposed fcc structure and unlikely to be relevant for real nanoclusters . the application of the explicit expressions for the effective potentials to numerical studies of spherical nanoparticles is in principle straightforward . in fact , the potentials in eqs . ( [ vljsexplicit ] ) and ( [ vljssexplicit ] ) have already been used in a numerical study of single particle transport in an equilibrium nanofluid composed of solid nanoparticles and fluid particles interaction through lennard - jones interactions , where the validity of a gaussian approximation of the van hove self - correlation function was investigated , and found to hold up to picosecond time scales for the fluid particles , and up to five to ten times longer ( depending on temperature ) for nanoparticles with a size of about 2 nm.@xcite given the explicit expressions for the effective potentials , the description allows a fairly direct route toward a qualitative model for a given system of nanoparticles in a fluid , since reasonable values for the parameters for commonly used pair potentials are available in the literature,@xcite while the number of atoms in a nanoparticle and its radius could be taken from experiments or theoretical calculations.@xcite furthermore , the effective potentials have a physical range based on the interaction of their constituents rather than on their radius . therefore , the effective potentials that were derived here are expected to be useful for the qualitative description of a wide variety of systems , from mono - disperse nanoparticles in a fluid to mixtures of different kinds of fluid particles , nanoclusters or buckyballs . a number of interesting extensions present themselves for future research . for instance , while the nanoparticles were assumed to be composed of one kind of particle only , potentials for nanoparticles composed of several types of particles can also be derived within the current context if the distribution of the types is either homogeneously mixed or distributed in spherical shells ( so - called core - shell nanoparticles@xcite ) . the spherical symmetry of the effective potentials , which decouples the rotational and translational degrees of freedom , could be lifted to extend the model to include rotational motion . this may be done by adding interaction sites on the surface of the nanoparticle or a multipole expansion . as long as the orientationally dependent potential is available , there are no obstacles in molecular dynamics simulations of such systems.@xcite furthermore , combining the current model with the mesoscopic fluid model of malevanets and kapral@xcite would yield a numerically efficient model of larger nanoparticles and colloids that includes hydrodynamic effects . these avenues are currently being investigated . the author wishes to thank profs . e. g. d. cohen , r. kapral , and j. schofield for useful discussions . this work was supported by the national sciences and engineering research council of canada and a petroleum research fund from the american chemical society .

an effective description for spherical nanoparticles in a fluid of point particles is presented . the resulting effective pair interactions between a nanoparticle and a point particle , as well as between two nanoparticles , are then given by spherically symmetric potentials . if overlap between particles is allowed , the effective potential generally has non - analytic points , but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential . effective potentials for hollow nanoparticles ( appropriate e.g. for buckyballs ) are also considered , and shown to be related to those for solid nanoparticles .

an effective description for spherical nanoparticles in a fluid of point particles is presented . the points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials , while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth . the resulting effective pair interactions between a nanoparticle and a point particle , as well as between two nanoparticles , are then given by spherically symmetric potentials . if overlap between particles is allowed , the effective potential generally has non - analytic points , but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential . effective potentials for hollow nanoparticles ( appropriate e.g. for buckyballs ) are also considered , and shown to be related to those for solid nanoparticles . finally , explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form , as well as from the commonly used london - van der waals , morse , buckingham , and lennard - jones potential . the applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure .

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entanglement is one of the key features of quantum mechanics , and during the past decades it has been demonstrated experimentally in many different physical systems . by coherent control of interacting quantum systems , entangled states can be engineered directly @xcite . alternatively , entanglement can be established as a consequence of the outcome of a measurement process either as a continuous ( possibly quantum - non - demolition ( qnd ) ) measurement @xcite or as a consequence of a single quantum jump @xcite . some of the above examples employ cavity quantum electrodynamics ( qed ) @xcite for mediating the interaction between the quantum systems , which allows for the direct engineering of entangled states in the strong - coupling regime @xcite . the present paper considers a different case the bad - cavity limit of qed , in which the damping rate of the cavity field is fast compared to the coupling rate between qubits and the cavity field . hence , any information of qubit coherence being encoded into the cavity field will immediately be lost from the cavity and the above - mentioned direct - engineering schemes are inapplicable . however , turning to a measurement - based protocol , the detection of a field transmitted through the cavity allows for re - establishing a firm knowledge of the qubit state and hence for the creation of entangled states through measurement back action . the measurement is of the continuous type , which is theoretically well - described by stochastic master - equation methods @xcite . in contrast to the work of ref . @xcite using similar theoretical methods , our calculations are not restricted to the dispersive and linear regime of the coupling between the cavity field and the qubits but allow instead for a more generalized set of parameters ( even a resonant coupling ) in search for the optimal choice for entanglement generation . we consider feasible experimental approaches and discuss the physical limitations imposed both fundamentally by the measurement process and practically by decoherence mechanisms . this paper is arranged as follows : the basic idea for the protocol is outlined in sec . [ sec : the_baisc_idea ] , while the theoretical modeling is elaborated on in sec . [ sec : stochastic_me ] . various practical measurement schemes are analyzed in sec . [ sec : ent - generation - no - decay ] , while qubit decoherence and inhomogeneities are added in sec . [ sec : decoherence_processes ] . after a general discussion in sec . [ sec : discussion ] , we summarize the conclusions of the paper in sec . [ sec : conclusion ] . some mathematical details are deferred to the appendix .

an entanglement - generating protocol is described for two qubits coupled to a cavity field in the bad - cavity limit . by measuring the amplitude of a field transmitted through the cavity , an entangled spin - singlet state can be established probabilistically . the measurement - based protocol provides criteria for selecting states with an infidelity scaling linearly with the qubit - decoherence rate .

an entanglement - generating protocol is described for two qubits coupled to a cavity field in the bad - cavity limit . by measuring the amplitude of a field transmitted through the cavity , an entangled spin - singlet state can be established probabilistically . both fundamental limitations and practical measurement schemes are discussed , and the influence of dissipative processes and inhomogeneities in the qubits are analyzed . the measurement - based protocol provides criteria for selecting states with an infidelity scaling linearly with the qubit - decoherence rate .

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we conclude this paper by summarizing the results that we have found . we have examined the self - stabilization of a bec against se by performing a stability analysis of a macroscopically occupied state for photons and two - level atoms , which describes a bec that is coherently coupled to a laser beam . the presence of the ground - state bec thereby leads to the formation of polaritons and introduces non - markovian effects in the spontaneous decay of excited atoms . in the case of a bec in a traveling - wave laser , the polariton spectrum displays an avoided crossing around the resonance frequency which causes similar changes in the se rate as a pbg in periodic dielectrics . its magnitude depends on the ratio @xmath155 between the total number of excited atoms @xmath94 and the number of bec - atoms inside a cube of the size of an optical wavelength @xmath156 . if this ratio is much larger than 1 the se rate will essentially remain unchanged . otherwise the change can be significant as the numerical examples shown in fig . [ resultsfigrun ] demonstrate . the change of the se rate displayed in fig . [ resultsfigrun ] depends on the detuning of the laser because the coherently excited atoms are driven at the laser s frequency @xmath21 . for a bec in a 1d optical lattice two new effects do appear . being a kind of periodic dielectric the bec then produces a real polaritonic band gap . the size of this band gap is determined by @xmath125 . as in the case of a traveling wave laser , se is only significantly altered if there are very few excited atoms . this in turn does imply that the optical lattice must be very weak and therefore produces only a small band gap which has only a very small influence on the se rate . the second new effect in a periodic bec is the appearance of a new channel for se which arises from the interference between different momentum components of the excited - state wavefunction and the photon modes . though its effect in a bec is as small as that of the band gap it should also be present in the case of a pbg in an ordinary periodic dielectric where it can be large . it should be pointed out clearly where exactly the difference between an ordinary periodic dielectric and a bec in an optical lattice comes into play . in an ordinary dielectric medium the periodicity is produced by whatever forces determine the stability of the medium . the excitation of an atom inside such a medium is done by a light beam , i.e. , a completely different physical system . in the case of a bec in an optical lattice , however , the excitation of the atoms and the potential that produces the periodicity of the bec both are provided by the same device : the laser beams of the optical lattice . these lattice beams have to achieve two competing goals : to provide a strong periodic potential ( to produce a large band gap ) and to cause only a weak excitation ( to have few excited atoms ) . as the achievement of both goals is impossible the periodicity of the bec will only have a tiny influence on the se rate and it will essentially cause the same effect as a homogeneous bec in a running laser wave . this argument also provides the answer to the question whether self - stabilization of a bec against se is possible . since the se rate is only significantly changed if there are very few excited atoms , and since a large pbg does only form for strong laser beams , a self - stabilization is not possible for becs with a density in the order of @xmath0 @xmath1 . we finally remark that our results are not applicable to becs confined in a micrometer - sized trap , a case discussed in the literature @xcite . our work is concerned with becs which are extended enough to allow the formation of polaritons . the necessary extension of the bec can be estimated by considering the typical interaction energy for the formation of polaritons which is given by @xmath157 ( see appendix [ polaritoneigenmodesrun ] ) . for a bec with a density of @xmath0 @xmath1 this energy is in the order of @xmath158 hz . for the formation of polaritons a photon must therefore be inside the bec longer than @xmath159 seconds . since it travels at the speed of light the bec must therefore be larger than about 3 mm . * acknowledgment * : this work has been supported by the australian research council and the optik zentrum konstanz .

we find that self - stabilization is not possible for becs with a density in the order of . however , the corresponding non - markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous bec interacting with a weak laser beam . we also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes . this new channel should also occur in ordinary periodic dielectrics .

an extended bose - einstein condensate ( bec ) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it . we examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the bec , and whether they can lead to a self - stabilization of the bec against spontaneous emission . we find that self - stabilization is not possible for becs with a density in the order of . however , the corresponding non - markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous bec interacting with a weak laser beam . these effects are caused by the occurrence of an avoided crossing in the photon ( or rather polariton ) spectrum . we also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes . this new channel should also occur in ordinary periodic dielectrics . + pacs : 03.75.fi , 32.80.-t , 42.70.qs + shortened title : spontaneous emission in bose - einstein condensates

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when inflation surpasses moderate levels it damages real economic activities . for instance , it affects government s tax revenues because they are effectively received a period later after the declaration that fix them @xcite . the perception of relative prices changes becomes more difficult since it is not easy to distinguish whether some price grows as a consequence of a relative price change or it is part of general inflation ( the lucas problem @xcite ) . it produces inefficient changes of relative prices @xcite if the adjustment process is different for different kinds of goods inducing misleading allocation of resources @xcite . inflation also affects currency in its property as medium of exchange , store of value , and unit of account . the degree of perturbation is greater the higher the inflation . if consumption goods become relatively more expensive than leisure due to inflation , labor market may be negatively perturbed by reduction of working hours supply @xcite . unanticipated increase in prices reduces real wages and expand employment @xcite , although the positive employment effect could be lowered or reversed by the effects of falling investment . furthermore , investment demand may be especially affected because of the shorter planning time scope and growing uncertainty . in general , when the inflation is higher then the decision horizon is shorter . moreover , with no alternative allocation to money , savings decline and investment falls at expenses of actual consumption , lowering the capital stock growth . therefore inflation is not a pure nominal problem , m but it is linked to real economy in many non trivial ways @xcite . consequently , governments try to prevent high inflation , and to lower it when reach elevated levels . parameters can change once policy changes @xcite . the relation between sources of inflation and the evolution of parameters is complex and not direct . these issues are also analyzed in text books on econophysics @xcite . models of hyperinflation are especially suitable to emphasize that inflation implies bad `` states of nature '' in economy . wars , changes of social regimens , states bankruptcies are the characteristics of such regimens . these factors together with the influence of pure economical variables like expectations , money demand , velocity of circulation and quantity of money , give an increase of the consumer price index ( cpi ) larger than exponential as can be observed in the investigated cases . in turn , this behavior affects negatively the social network causing unpleasant situations . the model for hyperinflation available in the literature is based on a nonlinear feedback ( nlf ) characterized by an exponent @xmath1 of a power law . in such an approach the cpi exhibits a finite time singularity of the form @xmath8 , allowing a determination of a critical time @xmath2 at which the economy would crash . this model has been successfully applied to many cases . however , in the most recent paper @xcite , it is shown that for the episode of weak hyperinflation occurred in israel it is impossible to determine a value for @xmath2 within the nlf model because @xmath6 goes to zero . in this limit one gets the linear feedback approach which does not contain information on @xmath2 @xcite . this drawback was attributed to a permanent but partially successful efforts for stopping inflation in israel . in order to include in the nlf formalism information on efforts for stabilization like those observed in the case of israel , we developed an extension of this model introducing a parameter @xmath3 , which multiplies all the past growth rate index ( gri ) contributions changing the relative weight of the therm with the power law . the interplay between @xmath6 and @xmath3 leads to multiple equilibria phenomena for episodes of high inflation . the literature on this kind of behavior in models of economics is large and diverse @xcite , see also e.g. refs.@xcite . we use the well known multiple equilibria expression to indicate the existence of multiple trajectories compatible with data which lead to very different states of nature of the economy where the final outcome is stable or not . in the extended nlf approach the solution for cpi becomes proportional to the gaussian hypergeometric function @xmath4 , where @xmath5 is a function of @xmath6 , @xmath3 , and @xmath2 . since for @xmath7 this hypergeometric function diverges , a finite time singularity shows up allowing a determination of @xmath2 . it is important to notice that the gaussian hypergeometric appears in a variety of physical and mathematical problems . in quantum mechanics , the solution of the schrdinger equation for some potentials is expressed in terms of @xmath9 @xcite . moreover , the eigenfunctions of the angular momentum operators are sometimes written in terms of @xmath9 functions @xcite . in the present work we also investigated the effects of the parameter @xmath3 on the non linear dynamic evolution of real inflations . firstly , the robustness of the novel model is tested analyzing the severe hyperinflation occurred in hungary after world war ii . next , it is successfully applied for studying the weaker hyperinflation developed in israel and the high - inflation episodes observed in mexico and iceland . in order to understand better the evolution of prices in these countries , brief descriptions of historical events are provided . in these cases we found multiple equilibria . the paper is organized in the following way . in sec.[sec : theory ] the nlf model is outlined with some details because it is the starting point for the extension proposed in sec . [ sec : general ] . the limit @xmath10 is discussed . section [ sec : results ] is devoted to report and discuss the results obtained by applying the novel approach . finally , the main conclusions are summarized in sec . [ sec : summary ] .

the consumer price index ( cpi ) exhibits a finite time singularity of the type , with , predicting a blow up of the economy at a critical time . however , this model fails in determining in the case of weak hyperinflation regimes like , e.g. , that occurred in israel . to overcome this trouble , the nlf model is extended by introducing a parameter , which multiplies all therms with past growth rate index ( gri ) . in this novel approach the solution for cpi is also analytic being proportional to the gaussian hypergeometric function , where is a function of , , and . for it is shown that the interplay between parameters and may produce phenomena of multiple equilibria .

an extension of the nonlinear feedback ( nlf ) formalism to describe regimes of hyper- and high - inflation in economy is proposed in the present work . in the nlf model the consumer price index ( cpi ) exhibits a finite time singularity of the type , with , predicting a blow up of the economy at a critical time . however , this model fails in determining in the case of weak hyperinflation regimes like , e.g. , that occurred in israel . to overcome this trouble , the nlf model is extended by introducing a parameter , which multiplies all therms with past growth rate index ( gri ) . in this novel approach the solution for cpi is also analytic being proportional to the gaussian hypergeometric function , where is a function of , , and . for this hypergeometric function diverges leading to a finite time singularity , from which a value of can be determined . this singularity is also present in gri . it is shown that the interplay between parameters and may produce phenomena of multiple equilibria . an analysis of the severe hyperinflation occurred in hungary proves that the novel model is robust . when this model is used for examining data of israel a reasonable is got . high - inflation regimes in mexico and iceland , which exhibit weaker inflations than that of israel , are also successfully described .

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in the present work we treated regimes of hyper- and high - inflation in economy . in a previous work @xcite it has been found that for a weak hyperinflation , like e.g. that developed in israel , was impossible to determine a value of @xmath2 within the frame of the nlf model . this model is based on a power law with an exponent @xmath1 , see eq . ( [ rate00 ] ) . the mentioned drawback has been attributed to a permanent but incomplete effort for stopping inflation . therefore , in the present work we suggested to include in the theory information on saturation by introducing a parameter @xmath3 , which multiplies all the past inflation growth rates . this parameter would account for the effort done by the government for coping inflation . in the extended approach , enlf , reported in the present paper the solutions for gri and cpi are also analytic as in the nlf model . in particular , the cpi is expressed in therms of the gaussian hypergeometric function @xmath4 , where @xmath5 is a function of @xmath3 , @xmath6 , @xmath102 , and @xmath2 , see eqs . ( [ defxb0])-([defxb ] ) . it is pertinent to notice that @xmath9 appears in a variety of mathematical and physical problems . for @xmath7 this hypergeometric function diverges leading to a finite time singularity , from which a value of @xmath2 can be determined . the same singularity is present in eq.([rate57 ] ) for gri . so , the enlf model proposed in the present work preserves the well - defined singularities yielded by the power law stemmed from a simple positive nonlinear feedback . this mechanism is important for understanding processes in financial crashes ( see ref . @xcite and references therein ) . for completeness , in the appendix it is shown that for the limit @xmath10 from above , one retrieves all the expressions of the nlf model . an analysis of the severe hyperinflation occurred in hungary after the world war ii proves that the novel enlf approach is robust . when it is used for examining data of israel there are two sorts of solutions . one yields @xmath6 consistent with zero ( lf model ) and the other one gives a well determined and reasonable @xmath2 . as a further application , high - inflation regimes exhibiting weaker inflations than that of israel were also analyzed . the episodes occurred in mexico and iceland are reported in the present work . data of both series of inflation can be described , as in the case of israel , with the lf model . however , the enlf(@xmath2 ) model also provides additional solutions forecasting possible blow up of the economies in case the high inflation regimes would become spirals of hyperinflation . the corresponding fits are very good and the predicted values of @xmath2 for crashes are acceptable . the phenomena of multiple equilibria , a known feature in models of economics , appears due to the fact that the introduction of @xmath3 enlarges the dimension of the @xmath101 hyper - surface , which now also presents minimums in domains where the parameters @xmath2 and @xmath6 are not strongly correlated . so , we can state that the parameter @xmath3 allows a more complete representation of inflationary processes . it is interesting to note that the exponent of the nonlinear feedback of inflation can be controlled by a parameter multiplying the growth rate . different combinations of parameters may be interpreted as forces acting with its own strength , producing dynamical paths that lead to very different outcomes . this work was supported in part by the ministry of science and technology of argentina through grants pip 0546/09 from conicet and pict 2011/01217 from anpcyt , and grant ubacyt 01/k156 from university of buenos aires .

an extension of the nonlinear feedback ( nlf ) formalism to describe regimes of hyper- and high - inflation in economy is proposed in the present work . in the nlf model this hypergeometric function diverges leading to a finite time singularity , from which a value of can be determined . this singularity is also present in gri . an analysis of the severe hyperinflation occurred in hungary proves that the novel model is robust . when this model is used for examining data of israel a reasonable high - inflation regimes in mexico and iceland , which exhibit weaker inflations than that of israel , are also successfully described .

an extension of the nonlinear feedback ( nlf ) formalism to describe regimes of hyper- and high - inflation in economy is proposed in the present work . in the nlf model the consumer price index ( cpi ) exhibits a finite time singularity of the type , with , predicting a blow up of the economy at a critical time . however , this model fails in determining in the case of weak hyperinflation regimes like , e.g. , that occurred in israel . to overcome this trouble , the nlf model is extended by introducing a parameter , which multiplies all therms with past growth rate index ( gri ) . in this novel approach the solution for cpi is also analytic being proportional to the gaussian hypergeometric function , where is a function of , , and . for this hypergeometric function diverges leading to a finite time singularity , from which a value of can be determined . this singularity is also present in gri . it is shown that the interplay between parameters and may produce phenomena of multiple equilibria . an analysis of the severe hyperinflation occurred in hungary proves that the novel model is robust . when this model is used for examining data of israel a reasonable is got . high - inflation regimes in mexico and iceland , which exhibit weaker inflations than that of israel , are also successfully described .

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star cluster pairs are common objects in the magellanic clouds and it is important to understand their formation and evolution processes . a list of 30 cluster pairs in the smc was first presented by hatzidimitriou & bhatia ( 1990 ) . bica & schmitt ( 1995 , hereafter bs95 ) revised previous data on smc extended objects ( star clusters , associations and emission nebulae ) and identified new ones using sky survey eso / serc r and j films . they presented a list of 40 pairs and 2 triple star clusters . pietrzyski & udalski ( 1999a ) reported 23 pairs and 4 triplets derived from pietrzyski et al.s ( 1998 ) star cluster catalogue in the ogle survey area . bica & dutra ( 2000 ) updated bs95 s catalogue considering the entries in pietrzyski et al s catalogue . bica & dutra ( 2000 ) indicated 75 pairs and multiplets comprising 176 individual objects . in recent years there has been growing evidence of interacting star clusters in the magellanic clouds , especially in the lmc . bhatia & hatzidimitriou ( 1988 ) concluded that more than 50% of lmc pairs must be physical systems . bhatia & mcgillivray ( 1988 ) found evidence that ngc2214 is a merging binary star cluster , based on the presence of a flattened core and an extended halo . indeed sagar et al . ( 1991 ) detected two turnoff points revealing the presence of two interacting clusters . bica et al . ( 1992 ) studied cluster pairs and multiplets in the lmc bar by means of integrated colours and found systems which resulted coeval and some with age differences . vallenari et al ( 1998 ) confirmed such scenarios by means of colour - magnitude diagrams . they also presented isophotal contours indicating physical interaction . several other studies have found binarity evidence in lmc cluster pairs ( e.g. kontizas et al . 1993 , dieball & grebel 2000a , 2000b ) . bhatia et al . ( 1991 ) presented a photographic atlas of binary star cluster candidates in the lmc . for the smc no morphological atlas is available and isophotal maps are required to test possible physical interactions . indeed comparisons of isophotes with isopleth maps of n - body simulations proved to be a useful tool ( rodrigues et al . 1994 , de oliveira et al . 1998 , hereafter odb98 ) , since the simulations produce features such as bridges , common envelopes and extensions . the observational importance of tidal tails as interaction signatures was also indicated by leon et al . ( 1999 ) . in this work we provide isophotal maps for smc pairs and multiplets to study the following properties of these candidate physical systems : ( i ) angular distribution ; ( ii ) projected centre - to - centre separation of members ; ( iii ) isophotal structures using the digitized sky survey@xmath6 ( hereafter dss ) ; ( iv ) ages derived by means of isochrone fitting , when possible . we discuss candidate physical systems and infer a scenario for their formation and evolution . in sect . 2 we gather the objects providing coordinates , sizes , centre - to - centre separations and other details for the smc pairs and multiplets . in sect . 3 we provide the isophotal contour atlas together with classifications of interaction features whenever present . a preliminary version of the present isophotal smc atlas together with one for the lmc was given in de oliveira ( 1996 ) . in sect . 4 we derive cluster ages by means of colour - magnitude diagrams extracted from the ogle - ii bvi photometric survey ( udalski et al . 1998 ) . in sect . 5 we discuss the properties of the systems and the possible scenarios for their origin and evolution . finally , concluding remarks are given in sect .

previous n - body simulations indicate that such shapes could be due to tidal tails , bridges or common envelopes . the plates were processed into the present compressed digital form with their permission . the digitized sky survey was produced at the space telescope science institute under us government grant nag w-2166 . ]

an isophotal atlas of 75 star cluster pairs and multiplets in the small magellanic cloud is presented , comprising 176 objects . they are concentrated in the smc main body . the isophotal contours were made from digitized sky survey images and showed relevant structural features possibly related to interactions in about 25% of the sample . previous n - body simulations indicate that such shapes could be due to tidal tails , bridges or common envelopes . the diameter ratio between the members of a pair is preferentially in the range , with a peak at . the projected separation is in the range pc with a pronounced peak at pc . for 91 objects it was possible to derive ages from colour - magnitude diagrams using the ogle - ii photometric survey . the cluster multiplets in general occur in ob stellar associations and/or hii region complexes . this indicates a common origin and suggests that multiplets coalesce into pairs or single clusters in a short time scale . pairs in the smc appear to be mostly coeval and consequently captures are a rare phenomenon . we find evidence that star cluster pairs and multiplets may have had an important role in the dynamical history of clusters presently seen as large single objects . the images in this study are based on photographic data obtained using the uk schmidt telescope , which was operated by the royal observatory edinburgh , with funding from the uk science and engineering research council , until 1988 june , and thereafter by the anglo - australian observatory . original plate material is copyright by the royal observatory edinburgh and the anglo - australian observatory . the plates were processed into the present compressed digital form with their permission . the digitized sky survey was produced at the space telescope science institute under us government grant nag w-2166 . ]

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we overlap two age histograms in fig . [ fig : age ] . the dotted line histogram shows objects from table [ tab : interact ] with ages via cmds . there are three peaks , at about 80 , 220 and 450 myr . the first two peaks appear to be present in grebel et al.s ( 2000 ) sample for 200 smc clusters based on ogle - ii data , reported at t @xmath3 100 and 200 myr respectively . they suggested them as enhanced star formation epochs . considering pietrzyski & udalski s ( 1999b ) sample with cmd ages for 93 smc clusters , no peak is seen at t = 80 - 100 myr , having their histogram a maximum at the youngest bin . in their histogram there occurs a local maximum at t @xmath3 250 - 300 myr , but the statistics is low . the third peak in the present study has no counterpart in both previous analyses , and it is probably an artifact from the low isochrone age step resolution in that range . the solid line histogram in fig . [ fig : age ] shows additionally the embedded objects in hii regions for which we assumed an age of 3 myr , and the objects from table [ tab : interact ] with lower or upper limits by assuming them as the ages themselves . we can observe again a three peak distribution but the first peak is now shifted to the youngest bin similarly to pietrzyski & udalski s ( 1999b ) histogram . this suggests that only the 200 myr peak is relevant , being related to the smc / lmc last encounter ( gardiner et al . 1994 , grebel et al.s 2000 ) . the maximum seen in the youngest bin is possibly related to the cluster formation / destruction rates . since the present sample deals with pairs and multiplets a fast destruction rate might be caused by the internal dynamical evolution in each cluster complex , caused by merger and/or other effects . approximately 55% of cluster pairs and multiplets in table [ tab : interact ] present similar ages between their members indicating that they are coeval . this suggests that most of the pairs and multiplets had a common origin , possibly from the same molecular complex . note that about 60% of the pairs and multiplets embedded in ob associations ( h - a , hodge 1985 ) , as indicated in column 9 of table [ tab : catalog ] , have comparable ages between their members . this could be an explanation for the origin of cluster systems . considering triplet and multiplet members , we found that about 70% of them are younger than 100 myr . these results suggest a possible binary cluster formation scenario : clusters can be born in multiplet systems and coalesce by mergers and tidal disruptions forming binary clusters in a timescale of @xmath3 100 myr . this time is in agreement with dynamical times required for an interacting pair to merge into a single cluster ( odb98 , de oliveira et al . 2000 ) . the pairs with a bridge in the isophotal maps have comparable ages for their components ( table [ tab : interact ] ) . as examples , the pairs ngc241/ngc242 and b39/bs30 in fig . [ fig : atlas2 ] show a bridge linking their members which could be interpreted as a sign of interaction ( see the similarity with the n - body simulation model in fig . 11 of odb98 ) . a typical timescale for the bridge phenomenon is @xmath3 30 myr , as deduced from a series of n - body simulations related to bridge formation and evolution ( odb98 ) . another interesting isophotal feature is related to the cluster triplet ngc220/ngc222/b23 which shows distortions for the small cluster in a direction almost perpendicular to the line connecting itself to the large components ngc220 and ngc222 . this configuration and morphologies are compatible with a fast hyperbolic encounter with small impact parameter ( e.g. fig . 12 of odb98 ) . [ fig : distr_smc ] shows the angular distribution of pairs and multiplets together with smc hi column density isophotes from mathewson & ford ( 1984 ) . it can be seen that most of the objects are concentrated in the smc main body , close to the higher concentration of hi , so it is not unexpected that in general they result young ( sect . 4 ) . the objects appear to be distributed along an axis . such distribution is present in the overall smc cluster sample and there is growing evidence that it is related to a nearly edge - on disk containing the bulk of the young stellar population in the smc ( bica _ et al . _ 1999 , westerlund 1990 ) . a nearly edge - on disk in a low internal reddening galaxy like the smc would imply an increase of projection effects as compared to a simulation such as that carried out by bhatia & hatzidimitriou ( 1988 ) for the nearly face - on lmc disk where the physical pairs would be about 50% . consequently the fraction of physical pairs in the smc would be lower . the present approach including morphological evidence of interaction is an attempt to constrain this aspect . indeed the fraction with isophotal distortions is only 25% ( sect . projection effects can be responsible for the age spread in some multiplets . for example the sextuplet ( table [ tab : interact ] ) has component ages 80 myr ( b72 ) , 200 myr ( h86 - 143 ) , 50 myr ( bs257 ) , 3 myr ( smc - n52a and smc - n52b ) and 400 myr ( h86 - 148 ) . possibly only the 3 or 4 younger components could be related to ob - association h - a35 , the remaining objects would be captures or projection effects . this age spread is also present in ic1611 s quadruplet and in some triplets . on the other hand the quintuplet in the star forming complex ngc395 has all its members with the same age ( 3 myr ) thus forming a physical system . in fig . [ fig : diam_smc ] we show the distribution of the diameter ratio between members for all pairs in the sample . the diameter ratio is mostly in the range @xmath19 , with a peak at @xmath2 indicating that the majority of pair members have a comparable size . this effect was also observed in the lmc ( bhatia et al . 1991 ) . [ fig : separ_smc ] shows the distribution of the centre - to - centre angular separation between pair members . the separation range is @xmath3 @xmath20 arcsec ( @xmath33 - 22 pc ) with a pronounced peak at @xmath3 @xmath21 arcsec ( 13 pc ) . a similar peak was also observed by bhatia et al . ( 1991 ) and de oliveira ( 1996 ) who found a bimodal distribution for the lmc pairs with peaks at @xmath3 5 and 13 pc . the observed upper limit of the projected centre - to - centre linear separation @xmath3 23 pc ( 80 arcsec ) is comparable to bhatia & hatzidimitriou s ( 1988 ) separation criterion for pairs in the lmc ( 18.7 pc ) . the frequent separation value around 13 pc may reflect a preferred survival distance for the systems , combined to projection effects .

they are concentrated in the smc main body . the diameter ratio between the members of a pair is preferentially in the range , with a peak at . the images in this study are based on photographic data obtained using the uk schmidt telescope , which was operated by the royal observatory edinburgh , with funding from the uk science and engineering research council , until 1988 june , and thereafter by the anglo - australian observatory .

an isophotal atlas of 75 star cluster pairs and multiplets in the small magellanic cloud is presented , comprising 176 objects . they are concentrated in the smc main body . the isophotal contours were made from digitized sky survey images and showed relevant structural features possibly related to interactions in about 25% of the sample . previous n - body simulations indicate that such shapes could be due to tidal tails , bridges or common envelopes . the diameter ratio between the members of a pair is preferentially in the range , with a peak at . the projected separation is in the range pc with a pronounced peak at pc . for 91 objects it was possible to derive ages from colour - magnitude diagrams using the ogle - ii photometric survey . the cluster multiplets in general occur in ob stellar associations and/or hii region complexes . this indicates a common origin and suggests that multiplets coalesce into pairs or single clusters in a short time scale . pairs in the smc appear to be mostly coeval and consequently captures are a rare phenomenon . we find evidence that star cluster pairs and multiplets may have had an important role in the dynamical history of clusters presently seen as large single objects . the images in this study are based on photographic data obtained using the uk schmidt telescope , which was operated by the royal observatory edinburgh , with funding from the uk science and engineering research council , until 1988 june , and thereafter by the anglo - australian observatory . original plate material is copyright by the royal observatory edinburgh and the anglo - australian observatory . the plates were processed into the present compressed digital form with their permission . the digitized sky survey was produced at the space telescope science institute under us government grant nag w-2166 . ]

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we presented an isophotal atlas for 75 star cluster pairs and multiplets in the small magellanic cloud , comprising 176 objects . it was possible to derive ages from colour - magnitude diagrams using the ogle - ii photometric survey for 91 objects . in addition we included in the analysis ages for 21 embedded objects in hii regions . the age distribution has a maximum in the youngest bin with a profile related to the cluster formation / destruction rates , in particular cluster multiple systems can have a fast destruction rate caused by their internal dynamical evolution . there is a second peak around 220 myr which is probably related to the smc / lmc last encounter . we find that 55% of the pairs and multiplets in the sample are in general coeval , indicating that captures are a rare phenomenon . most of the cluster multiplets occur in ob stellar associations and/or hii region complexes which indicates a common origin and suggests that multiplets coalesce into pairs or single clusters in a short time scale ( @xmath3 100 myr ) . the majority of the cluster members have comparable sizes , with a diameter ratio ranging mostly between @xmath19 . the projected separation distribution between the members of a pair has a pronounced peak at @xmath3 13 pc . these observational results are important constraints to theoretical models of star cluster pair encounters and could be related with the formation process and subsequent dynamical evolution of cluster systems . the angular distribution of cluster pairs and multiplets shows that most of the objects are located in the smc main body . the overall smc cluster sample presents a similar distribution and there is evidence that it is related to a nearly edge - on disk in the smc . considering this , it is expected an increase of projection effects as compared to estimates for the lmc disk where physical pairs would be about 50% ( bhatia & hatzidimitriou 1988 ) . the atlas shows that around 25% of the isophote maps present relevant structures like bridges , common envelopes or detached distorted isophotes . n - body simulations have indicated that these structures arise from interactions between the members of the cluster systems . indeed cluster pairs as ngc241/ngc242 and b39/bs30 show in their isophotal maps bridges linking their members and have comparable ages . we conclude that multiplicity may have an important role in the early dynamical evolution of star clusters in general , and signatures of that may survive in the long term structure of large single clusters ( de oliveira et al . 2000 ) . grebel e.k . , zaritsky d. , harris j. , 2000 . in _ news views of the magellanic clouds . in : proceedings of the iau symp . 190 _ , eds . you - hua chu , nicholas b. suntzeef , james e. hesser , david a.bohlender ( eds ) . , pasp conf . series , p. 405 .

an isophotal atlas of 75 star cluster pairs and multiplets in the small magellanic cloud is presented , comprising 176 objects . the projected separation is in the range pc with a pronounced peak at pc . for 91 objects it was possible to derive ages from colour - magnitude diagrams using the ogle - ii photometric survey . the cluster multiplets in general occur in ob stellar associations and/or hii region complexes . this indicates a common origin and suggests that multiplets coalesce into pairs or single clusters in a short time scale . pairs in the smc appear to be mostly coeval and consequently captures are a rare phenomenon . we find evidence that star cluster pairs and multiplets may have had an important role in the dynamical history of clusters presently seen as large single objects .

an isophotal atlas of 75 star cluster pairs and multiplets in the small magellanic cloud is presented , comprising 176 objects . they are concentrated in the smc main body . the isophotal contours were made from digitized sky survey images and showed relevant structural features possibly related to interactions in about 25% of the sample . previous n - body simulations indicate that such shapes could be due to tidal tails , bridges or common envelopes . the diameter ratio between the members of a pair is preferentially in the range , with a peak at . the projected separation is in the range pc with a pronounced peak at pc . for 91 objects it was possible to derive ages from colour - magnitude diagrams using the ogle - ii photometric survey . the cluster multiplets in general occur in ob stellar associations and/or hii region complexes . this indicates a common origin and suggests that multiplets coalesce into pairs or single clusters in a short time scale . pairs in the smc appear to be mostly coeval and consequently captures are a rare phenomenon . we find evidence that star cluster pairs and multiplets may have had an important role in the dynamical history of clusters presently seen as large single objects . the images in this study are based on photographic data obtained using the uk schmidt telescope , which was operated by the royal observatory edinburgh , with funding from the uk science and engineering research council , until 1988 june , and thereafter by the anglo - australian observatory . original plate material is copyright by the royal observatory edinburgh and the anglo - australian observatory . the plates were processed into the present compressed digital form with their permission . the digitized sky survey was produced at the space telescope science institute under us government grant nag w-2166 . ]

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a remnant s outermost debris may carry clues about both the chemistry of the progenitor s outer layers and about the dynamics of the sn explosion . our _ hst _ imaging of the cas a remnant has revealed a surprisingly large population of fast - moving ejecta outside of the ne and sw jet regions . these ejecta knots lie coincident with or out beyond the remnant s current forward shock front position ( as seen in x - rays ; see fig . 1 ) and exhibit a wide range of filter flux ratios indicative of a significant chemical diversity , confirmed by spectral data ( figs . while optically emitting debris constitute only a small fraction of the total ejected mass , the remnant s fastest moving material is perhaps best studied optically . for example , the ne and sw jets can be optically traced about 80 arcsec farther out than in radio or x - rays and only a handful of outer ejecta knots around the rest of the remnant are visible in even the deepest radio or x - ray images . on the other hand , outlying ejecta knots are seen in the optical due to their interaction with surrounding ism / csm which generate @xmath12100 km s@xmath2 internal shocks driven into the knot by the high stagnation pressure behind the knot s bow shock . consequently , what one sees may be a biased view of the distribution of outer ejecta . because the visibility of outlying optical knots depends upon whether they have recently encountered local ism / csm clouds or the forward and reverse shock fronts , combining results from different regions around the remnant might lead to a seemingly greater dispersion of chemical abundance variations with radial distance . this , plus the unlikely smooth and spherical expansion of the progenitor s outer layers , make uncertain apparent correlations of outer ejecta kinematic versus chemical properties when summed across the whole remnant . consequently , we restricted the present study to just a relatively small , limited region along the cas a remnant s eastern boundary where the ejecta appear to be interacting with an extended csm cloud . general spectral properties of outer emission knots were determined by the use of filter flux ratios and we have identified three main classes of outer ejecta : 1 ) knots dominated by [ n ii ] @xmath16548,6583 emission ; 2 ) knots dominated by oxygen emission lines especially [ o ii ] @xmath17319,7330 ; and 3 ) knots with emission line strengths much like those seen in the fmks found in the main shell . the histograms shown in figure 5 make a compelling case that , at least for the eastern limb region studied , the emission - line properties and hence likely chemical properties of cas a s highest velocity ejecta correlate fairly well with expansion velocity . because few spectra are available for the nearly 230 outer knots found within our selected eastern limb region , accurate and unambiguous abundance ranges are not possible for the different knot types from the broadband filter measurements . however , the observed range of flux values , when taken together with representative knot spectra ( see fig . 2 ) , offer qualitative estimates on relative nitrogen , oxygen , and sulfur abundances . using the modified @xcite shock code described in @xcite , several models were run for shock speeds of 50 100 km s@xmath2 assuming knot preshock densities @xmath72 @xmath73 . the log of the abundances of oxygen and nitrogen were varied from 14 to 16 ( h = 12.00 ) with a sulfur abundance of 14 and other elements heavier than ne set at or below solar values . these model results indicate that while [ s iii]/[o ii ] is sensitive to shock velocity , the ratio of [ n ii ] @xmath16548,6583/[o ii ] @xmath17319,7330 is fairly independent of shock speed and the abundances of other elements . for n / o abundance ratios of 0.1 and 10 , we found [ n ii]/[o ii ] values of @xmath0 0.5 and @xmath0 100 , respectively . such values suggest that for strong [ n ii ] emission outer knots , i.e. , knots plotted in the uppermost portion of figure 4 such as east 1 and knot 15 and having spectra with [ n ii]/[o ii ] @xmath74 20 ( cf . fig . 2 ) , the n / o abundance ratio exceeds unity indicating a nitrogen overabundance at least an order of magnitude over solar . the highest - velocity ejecta in the east limb region are clearly those with dominate [ n ii ] emission ( see figs . 5 and 6 ) . this fact , when taken together with the presence of n - rich circumstellar material ( qsfs ) and the observed lack of appreciable hydrogen emission in all but a couple of outermost ejecta @xcite support the notion that the cas a progenitor was probably a wn wolf - rayet star that exploded as a core - collapse sn ib event ( fesen et al.1987 , fesen & becker 1991 , vink 2004 ) . although recent estimates for the progenitor mass based on x - ray abundance analysis have difficulty explaining the lack of c - burning products such as ne and mg , the remnant s estimated oxygen mass of 13 m@xmath75 plus the excellent correlation between si , s , ar , and ca abundances suggest a relatively high main sequence mass @xmath0 1525 m@xmath75 @xcite not unlike that expected for a wr star progenitor . for the strong [ o ii ] emission knots , both our shock models as well as the metal - rich shock models presented in @xcite which assumed somewhat lower preshock densities suggest that a near solar abundance ratio for o / s @xmath12 10 yields an observed [ o ii ] @xmath17319,7330/[s ii ] @xmath16716,6731 ratio of around 1 2 and a f775w / f850lp filter ratio of around one ( after correcting for an a@xmath25 = 5 mag and the acs / wfc throughput ) . because [ o ii ] strong knots show f775w / f850lp ratios above 1.5 ( and can exceed 10 ) and are unlikely to have strong [ s ii ] @xmath16716,6731 emission in light of f625w/(f775w + f850lp ) ratios between 0.07 0.5 , such knots appear to possess o / s abundance ratios many times above the solar value . this qualitative assessment is consistent with spectra taken of of such knots , ( e.g. , knot east 2 and knot 17 ; see fig . 2 ) for which only emission lines of oxygen are detected in the 6000 7500 region . our discovery of a significant population of o - rich ejecta outside the forward shock front both here along the eastern limb region and elsewhere around the remnant @xcite may help in understanding the degree and asymmetry of compositional mixing of the cas a sn debris . on the one hand , the very high - velocity si and s rich ejecta in the ne and sw jets plus the presence of highly fe - rich ejecta produced by explosive si burning appearing outside the remnant s si - rich shell along the nw and se limbs has been taken as evidence for large scale turbulence and mixing due to a non - spherical expansion @xcite . this would appear consistent with some core - collapse models which show significant mixing and overturning of ejecta through rayleigh - taylor instabilities @xcite , and which sn 1987a gave direct evidence for in the form of the apparent transport of freshly synthesized @xmath76ni from the core to the h - rich envelope @xcite . however , the presence of a layer of o - rich ejecta knots situated in between the apparent n - rich outer photospheric layer and the s - rich , fmk - like ejecta layer suggests that , at least for this limited eastern limb region away from the remnant s ne and sw jets , cas a s chemical layers do not appear to have been completely mixed or disrupted all the way out to the surface . the outlying o - rich knots we see in cas a exhibit spectral properties not unlike the o - rich ejecta seen in the lmc / smc remnants n132d and 1e 0102.2 - 7219 where there is no evidence supporting mixing of o - rich ejecta with o - burning products , i.e. , si , s , ar , and ca rich ejecta @xcite . this raises questions about just how well mixed were the o - rich and s - rich layers in the cas a sn on both a local and global scale . the degree and uniformity of elemental mixing in cas a has been a long standing question ( chevalier & kirshner 1978 , 1979 ; johnson & yahil 1984 ; winkler et al . 1991 ; douvion et al . 1999 ; hwang et al . 2000 , willingale et al . strong o and s lines in most main shell ejecta knots indicate that substantial mixing of the o - rich and si+s - rich layers did indeed occur . however , there is also compelling evidence that this mixing was neither microscopic nor homogeneous on large scales . some ejecta clumps have optical spectra with nearly only oxygen emission lines visible @xcite , while others have very weak or nearly absent oxygen emissions but unusually strong lines of ca , ar , and s @xcite . compared to the range of [ s ii]/[o ii ] emission line ratios for optical knots in the main shell , there is a fairly constant [ ar iii ] @xmath317136/[s iii ] @xmath319069 ratio suggesting ar and s formed at about a constant ratio from oxygen burning , in sharp contrast to the observed [ o iii ] @xmath315007/[s iii ] @xmath319069 ratio which varies by as much as a factor of 100 . the observed range of ejecta spectral properties could reflect either different degrees of explosive oxygen burning @xcite or varying levels of mixing between outer o - rich material with inner layers of o - burning products @xcite . ne and ar line emission maps made from mid - infrared observations show an anti - correlation between the presence of neon ( which is most abundant in the outermost o - rich layers ) and silicon - rich ejecta pointing to a mixing process that was not homogeneous on large scales ( douvion et al . 1999 ) . the fact that there is no correlation of main shell ejecta abundances with expansion velocity means that there had to be some inversion of the s - rich inner layers relative to the o - rich outer layers @xcite . large scale rayleigh - taylor instability ` fingers ' or incomplete explosive o - burning across different regions might help explain the degree of mixing observed . in and around r - t fingers , considerable mixing would be expected leading to o - rich and s - rich ejecta regions with a lack of element vs. ejection velocity correlation like that observed . @xcite found for a type ib sn model with 4.2 m@xmath75 that r - t instabilities form at the si / o and o / he compositional interfaces . this lead to fragmentations of the fe - rich core and considerable mixing of the inner 2 m@xmath75 which ends up with an expansion velocity as high as 3500 5500 km s@xmath2 . however , this velocity is less than that seen in cas a and nearly pure fe - rich material out beyond the si - rich layers in cas a s nw and se sections @xcite would seem more consistent with a picture of strong but only regional overturning . @xcite also noted that the pattern of r - t overturning carries information about the geometry of neutrino - driven convection that seeds the r - t instabilities . if that is true , then the observed @xmath77 angular size of the fe - rich areas in cas a may be indicating the rough scale of such neutrino - driven convection seeds . on the other hand , high - velocity ( v = @xmath78 km s@xmath2 ) n - rich and o - rich ejecta at projected locations along the eastern limb out beyond the remnant s fastest moving fe - rich x - ray emission material ( 6000 km s@xmath2 ) show that even though fe - rich core fragments apparently penetrated the s + si - rich mantle ejecta layer , they did not expand past the n or o - rich outer layers as happened in sn 1987a . thus in cas a , at some distance radially above the r - t finger instabilities , the he + n - rich and o - rich layering structure appears to have survived largely intact . a nitrogen - oxygen - iron layering can be seen in figure 7 where the majority of optical n - rich and o - rich knots lie in projection ahead of the fe - rich ejecta detected in the x - rays . while not lying exactly in the plane of the sky , this fe - rich material is seen to extend out to a maximum radius of @xmath79 , in this region , corresponding to an average expansion velocity of around @xmath80 km s@xmath2 . de - projection of its observed radial velocity of @xmath81 to @xmath82 km s@xmath2 @xcite would only move it a few arcseconds farther eastward , insufficient to extend it out beyond either the n - rich or o - rich outer ejecta knots which lie at radial distances of @xmath83 and @xmath84 , respectively ( see fig . @xcite and @xcite comment that any fe - rich debris ejected farther out than seen in the _ chandra _ image would have encountered the reverse shock at an earlier epoch and thus could have cooled down below the x - ray emitting temperature range . however , the coincidence of the inner edge of the o - rich ejecta we have detected with the outermost fe - rich x - ray emitting material seen in _ chandra _ fe k image is striking ( left panel , fig . 7 ) suggesting that we re seeing most of the fastest - moving fe - rich material in this region . this holds true for the cooler fe l emission as well which has about the same spatial distribution and extent as that of fe k @xcite . however , there may be a causal relation between fe - rich ejecta and formation of these outlying ejecta knots . as can been seen from figure 7 , the projected space density of the outer optical ejecta knots may be correlated with the outermost fe - rich x - ray emitting ejecta . for example , the cluster of optical knots around knot e2 lies at the easternmost tip of the detected fe - rich x - ray emission , with the number of knots showing a noticeable decline to both the north and south . without knot radial velocity information , one can not test if such projected correlations are in fact spatially real , yet the coincidences seen here are intriguing . while radially limited layer mixing may explain the abundance pattern seen along the remnant s east limb , this process clearly did not operate in the ne and sw jet regions . thus the global picture of the cas a sn explosion which emerges is one of regional and radially limited overturning of mantle and core material . added to this scenario are the seemingly opposing ne and sw jets of much higher velocity ejecta , rich in explosive o - burning products , whose nature is not well understood . this all created the fairly complex sn remnant ejecta structure exhibiting regionally diverse abundance mixing patterns we observe today .

acs filter flux ratios along with follow - up , ground - based spectra are used to investigate some of the kinematic and chemical properties of these outermost ejecta . in this paper , we concentrate on a.5 sq arcmin region located along the eastern limb of the remnant where numerous outer emission knots are optically visible due to an interaction with a local circumstellar cloud , thereby providing a more complete and unbiased look at the remnant s fastest debris fragments . from a study of this region , we identify three main classes of outer ejecta : 1 ) knots dominated by [ n ii ],6583 emission ; 2 ) knots dominated by oxygen emission lines especially [ o ii ],7330 ; and 3 ) knots with emission line strengths similar to the [ s ii ] strong fmk ejecta commonly seen in the main emission shell . chandra _ and _ xmm _ data along the eastern limb .

analysis of broadband _ hst _ acs and wfpc2 images of the young galactic supernova remnant cassiopeia a reveals a far larger population of outlying , high - velocity knots of ejecta with a broader range of chemical properties than previously suspected . acs filter flux ratios along with follow - up , ground - based spectra are used to investigate some of the kinematic and chemical properties of these outermost ejecta . in this paper , we concentrate on a.5 sq arcmin region located along the eastern limb of the remnant where numerous outer emission knots are optically visible due to an interaction with a local circumstellar cloud , thereby providing a more complete and unbiased look at the remnant s fastest debris fragments . from a study of this region , we identify three main classes of outer ejecta : 1 ) knots dominated by [ n ii ],6583 emission ; 2 ) knots dominated by oxygen emission lines especially [ o ii ],7330 ; and 3 ) knots with emission line strengths similar to the [ s ii ] strong fmk ejecta commonly seen in the main emission shell . we identified a total of 69 [ n ii ] , 40 [ o ii ] , and 120 [ s ii ] knots in the small eastern limb region studied . mean transverse velocities derived from observed proper motion for 63 n - rich , 37 o - rich , and 117 fmk - like knots identified in this region were found to be 8100 , 7900 , and 7600 km s , respectively . the discovery of a significant population of o - rich ejecta situated in between the suspected n - rich outer photospheric layer and s - rich fmk - like ejecta suggests that the cas a progenitor s chemical layers were not completely disrupted by the supernova explosion outside of the remnant s ne and sw high velocity ` jet ' regions . in addition , we find the majority of o - rich outer ejecta at projected locations out beyond ( v = km s ) the remnant s fastest moving fe - rich x - ray emission material ( 6000 km s ) seen in _ chandra _ and _ xmm _ data along the eastern limb . this suggests that penetration of fe - rich material up through the s and si - rich mantle did not extend past the progenitor s n or o - rich outer layers for at least this section of the remnant .

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we present an analysis of broadband _ hst _ acs and wfpc2 images of the young galactic supernova remnant cassiopeia a , and concentrate specifically on a @xmath01.5 sq arcmin region located along the easternmost limb of the remnant . this region exhibits numerous outer emission knots that are optically visible due to an apparent interaction with a local circumstellar cloud , and therefore provide a more complete and unbiased look at the remnant s fastest debris fragments . calibrated acs filter flux ratios along with follow - up , ground - based spectra were used to investigate some of the kinematic and chemical properties of these outermost ejecta . these data revealed the following : \1 ) a substantial population of outlying , high - velocity ejecta knots exists around the remnant which exhibit a broader range of chemical properties than previously recognized . based on the outlying knots found in the east limb region , we identify three main classes of outer ejecta : a ) knots dominated by [ n ii ] @xmath16548,6583 emission , b ) knots dominated by oxygen emission lines especially [ o ii ] @xmath17319,7330 , and c ) ejecta with emission line strengths similar to the common [ s ii ] strong fmk ejecta of the main shell . mean transverse velocities derived from observed proper motion for 63 n - rich , 37 o - rich , and 117 fmk - like knots found in this region are 8100 , 7900 , and 7600 km s@xmath2 , respectively . \2 ) the discovery of a significant population of o - rich ejecta situated in between the suspected n - rich outer photospheric layer and s - rich fmk - like ejecta suggests that the cas a progenitor s chemical layers were not completely disrupted by the supernova explosion outside of the remnant s ne and sw high velocity ` jet ' regions . \3 ) we find that most o - rich outer ejecta along the remnant s eastern limb lie at projected locations out beyond ( v = @xmath3 km s@xmath2 ) the remnant s fastest moving fe - rich x - ray emission material ( 6000 km s@xmath2 ) along the eastern limb . this suggests that penetration of fe - rich material up through the s and si - rich mantle did generally not extend past the progenitor s n or o - rich outer layers as had been previously assumed . the chemical and dynamical picture of cas a that emerges is one of large , regional overturning involving both mantle and core material , separated by areas where the initial he + n - rich , o - rich , and si + s - rich layering survived fairly intact . this generated a fairly complex remnant structure with numerous clumps of reverse shocked ejecta showing a wide diversity of chemical abundances . future investigations of the cas a remnant using this _ hst _ image data set will include a full catalog of all optically visible outlying ejecta knots , analysis of the remnant s ejecta expansion asymmetries , and knot emission variability and ablation effects due to high speed passage through the local ism / csm . we thank p. hoeflich for helpful discussions , d. patnaude for help with the chandra x - ray data reduction , and j. thorstensen for assistance with the celestial coordinate transformations . this work was supported by nasa through grants go-8281 , go-9238 , go-9890 , and go-10286 to raf and jm from the space telescope science institute , which is operated by the association of universities for research in astronomy . rac is supported by nsf grant ast-0307366 and clg is supported through uk pparc grant ppa / g / s/2003/00040 . arnett , d. , fryxell , b. , & mueller , e. 1989 , , 341 , l63 bertin , e. , & arnouts , s. 1996 , , 117 , 393 blair , w. p. , morse , j. a. , raymond , j. c. , kirshner , r. p. , hughes , j. p. , dopita , m. a. , sutherland , r. s. , long , k. s. , & winkler , p. f. 2000 , , 537 , 667 chevalier , r. a. , & kirshner , r. p. 1978 , , 219 , 931 chevalier , r. a. , & kirshner , r. p. 1979 , , 233 , 154 delaney , t. , & rudnick , l. 2004 , advances in space research , 33 , 422 douvion , t. , lagage , p. o. , & cesarsky , c. j. 1999 , , 352 , l111 fabian , a. c. , willingale , r. , pye , j. p. , murray , s. s. , & fabbiano , g. 1980 , , 193 , 175 fesen , r. a. 2001 , , 133 , 161 fesen , r. a. , morse , j. a. , chevalier , r. a. , borkowski , k. j. , gerardy , c. l. , lawrence , s. s. , & van den bergh , s. 2001 , , 122 , 2644 fesen , r. a. , & becker , r. h. 1991 , , 371 , 621 fesen , r. a. , becker , r. h. , & blair , w. p. 1987 , , 313 , 378 fesen , r. a. , & gunderson , k. s. 1996 , , 470 , 967 ford , h. c. , et al . 1998 , proc . spie , 3356 , 234 garca - segura , g. , langer , n. , & mac low , m 1996 , , 316 , 133 gotthelf , e. v. , koralesky , b. , rudnick , l. , jones , t. w. , hwang , u. , & petre , r. 2001 , , 552 , l39 hammell , m. c. , & fesen , r. a. 2006 , in preparation hughes , j. p. , rakowski , c. e. , burrows , d. n. , & slane , p. o. 2000 , , 528 , l109 hurford , a. p. , & fesen , r. a. 1996 , , 469 , 246 hwang , u. , holt , s. s. , & petre , r. 2000 , 537 , l119 hwang , u. , & laming , j. m. 2003 , , 597 , 362 hwang , u. , et al . 2004 , , 615 , l117 kamper , k. & van den bergh , s. 1976 , , 32 , 351 kifonidis , k. , plewa , t. , janka , h .- t . , & m " uller , e. 2000 , , 531 , l123 kifonidis , k. , plewa , t. , janka , h .- , & m " uller , e. 2003 , , 408 , 621 kirshner , r. . , & chevalier , r. a. 1977 , , 218 , 142 laming , j. m. , & hwang , u. 2003 , , 597 , 347 laming , j. m. , & hwang , u. 2005 , , 298 , 33 langer , n. , & el eid , m. f. 1986 , , 167 , 265 lawrence , s. s. , macalpine , g. m. , uomoto , a. , woodgate , b. e. , brown , l. w. , oliversen , r. j. , lowenthal , j. d. , & liu , c. 1995 , , 109 , 2635 massey , p. , & gronwald , c. 1990 , , 358 , 344 minkowski , r. 1968 , in `` stars and stellar systems '' , 7 , 623 morse , j. a. , fesen , r. a. , chevalier , r. a. , borkowski , k. j. , gerardy , c. l. , lawrence , s. s. , & van den bergh , s. 2004 , , 614 , 727 pavlovsky , c. , et al . `` acs instrument handbook '' , version 5.0 , ( baltimore : stsci ) peimbert , m. , & van den bergh , s. 1971 , , 167 , 223 raymond , j. c. 1979 , , 39 , 1 reed , j. e. , hester , j. j. , fabian , a. c. , & winkler , p. f. 1995 , , 440 , 706 reynoso , e. m. , & goss , w. m. 2002 , , 575 , 871 sirianni , m. , et al . 2005 , preprint ( astro - ph/0507614 ) thorstensen , j. r. , fesen , r. a. , & van den bergh , s. 2001 , , 122 , 297 van den bergh , s. 1971 , , 165 , 457 van den bergh , s. , & dodd , w. w. 1970 , , 162 , 485 vink , j. , bloemen , h. , kaastra , j. s. , bleeker , j. a. m. 1998 , , 339 , 201 vink , j. 2004 , new astronomy review , 48 , 61 willingale , r. , bleeker , j. a. m. , van der heyden , k. j. , kaastra , j. s. , & vink , j. 2002 , , 381 , 1039 willingale , r. , bleeker , j. a. m. , van der heyden , k. j. , & kaastra , j. s. 2003 , , 398 , 1021 winkler , p. f. , roberts , p. f. , kirshner , r. p. 1991 , in `` supernovae : the tenth santa cruz summer workshop in astronomy and astrophysics '' , ed . woosley ( springer - verlag : new york ) , p 652 woosley , s. e. , langer , n. , & weaver , t. a. 1993 , , 411 , 823 woosley , s. e. , & weaver , t. a. 1995 , , 448 , 315 lcclccc f625w & @xmath85 s & 54507100 & [ o i ] 6300,6364 & 0.42 & 39 & 16 + ( sdss r ) & & & [ s ii ] 6716,6731 & 0.44 & 100 & 44 + & & & [ n ii ] 6548,6583 & 0.43 & 0 & 0 + & & & & & & + f775w & @xmath27 s & 68508600 & [ ar iii ] 7136 & 0.38 & 41 & 15 + ( sdss i ) & & & [ o ii ] 7319,7320 & 0.42 & 171 & 72 + & & & [ ar iii ] 7751 & 0.38 & 14 & 5 + & & & & & + f850lp & @xmath27 s & 850010500 & [ s iii ] 9069 & 0.20 & 210 & 42 + ( sdss z ) & & & [ s iii ] 9531 & 0.14 & 600 & 85 + & & & [ s ii ] 1028710370 & 0.05 & 380 & 19 + lcccccccc [ o i ] 6300,6364 & 55 & 39 & 29 & 152 & 157 & 7 & @xmath865 & 22 + [ n ii ] 6548,6583 & @xmath871 & @xmath871 & @xmath871 & @xmath871 & @xmath871 & 130 & 100 & @xmath868 + [ s ii ] 6716,6731 & 100 & 100 & 100 & 100 & 100 & 62 & @xmath865 & @xmath868 + [ o ii ] 7319,7330 & 275 & 171 & 104 & 1530 & 112 & 33 & @xmath865 & 100 + [ s iii ] 9069,9531 & 689 & 810 & 440 & 1190 & 558 & & & + & & & & & & & & + f625w ( f1 ) & 67 & 60 & 56 & 108 & 55 & 100 & 100 & 100 + f775w ( f2 ) & 134 & 92 & 55 & 673 & 58 & 24 & @xmath868 & 253 + f850lp ( f3 ) & 135 & 146 & 78 & 234 & 103 & 78 & @xmath8610 & 30 + & & & & & & & & + f625w / f775w & 0.50 & 0.65 & 1.00 & 0.16 & 0.95 & 4.17 & @xmath4112.0 & 0.40 + f775w / f850lp & 1.02 & 0.63 & 0.71 & 2.88 & 0.56 & 0.31 & @xmath00.80 & 8.34 + f625w / f850lp & 0.49 & 0.41 & 0.72 & 0.46 & 0.53 & 1.28 & @xmath4110.0 & 3.30 + f1/(f2 + f3 ) & 0.25 & 0.25 & 0.42 & 0.11 & 0.34 & 0.98 & @xmath415.5 & 0.35 +

we identified a total of 69 [ n ii ] , 40 [ o ii ] , and 120 [ s ii ] knots in the small eastern limb region studied . mean transverse velocities derived from observed proper motion for 63 n - rich , 37 o - rich , and 117 fmk - like knots identified in this region were found to be 8100 , 7900 , and 7600 km s , respectively . the discovery of a significant population of o - rich ejecta situated in between the suspected n - rich outer photospheric layer and s - rich fmk - like ejecta suggests that the cas a progenitor s chemical layers were not completely disrupted by the supernova explosion outside of the remnant s ne and sw high velocity ` jet ' regions . in addition , we find the majority of o - rich outer ejecta at projected locations out beyond ( v = km s ) the remnant s fastest moving fe - rich x - ray emission material ( 6000 km s ) seen in _ this suggests that penetration of fe - rich material up through the s and si - rich mantle did not extend past the progenitor s n or o - rich outer layers for at least this section of the remnant .

analysis of broadband _ hst _ acs and wfpc2 images of the young galactic supernova remnant cassiopeia a reveals a far larger population of outlying , high - velocity knots of ejecta with a broader range of chemical properties than previously suspected . acs filter flux ratios along with follow - up , ground - based spectra are used to investigate some of the kinematic and chemical properties of these outermost ejecta . in this paper , we concentrate on a.5 sq arcmin region located along the eastern limb of the remnant where numerous outer emission knots are optically visible due to an interaction with a local circumstellar cloud , thereby providing a more complete and unbiased look at the remnant s fastest debris fragments . from a study of this region , we identify three main classes of outer ejecta : 1 ) knots dominated by [ n ii ],6583 emission ; 2 ) knots dominated by oxygen emission lines especially [ o ii ],7330 ; and 3 ) knots with emission line strengths similar to the [ s ii ] strong fmk ejecta commonly seen in the main emission shell . we identified a total of 69 [ n ii ] , 40 [ o ii ] , and 120 [ s ii ] knots in the small eastern limb region studied . mean transverse velocities derived from observed proper motion for 63 n - rich , 37 o - rich , and 117 fmk - like knots identified in this region were found to be 8100 , 7900 , and 7600 km s , respectively . the discovery of a significant population of o - rich ejecta situated in between the suspected n - rich outer photospheric layer and s - rich fmk - like ejecta suggests that the cas a progenitor s chemical layers were not completely disrupted by the supernova explosion outside of the remnant s ne and sw high velocity ` jet ' regions . in addition , we find the majority of o - rich outer ejecta at projected locations out beyond ( v = km s ) the remnant s fastest moving fe - rich x - ray emission material ( 6000 km s ) seen in _ chandra _ and _ xmm _ data along the eastern limb . this suggests that penetration of fe - rich material up through the s and si - rich mantle did not extend past the progenitor s n or o - rich outer layers for at least this section of the remnant .

1103.3244

i

the search for supersymmetry and its breaking , in addition to the direct searches at lep , b - factories , tevatron and the large hadron collider ( lhc ) , is actively pursued using the wmap limits on the relic density constraints . however the sensitivity of the lightest supersymmetric particle relic density calculation to the variation of the cosmological expansion rate before big - bang nucleosynthesis ( bbn ) , even if modest and with no consequences on the cosmological observations , can modify considerably the relic density , and therefore change the constraints on the supersymmetric parameter space @xcite . in the standard cosmology the dominant component before bbn is radiation , however energy density and entropy content can be modified . in the following we consider the impact of different scenarios of alternative cosmologies . the precision of the wmap data should therefore not make us forget the hypothesis which are implied by the use of standard cosmology . we discuss in the following the implications of precision b - physics , direct searches and cold dark matter relic abundance for the case of anomaly mediated models , from a minimal anomaly mediation supersymmetry breaking @xcite , to mixed moduli - anomaly mediated @xcite and to hypercharge anomaly mediation @xcite . we also discuss similar supersymmetry breaking scenarios in the case of the next - to - minimal supersymmetric standard model . in section [ sec : models ] we discuss the different anomaly mediated supersymmetry breakings in the minimal supersymmetric standard model ( mssm ) in terms of the parameter spaces for these models and discuss the limits which can be applied due to the present data from particle physics experiments and from relic dark matter density assuming the standard model of cosmology . in section [ sec : models2 ] similar scenarios are considered in the next - to - minimal supersymmetric standard model ( nmssm ) and the corresponding particle and cosmological bounds are discussed . in section [ sec : cosmologies ] we discuss how alternative cosmological models can affect dramatically the bounds on the parameter space of the models we have considered while letting unchanged the observable cosmology . four different alternatives to the standard cosmology are discussed which share this behaviour . section [ sec : constr ] and section [ sec : lhc ] discuss respectively the constraints implied by these different cosmological scenarios and the perspectives at the lhc for a list of benchmark points which are representative of the available parameter space for these amsb models . our conclusions are given in section [ sec : conclusion ] .

apart from limits coming from flavour , low energy physics and direct collider searches , these models are usually constrained by the requirement of reproducing the observations on dark matter density in the universe . we reanalyse these bounds and in particular we focus on the dark matter bounds both considering the standard cosmological model and alternative cosmological scenarios . we also discuss briefly the implications for phenomenology and in particular at the large hadron collider . cern - ph - th-2011 - 052 + lycen 2011 - 01 * anomaly mediated susy breaking scenarios in the light of cosmology and in the dark ( matter ) * a. arbey , a. deandrea and a. tarhini + _ universit de lyon , france ; universit lyon 1 , cnrs / in2p3 , umr5822 ipnl , f-69622 villeurbanne cedex , france _ + + +

anomaly mediation is a popular and well motivated supersymmetry breaking scenario . different possible detailed realisations of this set - up are studied and actively searched for at colliders . apart from limits coming from flavour , low energy physics and direct collider searches , these models are usually constrained by the requirement of reproducing the observations on dark matter density in the universe . we reanalyse these bounds and in particular we focus on the dark matter bounds both considering the standard cosmological model and alternative cosmological scenarios . these scenarios do not change the observable cosmology but relic dark matter density bounds strongly depend on them . we consider few benchmark points excluded by standard cosmology dark matter bounds and suggest that loosening the dark matter constraints is necessary in order to avoid a too strong ( cosmological ) model dependence in the limits that are obtained for these models . we also discuss briefly the implications for phenomenology and in particular at the large hadron collider . cern - ph - th-2011 - 052 + lycen 2011 - 01 * anomaly mediated susy breaking scenarios in the light of cosmology and in the dark ( matter ) * a. arbey , a. deandrea and a. tarhini + _ universit de lyon , france ; universit lyon 1 , cnrs / in2p3 , umr5822 ipnl , f-69622 villeurbanne cedex , france _ + + +

1103.3244

c

we have considered in details the constraints on different possible realisations of superconformal anomaly mediation breaking mechanisms in supersymmetry . these constraints include the usual lep , b - factories , tevatron and lhc searches , but also precision constraints of cosmological origin , namely the wmap limits on the relic density of cold dark matter . we have discussed the standard cosmological approach and also alternative cosmological scenarios which do not change the cosmological observations but which can affect strongly the constraints on the parameter space of these supersymmetric models based on the relic abundance of dark matter . we therefore show how the dark matter constraints can be weakened in order to avoid strong model dependent assumptions in the choice of the cosmological model . based on different benchmark points for amsb models , we performed a detailed analysis of the constraints imposed by particle data and cosmology ( both standard and alternative ) and finally we gave the typical mass spectra and decay modes relevant for the lhc searches . the main lesson that can be learnt in such an exercice is that usual bounds on the parameter space of these models are too restrictive and bear a strong hidden cosmological model dependence in the assumption of the standard cosmological scenario . concerning the lhc searches , points which are excluded in the standard analysis but permitted in this more general approach , may be quite relevant for testing not only the particle theory models themselves but also alternative cosmological scenarios at the lhc , as in many cases relatively low mass supersymmetric particles are allowed with a peculiar spectrum where the lightest neutralino and chargino are very close in mass . 99 a. arbey and f. mahmoudi , `` susy constraints from relic density : high sensitivity to pre - bbn expansion rate , '' phys . b * 669 * ( 2008 ) 46 [ arxiv:0803.0741 ] . a. arbey and f. mahmoudi , `` susy constraints , relic density , and very early universe , '' jhep * 1005 * ( 2010 ) 051 [ arxiv:0906.0368 ] ; a. arbey and f. mahmoudi , `` lhc and ilc data and the early universe properties , '' nuovo cim . c * 33 * ( 2010 ) 151 [ arxiv:1002.4096 ] . l. randall and r. sundrum , `` out of this world supersymmetry breaking , '' nucl . b * 557 * ( 1999 ) 79 [ hep - th/9810155 ] ; g.f . giudice , m.a . luty , h. murayama and r. rattazzi , `` gaugino mass without singlets , '' jhep * 9812 * ( 1998 ) 027 [ hep - ph/9810442 ] ; a. pomarol and r. rattazzi , `` sparticle masses from the superconformal anomaly , '' jhep * 9905 * ( 1999 ) 013 [ hep - ph/9903448 ] ; d.w . jung and j.y . lee , `` anomaly - mediated supersymmetry breaking demystified , '' jhep * 0903 * ( 2009 ) 123 [ arxiv:0902.0464 ] . k. choi , k.s . jeong and k.i . okumura , `` phenomenology of mixed modulus - anomaly mediation in fluxed string compactifications and brane models , '' jhep * 0509 * ( 2005 ) 039 [ hep - ph/0504037 ] . r. dermisek , h. verlinde and l.t . wang , `` hypercharged anomaly mediation , '' phys . * 100 * ( 2008 ) 131804 [ arxiv:0711.3211 ] . h. baer , r. dermisek , s. rajagopalan and h. summy , `` neutralino , axion and axino cold dark matter in minimal , hypercharged and gaugino amsb , '' jcap * 1007 * ( 2010 ) 014 [ arxiv:1004.3297 ] . f. e. paige , s. d. protopopescu , h. baer and x. tata , `` isajet 7.69 : a monte carlo event generator for p p , anti - p p , and e+ e- reactions , '' hep - ph/0312045 . f. mahmoudi , `` superiso : a program for calculating the isospin asymmetry of @xmath143 in the mssm , '' comput . commun . * 178 * ( 2008 ) 745 [ arxiv:0710.2067 ] ; f. mahmoudi , `` superiso v2.3 : a program for calculating flavor physics observables in supersymmetry , '' comput . commun . * 180 * ( 2009 ) 1579 [ arxiv:0808.3144 ] ; ` http://superiso.in2p3.fr ` f. mahmoudi , `` superiso v3.0 , flavor physics observables calculations : extension to nmssm , '' comput . commun . * 180 * ( 2009 ) 1718 , ` http://superiso.in2p3.fr ` a. arbey and f. mahmoudi , `` superiso relic : a program for calculating relic density and flavor physics observables in supersymmetry , '' comput . phys . commun . * 181 * ( 2010 ) 1277 [ arxiv:0906.0369 ] , ` http://superiso.in2p3.fr/relic ` f. mahmoudi , `` new constraints on supersymmetric models from @xmath144 , '' jhep * 0712 * ( 2007 ) 026 [ arxiv:0710.3791 ] . cdf collaboration , `` search for @xmath145 and @xmath146 decays in 3.7 fb@xmath147 of @xmath148 collisions with cdf ii , '' cdf public note * 9892 * ( 2009 ) . a. g. akeroyd and f. mahmoudi , `` constraints on charged higgs bosons from @xmath149 and @xmath150 , '' jhep * 0904 * ( 2009 ) 121 [ arxiv:0902.2393 ] . m. antonelli _ et al . _ [ flavianet working group on kaon decays ] , `` precision tests of the standard model with leptonic and semileptonic kaon decays , '' arxiv:0801.1817 [ hep - ph ] . e. komatsu _ et al . _ [ wmap collaboration ] , `` seven - year wilkinson microwave anisotropy probe ( wmap ) observations : cosmological interpretation , '' astrophys . j. suppl . * 192 * ( 2011 ) 18 [ arxiv:1001.4538 ] . h. baer , r. dermisek , s. rajagopalan and h. summy , `` prospects for hypercharged anomaly mediated susy breaking at the lhc , '' jhep * 0910 * ( 2009 ) 078 [ arxiv:0908.4259 ] . h. baer , e.k . park , x. tata and t.t . wang , `` collider and dark matter searches in models with mixed modulus - anomaly mediated susy breaking , '' jhep * 0608 * ( 2006 ) 041 [ hep - ph/0604253 ] . for recent reviews , see : m. maniatis , `` the next - to - minimal supersymmetric extension of the standard model reviewed , '' int . j. mod . phys . a * 25 * ( 2010 ) 3505 [ arxiv:0906.0777 ] ; u. ellwanger , c. hugonie and a.m. teixeira , `` the next - to - minimal supersymmetric standard model , '' phys . * 496 * ( 2010 ) 1 [ arxiv:0910.1785 ] . u. ellwanger and c. hugonie , `` nmspec : a fortran code for the sparticle and higgs masses in the nmssm with gut scale boundary conditions , '' comput . commun . * 177 * ( 2007 ) 399 [ hep - ph/0612134 ] . p. gondolo and g. gelmini , `` cosmic abundances of stable particles : improved analysis , '' nucl . b * 360 * ( 1991 ) 145 ; j. edsjo and p. gondolo , `` neutralino relic density including coannihilations , '' phys . rev . d * 56 * ( 1997 ) 1879 [ hep - ph/9704361 ] . p. salati , `` quintessence and the relic density of neutralinos , '' phys . b * 571 * ( 2003 ) 121 [ astro - ph/0207396 ] . a. arbey , in preparation , ` http://superiso.in2p3.fr/relic/alterbbn ` . g.b . gelmini and p. gondolo , `` neutralino with the right cold dark matter abundance in ( almost ) any supersymmetric model , '' phys . d * 74 * ( 2006 ) 023510 [ hep - ph/0602230 ] . g. gelmini , p. gondolo , a. soldatenko and c.e . yaguna , `` the effect of a late decaying scalar on the neutralino relic density , '' phys . d * 74 * ( 2006 ) 083514 [ hep - ph/0605016 ] . gelmini and p. gondolo , `` neutralino with the right cold dark matter abundance in ( almost ) any supersymmetric model , '' phys . d * 74 * ( 2006 ) 023510 [ hep - ph/0602230 ] . g. gelmini , p. gondolo , a. soldatenko and c.e . yaguna , `` the effect of a late decaying scalar on the neutralino relic density , '' phys . d * 74 * ( 2006 ) 083514 [ hep - ph/0605016 ] . n. okada and o. seto , `` relic density of dark matter in brane world cosmology , '' phys . d * 70 * ( 2004 ) 083531 [ hep - ph/0407092 ] . k. jedamzik , `` big bang nucleosynthesis constraints on hadronically and electromagnetically decaying relic neutral particles , '' phys . rev . d * 74 * ( 2006 ) 103509 [ hep - ph/0604251 ] . w. beenakker , m. klasen , m. kramer , t. plehn , m. spira and p.m. zerwas , `` the production of charginos / neutralinos and sleptons at hadron colliders , '' phys . * 83 * ( 1999 ) 3780 [ erratum - ibid . * 100 * ( 2008 ) 029901 ] [ hep - ph/9906298 ] . h. baer and x. tata , `` probing charginos and neutralinos beyond the reach of lep at the tevatron collider , '' phys . d * 47 * ( 1993 ) 2739 . h. baer , c.h . chen , f. paige and x. tata , `` trileptons from chargino - neutralino production at the cern large hadron collider , '' phys . d * 50 * ( 1994 ) 4508 [ hep - ph/9404212 ] .

different possible detailed realisations of this set - up are studied and actively searched for at colliders . these scenarios do not change the observable cosmology but relic dark matter density bounds strongly depend on them . we consider few benchmark points excluded by standard cosmology dark matter bounds and suggest that loosening the dark matter constraints is necessary in order to avoid a too strong ( cosmological ) model dependence in the limits that are obtained for these models .

anomaly mediation is a popular and well motivated supersymmetry breaking scenario . different possible detailed realisations of this set - up are studied and actively searched for at colliders . apart from limits coming from flavour , low energy physics and direct collider searches , these models are usually constrained by the requirement of reproducing the observations on dark matter density in the universe . we reanalyse these bounds and in particular we focus on the dark matter bounds both considering the standard cosmological model and alternative cosmological scenarios . these scenarios do not change the observable cosmology but relic dark matter density bounds strongly depend on them . we consider few benchmark points excluded by standard cosmology dark matter bounds and suggest that loosening the dark matter constraints is necessary in order to avoid a too strong ( cosmological ) model dependence in the limits that are obtained for these models . we also discuss briefly the implications for phenomenology and in particular at the large hadron collider . cern - ph - th-2011 - 052 + lycen 2011 - 01 * anomaly mediated susy breaking scenarios in the light of cosmology and in the dark ( matter ) * a. arbey , a. deandrea and a. tarhini + _ universit de lyon , france ; universit lyon 1 , cnrs / in2p3 , umr5822 ipnl , f-69622 villeurbanne cedex , france _ + + +

astro-ph0510527

i

`` debris disks '' surrounding young stars are composed of optically thin dust ( see the reviews by artymowicz 2000 ; lagrange , backman , & artymowicz 2000 ; zuckerman 2001 ) . most debris disks are inferred to exist from measurements of infrared excesses ( e.g. , aumann et al . 1984 ; habing et al . 2001 ; zuckerman & song 2004 ) . a few disks are close enough to resolve in images , either in scattered starlight ( e.g. , smith & terrile 1984 ; schneider et al . 1999 ; kalas , graham , & clampin 2005 ) or in thermal emission ( e.g. , telesco et al . 2000 ; greaves et al . 2004 ) . is the observed dust primordial the remains of an optically thick , gas - rich disk from a previous herbig ae or t tauri phase ? or is it maintained in equilibrium continuously removed by processes such as poynting - robertson drag and replenished by the comminution of larger , colliding parent bodies ? a third possibility is that the observed dust represents the transient aftermath of recent cataclysmic events . dust might be freshly generated , unequilibrated debris from the catastrophic destruction of large planetesimals ( su et al . 2005 ; song et al . 2005 ) . the debris disk encircling the young m dwarf au microscopii is a promising place to investigate these questions . it is well resolved in scattered light from optical to near - infrared wavelengths ( kalas , liu , & matthews 2004 ; krist et al . 2005 , hereafter k05 ; liu 2004 ; metchev et al . 2005 ) . of central relevance to our study is the disk s surface brightness profile . within a projected distance @xmath0 from the star of 43 au , the surface brightness sb falls approximately as @xmath14 ( k05 ) . we refer to this region as the `` inner disk . '' outside 43 au , in the `` outer disk , '' the slope of the profile changes dramatically : sb @xmath15 ( k05 ) . this break is observed independently by other researchers ( liu 2004 ; metchev et al . the shape of the profile is all the more significant because it resembles that of the debris disk surrounding @xmath16 pictoris @xcite , and of the recently discovered disk encompassing hd 139664 @xcite . au mic s disk is also detected in unresolved thermal emission @xcite . the disk s infrared spectrum peaks at a wavelength of @xmath17@xmath18 and exhibits no excess at @xmath19 ; this behavior suggests that the disk contains an inner hole @xcite . here we offer a theory that explains these observations quantitatively . the reason why the surface brightness profile breaks at 43 au is that a narrow ring of parent bodies , analogous to the solar system s kuiper belt , orbits the star at a stellocentric radius @xmath20 . the subscript `` br '' refers to our term for the belt of parent bodies , the `` birth ring , '' wherein micron - sized dust grains are born through collisions of larger planetesimals . grain creation is balanced in steady state by destructive grain - grain collisions and removal by corpuscular and poynting - robertson ( cpr ) drag . ] corpuscular drag exerted by the young m dwarf s wind is probably at least a few times more effective at removing dust than poynting - robertson drag in the au mic system , a possibility first pointed out by plavchan , jura , & lipscy ( 2005 , hereafter pjl05 ) . the outer disk comprises grains that are only tenuously bound , moving on orbits rendered highly eccentric by stellar wind and radiation forces ( e.g. , lecavelier des etangs et al . 1996 ; augereau et al . these barely bound grains dominate scattering of starlight in the outer disk . by contrast , unbound grains escape the system too quickly for their steady - state population to contribute appreciably to the surface brightness . the inner disk is populated by grains that migrate inward by cpr drag quickly enough to evade collisional destruction . in cpr - dominated ( what we refer to as `` type a '' ) disks , a large fraction of grains meets this condition , unlike in collision - dominated ( `` type b '' ) disks . similar classifications were put forward by @xcite and @xcite in their considerations of disks composed of single - sized grains . we calculate simultaneously the steady - state spatial and size distributions of dust particles , and derive how the outer disk s optical depth scales with radius for type a and type b disks . our analysis accounts for destructive grain - grain collisions and the detailed dynamics of cpr drag , which reduces not only the orbital semi - major axes of grains but also their orbital eccentricities ( wyatt & whipple 1950 ) . the reduction of orbital eccentricity is not often considered but is a key component of our theory . whether type a or type b conditions apply to au mic s disk is determined in part by the strength of the stellar wind , which according to previous works is uncertain by orders of magnitude . in this work , we place a novel constraint on the stellar mass loss rate and decide the appropriate disk type by comparing our theoretical models to the observations . in [ oom ] , we lay down basic parameters of the au mic system : stellar properties , disk optical depths , timescales for grain - grain collisions , and how the star s wind and radiation alter orbits of dust grains . in [ theory ] , we employ order - of - magnitude physics and analytic scalings to understand how the interplay between collisions , blow - out , and drag shapes the observed surface brightness profiles of the inner and outer disks . there we derive the steady - state grain size distribution as a function of position , including the maximum sizes and total mass of parent bodies . in [ montecarlo ] , we verify and extend our analytic results with a monte carlo simulation of the disk s surface brightness , color , and spectral energy distribution ( sed ) . models are compared directly with observations . finally , in [ discussion ] , we summarize our theory , place it in context with our understanding of how planets form , and point out directions for future research .

au microscopii is a 12 myr old m dwarf that harbors an optically thin , edge - on disk of dust . the scattered light surface brightness falls with projected distance from the star as ; within , , while outside 43 au , . the `` inner disk '' at contains grains that migrate inward by corpuscular and poynting - robertson ( cpr ) drag . the `` outer disk '' at comprises grains just large enough to remain bound to the star , on orbits rendered highly eccentric by stellar wind and radiation pressure . these scaling relations , which we derive analytically and confirm numerically , are robust against uncertainties in the grain size distribution . by simultaneously modeling the surface brightness and thermal spectrum , we break model degeneracies to establish that the au mic system is collision - dominated , and that its narrow birth ring contains a lunar mass of decimeter - sized bodies .

au microscopii is a 12 myr old m dwarf that harbors an optically thin , edge - on disk of dust . the scattered light surface brightness falls with projected distance from the star as ; within , , while outside 43 au , . we devise a theory to explain this profile . at a stellocentric distance , we posit a ring of parent bodies on circular orbits : the `` birth ring , '' wherein micron - sized grains are born from the collisional attrition of parent bodies . the `` inner disk '' at contains grains that migrate inward by corpuscular and poynting - robertson ( cpr ) drag . the `` outer disk '' at comprises grains just large enough to remain bound to the star , on orbits rendered highly eccentric by stellar wind and radiation pressure . how the vertical optical depth scales with depends on the fraction of grains that migrate inward by cpr drag without suffering a collision . if this fraction is large , the inner disk and birth ring share the same optical depth , and in the outer disk . by contrast , under collision - dominated conditions , the inner disk is empty , and outside . these scaling relations , which we derive analytically and confirm numerically , are robust against uncertainties in the grain size distribution . by simultaneously modeling the surface brightness and thermal spectrum , we break model degeneracies to establish that the au mic system is collision - dominated , and that its narrow birth ring contains a lunar mass of decimeter - sized bodies . the inner disk is devoid of micron - sized grains ; the surface brightness at arises from light forward scattered by the birth ring . inside , the disk s color should not vary with ; outside , the disk must become bluer as ever smaller grains are probed .

astro-ph0510527

i

we have constructed a theory to explain the observed optical surface brightness profile and infrared emission spectrum of the debris disk encircling au mic . in our theory , the slope of surface brightness versus projected radius @xmath0 changes abruptly at @xmath348 because a birth ring of planetesimals exists at stellocentric radius @xmath20 . this ring has a full radial width @xmath349 and a vertical , geometric optical depth of @xmath350 . the parent bodies in the ring have sizes @xmath351 and a total mass of @xmath352 . collisional attrition of parent bodies generates micron - sized grains that scatter starlight at optical wavelengths . the population of visible grains is maintained in steady state : production by colliding parent bodies balances removal by grain - grain collisions and removal by corpuscular and poynting - robertson ( cpr ) drag . the timescales over which removal of visible grains occurs can be orders of magnitude shorter than the age of the system ( @xmath1712 myr ) , ensuring steady state . collisions between parent bodies initiate a collisional cascade that extends downward in particle size by several orders of magnitude . grains having sizes @xmath353 are expelled from the system by stellar wind and radiation ( swr ) pressure and contribute negligibly to the observed optical emission . instead , barely bound grains , having sizes just larger than @xmath171 and which occupy highly eccentric orbits , make the dominant contribution to the surface brightness in the outer disk at @xmath7 . the number of such grains rises more steeply than would be expected from a pure dohnanyi size spectrum as @xmath58 approaches @xmath171 from above , because grains on high - eccentricity orbits have prolonged lifetimes against cpr drag and collisions . the structure of the outer disk depends on whether these smallest of bound grains are removed principally by cpr drag ( type a conditions ) or by destructive grain - grain collisions ( type b conditions ) . as the luminosity and/or mass - loss rate of the central star increases , disk behavior grades from type b to type a. as the number of parent bodies in the birth ring increases , collision rates increase and disk behavior changes from type a to type b. in the outer reaches of type a disks , the vertical optical depth scales approximately as @xmath10 . under type b conditions , @xmath11 ( but see footnote [ faraway_almost ] ) . we have derived these scaling relations analytically and have verified them by monte carlo simulations . the inner regions at @xmath6 are populated by grains that survive long enough before suffering destructive collisions that their periastron distances diminish appreciably by cpr drag . in type a disks , a significant fraction of grains born in the birth ring meet this criterion , so the inner disk is characterized by the same vertical optical depth that characterizes the birth ring . by contrast , under type b conditions , the inner disk is practically empty . in the case of au mic , type b conditions prevail . by fitting simultaneously both the surface brightness profile and the thermal emission spectrum , we not only uniquely determine the vertical optical depth and radial width of the birth ring ( see the values cited above ) , but also constrain the stellar mass - loss rate @xmath35 to be @xmath354 . according to our theory , the inner disk of au mic at @xmath6 is empty . the observed surface brightness at @xmath344 is not zero because we are observing the disk edge - on . the primary contribution to the surface brightness at @xmath344 arises from starlight that is forward scattered by grains in the birth ring . our theory states that the observed structure of the au mic disk reflects processes that are balanced in steady state . equilibrium is likely since the timescales over which collisions and cpr drag operate , even in the rarefied outer disk , are shorter than the age of the system . the outer disk does not comprise `` primordial '' grains left behind from a now - evaporated gaseous disk , as has been speculated previously . nor is the manifestation of the debris disk phenomenon in au mic the outcome of a recent cataclysm that has not yet equilibrated . that our required parent body mass is modest ( equation [ [ parentmass ] ] ) supports our contention that the au mic disk is in steady state . as our paper was being completed , we became aware of an independent study of au mic by @xcite . these authors find by inverting the observed surface brightness profile that the underlying vertical optical depth of the au mic disk peaks near 35 au . it is heartening that their conclusion is consonant with one of ours , derived as they are using complementary approaches : detailed data - fitting procedures versus physical reasoning to understand dust dynamics under general circumstances . the ring of parent bodies at @xmath355 that we envision encircling au mic presents a youthful analogue to the solar system s kuiper belt ( see the protostars and planets v review by chiang et al . 2006 ) . the spatial dimensions of these systems are remarkably similar : the classical kuiper belt , containing those planetesimals thought to have formed _ in situ _ , extends in heliocentric distance from @xmath1740 au to @xmath1747 au ( e.g. , trujillo & brown 2001 ) . we conclude by pointing out directions for future work on au mic and other debris disks . 1 . _ disk thickness._by assuming that we are viewing the au mic disk perfectly edge - on , we estimated a full disk height of @xmath356 . the corresponding opening angle is @xmath357 . while our model of a type b disk succeeds in reproducing the observed scaling behavior of disk height ( @xmath358 in the inner disk and @xmath359 in the outer disk ) , we have not explained what sets the normalization . dissipative grain - grain collisions would be expected to damp the inclination dispersion and to reduce @xmath360 to values orders of magnitude smaller than our inferred value . _ application to other systems._the debris disk surrounding the a - star @xmath16 pictoris closely resembles the au mic disk @xcite . the surface brightness profile abruptly changes slope at @xmath361 , from sb @xmath362 to sb @xmath363 ( kalas & jewitt 1995 ) . moreover , the vertical scale height @xmath364 scales with @xmath0 the same way that it does in the au mic disk . pic s outer disk is red rather than blue ( by contrast to the case of au mic ) could be a consequence of the particular grain size required for blow - out in the @xmath16 pic system , since for certain grain sizes and compositions , @xmath365 can actually increase with increasing wavelength . see bohren & huffman ( 1983 ) for a discussion of this phenomenon of `` blueing . '' ] recently , another analogue to the au mic disk has been discovered : f - star hd 139664 hosts a debris disk whose surface brightness profile exhibits a sharp break at @xmath17@xmath366 @xcite . the theory we have laid out for au mic might find ready application to these other systems . uniqueness of au mic among m dwarfs._the pioneering keck survey conducted by pjl05 at @xmath367 reveals that au mic is distinguished among their sample of nine m dwarfs having ages of 10500 myr in emitting an infrared excess . do the other m dwarfs not possess disks ? as m dwarfs constitute the most numerous stars in the universe , understanding why au mic might be exceptional will help to determine the prevalence of planetary systems . many of the m dwarfs surveyed by pjl05 may simply be much older than au mic ; their parent body populations may have suffered near complete comminution . ubiquity of rings._that parent bodies are confined to a ring centered at @xmath368 in the au mic system calls for explanation . ring morphologies are so common witness the examples of hr 4796a ( schneider et al . 1999 ) , @xmath369 eridani ( greaves et al . 1998 ) , fomalhaut ( kalas et al . 2005 ) , and even the kuiper belt that the `` debris disk phenomenon '' might well be more precisely termed the `` debris ring phenomenon . '' while regions interior to rings might have been purged of material by planets , the physical processes that determine the outer edges of rings remain unclear . ideas proposed by takeuchi & artymowicz ( 2001 ) and klahr & lin ( 2005 ) for how interactions between solids and gas can concentrate planetesimals into rings might be relevant . that planetary systems have sharp outer edges suggests that planetesimal formation is not a continuous function of disk properties ; rather , the formation of planets may require disk properties to meet threshold conditions ( e.g. , youdin 2004 ) . this work was made possible by grants from the national science foundation and the alfred p. sloan foundation . we are grateful to peter plavchan for extensive and helpful discussions , and to john krist for supplying us with _ hst _ surface brightness data . we acknowledge encouraging exchanges with pawel artymowicz , doug baker , josh eisner , mike fitzgerald , james graham , lynne hillenbrand , mike jura , paul kalas , yoram lithwick , holly maness , stan metchev , reem sari , and yanqin wu . a portion of this work was completed in awaji island , japan , in the cheerful company of the participants of the 2005 kobe international planetary school . ccccccc @xmath370 & 2.0 & @xmath371 & @xmath372 & @xmath373 & @xmath374 & @xmath375 + @xmath208 & 2.0 & @xmath376 & @xmath372 & @xmath377 & @xmath378 & @xmath379 + @xmath380 & 2.4 & @xmath381 & @xmath382 & @xmath383 & @xmath384 & @xmath385 + @xmath386 & 6.4 & @xmath387 & @xmath388 & @xmath389 & @xmath390 & @xmath391 + allard , f. , hauschildt , p. h. , alexander , d. r. , tamanai , a. , & schweitzer , a. , , 556 , 357 artymowicz , p. 2000 , space science reviews , 92 , 69 augereau , j .- c . , et al . 2001 , a&a , 370 , 447 augereau , j .- c . , & beust , h. 2006 , a&a , accepted aumann , h. h. , et al . 1984 , , 278 , l23 bohren , c. f. & huffman , d. r. 1983 , absorption and scattering of light by small particles , new york : wiley - 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madjar , a. , & ferlet , r. 1996 , a&a , 307 , l542 liu , m. c. , 2004 , science , 305 , 1442 liu , m. c. , matthews , b. c. , williams , j. p. , & kalas , p. g. 2004 , , 608 , 526 magee , h. r. m. , gdel , m. , audard , m. , & mewe , r. 2003 , advances in space research , 32 , 1149 metchev , s. a. , eisner , j. a. , hillenbrand , l. a. , & wolf , s. 2005 , , 622 , 451 meyer , m. r. , backman , d. e. , weinberger , a. j. , & wyatt , m. c. 2006 , in protostars and planets v , eds . b. reipurth , d. jewitt , & k. keil , tucson : university of arizona press , in press murray , c. d. & dermott , s. f. 1999 , solar system dynamics , cambridge : cambridge university press obrien , d. p. & greenberg , r. 2003 , icarus , 164 , 334 pan , m. & sari , r. 2005 , icarus , 173 , 342 parker , e. n. 1964 , , 139 , 93 plavchan , p. , jura , m. , & lipscy , s. j. 2005 , , 631 , 1161 ( pjl05 ) roberge , a. , weinberger , a. j. , redfield , s. , & feldman , p. d. 2005 , , 626 , l105 schneider , g. , et al . 1999 , , 513 , l127 schrijver , c. j. , & title , a. m. 2001 , , 551 , 1099 smith , b. a. & terrile , r. j. 1984 , science , 226 , 1421 song , i. , zuckerman , b. , weinberger , a. j. , & becklin , e. e. 2005 , nature , 436 , 363 strassmeier , k. g. 2002 , astronomische nachrichten , 323 , 309 su , k. , et al . 2005 , , 628 , 487 takeuchi , t. , & artymowicz , p. 2001 , , 557 , 990 telesco , c. m. , et al . 2000 , , 530 , 329 torres , c. a. o. & ferraz mello , s. 1973 , a&a , 27 , 231 trujillo , c. a. & brown , m. e. 2001 , , 554 , l95 warren , s. g. 1984 , applied optics , 23 , 1206 weber , e. j. & davis , l. 1967 , , 148 , 217 wood , b. e. , m " uller , h .- r . , zank , g. p. , linsky , j. l. 2002 , , 574 , 412 wood , b. e. , mller , h .- , zank , g. p. , linsky , j. l. , & redfield , s. 2005 , apjl , 628 , l143 wyatt , m. c. 2005 , a&a , 433 , 1007 wyatt , s. p. & whipple , f. l. 1950 , , 111 , 134 youdin , a. n. 2004 , in asp conference series 323 : star formation in the interstellar medium : in honor of david hollenbach , 319 zuckerman , b. 2001 , , 39 , 549 zuckerman , b. , & song , i. 2004 , , 603 , 738

we devise a theory to explain this profile . at a stellocentric distance , we posit a ring of parent bodies on circular orbits : the `` birth ring , '' wherein how the vertical optical depth scales with depends on the fraction of grains that migrate inward by cpr drag without suffering a collision . if this fraction is large , the inner disk and birth ring share the same optical depth , and in the outer disk . by contrast , under collision - dominated conditions , the inner disk is empty , and outside . the inner disk is devoid of micron - sized grains ; the surface brightness at arises from light forward scattered by the birth ring . inside ,

au microscopii is a 12 myr old m dwarf that harbors an optically thin , edge - on disk of dust . the scattered light surface brightness falls with projected distance from the star as ; within , , while outside 43 au , . we devise a theory to explain this profile . at a stellocentric distance , we posit a ring of parent bodies on circular orbits : the `` birth ring , '' wherein micron - sized grains are born from the collisional attrition of parent bodies . the `` inner disk '' at contains grains that migrate inward by corpuscular and poynting - robertson ( cpr ) drag . the `` outer disk '' at comprises grains just large enough to remain bound to the star , on orbits rendered highly eccentric by stellar wind and radiation pressure . how the vertical optical depth scales with depends on the fraction of grains that migrate inward by cpr drag without suffering a collision . if this fraction is large , the inner disk and birth ring share the same optical depth , and in the outer disk . by contrast , under collision - dominated conditions , the inner disk is empty , and outside . these scaling relations , which we derive analytically and confirm numerically , are robust against uncertainties in the grain size distribution . by simultaneously modeling the surface brightness and thermal spectrum , we break model degeneracies to establish that the au mic system is collision - dominated , and that its narrow birth ring contains a lunar mass of decimeter - sized bodies . the inner disk is devoid of micron - sized grains ; the surface brightness at arises from light forward scattered by the birth ring . inside , the disk s color should not vary with ; outside , the disk must become bluer as ever smaller grains are probed .

0801.4545

i

high transverse momentum ( ) partons are informative probes of the high energy density matter created in nuclear collisions at the relativistic heavy - ion collider ( rhic ) . these partons lose a large fraction of their energy in the matter prior to forming final state hadrons . such an energy loss is predicted to lead to a reduction of both single hadron and correlated dihadron yields at high @xcite , a phenomenon known as jet - quenching . indeed , current results for high have revealed a strong suppression of inclusive hadron yields @xcite , as well as the suppression of correlated away - side hadron pairs @xcite . despite this strong suppression , particle production for @xmath10 gev/@xmath2 appears to have a significant contribution from in - vacuum jet fragmentation . this is suggested by a -independent suppression factor for single hadrons @xcite , which implies a @xmath4-like power law spectral shape in au+au collisions , and similar @xmath11 to @xmath12 meson @xcite and proton to pion @xcite ratios between au+au and p+p collisions . more direct evidence has been provided by high - dihadron azimuthal angle ( @xmath0 ) correlations measurements . in particular , our current measurements , as well as prior ones @xcite , reveal characteristic jet - like peaks for the near - side ( @xmath13 ) and the away - side ( @xmath5 ) at high . in most energy loss models , the stopping power of the medium is normally characterized by the transport coefficient @xmath14 , defined as the squared average momentum transfer from the medium to the hard parton per unit path length . however , due to the steeply falling parton spectra and strong jet quenching , the observed high - single hadrons and hadron pairs mainly come from ( di)jets that suffer minimal interaction with the medium . thus , the overall suppression factor is sensitive to the full energy loss probability distribution instead of just the average energy loss itself . in fact , simple calculations @xcite with different energy loss probability distributions have been shown to match the data quite well . however , the extracted @xmath15 values are sensitive to the theoretical models and their associated assumptions @xcite . additional experimental constraints on the dynamics of the energy loss processes are clearly needed . in order to improve our understanding of the parton - medium interactions , it is important to study the fate of partons that suffer energy loss in the medium . these partons are quenched by the medium and their energy is believed to be transported to lower - hadrons ( @xmath8 gev/@xmath2 ) . prior measurements @xcite in this region , as well as the present study , indicate strong modifications of the near- and the away - side @xmath0 distributions . the near - side jet - induced pairs peak at @xmath13 , but the peak is broadened and enhanced with respect to @xmath4 collisions . the away - side jet - induced pairs are observed to peak at @xmath16 @xcite with a local minimum at @xmath5 . these modification patterns reflect characteristics of the energy transport of the quenched partons in both and @xmath0 . many mechanisms for this energy transport have been proposed for the near - side @xcite and away - side @xcite . such energy transport is expected to enhance jet contributions to the production of low - hadrons . however , jet - induced hadron pair correlations can be affected by soft processes such as hydrodynamical flow @xcite and quark coalescence @xcite , which dominate the hadron production in the intermediate region . the coupling of partons with hydrodynamical flow could modify the jet shape and yield . similarly , quark coalescence could modify the particle composition in the near- and away - side jets @xcite . therefore , detailed correlation studies for @xmath8 gev/@xmath2 can improve our knowledge of the interplay between soft and hard processes for hadron production . in this paper we present a detailed survey of the trigger , partner and centrality dependence of the near- and away - side jet shapes and yields from au+au collisions . these measurements provide a comprehensive overview of the different physical features that come into play for different ranges , and provide new insights on the interplay between the processes leading to jet energy loss and the response of the medium to the lost energy . in addition , they allow a detailed study of the similarities and differences between the correlation patterns for the near- and away - side jets . when coupled with inclusive hadron production , these measurements also allow quantification of the role of jets at intermediate , where the particle production is believed to be dominated by the soft processes . the results reported here comprise significant extensions to results published earlier @xcite . in section ii , we introduce variables used to quantify the jet properties and their in - medium modifications . in section iii , we present data analysis details , jet signal extraction and background subtraction , and several sources of systematic errors related to the measurements . the main results are presented in section iv and model comparisons and discussions are given in section v. several technical issues related to the correlation analysis are addressed in appendices a - c , and tabulated data are given in appendix d.

comparisons to data suggest that the away - side distribution can be divided into a partially suppressed `` head '' region centered at , and an enhanced `` shoulder '' region centered at . these observations suggest that both the away- and near - side distributions contain a jet fragmentation component which dominates for gev and a medium - induced component which is important for gev/ .

azimuthal angle ( ) correlations are presented for a broad range of transverse momentum ( gev/ ) and centrality ( 0 - 92% ) selections for charged hadrons from di - jets in au+au collisions at = 200 gev . with increasing , the away - side distribution evolves from a broad and relatively flat shape to a concave shape , then to a convex shape . comparisons to data suggest that the away - side distribution can be divided into a partially suppressed `` head '' region centered at , and an enhanced `` shoulder '' region centered at . the spectrum for the associated hadrons in the head region softens toward central collisions . the spectral slope for the shoulder region is independent of centrality and trigger . the properties of the near - side distributions are also modified relative to those in collisions , reflected by the broadening of the jet shape in and , and an enhancement of the per - trigger yield . however , these modifications seem to be limited to gev/ , above which both the hadron pair shape and per - trigger yield become similar to collisions . these observations suggest that both the away- and near - side distributions contain a jet fragmentation component which dominates for gev and a medium - induced component which is important for gev/ . we also quantify the role of jets at intermediate and low through the yield of jet - induced pairs in comparison to binary scaled pair yield . the yield of jet - induced pairs is suppressed at high pair proxy energy ( sum of the magnitudes of the two hadrons ) and is enhanced at low pair proxy energy . the former is consistent with jet quenching ; the latter is consistent with the enhancement of soft hadron pairs due to transport of lost energy to lower .

0906.1393

i

the isolation of single layers of carbon ( graphene ) whose low - energy spectrum is described by the dirac - weyl hamiltonian of massless spin-@xmath7 fermions @xcite , has offered physicists the unique possibility to test the predictions of relativistic quantum mechanics in a condensed phase . a particular attention focuses on ballistic transport @xcite , as the unusual band structure of a carbon monolayer @xcite leads simultaneously to a divergent fermi wavelength @xmath8 in the undoped graphene limit , and to a zero bandgap . for these reasons , the quantum - mechanical wave character of an electron plays an essential role in transport even through a macroscopic graphene sample , provided that the influence of disorder is negligible @xcite . a separate issue concerns the fact that dirac fermions in graphene occur in two degenerate families , resulting from the presence of two different valleys in the band structure . this valley degree of freedom offers conceptually new possibilities to control charge carriers the so - called `` valleytronics '' @xcite . so far , extensive theoretical studies of ballistic transport , based on mode - matching analysis for the dirac equation @xcite , are available for a _ rectangular _ graphene sample of width @xmath9 , length @xmath10 , and various types of boundary conditions . in the regime of large aspect ratios @xmath11 , the conductance of an undoped sample scales as @xmath12 , with the universal conductivity @xmath0 , regardless of boundary conditions @xcite . moreover , as shown by tworzydo _ @xcite , the fano factor in this case coincides with that of a diffusive wire ( @xmath1 ) . also , the transmission eigenvalues of these two systems display the same distribution . this analogy coined the term of _ pseudodiffusive transport _ , which describes ballistic graphene properties in the universal conductivity limit . recent experiments report an agreement with the theoretical predictions of refs . @xcite for either the conductance @xcite or the fano factor @xcite . furthermore , the temperature dependence of the conductivity @xcite also shows an approximate agreement with the ballistic theory generalized to finite temperatures @xcite . however , even for low temperatures , the convergence with @xmath13 is much slower than predicted . in particular , for the largest aspect ratio @xmath14 studied in ref . @xcite the deviations from the limiting values @xmath15 and @xmath1 are close to @xmath16 , whereas results of ref . @xcite show the convergence should be already reached for moderate aspect ratios @xmath17 . a clear explanation of this discrepancy is missing , but it is usually attributed to the fact that boundary conditions used in theoretical works , which describe either an abrupt termination of a perfect honeycomb lattice or an infinite mass confinement @xcite , may not model the real - sample edges correctly @xcite . in this work , we consider ballistic graphene systems of geometries for which the boundary effects are absent or suppressed . the paper is organized as follows : in sec . [ conmap ] we briefly recall the mode - matching analysis for a graphene strip , and show how to employ the conformal symmetry of the dirac equation for undoped graphene @xcite to obtain analytically the transmission eigenvalues for other systems . then , in sec . [ corbdi ] the method is applied to the corbino disk . the results are compared with those obtained by direct mode - matching for angular momentum eigenstates , a relation with the nonrelativistic electron gas in the disk setup is also discussed . in sec . [ bimass ] we study two basic billiards bounded with mass confinement : a finite section of the corbino disk and a quantum dot with circular edges . the results obtained with the conformal mapping technique are confirmed by the computer simulation of transport using the tight - binding model on a honeycomb lattice . finally , in sec . [ ribb ] we study numerically the transport _ across _ an infinitely long nanoribbon by utilizing the @xmath18-terminal recursive green s function algorithm @xcite , as well as across a finite section of a nanoribbon with an abrupt lattice termination . all the systems show pseudodiffusive transport behavior in a wide range of geometrical parameters . a further analogy between them appears when ( at least ) one of the leads is narrow in comparison to the characteristic length of the conducting region @xmath19 . namely , the conductance in such a _ quantum tunneling _ regime shows a power - law decay @xmath20 , where @xmath21 is a nonuniversal ( geometry - dependent ) exponent . moreover , it is related to the shot noise by @xmath22 , so that the poissonian limit ( @xmath2 ) is approached for large @xmath19 . the symmetry - dependent factor @xmath4 in the presence of full spin , valley and symplectic degeneracy ( the case of the corbino disk ) , or @xmath5 when the mass confinement breaks symplectic symmetry of the dirac equation . a final reduction to @xmath6 may be reached by adding abrupt ( i.e. armchair ) edges , which scatter the valleys . the original feature of the geometries studied in this article is that the influence of sample edges are eliminated ( for the corbino setup ) or irrelevant , as the spatial current distribution is not uniform , but concentrated far away from the edges . this is why we believe that our theoretical findings could be confirmed experimentally with better precision than that for rectangular samples , as the role of boundary conditions is strongly suppressed .

the degeneracy for the corbino disk , which preserves the full symmetry of the dirac equation , for billiards bounded with smooth edges which break the symplectic symmetry , and when abrupt edges lead to strong intervalley scattering . an alternative , analytical or numerical technique , is utilized for each of the billiards to confirm the applicability of the conformal mapping for various boundary conditions .

ballistic transport through a collection of quantum billiards in undoped graphene is studied analytically within the conformal mapping technique . the billiards show _ pseudodiffusive _ behavior , with the conductance equal to that of a classical conductor characterized by the conductivity , and the fano factor . by shrinking at least one of the billiard openings , we observe a _ tunneling _ behavior , where the conductance shows a power - law decay with the system size , and the shot noise is poissonian ( ) . in the crossover region between tunneling and pseudodiffusive regimes , the conductance . the degeneracy for the corbino disk , which preserves the full symmetry of the dirac equation , for billiards bounded with smooth edges which break the symplectic symmetry , and when abrupt edges lead to strong intervalley scattering . an alternative , analytical or numerical technique , is utilized for each of the billiards to confirm the applicability of the conformal mapping for various boundary conditions . = 1

1304.6573

c

in conclusion , we have investigated , by means of morphodynamic modeling of aeolian dunes , the respective roles of bimodal wind regimes , topography , influx asymmetry and dune collisions on the formation and evolution of asymmetric barchan dune shapes . the conclusions of our numerical simulations can be summarized as follows : * _ bimodal wind regimes _ the limb opposite to the secondary wind elongates into the resultant transport direction if the divergence angle of the bimodal wind is obtuse and the ratio @xmath196}/{\left[{q_1t_{{\mathrm{w}}1}}\right]}$ ] where @xmath89 ( @xmath88 ) and @xmath66 ( @xmath68 ) stand for the bulk sand flux and the duration of the primary ( secondary ) wind , respectively exceeds @xmath1 . these conditions are the same as the ones for oblique alignment of bedforms in dense sand beds @xcite , the asymmetric barchan being the corresponding morphology under low amount of available sand . * _ topography _ a barchan crossing a topographic rise can become asymmetric ; the limb closest to the topographic rise elongates downwind . the migration velocity of a barchan that is on a tilted surface has a downhill component proportional to the tilting slope ; the preferential limb extension is downhill rather than downwind . * _ influx asymmetry _ the side of the barchan subjected to the larger influx increases in volume , whereas the opposite limb elongates downwind . the typical asymmetric morphology is a barchan with an elongated arm ( the one subjected to lower influx ) . the asymmetry is of transient nature , since the dune migrates laterally towards the region of higher influx . * _ dune collisions _ asymmetry can be triggered due to barchan collisions with lateral offset . binary collisions with large offset can lead to extension of the limb resulting from the merging of the two limbs participating at the collision . collisions between multiple barchans in a field can trigger more complex asymmetric patterns . some patterns produced in these simulations involve the elongation of one limb of the upwind dune , as reported from previous observations @xcite . in order to improve the quantitative assessment of asymmetric barchans , the model should be extended in order to account for secondary flow effects at the dune lee @xcite , which may be relevant for the dynamics of limb elongation due to bimodal wind regimes or due to topographic ridges with sharp slopes @xcite . indeed , the separation bubble model of section [ sec : wind_field ] does not account for the occurrence of three - dimensional flow structures within the zone of recirculating flow , which affect the dune shape at the lee and can contribute to the elongation of the limb . realistic simulations of bimodal wind regimes should further account for multiple secondary wind trends in consistence with the complex sand roses of real dune fields @xcite . moreover , real winds can be very gusty , with changes in direction of 45 degrees or more taking place in most cases in less than 15 minutes , while in some instances the changes may be gradual or abrupt @xcite . this effect of changes in wind directions should be considered in the future . finally , we also note that there are examples of seif dunes formation from vegetated linear dunes that lost their vegetation due to human impact @xcite . the formation of seif dunes in the presence of a dynamic vegetation cover remains to be investigated in the future . the results of our calculations are potentially useful for inferring local wind regimes or spatial variations either in topography or in availability of mobile sediments in planetary dune fields where asymmetric barchans occur .

several factors have been identified as potential causes for barchan dune asymmetry on earth and mars : asymmetric bimodal wind regime , topography , influx asymmetry and dune collision . however , the dynamics and potential range of barchan morphologies emerging under each specific scenario that leads to dune asymmetry are far from being understood . in the present work , asymmetric barchans migrating along a tilted surface move laterally , with transverse migration velocity proportional to the slope of the terrain . limb elongation induced by topography can occur when a barchan crosses a topographic rise . our findings can be useful for making quantitative inference on local wind regimes or spatial heterogeneities in transport conditions of planetary dune fields hosting asymmetric barchans .

barchan dunes crescent - shaped dunes that form in areas of unidirectional winds and low sand availability commonly display an asymmetric shape , with one limb extended downwind . several factors have been identified as potential causes for barchan dune asymmetry on earth and mars : asymmetric bimodal wind regime , topography , influx asymmetry and dune collision . however , the dynamics and potential range of barchan morphologies emerging under each specific scenario that leads to dune asymmetry are far from being understood . in the present work , we use dune modeling in order to investigate the formation and evolution of asymmetric barchans . we find that a bimodal wind regime causes limb extension when the divergence angle between primary and secondary winds is larger than , whereas the extended limb evolves into a seif dune if the ratio between secondary and primary transport rates is larger than . calculations of dune formation on an inclined surface under constant wind direction also lead to barchan asymmetry , however no seif dune is obtained from surface tilting alone . asymmetric barchans migrating along a tilted surface move laterally , with transverse migration velocity proportional to the slope of the terrain . limb elongation induced by topography can occur when a barchan crosses a topographic rise . furthermore , transient asymmetric barchan shapes with extended limb also emerge during collisions between dunes or due to an asymmetric influx . our findings can be useful for making quantitative inference on local wind regimes or spatial heterogeneities in transport conditions of planetary dune fields hosting asymmetric barchans . barchan dunes , dune asymmetry , wind erosion , sand transport , dune model

cond-mat9805013

i

for a long time , there has been a continuing interest in the definition of atomic charges in solid state physics as well as in chemistry @xcite . this interest lies essentially in the fact that the concept of atomic charge naturally arises in a large diversity of frameworks and is frequently helpful for a simple description of solids and molecules . the variety of contexts in which the charge is involved ( ir spectrum analysis , xps chemical shifts analysis , theory of ionic conductivity of oxides , determination of electrostatic potential , definition of oxidation states ... ) underlines its central role but also reveals a concomitant problem : inspired by various models or by the description of various physical phenomena , many different definitions have been proposed that , unfortunately , are not equivalent @xcite . following a distinction already made by cochran @xcite , it seems possible to classify the different concepts into static and dynamical charges . the _ static _ charge is an intuitive concept , usually based on a partitioning of the ground - state electronic density into contributions attributed to the different atoms . it is an ill - defined quantity that depends on the convention artificially chosen to affect a given electron to a particular ion @xcite . on the other hand , the _ dynamical _ charge is directly related to the change of polarization ( or dipole moment , for molecules ) created by an atomic displacement . this change of polarization is a quantity that can be experimentally measured , at least in principles , giving the dynamical charge a well - defined character . in order to clarify the concept of atomic charge , it was important to compare on practical examples the numerical results obtained from its different definitions . recent studies of the statistical correlation between various atomic charges using a principal component analysis have suggested that the different definitions are not independent but correspond to different scales driven by a unique underlying physical factor @xcite . if this assertion seems plausible as far as static charges are concerned , we will argue that the dynamical charge should not reduce to the same physical factor but should also depend on an additional parameter : the rate of transfer of charge , influenced by the bonding with the other atoms of the system and additionally , for large systems , by the condition imposed on the macroscopic electric field . the born effective charge tensor @xmath1 alias transverse charge , that is at the center of the present study , is a dynamical quantity introduced by born @xcite in 1933 . in solid state physics , it is since a long time considered as a fundamental quantity because it monitors the long - range coulomb interaction responsible of the splitting between transverse and longitudinal optic phonon modes @xcite . during the seventies , the born effective charges were already investigated and discussed within empirical approaches ( see for example harrison @xcite ) . more recently , they became accessible to first - principles calculations @xcite , and accurate values have been reported for a large variety of materials . for the case of abo@xmath0 compounds , old experimental data @xcite and empirical studies @xcite had suggested that the amplitude of the born effective charges should deviate substantially from the amplitude of the static atomic charge . surprisingly , this result remained in the dark until first - principles calculations confirmed that the components of @xmath1 are anomalously large in these oxides @xcite . it was observed that the components of @xmath1 can reach twice that of the nominal ionic charges . this result reopened the discussion on the physics of the born effective charges and different recent studies tried to clarify the microscopic processes monitoring the amplitude of @xmath1 . in this paper , we first clarify the relationship between various atomic charges . we then present results concerning batio@xmath0 and srtio@xmath0 in order to illustrate how a careful analysis of the born effective charges can teach us interesting physics concerning these compounds . it reveals the mixed ionic and covalent character of the bond @xcite . it allows to visualize the mechanism of polarization as electronic currents produced by dynamical changes of orbital hybridizations @xcite . it also clarifies the origin of the giant destabilizing dipole - dipole interaction producing the ferroelectric instability of these materials @xcite . in section ii and iii , we contrast the concepts of static and dynamical charges and we reintroduce the born effective charge that is at the center of the present discussion . in section iv , we compare various results obtained within different frameworks for the cubic phase of batio@xmath0 and srtio@xmath0 . the bond orbital model of harrison is explicitely applied to srtio@xmath0 ( appendix a ) . we also discuss the origin of the large anomalous contributions in terms of local electronic polarizability and dynamical changes of orbital hybridization . a decomposition of the role played by the different bands is reported in section v. section vi is devoted to the evolution of the born effective charges in the three ferroelectric phases of batio@xmath0 as well as in the cubic phase under hydrostatic pressure . this points out the role of the anisotropy of the atomic environment on the amplitude of @xmath1 . finally , in section vii , we report the evolution of the effective charges all along the path of atomic displacements from the cubic to the rhombohedral phase and we estimate the spontaneous polarization of the three ferroelectric phase of batio@xmath0 .

based on recent first - principles computations in perovskite compounds , especially batio , we examine the significance of the born effective charge concept and contrast it with other atomic charge definitions , either static ( mulliken , bader ... ) or dynamical ( callen , szigeti ... ) . various results concerning barium and strontium titanates are presented . the sensitivity of the born effective charges to microscopic and macroscopic strains is examined .

based on recent first - principles computations in perovskite compounds , especially batio , we examine the significance of the born effective charge concept and contrast it with other atomic charge definitions , either static ( mulliken , bader ... ) or dynamical ( callen , szigeti ... ) . it is shown that static and dynamical charges are not driven by the same underlying parameters . a unified treatment of dynamical charges in periodic solids and large clusters is proposed . the origin of the difference between static and dynamical charges is discussed in terms of local polarizability and delocalized transfers of charge : local models succeed in reproducing anomalous effective charges thanks to large atomic polarizabilities but , in abo compounds , ab initio calculations favor the physical picture based upon transfer of charges . various results concerning barium and strontium titanates are presented . the origin of anomalous born effective charges is discussed thanks to a band - by - band decomposition which allows to identify the displacement of the wannier center of separated bands induced by an atomic displacement . the sensitivity of the born effective charges to microscopic and macroscopic strains is examined . finally , we estimate the spontaneous polarization in the four phases of barium titanate .

cond-mat9805013

c

in this paper , we first analyzed the links between different definitions of atomic charge . we have shown that , contrary to the static definitions , dynamical effective charges also depend on the electronic charge reorganisation induced by an atomic displacement . the amplitude of this dynamical contribution is monitored not only by the bonding with the other atoms but also , for large systems , by the condition imposed on the macroscopic electric field . a unified treatment of the concept of dynamical charge in molecules , large clusters , and truly periodic systems has been presented , in which the born effective charge and the optical dielectric constant appear as the two fundamental quantities . the microscopic origin of the dynamical contribution has been discussed in terms of local polarizability and delocalized transfers of electrons . based on various first - principles results , we have then emphasized that the born effective charges are anomalously large in the family of abo@xmath0 compounds : their amplitude can reach more than twice that of the nominal ionic charges . this feature was explained in terms of interatomic transfers of charge , produced by `` off - site '' dynamical changes of hybridization . for batio@xmath0 and srtio@xmath0 , we have brought to light complex dynamical changes of hybridization , concerning not only ti and o but also ba and sr orbitals . the hybridizations restricted to occupied states generate however compensating anomalous contributions so that , finally , the total value of @xmath1 is essentially affected by dynamical changes of hybridization between o 2p and ti 3d orbitals . as a more general issue , it appears that the existence of partial hybridizations between occupied and unoccupied states is an important feature for candidate to large anomalous born effective charges . moreover , the dynamical transfers of charge are expected to be larger when such a hybridization involve d states , for which the interactions parameters with other orbitals are particularly sensitive to the interatomic distance . investigating the evolution of @xmath1 to the structural features , we have shown that they are strongly affected by the ferroelectric atomic displacements and much less sensitive to isotropic pressure . the results have clarified that the amplitude of @xmath1 is not monitored by a particular interatomic distance but is dependent on the anisotropy of the ti environment along the ti - o chains . finally , the effective charges were used to estimate the spontaneous polarization in the ferroelectric phases of batio@xmath0 . for that purpose , their evolution was investigated all along the path of atomic displacement from the cubic to the rhombohedral structure . all along this work , we only focused on the _ microscopic _ mechanisms that govern the amplitude of the born effective charges . in independent studies , it was also emphasized that the anomalously large born effective charges produce a giant lo - to splitting in abo@xmath0 compounds , specially for the ferroelectric phonon mode @xcite . moreover , it was demonstrated that this feature is associated to the existence of an anomalously large destabilizing dipole - dipole interaction , sufficient to compensate the stabilizing short - range forces and induce the ferroelectric instability @xcite . in materials where polar modes play a major role , the born effective charge appears therefore also as a `` key concept '' to relate the electronic and structural properties @xcite . g. would like to thank r. resta for numerous illuminating discussions , ph . lambin for his help in shell - model calculations , l. l. boyer for clarifying some aspects of the scad model , and n. marzari and d. vanderbilt for providing an early copy of their recent results . x.g . is grateful to the national fund for scientific research ( fnrs - belgium ) for financial support . we acknowledge the use of ibm - rs 6000 work stations from common projects between ibm belgium , ucl - pcpm and fundp - scf , as well as the use of the maui high performance computing center ibm - sp2 . we thank corning incorporated for the availability of the planewave code , as well as j .- beuken for his kind and permanent computer assistance . we also acknowledge financial support from the pai - uiap p4/10 .

the origin of the difference between static and dynamical charges is discussed in terms of local polarizability and delocalized transfers of charge : local models succeed in reproducing anomalous effective charges thanks to large atomic polarizabilities but , in abo compounds , ab initio calculations favor the physical picture based upon transfer of charges . finally , we estimate the spontaneous polarization in the four phases of barium titanate .

based on recent first - principles computations in perovskite compounds , especially batio , we examine the significance of the born effective charge concept and contrast it with other atomic charge definitions , either static ( mulliken , bader ... ) or dynamical ( callen , szigeti ... ) . it is shown that static and dynamical charges are not driven by the same underlying parameters . a unified treatment of dynamical charges in periodic solids and large clusters is proposed . the origin of the difference between static and dynamical charges is discussed in terms of local polarizability and delocalized transfers of charge : local models succeed in reproducing anomalous effective charges thanks to large atomic polarizabilities but , in abo compounds , ab initio calculations favor the physical picture based upon transfer of charges . various results concerning barium and strontium titanates are presented . the origin of anomalous born effective charges is discussed thanks to a band - by - band decomposition which allows to identify the displacement of the wannier center of separated bands induced by an atomic displacement . the sensitivity of the born effective charges to microscopic and macroscopic strains is examined . finally , we estimate the spontaneous polarization in the four phases of barium titanate .

1509.04839

i

optimal insurance contract design is an important problem , manifested not only in theory but also in insurance and financial practices . the problem is to determine the optimal amount of compensation as a function of the loss called indemnity so as to maximize the insured s satisfaction , subject to the participation constraint of the insurer . in the insurance literature , most of the work assume that the insurer is risk neutral while the insured is a risk - averse expected utility ( eu ) maximizer ; see e.g. arrow ( 1963 ) , raviv ( 1979 ) , and gollier and schlesinger ( 1996 ) . in this case , the optimal contract is in general a deductible one that covers part of the loss in excess of a deductible level . however , the eu theory has received many criticisms , for it fails to explain numerous experimental observations and theoretical puzzles . in the context of insurance contracting , the classical eu - based models can not explain some behaviors in insurance demand such as that for small losses ( e.g. demand for warranties ) ; see a detailed discussion in bernard et al . ( 2015 ) . in order to overcome this drawback of the eu theory , different measures of evaluating uncertain outcomes have been put forward to depict human behaviors . a notable one is the rank - dependent utility ( rdu ) proposed by quiggin ( 1982 ) , which consists of a concave utility function and an inverse-@xmath0 shaped probability weighting ( or distortion ) function . through the probability weighting , the rdu theory captures the common observation that people tend to exaggerate small probabilities of extremely good and bad outcomes . with the development of advanced mathematical tools , the rdu preference has been applied to many areas of finance , including portfolio choice and option pricing . on the other hand , barseghyan et al . ( 2013 ) use data on households insurance deductible decisions in auto and home insurance to demonstrate the relevance and importance of the probability weighting and suggest the possibility of generalizing their conclusions to other insurance choices . there have been also studies in the area of insurance contract design within the rdu framework ; see for example chateauneuf , dana and tallon ( 2000 ) , dana and scarsini ( 2007 ) , and carlier and dana ( 2008 ) . however , all these papers assume that the probability weighting function is convex . bernard et al . ( 2015 ) are probably the first to study rdu - based insurance contracting with _ inverse-@xmath0 shaped _ weighting functions , using the quantile formulation originally developed for portfolio choice ( jin and zhou 2008 , he and zhou 2011 ) . they derive optimal contracts that not only insure large losses above a deductible level but also cover small ones . however , their contracts suffer from a severe problem of moral hazard , since they are not increasing with respect to the losses . is increasing if @xmath1 whenever @xmath2 . we say @xmath3 is `` strictly increasing '' if @xmath4 whenever @xmath2 . similar conventions are used for `` decreasing '' and `` strictly decreasing '' functions . ] as a consequence , insureds may be motivated to hide their true losses in order to obtain additional compensations ; see a discussion on pp . 175176 of bernard et al . ( 2015 ) . this paper aims to address this setback . we consider the same insurance model as in bernard et al . ( 2015 ) , but adding an explicit constraint that both the indemnity function and the insured s retention function ( i.e. the part of the losses to be born by the insured ) must be globally increasing with respect to the losses . this constraint will rule out completely the aforementioned behaviour of moral hazard ; yet mathematically it gives rise to substantial difficulty . the approach used in bernard et al . ( 2015 ) no longer works . we develop a general approach to overcome this difficulty . specifically , we first derive the necessary and sufficient conditions for optimal solutions via calculus of variations . then we deduce explicitly expressed optimal contracts by a fine analysis on these conditions . an interesting finding is that , for a good and reasonable range of parameters specifications , there are only two types of optima contracts , one being the classical deductible one and the other a three - fold " one covering both small and large losses . the remainder of the paper is organized as follows . section 2 presents the optimal insurance model under the rdu framework including its quantile formulation . section 3 applies the calculus of variations to derive a general necessary and sufficient condition for optimal solutions . we then derive optimal contracts for yaari s criterion and the general rdu in sections 4 and 5 , respectively . section 6 provides a numerical example to illustrate our results . finally , we conclude with section 7 . proofs of some lemmas are placed in an appendix .

. however , their contracts suffer from a problem of moral hazard for paying more compensation for a smaller loss . this paper addresses this setback by exogenously imposing the constraint that both the indemnity function and the insured s retention function be increasing with respect to the loss . we characterize the optimal solutions via calculus of variations , and then apply the result to obtain explicitly expressed contracts for problems with yaari s dual criterion and general rdu . ( 2015 ) . * keywords : * optimal insurance design , rank - dependent utility theory , yaari s dual criterion , probability weighting function , moral hazard , indemnity function , retention function , quantile formulation .

bernard et al . ( 2015 ) study an optimal insurance design problem where an individual s preference is of the rank - dependent utility ( rdu ) type , and show that in general an optimal contract covers both large and small losses . however , their contracts suffer from a problem of moral hazard for paying more compensation for a smaller loss . this paper addresses this setback by exogenously imposing the constraint that both the indemnity function and the insured s retention function be increasing with respect to the loss . we characterize the optimal solutions via calculus of variations , and then apply the result to obtain explicitly expressed contracts for problems with yaari s dual criterion and general rdu . finally , we use a numerical example to compare the results between ours and that of bernard et al . ( 2015 ) . * keywords : * optimal insurance design , rank - dependent utility theory , yaari s dual criterion , probability weighting function , moral hazard , indemnity function , retention function , quantile formulation .

0806.0845

i

in recent years , it has been debated in the literature about possible alternatives to black holes , the black hole mimickers , which would look observationally almost like black holes but would have no horizon . the existence of such objects can , in principle , put in doubt astrophysical data which otherwise are considered as observational confirmation in favor of black holes @xcite . on one hand , it is clear that the properties in the near - horizon region where gravity is strong can be quite different for both type of objects . on the other hand , the statements about the difficulties in discerning black holes from their mimickers are usually related to measurements at spatial infinity . thus , one should insist on the question : can an observer at infinity catch the difference between both type of objects in some indirect way , or even rule out some possible mimicker ? in our view , the answer is positive and is connected with key properties , namely , regularity or singularity , of the corresponding geometries . it turns out that the requirement of full regularity up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out the potential mimickers in most of the cases . the goal of the present work is to examine the near - horizon properties , and their connection with far away asymptotic properties , of some candidates to black mimickers . we study spherically symmetric configurations , and make , two major divisions , or classes , on those candidates . first , uncharged or charged but non - extremal objects , and second extremal objects . within the uncharged or charged but non - extremal one can invoke as black hole mimickers , non - extremal @xmath0-wormholes on the threshold of the formation of an event horizon , some of which are called black foils @xcite ( see @xcite for the construction with other purposes of @xmath0-wormholes , which actually can also act as mimickers ) , and gravastars @xcite . within the extremal charged class one can invoke extremal @xmath2-wormholes on the threshold of the formation of an event horizon , quasi - black holes @xcite ( see also @xcite ) , and wormholes on the basis of quasi - black holes from bonnor stars , to name a few . we want to elucidate , whether or not the objects belonging to these two classes remain regular in the near - horizon limit . the arguments of @xcite which rule out non - extremal limiting configurations as becoming singular do not apply to the wormhole case @xcite . thus , we carry out the corresponding analysis anew for both classes of objects .

black hole mimickers are possible alternatives to black holes , they would look observationally almost like black holes but would have no horizon . the properties in the near - horizon region where gravity is strong can be quite different for both type of objects , but at infinity it could be difficult to discern black holes from their mimickers . to disentangle this possible confusion , we examine the near - horizon properties , and their connection with far away asymptotic properties , of some candidates to black mimickers . we study spherically symmetric uncharged or charged but non - extremal objects , as well as spherically symmetric charged extremal objects . within the uncharged or charged but non - extremal black hole mimickers , we study non - extremal-wormholes on the threshold of the formation of an event horizon , of which a subclass are called black foils , and gravastars . within the charged extremal black hole mimickers we study extremal-wormholes on the threshold of the formation of an event horizon , quasi - black holes , and wormholes on the basis of quasi - black holes from bonnor stars . we elucidate , whether or not the objects belonging to these two classes remain regular in the near - horizon limit .

black hole mimickers are possible alternatives to black holes , they would look observationally almost like black holes but would have no horizon . the properties in the near - horizon region where gravity is strong can be quite different for both type of objects , but at infinity it could be difficult to discern black holes from their mimickers . to disentangle this possible confusion , we examine the near - horizon properties , and their connection with far away asymptotic properties , of some candidates to black mimickers . we study spherically symmetric uncharged or charged but non - extremal objects , as well as spherically symmetric charged extremal objects . within the uncharged or charged but non - extremal black hole mimickers , we study non - extremal-wormholes on the threshold of the formation of an event horizon , of which a subclass are called black foils , and gravastars . within the charged extremal black hole mimickers we study extremal-wormholes on the threshold of the formation of an event horizon , quasi - black holes , and wormholes on the basis of quasi - black holes from bonnor stars . we elucidate , whether or not the objects belonging to these two classes remain regular in the near - horizon limit . the requirement of full regularity , i.e. , finite curvature and absence of naked behavior , up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out potential mimickers in most of the cases . a list ranking the best black hole mimickers up to the worse , both non - extremal and extremal , is as follows : wormholes on the basis of extremal black holes or on the basis of quasi - black holes , quasi - black holes , wormholes on the basis of non - extremal black holes ( black foils ) , and gravastars . since , in observational astrophysics it is difficult to find extremal configurations ( the best mimickers in the ranking ) , whereas non - extremal configurations are really bad mimickers , the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of it .

0806.0845

c

we have studied wormhole and other configurations as possible mimickers of black holes . we have separated the configurations into non - extremal and extremal . for wormholes , we have examined separately two limiting procedures in which the wormhole throat approaches the black hole horizon . in the first procedure , we fix the location of an observer ( exactly on the throat ) . then , we change the spacetime ( making a wormhole on the verge of being a black hole ) . this is the situation bt . in the second , we change spacetime ( making a wormhole on the verge of a black hole ) , then place the shell outside the throat and move it toward the throat ( which coincides with the horizon ) this is the situation tb . this procedure is carried out for non - extremal and extremal configurations separately . in the non - extremal case it turned out that each of the limits under discussion is singular : either the kretschmann scalar or surface stresses on the throat ( or both ) diverge . thus , the limit is singular . in other words , a mimicker of a non - extremal black hole , made from a non - extremal wormhole , including the black foil of @xcite , is not smooth . we have summarized the results for the non - extremal case in a table . for the extremal case both the kretschmann scalar and surface stresses remain finite . this pronounced distinction between properties of the limiting configurations in the non - extremal and extremal cases is one counterpart of the conclusion made in @xcite that quasi - black holes can be only extremal . however , one should not forget about some subtleties connected with the fact that singular behavior can , in general , manifest itself not only in the value of the kretschmann scalar . even if this scalar is finite , a naked behavior is possible or even inevitable as was shown in in the present paper and in @xcite ( see , e.g. , sec . v of @xcite for a discussion about other subtleties in which the singular features of quasi - black holes are revealed ) . there is also another candidate for the role of a non - extremal black hole mimicker , a gravastar @xcite . however , the corresponding surface stresses grow unbound when the radius approaches the gravitational radius , as we have seen . from an astrophysical viewpoint , the situation bt in the non - extremal case , i.e. , a black foil , is more interesting since it implies no necessity of making a shell by hand . it is the case considered in @xcite . one of the questions raised in @xcite is whether it is possible or not to distinguish between a true non - extremal black hole , a schwarzschild black hole say , and a wormhole . the main conclusion of @xcite is that it is impossible to distinguish for any finite time in the limit under discussion . this conclusion is reached on the basis of considering properties of bodies moving along separate fixed geodesics and emitting signals detected at infinity . however , if from single geodesics we shift our attention to a congruence of geodesics , it turns out that the strong gravity forces , on the near horizon region , leave their imprint on the form of a moving body and , thus , on the properties of signals which an observer at infinity is detecting . if the surface of the body is luminescent , an observer at infinity would see either a finite width instead of a point , a continuous detection instead of separate pulses , and so on . it is essential that in the case discussed in @xcite the corresponding proper time of deformation tends to zero when the curvature grows unbound , with the time at infinity being finite . thus , at least in principle , an observer can distinguish between a black hole and an almost singular wormhole . the singular nature of the limit in the non - extremal case makes also questionable the applicability of the membrane paradigm used in @xcite . the key point in this paradigm consists in boundary conditions according to which a free - falling observer sees a finite value of physical fields on the horizon ( see @xcite , sec . ii ) . however , in the problem under discussion , typically , this observer as well as the geometry itself become ill - defined . only in some cases ( see model 2 , situation tb ) the curvature components remain finite in the free - falling frame . but even in such situations the infinite surface stresses on the horizon surface makes the physical meaning of the membrane paradigm unclear since this paradigm relies heavily on the concept of a regular surface . objects based on nearly extremal wormholes , although of less interest astrophysically perhaps , have a much better behavior in the sense that both the geometry and surface stresses remain finite . moreover , typically , there is no naked behavior . in this case , the effect of strong curvature is much less pronounced than in the case of quasi - black holes where a naked behavior is typical @xcite . in this sense , a wormhole composed on the basis of two extremal black holes seems to be the best mimicker of an extremal black hole . as by - product , we have obtained a model of a regular black hole ! thus , if we try to arrange a ranking of black hole mimickers , both non - extremal and extremal , the list looks as follows from top to bottom : wormholes on the basis of extremal black holes or on the basis of quasi - black holes , quasi - black holes , wormholes on the basis of non - extremal black holes ( and within these the best are black foils ) , and gravastars . bearing in mind that in observational astrophysics it is difficult to find extremal configurations ( the would be best mimickers ) , whereas non - extremal configurations are really bad mimickers , the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of it . in the present paper we have restricted ourselves to static spherically symmetric spacetimes . meanwhile , in a recent work @xcite the status of black hole mimickers is undermined in the rapidly rotating case as well since it is argued that they are unstable . we have also circumscribed our discussion to particular wormholes , gravastars and quasi - black holes @xcite-@xcite , since these objects are well adapted to our goal of examining the near - horizon properties and their connection with far away asymptotic properties . however , there are many other objects with properties that make them also potential black hole mimickers ( see , e.g. , @xcite ) and which are worthy of study within our formalism . o. z. thanks centro multidisciplinar de astrofsica centra for hospitality and a stimulating working atmosphere . this work was partially funded by fundao para a cincia e tecnologia ( fct ) - portugal , through project poci / fp/63943/2005 .

the requirement of full regularity , i.e. , finite curvature and absence of naked behavior , up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out potential mimickers in most of the cases . a list ranking the best black hole mimickers up to the worse , both non - extremal and extremal , is as follows : wormholes on the basis of extremal black holes or on the basis of quasi - black holes , quasi - black holes , wormholes on the basis of non - extremal black holes ( black foils ) , and gravastars . since , in observational astrophysics it is difficult to find extremal configurations ( the best mimickers in the ranking ) , whereas non - extremal configurations are really bad mimickers , the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of it .

black hole mimickers are possible alternatives to black holes , they would look observationally almost like black holes but would have no horizon . the properties in the near - horizon region where gravity is strong can be quite different for both type of objects , but at infinity it could be difficult to discern black holes from their mimickers . to disentangle this possible confusion , we examine the near - horizon properties , and their connection with far away asymptotic properties , of some candidates to black mimickers . we study spherically symmetric uncharged or charged but non - extremal objects , as well as spherically symmetric charged extremal objects . within the uncharged or charged but non - extremal black hole mimickers , we study non - extremal-wormholes on the threshold of the formation of an event horizon , of which a subclass are called black foils , and gravastars . within the charged extremal black hole mimickers we study extremal-wormholes on the threshold of the formation of an event horizon , quasi - black holes , and wormholes on the basis of quasi - black holes from bonnor stars . we elucidate , whether or not the objects belonging to these two classes remain regular in the near - horizon limit . the requirement of full regularity , i.e. , finite curvature and absence of naked behavior , up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out potential mimickers in most of the cases . a list ranking the best black hole mimickers up to the worse , both non - extremal and extremal , is as follows : wormholes on the basis of extremal black holes or on the basis of quasi - black holes , quasi - black holes , wormholes on the basis of non - extremal black holes ( black foils ) , and gravastars . since , in observational astrophysics it is difficult to find extremal configurations ( the best mimickers in the ranking ) , whereas non - extremal configurations are really bad mimickers , the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of it .

1310.8303

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low mass x - ray binaries ( lmxbs ) , comprising a black hole or neutron star primary ( @xmath8 ) and a low mass main sequence or evolved secondary ( @xmath9 ) , produce x - rays through the accretion of matter onto their primaries ( see reviews by e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? all black hole and many neutron star lmxbs are transient , experiencing occasional outbursts during which their mass accretion rate and x - ray luminosity increase by several orders of magnitude . these outbursts have typical durations spanning days to months . the cycle of outburst and quiescence in lmxbs is explained by the disc instability model ( see e.g. the review by * ? ? ? mass transferred from the secondary builds up in an accretion disc around the primary . as the disc density increases , the temperature rises to the point at which hydrogen ionizes . the change in ionization state is associated with a switch to higher viscosity , increasing mass accretion onto the primary and causing an outburst . this enhanced accretion eventually lowers the disc density and temperature to the point at which the viscosity returns to its original value . unlike cataclysmic variables , where outbursts are terminated by a cooling wave after a few days , the outbursts of lmxbs are prolonged by x - ray irradiation , which heats the disc and traps it in the hot , ionized state @xcite . in sufficiently short period systems the whole disc is irradiated and the majority of the disc mass is accreted . the accretion rate during an outburst is known to decay exponentially ( e.g. * ? ? ? * ; * ? ? ? * ) , unless the disk is entirely irradiated ( see section 3.2 ) . it was characterised by @xcite as : @xmath10 here @xmath11 is the disc density and @xmath12 is the viscosity , where @xmath13 is the hot state viscosity parameter , @xmath14 is the sound speed , and h is the vertical scale height of the disk . the maximum extent of the disc , @xmath15 , is limited by the size of the roche lobe of the primary and can be related to the orbital period ( @xmath16 ) . for typical mass ratios ( @xmath17 ) , @xmath18 cm , where @xmath19 is the orbital period in hours and @xmath20 is the primary mass in solar masses . both the peak accretion rate ( @xmath21 ) and outburst duration ( @xmath22 , where @xmath23 is the disc mass ; c.f . section 3 ) depend inherently on the orbital period . the radiative efficiency of accretion in an lmxb is given by @xmath24 , where @xmath25 for a radiatively efficient flow through a thin accretion disc ( see e.g , * ? ? ? * ) . at low accretion rates cooling becomes inefficient and a radiatively inefficient , advection dominated accretion flow ( adaf ) can occur @xcite . the adaf model is a solution to the hydrodynamical equations of viscous differentially rotating flows with low sub - eddington accretion rates . the accreting gas has a very low density , leading to an optically thin flow which can not cool efficiently within an accretion time . the viscous energy is stored in the gas as thermal energy rather than being radiated away , and is advected onto the central compact object . the transition from radiatively efficient to inefficient flow is expected to take place once the accretion luminosity reaches a few percent of the eddington luminosity ( @xmath3 ) . for black hole primaries , which lack a hard surface , @xmath26 and the accretion energy is carried with the mass flow into the hole or transferred elsewhere , e.g as radio jets or mechanical outflows . neutron star primaries do not experience a drop in accretion efficiency because the advected energy must always be radiated from the stellar surface . hence , at sufficiently short periods ( and thus small disc radii and peak accretion rates ) black hole lmxbs will undergo fainter , shorter outbursts than comparable neutron star systems , making them more difficult to detect . the relationship between orbital period and peak outburst luminosity for lmxbs is well established ( e.g. * ? ? ? * ; * ? ? ? @xcite studied the outburst luminosities of a sample of transient lmxbs observed by the rossi x - ray timing explorer ( _ rxte _ ) . they showed that there was no distinguishable difference in the orbital period - peak outburst luminosity relation of black holes compared to neutron star primaries , when luminosities were measured in eddington units . however , they suggest that the two populations may diverge at short periods . along similar lines , note that the low peak outburst luminosities in short period black hole lmxbs can cause them to remain in a low luminosity - hard spectral state , rather than entering the high luminosity - soft state expected for radiatively efficient accretion . this breed of outburst , where sources remain in the low - hard state throughout , has been observed in several sources @xcite in addition to establishing a relation between orbital period and peak outburst luminosity , @xcite point out that the absence , in their dataset , of black holes with orbital periods of @xmath27hr , may be caused by radiatively inefficient accretion lowering the peak outburst luminosities of these systems . in this paper , we investigate this hypothesis , using the ritter - kolb catalogue @xcite to show that there is statistical evidence for a dearth of black holes in lxmbs at short orbital periods . we suggest that this is caused by the increasing importance of radiatively inefficient accretion in black hole systems lowering not only peak outburst luminosities but also outburst durations and x - ray duty cycles . additionally , we investigate the nature of the transition to radiatively inefficient accretion , modelling it as an instantaneous change to @xmath1 = 0 at a fraction @xmath2 of the eddington luminosity ( @xmath3 ) and as a power law decrease , @xmath4 , below @xmath28 . in section 2 we present the sample of systems and the statistical evidence for the lack of black hole lmxbs at short orbital periods . in section 3 we study the effect of a radiative efficiency switch on the peak luminosities and outburst timescales of black hole lmxbs . we determine the conditions under which these effects can hide a short orbital period black hole population in section 4 . this is followed by a discussion of our findings and our conclusions .

by comparing the orbital period distributions of black hole and neutron star low mass x - ray binaries ( lmxbs ) in the ritter - kolb catalogue we show that there is statistical evidence for a dearth of black hole systems at short orbital periods ( h ) . this could either be due to a true divergence in orbital period distributions of these two types of system , or to black hole lmxbs being preferentially hidden from view at short orbital periods . the peak luminosity and the duration of x - ray binary outbursts are related to the disc radius and , hence , the orbital period . at short periods , where the peak outburst luminosity drops close to the threshold for radiatively inefficient accretion , black hole lmxbs have lower outburst luminosities , shorter outburst durations and lower x - ray duty cycles than comparable neutron star systems . we estimate the outburst properties and orbital period distribution of black hole lmxbs using two models of the transition to radiatively inefficient accretion : an instantaneous drop in accretion efficiency ( ) to zero , at a fraction ( ) of the eddington luminosity ( ) and a power - law efficiency decrease , , for l l . we show that a population of black hole lmxbs at short orbital periods can only be hidden by a sharp drop in efficiency , either instantaneous or for . [ firstpage ] stars : binaries x - rays : binaries black hole physics accretion accretion discs

by comparing the orbital period distributions of black hole and neutron star low mass x - ray binaries ( lmxbs ) in the ritter - kolb catalogue we show that there is statistical evidence for a dearth of black hole systems at short orbital periods ( h ) . this could either be due to a true divergence in orbital period distributions of these two types of system , or to black hole lmxbs being preferentially hidden from view at short orbital periods . we explore the latter possibility , by investigating whether black hole lmxbs could be concealed by a switch to radiatively inefficient accretion at low luminosities . the peak luminosity and the duration of x - ray binary outbursts are related to the disc radius and , hence , the orbital period . at short periods , where the peak outburst luminosity drops close to the threshold for radiatively inefficient accretion , black hole lmxbs have lower outburst luminosities , shorter outburst durations and lower x - ray duty cycles than comparable neutron star systems . these factors can combine to severely reduce the detection probability of short period black hole lmxbs relative to those containing neutron stars . we estimate the outburst properties and orbital period distribution of black hole lmxbs using two models of the transition to radiatively inefficient accretion : an instantaneous drop in accretion efficiency ( ) to zero , at a fraction ( ) of the eddington luminosity ( ) and a power - law efficiency decrease , , for l l . we show that a population of black hole lmxbs at short orbital periods can only be hidden by a sharp drop in efficiency , either instantaneous or for . this could be achieved by a genuine drop in luminosity or through abrupt spectral changes that shift the accretion power out of a given x - ray band . [ firstpage ] stars : binaries x - rays : binaries black hole physics accretion accretion discs

1211.2362

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to express macroscopic observables in terms of the microscopic parameters of composite particles , one has to reduce an infinite number of mechanical degrees of freedom to a few hydrodynamical degrees of freedom@xcite . two typical techniques are projection and coarse - graining . in the projection method , one can either project the density matrix to a reduced density matrix for the relevant degrees of freedom ( schrodinger picture)@xcite or project a sum of microscopic mechanical variables to a macroscopic slow variable ( heisenberg picture)@xcite . while in the coarse - graining method , excepting the obligatory ensemble average , one still has to carry out at least one of three average procedures : ( 1 ) coarse - graining in time@xcite ; ( 2 ) coarse - graining in space@xcite ; or ( 3 ) coarse - graining in the eigenvalue spectrum of energy and other collective variables@xcite . in the coarse - graining techniques , the spatial coarse grained average plays an essential role in formulating all macroscopic problems . macroscopically , a non - equilibrium process in a fluid is described by some local hydrodynamic ( thermodynamic , macroscopic ) variables : temperature , stress , concentration and macroscopic velocity field etc@xcite . the fundamental assumption behind this macroscopic description is that there exists a local equilibrium at each coarse - grained spatial ` point ' and at every coarse - grained temporal ` moment'@xcite . similarly in the kinetic theories , at least three of the arguments of the single - particle distribution function , time , position and translational momentum are defined in a coarse - grained sense ( far more coarse - grained than the requirement of uncertainty principle)@xcite . as an alternative to the distribution function in phase space , onsager introduced a distribution function for the coarse grained moments of the conserved quantities ( displacements)@xcite . to obtain hydrodynamic equations and transport coefficients , m. s. green noticed that the resolution of a macroscopic measurement is finite , so that one must eliminate the high wave number components of a collective variable which are are unmeasurable . the observed value of a hydrodynamic variable is given by averaging the truncated@xcite collective variable over the distribution function of markoff process@xcite . it is well - known that temporal coarse - graining ( tcg ) is not necessary for deriving the macroscopic maxwell equations ( mame ) from the microscopic ones@xcite . a safe lower limit of length @xmath0 for a macroscopic description of reflection and refraction of visible light can be taken as @xmath1@xcite . the time scale @xmath2 associated with @xmath0 is in the range of atomic or molecular motions , a tcg at a time scale @xmath2 is meaningless@xcite . moreover , if one averages the motion of the particles over a time scale longer than @xmath2 , the scattering phenomena will be smeared@xcite . in the mame , the sources of fields are the total charge density and the total current density@xcite . at the same time , the induced charge density and the induced current density are also the responses of the system to the external fields . since no tcg is taken in deriving mame , one should not require tcg in computing current density ( conductivity)@xcite . the energy dissipation of system is taken care of by the thermal contact with a thermal bath@xcite . it seems that tcg is not needed for the irreversible processes caused by the mechanical distrubances@xcite . an open question is whether tcg is necessary to describe an irreversible process induced by an internal ( thermal ) disturbance@xcite . several schemes have been designed to replace an internal disturbance with a fictitious mechanical disturbance@xcite . but these methods assume _ a priori _ that the navier - stokes equation is valid@xcite . in other theories , tcg is often taken along with spatial coarse - graining and ensemble average@xcite . in particularly , tcg is viewed as a critical step producing irreversibility in the kinetic approach ( master or boltzmann equation)@xcite . although a velocity gradient is often viewed as an _ internal _ disturbance , it can be realized in a ` mechanical ' manner . in a fluid , two obvious ways to produce a velocity gradient are ( i ) moving a boundary plate which confines the fluid ; and ( ii ) stirring the fluid with a rod in the middle . in both situations , a velocity gradient is produced by the interaction between the fluid and an external object at the solid - fluid interface . a non - equilibrium ` hamiltonian ' has been phenomenologically introduced to effectively compute viscosity@xcite . in addition , for a mechanical disturbance@xcite , one may define microscopic response in a pure state . the observed macroscopic response ( consequently transport coefficient ) is given by spatial coarse graining the microscopic response and averaging over possible initial conditions@xcite . it is worthwhile to explore whether we could describe viscosity in a more ` mechanical ' manner : ( i ) not invoking temporal coarse - graining ; and ( ii ) not assuming local equilibrium as the starting point . in this paper , we show that shear viscosity can be strictly calculated from a time - dependent schrodinger equation , and time coarse - graining can be avoided . one may repeat the same procedure for bulk viscosity _ mutatis mutandis_. in the discussion , we will only use the schrodinger picture . because a hydrodynamic quantity is a bilinear form of the many - body wave function , all the conclusions are valid for any set of identical particles : bosons or fermions . only when we take concrete approximations for the many - body wave functions , do we need to know whether the particles are fermions or bosons . in sec . [ cons ] , we first express the velocity gradient in a fluid as a constraint on the wave function of the fluid , cf . eq.([bc ] ) . to prescribe an internal disturbance like velocity gradient , one needs the wave function of the system . the wave function must be determined self - consistently with the given velocity gradient . with velocity gradient as a constraint , the evolution equation for wave function is then derived using the lagrange multiplier method@xcite , cf . eqs.([eu1],[eu3],[eu4 ] ) . from the appearance , it is a time - dependent schrodinger equation . two additional terms [ eqs.([eu3],[eu4 ] ) ] appear in the ` hamiltonian ' . both of them contain the occupation probabilities of admissible initial states , which reflects the fact that a velocity gradient is an internal disturbance . on the other hand a mechanical perturbation is completely specified by the time dependence of external field@xcite . in sec . [ shou ] , we first discuss the entropy production rate of the system + bath , cf . eqs.([entr],[tre ] ) . secondly , we check the mass conservation law , cf . eqs.([hmc0],[hmc ] ) . thirdly , the microscopic response eq.([flu ] ) to the velocity gradient ( the momentum flux in a pure state ) is obtained from the momentum conservation law in a pure state . the dissipation caused by a mechanical perturbation depends on the occupation probabilities of admissible initial states . because a velocity gradient is an internal disturbance , the dissipation caused by a velocity gradient depends on the _ squares _ of the occupation probabilities of admissible initial states this feature is clearly seen in the time rates of change of energy , mass and momentum . representing velocity gradient as a constraint on the wave function [ eq.([bc ] ) ] depends critically on the assumption that a suitable spatial coarse - graining is adequate@xcite to describe internal friction . in sec . [ put ] we show that the spatial coarse - graining average automatically contains a coarse - graining in time [ eq.([3 ] ) ] and a coarse - graining in eigenvalue spectrum of collective variables [ sec . [ egcr ] ] . in sec . [ dirac ] , we apply the method of variation constants to obtain the lagrange multipliers which appear in the solution of the time - dependent schrodinger equation . the lagrange multipliers characterize the interaction on the system exerted by the boundary plates . the phenomenological non - equilibrium ` hamiltonian'@xcite can be obtained from @xmath3 , the interaction of system with plates linear in velocity gradient . the shear viscosity is read from the macroscopic momentum flux ( [ mrf ] ) which is deduced from the wave function of system at some moment . in sec . [ tcd ] , we explain that applying dirac perturbation theory to transport process is valid . various time scales in the momentum transport process are discussed . we show that the length scale of spatial coarse - graining is determined by an intrinsic time scale . in sec . [ fph ] , we show that the macroscopic stress tensor derived from the microscopic response method is the same as that derived from averaging the momentum flux operator over the density matrix . we developed a cumulant expansion for the density operator . when we replace the operator in the exponent with its expectation value , we reproduce the non - equilibrium density matrix obtained from other approaches .

it allows us to define the microscopic response to a velocity gradient in a pure state . the dissipation caused by a velocity gradient depends on the square of initial occupation probability , whereas the dissipation caused by a mechanical perturbation depends on the initial occupation probability itself . we apply the method of variation of constants to solve the time - dependent schrodinger equation with constraints . the various time scales appearing in the momentum transport are estimated .

by viewing a velocity gradient in a fluid as an internal disturbance and treating it as a constraint on the wave function of a system , a linear evolution equation for the wave function is obtained from the lagrange multiplier method . it allows us to define the microscopic response to a velocity gradient in a pure state . taking a spatial coarse - graining average over this microscopic response and averaging it over admissible initial states , we achieve the observed macroscopic response and transport coefficient . in this scheme , temporal coarse - graining is not needed . the dissipation caused by a velocity gradient depends on the square of initial occupation probability , whereas the dissipation caused by a mechanical perturbation depends on the initial occupation probability itself . we apply the method of variation of constants to solve the time - dependent schrodinger equation with constraints . the various time scales appearing in the momentum transport are estimated . the relation between the present work and previous theories is discussed .

1001.2037

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the discovery of strong gravitational lensing in q0957@xmath6561 @xcite opened up the possibility of using strong lens systems to study cosmology and astrophysics . roughly a few hundred strong lens systems produced by massive galaxies have been discovered to date , with quasars ( e.g. , * ? ? ? * ) , radio sources ( e.g. , * ? ? ? * ; * ? ? ? * ) , and galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) appearing as source populations . these samples of strong lenses have been extensively used to constrain dark energy , the density profile of lensing galaxies , and the evolution of massive ellipticals ( see , e.g. , * ? ? ? * for a review ) . it is expected that large new samples of strong lenses will be obtained in future wide - field imaging surveys ( e.g. , * ? ? ? * ; * ? ? ? * ) . for instance , the large synoptic survey telescope ( lsst ; * ? * ) will observe a 20,000 deg@xmath7 region with a final limiting magnitude of @xmath8 , which is considerably wider and deeper than existing optical imaging surveys such as the sloan digital sky survey ( sdss ; * ? ? ? more importantly , future imaging surveys such as lsst s will pay particular attention to the acquisition of time - domain data , mostly in order to study transient objects including supernovae ( sne ) . in this paper , we present detailed predictions of the numbers of time - variable sources we can expect to be strongly lensed in ongoing and future time domain optical imaging surveys . we focus on time - variable sources for two reasons . first , time domain data enable us to identify strong lenses by taking advantage of time variability @xcite . @xcite proposed to find strong lenses by looking for `` extended variable sources '' in time - domain data , and argued that this technique should be very efficient due to the low levels of contamination in the difference images . second , time - variable sources allow us to measure time delays between multiple images ; these time delays contain rich information on the lens potentials as well as cosmology ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the obvious and traditional example of such a strongly lensed time - variable source is a quasar ( qso ) . of @xmath9 gravitationally lensed quasars currently known , time delays have been measured for only @xmath10 ( see * ? ? ? * for a recent compilation ) . a major advance offered by the upcoming imaging surveys is their potential not only to discover new lenses but also monitor them as well . some of the survey telescopes we will consider do have larger static surveys planned , but we do not consider them on the grounds that if they are wide enough to be competitive , they will be limited by the required monitoring follow - up . synoptic surveys ( such as those designed to discover supernovae ) should provide some estimate of the lens time delays we are careful to point out where this may not be the case . the scope of several planned surveys allows us also to consider sne as time - variable sources . while a distant sn highly magnified by a foreground massive cluster has recently been identified @xcite , no multiply - imaged sn has yet been discovered . however , the possibility of discovering such strongly - lensed sne by future time - domain surveys such as the joint dark energy mission ( jdem ) and the lsst has been pointed out @xcite . a particularly enticing feature of lensed sne is that , if they are type - ia , the `` standardizable candle '' nature of the peak brightness allows a direct determination of the lensing magnification factor , which breaks the degeneracy between the lens potential and the hubble constant @xcite . indeed , we expect any large sample of time delay lenses to be useful in constraining cosmological parameters . the idea of using strong gravitational lens systems with time - variable sources to measure the hubble constant is an old one @xcite ; in fact , the time delays between images provide a way of measuring the `` time - delay distance '' to the lens . this quantity is a combination of the angular diameter distances to the lens , source , and between the two , and while primarily sensitive to @xmath11 , it does also depend on the other cosmological parameters ( see e.g. , * ? ? ? * for a recent high - precision measurement ) . attempts to measure the hubble constant from the statistical analysis of the current lensed quasar sample @xcite have yielded values consistent with constraints from other cosmological probes ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in future , larger samples covering a wide range of lens and source redshift permutations should provide interesting constraints on the dark energy equation of state as well as hubble constant @xcite . in this work , we revisit the forecast constraints on dark energy parameters for the lsst , using new , realistic predicted distributions of strong lenses . this paper is organised as follows . in section [ sec : calc ] we describe the ingredients of our lens abundance calculation , including our assumptions about both the lens and source populations . we then present our predictions for various survey depths and areas in section [ sec : survey ] . we then present monte carlo realisations of some fiducial survey lens catalogues in section [ sec : mock ] , and use these to explore the potential of some of these in constraining cosmological parameters via the time delay distances to the lenses in section [ sec : cosmo ] . after a brief discussion ( section [ sec : discuss ] ) we conclude in section [ sec : concl ] . we take as the parameters of a fiducial cosmological model @xmath12 , @xmath13 , @xmath14 , @xmath15 and @xmath16 . we denote the angular diameter distance from observer to lens as @xmath17 , from observer to source as @xmath18 , and from lens to source as @xmath19 .

the lsst should also find some 130 lensed supernovae during the 10-year survey duration , which is compared with lensed supernovae predicted to be found by a deep , space - based supernova survey done by the joint dark energy mission ( jdem ) . while this is encouraging in the sense that these uncertainties are only 50% larger than those predicted for a space - based type - ia supernova sample , we show how the dark energy figure of merit degrades with decreasing knowledge of the the lens mass distribution . - .5 in [ firstpage ] cosmological parameters cosmology : theory gravitational lensing

cadenced optical imaging surveys in the next decade will be capable of detecting time - varying galaxy - scale strong gravitational lenses in large numbers , increasing the size of the statistically well - defined samples of multiply - imaged quasars by two orders of magnitude , and discovering the first strongly - lensed supernovae . we carry out a detailed calculation of the likely yields of several planned surveys , using realistic distributions for the lens and source properties and taking magnification bias and image configuration detectability into account . we find that upcoming wide - field synoptic surveys should detect several thousand lensed quasars . in particular , the large synoptic survey telescope ( lsst ) should find more than some 8000 lensed quasars , some 3000 of which will have well - measured time delays . the lsst should also find some 130 lensed supernovae during the 10-year survey duration , which is compared with lensed supernovae predicted to be found by a deep , space - based supernova survey done by the joint dark energy mission ( jdem ) . we compute the quad fraction in each survey , predicting it to be for the lensed quasars and for the lensed supernovae . generating a mock catalogue of around 1500 well - observed double - image lenses , as could be derived from the lsst survey , we compute the available precision on the hubble constant and the dark energy equation parameters for the time delay distance experiment ( assuming priors from planck ) : the predicted marginalised 68% confidence intervals are , , and . while this is encouraging in the sense that these uncertainties are only 50% larger than those predicted for a space - based type - ia supernova sample , we show how the dark energy figure of merit degrades with decreasing knowledge of the the lens mass distribution . - .5 in [ firstpage ] cosmological parameters cosmology : theory gravitational lensing

1001.2037

c

we have presented detailed calculations of the likely yields of several planned cadenced surveys , adopting realistic distributions for the lens and source properties , and taking account of the selection functions , including the magnification bias . we find that , for example , the lsst will discover @xmath243 lensed quasars ( @xmath244 of which will have time delay measurements ) and @xmath9 lensed sne . approximately one third of lensed sne will be type - ia . the lenses are dominated by double ( two - image ) lenses , with expected quad fractions of @xmath245% for lensed quasars and @xmath246% for lensed sne . we have also produced mock catalogues of lenses , which are useful for probing strong lensing selection effects and the feasibility of various science projects . we have used a mock catalogue of @xmath247 well - observed double lenses in lsst to derive expected cosmological constraints . specifically , we derived precisions on the hubble constant and the dark energy equation of state parameters from this sample of time delay measurements , assuming priors from planck . the resulting predicted marginalised 68% confidence intervals are @xmath3 , @xmath4 , and @xmath5 , implying that time delays can improve constraints from a jdem supernova type - ia sample . however , this result holds only if we have accurate prior knowledge of the lens population s mean effective density profile : we find that the prior on the mean radial density slope has to be @xmath248 in order for time delays from the lsst strong lens to be a useful future cosmological probe .

we carry out a detailed calculation of the likely yields of several planned surveys , using realistic distributions for the lens and source properties and taking magnification bias and image configuration detectability into account . we find that upcoming wide - field synoptic surveys should detect several thousand lensed quasars . in particular , the large synoptic survey telescope ( lsst ) should find more than some 8000 lensed quasars , some 3000 of which will have well - measured time delays . , we compute the available precision on the hubble constant and the dark energy equation parameters for the time delay distance experiment ( assuming priors from planck ) : the predicted marginalised 68% confidence intervals are , , and .

cadenced optical imaging surveys in the next decade will be capable of detecting time - varying galaxy - scale strong gravitational lenses in large numbers , increasing the size of the statistically well - defined samples of multiply - imaged quasars by two orders of magnitude , and discovering the first strongly - lensed supernovae . we carry out a detailed calculation of the likely yields of several planned surveys , using realistic distributions for the lens and source properties and taking magnification bias and image configuration detectability into account . we find that upcoming wide - field synoptic surveys should detect several thousand lensed quasars . in particular , the large synoptic survey telescope ( lsst ) should find more than some 8000 lensed quasars , some 3000 of which will have well - measured time delays . the lsst should also find some 130 lensed supernovae during the 10-year survey duration , which is compared with lensed supernovae predicted to be found by a deep , space - based supernova survey done by the joint dark energy mission ( jdem ) . we compute the quad fraction in each survey , predicting it to be for the lensed quasars and for the lensed supernovae . generating a mock catalogue of around 1500 well - observed double - image lenses , as could be derived from the lsst survey , we compute the available precision on the hubble constant and the dark energy equation parameters for the time delay distance experiment ( assuming priors from planck ) : the predicted marginalised 68% confidence intervals are , , and . while this is encouraging in the sense that these uncertainties are only 50% larger than those predicted for a space - based type - ia supernova sample , we show how the dark energy figure of merit degrades with decreasing knowledge of the the lens mass distribution . - .5 in [ firstpage ] cosmological parameters cosmology : theory gravitational lensing

1304.0552

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given a @xmath0-regular rooted tree , attach to each edge @xmath2 a random variable @xmath3 , such that the variables are independent and identically distributed . for a vertex @xmath4 in the tree , denote by @xmath5 the sum of the variables @xmath3 over all edges @xmath2 on the path from the root to @xmath4 . this defines a branching random walk , a basic model for a disordered tree . it is natural to ask for an efficient algorithm which explores the vertices of this tree in order to find vertices @xmath4 with a large value of @xmath5 . in fact , aldous @xcite proposed this problem as a benchmark problem for comparing different generic optimization algorithms , since the nave approach , which would be to simply explore all vertices down to the level @xmath7 in the tree and taking the one with the maximal value of @xmath5 , is a bad choice for an algorithm because the number of vertices grows exponentially in @xmath7 . the metropolis algorithm is a general recipe for constructing a discrete - time markov chain on a finite state space for which a given distribution @xmath9 is stationary and whose transitions respect a given graph structure of the state space . in the context of the comparison of algorithms discussed earlier , aldous @xcite suggested using the metropolis algorithm to `` sample '' a certain gibbs measure on the vertices of a branching random walk tree , namely the one which assigns mass @xmath10 to a vertex @xmath4 , for some parameter @xmath11 . in the case where this measure is infinite , for example when there is an infinite number of vertices @xmath4 with @xmath12 , this algorithm should `` walk down the tree '' and , for an appropriate choice of the parameter @xmath13 , find vertices @xmath4 with high values of @xmath5 . let @xmath14 denote the level of the vertex @xmath4 in the tree , and let @xmath15 be the vertex visited by the metropolis algorithm at the time @xmath16 . aldous raised the following natural question : if the maximum of the branching random walk has positive speed , that is , if @xmath17 , does there exist a choice of the parameter @xmath13 , such that @xmath18 ? we will answer this question in the affirmative for a certain class of laws of the variables @xmath3 , including the binomial distribution . in fact , we show more : let @xmath19 , which exists almost surely @xcite . we show that there exists a parameter @xmath20 , such that @xmath21 and @xmath22 , where @xmath23 is the asymptotic variance of @xmath24 , which we show to be positive and finite . this result was conjectured by aldous , who gave heuristic arguments and numerical evidence for it [ in the case where the variables @xmath3 only take the values @xmath25 and @xmath26 . results of this type are also known as _ einstein relations _ in the domain of random walks in random environments and our methods of proof will indeed rely on many techniques from this field , some of which have been obtained recently . we are given a @xmath0-regular infinite rooted tree , @xmath27 . the root is denoted by @xmath28 and the level / depth of a vertex @xmath4 in the tree by @xmath14 . the notation @xmath29 denotes that @xmath30 and @xmath4 are connected by an edge . the parent of a vertex @xmath4 is denoted by @xmath31 ( with the convention @xmath32 ) . we write @xmath33 if @xmath30 is an ancestor of @xmath4 and @xmath34 if @xmath33 but @xmath35 . we furthermore use the following handy notation : if @xmath33 , then @xmath36 $ ] denotes the set of vertices on the path from @xmath30 to @xmath4 , including @xmath30 and @xmath4 . the notation @xmath37 $ ] , @xmath38 and @xmath39 then has obvious meaning . to each edge @xmath40 , we then attach a random variable @xmath3 , such that the collection @xmath41 ) is i.i.d . according to the law of a random variable @xmath42 . here , orientation of the edges matters , and we will set @xmath43 for all @xmath4 . in what follows , we will introduce several assumptions , _ which we assume to hold throughout the paper_. we begin with the following assumptions on the law of @xmath42 . the law of @xmath42 is of compact support , that is , @xmath44 . there exists @xmath20 , such that @xmath45=e[f(-x)]$ ] for all bounded measurable functions @xmath46 . @xmath47 , where @xmath48 + \log(d-1)$ ] . note that ( xr ) is equivalent to the laplace transform @xmath49 $ ] being symmetric around @xmath50 . in particular , the constant @xmath51 is necessarily unique unless @xmath52 almost surely . an example for a law satisfying ( xs ) , ( xr ) and ( xm ) is the distribution of @xmath53 , where @xmath54 follows a binomial distribution of parameters @xmath7 and @xmath55 , with @xmath56 , where @xmath57 . in this case , @xmath58 . in general , in order to construct a law satisfying ( xs ) and ( xr ) , one can start from a symmetric random variable @xmath42 taking values in a compact interval @xmath59 $ ] and define a law with radon nikodym derivative proportional to @xmath60 with respect to the law of @xmath42 . this law will then satisfy ( xm ) for @xmath51 small enough . we remark that assumption ( xs ) seems not to be crucial , and the argument extends to certain distributions with non compact support , at the cost of more complicated technical arguments . to avoid this complication we chose to present the result under this simplifying assumption . on the other hand , assumption ( xr ) is essential for our treatment , as it ensures , at @xmath51 , the reversibility of the markov chain consisting of the environment viewed from the point of view of the particle ; see proposition [ prop : rev_erg ] . the reversibility will be crucial both in the application of the kipnis varadhan theory , as well as in the proof of validity of the einstein relation ( one may expect a correction term for non reversible chains ) . we now define the branching random walk by @xmath61 } x({\vec}u , u),\qquad s ( \root ) = 0.\ ] ] note that @xmath62 for every two vertices @xmath30 and @xmath4 with @xmath29 , by the above convention that @xmath63 . since @xmath64 is the log - laplace transform of this branching random walk , it is known @xcite that @xmath65 exists and is positive under assumption ( xm ) . note further that assumptions ( xm ) and ( xr ) together imply that @xmath66 for all @xmath67 , such that @xmath68 exists and is negative @xcite . in order to define the metropolis algorithm , we are given a function @xmath69 satisfying the following conditions [ examples are @xmath70 and @xmath71 : @xmath72 takes values in @xmath73 $ ] , is nondecreasing and satisfies @xmath74 and @xmath75 . it is lipschitz - continuous and continuously differentiable on @xmath76 . it satisfies the functional equation @xmath77 for all @xmath78 . for a given realization of the branching random walk and a parameter @xmath67 , the metropolis algorithm is then the markov chain @xmath79 on the vertices of the tree with the transition probabilities @xmath80 given by @xmath81 we denote the ( annealed , i.e. , averaged over the environment ) law of the metropolis algorithm on the branching random walk tree by @xmath82 and expectation with respect to this law by @xmath83 . our main theorem is the following : [ th : einstein ] set @xmath84 . the limit @xmath85 exists @xmath86-almost surely and is a strictly positive and finite constant . for each @xmath67 , the deterministic limit @xmath87 exists @xmath82-almost surely and satisfies @xmath88 we note that the existence of @xmath89 and the fact that it vanishes at @xmath90 were already shown in @xcite ( in a slightly more restrictive setup ) . the main novelty in theorem [ th : einstein ] is the proof of the einstein relation ( [ eq - einsteinfinal ] ) , as well as the fact that the right side is strictly positive . our main inspiration , as noted above , is aldous s work @xcite . in that paper , aldous makes the crucial observation that a reversible invariant measure for the environment viewed from the point of view of the particle exists at @xmath90 , and derives from this that @xmath91 , and the existence of the limit @xmath23 under @xmath86 ; he also completely analyzes a greedy algorithm and formulates a series of conjectures , some answered here . in the same paper , aldous also refers speculatively to @xcite as relevant to the analysis near @xmath90 ; indeed , the approach of the latter to proofs of the einstein relation forms the basis of the current paper , as well to recent advances in the analysis of the einstein relation for disordered systems , as we now discuss . the einstein relation ( er ) links the asymptotic variance of additive functionals of ( reversible ) markov chains in equilibrium to the chains response to small perturbations . in a weak limit ( where the time - scale is related to the strength of the perturbation ) , lebowitz and rost @xcite provide a general recipe ( based on the kipnis varadhan theory , see @xcite for a comprehensive account ) for the validity of a weak form of the er in disordered systems . for the tagged particle in the symmetric exclusion process , the er was proved by loulakis in @xmath27 @xcite by perturbative methods ( using transience in an essential way ) ; this approach was adapted to bond diffusion in @xmath92 in special environment distributions @xcite . for mixing dynamical random environments with spectral gap , a full perturbation expansion was proved in @xcite . significant recent progress was achieved by @xcite , where the lebowitz rost approach was combined with good _ uniform in the environment _ estimates on certain regeneration times in the transient regime , that are used to pass from a weak er to a full er . these uniform estimates are typically not available for random walks on ( random ) trees , and a completely different approach , based on explicit recursions , was taken in @xcite , where ( biased ) random walks on galton watson trees were analyzed . while we still consider walks on trees , the approach we take is closer to that of @xcite , while replacing their uniform regeneration estimates with probabilistic estimates , in the spirit of @xcite . see also @xcite for another approach to the proof of the er in the context of balanced random walks . as mentioned above , the starting point is aldous s observation that under @xmath86 , the environment viewed from the point of view of the particle forms a _ reversible _ markov chain . we begin by proving this ( proposition [ prop : rev_erg ] ) , and then apply the kipnis varadhan theory to deduce an invariance principle for anti - symmetric additive functionals ( lemma [ lem : antisym ] ) . this allows us to prove the weak er , theorem [ th : weak_er ] , following the lebowitz rost recipe . to handle the perturbation , estimates on regeneration times and distances are crucial . we work with _ level _ regeneration times that are introduced in section [ sec - reg ] ; these involve the random walk location @xmath93 , not the vertices values @xmath94 ; of course , the latter influence the transition probabilities of the random walk . in order to transform the weak er to a full er , we need uniform bounds on the moments of the regeneration times . these are obtained in proposition [ prop : tau_moments ] , where it is proved that the regeneration times exhibit uniform annealed stretched - exponential bounds . the proof has two main steps : first , exponential moments are proved for regeneration _ distances _ , using in a crucial way a structure lemma of grimmett and kesten ; see lemma [ lem : excursion_tail ] . then , the estimates for regeneration times are obtained , using that the walk must visit many well - separated fresh vertices , and between two such visits , the walk has a large enough probability to hit distant levels . in proving the last statement , an argument of aidkon @xcite is used ; see lemma [ lem : fresh ] .

consider a-ary rooted tree ( ) where each edge is assigned an i.i.d . ( bounded ) random variable of negative mean . assign to each vertex the sum of over all edges connecting to the root , and assume that the maximum of over all vertices at distance from the root tends to infinity ( necessarily , linearly ) as tends to infinity .

consider a-ary rooted tree ( ) where each edge is assigned an i.i.d . ( bounded ) random variable of negative mean . assign to each vertex the sum of over all edges connecting to the root , and assume that the maximum of over all vertices at distance from the root tends to infinity ( necessarily , linearly ) as tends to infinity . we analyze the metropolis algorithm on the tree and show that under these assumptions there always exists a temperature of the algorithm so that it achieves a linear ( positive ) growth rate in linear time . this confirms a conjecture of aldous [ _ algorithmica _ * 22 * ( 1998 ) 388412 ] . the proof is obtained by establishing an einstein relation for the metropolis algorithm on the tree

1611.04084

c

recently , a novel type of rnyi entropy on a black - hole horizon was proposed by bir and czinner @xcite , in which a logarithmic formula of the original rnyi entropy was used and the bekenstein hawking entropy was regarded as a nonextensive tsallis entropy . in this study , the modified rnyi entropy has been applied to the holographic equipartition law proposed by padmanabhan @xcite , to investigate the cosmological constant problem and alternative dark energy models based on the holographic equipartition law . consequently , the acceleration equation , which includes an extra driving term , can be derived in a homogeneous , isotropic , and spatially flat universe . the extra driving term is a logarithmic formula which can explain the accelerated expansion of the late universe , as for alternative ( effective ) dark energy . under two specific conditions , the extra driving term is found to be the constant - like and @xmath111-like terms , respectively . in particular , when a specific condition is satisfied , the extra driving term is found to be constant - like , i.e. , @xmath112 , as if it is a cosmological constant @xmath0 . in the present model , @xmath155 is required to obtain the constant - like term from the most severe constraint . in other words , the constant - like term must be extremely small when the extra driving term behaves as if it is constant . the present model may imply that the cosmological constant is related to a small deviation from the bekenstein hawking entropy . in addition , interestingly , the order of the constant - like term is naturally consistent with the order of the cosmological constant measured by observations because , without tuning , the specific condition constrains the value of the constant - like term . the present model is expected to provide new insights into not only alternative dark energy models but also the cosmological constant problem . this paper focuses on the derivation of the extra driving term and the specific condition for the constant - like term . accordingly , general solutions for the present model that includes a logarithmic driving term have been separately studied in appendix [ solutions for the present model and evolutions of the universe ] . to solve the cosmological equations , the present model is assumed to be a particular case of @xmath2cdm models . from the obtained solution , the background evolutions of the universe in the present model are found to agree well with those in the standard @xmath0cdm model when both @xmath156 and @xmath157 are small . for lower redshift , the present model gradually deviates from the @xmath0cdm model , due to the logarithmic term . therefore , the present model can be distinguished from the standard @xmath0cdm model .

consequently , the acceleration equation including an extra driving term can be derived in a homogeneous , isotropic , and spatially flat universe . when a specific condition is mathematically satisfied , the extra driving term is found to be constant - like as if it is a cosmological constant . interestingly , the order of the constant - like term is naturally consistent with the order of the cosmological constant measured by observations because , without tuning , the specific condition constrains the value of the constant - like term . the present model should provide new insights into both alternative dark energy and the cosmological constant problem .

cosmological equations were recently derived by padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space . in this study , a modified rnyi entropy is applied to padmanabhan s ` holographic equipartition law ' , by regarding the bekenstein hawking entropy as a nonextensive tsallis entropy and using a logarithmic formula of the original rnyi entropy . consequently , the acceleration equation including an extra driving term can be derived in a homogeneous , isotropic , and spatially flat universe . when a specific condition is mathematically satisfied , the extra driving term is found to be constant - like as if it is a cosmological constant . interestingly , the order of the constant - like term is naturally consistent with the order of the cosmological constant measured by observations because , without tuning , the specific condition constrains the value of the constant - like term . the present model should provide new insights into both alternative dark energy and the cosmological constant problem .

1310.0324

i

in this paper it will be shown how the generalisation of symmetry properties of perfect solid crystals to crystals with certain uniform distributions of defects leads to a classification of the symmetries of discrete defective crystals as elastic or inelastic . we show that , in contrast with the perfect crystal case , some of the symmetries of a discrete defective crystal do not extend uniquely to a symmetry of the continuum model of the defective crystal . this allows us to classify the symmetries which do nt extend as inelastic symmetries of the discrete defective crystal , while those which do extend uniquely are restrictions of elastic deformations of the continuous crystal and we call these symmetries elastic symmetries of the discrete crystal . a starting point for the study of the mechanics of perfect solid crystals is to consider the geometrical symmetries of perfect lattices in @xmath0 : @xmath1 where @xmath2 are defining basis vectors and the summation convention operates on repeated indices . the perfect lattice @xmath3 defines a discrete set of points in @xmath0 and can also be thought of as a discrete subgroup of the continuous lie group @xmath0 with addition as group composition . the discrete structures @xmath3 in @xmath0 have geometrical symmetries @xmath4 given by @xmath5 the symmetries of @xmath3 are bijective and preserve addition as well as the set of points in @xmath0 defined by @xmath3 . moreover , every symmetry @xmath6 of a perfect lattice @xmath3 extends uniquely to a bijection of @xmath0 . here we extend and generalise these properties of the symmetries of perfect crystals to a certain class of defective crystal where the distribution of defects is uniform . we use davini s continuum model of defective crystals @xcite , in which the dislocation density tensor @xmath7 , @xmath8 is defined by @xmath9 where the fields @xmath10 are dual to the smooth _ lattice vector fields _ @xmath11 , which represent the crystal geometry in a region @xmath12 . a crystal with a uniform distribution of defects has dislocation density tensor which is constant in space . ( note that for perfect crystals @xmath13 . ) suppose that @xmath14 is a set of lattice vector fields which are elastically related to @xmath15 in the sense that there exists a smooth invertible mapping @xmath16 such that @xmath17 we say that @xmath18 is an elastic deformation . if @xmath19 is calculated via the analogue of , using fields dual to @xmath20 , then @xmath21 therefore , each component @xmath22 of the dislocation density tensor is an ` elastic ' scalar invariant so that the value of the dislocation density is unchanged by elastic deformations of the crystal . due to this elastic invariance , for a given dislocation density tensor @xmath23 there are infinitely many choices of ( elastically related ) sets of corresponding lattice vector fields . it is a commonly held idea in the elasticity theory of perfect crystals that there is a continuum energy density @xmath24 which depends on the underlying perfect lattice @xmath3 ; that is @xmath25 where @xmath26 denotes the set of vectors @xmath27 . if the basis vectors @xmath28 generate the same lattice @xmath3 ( i.e. @xmath29 in ) then @xmath30 in other words the geometrical symmetries of @xmath3 correspond to the material symmetries of the energy density function @xmath24 . here we use a generalisation of this theory which accounts for the presence of a continuous distribution of defects in the crystal . it is assumed that the strain energy density per unit volume in such a crystal depends on the values of the lattice vector fields @xmath31 , @xmath32 , @xmath33 and dislocation density tensor @xmath34 at some point in @xmath12 . thus @xmath35 where @xmath26 denotes the set of vectors @xmath27 which are the values of the lattice vector fields at some point in @xmath12 , and @xmath23 denotes the dislocation density tensor evaluated at the same point . as we shall see in section [ sec : structure ] , the arguments of the energy density function determine a structure @xmath36 which under certain conditions will be a discrete set of points . if another set of arguments , say @xmath37 , determine the same discrete structure then it is assumed that @xmath38 hence for crystals with defects we are associating that the symmetries of the energy density function with the geometrical symmetries of the structure @xmath36 . therefore the structure @xmath36 is taken to be the defective crystal analogue of the perfect lattice @xmath3 underlying perfect crystals , and it is a central task to determine the geometrical symmetries of @xmath36 . notice that the arguments @xmath39 of @xmath24 give no information regarding gradients of @xmath23 , and we shall assume that they are zero . therefore the dislocation density tensor @xmath23 is constant in space and the crystal has a uniform distribution of defects . it is this assumption that endows the crystal with a lie group structure . suppose that the vector fields @xmath31 , @xmath32 , @xmath33 , defined here and henceforth on @xmath40 , give constant @xmath23 . then according to pontryagin @xcite , the system of partial differential equations @xmath41 has a solution for the function @xmath42 , where @xmath43 denotes the gradient of @xmath42 with respect to its first argument . moreover , the function @xmath44 can be taken to satisfy the properties required for it to be a lie group composition function on @xmath0 , i.e. @xmath45 where @xmath46 is the group identity element and @xmath47 is the unique inverse of the element @xmath48 @xcite . here , the lie group @xmath49 has underlying manifold @xmath0 so that an element @xmath50 can be uniquely specified by @xmath51 where @xmath52 and @xmath53 is a basis of @xmath0 . we will often use the alternative notation @xmath54 . ( note that in the perfect crystal case where @xmath55 , we can take @xmath42 to be addition so that @xmath56 . ) relation expresses the _ right invariance _ of the fields @xmath57 with respect to the lie group @xmath58 . suppose that the fields @xmath59 are elastically related to @xmath57 via @xmath18 as in . then if @xmath60 is defined by @xmath61 then @xmath62 hence the fields @xmath59 are right invariant with respect to the lie group @xmath63 and since @xmath64 is invertible , the groups @xmath65 and @xmath66 are isomorphic . thus , elastically related crystal states have isomorphic corresponding lie groups . recall that the dislocation density tensor @xmath23 is an elastic invariant so there is an infinite choice of elastically related lattice vector fields which have duals which satisfy for a given constant dislocation density . therefore , there is also an infinite number of choices of isomorphic lie groups @xmath49 corresponding to @xmath23 . hence a given constant @xmath23 determines up to lie group isomorphism a lie group @xmath65 . in this paper we make a ` canonical ' choice of the lie group @xmath65 to simplify the computations . we identify material points of the crystal with elements of the lie group . when @xmath65 has a uniform discrete subgroup @xmath36 ( where @xmath67 is uniform if the left coset space @xmath68 is compact ) the material points corresponding to the elements in @xmath36 have a minimum separation distance and form discrete geometrical structures which we take to the defective crystal analogue of the perfect lattice @xmath3 . the requirement that @xmath68 be compact is a generalisation of the fact that in the perfect crystal case that @xmath69 ( the unit cell of the lattice @xmath3 with appropriate identification of boundary points ) is compact . according to auslander , green and hahn @xcite there are precisely three classes of non - abelian , three dimensional lie groups @xmath65 with uniform discrete subgroups . these are a certain class of nilpotent lie groups and two non - isomorphic classes of solvable lie groups . for each of these cases we are interested in the form of the geometrical structures corresponding to the discrete subgroups @xmath36 and the geometrical symmetries of these structures ( i.e. the changes of generators of @xmath36 which preserve the points in the geometrical structure ) . these have already been determined in all three cases : * when the lie group @xmath65 is nilpotent ( with corresponding lie algebra with rational structure constants ) , cermelli and parry @xcite have shown that the corresponding discrete subgroups give either a simple lattice or a 4-lattice ( in pitteri and zanzotto s terminology @xcite ) even though the composition function in @xmath65 is not additive . for such groups , parry and sigrist @xcite construct explicitly all sets of generators of a given discrete subgroup . the formulae that connect different sets of generators generalise the perfect crystal case given by . * auslander et al . @xcite call the two classes of solvable groups @xmath70 and @xmath71 . it has been shown by parry and nicks that in both cases the geometrical structures corresponding to the discrete subgroups of these solvable groups are simple lattices . the changes of generators preserving these structures were also determined ( see @xcite for the @xmath70 case and @xcite for the @xmath71 case ) . in this paper we focus on a property of the symmetries of perfect lattices which does not hold in the generalisation to the symmetries of discrete structures underlying crystals with uniform distributions of defects . recall that the geometrical symmetries of a perfect lattice @xmath3 are bijections @xmath4 as in which preserve addition . each of these symmetries extends uniquely to a bijection @xmath72 defined by @xmath73 thus every symmetry of @xmath3 represents a ( restriction of an ) elastic deformation of the continuum perfect crystal . this is not the case for crystals with constant @xmath74 where the underlying lie group , @xmath58 , is solvable or nilpotent . in these cases there is a difference between the set of all geometrical symmetries of a discrete structure @xmath75 and the subset of these symmetries which preserve the group structure of @xmath36 and extend uniquely to elastic deformations of @xmath0 . this allows us to classify the symmetries of the discrete structures @xmath36 which preserve the group structure as elastic or inelastic depending on whether or not they are restrictions of elastic deformations of the continuum defective crystal . the observation that such a classification can be made is interesting because it indicates a possible link between the inelastic symmetries of the discrete crystal @xmath36 ( which preserve the elastic invariant @xmath23 and the discrete structure ) and observed inelastic processes in crystal behaviour such as slip in particular planes and directions determined by geometry . notice that we consider here only symmetries of discrete structures @xmath36 which additionally preserve the group structure . we do not discuss here symmetries where the discrete structure represents discrete subgroups of different lie groups , isomorphic or not . our simplified task then is to identify which of the geometrical symmetries of discrete subgroups @xmath75 extend uniquely to elastic deformations of @xmath0 . this task breaks down into two stages . first we must determine which of the geometrical symmetries of @xmath36 preserve the group structure of @xmath36 ; that is which of the symmetries will extend to _ automorphisms _ of @xmath36 . secondly we need to determine if these automorphisms of @xmath36 extend uniquely to automorphisms of the ambient lie group @xmath65 . for a geometrical symmetry of @xmath36 to be classified as an elastic symmetry it must extend to an automorphism of @xmath36 and that automorphism must extend uniquely to an automorphism of @xmath65 , since these are requirements that must be satisfied in order that the geometrical symmetry is a restriction of an elastic deformation of the defective crystal . in the cases where the structure @xmath36 is a discrete subgroup of a nilpotent lie group or a solvable lie group in the class @xmath70 such a classification of the geometrical symmetries of @xmath36 has been carried out . the automorphisms of the discrete subgroups @xmath36 have been computed ( see @xcite for the nilpotent case and @xcite for the @xmath70 case ) and it has been observed that theorems of malcev @xcite and gorbatsevich @xcite guarantee that every automorphism of @xmath36 extends uniquely to an automorphism of the ambient lie group @xmath65 . in this paper we will complete the analysis by classifying the geometrical symmetries of discrete subgroups @xmath36 of solvable groups in the class @xmath71 . in this case we must work a little harder since although it remains relatively straightforward to compute which of the geometrical symmetries of @xmath36 correspond to automorphisms of @xmath36 , there is no analogue of the theorems of malcev and gorbatsevich for solvable groups of this class . therefore we must determine directly whether or not automorphisms of @xmath36 extend uniquely to automorphisms of @xmath71 . the difficulties arise for the @xmath71 class due to the fact that the exponential mapping from the corresponding lie algebra @xmath76 to @xmath71 is not one - to - one . we begin by recalling how to construct discrete structures @xmath36 corresponding to a particular set of arguments @xmath39 of the energy density function @xmath24 . these are discrete subgroups of lie groups @xmath65 and we will also recall elements of lie group theory that will be required in this paper , including facts about lie group isomorphisms . in section [ sec : solvable ] , following auslander et al . @xcite and nicks and parry @xcite we introduce the group @xmath71 and the canonical group in the isomorphism class which we will work with . we also introduce the lie algebra @xmath76 of the lie group @xmath71 and calculate the automorphisms of @xmath71 . in section [ sec : discrete ] we discuss the discrete subgroups @xmath36 of @xmath71 , recalling results from nicks and parry @xcite concerning their geometrical symmetries . we next compute the automorphisms of these discrete subgroups @xmath36 which amounts to determining the matrices @xmath77 which commute with a given matrix @xmath78 which is related to the dislocation density . this is a number theoretic problem studied by baake and roberts @xcite and here we summarize their results which are relevant to this work . finally in section [ sec : extensions ] we demonstrate explicitly that each of these automorphisms of @xmath36 extends uniquely to an automorphism of @xmath71 .

these structures are in fact the discrete subgroups of the ambient lie group . the geometrical symmetries of these structures can be computed in terms of the changes of generators of the discrete subgroup which preserve the discrete set of points . here a classification of the symmetries for the discrete subgroups of a particular class of three - dimensional solvable lie group is presented . it is a fact that there are only three mathematically distinct types of lie groups which model uniform defective crystals , and the calculations given here complete the discussion of the symmetries of the corresponding discrete structures . we show that those symmetries corresponding to automorphisms of the discrete subgroups extend uniquely to symmetries of the ambient lie group and we regard these symmetries as ( restrictions of ) elastic deformations of the continuous defective crystal . other symmetries of the discrete structures are classified as ` inelastic ' symmetries .

crystals which have a uniform distribution of defects are endowed with a lie group description which allows one to construct an associated discrete structure . these structures are in fact the discrete subgroups of the ambient lie group . the geometrical symmetries of these structures can be computed in terms of the changes of generators of the discrete subgroup which preserve the discrete set of points . here a classification of the symmetries for the discrete subgroups of a particular class of three - dimensional solvable lie group is presented . it is a fact that there are only three mathematically distinct types of lie groups which model uniform defective crystals , and the calculations given here complete the discussion of the symmetries of the corresponding discrete structures . we show that those symmetries corresponding to automorphisms of the discrete subgroups extend uniquely to symmetries of the ambient lie group and we regard these symmetries as ( restrictions of ) elastic deformations of the continuous defective crystal . other symmetries of the discrete structures are classified as ` inelastic ' symmetries .

cond-mat0506425

r

ybptin is one of the rptin compounds , reported to crystallize in zrnial hexagonal structure@xcite , space group p@xmath23 . single crystals of this compound were obtained by two methods : from high - temperature ternary solution , as described in ref . [ 15 ] , and from stoichiometric on - line melt@xcite . the initial concentration used for the solution growth was yb@xmath24pt@xmath25in@xmath26 , and the ternary solution , sealed in a 3-cap ta crucible@xcite under partial argon pressure , was slow - cooled from 1200@xmath27 c to 1000@xmath27 c over approximately 100 hours . subsequently , the excess liquid solution was decanted , and the resulting hexagonal rods were briefly etched in hcl to remove residual flux from the surface . for the on - line melt , 1:1:1 atomic ratios of yb , pt and in were sealed in a ta crucible under partial argon atmosphere . after briefly heating the sealed crucible up to approximately 1650@xmath27 c in an induction furnace , the crucible was sealed in a quartz ampoulle and annealed at 700@xmath27 c for 120 hours . small rods were subsequently extracted from the resulting crystalline conglomerate . anisotropic magnetization measurements as a function of temperature and applied field m(h , t ) were performed in a quantum design mpms squid magnetometer ( t @xmath28 k , h@xmath29 kg ) . temperature- and field - dependent specific heat c@xmath30(h , t ) , resistivity @xmath31(h , t ) and hall resistivity @xmath32(h , t ) measurements were taken in a quantum design ppms-14 instrument with he-3 option , for temperatures down to 0.4 k , and applied magnetic fields between 0 and 140 kg . for the anisotropic ( _ i.e. , _ @xmath33 or @xmath34 ) specific heat measurements a relaxation technique with fitting of the whole calorimeter ( sample with sample platform and puck ) was used . the sample platform and grease background , measured separately for all necessary ( h , t ) values , was subtracted from the sample response . also , the non - magnetic contribution to the total specific heat was estimated based on measurements on flux - grown luptin , used as the non - magnetic analogue of ybptin . the single crystals of luptin were grown using similar initial composition ( r@xmath35pt@xmath35in@xmath36 ) and temperature profile ( slow cooling from 1190@xmath27c to 800@xmath27c over @xmath19100 hours ) that yielded fully - occupied rptin single crystals for the lighter members of the series@xcite . we therefore anticipate that the luptin crystals are also fully - occupied , and we used this system as the non - magnetic analogue for our both yb compounds . it should be noted that we made the assumption that the non - magnetic background is insensitive to the 2@xmath13 pt - deficiency in the solution - grown compound . the specific heat for luptin was measured in the same temperature range as for ybptin and ybpt@xmath1 in , for 0 and 140 kg applied field , and was found to be virtually field - independent over the measured temperature range . a standard ac four - probe resistance technique ( @xmath37 hz , @xmath38 ma ) was used for the field- and temperature - dependent resistivity measurements . given the rod - like geometry of the samples , the current was always flowing along the crystallographic c - axis , whereas the field was either parallel ( for longitudinal magnetoresistance ) , or perpendicular ( for transverse magnetoresistance ) to the direction of current flow . the hall resistivity measurements were performed on a sample that was polished down to a plate - like shape . this sample geometry restricted the hall resistivity measurements to the field applied within the hexagonal crystallographic plane ( @xmath39 ) . the hall resistivity @xmath32(h , t ) was measured for field perpendicular to both the current and the hall voltage directions . in order to minimize the inherent ( small ) misalignment of the voltage contacts , these measurements were taken for two opposite directions of the applied field , h and -h , and the odd component , ( @xmath32(h ) - @xmath32(-h))@xmath40 was taken as the hall resistivity . for each of the two systems ( ybptin and ybpt@xmath1 in ) , we will compare the similar data for the the two orientations of the applied field ( _ i.e. _ , for @xmath39 and @xmath41 ) , as well as the resulting t - h phase diagrams . the criteria used for determining the points on all presented phase diagrams will be discussed in more detail in the appropriate sections , but in general they were maxima in the c@xmath30(h , t ) data , and derivative maxima or onset values for the transport data . for @xmath39 , the maximum temperature for which the @xmath42 could be fit to a straight line was the criterium used in determining the upper limit of this fermi liquid - like region . additional hall resistivity measurements were performed for the field applied within the basal plane , for the ybpt@xmath1 in ( flux - grown ) compound . various criteria were used for determining critical points similar to the hall line for the ybrh@xmath15si@xmath15@xcite and ybagge@xcite systems .

detailed anisotropic ( hab and hc ) resistivity and specific heat measurements were performed on online - grown ybptin and solution - grown ybpt in single crystals for temperatures down to 0.4 k , and fields up to 140 kg ; hab hall resistivity was also measured on the ybpt in system for the same temperature and field ranges .

detailed anisotropic ( hab and hc ) resistivity and specific heat measurements were performed on online - grown ybptin and solution - grown ybpt in single crystals for temperatures down to 0.4 k , and fields up to 140 kg ; hab hall resistivity was also measured on the ybpt in system for the same temperature and field ranges . all these measurements indicate that the small change in stoichiometry between the two compounds drastically affects their ordering temperatures ( t k in ybptin , and k in ybpt in ) . furthermore , a field - induced quantum critical point is apparent in each of these heavy fermion systems , with the corresponding critical field values of ybpt in ( h around 35 - 45 kg and h kg ) also reduced compared to the analogous values for ybptin ( h kg and h kg ) .

cond-mat0506425

r

for both solution and on - line grown crystals , the crystal structure was confirmed by powder x - ray diffraction , with no detectable impurity peaks . however , additional single crystal x - ray measurements were performed on the two types of ybptin compounds . crystals with dimensions @xmath43 and @xmath44 were extracted from the flux and on - line grown samples respectively . room - temperature x - ray diffraction data were collected on a stoe ipdsii image plate diffractometer with mo k@xmath45 radiation , and were recorded by taking @xmath46 scans in @xmath47 in the full reciprocal sphere . the range of 2 @xmath47 extended from @xmath48 to @xmath49 . numerical absorption corrections for both crystals were based on crystal face indexing , followed by a crystal shape optimization . structure solution and refinement were done using the shelxtl program . the crystallographic and structural data are summarized in tables [ t1 ] - [ t2 ] . .atomic coordinates and equivalent isotropic displacement parameters ( @xmath50 ) for the flux - grown ybptin system . u(eq ) is defined as one third of the trace of the orthogonal u@xmath51 tensor . space group _ p @xmath52 2 m _ , a @xmath53 , c @xmath54 , r = 0.0273 , r@xmath55 = 0.0598 . [ cols="^,^,^,^,^,^ " , ] a high temperature factor was inferred for pt(1 ) of the flux - grown crystal during final stages of the refinement , which is usually indicative of possible atomic deficiencies , symmetry reduction or superstructure formation . no superstructure reflections were observed , and symmetry reduction did not resolve the issue . however , relaxing pt(1 ) site occupancy resulted in a statistically significant deficiency ( 0.06(1 ) , table [ t1 ] ) , and led to improvements in the pt(1 ) temperature factor and overall residual r value . we also tested for possible deficiencies on the other atomic sites in this crystal , but refined occupancies for yb ( 1.00(6 ) ) , pt(2 ) ( 1.00(6 ) ) and in ( 1.02(2 ) ) did not suggest presence of atomic deficiencies . thus the composition of the flux - grown crystal can be written as ybpt@xmath1 in , noting that the pt@xmath1 value reflects the pt stoichiometry of the whole unit cell , not just of the pt(1 ) site . in contrast to the flux - grown sample , the pt(1 ) temperature factor of the on - line grown crystal had a reasonable value . relaxing the pt(1 ) occupancy yielded only a slight and statistically insignificant deficiency of 0.014(9 ) ( table [ t2 ] ) . occupancy refinement for other atomic sites showed no deviations from unity . although small deficiencies on the pt(1 ) site could not be excluded , the ybptin formula is a good presentation of the composition of the on - line crystal in terms of sensitivity of our x - ray diffraction experiments . this difference in the stoichiometry of the solution and on - line grown samples is consistent with ybptin having a small width of formation extending towards the pt - deficient side ; given that the initial melt composition is very pt - poor ( _ i.e. _ , yb@xmath24pt@xmath25in@xmath26 ) , it is expected to be sensitive to such a small width of formation . a closer look at the atoms positions given in tables [ t1]-[t2 ] suggests that two compounds might be mirror images of each other ; whereas racemic twinning could not be excluded for either the solution or the on - line grown compounds , no evidence of the existence of both `` left '' and `` right '' structures in each system could be found . the lattice parameters and unit cell volume for the solution - grown , ybpt@xmath1 in crystals were @xmath56 , @xmath57 @xmath58and @xmath59 @xmath60 . the analogous unit cell dimensions on the on - line grown crystals were slightly smaller : @xmath61 , @xmath62 @xmath58and @xmath63 @xmath60 . anisotropic magnetization measurements are presented in fig.[f01 ] for both the ybpt@xmath1 in ( full symbols ) and the ybptin ( open symbols ) compounds . as can be observed in fig.[f01]a , the paramagnetic susceptibility indicates moderate anisotropy for both systems ( with @xmath64 at the lowest temperature ) , and no clear sign of magnetic ordering down to @xmath65 k. the anisotropic m(h ) isotherms show a continuous increase of the magnetization , with a trend towards saturation above 40 kg ( fig.[f01]b ) for h applied within the ab - plane ; the axial magnetization remains linear and significantly smaller than m@xmath66 up to our maximum field available for these measurements ( 55 kg ) . whereas qualitatively there is an overall similarity between the corresponding data of the two compounds , the absolute values of both susceptibility and field - dependent magnetization are slightly larger for ybpt@xmath1 in than for ybptin . we believe the @xmath19 10 to 20@xmath13 difference to be too large to have been caused by weighing errors alone , and thus we conclude that it may reflect the different kondo temperatures and exchange coupling due to the change of stoichiometry in the two compounds . the zero - field specific heat and resistivity data shown in fig.[f02 ] are consistent with magnetic ordering in both compounds , however at different temperatures : two well defined peaks at t@xmath67 k and 1.4 k are visible in the ybptin c@xmath30(t ) data ( open symbols , fig.[f02]a ) , whereas only one peak can be distinguished , around 2 k , in the ybpt@xmath1 in data ( full symbols ) . these transition temperatures are marked by the vertical dotted lines for the former compound , and by one dashed line for the latter . it can be seen that the corresponding resistivity measurements ( fig.[f02]b ) show changes in slope around the respective transition temperatures . another noticeable difference between ybptin and ybpt@xmath1 in manifests in the resistivity values ( fig.[f02]b and [ frt300 ] ) with the ones for the former compound being approximately three times smaller in the latter one . the error bars shown for the lowest temperature @xmath31 values give a caliper of the uncertainty in estimating the resistivity values for the two compounds , further confirming the aforementioned difference . the larger residual resistivity in ybpt@xmath1 in is consistent with the additional disorder ( _ i.e. _ , site disorder ) or presence of additional vacancies in this type of crystals . thus the zero - field measurements indicate a dramatic effect of the small pt - deficiency on the ordered state in ybptin : the upper transition is shifted down in temperature in the pt - deficient compound , whereas a second one is clearly identifiable only in ybptin . in order to explore the differences between these two samples more thoroughly , a systematic study of the field - dependence of @xmath68 and c@xmath69 was undertaken . * @xmath39 * + the low - temperature specific heat data for the on - line grown compound ybptin is shown in fig.[f11]a , for various values of the applied field . as already seen , two sharp peaks present in the h = 0 data can be associated with magnetic phase transitions at t @xmath70 k and 1.4 k. as the applied field is increased , these transitions ( indicated by small arrows in fig.[f11]a ) move to lower temperatures , and eventually drop below 0.4 k around 20 kg , and 60 kg respectively . trovarelli _ _ et al.__@xcite have reported similar measurements up to 80 kg , which are consistent with our data ; however , their study did not include a systematic analysis of the h - t phase diagram or the potential quantum critical behavior in this compound . from the linear extrapolation of the zero - field c@xmath71 _ vs. _ t@xmath11 data from t @xmath19 5 k down to t = 0 ( dotted line in the inset , fig.[f11]a ) , the electronic specific heat coefficient @xmath72 can be roughly estimated as @xmath73 mj / mol k@xmath11 . the magnetic component of the specific heat is defined as @xmath74(ybptin)@xmath75(luptin ) , and is shown in fig.[f11]b as @xmath76 _ vs. _ t@xmath11 , for the same field values as before . when the magnetic specific heat is plotted in c@xmath77 vs. @xmath78 t coordinates ( fig.[f11a ] ) , a reduced region of logarithmic divergency ( non - fermi liquid nfl behavior ) is apparent ; however this linear region in c@xmath79 is more ambiguous than in other heavy fermion compounds displaying nfl behavior ( _ e.g. _ , ybrh@xmath15si@xmath15@xcite and ybagge@xcite ) . because of a downturn in the high field data ( h @xmath80 50 kg [ fig.[f11a]b ] ) around 5 k for h = 50 kg , the largest logarithmic divergency which occurs for h @xmath19 60 kg , is limited to only a fraction of a decade in temperature ( 1.5 k @xmath81 t @xmath81 6.5 k ) . the above observations suggests that a qcp may exist around a critical field value h@xmath4 just above 60 kg , but the presence of a nfl region at intermediate field values is less clearly defined than in the previously studied yb - based heavy fermion compounds . one of the expressions considered in the scaling analysis at a qcp@xcite is the cross - over function @xmath82~/~t$ ] _ vs. _ @xmath83 . in the case of ybrh@xmath15si@xmath15@xcite and ybagge@xcite , the @xmath83 range over which universal scaling was observed in high fields corresponded to 1@xmath10 t @xmath81 3 k@xmath84 , and 1.2 k@xmath84 respectively ( with @xmath85 ) . due to the slightly enhanced magnetic ordering temperature @xmath86 k in ybptin , the analogous @xmath87 t range is drastically reduced ( 1@xmath10 t @xmath81 0.3 k@xmath84 ) , making the unambiguous determination of the critical exponent @xmath88 essentially impossible . low - temperature resistivity curves for different values of the applied magnetic field are shown in fig.[f12 ] . the @xmath89 data are consistent with the presence of two magnetic phase transitions at low fields ; the small arrows indicate these transition temperature values , as determined from maxima in the d@xmath90 . both these transitions are suppressed by increasing applied field . whereas the upper transition can still be detected for h @xmath91 kg , a field of about 20 kg is sufficient to drive the lower one below our base temperature of 0.4 k. it is worth noting that the critical field h@xmath92 kg , determined from the @xmath31(t , h ) data as the field required to suppress the magnetic ordering , is close to the position of the qcp as inferred based on the c@xmath30 data ( fig.[f11]-[f11a ] ) . as fig.[f12sqab ] indicates , when the magnetic field is increased beyond h@xmath4 , the temperature dependence of the resistivity is ambiguous ; particularly at fields just above h@xmath4 ( h @xmath93 100 kg ) , it is difficult to distinguish between linear or quadratic behavior of the resistivity as a function of temperature . consequently we leave the complete analysis of the temperature - dependent resistivity outside the ordered state for the discussion section . when magnetoresistance measurements ( @xmath94 ) are performed ( fig.[f13 ] ) three features are apparent at very low temperatures , as indicated for t = 0.4 k by the small arrows . the inset shows @xmath31(h ) at t = 0.8 k , to exemplify how these transition temperatures were inferred from these data . for t @xmath80 1 k , the two lower transitions merge and the resulting one is still distinguishable up to approximately 1.4 k. the upper transition moves down towards zero field as the temperature approaches t@xmath95 k. based on the above field- and temperature - dependent thermodynamic and transport measurements , a @xmath96 phase diagram for @xmath21 can be constructed ( fig.[f14 ] ) : in zero magnetic field , two magnetic phase transitions can be observed , around t@xmath95 k and t@xmath97 k. increasing magnetic field splits the lower transition into two separate ones around h @xmath98 kg ; one of these phase lines drops towards our lowest temperature at almost constant field , whereas the second one has a slower decrease with field , such that it approaches t = 0.4 k around h = 20 kg . in a similar manner , the upper transition is driven down towards 0 around @xmath99 kg . + * @xmath41 * + fig.[f20 ] presents specific heat data for ybptin , @xmath100 , for fields up to 80 kg . high torques on this sample for this orientation of the field prevented us from completing these measurements up to 140 kg . moreover , as will be shown below , there are significant discrepancies between the transition temperatures determined even from the intermediate - field specific heat data and transport measurements ( _ i.e. _ , for h @xmath80 40 kg ) . this observation prompts us to suspect that significant torques may have changed the sample orientation for the specific heat measurements , even for fields significantly lower than 80 kg . in zero field , we can confirm the two magnetic transitions observed before , at t@xmath95 k , and t@xmath97 k respectively ; as the small arrows indicate , the lower - t transition is driven down in field , and falls below 0.4 k for h @xmath101 kg , whereas the upper transition persists above 80 kg . the temperature and field dependent resistivity data ( fig.[f21]-[f21rh ] ) indicate a much slower suppression of the magnetic order with the applied field . in fig.[f21]a , @xmath68 curves are shown , with the arrows indicating the transition temperatures as determined from @xmath102 . fig.[f21]b presents a subset of these derivatives , to illustrate the criteria for determining the temperatures : for the lower transition , a peak in @xmath102 broadens as field is increased , and disappears for h @xmath103 80 kg ; the upper transition is marked by a step in these derivatives , which also broadens as h increases . at the highest measured field ( _ i.e. _ , 140 kg ) we are unable to distinguish between a very broad step ( with a possible transition temperature marked by the small arrow ) or a cross - over in corresponding @xmath102 . the field - dependent resistivity data ( fig.[f21rh ] ) are indicative of a low temperature transition consistent with that seen in @xmath68 , with the critical fields determined from onsets . given the above c@xmath30(t , h ) and @xmath31(t , h ) data , we suspect that magnetic fields h @xmath103 20 kg deform the four wires supporting the he-3 specific heat platform used for the c@xmath30(t , h ) measurements , whereas the resistivity sample appears to be well held in place by grease on the rigid platform . consequently , at high fields , the two sets of data ( c@xmath30(t , h ) and @xmath31(t , h ) ) may not correspond to the same orientation of the field ( @xmath41 ) , yielding different transition temperature values for the corresponding applied fields . as a result , in constructing the t - h phase diagram for h@xmath104 ( fig.[f22 ] ) , we will consider the t@xmath105 values as determined from the @xmath31(t , h ) data up to h = 140 kg , and only the h @xmath106 20 kg ones based on specific heat measurements . also shown are error bars for points determined from @xmath31(t ) data at several field values ( _ i.e. _ , for h = 20 , 80 , 100 , 120 and 140 kg ) , and for the point obtained from @xmath31(h ) at our minimum temperature ( t = 0.4 k ) ; these give a caliper of the errors bars in determining the points on this phase diagram for the whole field and temperature range . two transitions can be observed in fig.[f22 ] , at low fields , around 3.4 k , and 1.4 k respectively . as h is being increased , the low temperature line slowly approaches t = 0 around h @xmath107 kg . the step in @xmath102 associated with the upper transition ( fig.[f21]b ) broadens as the field increases , resulting in increasingly large error bars in determining these transition temperatures . as already mentioned , it is uncertain if the transition persists up to h = 140 kg , or if cross - over occurs between 120 and 140 kg . * @xmath39 * + given the differences between ybptin and ybpt@xmath1 in evidenced by both thermodynamic and transport data ( figs.[f01]-[frt300 ] ) , it is desirable to compare similar measurements on the two compounds , and to study the effect of the small stoichiometry change on the field - induced qcp . consequently , in fig.[f03 ] we present the low - temperature specific heat data of ybpt@xmath1 in , for various values of the applied field h @xmath108 . a well - defined peak at t @xmath109 k in the h @xmath110 data may be associated with the magnetic ordering of this compound . as the applied magnetic field is increased , this transition ( indicated by small arrows ) moves to lower temperatures , and eventually drops below 0.4 k around 35 kg . from the linear extrapolation of the h = 0 data from t @xmath111 k down to t = 0 ( inset , fig.[f03]a ) , we can estimate the electronic specific heat coefficient @xmath72 as @xmath112 mj / mol k@xmath11 . fig.[f03]b the magnetic specific heat data for the same field values , @xmath74(ybpt@xmath1in)@xmath75(luptin ) , plotted as c@xmath113 _ vs. _ t@xmath11 . fig.[f03b ] shows the magnetic specific heat as @xmath114 _ vs. _ @xmath115 , for the same field values as before . a logarithmic divergence can be observed in these data , with the largest temperature region where @xmath116 occurring around h = 35 kg ( dotted line ) . however , on the next measured curve ( _ i . , for h = 40 kg ) the linear region extends over a comparable temperature interval , at slightly higher temperatures than in the h = 35 kg case . it thus appears that the largest temperature region ( close to a decade ) for the logarithmic divergency of the c@xmath113 data may occur for some intermediate field value ( 35 kg @xmath81 h @xmath81 40 kg ) . these data could be described as @xmath117 , with the ranges for @xmath118 and t@xmath119 determined from the linear fits on the h = 35 and 40 kg curves : 420 mj@xmath10mol k@xmath120 430 mj@xmath10mol k@xmath11 , and 14.7 k @xmath103 t@xmath121 13.5 k. the above observations seem consistent with a qcp in this compound with critical field just above 35 kg . fig.[f04 ] shows the low - temperature resistivity data for various values of the applied magnetic field . a maximum in d@xmath90 , associated with the magnetic ordering can be identified at t @xmath122 k in the h = 0 data , and is marked by small arrow in fig.[f04]a ; as the field is increased above 35 kg , small arrows indicate that this transition temperature drops below 0.4 k , consistent with the specific heat data . as was the case of ybptin , in ybpt@xmath1 in the temperature dependence of the resistivity outside the ordered state is ambiguous . from figs.[f04]b-[f04sqab ] it is unclear whether the resistivity is linear or quadratic in field for h @xmath123 , particularly for intermediate field values ( h @xmath106 55 kg ) . a detailed analysis of the resistivity data above the critical field will be performed in the discussion section , for both compounds . this should allow us to better clarify the position of the qcp and the existence of a fermi liquid - like ( fl ) regime in these systems . transverse magnetoresistance measurements were taken at constant temperatures ranging from 0.4 k to 10 k. as shown in fig.[f05 ] , two different temperature regimes can be identified in these data : for t @xmath124 k ( fig.[f05]a ) , two transitions can be distinguished . the small arrows mark the positions for these two transitions for t = 0.4 k , whereas the inset illustrates how these critical field values were determined . as the temperature increases up to about 1.8 k , the upper transition moves down in field and broadens , whereas the position of the lower one seems almost unaffected by the change in temperature . for temperatures higher than 2 k ( fig.[f05]b ) , the magnetoresistance isotherms display only a broad feature that looks more like a cross - over rather than a transition . using the detailed c@xmath30(t , h ) and @xmath31(t , h ) measurements discussed above , the ybpt@xmath1 in t - h phase diagram for h@xmath125 can be constructed . as can be seen in fig.[f06 ] , it is qualitatively similar to the corresponding t - h phase diagram for the stoichiometric compound ( fig.[f14 ] ) : in ybpt@xmath1 in magnetic ordering occurs at around 2.2 k. an almost field independent phase line is apparent in the @xmath94 data around 8 kg , and it appears to persist close to the magnetic ordering temperature . increasing applied field drives the higher transition towards t = 0 at a critical field values around 35 kg . + * @xmath41 * + the similarities observed previously between ybptin and ybpt@xmath1 in are also present for the @xmath41 direction , as the c@xmath30(t , h ) and @xmath31(t , h ) measurements indicate . as in the case of the stoichiometric compound , significant torques on the specific heat platform and sample for h @xmath80 50 kg may be the cause of the different transition temperature values , as determined by the two data sets mentioned above . therefore we will only take into consideration c@xmath30(t , h ) data for h @xmath81 50 kg ( fig.[f17 ] ) . similar to the @xmath39 measurements ( fig.[f03 ] ) , the @xmath41 c@xmath30 curves reveal a magnetic transition around 2.1 k for h = 0 ( fig.[f17 ] ) , which drops to @xmath19 2 k for h = 40 kg , before the sample torques significantly ; small arrows indicate the position of the transition temperature for the three curves shown in fig.[f17 ] . the temperature and field dependent resistivity data ( fig.[f18 ] ) indicate a slow suppression of the magnetic order with the applied field . fig.[f18]a shows the @xmath31(t ) curves in various applied fields , with the large circles marking the phase transition as determined from d@xmath90 ; the inset illustrates how the transition temperature was determined for h = 0 . the critical field required to suppress this transition below our base temperature appears to be around 120 kg . given the limited temperature range at these high fields , for h = 130 and 140 kg we were unable to distinguish a linear or quadratic temperature dependence of the resistivity . the magnetoresistance isotherms are presented in fig.[f18]b , and the large squares on this plot also indicate the high - t magnetic phase transition ; in the inset , a few d@xmath126 curves are shown to illustrate how the critical field values for the transition were determined . based on the c@xmath30(t , h ) and @xmath31(t , h ) presented above , the @xmath41 t - h phase diagram for ybpt@xmath1 in can be obtained , as shown in fig.[f19 ] . at low fields , this t - h phase diagram is consistent with the in - plane one for this compound : a magnetic transition is apparent around 2.2 k , but the possible second one around 1.0 k is not visible in the h@xmath0c measurements ; the t @xmath127 2.2 k transition is driven down in temperature by increasing applied fields , and it approaches our base temperature ( _ i.e. _ , 0.4 k ) around 120 kg . lack of measurements below 0.4 k or above 140 kg limits our ability to probe the existence of a qcp in this orientation , similar to the one at h@xmath128 kg for @xmath39 .

furthermore , a field - induced quantum critical point is apparent in each of these heavy fermion systems , with the corresponding critical field values of ybpt in ( h around 35 - 45 kg and h kg ) also reduced compared to the analogous values for ybptin ( h kg and h kg ) .

detailed anisotropic ( hab and hc ) resistivity and specific heat measurements were performed on online - grown ybptin and solution - grown ybpt in single crystals for temperatures down to 0.4 k , and fields up to 140 kg ; hab hall resistivity was also measured on the ybpt in system for the same temperature and field ranges . all these measurements indicate that the small change in stoichiometry between the two compounds drastically affects their ordering temperatures ( t k in ybptin , and k in ybpt in ) . furthermore , a field - induced quantum critical point is apparent in each of these heavy fermion systems , with the corresponding critical field values of ybpt in ( h around 35 - 45 kg and h kg ) also reduced compared to the analogous values for ybptin ( h kg and h kg ) .

0912.2960

i

the desire for ever increasing computational speeds has led to the conception of spintronics technologies that make use of both the charge and spin properties of electrical charge carriers in solids@xcite . realization of these devices for useful technologies requires the discovery and development of materials that have easily controllable electronic and magnetic properties to the same extent that semiconductors allow control over charge properties . this demand has led to an enormous interest in magnetic semiconductors to investigate if traditional semiconductors can be manipulated by chemical substitution of transition metal elements , or other creative means , into offering control over the spin properties of electrons@xcite . because so many of the suggested devices rely on the production and detection of spin polarized currents , magnetic semiconductors with curie temperatures above room temperature that are compatible with silicon technology are highly desired . however , this goal has thus far not been met and it has become increasingly apparent that to make progress , fundamental knowledge and understanding of the electronic and magnetic properties of magnetic semiconductors are necessary . although some headway in this direction has been made , the complexity of disordered materials with strong interactions makes magnetic semiconductors difficult to model and understand@xcite . in a recent paper we presented the results of an exploration into the magnetic and electronic properties of one such magnetic semiconducting compound , fe@xmath5co@xmath6s@xmath0 based on the diamagnetic insulating parent compound iron pyrite ( fes@xmath0)@xcite . we found that the insulator - to - metal transition that occurs for low concentrations of co doping was followed by a transition from a paramagnet to a disordered ferromagnet first apparent for small dopant concentrations , @xmath2 , at very low temperatures . increased co doping led to an increased transition temperature and to a more ordered ferromagnetic phase@xcite . the main conclusion of our paper was that the quenched disorder associated with the chemical substitution has important consequences on the formation of the magnetic state at small @xmath2 and on the finite temperature phase transitions at larger @xmath2 . unusual power law temperature , @xmath7 , and magnetic field , @xmath8 , dependencies of the magnetic susceptibility , magnetization , and specific heat were measured at low-@xmath7 for @xmath2 near the critical concentration for nucleation of a magnetic phase , @xmath9 , as well as at @xmath7 s just above the curie temperature , @xmath10 for @xmath11 . these were attributed to large , rare disorder fluctuations consisting of regions of local magnetic order which fluctuate as a single large magnetic moment and that grow in size as @xmath12 or @xmath13 . fluctuating rare region phenomena associated with phase transitions in systems with quenched disorder are known under the heading of griffiths phases@xcite . theorists have found the subject of griffiths phases fascinating since griffiths discovered the non - intuitive feature in his calculations that , under certain conditions , exponentially rare regions in disordered systems can dominate the thermodynamic response when in proximity to a phase transition@xcite . this is in contrast to many aspects of phase transitions where disorder can be treated perturbatively or simply ignored . these ideas have drawn even more interest as evidence for non - fermi liquid behavior in disordered systems has been discovered while explanations remain tentative@xcite . while it is clear that the disorder and strong electron correlations are responsible for the breakdown of fermi liquid behavior in some cases , the microscopic origins remain poorly understood@xcite . in this context , the unusual power law behavior associated with the formation of griffiths phases have been discussed as one mechanism for disorder driven non - fermi liquid behavior@xcite . experimental evidence that griffiths phases are observable in condensed matter systems has only recently been reported for a small number of systems@xcite , and in our previous publication we presented evidence for the importance of griffiths phase formation near the critical concentration for magnetic ordering in the magnetic semiconducting system fe@xmath5co@xmath6s@xmath0 . the purpose of the present paper is to present a more thorough rendering of our magnetic susceptibility , magnetization , and specific heat experiments and analysis , as well as to present the results of some more recent ac magnetic susceptibility measurements made at ambient and applied pressures of up to 7 kbar . in a separate accompanying article we present the results of our hall effect and resistivity measurements of these same materials@xcite . we chose to investigate co doped fes@xmath0 since fes@xmath0 is a simple diamagnetic band insulator with the same pyrite crystal structure as cos@xmath0 , a itinerant ferromagnet@xcite . the two compounds had been shown earlier to be miscible such as to form the substitutional series fe@xmath5co@xmath6s@xmath0 without observation of second phases or any phase segregation that occurs in many magnetic semiconducting compounds . as such , it allowed the investigation of the transition from diamagnetic insulator to a paramagnetic metal , then to a ferromagnetic metal with co substitution . in addition , band structure calculations have predicted that at large @xmath2 , @xmath14 , fe@xmath5co@xmath6s@xmath0 is half metallic having a fully spin polarized ground state@xcite we begin our discussion by presenting the details of the experimental techniques that we have used to investigate the extrinsic properties of fe@xmath5co@xmath6s@xmath0 . this is followed by a presentation of the magnetic susceptibility , magnetization , and specific heat over a wide range of @xmath2 covering insulating , paramagnetic metallic , and ferromagnetic metallic behaviors . in section [ griffneartc ] we explore in detail the behavior of our crystals nearest @xmath9 at low temperatures where the power - law in @xmath7 and @xmath8 behaviors are found . this is followed by a discussion of the magnetic properties of crystals with @xmath11 in proximity to @xmath10 displaying similar behavior . we conclude the paper with a summary and discussion of our results .

the lattice constant , ac and dc magnetic susceptibility , magnetization , and specific heat have been measured over the range of co concentration . the variation of the ac susceptibility with hydrostatic pressure has also been measured in a small number of our samples . all of these quantities show systematic variation with including a paramagnetic to disordered ferromagnetic transition at . a detailed analysis of the changes with temperature and magnetic field reveal small power law dependencies at low temperatures for samples near the critical concentration for magnetism , and just above the curie temperature at higher . we interpret this behavior as due to the formation of griffiths phases that result from the quenched disorder inherent in a doped semiconductor .

doping of the band insulator fes with co on the fe site introduces a small density of itinerant carriers and magnetic moments . the lattice constant , ac and dc magnetic susceptibility , magnetization , and specific heat have been measured over the range of co concentration . the variation of the ac susceptibility with hydrostatic pressure has also been measured in a small number of our samples . all of these quantities show systematic variation with including a paramagnetic to disordered ferromagnetic transition at . a detailed analysis of the changes with temperature and magnetic field reveal small power law dependencies at low temperatures for samples near the critical concentration for magnetism , and just above the curie temperature at higher . in addition , the magnetic susceptibility and specific heat are non - analytic around displaying an extraordinarily sharp field dependence in this same temperature range . we interpret this behavior as due to the formation of griffiths phases that result from the quenched disorder inherent in a doped semiconductor .

1412.0670

i

the neutrino and antineutrino flux spectra emitted by a core - collapse supernova ( sn ) significantly depend on flavor . therefore , flavor conversion can strongly modify what neutrinos do after decoupling , notably in driving the explosion , determining nucleosynthesis yields in the neutrino - driven wind , and the expected signal in large - scale detectors @xcite . even though neutrino mixing angles are large , in a dense medium the eigenstates of propagation and those of interaction are very nearly the same @xcite . therefore , significant flavor conversion would only occur by the msw effect @xcite at a large distance from the collapsed core . this situation can fundamentally change when taking neutrino - neutrino refraction into account @xcite . it can lead to self - induced flavor conversion @xcite even when the matter density is large and therefore the effective mixing angle is small @xcite . the propagation eigenmodes of the collective neutrino ensemble include run - away solutions in flavor space @xcite , leading to this phenomenon . one question is if self - induced flavor conversion would occur in regions below the stalled shock wave during the sn accretion phase . flavor conversion could then modify neutrino energy deposition and impact the explosion dynamics in the framework of the neutrino - driven mechanism of sn explosion . while self - induced flavor conversion can occur at much higher density than msw conversion , it is still suppressed by the `` multi - angle matter effect '' @xcite , although the exact conditions where conversions would occur require a linearized stability analysis or a numerical solution of the neutrino - flavor equations of motion . dedicated studies , using one - dimensional ( 1d ) sn models found that the `` onset radius '' of self - induced flavor conversion would always lie beyond the shock front where matter densities are much smaller @xcite . subsequent studies using other sn models found similar results @xcite . since that time , our theoretical understanding of both self - induced flavor conversion and of flavor - dependent sn neutrino emission have both evolved . we are here especially concerned with developments having to do with spontaneous breaking of symmetries that were previously taken for granted . axial symmetry of the neutrino radiation field around a given radial direction had been assumed in studies of collective flavor oscillations . however , a new class of run - away solutions breaks this symmetry spontaneously , allowing self - induced flavor conversion for both neutrino mass orderings @xcite . moreover , spatial uniformity can also be broken spontaneously , leading to small - scale instabilities @xcite . however , very recently it was shown that in the sn context , after including multi - angle matter effects , the uniform mode provides the most sensitive test for instability @xcite . therefore , in our present study we do not worry about small - scale instabilities when addressing the impact of an unusually small lepton - number flux . the other new finding is that sn neutrino emission in 3d models can develop a global dipole pattern termed lesa for lepton emission self - sustained asymmetry @xcite . while the overall neutrino luminosity remains nearly spherically symmetric , the deleptonization flux ( @xmath0 minus @xmath4 ) develops a strong dipole pattern within the first @xmath5150 ms after collapse irrespective of other hydrodynamical instabilities , notably even in the presence of the standing accretion shock instability ( sasi ) . more recent 3d models of the garching group @xcite as well as the oak ridge group @xcite show explosions . while all garching models exhibit the lesa effect very clearly and suggest that it persists at least until some 100 ms after the onset of the explosion @xcite , the 3d explosion model of oak ridge shows a less stationary dipole with an amplitude of just about 10% of the monopole over most of the pre - explosion evolution and a more lesa - like episode with a dipole - to - monopole ratio of @xmath525% and stable direction only in a time interval between 360 and 410 ms after bounce @xcite . the reason for these differences between the garching and oak ridge models is not clear yet , but they may be connected to different structural or transport conditions in the newly formed neutron star . the lesa phenomenon , when it is fully developed , implies that during the accretion phase , the deleptonization flux emerges primarily in one hemisphere . in some directions of the opposite hemisphere , it can be very small and sometimes even slightly negative . one may wonder if an unusually small lepton - number flux would facilitate self - induced flavor conversion , perhaps even below the shock front , and thus would require a fundamental re - examination of neutrino heating in directions of small lepton - number flux . for isotropic neutrinos or sn neutrinos in the single - angle approximation , self - induced flavor conversion is unavoidable in a @xmath0-@xmath4 symmetric ensemble @xcite . on the other hand , multi - angle effects caused by matter or even by neutrinos themselves can suppress the instability . the main purpose of our work is a parametric study of the impact of the @xmath0-@xmath4 flux asymmetry on self - induced flavor conversion . we use a linearized stability analysis , where we neglect several issues that have been discussed in the recent literature . we ignore spin - flip effects caused by neutrino magnetic dipole moments @xcite or simply by refraction in inhomogeneous or anisotropic media @xcite , and we ignore the role of anomalous neutrino - antineutrino pair correlations @xcite . realistically , all of these are probably small effects . it could be more questionable that we also ignore the `` halo flux '' produced by residual scattering beyond the neutrino sphere and especially its `` backward going '' component @xcite . moreover , we do not worry about the question if our assumed quasi - stationary neutrino source indeed produces a quasi - stationary solution . a true assessment of these latter assumptions requires a deeper conceptual development irrespective of the lesa context . we begin in sec . [ sec : flv - evol ] with setting up the linear stability analysis and clarifying our conventions and normalizations of crucial input parameters . in sec . [ sec : analysis ] we perform the stability analysis for a simplified setup and we discuss the role of the @xmath0-@xmath4 asymmetry . we conclude in sec . [ sec : conclusions ] with a summary and discussion of our findings .

during the accretion phase of a core - collapse supernova ( sn ) , the deleptonization flux has recently been found to develop a global dipole pattern ( lesa lepton emission self - sustained asymmetry ) . we use a linearized stability analysis in a simplified sn model to study the impact of the flux asymmetry on self - induced neutrino flavor conversion . overall we find that for large matter densities which are relevant below the shock wave , self - induced flavor conversion remains suppressed in the lesa context and thus irrelevant for neutrino - driven explosion dynamics .

during the accretion phase of a core - collapse supernova ( sn ) , the deleptonization flux has recently been found to develop a global dipole pattern ( lesa lepton emission self - sustained asymmetry ) . the number flux is much larger than in one direction , whereas they are approximately equal , or even , in the opposite direction . we use a linearized stability analysis in a simplified sn model to study the impact of the flux asymmetry on self - induced neutrino flavor conversion . while a small lepton - number flux facilitates self - induced flavor conversion , `` multi - angle matter suppression '' is more effective . overall we find that for large matter densities which are relevant below the shock wave , self - induced flavor conversion remains suppressed in the lesa context and thus irrelevant for neutrino - driven explosion dynamics .

1606.06614

i

in just 20 years the complexity of systems studied in surface science has increased by orders of magnitude . @xcite whereas previous major problems where associated with the adsorption behavior of small adsorbates such as co on pt(111 ) , @xcite typical challenges that dominate surface science nowadays are associated with the structural , electronic , and chemical properties of large organic adsorbates and molecular networks on metal and semiconductor surfaces . @xcite here the interaction strength and geometry of systems and the implications for nanoarchitectures , self - assembly , or atomic - scale manipulation is studied by two complementary sets of techniques , namely by _ in vacuo _ surface science experiments @xcite and _ ab initio _ electronic structure simulations . @xcite the capabilities of both experiment and simulation have increased tremendously . on the computational side , previously unthinkable system sizes can be dealt with thanks to the immense increase in computational power and the numerical , as well as algorithmic efficiency of density - functional theory ( dft ) . @xcite owing to the latest advances in particular in the treatment of dispersive interactions , such calculations are nowadays able to provide a reliable description of the adsorption structure and energetics of highly complex organic adsorbates on metal surfaces . @xcite an especially important aspect of theoretical surface science that should benefit from this progress is the ability to conduct computational screenings of possible geometries of complex interfaces , be it for determining the atomic configuration of surface reconstructions , @xcite topologies of organic crystals , @xcite or identifying the manifold of all possible compositions and adsorption sites in processes of heterogeneous catalysis and in compound materials . @xcite however , one thing that has not changed much in recent years is how , in simulations , optimal adsorption structures are identified . the large number of degrees of freedom in a complex adsorbate , as well as the structural complexity of large surface nanostructures , necessitates a full global search for optimal structures and overlayer phases that includes all possible binding modes and chemical changes that can occur upon adsorption . knowing the geometric structure of an interface is an important prerequisite to investigating its electronic properties and level alignment , which in turn determines the performance in potential electronic or catalytic applications . an efficient potential energy surface ( pes ) sampling tool is necessary to enable this , as opposed to just conventional local optimization of several chemically sensible initial guesses . in general , this problem can be solved by applying global geometry optimization methods . @xcite the goal of a majority of such global optimization approaches is to efficiently traverse the pes by generating new trial configurations that are subsequently accepted or rejected based on certain criteria . multiple reviews on global optimization methods specific to certain types of systems , ranging from small clusters to large biomolecules , have been published recently . @xcite in particular , much attention has been attracted by the application of global optimization methods to the study of metal clusters , @xcite binary nanoalloys , @xcite proteins , @xcite water clusters , @xcite and molecular switches . @xcite recently , global geometry optimization schemes have been specifically developed and applied in the growing field of heterogeneous catalysis , @xcite including application in reaction coordinate prediction , @xcite and biomolecular simulations . @xcite a wide range of different global optimization algorithms has thereby been suggested over the last two decades , ranging from simple classical statistical mechanics simulated annealing schemes @xcite to sophisticated landscape paving , @xcite puddle - jumping , @xcite or neural - network controlled dynamic evolutionary approaches . @xcite two prominent and most popular families of global geometry optimization techniques include monte - carlo based methods , such as basin hopping ( bh ) , @xcite and evolutionary principles based genetic algorithms ( ga ) . @xcite however , no general rule of preference to a specific algorithm exists , as the efficiency of classical global optimization methods is highly system dependent . @xcite there are many technical aspects that influence the performance of any global sampling technique , such as the choice of initial geometry , the ways of disturbing the configuration during the trial move , the definition of acceptance criteria , the methods employed to calculate potential energies and forces _ many authors were concerned with the efficiency of applied sampling methods and suggested various improvements . @xcite moreover , the possibility of moving from the total energy as the main sampling criterion towards observable - driven @xcite and grand - canonical @xcite global sampling schemes has been suggested . the parameter that plays the most crucial role in method performance , however , is the choice of coordinates suitable for representing the geometries and , most importantly , changes in geometries during the sampling , _ _ i.e.__the so - called trial moves . @xcite the essential importance of the trial geometry generation step has already been noticed in early system - specific publications . @xcite for instance , simple group rotations within proteins@xcite or clusters@xcite already led to significant gains in sampling efficiency . furthermore , several computationally more expensive ways to produce elementary trial moves were suggested based on short high - temperature molecular dynamics ( md ) runs.@xcite for certain systems they have indeed proven to be much more effective , allowing to _ e.g. _ optimize large metallic clusters within atomistic models . @xcite from a programmer s point of view , the perhaps most intuitive representation of the atomic coordinates of trial moves are cartesian coordinate ( cc ) displacements . it has been noted though that this most popular representation is often inefficient , @xcite due to its chemical blindness , which may easily lead to unphysical configurations ( _ _ e.g.__dissociated structures ) . cc displacements do not account for the overall geometry and the coupling between coordinates . different approaches have been proposed to overcome this difficulty , such as virtual - alphabet genetic algorithms , @xcite employing the idea that coordinates should stand as meaningful building blocks , @xcite or genetic algorithms with space - fixed ccs , @xcite introducing non - traditional genetic operators . the main limitation of these methods , however , is that they remain rather system specific . the choice of suitable coordinates for global optimization should rather be system independent , while at the same time adapted to the chemical structure . especially in the case of large adsorbates the completely unbiased way in which the structural phase space is sampled in ccs does not allow for an efficient structural search for conformational changes upon adsorption that leave the molecular connectivity intact . the chemically most intuitive set of coordinates for such a situation would instead be internal coordinates ( ics ) , namely bond stretches , angle bends , or torsions . already in the seminal work on bh of wales and doye , the potential usefulness of such coordinates has been noted , @xcite and later shown to be beneficial for structures connected by double - ended pathways.@xcite one of the first applications of the idea of using ics for global geometry optimization was reported in the context of protein - ligand docking , which developed into the so - called internal coordinate mechanics ( icm ) model , @xcite further extending the above mentioned concept of meaningful building blocks . @xcite another example of global optimization in ics was the attempt of introducing dihedral angles into the framework of the so - called deterministic global optimization . @xcite global optimization of clusters and molecules in ics using the z - matrix representation was suggested by dieterich and hartke . @xcite however , automatic construction of a z - matrix is close to impossible for larger , more complicated systems , especially organic molecules containing rings . besides , it also does not eliminate the problem of coordinate redundancies , which generally limits the applicability of this approach . especially suitable for a system independent description of complex molecular structures are instead so - called delocalized internal coordinates ( dics ) , _ i.e. _ non - redundant linear combinations of ics , that have been extensively used for efficient local structure optimization of covalent molecules , @xcite crystalline structures , @xcite and for vibrational calculations . @xcite in our recent work @xcite , we implemented such automatically generated collective curvilinear coordinates in a bh global sampling procedure . the similarity of these coordinates to molecular vibrations does yield an enhanced generation of chemically meaningful trial structures , especially for covalently bound systems . in the application to hydrogenated si clusters , we correspondingly observed a significantly increased efficiency in identifying low - energy structures when compared to cc trial moves and exploited this enhancement for an extensive sampling of potential products of silicon cluster soft landing on the si(001 ) surface . in the present work , we provide a detailed methodological account of this curvilinear coordinate global optimization approach , @xcite and extend it to a conformational screening of adsorbates on surfaces . we do this by introducing constraints and extending the coordinate system to include lateral surface translations and rigid adsorbate rotations . these curvilinear coordinates are constructed automatically at every global optimization step and , similarly to the original bh scheme , we pick a random set of coordinate displacements with which a trial move is attempted . testing this for the _ trans_-@xmath0-ionylideneacetic acid molecule adsorbed on a au(111 ) surface ( as an example of a complex functionalized organic adsorbate ) , and for methane adsorbed on a ag(111 ) surface ( as an example of a small adsorbate with a shallow pes and many minima ) , we find that dic trial moves increase the efficiency of bh by both a more complete sampling of the possible surface adsorption sites and by reducing the number of molecular dissociations . the paper is organized as follows : in chapter [ methods ] we outline traditional approaches to global structure optimization , explain the construction of dics and our definition of a complete coordinate set for adsorbates on surfaces , and how these coordinates are applied for conformational structure searches in a global optimization framework such as basin hopping . in chapter [ computational ] we summarize the computational details of our benchmark studies on the surface - adsorbed aggregates presented in chapter [ results ] . we conclude our work in chapter [ conclusions ] . additional remarks on software and algorithms can be found in appendix [ appendix - winak ] , details on dft calculated diol stability can be found in appendix [ appendix - dft ] .

the employed automatically constructed delocalized internal coordinates are similar to molecular vibrations , which enhances the generation of chemically meaningful trial structures . by introducing flexible constraints and local translation and rotation of independent geometrical subunits we enable the use of this method for molecules adsorbed on surfaces and interfaces . for two test systems , _ trans_--ionylideneacetic acid adsorbed on a au(111 ) surface and methane adsorbed on a ag(111 ) surface , we obtain superior performance of the method compared to standard optimization moves based on cartesian coordinates .

efficient structure search is a major challenge in computational materials science . we present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves . this approach has recently been shown to be efficient in structure determination of clusters [ nano letters 15 , 80448048 ( 2015 ) ] and is here extended for its application to covalent , complex molecules and large adsorbates on surfaces . the employed automatically constructed delocalized internal coordinates are similar to molecular vibrations , which enhances the generation of chemically meaningful trial structures . by introducing flexible constraints and local translation and rotation of independent geometrical subunits we enable the use of this method for molecules adsorbed on surfaces and interfaces . for two test systems , _ trans_--ionylideneacetic acid adsorbed on a au(111 ) surface and methane adsorbed on a ag(111 ) surface , we obtain superior performance of the method compared to standard optimization moves based on cartesian coordinates .

1606.06614

c

we presented a modification of the basin hopping algorithm by performing global optimization trial moves in chemically - motivated curvilinear coordinates that resemble molecular vibrations . this approach has recently been shown to be efficient in structure determination of clusters @xcite and was here investigated and extended for the application to organic molecules both in gas phase and adsorbed on metal surfaces . the chemical nature of the collective displacements enables straightforward inclusion of rotations , translations , as well as constraints on these and arbitrary internal degrees of freedom . this allows for a finely tunable sampling of practically relevant areas of phase space for complex systems that appear in nanotechnology and heterogeneous catalysis , such as hybrid organic - inorganic interfaces , @xcite organic crystals , self - assembled nanostructures , and reaction networks on surfaces . these systems feature heterogeneous chemical bonding , where stiff energetically favorable bonding moieties , such as covalent molecules , coexist with weak and flexible bonding forces such as interactions between molecules or between a molecule and a surface . for the show cases @xmath0-acid adsorbed on au(111 ) and methane adsorbed on ag(111 ) we find that collective internal coordinate based trial moves outperform cartesian trial moves in several ways : _ i ) _ cdics systematically identify a larger number of structures at equal number of global optimization steps , thus allowing to reduce the number of necessary global optimization steps ; _ ii ) _ constr.cdics are able to restrict structure searches to well defined chemically - motivated subdomains of the configurational space and thus find more relevant structures ; _ iii ) _ dics generate less strained structures and reduce the computational cost associated with a single global optimization step . in future work we plan to utilize the variability of singular - value decomposed collective coordinates in the context of materials structure search to facilitate simulation of surface reconstructions and defect formation , as well as crystal polymorphism and phase stability in organic crystals and layered materials . so far we have only discussed the relevance of these coordinate systems in the context of basin hopping , however displacement moves are a common element of many different stochastic global optimization strategies , such as , for example , minima hopping , where curvilinear constraints can help guide the md . @xcite our implementation can easily be extended to feature such algorithms as well .

we present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves . this approach has recently been shown to be efficient in structure determination of clusters [ nano letters 15 , 80448048 ( 2015 ) ] and is here extended for its application to covalent , complex molecules and large adsorbates on surfaces .

efficient structure search is a major challenge in computational materials science . we present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves . this approach has recently been shown to be efficient in structure determination of clusters [ nano letters 15 , 80448048 ( 2015 ) ] and is here extended for its application to covalent , complex molecules and large adsorbates on surfaces . the employed automatically constructed delocalized internal coordinates are similar to molecular vibrations , which enhances the generation of chemically meaningful trial structures . by introducing flexible constraints and local translation and rotation of independent geometrical subunits we enable the use of this method for molecules adsorbed on surfaces and interfaces . for two test systems , _ trans_--ionylideneacetic acid adsorbed on a au(111 ) surface and methane adsorbed on a ag(111 ) surface , we obtain superior performance of the method compared to standard optimization moves based on cartesian coordinates .

cond-mat9804060

i

since the last few years , identifying the symmetry of the pairing state has been the expected major step towards an understanding of high @xmath14 superconductivity . the controversy is not yet resolved : while there seems to be an agreement on the existence of nodes in the gap , some experiments appear to advocate in favor of a pure @xmath12 symmetry @xcite , whereas others seem to exhibit a significant s - wave contribution @xcite . with respect to this problem , inelastic light scattering has been shown very early to be a powerful tool because , besides probing the bulk ( in contrast with photoemission and tunneling ) , the polarization selection rules on the incident and scattered light make the spectra sensitive to the wave - vector of the electronic excitations @xcite . a theoretical approach of electronic raman scattering has been developed , in the case of @xmath12 symmetry . the emphasis is put on the low energy spectrum , which is expected in this case to exhibit well defined power laws , according to the symmetry channel , e.g. the polarization of the incoming and outgoing light . more precisely , the so - called @xmath8 and @xmath15 symmetry should display a linear dependence versus frequency , as these channels are sensitive to the nodes in the @xmath16 direction , whereas the @xmath9 symmetry probes mainly directions around the @xmath17 @xmath18 directions and should display a @xmath19 frequency dependence @xcite . such calculations omit other excitations such as phonons . the experimental major difficulty lies then in the fact that in most investigated compounds , e.g. @xmath20 @xmath21 ( y-123 ) , @xmath22 ( bi-2212 ) and @xmath23 ( tl-2201 ) , a large phonon contribution is superimposed to the electronic excitations in particular at low frequency and has therefore to be subtracted , which precludes an accurate determination of the shape of the electronic contribution in the superconducting state @xcite . despite this difficulty , in a number of reports , a satisfactory agreement is claimed to be found between the electronic response obtained after subtraction of the phonon lines , and the @xmath12 model @xcite in this work , we report _ pure _ electronic raman spectra in @xmath0 ( hg-1223 ) single crystals , belonging to the highest @xmath14 cuprate family . this provides a large spectral range below the superconducting gap frequency where the low energy electronic spectrum can be analyzed . moreover , within this range , no subtraction of the phonons is required to discuss the electronic response @xcite . indeed , as shown in our previous work [ 16 - 18 ] , the very low intensity of the raman phonon peaks for electric fields within the @xmath24 planes allows a reliable analysis of the electronic excitations in the superconducting state . the crystallographic structure of hg-1223 is tetragonal ( @xmath25 ) @xcite , which yields an unambiguous comparison with theoretical calculations based on tetragonal symmetry , without the complications due to the orthorhombic distortion as in y-123 @xcite . hg-1223 is therefore particularly well suited for the study of the electronic raman scattering . our most striking results are i ) the existence of two electronic maxima at @xmath26 and @xmath27 , both detected in @xmath28 symmetry . these two maxima disappear at @xmath14 . ii ) the low frequency behavior of the @xmath29 spectrum displays what we believe to be an intrinsic linear term , which is observed for all excitation energies used in this work ( 476.5 - 647.1 nm spectral range ) . such observations imply that the gap is strongly anisotropic with two distinct maxima and that nodes exist outside the [ 110 ] and [ 1,@xmath13,0 ] directions . we argue that our results , which are at odds with a pure @xmath12 gap symmetry , imply an order parameter with two maximum gap values and eight nodes .

pure electronic raman spectra with no phonon structures hindering the analysis of the electronic continuum have been obtained . as a consequence , these two maxima disappear at and do not soften significantly as the temperature is raised up to the low energy frequency dependence of the electronic response is strongly linear , for various excitation lines in the 476.5 to 647.1 nm range . instead , they strongly advocate in favor of an anisotropic superconducting gap with two distinct gap maxima and of nodes existing outside the [ 110 ] and [ 1,,0 ] directions in * k*-space .

electronic raman scattering measurements have been performed on single crystals in the superconducting state . pure electronic raman spectra with no phonon structures hindering the analysis of the electronic continuum have been obtained . as a consequence , the spectra in the pure and symmetries are directly and reliably analyzed and the pure contribution can be easily identified . below the critical temperature two electronic structures at and are clearly seen . both are observed simultaneously in pure symmetry , the highest energy one being located at the energy of the maximum . these two maxima disappear at and do not soften significantly as the temperature is raised up to the low energy frequency dependence of the electronic response is strongly linear , for various excitation lines in the 476.5 to 647.1 nm range . such experimental data can not be reconciled with a pure symmetry . instead , they strongly advocate in favor of an anisotropic superconducting gap with two distinct gap maxima and of nodes existing outside the [ 110 ] and [ 1,,0 ] directions in * k*-space . we discuss in detail the simplest order parameter compatible with our experimental findings .

1010.3112

i

the probability of a sample configuration provides a useful ground for analyzing genetic data . popular applications include obtaining maximum likelihood estimates of model parameters and performing ancestral inference [ see @xcite ] . in principle , model - based full - likelihood analyses , such as that based on the coalescent [ kingman ( @xcite , @xcite ) ] , should be among the most powerful methods since they make full use of the data . however , in most cases , it is intractable to obtain a closed - form formula for the probability of a given data set . a well - known exception to this hurdle is the ewens sampling formula ( esf ) , which describes the stationary probability distribution of a sample configuration under the one - locus infinite - alleles model in the diffusion limit [ @xcite ] . notable biological applications of this closed - form formula include the test of selective neutrality [ see @xcite , slatkin ( @xcite , @xcite ) ] . @xcite provided a plya - like urn model interpretation of the formula , and recently @xcite provided a new combinatorial proof of the esf and extended the framework to obtain new results for the case with a variable population size . we refer the reader to the latter paper for a nice summary of previous works related to the esf . note that the esf also arises in several interesting contexts outside biology , including random partition structures and bayesian statistics ; see @xcite for examples of intricate combinatorial connections . the esf is a special case of the two - parameter sampling formula constructed by pitman ( @xcite , @xcite ) for exchangeable random partitions . @xcite considered generalizing the infinite - alleles model to include recombination and constructed a recursion relation satisfied by the two - locus sampling probability distribution at stationarity in the diffusion limit . @xcite later undertook a more mathematical analysis of the two - locus model and provided several interesting results . however , to date , a general closed - form formula for the two - locus sampling distribution remains unknown . indeed , it is widely recognized that recombination adds a formidably challenging layer of complexity to population genetics analysis . because obtaining exact analytic results in the presence of recombination is difficult , recent research has focused on developing sophisticated and computationally - intensive monte carlo techniques . examples of such techniques applied to the coalescent include monte carlo simulations [ see hudson ( @xcite , @xcite ) ] , importance sampling [ see @xcite , @xcite , @xcite , de iorio and griffiths ( @xcite , @xcite ) , @xcite ] and markov chain monte carlo methods [ see @xcite , @xcite , @xcite ] . being the simplest model with recombination , the two - locus case has been extensively studied in the past [ @xcite , @xcite , @xcite , @xcite , @xcite ] and a renewed wave of interest was recently sparked by @xcite , who proposed a composite likelihood method which uses two - locus sampling probabilities as building blocks . ldhat , a widely - used software package for estimating recombination rates , is based on this composite likelihood approach , and it has been used to produce a fine - scale map of recombination rate variation in the human genome [ @xcite , @xcite ] . ldhat assumes a symmetric diallelic recurrent mutation model at each locus and relies on the importance sampling scheme proposed by @xcite for the coalescent with recombination , to generate exhaustive lookup tables containing two - locus probabilities for all inequivalent sample configurations and a range of relevant parameter values . this process of generating exhaustive lookup tables is very computationally expensive . a fast and accurate method of estimating two - locus probabilities would be of practical value . in this paper , we revisit the tantalizing open question of whether a closed - form sampling formula can be found for the coalescent with recombination . we show that , at least for the two - locus infinite - alleles model with the population - scaled recombination rate @xmath0 large but not necessarily infinite , it is possible to obtain useful closed - form analytic results . note that the aforementioned monte carlo methods generally become less efficient as @xmath0 increases . those methods involve sampling a large collection of genealogical histories consistent with the observed sample configuration , and , when @xmath0 is large , the sampled genealogies tend to be very complicated ; they typically contain many recombination events , and it may take a long time for every locus to reach a most recent common ancestor . however , contrary to this increased complexity in the standard coalescent , we actually expect the evolutionary dynamics to be easier to describe for large @xmath0 , since the loci under consideration would then be less dependent . hence , it seems reasonable to conjecture that there may exist a stochastic process simpler than the standard coalescent with recombination that describes the relevant degrees of freedom in the large @xmath0 limit . we believe that our sampling formula may provide some hints as to what that dual process should be . the work discussed here generalizes previous results [ @xcite , @xcite ] for @xmath1 , in which case the loci become independent and the two - locus sampling distribution is given by a product of one - locus esfs . our main results can be summarized as follows . consider the diffusion limit of the two - locus infinite - alleles model with population - scaled mutation rates @xmath2 and @xmath3 at the two loci . for a sample configuration @xmath4 ( defined later in the text ) , we use @xmath5 to denote the probability of observing @xmath4 given the parameters @xmath6 and @xmath0 . for an arbitrary @xmath4 , our goal is to find an asymptotic expansion of @xmath5 in inverse powers of @xmath0 , that is , for large values of the recombination rate @xmath0 , our goal is to find @xmath7 where @xmath8 , and @xmath9 are independent of @xmath0 . as mentioned before , @xmath10 is given by a product of one - locus esfs . in this paper , we derive a closed - form formula for the first - order term @xmath11 . further , we show that the second - order term @xmath12 can be decomposed into two parts , one for which we obtain a closed - form formula and the other that satisfies a simple strict recursion . the latter can be easily evaluated using dynamic programming . details of these results are described in section [ sec : asy ] . in a similar vein , in section [ sec : joi ] , we obtain a simple asymptotic formula for the joint probability distribution of the number of alleles observed at the two loci . we remark that our work has practical value in genetic analysis . while this paper was under review , we applied the technique developed here to obtain analogous results for an arbitrary finite - alleles recurrent mutation model . see @xcite for details . in that paper , we performed an extensive assessment of the accuracy of our results for a particular finite - alleles model of mutation , and showed that they may be accurate even for moderate values of @xmath0 , including a range that is of biological interest . the accuracy ( not discussed here ) of our results for the infinite - alleles model is very similar to that finite - alleles case .

ewens sampling formula ( esf ) is a one - parameter family of probability distributions with a number of intriguing combinatorial connections . specifically , we consider an asymptotic expansion of the two - locus sampling formula in inverse powers of and obtain closed - form expressions for the first few terms in the expansion .

ewens sampling formula ( esf ) is a one - parameter family of probability distributions with a number of intriguing combinatorial connections . this elegant closed - form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite - alleles model of mutation . since its discovery in the early 1970s , the esf has been used in various biological applications , and has sparked several interesting mathematical generalizations . in the population genetics community , extending the underlying random - mating model to include recombination has received much attention in the past , but no general closed - form sampling formula is currently known even for the simplest extension , that is , a model with two loci . in this paper , we show that it is possible to obtain useful closed - form results in the case the population - scaled recombination rate is large but not necessarily infinite . specifically , we consider an asymptotic expansion of the two - locus sampling formula in inverse powers of and obtain closed - form expressions for the first few terms in the expansion . our asymptotic sampling formula applies to arbitrary sample sizes and configurations . and . .

1010.3112

r

in what follows , we provide proofs of the results mentioned in the previous two sections . first , assume @xmath146 . substitute the expansion ( [ expansion ] ) into golding s recursion ( [ golding ] ) , divide by @xmath147 and let @xmath148 . we are then left with @xmath149 now , applying ( [ unwrap0 ] ) repeatedly gives @xmath150\times[l]}c_{ij}!}{c ! } q_0({\mathbf{a}}+{\mathbf{c}}_a,{\mathbf{b}}+{\mathbf{c}}_b , \mathbf{0}),\ ] ] where the summation is over all distinct orderings of the @xmath143 gametes with multiplicity @xmath66 . there are @xmath151 such orderings and since the summand is independent of the ordering , we conclude @xmath152 clearly , ( [ unwrap0b ] ) also holds for @xmath153 . from a coalescent perspective , this equation tells us that any gamete with specified alleles ( i.e. , `` carrying ancestral material '' ) at both loci must undergo recombination instantaneously backward in time . now , by substituting the asymptotic expansion ( [ expansion ] ) with @xmath104 into golding s recursion ( [ golding ] ) and letting @xmath148 , we obtain @xmath154q_0({\mathbf { a}},{\mathbf{b}},\mathbf{0 } ) \nonumber\\ & & \qquad= \sum_{i=1}^k a_i(a_i-1)q_0({\mathbf{a}}-{\mathbf{e}}_i,{\mathbf { b}},\mathbf{0 } ) + \sum_{j=1}^l b_j(b_j-1)q_0({\mathbf{a}},{\mathbf { b}}-{\mathbf{e}}_j,\mathbf{0 } ) \nonumber\\[-8pt]\\[-8pt ] & & \qquad\quad { } + 2\sum_{i=1}^k\sum_{j=1}^l a_i b_j q_0({\mathbf{a}}-{\mathbf{e } } _ i,{\mathbf{b}}-{\mathbf{e}}_j,{\mathbf{e}}_{ij } ) \nonumber\\ & & \qquad\quad { } + \theta_a\sum_{i=1}^k \delta_{a_i,1}q_0({\mathbf { a}}-{\mathbf{e } } _ i,{\mathbf{b}},\mathbf{0 } ) + \theta_b\sum_{j=1}^l\delta _ { b_j,1}q_0({\mathbf{a}},{\mathbf{b}}-{\mathbf{e}}_j,\mathbf{0}).\nonumber\end{aligned}\ ] ] equation ( [ unwrap0b ] ) implies @xmath155 , so with a bit of rearranging we are left with @xmath156q_0({\mathbf { a}},{\mathbf{b}},\mathbf{0 } ) \nonumber\\ & & \qquad= \sum_{i=1}^k a_i(a_i-1)q_0({\mathbf{a}}-{\mathbf{e}}_i,{\mathbf { b}},\mathbf{0 } ) + \sum_{j=1}^l b_j(b_j-1)q_0({\mathbf{a}},{\mathbf { b}}-{\mathbf{e}}_j,\mathbf{0 } ) \\ & & \qquad\quad { } + \theta_a\sum_{i=1}^k \delta_{a_i,1}q_0({\mathbf { a}}-{\mathbf{e } } _ i,{\mathbf{b}},\mathbf{0 } ) + \theta_b\sum_{j=1}^l\delta _ { b_j,1}q_0({\mathbf{a}},{\mathbf{b}}-{\mathbf{e}}_j,\mathbf{0})\nonumber\end{aligned}\ ] ] with boundary conditions @xmath157 for all @xmath50 $ ] and . noting that ( [ goldingc=0 ] ) is the sum of two independent recursions of the form ( [ one - locus - recursion ] ) , one for each locus and each with appropriate boundary condition , we conclude that @xmath158 is given by @xmath159 a product of two ( ordered ) esfs . it is straightforward to verify that ( [ esfx2 ] ) satisfies ( [ goldingc=0 ] ) . finally , using ( [ unwrap0b ] ) and ( [ esfx2 ] ) , we arrive at ( [ leading ] ) . first , assume @xmath160 . substitute the asymptotic expansion ( [ expansion ] ) into golding s recursion ( [ golding ] ) , eliminate terms of order @xmath0 by applying ( [ unwrap0 ] ) , and let @xmath148 . after applying ( [ unwrap0b ] ) to the remaining terms and invoking ( [ goldingc=0 ] ) , with some rearrangement we obtain @xmath161 now , by utilizing ( [ esfx2 ] ) , this can be written in the form @xmath162 where @xmath163\\[-8pt ] & & { } -q^a({\mathbf{a}}+{\mathbf{c}}_a)\sum_{j=1}^l \frac { c_{\cdot j}(c_{\cdot j}-1)}{c}q^b({\mathbf{b}}+{\mathbf{c}}_b -{\mathbf{e}}_j ) \nonumber\\ & & { } + \sum_{i=1}^k\sum_{j=1}^l \frac{c_{ij}(c_{ij}-1)}{c}q^a ( { \mathbf{a}}+{\mathbf{c}}_a-{\mathbf{e}}_i)q^b({\mathbf { b}}+{\mathbf { c}}_b-{\mathbf{e}}_j).\nonumber\end{aligned}\ ] ] above , we assumed @xmath146 . we define @xmath164 if @xmath165 . iterating the recursion ( [ q1+f ] ) , we may write @xmath108 as @xmath166.\end{aligned}\ ] ] similarly , repeatedly iterating ( [ q1+f ] ) yields @xmath167 the key observation is that the right - hand side of ( [ expandf ] ) has a nice probabilistic interpretation which allows us to obtain a closed - form formula . to be more precise , consider the first summation @xmath168 for a fixed sample configuration @xmath79 , this can be interpreted as the sum over all possible ways of throwing away a gamete at random and calculating @xmath169 based on the remaining subsample , which we will denote @xmath170 . equivalently , it is the expected value of @xmath169 with respect to subsampling without replacement @xmath171 of the gametes in @xmath79 . write this as @xmath172,\ ] ] where @xmath173 is the random subsample obtained by sampling without replacement @xmath171 gametes from @xmath79 , and @xmath174 , @xmath175 . note that once the subsample @xmath176 is obtained , then @xmath177 and @xmath178 are fully specified . more generally , consider the @xmath179th sum in ( [ expandf ] ) . a particular term in the summation corresponds to an ordering of @xmath180 gametes in @xmath79 , which , when removed leave a subsample @xmath181 . with respect to this subsample , the summand is @xmath182 and for each such subsample @xmath183 there are @xmath184 distinct orderings of the remaining types in @xmath79 , with each ordering contributing the same amount to the sum . here , @xmath185 denotes the multinomial coefficient : @xmath186 gathering identical terms , the @xmath179th sum in ( [ expandf ] ) can therefore be written over all distinct subsamples of @xmath79 of size @xmath187 : @xmath188,\end{aligned}\ ] ] where , for a fixed @xmath187 , @xmath189 is a multivariate hypergeometric@xmath190 random variable ; that is , @xmath191\times[l ] } \bigl[c_{ij}^{(m ) } = c_{ij}^{(m ) } \bigr ] \biggr ) = \frac{1}{{c\choose m } } \prod_{(i , j)\in[k]\times[l ] } \pmatrix{c_{ij}\cr c_{ij}^{(m)}}.\ ] ] furthermore , marginally we have @xmath192 in summary , ( [ expandf ] ) can be written as @xmath193.\ ] ] according to lemma [ lemma : first ] , the first term @xmath194 vanishes , so we are left with @xmath195.\ ] ] finally , since @xmath196 and @xmath197 , ( [ eq : f ] ) and ( [ subsampling ] ) together imply @xmath198q^a({\mathbf{a}}+{\mathbf { c}}_a-{\mathbf{e}}_i ) \\ & & \qquad\quad\hspace*{21.2pt } { } - q^a({\mathbf{a}}+{\mathbf{c}}_a)\frac{1}{m}\sum_{j=1}^l \mathbb{e}\bigl[c_{\cdot j}^{(m)}\bigl(c_{\cdot j}^{(m)}-1\bigr)\bigr]q^b({\mathbf { b}}+{\mathbf{c}}_b-{\mathbf{e}}_j ) \\ & & \qquad\quad\hspace*{21.2pt } { } + \frac{1}{m}\sum_{i=1}^k \sum_{j=1}^l \mathbb{e } \bigl[c_{ij}^{(m)}\bigl(c_{ij}^{(m)}-1\bigr)\bigr]q^a({\mathbf{a}}+{\mathbf{c}}_a -{\mathbf{e}}_i)q^b({\mathbf{b}}+{\mathbf{c}}_b-{\mathbf{e}}_j)\biggr].\end{aligned}\ ] ] the moments in this equation are easy to compute and one can sum them over @xmath187 to obtain the desired result ( [ firstorder ] ) . first , note that for any sample @xmath199 and any subsample of the form @xmath200 , we have @xmath201 , since every term on right - hand side of ( [ eq : f ] ) has a vanishing coefficient . so , equation ( [ q1concise ] ) implies @xmath202 for any @xmath203\times[l]$ ] . now , substitute the asymptotic expansion ( [ expansion ] ) with @xmath104 into golding s recursion ( [ golding ] ) . note that terms of order @xmath0 are absent since @xmath204 . eliminate terms with coefficients independent of @xmath0 by applying ( [ goldingc=0preliminary ] ) , multiply both sides of the recursion by @xmath0 , and let @xmath148 to obtain the following : @xmath205q_1({\mathbf{a}},{\mathbf { b}},\mathbf{0 } ) \\ & & \qquad= \sum_{i=1}^k a_i(a_i-1)q_1({\mathbf{a}}-{\mathbf{e}}_i,{\mathbf { b}},\mathbf{0 } ) + \sum_{j=1}^l b_j(b_j-1)q_1({\mathbf{a}},{\mathbf { b}}-{\mathbf{e}}_j,\mathbf{0 } ) \\ & & \qquad\quad { } + 2\sum_{i=1}^k \sum_{j=1}^l a_i b_j q_1({\mathbf{a}}-{\mathbf{e } } _ i,{\mathbf{b}}-{\mathbf{e}}_j,{\mathbf{e}}_{ij } ) \\ & & \qquad\quad { } + \theta_a\sum_{i=1}^k \delta_{a_i,1}q_1({\mathbf { a}}-{\mathbf{e } } _ i,{\mathbf{b}},\mathbf{0 } ) + \theta_b\sum_{j=1}^l\delta _ { b_j,1}q_1({\mathbf{a}},{\mathbf{b}}-{\mathbf{e}}_j,\mathbf{0})\end{aligned}\ ] ] with boundary conditions @xmath206 for all @xmath50 $ ] and @xmath75 $ ] . this equation can be made strictly recursive by applying ( [ unwrap1b ] ) to @xmath207 . it therefore follows from the boundary conditions ( for example , by induction ) that @xmath208 . here , we provide only an outline of a proof ; details are similar to the proof of theorem [ thm : first ] . substitute the asymptotic expansion ( [ expansion ] ) into golding s recursion ( [ golding ] ) , eliminate terms with coefficients proportional to @xmath0 or independent of @xmath0 . then , multiply both sides of the recursion by @xmath0 and let @xmath148 to obtain @xmath209 \nonumber\\[-8pt]\\[-8pt ] & & \qquad\quad { } + \theta_a\sum_{i=1}^k \biggl[\sum_{j=1}^l \delta _ { a_i+c_{i\cdot},1}\delta_{c_{ij},1}q_1({\mathbf{a}},{\mathbf { b}}+{\mathbf{e } } _ j,{\mathbf{c}}-{\mathbf{e}}_{ij})\nonumber\\ & & \qquad\quad\hspace*{93.3pt } { } + \delta_{a_i,1}\delta _ { c_{i\cdot } , 0}q_1({\mathbf{a}}-{\mathbf{e}}_i,{\mathbf{b}},{\mathbf { c } } ) \biggr ] \nonumber\\ & & \qquad\quad { } + \theta_b\sum_{j=1}^l \biggl[\sum_{i=1}^k \delta _ { b_j+c_{\cdot j},1}\delta_{c_{ij},1}q_1({\mathbf{a}}+{\mathbf { e}}_i,{\mathbf { b}},{\mathbf{c}}-{\mathbf{e}}_{ij})\nonumber\\ & & \qquad\quad\hspace*{89.3pt } { } + \delta_{b_j,1}\delta _ { c_{\cdot j},0}q_1({\mathbf{a}},{\mathbf{b}}-{\mathbf{e}}_j,{\mathbf { c } } ) \biggr ] \nonumber\\ & & \qquad\quad { } - [ n(n-1 ) + \theta_a(a+c ) + \theta _ b(b+c)]q_1({\mathbf { a}},{\mathbf{b}},{\mathbf{c } } ) . \nonumber\end{aligned}\ ] ] by substituting our expression ( [ firstorder ] ) for @xmath108 , the right - hand side can be expressed as a function @xmath210 which is completely known but rather cumbersome to write down . as in the proof of theorem [ thm : first ] , the same `` unwrapping '' maneuver can be applied to rearrange ( [ secondrec ] ) into the form ( [ q2concise ] ) , where @xmath211.\ ] ] this time @xmath212 $ ] is a function of fourth - order moments of the multivariate hypergeometric distribution . the formula shown in the is obtained by evaluating the expectations and summing over @xmath187 . we now show that @xmath115 satisfies the recursion shown in ( [ q2(a , b,0 ) ] ) . we will use the fact that for a sample @xmath213 , we have @xmath214 for an arbitrary @xmath79 , @xmath215 is much more complicated . now , one can adopt the approach used in the proof of lemma [ lemma : first ] to obtain a strict recursion for @xmath118 . first , note that ( [ q2concise ] ) and ( [ g(a1,b1,c1 ) ] ) imply @xmath216 \nonumber\\ & & \qquad= q_2({\mathbf{a}},{\mathbf{b}},\mathbf{0 } ) + g({\mathbf { a}}-{\mathbf{e } } _ i,{\mathbf{b}}-{\mathbf{e}}_j,{\mathbf{e}}_{ij } ) \nonumber\\ & & \qquad= q_2({\mathbf{a}},{\mathbf{b}},\mathbf{0 } ) + 2(a-1)(b-1)q^a ( { \mathbf{a}})q^b({\mathbf{b } } ) \\\ & & \qquad\quad { } - 2(b-1)(a_i-1)q^a({\mathbf{a}}-{\mathbf{e}}_i)q^b({\mathbf{b } } ) \nonumber\\ & & \qquad\quad { } - 2(a-1)(b_j-1)q^a({\mathbf{a}})q^b({\mathbf{b}}-{\mathbf{e}}_j ) \nonumber\\ & & \qquad\quad { } + 2(a_i-1)(b_j-1)q^a({\mathbf{a}}-{\mathbf{e}}_i)q^b({\mathbf { b}}-{\mathbf{e}}_j).\nonumber\end{aligned}\ ] ] as before , substitute the asymptotic expansion ( [ expansion ] ) for @xmath217 into golding s recursion ( [ golding ] ) , eliminate terms with coefficients independent of @xmath0 or proportional to @xmath218 , and let @xmath148 to obtain @xmath205q_2({\mathbf{a}},{\mathbf { b}},\mathbf{0 } ) \\ & & \qquad= \sum_{i=1}^k a_i(a_i-1)q_2({\mathbf{a}}-{\mathbf{e}}_i,{\mathbf { b}},\mathbf{0 } ) + \sum_{j=1}^l b_j(b_j-1)q_2({\mathbf{a}},{\mathbf { b}}-{\mathbf{e}}_j,\mathbf{0 } ) \\ & & \qquad\quad { } + 2\sum_{i=1}^k \sum_{j=1}^l a_i b_j q_2({\mathbf{a}}-{\mathbf{e } } _ i,{\mathbf{b}}-{\mathbf{e}}_j,{\mathbf{e}}_{ij } ) \\ & & \qquad\quad { } + \theta_a\sum_{i=1}^k \delta_{a_i,1}q_2({\mathbf { a}}-{\mathbf{e } } _ i,{\mathbf{b}},\mathbf{0 } ) + \theta_b\sum_{j=1}^l\delta _ { b_j,1}q_2({\mathbf{a}},{\mathbf{b}}-{\mathbf{e}}_j,\mathbf{0})\end{aligned}\ ] ] with boundary conditions @xmath117 for all @xmath50 $ ] and @xmath75 $ ] . this equation can be made strictly recursive by applying ( [ unwrap2 ] ) to @xmath219 . after some simplification , this leads to the recursion ( [ q2(a , b,0 ) ] ) . the proof is similar to the proof of proposition [ prop : leading ] , working with the system ( [ kl ] ) rather than golding s recursion ( [ golding ] ) . first , assume @xmath146 . substitute the expansion ( [ expansionkl ] ) into the recursion ( [ kl ] ) , divide by @xmath147 and let @xmath220 . we are left with @xmath221 which implies @xmath222 clearly , ( [ unwrapkl ] ) also holds for @xmath153 . now , by substituting the asymptotic expansion ( [ expansionkl ] ) with @xmath141 into ( [ kl ] ) and letting @xmath148 , we obtain @xmath223p_0(a , b,0;k , l ) \nonumber\\ & & \qquad= a(a-1)p_0(a-1,b,0;k , l ) + b(b-1)p_0(a , b-1,c;k , l ) \nonumber\\ & & \qquad\quad { } + 2ab p_0(a-1,b-1,1;k , l ) \\ & & \qquad\quad { } + \theta_aa p_0(a-1,b,0;k-1,l)\nonumber\\ & & \qquad\quad { } + \theta_bb p_0(a , b-1,0;k , l-1).\nonumber\end{aligned}\ ] ] after invoking ( [ unwrapkl ] ) on @xmath224 and rearranging , we are left with @xmath225p_0(a , b,0;k , l ) \nonumber\\ & & \qquad = a(a-1)p_0(a-1,b,0;k , l ) + b(b-1)p_0(a , b-1,0;k , l ) \nonumber\\[-8pt]\\[-8pt ] & & \qquad\quad{}+ \theta_aa p_0(a-1,b,0;k-1,l)\nonumber\\ & & \qquad\quad { } + \theta_bb p_0(a , b-1,0;k , l-1)\nonumber\end{aligned}\ ] ] with boundary conditions @xmath226 and @xmath227 . equation ( [ klc=0 ] ) can be expressed as a linear sum of two independent recursions : @xmath228 with respective boundary conditions @xmath229 and @xmath230 . these recursions are precisely those considered by ewens [ ( @xcite ) , ( 21 ) ] , with respective solutions ( [ k ] ) and ( [ l ] ) . hence , @xmath231 and @xmath232 , and it is straightforward to verify that @xmath233 satisfies ( [ klc=0 ] ) . substituting this solution into ( [ unwrapkl ] ) , we arrive at ( [ leadingkl ] ) , as required . first , assume @xmath146 . substitute the asymptotic expansion ( [ expansionkl ] ) into the recursion ( [ kl ] ) , eliminate terms with coefficients linear in @xmath0 by applying ( [ unwrapkl ] ) , and let @xmath148 . after applying ( [ unwrapkl ] ) to the remaining terms and invoking ( [ klc=0 ] ) , with some rearrangement we obtain @xmath234\\[-8pt ] & & \qquad\quad\hspace*{33pt}{}- p_0(a+c , b+c-1,0;k , l)\nonumber\\ & & \qquad\quad\hspace*{120.04pt } { } + p_0(a+c-1,b+c-1,0;k , l)].\nonumber\end{aligned}\ ] ] applying the recursion repeatedly , this becomes @xmath235\\[-8pt ] & & \qquad\quad\hspace*{14.05pt } { } - p_0(a+c , b+c-1,0;k , l ) \nonumber\\ & & \qquad\quad\hspace*{100.5pt}{}+ p_0(a+c-1,b+c-1,0;k , l)]\nonumber\\ & & \qquad\quad\hspace*{10.6pt}{}\times\sum_{m=0}^{c-1 } ( c-1-m).\nonumber\end{aligned}\ ] ] according to lemma [ lemma : firstkl ] , the first term @xmath236 vanishes . hence , since @xmath139 is given by ( [ leadingkl ] ) , the right - hand side of ( [ p1+f ] ) is fully known . with some rearrangement , we are left with ( [ firstorderkl ] ) . first , note that ( [ firstreckl ] ) implies @xmath237 now , substitute the asymptotic expansion ( [ expansionkl ] ) with @xmath238 into ( [ kl ] ) , eliminate leading - order terms by applying ( [ klc=0preliminary ] ) , and let @xmath148 . the result is made strictly recursive by invoking ( [ unwrap1kl ] ) , and we obtain @xmath239p_1(a , b,0;k , l ) \\ & & \qquad= a(a-1)p_1(a-1,b,0;k , l)\\ & & \qquad\quad { } + b(b-1)p_1(a , b-1,0;k , l ) \\ & & \qquad\quad{}+ \theta_aa p_1(a-1,b,0;k-1,l)\\ & & \qquad\quad { } + \theta_bb p_1(a , b-1,0;k , l-1)\end{aligned}\ ] ] with boundary conditions @xmath240 , for @xmath241 . it therefore follows ( e.g. , by induction ) that @xmath242 . [ appendixa ]

this elegant closed - form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite - alleles model of mutation . since its discovery in the early 1970s , the esf has been used in various biological applications , and has sparked several interesting mathematical generalizations . in the population genetics community , extending the underlying random - mating model to include recombination has received much attention in the past , but no general closed - form sampling formula is currently known even for the simplest extension , that is , a model with two loci . in this paper , we show that it is possible to obtain useful closed - form results in the case the population - scaled recombination rate is large but not necessarily infinite .

ewens sampling formula ( esf ) is a one - parameter family of probability distributions with a number of intriguing combinatorial connections . this elegant closed - form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite - alleles model of mutation . since its discovery in the early 1970s , the esf has been used in various biological applications , and has sparked several interesting mathematical generalizations . in the population genetics community , extending the underlying random - mating model to include recombination has received much attention in the past , but no general closed - form sampling formula is currently known even for the simplest extension , that is , a model with two loci . in this paper , we show that it is possible to obtain useful closed - form results in the case the population - scaled recombination rate is large but not necessarily infinite . specifically , we consider an asymptotic expansion of the two - locus sampling formula in inverse powers of and obtain closed - form expressions for the first few terms in the expansion . our asymptotic sampling formula applies to arbitrary sample sizes and configurations . and . .

1411.1319

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* background . * finding the node with the largest label in a labeled network is one of the fundamental problems in distributed computing . this is the way in which _ leader election _ is usually solved . ( in leader election , one node of a network has to become a _ leader _ and all other nodes have to become _ non - leaders _ ) . in fact , to the best of our knowledge , all existing leader election algorithms performed in labeled networks choose , as leader , the node with the largest label or the node with the smallest label @xcite . the classic problem of leader election first appeared in the study of local area token ring networks @xcite , where , at all times , exactly one node ( the owner of a circulating token ) has the right to initiate communication . when the token is accidentally lost , a leader is elected as the initial owner of the token . * model and problem description . * the network is modeled as an undirected connected graph with @xmath0 labeled nodes and with diameter @xmath3 at most @xmath2 . we denote by @xmath10 the diameter of graph @xmath11 . labels are drawn from the set of integers @xmath12 , where @xmath13 is polynomial in @xmath0 . each node has a distinct label . initially each node knows its label and its degree . the node with the largest label in a graph will be called its _ largest node_. we use the extensively studied @xmath14 communication model @xcite . in this model , communication proceeds in synchronous rounds and all nodes start simultaneously . in each round , each node can exchange arbitrary messages with all of its neighbours and perform arbitrary local computations . for any @xmath15 and any node @xmath16 , we use @xmath17 to denote the knowledge acquired by @xmath16 within @xmath18 rounds . thus , @xmath17 consists of the subgraph induced by all nodes at distance at most @xmath18 from @xmath16 , except for the edges joining nodes at distance exactly @xmath18 from @xmath16 , and of degrees ( in the entire graph ) of all nodes at distance exactly @xmath18 from @xmath16 . hence , if no additional knowledge is provided _ a priori _ to the nodes , the decisions of @xmath16 in round @xmath18 in any deterministic algorithm are a function of @xmath17 . we denote by @xmath19 the set of labels of nodes in the subgraph induced by all nodes at distance at most @xmath18 from @xmath16 . the _ time _ of a task is the minimum number of rounds sufficient to complete it by all nodes . it is well known that the synchronous process of the @xmath14 model can be simulated in an asynchronous network . this can be achieved by defining for each node separately its asynchronous round @xmath20 ; in this round , a node performs local computations , then sends messages stamped @xmath20 to all neighbours , and waits until it gets messages stamped @xmath20 from all neighbours . to make this work , every node is required to send at least one ( possibly empty ) message with each stamp , until termination . all of our results can be translated for asynchronous networks by replacing `` time of completing a task '' by `` the maximum number of asynchronous rounds to complete it , taken over all nodes '' . we consider two distinct tasks in which the largest node is found deterministically . in _ selection _ , this node has to output 1 and all other nodes have to output 0 . in _ election _ , all nodes must output the largest label . note that in election all nodes perform selection and additionally learn the identity of the largest node . both variations are useful in different applications . in the aforementioned application of recovering a lost token , selection is enough , as the chosen node will be the only one to get a single token and then the token will be passed from node to node . in this case , other nodes do not need to know the identity of the chosen leader . the situation is different if all nodes must agree on a label of one of the nodes , e.g. , to use it later as a common parameter for further computations . then the full strength of election is needed . likewise , learning the largest label by all nodes is important when labels carry some additional information apart from the identities of nodes , e.g. , some values obtained by sensors located in nodes . our results also remain valid in such situations , as long as the `` informative label '' can be represented as an integer polynomial in @xmath0 . our aim is to compare the difficulty of the two seemingly similar tasks of selection and election executed under stringent running time constraints . the measure of difficulty is the amount of information that nodes of the network must initially possess in order to solve the given task in an imposed amount of time . following the standard framework of _ algorithms with advice _ , see , e.g. , @xcite , this information ( a single binary string ) is provided to all nodes at the start by an oracle knowing the entire graph . the length of this string is called the _ size of advice_. the paradigm of algorithms with advice has a far - reaching importance in the realm of network algorithms . establishing a tight bound on the minimum size of advice sufficient to accomplish a given task permits to rule out entire classes of algorithms and thus focus only on possible candidates . for example , if we prove that @xmath4 bits of advice are needed to perform a certain task in @xmath0-node graphs , this rules out all potential algorithms that can work using only some linear upper bound on the size of the network , as such an upper bound could be given to the nodes using @xmath21 bits by providing them with @xmath22 . lower bounds on the size of advice give us impossibility results based strictly on the _ amount _ of initial knowledge outlined in a model s description . this more general approach should be contrasted with traditional results that focus on specific _ kinds _ of information available to nodes , such as the size , diameter , or maximum node degree . * our results . * consider the class of @xmath0-node graphs with any diameter @xmath1 , for some integer @xmath2 . first observe that if time is larger than @xmath3 , then both tasks can be solved without advice , as nodes learn the entire network and _ learn that they have learned it_. thus they can just choose the maximum of all labels seen . for the task of _ election _ , we show that if time is smaller than @xmath3 , then the optimal size of advice is @xmath4 , and if time is exactly @xmath3 , then the optimal size of advice is @xmath5 . here our contribution consists in proving two lower bounds on the size of advice . we prove one lower bound by exhibiting , for any positive integers @xmath23 , networks of size @xmath24 and diameter @xmath25 , for which @xmath26 bits of advice are needed for election in time below @xmath3 . to prove the other lower bound , we present , for any positive integer @xmath2 , networks of diameter @xmath1 for which @xmath27 bits of advice are needed for election in time exactly @xmath3 . these lower bounds are clearly tight , as even for time 0 , @xmath28 bits of advice are enough to provide the largest label in the network , and , for time @xmath3 when nodes know the entire network , but they _ do not know that they know it _ @xmath29 bits of advice are enough to give the diameter @xmath3 to all nodes and thus reassure them that they have seen everything . in this case , they can safely choose the maximum of all labels seen . hence , a high - level statement of our results for election is the following . if time is too small for all nodes to see everything , then no more efficient help in election is possible than just giving the largest label . if time is sufficient for all nodes to see everything , but too small for them to realize that they do , i.e. , the time is exactly @xmath3 , then no more efficient help in election is possible than providing @xmath3 , which supplies nodes with the missing certainty that they have seen everything . it should be noted that @xmath0 could be exponential in @xmath2 , as in hypercubes , or @xmath2 can even be constant with respect to arbitrarily large @xmath0 . thus , our results for election show that , for some networks , there is an exponential ( or even larger ) gap of difficulty of election ( measured by the size of advice ) between time smaller than @xmath3 and time exactly @xmath3 . another such huge gap is between time @xmath3 , when advice of size @xmath5 is optimal , and time larger than @xmath3 , when 0 advice is enough . these gaps could be called _ intra - task _ jumps in difficulty for election with respect to time . for the task of _ selection _ , the situation changes dramatically , even within the class of rings . indeed , for the class of rings , we show that , if time is @xmath6 , for any @xmath7 , then the optimal size of advice is @xmath5 , and , if time is @xmath8 ( and at most @xmath3 ) then this optimal size is @xmath9 . here our contribution is three - fold . for selection in time @xmath6 , for any @xmath7 , we exhibit , for any positive integer @xmath2 , a class of rings with diameter at most @xmath2 which requires advice of size @xmath27 . as before , this lower bound is tight , even for time 0 . further , for selection in time at most @xmath30 , for @xmath31 , we construct a class of rings with diameter @xmath1 which requires advice of size @xmath32 . at first glance , it might seem that this lower bound is too weak . indeed , providing either the diameter or the largest label , which are both natural choices of advice , would not give a tight upper bound , as this may require @xmath33 bits . however , we use a more sophisticated idea that permits us to construct a very compact advice ( of matching size @xmath34 ) and we design a selection algorithm , working for all rings of diameter @xmath1 in time at most @xmath30 , for which this advice is enough . thus there is an _ exponential _ increase of difficulty ( measured by the size of advice ) between selection in time @xmath6 , for any @xmath7 , and selection in time @xmath8 . as in the case of election , another huge increase of difficulty occurs between time @xmath3 and time larger than @xmath3 . these gaps could be called _ intra - task _ jumps of difficulty for selection with respect to time . as for the comparison between election and selection , our results show that , perhaps surprisingly , while for small time , the difficulty of these two tasks on rings is similar , for time @xmath8 the difficulty of election ( measured by the size of advice ) is exponentially larger than that of selection , even for the class of rings . while both in selection and in election the unique leader having the maximum label is chosen , these tasks differ in how widely this label is known . it follows from our results that , if linear time ( not larger than the diameter ) is available , then the increase of difficulty ( in terms of advice ) of making this knowledge widely known is exponential . this could be called the _ inter - task _ jump of difficulty between election and selection . figure [ summarytable ] provides a summary of our results . ] * related work . * the leader election problem was introduced in @xcite . this problem has been extensively studied in the scenario adopted in the present paper , i.e. , where all nodes have distinct labels . as far as we know , this task was always solved by finding either the node with the largest or that with the smallest label . leader election was first studied for rings . a synchronous algorithm based on label comparisons and using @xmath35 messages was given in @xcite . it was proved in @xcite that this complexity is optimal for comparison - based algorithms . on the other hand , the authors showed an algorithm using a linear number of messages but requiring very large running time . an asynchronous algorithm using @xmath35 messages was given , e.g. , in @xcite , and the optimality of this message complexity was shown in @xcite . deterministic leader election in radio networks has been studied , e.g. , in @xcite , as well as randomized leader election , e.g. , in @xcite . in @xcite , the leader election problem was approached in a model based on mobile agents for networks with labeled nodes . many authors @xcite studied leader election in anonymous networks . in particular , @xcite characterize message - passing networks in which leader election can be achieved when nodes are anonymous . characterizations of feasible instances for leader election were provided in @xcite . memory needed for leader election in unlabeled networks was studied in @xcite . providing nodes or agents with arbitrary kinds of information that can be used to perform network tasks more efficiently has previously been proposed in @xcite . this approach was referred to as _ algorithms with advice_. the advice is given either to nodes of the network or to mobile agents performing some network task . in the first case , instead of advice , the term _ informative labeling schemes _ is sometimes used , if ( unlike in our scenario ) different nodes can get different information . several authors studied the minimum size of advice required to solve network problems in an efficient way . in @xcite , given a distributed representation of a solution for a problem , the authors investigated the number of bits of communication needed to verify the legality of the represented solution . in @xcite , the authors compared the minimum size of advice required to solve two information dissemination problems using a linear number of messages . in @xcite , it was shown that advice of constant size given to the nodes enables the distributed construction of a minimum spanning tree in logarithmic time . in @xcite , the advice paradigm was used for online problems . in @xcite , the authors established lower bounds on the size of advice needed to beat time @xmath36 for 3-coloring cycles and to achieve time @xmath36 for 3-coloring unoriented trees . in the case of @xcite , the issue was not efficiency but feasibility : it was shown that @xmath37 is the minimum size of advice required to perform monotone connected graph clearing . in @xcite , the authors studied radio networks for which it is possible to perform centralized broadcasting in constant time . they proved that constant time is achievable with @xmath38 bits of advice in such networks , while @xmath39 bits are not enough . in @xcite , the authors studied the problem of topology recognition with advice given to nodes . to the best of our knowledge , the problems of leader election or maximum finding with advice have never been studied before .

finding the node with the largest label in a labeled network , modeled as an undirected connected graph , is one of the fundamental problems in distributed computing . this is the way in which _ leader election _ is usually solved . we consider two distinct tasks in which the largest - labeled node is found deterministically . in _ selection _ , this node has to output 1 and all other nodes have to output 0 . in _ our aim is to compare the difficulty of these two seemingly similar tasks executed under stringent running time constraints . the measure of difficulty is the amount of information that nodes of the network must initially possess , in order to solve the given task in an imposed amount of time . following the standard framework of _ algorithms with advice _ , this information ( a single binary string ) is provided to all nodes at the start by an oracle knowing the entire graph . the length of this string is called the _ size of advice_. the paradigm of algorithms with advice has a far - reaching importance in the realm of network algorithms . lower bounds on the size of advice give us impossibility results based strictly on the _ amount _ of initial knowledge outlined in a model s description . this more general approach should be contrasted with traditional results that focus on specific _ kinds _ of information available to nodes , such as the size , diameter , or maximum node degree . consider the class of-node graphs with any diameter , for some integer . if time is larger than , then both tasks can be solved without advice . for the task of _ election _ , we show that if time is smaller than , then the optimal size of advice is , and if time is exactly , then the optimal size of advice is . for the task of _ selection _ , the situation changes dramatically , even within the class of rings . indeed , for the class of rings , we show that , if time is , for any , then the optimal size of advice is , and , if time is ( and at most ) then this optimal size is . thus there is an _ exponential _ increase of difficulty ( measured by the size of advice ) between selection in time , for any , and selection in time . as for the comparison between election and selection , our results show that , perhaps surprisingly , while for small time , the difficulty of these two tasks on rings is similar , for time the difficulty of election ( measured by the size of advice ) is exponentially larger than that of selection . * keywords : * election , selection , maximum finding , advice , deterministic distributed algorithm , time . 0.18 in 0.0 in 0.2 in

finding the node with the largest label in a labeled network , modeled as an undirected connected graph , is one of the fundamental problems in distributed computing . this is the way in which _ leader election _ is usually solved . we consider two distinct tasks in which the largest - labeled node is found deterministically . in _ selection _ , this node has to output 1 and all other nodes have to output 0 . in _ election _ , the other nodes must additionally learn the largest label ( everybody has to know who is the elected leader ) . our aim is to compare the difficulty of these two seemingly similar tasks executed under stringent running time constraints . the measure of difficulty is the amount of information that nodes of the network must initially possess , in order to solve the given task in an imposed amount of time . following the standard framework of _ algorithms with advice _ , this information ( a single binary string ) is provided to all nodes at the start by an oracle knowing the entire graph . the length of this string is called the _ size of advice_. the paradigm of algorithms with advice has a far - reaching importance in the realm of network algorithms . lower bounds on the size of advice give us impossibility results based strictly on the _ amount _ of initial knowledge outlined in a model s description . this more general approach should be contrasted with traditional results that focus on specific _ kinds _ of information available to nodes , such as the size , diameter , or maximum node degree . consider the class of-node graphs with any diameter , for some integer . if time is larger than , then both tasks can be solved without advice . for the task of _ election _ , we show that if time is smaller than , then the optimal size of advice is , and if time is exactly , then the optimal size of advice is . for the task of _ selection _ , the situation changes dramatically , even within the class of rings . indeed , for the class of rings , we show that , if time is , for any , then the optimal size of advice is , and , if time is ( and at most ) then this optimal size is . thus there is an _ exponential _ increase of difficulty ( measured by the size of advice ) between selection in time , for any , and selection in time . as for the comparison between election and selection , our results show that , perhaps surprisingly , while for small time , the difficulty of these two tasks on rings is similar , for time the difficulty of election ( measured by the size of advice ) is exponentially larger than that of selection . * keywords : * election , selection , maximum finding , advice , deterministic distributed algorithm , time . 0.18 in 0.0 in 0.2 in

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eighteen years of doppler shift measurements of the primary star in the nearby binary system 55 cancri ( hd 75732 ; hereafter 55 cnc ) have gradually raised the number of orbiting planets from 1 ( butler et al . 1997 ) , to 3 ( marcy et al . 2002 ) , to 4 ( mcarthur et al . 2004 ) , and recently to 5 ( fischer et al . 2008 ) . although the 4 inner planets are closely packed together ( their semimajor axes @xmath2 au ) , the orbits of all 5 planets are remarkably circular ( see table 1 ) and presumably coplanar . the system exhibits astonishing regularity , reminiscent only of the planetary order in our solar system and unmatched by any other currently known multiple planet extrasolar system ( for reviews of orbital and dynamical characteristics of exoplanets , see marcy et al . [ 2005 ] and butler et al . [ 2006 ] ) . the most massive planet , 55 cnc d with @xmath3 au and a minimum mass ( mcarthur et al . 2004 ) , which increases all masses by 25% . ] of 3.835 jupiter masses ( table 1 ) , is the most distant gaseous giant known among exoplanets with well defined orbits and , like jupiter , it orbits beyond 5 au from the star . furthermore , there are no giant planets in the area roughly between 1 and 5 au , just like in our solar system . in fact , no planets have been found to date in the 5 au gap between the two outermost planets , f and d , with semimajor axes @xmath4 au and @xmath5 au , respectively . cccccc + + index & planet & orbital & semimajor & minimum & orbital + @xmath6 & designation & period & axis & mass & eccentricity + & & @xmath7 ( days ) & @xmath8 ( au ) & @xmath9 ( @xmath10)@xmath11 & @xmath12 + 1 & e & 2.817 & 0.038 & 0.034 & 0.070 + 2 & b & 14.65 & 0.115 & 0.824 & 0.014 + 3 & c & 44.34 & 0.240 & 0.169 & 0.086 + 4 & f & 260.0 & 0.781 & 0.144 & . . . @xmath13 + 5 & d & 5218 & 5.77 & 3.835 & 0.025 + + + + despite the similarities in orbital characteristics , the planetary system of 55 cnc exhibits some conspicuous differences when compared to our solar system ( fischer et al . [ 2008 ] and table 1 ) : ( a ) three of the planets orbit too close to the star ( within 0.24 au ) , that is closer than the orbit of mercury around the sun . ( b ) the second planet , 55 cnc b ( @xmath14 au ) , is also the second largest with a mass of @xmath15 jupiter masses . this planet also shows the lowest orbital eccentricity ( @xmath16 ) among all 5 planets . ( c ) the 4 inner planets are all quite massive , with the innermost planet , 55 cnc e ( @xmath17 au ) , having the smallest mass ( @xmath18 earth masses ) , a value roughly comparable to the mass of uranus . most , if not all , of these planets are expected to be gaseous giants in contrast to the terrestrial planets in our solar system . the central star of 55 cnc and the dynamics of its system have kept observers occupied for other reasons as well : 1 . this star is the primary in a visual binary ( separation @xmath1910@xmath20 au ) and belongs to a group of @xmath1930 multiple stellar systems in which giant planets are seen orbiting very close to the primary stars ( eggenberger et al . 2004 ; raghavan et al . in fact , the most massive inner planets tend to be found in multiple stellar systems and those with the shorter periods ( @xmath21 days ) tend to also have very low eccentricities . the three inner planets of 55 cnc , with orbital periods @xmath22 days and eccentricities @xmath23 , all fit precisely this trend . 2 . the primary star of 55 cnc has very high metallicity compared to the sun ( @xmath24 ; gonzalez & vanture 1998 ; valenti & fischer 2005 ) , a property that has been associated with a higher probability of forming massive protoplanetary cores and gaseous giant planets in the surrounding , also metal rich , disk by the process of core accretion ( ida & lin 2004b ; bodenheimer & pollack 1986 ; pollack et al . it seemed for a time that an extended disk of dust was visible in the infrared , but this result was negated when additional infrared observations failed to detect a disk ( schneider et al . 2001 ; bryden et al . 2006 ) and submillimeter observations indicated that the excess flux could be attributed to background sources ( jayawardhana et al . 4 . the orbits of the two more massive of the inner planets , 55 cnc b and c , appear to be close to but not quite in mean motion resonance with a period ratio of nearly 3:1 ( marcy et al . 2002 ; fischer et al . this is the only known 3:1 apparent resonant pair , whereas in all the other known cases the planets appear to have been captured in 2:1 resonances ( butler et al . 2006 ) . the picture that emerges from the observations of 55 cnc is enigmatic . the most important questions can be summarized as follows ( fischer et al . 2008 ) : why did this star end up with so many massive planets when 90% of the observed stars do not have any giants at all ? the similarities to our solar system seem to indicate that multiple planet systems like 55 cnc ( and @xmath25 ara ara ( hd 160691 , gj 691 ) also has a gaseous giant orbiting beyond 5 au ( @xmath26 au ) and 3 additional giants orbiting close to the star ( santos et al . 2004 ; pepe et al . 2007 ; and table 5 below ) . their distribution shows a large gap between 1.5 and 5.2 au ; but the orbital eccentricities of the inner planets are comparatively larger ( @xmath27 ) than those in 55 cnc ( see also [ muara ] ) . ] ) should be common , but why have they not been observed in larger numbers ? and if such multi planet systems around metal rich stars represent the new norm of planet evolution ( ida & lin 2004b ) , where are the systems with central stars chemically similar to our sun ? one would certainly be reluctant to admit that our solar system is special because of the inherent bias associated with such a proposition . in addition , were the inner planets of 55 cnc ( and @xmath25 ara ) formed `` in situ '' on the observed orbits ( lissauer 1995 ; bodenheimer et al . 2000 ) , or are they the result of inward migration ( ward & hahn 2000 ; lin et al . 2000 ; armitage et al . 2002 ; alibert et al . 2004 , 2005a , 2006 ) that terminated conveniently ( marcy et al . 2000 ; trilling et al . 2002 ; eggenberger et al . 2004 ) to allow for the planets to survive and circularize their orbits ? and why are all the planetary orbits in 55 cnc so nearly circular when large eccentricities are quite common in exoplanets ( marcy et al . 2000 , 2005 ) and it appears that resonant tidal interactions did not take hold since an actual 3:1 commensurability was not established ? finally , could there be smaller planets or an asteroid belt in the 5 au gap and , in any case , why was matter acquisition so disparate as to produce a series of smaller planets surrounded by two very massive planets , 55 cnc b and d ? finding answers to even some of these questions can be a giant step toward understanding planet formation and evolution . we will revisit the underlying issues in [ questions ] below . the observations of 55 cnc have motivated several empirical modeling efforts that attempted to explore the various compelling issues that arise from the impressive regularity of this planetary system , the existence of the 5 au gap , and the unusual chemical properties of the parent star : 1 . _ metal rich environment for planet formation_. ida & lin ( 2004a , b , 2005 ) carried out monte carlo simulations of protoplanetary core growth , orbital migration , and gas acquisition . their model predicts that the probability of forming gas giants increases rapidly with increasing metal abundances in the host stars and the surrounding disks , which is consistent with the multitude of planets observed in 55 cnc and @xmath25 ara . on the other hand , the physical and orbital properties of these planets are in disagreement with the main features of this model , namely that there should not be planets with @xmath28 earth masses at @xmath29 au and that short period , neptune size planets should not be common around such g - type stars as opposed to m dwarfs . this led ida & lin ( 2005 ) to speculate that the planets seen in 55 cnc and @xmath25 ara have not migrated to their present locations but they were instead formed in situ with the help of sweeping mean motion or secular resonances . however , there is no evidence that gas - giant migration or resonances ever played a role in the formation of these planets , and this adds to the mystery surrounding such well ordered planetary systems . 2 . _ long term orbital stability_. the stability of the planetary orbits in 55 cnc has been investigated independently by several groups : raymond & barnes ( 2005 ) integrated the orbits of the 3 most massive planets ( b d ) for 100 myr and found that the system could afford to have more planets in stable orbits between planets c and d. fischer et al . ( 2008 ) integrated the orbits of all 5 planets for 1 myr and found that planets b and c are not locked into a 3:1 mean motion resonance . gayon et al . ( 2008 ) integrated the orbits of all 5 planets for 400 myr and showed that the system represents a case of stable chaos in which , however , close encounters between planets are avoided . all of these models indicate clearly that the system is dynamically stable over long time scales ( @xmath30 0.1 gyr ) . 3 . _ apparent 3:1 mean motion resonance_. the apparent 3:1 mean motion resonance between the orbits of planets b and c in 55 cnc was initially hailed as a new example of a low order commensurability in a `` resonant system '' ( barnes & quinn 2004 ) , with 2:1 resonances providing the only previous example in observed systems . although barnes & quinn ( 2004 ) did not study 55 cnc explicitly , their models showed that planets in resonant systems have very narrow zones of stability and raised the possibility that such systems are only marginally stable . modeling of 55 cnc was undertaken by zhou et al . ( 2008 ) who showed that planets b and c can be captured in a 3:1 resonance if they start with modest eccentricities ( @xmath31 ) and migrate slowly ( for @xmath190.1 myr ) . the above models would indicate that the arrangement of the inner planets in 55 cnc is the result of special circumstances , an uncomfortable notion . since we now know that planets b and c are not in resonance ( fischer et al . 2008 ; gayon et al . 2008 ) , a more palatable conjecture is that no special migration has ever occurred in 55 cnc and that its inner planets form a typical `` interacting system '' ( barnes & quinn 2004 ) in which the planets are able to perturb one another and have broad zones of stability available to them . modeling efforts and related conjectures concerning the apparent 3:1 resonance in 55 cnc demonstrate how difficult it is to simulate such complex systems because we do not have a handle on the initial conditions ; numerical models that start from arbitrary but convenient initial conditions are capable of producing `` easily '' just about all of the observed results . so it is not surprising that more recent modeling efforts ( although they did not address 55 cnc directly ) now seem to provide evidence against 3:1 resonant captures of planets in general : pierens & nelson ( 2008 ) found that massive planets captured by a dominant , jupiter size planet tend to end up exclusively in 2:1 or 3:2 mean motion resonances , depending on their mass . furthermore , adams et al . ( 2008 ) and lecoanet et al . ( 2008 ) found that turbulence in the host protoplanetary disk can upset mean motion resonances and thus resonant systems should be rarely observed . _ packed planetary systems hypothesis_. the orbital stability calculations of barnes & quinn ( 2004 ) and related simulations by barnes & raymond ( 2004 ) used massless test particles in models of several known extrasolar multiplanetary systems in order to identify broad regions full of dynamically stable orbits and to predict the possible existence of additional , yet unseen planets . these calculations were extended by raymond & barnes ( 2005 ) , raymond et al . ( 2006 ) , and barnes et al . ( 2008 ) to include various saturn mass and terrestrial mass particles in between the orbits of the known planets in each simulated system . although it was easy to find stable orbits for additional planets with terrestrial or smaller masses in some of these systems , the main result of these numerical experiments came as a surprise : many systems are on the edge of stability and small changes to the values of @xmath32 or @xmath33 push them to become unstable . following the ideas of laskar ( 1996 ) , barnes & raymond ( 2004 ) conjectured that the remaining apparently stable systems are also packed with enough planets to be marginally stable . this is the packed planetary systems ( pps ) hypothesis and it predicts that stable systems may contain unseen planets that bring them to the edge of stability . the pps models successfully predicted the existence of hd 74156 d ( barnes et al . 2008 ) before its discovery ( bean et al . 2008 ) and proved to be consistent with the presence of 55 cnc f that was found ( fischer et al . 2008 ) orbiting at the inner edge of the predicted stable zone ( @xmath34 au @xmath35 3.2 au , @xmath36 ; barnes & raymond 2004 ) . the stable zone in 55 cnc is too wide , as a result the 5planet system is still not packed and there could be more undetected planets between the planets f and d ( raymond et al . 2008 ) . specifically , the pps models suggest the following interesting possibilities : ( a ) a giant planet with up to saturn mass may exist near 2 au ( the center of the stable zone ) with @xmath37 ( raymond & barnes 2005 ) . ( b ) alternatively , several terrestrial planets with up to 0.63 earth masses may exist at 1.13.6 au with @xmath38 ( raymond et al . although the possibility of having earth like planets in the `` habitable zone '' around 1 au is intriguing , our own interest in this work is focused entirely on the possibility of having a gas giant orbiting at @xmath192 au for the reasons that we explain in [ newmodel ] below . the current observations of 55 cnc do not rule out such a planet : at a distance of @xmath192 au , a giant planet could avoid detection if its minimum mass is smaller than 100 earth masses ( fischer et al . 2008 ) , i.e. , approximately equal to or less than the mass of saturn . 5 . _ empirical titius bode relation_. poveda & lara ( 2008 ) presented an exponential fit of the semimajor axes of the 5 known planets in 55 cnc . this empirical relation is akin to the titius bode ( tb ) rule for the solar system , but it works only if there exists a hypothetical sixth planet at @xmath39 au . based on this result , poveda & lara ( 2008 ) proposed that an unseen planet with @xmath40 au should be present in 55 cnc . there is no physical basis for this prediction , yet it is quite interesting that the empirical tb relation of 55 cnc is in complete agreement with the prediction of the pps model for a gas giant at the same orbital distance . since the pps model and the tb relation converge to the same prediction , they can both be tested by additional doppler shift measurements of the primary star of 55 cnc . by extending their baseline , future observations should be able to search for an additional periodicity in the 5 au gap of 55 cnc and , irrespective of the outcome , the result can be pivotal for planet formation theories ( see also [ newmodel].5 ) . 6 . _ the protoplanetary disk of 55 cnc_. fischer et al . ( 2008 ) made an attempt to estimate some key parameters of the minimum mass protoplanetary disk of 55 cnc . using a typical surface density profile for the disk that varied with distance @xmath0 as @xmath1 and an estimate of the core masses of the 5 observed planets that took into account the excessive metallicity of the system , they found a total mass of 0.031 @xmath41 out to 6 au and a surface density for the dust of @xmath42 at 5 au . the dust - to - gas mass ratio was set to the nominal value of 1% and the mass estimate also took into account the intermediate inclination of the orbital plane of the system ( @xmath43 , as derived by mcarthur et al . [ 2004 ] for 55 cnc d ) . the assumed @xmath44 profile was first established for the minimum mass solar nebula ( mmsn ) by weidenschilling ( 1977 ) and hayashi ( 1981 ) and it has been commonly used ever since in calculations of this type . recently , this profile was investigated again in our solar system ( davis 2005 ) , in extrasolar systems ( kuchner 2004 ) , and in dusty circumstellar disks around t tauri stars ( kitamura et al . 2002 ; andrews & williams 2007 ) . due to large systematic uncertainties , none of these investigations has been able to directly confirm or reject the original @xmath44 relation , although all of them provide useful hints about possible improvements of the `` typical '' surface density profile of the solar nebula and extrasolar protoplanetary disks . for what follows , it is interesting to note that the the model of davis ( 2005 ) indicates that the original power law @xmath45 with @xmath46 tends to overestimate the surface density within the central 1 au of the solar nebula . also , kuchner ( 2004 ) finds a steeper profile with @xmath47 for the surface density of the typical minimum mass `` extrasolar nebula '' ( mmen ) constructed by weidenschilling s ( 1977 ) method from 26 exoplanets found in multi planet systems . the @xmath47 power law index results , again , in an overestimate of the surface density within the central 1 au of the mmen . the lack of a central core region , such as that suggested for the mmsn ( lissauer 1987 ; davis 2005 ) and for circumstellar disks ( garaud & lin 2007 ) , is the obvious reason for the excessive central densities in models that adopt a single power law density profile for the entire protoplanetary disk . we are interested in 55 cnc because this is the only extrasolar system with so many planets in well ordered , long lived , circular orbits . we believe that the high degree of regularity seen in this system makes it an ideal laboratory for exploring the above discussed issues and for testing the leading current hypotheses and models about planet formation in protostellar disks . our work starts with a new physical model that we formulated rigorously based on exact solutions of the isothermal lane emden equation with rotation and that relates the observed planets in a well ordered , multi planet system to key physical properties of the protoplanetary disk that hosted their formation . first we applied this model successfully to the 11 largest planets of our solar system ( christodoulou & kazanas 2008 , hereafter ck ) and we proceed here to apply it to the 5 known planets of 55 cnc . the results obtained from our modeling are tied to the theoretical models of [ th ] in the following ways : 1 . our model uses all the planets in regular orbits irrespective of size , mass , and metal abundances . as such , it works equally well for solar type systems like our solar system and for systems with different metallicities or with gas giants in short period orbits like 55 cnc . we do expect however that the modeling results will have to be interpreted consistently with the physical and the chemical properties of the detected planets and their parent stars . it is important that the planetary orbits of 55 cnc were found to be dynamically stable over long time scales because our model associates such long lived orbits with local minima of the gravitational potential well in the midplane of the original protoplanetary disk . this association does not hold for many odd systems in which one or two planets have migrated inward and are now seen very close to their parent stars . however , the regular spacing of the planets and the stability of 55 cnc argue against migration as a process that dominated its evolution . it is now clear that 55 cnc b and c are not caught in a 3:1 mean motion resonance . this result also suggests that no significant migration has taken place in the disk of 55 cnc and it supports our picture of a well - ordered system in which the planets formed in situ by core accretion . in turn , such regular planetary orbits readily provide information about the locations of density enhancements ( the local potential minima ) in the disk during the planet formation stage . the pps models predict that there must exist at least one more planet in the 5 au gap of 55 cnc and they will be tested by future observations for the first time in such a well ordered , multi planet , extrasolar system . our model is also not impervious to the possible existence of an additional planet , but it does not necessarily need a 6@xmath48 planet in order to work . as it predicts entirely different physical characteristics for the disk of 55 cnc depending on whether 5 or 6 planets are used ( see [ properties ] ) , our model too needs an observational resolution of this dilemma . 5 . based on the work of ck , we now understand that the tb relation can be accommodated within our approach , but the rule has no inherent physical significance for our solar system or for 55 cnc . since the tb relation of 55 cnc necessarily predicts a 6@xmath48 planet at @xmath40 au , the absence of such a planet from the 5 au gap will settle this issue without a doubt . such an observational result will however be detrimental to the pps hypothesis as well . alternatively , if an additional planet is found in the 5 au gap , then the doubts will persist , the pps hypothesis will persevere , and our model ( and presumably models such as those of weidenschilling [ 1977 ] and davis [ 2005 ] ) will then show a clear preference for a different radial density profile of the protoplanetary disk of 55 cnc ( see [ properties ] for details ) . the attempt of fischer et al . ( 2008 ) to estimate some of the properties of the minimum mass protoplanetary nebula ( mmpn ) of 55 cnc is noteworthy by insufficient . the main drawback of these estimates is that the authors assumed a @xmath49 profile for the disk without actually using weidenschilling s ( 1977 ) method or any of the competing methods cited in [ th].6 above . consequently , the particular density profile produced by our disk model of 55 cnc can not be compared to this previous work . some of the parameter values obtained by fischer et al . ( 2008 ) and by kuchner ( 2004 ) , who did use weidenschilling s method , can however be compared to the results of our modeling , and we do so in [ surface ] below . in [ model ] , we describe in detail the new physical model of the midplane of the protoplanetary disk of 55 cnc and we derive the fundamental dynamical parameters of this disk ( minimum mass , density profile , specific angular momentum , rotation frequency , and equation of state ) . we also examine the dynamical stability of the model and we describe the effects that a possible 6@xmath48 planet will have if it is discovered orbiting at @xmath40 au , as expected by the pps and tb models of the system ( [ th ] ) . in [ discussion ] , we interpret the results from our model and we discuss the issues and the questions mentioned above that pertain to the impressive regular structure of this planetary system and its intriguing 5 au gap . we also report briefly on our modeling effort of the related multi planet system @xmath25 ara .

five planets are presently believed to orbit the primary star of 55 cnc , but there exists a large 5 au gap in their distribution between the two outermost planets . this gap has attracted considerable interest because it may contain one or more lower mass planets whose existence is not contradicted by long - term orbit stability analyses , in fact it is expected according to the `` packed planetary systems '' hypothesis and an empirical titius bode relation recently proposed for 55 cnc . furthermore , the second largest planet is just the second farthest and it orbits very close to the star . its orbit , the most circular of all , appears to be nearly but not quite commensurable with the orbit of the third planet , casting doubt that any migration or resonant capture of the inner planets has ever occurred and lending support to the idea of `` in situ '' giant planet formation by the process of core accretion . all of the above ideas will be tested in the coming years in this natural laboratory as more observations will become available . the disk of 55 cnc was smaller , heavier , and less rotationally supported than the solar nebula , so this system represents a different mode of multi planet formation compared to our own solar system .

five planets are presently believed to orbit the primary star of 55 cnc , but there exists a large 5 au gap in their distribution between the two outermost planets . this gap has attracted considerable interest because it may contain one or more lower mass planets whose existence is not contradicted by long - term orbit stability analyses , in fact it is expected according to the `` packed planetary systems '' hypothesis and an empirical titius bode relation recently proposed for 55 cnc . furthermore , the second largest planet is just the second farthest and it orbits very close to the star . its orbit , the most circular of all , appears to be nearly but not quite commensurable with the orbit of the third planet , casting doubt that any migration or resonant capture of the inner planets has ever occurred and lending support to the idea of `` in situ '' giant planet formation by the process of core accretion . all of the above ideas will be tested in the coming years in this natural laboratory as more observations will become available . this opportunity presents itself in conjunction with a physical model that relates the orbits of the observed planets to the structure of the original protoplanetary disk that harbored their formation at the early stages of protostellar collapse . using only the 5 observed planets of 55 cnc , this model predicts that the surface density profile of its protoplanetary disk varied with distance precisely as , as was also found for the minimum mass solar nebula . despite this similarity , the disk of 55 cnc was smaller , heavier , and less rotationally supported than the solar nebula , so this system represents a different mode of multi planet formation compared to our own solar system .

0811.0868

i

in [ intro ] , we placed in proper context all the available information about the multi planetary system of 55 cnc . our knowledge of this system comes from 18 years of doppler shift observations of the central star ( fischer et al . 2008 ; mcarthur et al . 2004 ; marcy et al . 2002 ; butler et al . 1997 ) and from theoretical modeling of the inferred planetary orbits ( fischer et al . 2008 ; raymond et al . 2008 ; poveda & lara 2008 ; gayon et al . 2008 ; zhou et al . 2008 ; raymond & barnes 2005 ; ida & lin 2005 ; kuchner 2004 ) . the metal rich primary star of 55 cnc has 5 massive planets in remarkably circular orbits and , outside of our sun , this is the only star with so many planets in well ordered , perfectly stable , nonresonant orbits ( table 1 ) . the system does however exhibit a large 5 au gap between its two outermost planets and this vast empty region has sparked speculation that one or more additional planets may still remain undetected between planets f ( @xmath4 au ) and d ( @xmath5 au ) . our contribution to the investigation of 55 cnc is a new physical model of the midplane of the protoplanetary disk in which the planets were formed . this model was introduced in [ newmodel ] and it was described in detail in [ model ] . it is based on exact solutions of the isothermal lane emden equation with rotation ( eq . [ [ main1 ] ] ) subject to the appropriate central boundary conditions ( eq . [ [ bc ] ] ) . these solutions describe radial density profiles that are oscillatory by nature , despite the fact that the corresponding rotation profiles are strictly monotonic and well - behaved . the oscillations occur about an average ( baseline ) density ( eq . [ [ den ] ] ) that is a combination of two power laws , a flat uniform core and a decreasing outer section ( [ baseline ] ) . such baseline density profiles are also exact intrinsic solutions of the lane - emden equation but they are incapable of satisfying the central boundary conditions ( see ck for more details and for an application of the model to our solar system ) . the baselines do however obey the same rotation law ( eq . [ [ den31 ] ] ) as the corresponding oscillatory solutions . some typical baselines and their rotation profiles are shown in fig . [ fig1 ] , while a typical oscillatory solution and its baseline are shown in fig . [ fig2 ] . the oscillatory density profile shown in fig . [ fig2 ] represents the best fit model for the midplane of the protoplanetary disk of 55 cnc . the fit was obtained by nonlinear unconstrained optimization that matches the orbital semimajor axes of the observed planets to consecutive density maxima ( or gravitational potential minima ) of the oscillatory profile ( see [ exact ] and table 2 ) and that uses the semimajor axis of the third planet from the star to set the physical scale of the model . the dynamical parameters of the best fit model are listed in eq . ( [ neb ] ) and its physical properties are summarized in [ properties][surface ] and in table 3 . the midplane of the disk of 55 cnc was composed of a very small ( @xmath190.05 au ) and very dense ( @xmath1910@xmath177 ) uniform core in slow rotation ( period @xmath191 yr ) , followed by a power law gradient such that the surface density varied with distance as @xmath178 ( eq . [ [ sigma ] ] ) out to @xmath196 au . this configuration is stable to both axisymmetric and nonaxisymmetric perturbations ( [ stability ] ) . the @xmath178 dependence of the surface density profile of 55 cnc is effectively identical to that found by ck for the solar nebula . despite this resemblance , the detailed comparison between the two nebular disks shown in table 3 indicates that the two models are generally dissimilar , and the differences seen in table 3 are also reflected in the differing characteristics of the planetary systems that were created around these two stars . specifically , the inner disk of 55 cnc was denser and heavier , and this explains why 4 massive planets were formed within the inner 0.8 au . these high densities are also responsible for the large growth of the second planet from the star , 55 cnc b , which is the most massive of the inner 4 planets . this planet was free to grow in a high density environment , while the area around the orbit of the first planet could have been depleted by the protostar ( just as mercury s growth was severely limited by the protosun ) . on the other hand , the same disk showed much smaller densities beyond 2 au , and this explains why only one massive planet managed to form at the bottom of the single , very wide potential well outside of 5 au . ccc + physical & large light disks & small heavy disks + property & ( solar system ) @xmath179 & ( 55 cancri a ) @xmath180 + & & + disk & & + & & + metallicity ( @xmath181 ) & @xmath182 & @xmath183 + radial scale ( @xmath103 ) & 0.02 au & 0.001 au + radial size & 4070 au & 610 au + core size ( @xmath151 ) & 1 au & 0.05 au + core density ( @xmath131 ) & @xmath184 & @xmath185 + & & + rotation & & + & & + @xmath97 & 0.4 & 0.1 + rotation period ( @xmath139 ) & 12 yr & 1 yr + jeans period ( @xmath186 ) & 5 yr & 0.1 yr + & & + gas surface density & & + & & + @xmath153 & 2500 & 75000 + @xmath187 & 2000 & 1000 + @xmath188 & 200 & 100 + @xmath189 , @xmath190 & @xmath165 & @xmath165 + + + + + the planetary system of 55 cnc and the solar system are both remarkably well ordered despite the differences in structure and dynamical characteristics and the differences between their host stars . this comparison seems to indicate that there exist two modes of planet formation that lead to stable , well organized , multi planet systems . based on our modeling and on the results of ck , we can describe these two extremes of multiple planet formation in the isothermal regime of protostellar collapse as follows ( see also table 4 ) : 1 . _ large light disks._solar type protoplanetary disks with @xmath191 au cores and moderate rotational support ( no more than @xmath1940%50% of maximum rotation ) that have core densities a few times above those required to form planets ( @xmath1910@xmath191 ; lissauer 1993 ) are capable of forming rocky planets in the first 2 au and , due to the comparatively high densities in their outer regions , several gas giants beyond 5 au as well . such disks can extend for at least 4070 au in the radial direction . because their core densities are barely supercritical , these disks can form only terrestrial planets in the vicinity of the core radius . 2 . _ small heavy disks._metal rich protoplanetary disks with @xmath190.05 au cores and little rotational support ( no more than @xmath1910%15% of maximum rotation ) that have core densities @xmath191000 times above the critical value are capable of forming giant planets in the first 2 au and , due to the substantial density drop in their outer regions , only one gas giant beyond 5 au . such disks can not extend for more than 610 au ( and if they do , their densities are too low to form giant planets ) . because their core densities are strongly supercritical , these disks can easily form gas giants around 1 au , so terrestrial planets are not expected to be present in the habitable zone in this mode . returning now to the questions posed in [ obs ] , we can outline some feasible answers suggested by the above results : most of the observed stars ( @xmath1990% ) do not show any giant planets at all . some of them , especially those of solar type , may have planetary systems formed in large light disks ( llds ) , in which case their planets are not observable yet with the current resolution because the inner planets have very low masses and the outer planets are too distant from their stars . this is probably the reason why the solar system is currently the only example of a system formed in an lld . on the other hand , the inner giant planets formed in small heavy disks ( shds ) can be presently detected . besides the standard example of 55 cnc , all other planets found within 23 au from their stars in nearly circular orbits are good candidates for the shd mode . this also includes @xmath25 ara , hd 37124 , and the massive , short period ( @xmath21 days ) planets with low eccentricities found in multiple stellar systems ( see [ obs ] ) . on the question of in situ formation versus migration , the slow rotation found in our models ( table 4 ) and the structure of the disks that show several local potential minima strongly support the in situ formation of planets by planitesimal aggregation and gas accretion inside these potential wells . this does not mean that planetary migration can not occur at all , it just indicates that the multiple planets of well ordered systems do not migrate . migration may still be the dominant mechanism in systems with planets in highly eccentric and/or irregularly spaced orbits . but even in such cases , our modeling adds a new dimension to the migration problem that has not been previously explored : the ability of a planet to migrate can no longer be determined solely by the disk torques that redistribute the angular momentum of a planetary orbit . that was done in the past ( e.g. , lin et al . [ 2000 ] , ward & hahn [ 2000 ] , and references therein ) while the density profile of the underlying disk was assumed to be monotonically decreasing without any localized potential wells . in the present setting in which the planets are trapped inside gravitational potential minima , the energy content of each planet needs to be considered as well . a planet orbiting inside a local gravitational potential well can migrate only if the interaction with the disk provides enough energy for it to leap out of its well otherwise the torqing of the planetary orbit will simply lead to stable oscillations and the development of some eccentricity insde this potential minimum . on the question of the existence of additional planets in 55 cnc , our model boldly predicts that no other planet will be found in the future . in particular , we do not believe that there is room in the 5 au gap even for a small rocky terrestrial planet or an asteroid belt because the potential minima of planets f and d reach into the gap ( see fig . [ fig2 ] ) , and all debris must have been swept by these two massive planets . this prediction is in contrast to the predictions of the pps models ( raymond et al . 2008 ) and the tb conjecture ( poveda & lara 2008 ) for the system , and the disagreement can be resolved by future observations of 55 cnc ( see also [ properties ] above ) . the question of the impressive growth of inner planet 55 cnc b ( @xmath14 au , mass @xmath192 jupiter masses ) was discussed briefly in [ modes ] above . the density of the peak where this planet was formed ( table 2 ) is quite high ( @xmath193 ) . only planet e was formed in a higher density environment in the shd of 55 cnc , but this planet resides deep inside the core of the nebula and its gaseous envelope could have easily been ablated by the protostar at a later time . the situation is similar in the inner solar system , although venus is slightly less massive than the earth . the emerging paradigm , valid for both llds and shds , is that of a depleted innermost planet followed by planets that are free to grow as much as the local conditions in the disk would allow . this picture appears to be borne out also in another shd candidate , @xmath25 ara , but with some caveats that we discuss below . recent observations ( pepe et al . [ 2007 ] and table 5 ) of the metal rich star @xmath25 ara ( @xmath24 ; santos et al . 2004 ) indicate 4 orbiting planets in a configuration very similar to that of 55 cnc : a single massive outer planet , @xmath25 ara e , is separated from the 3 inner planets ( c , d , and b ) by a large empty region between 1.5 and 5.2 au . the minimum mass of the innermost planet is comparable to that of the innermost planet in 55 cnc , so this planet is also a low mass ( depleted ) giant while its two neighbors have minimum masses comparable to the mass of jupiter . cccccc + + index & planet & orbital & semimajor & minimum & orbital + @xmath6 & designation & period & axis & mass & eccentricity + & & @xmath7 ( days ) & @xmath8 ( au ) & @xmath9 ( @xmath10)@xmath11 & @xmath12 + 1 & c & 9.6386 & 0.091 & 0.03321 & 0.172 + 2 & d & 310.55 & 0.921 & 0.5219 & 0.0666 + 3 & b & 643.25 & 1.497 & 1.676 & 0.128 + 4 & e & 4205.8 & 5.235 & 1.814 & 0.0985 + + + although the eccentricities of its planetary orbits are larger than those of 55 cnc ( see tables 1 and 5 ) , @xmath25 ara appears to be a good example of an shd system . the size of the system is also comparable to that of 55 cnc ( @xmath196 au ) , so we expected our best fit model to produce parameter values similar to those of 55 cnc . we also thought that , by analogy , a pps model of the system would find a stable zone in the 3.7 au gap between planets b and e , and a tb model would predict a planet in the same gap . such models are not yet available , but the tb relation of poveda & lara ( 2008 ) can be easily applied to the observed semimajor axes . it turns out that the tb models are not particularly good fits to the data with or without a hypothetical 5@xmath116 planet in the 3.7 au gap . the planetary orbits of @xmath25 ara shown in table 5 can not be matched to the density maxima in any of our models . the reason for this failure is that planet d is too close to planet b , and this leaves an inconspicuous 0.8 au gap in the distribution between planets c and d. a hypothetical planet is needed in this gap to restore the regular spacing of the inner planets . this , of course , does not mean that an undetected planet necessarily exists in the 0.8 au gap , it just implies that a density maximum is needed in that area of the model for the distribution to be typical of a well organized shd system . by the same token , some models allow for yet another density maximum interior to the orbit of planet c , at @xmath190.05 au . such experimental models are characterized by different parameter sets , so a `` best fit model '' can not be determined , unless additional planets are discovered in @xmath25 ara by future observations . a surface density profile of the form @xmath194 is applicable outside the central core region of the protoplanetary disk of 55 cnc and the solar nebula ( table 4 ) . the presence of a roughly uniform core is strongly suggested by both theory and observations ( see [ th].6 ) , and our models suggest that llds and shds can be distinguished by their core sizes ( @xmath191 au and @xmath190.05 au , respectively ) . on the other hand , we do not know why both of the nebular disks in table 3 show the @xmath178 trend , although this fact that we independently obtained the same result ( as opposed to two different power laws ) from two different planetary systems argues in favor of our modeling assumptions . at this point , we do not have any more evidence of the ubiquity of the @xmath178 profile among llds and shds , but we can certainly argue that this density power law is more relevant to planet formation than the profiles from steady state viscous and irradiated accretion disks ( kitamura et al . [ 2002 ] , andrews & williams [ 2007 ] , garaud & lin [ 2007 ] , and references therein ) . the isothermal phase of protostellar collapse that our models address is an extended intermediate phase of the whole process during which the magnetic fields have diffused away , the central core mass is a minute fraction of the solar mass , matter continues being deposited onto the disk from above and below , most of the gas in the disk is molecular , and all the energy produced is efficiently radiated away ( see tohline [ 2002 ] for a recent review ) . at this stage , the evolution of the gas is not driven by viscosity or by ionization because the gas is transparent to radiation ; the gas responds fully to the effects of self gravity and ( non keplerian ) rotation , and this is why it is very encouraging to know that our modeled disks are dynamically stable ( [ stability ] ) . theoretical calculations of viscous , magnetized , or irradiated accretion disks are not applicable in this regime of protostellar collapse , while observations of thermal radiation from t tauri stars probe the disks long after the isothermal phase is over , the gas has become opaque to its own radiation , and the grown protostars have imposed nearly keplerian rotation profiles onto the disks . therefore , there is no reason to expect that the surface density profiles should have power law indices of @xmath195 or softer ( seen in t tauri disks ; kitamura et al . 2002 ; andrews & williams 2007 ) during the isothermal phase of collapse ; and if the planetary results of kuchner ( 2004 ) give any indication about extrasolar systems , we should expect instead @xmath196indices between @xmath165 and @xmath197 . adams , f. c. , laughlin , g. , & bloch , a. m. 2008 , , 683 , 1117 alibert , y. , baraffe , i. , benz , w. , et al . 2006 , a&a , 455 , l25 alibert , y. , mordasini , c. , & benz , w. 2004 , a&a , 417 , l25 alibert , y. , mordasini , c. , benz , w. , & winisdoerffer , c. 2005a , a&a , 434 , 343 alibert , y. , mousis , o. , mordasini , c. , & benz , w. 2005b , apj , 626 , l57 andrews , s. m. , & williams , j. p. 2007 , , 659 , 705 armitage , p. j. 2003 , , 582 , l47 armitage , p. j. , livio , m. , lubow , s. h. , & pringle , j. e. 2002 , mnras , 334 , 248 barnes , r. , gozdiewski , k. , & raymond , s. n. 2008 , , 680 , l57 barnes , r. , & quinn , t. 2004 , , 611 , 494 barnes , r. , & raymond , s. n. 2004 , , 617 , 569 bean , j. l. , mcarthur , b. e. , benedict , g. f. & armstrong , a. 2008 , , 672 , 1202 bodenheimer , p. , hubickyj , o. , & lissauer , j. j. 2000 , icarus , 143 , 2 bodenheimer , p. , & pollack , j. p. 1986 , icarus , 67 , 391 bryden , g. , beichman , c. a. , trilling , d. e. , et al . 2006 , , 636 , 1098 butler , r. p. , marcy , g. w. , williams , e. , hauser , h. , & shirts , p. 1997 , , 474 , l115 butler , r. p. , wright , j. t. , marcy , g. w. , et al . 2006 , , 646 , 505 christodoulou , d. m. , & kazanas , d. 2008 , , submitted ( astro - ph/0706.3205 ) ( ck ) christodoulou , d. m. , shlosman , i. , & tohline , j. e. 1995 , , 443 , 551 davis , s. s. 2005 , , 627 , l153 desort , m. , lagrange , a .- m . , galland , f. , et al . 2008 , a&a , preprint ( astro - ph/0809.3862 ) eggenberger , a. , udry , s. , & mayor , m. 2004 , a&a , 417 , 353 fischer , d. a. , marcy , g. w. , butler , r. p. , et al . 2008 , , 675 , 790 garaud , p. , & lin , d. n. c. 2007 , , 654 , 606 gayon , j. , marzari , f. , & scholl , h. 2008 , , 389 , l1 gonzalez , g. , & vanture , a. d. 1998 , a&a , 339 , l29 hayashi , c. 1981 , prog . suppl . , 70 , 35 ida , s. , & lin , d. n. c. 2004a , apj , 604 , 388 ida , s. , & lin , d. n. c. 2004b , apj , 616 , 567 ida , s. , & lin , d. n. c. 2005 , apj , 626 , 1045 jayawardhana , r. , holland , w. s. , kalas , p. , et al . 2002 , , 570 , l93 kitamura , y. , momose , m. , yokogawa , s. , et al . 2002 , , 581 , 357 kuchner , m. j. 2004 , apj , 612 , 1147 laskar , j. 1996 , celest . astron . , 64 , 115 lecoanet , d. , adams , f. c. , & bloch , a. m. 2008 , , preprint ( astro - ph/0810.4076 ) lin , d. n. c. , papaloizou , j. c. b. , terquem , c. , bryden , g. , & ida , s. 2000 , protostars and planets iv , ed . v. mannings , a. p. boss , & s. s. russell ( univ . of arizona press : tucson ) , 1111 lissauer , j. j. 1987 , icarus , 69 , 249 lissauer , j. j. 1993 , , 31 , 129 lissauer , j. j. 1995 , icarus , 114 , 217 marcy , g. w. , butler , r. p. , fischer , d. a. , et al . 2002 , , 581 , 1375 marcy , g. , butler , r. p. , fischer , d. , et al . 2005 , prog . suppl . , 158 , 24 marcy , g. w. , cochran , w. d. , & mayor , m. 2000 , protostars and planets iv , ed . v. mannings , a. p. boss , & s. s. russell ( univ . of arizona press : tucson ) , 1285 mcarthur , b. e. , endl , m. , cochran , w. d. , et al . 2004 , , 614 , l81 pepe , f. , correia , a. c. m. , mayor , m. 2007 , a&a , 462 , 769 pierens , a. , & nelson , r. p. 2008 , a&a , 482 , 333 pollack , j. b. , hubickyj , o. , bodenheimer , p. , et al . 1996 , icarus , 124 , 62 poveda , a. , & lara , p. 2008 , rmxaa , 44 , 243 raghavan , d. , henry , t. j. , mason , b. d. , et al . 2006 , apj , 646 , 523 raymond , s. n. , & barnes , r. 2005 , , 619 , 549 raymond , s. n. , barnes , r. , & gorelick , n. 2008 , , , preprint ( astro - ph/0808.3295 ) raymond , s. n. , barnes , r. , & kaib , n. a. 2006 , , 644 , 1223 santos , n. c. , bouchy , f. , mayor , m. , et al . 2004 , a&a , 426 , l19 schneider , g. becklin , e. e. , smith , b. a. , et al . 2001 , , 121 , 525 tohline , j. e. 2002 , , 40 , 349 trilling , d. e. , lunine , j. i. , & benz , w. 2002 , a&a , 394 , 241 valenti , j. a. , & fischer , d. a. 2005 , apjs , 159 , 141 vogt , s. s. , butler , r. p. , marcy , g. w. , et al . 2005 , , 632 , 638 ward , w. r. , & hahn , j. m. 2000 , protostars and planets iv , ed . v. mannings , a. p. boss , & s. s. russell ( univ . of arizona press : tucson ) , 1135 weidenschilling , s. j. 1977 , a&ss , 51 , 153 zhou , l .- y . , ferraz - mello , s. , & sun , y .- s . 2008 , exoplanets : detection , formation and dynamics , proc . iau symposium no . sun , s. ferraz - mello , & j .- zhou ( cambridge univ . press : cambridge ) , 119 0.5truein

this opportunity presents itself in conjunction with a physical model that relates the orbits of the observed planets to the structure of the original protoplanetary disk that harbored their formation at the early stages of protostellar collapse . using only the 5 observed planets of 55 cnc , this model predicts that the surface density profile of its protoplanetary disk varied with distance precisely as , as was also found for the minimum mass solar nebula . despite this similarity ,

five planets are presently believed to orbit the primary star of 55 cnc , but there exists a large 5 au gap in their distribution between the two outermost planets . this gap has attracted considerable interest because it may contain one or more lower mass planets whose existence is not contradicted by long - term orbit stability analyses , in fact it is expected according to the `` packed planetary systems '' hypothesis and an empirical titius bode relation recently proposed for 55 cnc . furthermore , the second largest planet is just the second farthest and it orbits very close to the star . its orbit , the most circular of all , appears to be nearly but not quite commensurable with the orbit of the third planet , casting doubt that any migration or resonant capture of the inner planets has ever occurred and lending support to the idea of `` in situ '' giant planet formation by the process of core accretion . all of the above ideas will be tested in the coming years in this natural laboratory as more observations will become available . this opportunity presents itself in conjunction with a physical model that relates the orbits of the observed planets to the structure of the original protoplanetary disk that harbored their formation at the early stages of protostellar collapse . using only the 5 observed planets of 55 cnc , this model predicts that the surface density profile of its protoplanetary disk varied with distance precisely as , as was also found for the minimum mass solar nebula . despite this similarity , the disk of 55 cnc was smaller , heavier , and less rotationally supported than the solar nebula , so this system represents a different mode of multi planet formation compared to our own solar system .

1402.0966

i

let @xmath1 with @xmath2 , be a sequence of random vectors . a common functional of interests @xmath3 of @xmath4 is defined by @xmath5,\qquad x\in r^d,\ ] ] where @xmath6 is a certain sequence of positive constants and @xmath7 is a real function on @xmath8 . such functionals arise in non - parametric estimation problems , where @xmath9 may be a kernel function @xmath10 or a squared kernel function @xmath11 and the sequence @xmath12 is the bandwidth used in the non - parametric regression . the uniform convergence of @xmath3 in the situation that the @xmath4 satisfy certain stationary conditions was studied in many articles . liero @xcite , peligrad @xcite and nze and doukhan @xcite considered the uniform convergence over a fixed compact set , while masry @xcite , bosq @xcite and fan and yao @xcite gave uniform results over an unbounded set . these work mainly focus on random sequence @xmath13 which satisfies different types of mixing conditions . investigating a more general framework , andrews @xcite gave result on kernel estimate when the data sequence is near - epoch dependent on another underlying mixing sequence . more recently , hansen @xcite provided a set of general uniform consistency results , allowing for stationary strong mixing multivariate data with infinite support , kernels with unbounded support and general bandwidth sequences . kristensen @xcite further extended hansen s results to the heterogenous dependent case under @xmath14-mixing condition . also see wu , huang and huang @xcite for kernel estimation in general time series settings . in comparison to the extensive results where the @xmath15 comes from a stationary time series data , there is little investigation on the the uniform convergence of @xmath3 for the @xmath15 being a non - stationary time series . in this regard , gao , li and tjstheim @xcite derived strong and weak consistency results for the case where the @xmath15 is a null - recurrent markov chain . wang and wang @xcite worked with partial sum processes of the type @xmath16 where @xmath17 is a general linear process . while the rate of convergence in gao , li and tjstheim @xcite is sharp , they impose the independence between @xmath18 and @xmath15 . using a quite different method , wang and wang @xcite allowed for the endogeneity between @xmath18 and @xmath15 , but their results hold only for the @xmath19 being in a fixed compact set . the aim of this paper is to present a general uniform consistency result for @xmath3 with broad applicability . as a framework , our assumption on the @xmath13 is only related to the conditional variance of the martingale , that is , @xmath20 $ ] . see assumption [ assumption2.3 ] in section [ sec2 ] . this of course is a `` high level '' condition , but it in fact is quite natural which holds true for many interesting and important examples , including stationary mixing time series , stationary iterated random function and harris recurrent markov chain . see sections [ sec22 ] and [ sec23 ] for the identification of assumption [ assumption2.3 ] . this condition also holds true for @xmath0 processes with innovations being a linear process , but the identification is complicated and requires quite different techniques . we will report related work in a separate paper . by using the established result , we investigate the uniform convergence of the nadaraya watson estimator in a non - linear cointegrating regression model . it confirms that the uniform asymptotics in wang and wang @xcite can be extended to a unbounded set and the independence between the @xmath21 and @xmath13 in gao , li and tjstheim @xcite can be removed . more importantly , our result not only provides sharp convergence rate , but also the optimal range for the uniform convergence to be held . it should be mentioned that our work on the uniform upper and lower bound estimation for a functional of harris recurrent markov chain is of independent interests . this paper is organized as follows . our main results are presented in next section , which includes the establishment of a framework on the uniform convergence for a class of martingale and uniform upper and lower bound estimation for a functional of harris recurrent markov chain . an application of the main results in non - linear cointegrating regression is given in section [ sec3 ] . all proofs are postponed to section [ sec4 ] . throughout the paper , we denote constants by @xmath22 which may be different at each appearance . we also use the notation @xmath23 .

for a class of martingales , this paper provides a framework on the uniform consistency with broad applicability . the main condition imposed is only related to the conditional variance of the martingale , which holds true for stationary mixing time series , stationary iterated random function , harris recurrent markov chains and processes with innovations being a linear process . using the established results , this paper investigates the uniform convergence of the nadaraya watson estimator in a non - linear cointegrating regression model . our results not only provide sharp convergence rate , but also the optimal range for the uniform convergence to be held . this paper also considers the uniform upper and lower bound estimates for a functional of harris recurrent markov chain , which are of independent interests .

for a class of martingales , this paper provides a framework on the uniform consistency with broad applicability . the main condition imposed is only related to the conditional variance of the martingale , which holds true for stationary mixing time series , stationary iterated random function , harris recurrent markov chains and processes with innovations being a linear process . using the established results , this paper investigates the uniform convergence of the nadaraya watson estimator in a non - linear cointegrating regression model . our results not only provide sharp convergence rate , but also the optimal range for the uniform convergence to be held . this paper also considers the uniform upper and lower bound estimates for a functional of harris recurrent markov chain , which are of independent interests .

1612.02160

i

all graphs in this paper are assumed to be finite , undirected , simple and without loops . for a graph @xmath11 ( or just @xmath12 if the graph under consideration is clear ) and vertices @xmath13 , let @xmath14 denote the distance between @xmath4 and @xmath5 in @xmath6 , that is , the number of edges contained in a shortest path between @xmath4 and @xmath5 . for a positive integer @xmath1 , the _ @xmath1-th power graph @xmath15 of @xmath6 _ is the graph with @xmath3 as its vertex set and @xmath16 contains the edge @xmath17 if and only if @xmath18 . problems related to the chromatic number @xmath19 of power graphs @xmath20 were first considered by kramer and kramer @xcite in 1969 and have enjoyed significant attention ever since . it is clear that for @xmath21 any power of a star is a clique , and hence there are not many classes of graphs for which @xmath19 can be bounded by a constant . an easy argument shows that for a graph @xmath6 with maximum degree @xmath22 we have @xmath23 however , there are many classes of graphs for which it is possible to find much better upper bounds . recall that a graph @xmath6 is _ @xmath24-degenerate _ if every subgraph of @xmath6 contains a vertex of degree at most @xmath24 . [ largepow ] + let @xmath24 and @xmath1 be positive integers . there exists a constant @xmath25 such that for every @xmath24-degenerate graph @xmath6 we have @xmath26 . in this result , the exponent on @xmath27 is best possible ( see below ) . in particular , @xmath28 is at most linear in @xmath27 for planar graphs @xmath6 . wegner @xcite conjectured that every planar graph @xmath6 with @xmath29 satisfies @xmath30 , and gave examples that show this bound would be tight . the conjecture has attracted considerable attention since it was stated in 1977 . for more on this conjecture we refer the reader to @xcite . in ( * ? ? ? * section 11.9 ) , neetil and ossona de mendez define the notion of _ exact power graph_. let @xmath0 be a graph and @xmath1 a positive integer . the _ exact @xmath1-power graph @xmath31 _ has @xmath3 as its vertex set , and @xmath17 is an edge in @xmath31 if and only if there is in @xmath6 a path of length @xmath1 ( i.e. with @xmath1 edges ) between the vertices @xmath4 and @xmath5 ( the path need not be induced , nor a shortest path ) . similarly , they define the _ exact distance-@xmath1 graph @xmath2}}$ ] _ as the graph with @xmath3 as its vertex set , and @xmath17 as an edge if and only if @xmath32 . since obviously @xmath33}})\subseteq e({g^{\natural p}})\subseteq e(g^p)$ ] , we have @xmath8}})\le\chi({g^{\natural p}})\le\chi(g^p)$ ] . for planar graphs @xmath6 , theorem [ largepow ] gives that the exact @xmath1-power graphs @xmath31 satisfy @xmath34 . this result is best possible , even for outerplanar graphs , as the following examples show . for @xmath35 and @xmath36 , let @xmath37 be the @xmath24-regular tree of radius @xmath38 with root @xmath39 . we say that a vertex @xmath5 is at level @xmath40 if @xmath41 . for every edge @xmath42 between vertices at levels @xmath40 and @xmath43 for some @xmath44 , we do the following : if @xmath1 is even , then add a path of length @xmath43 between @xmath45 and @xmath39 ; if @xmath1 is odd , then add paths of length @xmath43 and @xmath46 between @xmath45 and @xmath39 . call the resulting graph @xmath47 . it is straightforward to check that @xmath48 for even @xmath1 , that @xmath49 for odd @xmath1 , and that there is a path of length @xmath1 between any two vertices at level @xmath38 . since there are @xmath50 vertices at level @xmath38 , this immediately means that @xmath51 . surprisingly , for exact distance graphs , the situation is quite different . [ thm2 ] 1.5to1.5let @xmath1 be an odd positive integer . then there exists a constant @xmath52 such that for every planar graph @xmath6 we have @xmath8}})\le c$ ] . 1.5to1.5let @xmath1 be an even positive integer . then there exists a constant @xmath53 such that for every planar graph @xmath6 we have @xmath8}})\le c'\cdot\delta(g)$ ] . the results in theorem [ thm2 ] are actually special cases of the following more general results . we will recall the concept of a _ graph class with bounded expansion _ in the next subsection . [ thm3 ] + let @xmath54 be a class of graphs with bounded expansion . 1.5to1.5let @xmath1 be an odd positive integer . then there exists a constant @xmath55 such that for every graph @xmath56 we have @xmath8}})\le c$ ] . 1.5to1.5let @xmath1 be an even positive integer . then there exists a constant @xmath57 such that for every graph @xmath56 we have @xmath8}})\le c'\cdot\delta(g)$ ] . we will give two proofs of part(a ) . the two proofs give incomparable bounds . also , both proofs are considerably shorter and provide better bounds than the original proof of part(a ) of neetil and ossona de mendez ( * ? ? ? * theorem 11.8 ) . theorem [ thm3](b ) is new , as far as we are aware . as we showed above , if we consider exact powers instead of exact distance graphs , then we need to use bounds involving @xmath27 if we want to bound @xmath58 , even for odd @xmath1 and if @xmath6 is planar . however , by adding the condition that @xmath6 has sufficiently large _ odd girth _ ( length of a shortest odd cycle ) , @xmath58 can be bounded without reference to @xmath27 , for odd @xmath1 . it follows from theorem [ thm3](a ) that this is possible if the odd girth is at least @xmath59 . this is because odd girth at least @xmath59 guarantees that if there is a path of length @xmath1 between @xmath45 and @xmath39 , then any shortest @xmath42-path has odd length . with some more care we can reprove the following . [ thm4 ] + let @xmath54 be a class of graphs with bounded expansion and let @xmath1 be an odd positive integer . then there exists a constant @xmath60 such that for every graph @xmath56 with odd girth at least @xmath61 we have @xmath62 . theorem [ thm2](a ) and its general version theorem [ thm3](a ) are quite surprising , since the exact distance graphs @xmath2}}$ ] of a planar graph @xmath6 can be very dense . to see this , for @xmath63 let @xmath64 be obtained from the complete graph @xmath65 by subdividing each edge @xmath66 times ( i.e.by replacing each edge by a path of length @xmath67 ) . for @xmath68 , form @xmath69 by adding four sets of @xmath24 new vertices to @xmath64 and joining all @xmath24 vertices in the same set to one of the vertices of degree three in @xmath64 . see figure [ four ] for a sketch of @xmath70 . such that @xmath71}}$ ] has edge density approximately 3/4.,width=200 ] it is easy to check that @xmath69 is a planar graph with @xmath72 vertices , while @xmath73}}$ ] has @xmath74 edges . so for fixed @xmath67 and large @xmath24 , the graph @xmath73}}$ ] has approximately @xmath75 times the number of edges of the complete graph on the same number of vertices . it is interesting to see what actual upper and lower bounds we can get for the chromatic numbers of @xmath2}}$ ] for @xmath6 from some specific classes of graphs and for specific values of ( odd ) @xmath1 . using the proof in @xcite , it follows that for @xmath76 and for planar graphs @xmath6 we can get the upper bound @xmath77}})\le5\cdot2^{20,971,522}$ ] ( see also subsection [ ssec3.0 ] ) . on the other hand , ( * ? ? ? * exercise 11.4 ) gives an example of a planar graph @xmath6 with @xmath77}})=6 $ ] . our new proof of theorem [ thm3](a ) already gives a much smaller upper bound for @xmath77}})$ ] for planar graph @xmath6 . by a more careful analysis , we can reduce that upper bound even further , giving the bound in the following result . we also managed to increase the lower bound , although by one only . details can be found in section [ sec4 ] . [ thm5 ] 1.5to1.5for every planar graph @xmath6 we have @xmath77}})\le143 $ ] . 1.5to1.5there exists a planar graph @xmath78 such that @xmath79}})=7 $ ] . for outerplanar graphs @xmath6 we have that @xmath77}})\le13 $ ] , while there exists an outerplanar graph @xmath80 such that @xmath81}})=5 $ ] ( see the results in sections [ sec3 ] and [ sec4 ] ) . when solving an optimisation problem it is often useful to preorder the input so as to minimise some parameter . one such parameter is the _ colouring number _ @xmath82 of a graph @xmath6 . this is the minimum integer @xmath24 such that there is a linear ordering @xmath83 of @xmath3 such that every vertex @xmath5 has at most @xmath84 neighbours @xmath4 with @xmath85 . ( so the colouring number is one more than the _ degeneracy _ of a graph . ) it is well - known and easy to see that the chromatic number @xmath86 of a graph @xmath6 satisfies @xmath87 . although this bound is far from being tight in many cases , it is often used to show that a specific class of graphs has bounded chromatic number . different generalisations of the colouring number can be found in the literature . chen and schelp @xcite proved that the class of planar graphs has linear ramsey number by also controlling , for all vertices @xmath39 , the number of smaller vertices that can be reached by a path of length two , whose middle vertex is larger than @xmath39 . various versions of their idea were applied by kierstead and trotter @xcite , kierstead @xcite , and zhu @xcite to problems concerning the game chromatic number of graphs and gave rise to the 2-colouring number defined below . in their study of oriented game chromatic number of graphs , kierstead and trotter @xcite considered paths of length four with different configurations of `` large '' internal vertices , which later motivated the notions of 4-colouring number and weak 4-colouring number . kierstead and kostochka @xcite applied 2-colouring numbers to a ( non - game ) packing problem . all of these notions are encompassed in the concepts of the _ @xmath24-colouring number _ and the _ weak @xmath24-colouring number _ of a graph , both of which were first introduced by kierstead and yang @xcite . let @xmath0 be a graph , @xmath83 a linear ordering of @xmath3 , and @xmath24 a positive integer . we say that a vertex @xmath88 is _ @xmath24-accessible _ from @xmath89 if @xmath85 and there exists an @xmath90-path @xmath91 of length at most @xmath24 such that @xmath92 for all internal vertices @xmath93 of @xmath91 . similarly , if all internal vertices @xmath93 of @xmath91 satisfy the less restrictive condition that @xmath94 , then we say that @xmath4 is _ weakly _ from @xmath5 . let @xmath95 be the set of vertices that are @xmath24-accessible from @xmath5 , and @xmath96 the set of vertices that are weakly @xmath24-accessible from @xmath5 . @xmath24-colouring number @xmath97 _ and _ weak @xmath24-colouring number @xmath98 _ of a graph @xmath6 are defined as follows : @xmath99 if we allow paths of any length ( but still have restrictions on the position of the internal vertices ) , we get @xmath100 , @xmath101 , the _ @xmath102-colouring number @xmath103 _ and the _ weak @xmath102-colouring number @xmath104_. we now state the main results of this paper . [ thm10 ] 1.5to1.5for every odd positive integer @xmath1 and every graph @xmath6 we have @xmath8}})\le{\mathrm{wcol}}_{2p-1}(g)$ ] . 1.5to1.5for every even positive integer @xmath1 and every graph @xmath6 we have @xmath8}})\le{\mathrm{wcol}}_{2p}(g)\cdot\delta(g)$ ] . [ thm11 ] + let @xmath1 be an odd positive integer and @xmath6 a graph . set @xmath105 . 1.5to1.5we have @xmath8}})\le \bigl(\bigl\lfloor\frac12p\bigr\rfloor+2\bigr)^q$ ] . 1.5to1.5if @xmath6 has odd girth at least @xmath61 , then @xmath106 . an interesting aspect of generalised colouring numbers is that these invariants can also be seen as gradations between the colouring number @xmath82 and two important minor monotone invariants , namely the _ tree - width @xmath107 _ and the _ tree - depth @xmath108 _ ( which is the minimum height of a depth - first search tree for a supergraph of @xmath6 , see @xcite ) . more explicitly , for every graph @xmath6 we have the following relations . [ pro : coltwtd ] 1.5to1.5@xmath109 ; 1.5to1.5@xmath110 . the equality @xmath111 was first proved in @xcite . the equality @xmath112 is ( * ? ? ? * lemma 6.5 ) . relations between the two sets of numbers exist as well . clearly , @xmath113 and @xmath114 . for the converse , kierstead and yang @xcite proved that @xmath115 . note that this means that if one of the generalised colouring numbers is bounded for a class of graphs ( for some @xmath24 ) , then so is the other one . shortly after neetil and ossona de mendez @xcite introduced the notion of _ classes with bounded expansion _ , zhu provided , in @xcite , a way of characterising these classes in terms of the weak @xmath24-colouring numbers . we will use this characterisation as a definition . [ def7 ] + a class of graphs @xmath54 has _ bounded expansion _ if and only if there exist constants @xmath116 , @xmath117 such that @xmath118 for all @xmath24 and all @xmath56 . by this definition , theorem [ thm3](a ) follows directly from both theorems [ thm10](a ) and [ thm11](a ) . we give the proofs of theorems [ thm10 ] and [ thm11 ] in the next section . the proof of theorem [ thm11 ] actually proves a stronger result . for two graphs @xmath0 and @xmath119 on the same vertex set , define @xmath120 . then the upper bound in both parts of theorem [ thm11 ] holds for @xmath121}}\cup{g^{[\natural 3]}}\cup\cdots\cup{g^{[\natural p]}})$ ] and @xmath122 , respectively . a natural question is if for even @xmath1 we can generalise the bound in theorem [ thm10](b ) by a similar bound @xmath123 , where @xmath124 depends on the generalised colouring numbers . but this is not possible . let @xmath125 be the @xmath126-regular tree of radius 2 . then we have @xmath127 and @xmath128 for all @xmath35 . it is easy to check that @xmath129 , but @xmath130 . these examples generalise to larger distances . the results in theorem [ thm11 ] are best possible in the sense that they give upper bounds of @xmath8}})$ ] and @xmath58 that depend on @xmath131 only , whereas no such results are possible that depend on @xmath98 with @xmath132 . to see this , for @xmath133 let @xmath134 be the @xmath135-subdivision of the complete graph @xmath136 ( that is , the graph formed by replacing the edges of @xmath136 by paths of length @xmath1 ) . then we obviously have @xmath137}})=n$ ] . on the other hand we have @xmath138 . to verify this , order the vertices of @xmath134 as follows . first order the branch vertices ( the vertices in the original clique ) , and then order the subdivision vertices in any way . clearly , each branch vertex will not weakly @xmath135-access any other vertex . an internal vertex of a subdivided edge can only weakly @xmath135-access the other @xmath1 vertices on the path that replaced the edge ( including the two end - vertices of the path ) . so for fixed odd @xmath139 we can not bound @xmath137}})$ ] by an expression that involves @xmath140 only . the bound on the odd girth in theorem [ thm11](b ) is also best possible . to show this , for @xmath141 let @xmath142 be formed by taking the path @xmath143 of length @xmath144 , and adding @xmath24 new vertices that are adjacent to both end - vertices of @xmath143 only . it is clear that if @xmath1 is odd , then @xmath142 has odd girth @xmath1 . since between any of the @xmath24 extra vertices there is a path of length @xmath1 , we have @xmath145 . the ordering obtained by taking the two end - vertices of @xmath143 first , and then ordering the other vertices in any way , shows that @xmath146 . so for fixed odd @xmath139 we can not bound @xmath147 by an expression that involves @xmath148 only . neetil and ossona de mendez ( * ? ? ? * section 11.9.3 ) give examples that even if we replace `` there exists a path of length @xmath1 between @xmath4 and @xmath5 '' by `` there exists an _ induced _ path of length @xmath1 between @xmath4 and @xmath5 '' in the definition of @xmath31 , it is not possible to reduce the bound on the odd girth in theorem [ thm11](b ) . the upper bounds obtained by neetil and ossona de mendez in their proof of theorem [ thm3](a ) are very large , even for @xmath76 . their proof relies on the concept of _ @xmath1-centred colourings _ of graphs . a ( proper ) colouring of a graph @xmath6 is a _ @xmath1-centred colouring _ if for each connected induced subgraph @xmath149 of @xmath6 , either one colour appears exactly once on @xmath149 or @xmath149 gets at least @xmath1 colours . this is what is proved in @xcite . [ realprev ] + let @xmath1 be an odd positive integer . if a graph @xmath6 has a @xmath1-centred colouring that uses at most @xmath150 colours , then @xmath8}})\le n2^{n2^n}$ ] . given a graph @xmath6 , the _ star chromatic number _ @xmath151 is the smallest number of colours needed to properly colour @xmath6 such that every two colours induce a star forest ( a forest where every component is isomorphic to a _ star @xmath152 _ ) . it is easy to see that a colouring of a graph is 3-centred if and only if every two colours induce a star forest . albertson et al . @xcite showed that the star chromatic number of planar graphs is at most 20 , and there exist planar graphs with star chromatic number equal to 10 . this means that the best known upper bound on @xmath77}})$ ] for planar graphs given by theorem [ realprev ] is @xmath153 , while the best possible upper bound for planar graphs that can be found using that theorem directly is @xmath154 . an alternative bound can be obtained from theorem [ realprev ] using the following result . + every graph @xmath6 has a @xmath1-centred colouring that uses at most @xmath155 colours . [ first ] + let @xmath1 be an odd positive integer and @xmath6 a graph . setting @xmath156 we have @xmath8}})\le w2^{w2^w}$ ] . as far as we are aware , the best known upper bound for @xmath157 for planar is given by the following result . [ binomcol ] + for every positive integer @xmath24 and planar graph @xmath6 we have @xmath158 . so we have @xmath159 for planar graphs , which , when combined with corollary [ first ] , unfortunately gives a worse bound for @xmath77}})$ ] for planar graphs than the one obtained earlier . on the other hand , combining theorems [ thm10](a ) and [ binomcol ] already gives the significantly better upper bound @xmath77}})\le231 $ ] for planar graphs . in section [ sec3 ] we will show that this bound can be lowered further to 143 . the remainder of this paper is organised as follows . in the next section we prove our main results , theorems [ thm10 ] and [ thm11 ] . we use the results from that section in section [ sec3 ] to find explicit upper bounds for the chromatic number of exact distance graphs for some specific classes of graphs , including graphs with bounded genus , graphs with bounded tree - width , and graphs without a specified complete minor . in section [ sec4 ] we describe the graph promised in theorem [ thm5](b ) . we close with a number of open problems and directions for further study .

for any graph and positive integer , the _ exact distance- graph _ }}$ ] is the graph with vertex set , which has an edge between vertices and if and only if and have distance in . for odd , neetil and ossona de mendez proved that for any fixed graph class with _ bounded expansion _ , the chromatic number of }}$ ] is bounded by an absolute constant . using the notion of _ generalised colouring numbers _ , we give a much simpler proof for the result of neetil and ossona de mendez , which at the same time gives significantly better bounds . in particular , we show that for any graph and odd positive integer , the chromatic number of }}$ ] is bounded by the weak-colouring number of . for even , we prove that}})$ ] is at most the weak-colouring number times the maximum degree . for odd , the existing lower bound on the number of colours needed to colour}}$ ] when is planar is improved . similar lower bounds are given for-minor free graphs .

for any graph and positive integer , the _ exact distance- graph _ }}$ ] is the graph with vertex set , which has an edge between vertices and if and only if and have distance in . for odd , neetil and ossona de mendez proved that for any fixed graph class with _ bounded expansion _ , the chromatic number of }}$ ] is bounded by an absolute constant . using the notion of _ generalised colouring numbers _ , we give a much simpler proof for the result of neetil and ossona de mendez , which at the same time gives significantly better bounds . in particular , we show that for any graph and odd positive integer , the chromatic number of }}$ ] is bounded by the weak-colouring number of . for even , we prove that}})$ ] is at most the weak-colouring number times the maximum degree . for odd , the existing lower bound on the number of colours needed to colour}}$ ] when is planar is improved . similar lower bounds are given for-minor free graphs . key words : _ bounded expansion , chromatic number , exact distance graphs , generalised colouring numbers , planar graphs _

1109.1319

i

in @xmath3 interesting connections exist between the @xmath2-variable knot polynomials and invariants of legendrian knots . with respect to the standard contact structure on @xmath3 , fuchs and tabachnikov @xcite showed that an upper bound for the thurston - bennequin number arises from the kauffman and homfly - pt knot polynomials . furthermore , when this estimate is sharp some non - classical invariants exhibit nice properties . specifically , combining results from @xcite , @xcite , @xcite , and @xcite we have : [ thm : review ] for a legendrian link @xmath4 the following three statements are all equivalent : 1 . the estimate @xmath5 ( resp . @xmath6 ) is sharp where @xmath7 $ ] denote the kauffman and homfly - pt polynomials . 2 . a front diagram for @xmath8 has a @xmath0-graded ( resp . @xmath2-graded ) normal ruling . 3 . the chekanov - eliashberg dga of @xmath8 has a @xmath0-graded ( resp . @xmath2-graded ) augmentation . in addition , the conditions of theorem [ thm : review ] are necessary in order for @xmath8 to have a linear at infinity generating family . in this article , we establish analogous results for legendrian knots in the @xmath0-jet space of the circle , @xmath9 . the manifold @xmath9 is topologically an open solid torus and carries a standard contact structure . legendrian knots in @xmath9 have attracted a fair amount of attention in the literature ; see for instance @xcite , @xcite , @xcite . the @xmath0-jet space setting comes with convenient projections from which legendrian knots may be presented via front or lagrangian diagrams and legendrian isotopy may be described in a combinatorial manner . in addition , @xmath0-jet spaces provide a natural setting for the use of generating families . a convenient formal way to define a normal ruling , @xmath10 , of @xmath8 is as a family of fixed point free involutions of the strands of the front diagram of @xmath8 subject to many restrictions . at least locally , this may be viewed as a decomposition of the front diagram into pairs of paths . chekanov and pushkar introduced normal rulings in @xcite albeit with different terminology as well as related legendrian isotopy invariants which have become known as ruling polynomials . in connection with augmentations , fuchs independently defined normal rulings of knots in @xmath3 and , in the case of the kauffman polynomial , already conjectured the equivalence of ( 1 ) and ( 2 ) in @xcite . this conjecture was verified in @xcite where it was shown that in fact the @xmath0-graded and @xmath2-graded ruling polynomials appear as coefficients of the kauffman and homfly - pt polynomials respectively . relationships between the kauffman / homfly - pt invariants and legendrians knots in @xmath9 have already begun to be studied , and several factors make the situation more interesting . for instance , the homfly - pt polynomial , @xmath11 , of a solid torus link , @xmath8 , belongs to a polynomial algebra over @xmath12 $ ] with a countably infinite number of generators @xmath13 ; the kauffman polynomial has a similar form . chmutov and goryunov @xcite proved thurston - bennequin number estimates analogous to those appearing in ( 1 ) of theorem [ thm : review ] using these many variable kauffman and homfly - pt polynomials . in the case of the homfly - pt polynomial , it was shown in @xcite that the @xmath2-graded ruling polynomial can be recovered from the homfly - pt polynomial , but this requires first specializing via an @xmath14-module homomorphism @xmath15 \rightarrow r$ ] . in the present work we develop analogous results involving the @xmath0-graded ruling polynomial and the kauffman skein module . ( see theorems [ thm : front ] and [ thm : spec ] . ) the need to specialize the kauffman and homfly - pt invariants in order to recover the ruling polynomials has an interesting consequence . there are many solid torus links where the kauffman or homfly - pt polynomial estimate is sharp , yet the corresponding ruling polynomial vanishes . as a result , for legendrians in @xmath9 some adjustment is required to statement ( 2 ) of theorem [ thm : review ] . for this purpose , we introduce a quite natural notion of _ generalized normal ruling _ where the fixed point free condition is relaxed . our main result is the following analog of theorem [ thm : review ] : [ the : main ] let @xmath16 be a legendrian link . 1 . then , the estimate @xmath5 ( resp . @xmath6 ) is sharp if and only if @xmath8 has a @xmath0-graded ( resp . @xmath2-graded ) generalized normal ruling . 2 . suppose @xmath8 has been assigned a @xmath17-valued maslov potential . then , the chekanov - eliashberg dga of @xmath8 has a @xmath18-graded augmentation if and only if a front diagram for @xmath8 admits a @xmath18-graded generalized normal ruling . aside from allowing the more general @xmath18-graded condition in ( 2 ) , it is natural to organize the three statements into these two equivalences . even in @xmath3 , the authors do not know of any proof of an implication between the statements about the knot polynomial estimates and existence of augmentations which is able to avoid using normal rulings . there are settings , for instance certain contact lens spaces , where legendrian contact homology @xcite and homfly - pt polynomial estimates ( @xcite , @xcite ) for @xmath19 have been established while an appropriate notion of normal ruling has yet to be formulated . for this reason , establishing a more direct link between bennequin type inequalities and augmentations could prove interesting . the article is arranged as follows : in section 2 , we provide the necessary background about normal rulings and the kauffman and homfly - pt invariants and also introduce generalized normal rulings . section 3 runs parallel to the results on the homfly - pt skein module and @xmath2-graded rulings from @xcite . we show how to recover the @xmath0-graded ruling polynomial from an appropriate specialization of the kauffman skein module . a natural basis for the kauffman skein module is indexed by partitions , and for this basis we provide an explicit formula for the specialization . in section 4 we prove ( 1 ) of theorem [ the : main ] by combining the results of section 3 ( and @xcite for the homfly - pt case ) with a linear independence argument . the final section of the article deals with part ( 2 ) of theorem [ the : main ] . for the forward implication we base all of our arguments on the linear algebraic results of barannikov @xcite from which the reason behind the normality conditions , with or without fixed points , becomes clear . this work was initiated through the pruv program at duke university . we thank david kraines for supervising the program and encouraging our participation . also , we thank lenny ng for his interest in the project . a portion of the writing was carried out while the second author was a visitor at the max planck institute for mathematics in bonn , and it is a pleasure to acknowledge mpim for their hospitality . the first author received support from nsf career grant dms-0846346 .

is introduced . we show that the existence of such a generalized normal ruling is equivalent to sharpness of the kauffman polynomial estimate for the thurston - bennequin number as well as to the existence of an ungraded augmentation of the chekanov - eliashberg dga . parallel results involving the homfly - pt polynomial and-graded generalized normal rulings are established .

for legendrian links in the-jet space of we show that the-graded ruling polynomial may be recovered from the kauffman skein module . for such links a generalization of the notion of normal ruling is introduced . we show that the existence of such a generalized normal ruling is equivalent to sharpness of the kauffman polynomial estimate for the thurston - bennequin number as well as to the existence of an ungraded augmentation of the chekanov - eliashberg dga . parallel results involving the homfly - pt polynomial and-graded generalized normal rulings are established .

cond-mat0210534

i

immiscible two - phase flow in the vicinity of the contact line ( cl ) , where the fluid - fluid interface intersects the solid wall , is a classical problem that falls beyond the framework of conventional hydrodynamics @xcite . in particular , molecular dynamics ( md ) studies have shown relative slipping between the fluids and the wall , in violation of the no - slip boundary condition @xcite . there have been numerous ad - hoc models @xcite to address this phenomenon , but none was able to give a quantitative account of the md slip velocity profile in the molecular - scale vicinity of the cl . while away from the moving cl the small amount of relative slipping was found to follow the navier boundary condition ( nbc ) @xcite , i.e. , relative slipping proportional to the tangential viscous stress , in the molecular - scale vicinity of the cl the nbc failed totally to account for the near - complete slip . this failure casts doubts on the general applicability of the nbc to immiscible flows and hinders a continuum formulation of the hydrodynamics in the cl region . in particular , a ( possible ) breakdown in the hydrodynamic description for the molecular - scale cl region has been suggested @xcite . in another approach @xcite , it was shown the md results can be reproduced by continuum finite element simulations , provided the slip profile extracted from md is used as input . this work demonstrated the feasibility of the hybrid algorithm , but left unresolved the problem concerning the boundary condition governing the cl motion . without a continuum hydrodynamic formulation , it becomes difficult or impossible to have realistic simulations of micro- or nanofluidics , or of immiscible flows in porous media where the relative wetting characteristics , the moving cl dissipation , and behavior over undulating solid surfaces may have macroscopic implications . from md simulations on immiscible two - phase flows , we report the finding that the generalized navier boundary condition ( gnbc ) applies for all boundary regions , whereby the relative slipping is proportional to the sum of tangential viscous stress and the uncompensated young stress . the latter arises from the deviation of the fluid - fluid interface from its static configuration @xcite . by combining gnbc with the cahn - hilliard ( ch ) hydrodynamic formulation of two - phase flow @xcite , we obtained a consistent , continuum description of immiscible flow with material parameters ( such as viscosity , interfacial tension , etc ) directly obtainable from md simulations . the convective - diffusive dynamics in the vicinity of the interface and the moving cl also means the introduction of two phenomenological dynamic parameters whose values can be fixed by comparison with one md flow profile . once the parameter values are determined from md simulations , our continuum hydrodynamics can yield predictions matching those from md simulations ( for different couette and poiseuille flows ) . our findings suggest the no - slip boundary condition to be an approximation to the gnbc , accurate for most macroscopic flows but failing in immiscible flows . these results open the door to efficient simulations of nano- or microfluidics involving immiscible components , as well as to macroscopic immiscible flow calculations , e.g. , in porous media , that are physically meaningful at the molecular level @xcite . the latter is possible , for example , by employing the adaptive method based on the iterative grid redistribution introduced in ref . this method has demonstrated the capability of resolving , at the same time , both the global behavior of a partial differential equation solution with coarse mesh , and a strong singularity in a localized region with a refined local mesh of over @xmath0 ratio to the coarse mesh .

from extensive molecular dynamics simulations on immiscible two - phase flows , we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized navier boundary condition , in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated young stress . the latter arises from the deviation of the fluid - fluid interface from its static configuration . we give a continuum formulation of the immiscible flow hydrodynamics , comprising the generalized navier boundary condition , the navier - stokes equation , and the cahn - hilliard interfacial free energy . in particular , the behavior at high capillary numbers , leading to the breakup of the fluid - fluid interface , is accurately predicted . * molecular scale contact line hydrodynamics + of immiscible flows *

from extensive molecular dynamics simulations on immiscible two - phase flows , we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized navier boundary condition , in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated young stress . the latter arises from the deviation of the fluid - fluid interface from its static configuration . we give a continuum formulation of the immiscible flow hydrodynamics , comprising the generalized navier boundary condition , the navier - stokes equation , and the cahn - hilliard interfacial free energy . our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular - scale vicinity of the contact line . in particular , the behavior at high capillary numbers , leading to the breakup of the fluid - fluid interface , is accurately predicted . * molecular scale contact line hydrodynamics + of immiscible flows *

1207.5910

i

gaussian graphical models are popular tools for modelling complex associations in the multivariate continuous case . if the graph with vertex set @xmath0:=\{1,\ldots , m\}$ ] is complete , then the general linear group @xmath1 , consisting of all invertible @xmath2-matrices , acts on the space of concentration matrices in the model , as well as on the sample space . the maximum likelihood estimator ( mle ) of the concentration matrix is equivariant with respect to this group action , but many other equivariant estimators have been proposed , for example , by @xcite . for smaller graphs , only some proper subgroup of @xmath1 will act on the set of compatible concentration matrices . in this paper , we describe that subgroup explicitly , and pave the way for its use in designing invariant tests , ( robust ) equivariant estimators and improved inference procedures . having an explicit group acting on a statistical model has numerous advantages . this was first pointed out by @xcite in the context of the location and scale models , which then led to the notion of a transformation family , that is , a statistical model on which a group acts transitively . group actions give rise , for example , to the study of model invariants and distributional aspects of the maximum likelihood estimator ( mle ) or other equivariant estimators [ see @xcite ] . when a group acts on a model in a nontransitive manner , the model is sometimes called a composite transformation family [ see @xcite ] . in this case , the model can be decomposed into a family of transformation models each corresponding to a fixed value of some parameter . to set the stage , let @xmath3,e)$ ] be an undirected graph with set of vertices @xmath0 $ ] and set of edges @xmath4\choose2}$ ] . denote by @xmath5 the set of symmetric matrices in @xmath6 and by @xmath7 the cone of positive definite matrices . let @xmath8 denote the linear space of symmetric matrices whose @xmath9 off - diagonal entry is zero if @xmath10 , and by @xmath11 the cone of all positive definite matrices in @xmath12 . as a running example in this , we take @xmath13 to be the path @xmath14 . so @xmath15 consists of all symmetric matrices of the form @xmath16.\ ] ] let @xmath17}$ ] be a random vector with multivariate normal distribution @xmath18 . the _ gaussian graphical model _ is the statistical model for @xmath19 given by @xmath20 so @xmath21 is the space of concentration matrices compatible with the model [ see @xcite ] . the group @xmath22 acts on @xmath23 by matrix - vector multiplication , and this induces an action on @xmath24 and @xmath25 given by @xmath26indeed , note that this is the concentration matrix of @xmath27 if @xmath28 is the concentration matrix of @xmath29 . a leading role in this paper is played by the group @xmath30 this is a closed subgroup of the lie group @xmath1 ( see section [ secg ] ) . for example , if @xmath13 is the complete graph , then @xmath31 is all of @xmath1 . for _ any _ graph @xmath13 , the group @xmath31 contains the invertible diagonal matrices , which correspond to scaling the components of @xmath19 . furthermore , @xmath31 contains elements coming from graph automorphisms of @xmath13 . specifically , if @xmath32 \to[m]$ ] is such an automorphism , then the permutation matrix @xmath33 with ones on the positions @xmath34 $ ] lies in @xmath31 , since its action on @xmath24 stabilizes the zero pattern prescribed by @xmath13 . for our running example @xmath35 , the permutation matrix @xmath36\ ] ] lies in @xmath31 . our first result is an explicit description of @xmath31 in terms of @xmath13 , and requires the pre - order on @xmath0 $ ] defined by @xmath37 where @xmath38\dvtx \{i , j\ } \in e\}$ ] denotes the set of neighbors of @xmath39 in @xmath13 . so in our running example @xmath35 we have @xmath40 . consider the closed subset @xmath41 of @xmath1 defined by @xmath42 we show in section [ secg ] that this set is a subgroup of @xmath1 . for @xmath43 it consists of all invertible matrices of the form @xmath44.\ ] ] [ thmmg ] for any undirected graph @xmath3,e)$ ] , the group @xmath31 is generated by the group @xmath41 and the permutation matrices corresponding to the automorphism group of the graph @xmath13 . for @xmath35 , this theorem says that @xmath31 is the group of all matrices of the form above , together with all matrices of the form @xmath45.\ ] ] the two subgroups of @xmath31 in theorem [ thmmg ] can have a nontrivial intersection . for instance , when @xmath13 is the complete graph , the automorphism group of @xmath13 is contained in @xmath41 . in section [ secg ] , we state and prove a more refined statement that gets rid of that intersection . now that we know explicitly which matrix group @xmath31 acts on our graphical model @xmath46 , we can use this group to develop classical notions of multivariate statistics in the general context of graphical models . one of these notions is that of an equivariant estimator [ see , e.g. , @xcite ] . let @xmath47 denote the @xmath48 matrix , whose columns correspond to @xmath49 independent copies of the vector @xmath19 . then an equivariant estimator for the concentration matrix is a map @xmath50 , that is , a map from the space of @xmath49-samples @xmath47 to the parameter space of the model , that satisfies @xmath51 for all realisations @xmath52 of @xmath47 . the standard example is the maximum likelihood estimator ( mle ) . indeed , the likelihood of concentration matrix @xmath28 given an @xmath49-sample @xmath52 equals the likelihood of @xmath53 given @xmath54 , for any @xmath55 , and this implies that the mle is @xmath31-equivariant . other equivariant estimators of the concentration matrix for some special graphical models have been proposed in @xcite . for decomposable graphs , the mle exists with probability one if and only if @xmath49 is at least the size of the maximal clique of the given graph . however , in general , whether the mle exists , with probability one , for a given sample size @xmath49 and a given graph @xmath13 is a subtle matter ; see the recent paper by @xcite and the references therein . by contrast , the question whether for a given sample size _ any _ equivariant estimator exists , turns out to have a remarkably elegant answer for any graph @xmath13 . to state it , define the _ down set _ @xmath56 of an element @xmath57 $ ] to be the set of all @xmath58 $ ] with @xmath59 . [ thgeqexist ] let @xmath3,e)$ ] be an undirected graph . there exists a @xmath31-equivariant estimator @xmath60 if and only if @xmath61}|{\hspace*{-1pt}\downarrow\hspace{-3pt}}i|$ ] . to be precise , when @xmath49 is at least the bound in the theorem , a @xmath31-equivariant @xmath62 exists that is defined outside some measure - zero set ( in fact , an algebraic subvariety of positive codimension ) , while if @xmath49 is smaller than that bound , then not even any partially defined equivariant map @xmath62 exists . for our running example @xmath35 , we have @xmath63 and @xmath64 and @xmath65 , so theorem [ thgeqexist ] says that an equivariant estimator exists with probability one if and only if the sample size is at least @xmath66 , which in this case coincides with the condition for existence of the mle . theorem [ thgeqexist ] will be proved in section [ secequivariance ] , where we also establish upper bounds on the robustness of equivariant estimators , based on general theory from @xcite . another classical notion related to a group action on a statistical model is that of _ invariants _ on the sample space . in our case , these are maps @xmath67 defined on @xmath68 , possibly outside some measure - zero set , that are constant on @xmath31-orbits , that is , that satisfy @xmath69 for all @xmath55 . an invariant @xmath67 is called _ maximal _ if it distinguishes all @xmath31-orbits . in formulas this means that for @xmath49-samples @xmath70 , outside some set of measure zero , the equality @xmath71 implies that there exists a @xmath55 such that @xmath72 . any invariant map is then a function of @xmath67 . the relevance of maximal invariants in statistics lies in the fact that they facilitate inference for the maximum likelihood estimator in the case of transformation families [ see @xcite ] . in this case the maximal invariant is an ancillary statistics that one may chose to condition on . these ideas can be used also in the case of composite transformation families , where the inference for the index parameter @xmath73 is based on the marginal distribution of the maximal invariant statistics [ @xcite , section 5 ] . another important application of the maximal invariant is in the construction of _ invariant tests _ [ see @xcite ] . suppose , for instance , that we want to test the hypothesis that the distribution of the multivariate gaussian random vector @xmath19 lies in @xmath46 against the alternative that it does not , and suppose that for the @xmath49-sample @xmath74 the test would accept the hypothesis . then , since @xmath46 is stable under the action of any @xmath55 , it is natural to require that our test also accepts the hypothesis on observing @xmath75 . thus , the test itself would have to be @xmath31-invariant . our result on maximal invariants uses the equivalence relation @xmath76 on @xmath0 $ ] defined by @xmath77 if and only if both @xmath78 and @xmath59 , that is , if and only if @xmath79 . we write @xmath80 for the equivalence class of @xmath57 $ ] and @xmath0/\sim$ ] for the set of all equivalence classes . [ thmmmaxinv ] let @xmath3,e)$ ] be an undirected graph . suppose that @xmath81 . then the map @xmath82/\sim } { \mathbb{r}}^{n\times n}$ ] given by @xmath83^t \bigl(\mathbf{x } [ { { \hspace*{-1pt}\downarrow\hspace{-3pt}}}i ] \mathbf { x } [ { { \hspace*{-1pt}\downarrow\hspace{-3pt}}}i]^t\bigr)^{-1 } \mathbf{x } [ { { \hspace*{-1pt}\downarrow\hspace{-3pt}}}i ] \bigr)_{\bar{i}\in[m]/\sim},\ ] ] where @xmath84 \in{\mathbb{r}}^{| { { \hspace*{-1pt}\downarrow\hspace{-3pt}}}i|\times n}$ ] is the submatrix of @xmath52 given by all rows indexed by @xmath56 , is a maximal @xmath41-invariant . the lower bound on @xmath49 in the theorem ensures that the @xmath85-matrices @xmath84 \mathbf { x } [ { { \hspace*{-1pt}\downarrow\hspace{-3pt}}}i]^t$ ] are invertible for generic @xmath52 , and in particular for @xmath86 outside a set of measure zero . for the complete graph , theorem [ thmmmaxinv ] reduces to the known statement that @xmath87 is a maximal invariant , see example 6.2.3 in @xcite , while for our running example @xmath35 it says that the rank - one matrix @xmath88^t ( \mathbf{x}[1 ] \mathbf{x}[1]^t)^{-1 } \mathbf{x}[1]$ ] ( recording only the direction of the first row of @xmath52 ) and the rank - two matrices @xmath89^t ( \mathbf{x}[1,2 ] \mathbf { x}[1,2]^t)^{-1 } \mathbf{x}[1,2]$ ] and @xmath90^t ( \mathbf{x}[1,3 ] \mathbf{x}[1,3]^t)^{-1 } \mathbf{x}[1,3]$ ] together form a maximal invariant for @xmath41 . we stress that theorem [ thmmmaxinv ] gives a maximal invariant under the subgroup @xmath41 , rather than under all of @xmath31 . the proof of this theorem can be found in section [ secorbequiv ] . our final results concern the space @xmath92 of @xmath31-orbits in @xmath91 . when @xmath46 is a transformation family , this space consists of a single point and hence has dimension zero . conversely , it turns out that when the dimension of @xmath92 is zero , @xmath46 is a transformation family . by work of @xcite , it is known exactly for which graphs this happens . our result on @xmath92 is a combinatorial expression for its dimension . rather than capturing that expression in a formula , which we will do in section [ secorbits ] , we now describe it in terms of a combinatorial procedure . let @xmath3,e)$ ] be an undirected graph . color an edge @xmath93 red if @xmath77 , green if @xmath78 or @xmath59 but not both , and blue otherwise . next delete all green edges from @xmath13 , while retaining their vertices . then delete the blue edges sequentially , in each step not only deleting a blue edge but also its two vertices together with all further blue and red edges incident to those two vertices . continue this process until no blue edges are left . call the resulting graph @xmath94 ; it consists of red edges only . see figure [ figorbitspacedim ] for an example . one can show that , up to isomorphism , @xmath94 is independent of the order in which the blue edges with incident vertices were removed though in general it is larger than the graph obtained by deleting all blue edges , their vertices , and their incident edges at once . [ thmmorbitspacedim ] the dimension of @xmath92 equals the number of blue edges in the original graph @xmath13 minus the number of red edges in @xmath13 plus the number of remaining red edges in @xmath94 . in other words , that dimension equals the number of blue edges in @xmath13 minus the number of red edges deleted in the process going from @xmath13 to @xmath94 . this number is nonnegative : indeed , if in some step a blue edge @xmath95 is being deleted together with its vertices , then for each red edge @xmath96 being deleted along with @xmath39 there is also a blue edge @xmath97 being deleted , and for each red edge @xmath98 being deleted along with @xmath99 also a blue edge @xmath100 is deleted . this shows , in particular , that @xmath101 is zero if and only if @xmath13 has no blue edges , that is , if all edges run between vertices that are comparable in the pre - order . this is equivalent to the condition found in @xcite for @xmath46 to be a transformation family ; see theorem [ thmmmassam ] below . for our running example @xmath102 the model is a transformation family and similarly for complete graphs . for an example where @xmath92 has dimension @xmath103 , see figure [ figorbitspacedim ] . the proof of theorem [ thmmorbitspacedim ] can be found in section [ secorbits ] and in supplementary materials [ @xcite ] . has dimension @xmath103 . ] the remainder of the paper closely follows the structure of this introduction . first , in section [ secg ] we use structure theory of real algebraic groups to determine @xmath31 . in section [ secequivariance ] , we derive necessary and sufficient conditions for the existence , with probability one , of equivariant estimators of the concentration ( or covariance ) matrix , and we give an upper bound on the robustness of those estimators , measured by the finite sample breakdown point for generic samples . in section [ secorbequiv ] , we derive the maximal invariant of theorem [ thmmmaxinv ] . in section [ sectransitive ] , we discuss in some detail the case where @xmath31 acts transitively on @xmath91 providing general formula for an equivariant estimator , after which section [ secorbits ] is devoted to our combinatorial formula for the orbit space dimension in the general case . we conclude the paper with a short discussion . in the supplementary materials [ @xcite ] , we provide the proof of theorem [ thmmorbitspacedim ] . we also discuss further results on the combinatorial structure of the problem that link our work to @xcite .

we reveal this structure by explicitly describing , for any undirected graph , the ( maximal ) matrix group acting on the space of concentration matrices in the model . the continuous part of this group is captured by a poset naturally associated to the graph , while automorphisms of the graph account for the discrete part of the group . we compute the dimension of the space of orbits of this group on concentration matrices , in terms of the combinatorics of the graph ; and for dimension zero we recover the characterization by letac and massam of models that are transformation families . finally , we address the issue of robustness of these estimators by computing upper bounds on finite sample breakdown points . ,

gaussian graphical models have become a well - recognized tool for the analysis of conditional independencies within a set of continuous random variables . from an inferential point of view , it is important to realize that they are composite exponential transformation families . we reveal this structure by explicitly describing , for any undirected graph , the ( maximal ) matrix group acting on the space of concentration matrices in the model . the continuous part of this group is captured by a poset naturally associated to the graph , while automorphisms of the graph account for the discrete part of the group . we compute the dimension of the space of orbits of this group on concentration matrices , in terms of the combinatorics of the graph ; and for dimension zero we recover the characterization by letac and massam of models that are transformation families . furthermore , we describe the maximal invariant of this group on the sample space , and we give a sharp lower bound on the sample size needed for the existence of equivariant estimators of the concentration matrix . finally , we address the issue of robustness of these estimators by computing upper bounds on finite sample breakdown points . ,

0903.2039

i

the goal of the first part of this paper is to introduce a new object called plane overpartitions , and to give several enumeration formulas for these plane overpartitions . plane overpartition _ is a plane partition where ( 1 ) in each row the last occurrence of an integer can be overlined or not and all the other occurrences of this integer are not overlined and ( 2 ) in each column the first occurrence of an integer can be overlined or not and all the other occurrences of this integer are overlined . an example of a plane overpartition is @xmath0 this paper takes its place in the series of papers on overpartitions started by corteel and lovejoy @xcite . the motivation is to show that the generating function for plane overpartitions is : @xmath1 in this paper , we give several proofs of this result and several refinements and generalizations . namely , we prove the following results . content formula for the generating function for plane overpartitions of a given shape , see theorem [ t1 ] . the hook formula for the generating function for reverse plane overpartitions , see theorem [ reverse ] . the generating function formula for plane overpartitions with bounded parts , see theorem [ boundedparts ] . the goal of the second part of this paper is to extend the generating function formula for cylindric partitions due to borodin @xcite and the following 1-parameter generalized macmahon s formula due to the third author of this paper @xcite : @xmath2 where the weight @xmath3 is a polynomial in @xmath4 that we describe below . given a plane partition @xmath5 ( a ferrers diagram filled with positive integers that form nonincreasing rows and columns ) , a connected component of @xmath5 is the set of all connected boxes of its ferrers diagram that are filled with a same number . if a box @xmath6 belongs to a connected component @xmath7 then we define its level @xmath8 as the smallest positive integer such that @xmath9 does not belong to @xmath7 . a border component of level @xmath10 is a connected subset of a connected component whose all boxes have level @xmath10 , see figure [ fig11 ] . we associate to each border component of level @xmath10 , the weight @xmath11 . the polynomial @xmath3 is the product of the weights of its border components . for the plane partition from figure [ fig11 ] it is @xmath12 . [ htp ! ] we give a new proof of the 1-parameter generalized macmahon s formula . we also extend this formula to two more general objects : skew plane partitions and cylindric partitions . namely , we prove the following results . 1-parameter generalized formula for the generating function for skew plane partitions , see theorem [ skew ] . 1-parameter generalized formula for the generating function for cylindric partitions , see theorem [ uvodcyl ] . in the rest of this section we give definitions and explain our results in more detail . a partition @xmath13 is a nonincreasing sequence of positive integers @xmath14 . each @xmath15 is a part of the partition and the number of parts is denoted by @xmath16 . the weight @xmath17 of @xmath13 is the sum of its parts . a partition @xmath13 can be graphically represented by the ferrers diagram that is a diagram formed of @xmath16 left justified rows , where the @xmath18 row consists of @xmath15 cells ( or boxes ) . the conjugate of a partition @xmath13 , denoted by @xmath19 , is a partition that has the ferrers diagram equal to the transpose of the ferrers diagram of @xmath13 . for a cell @xmath6 of the ferrers diagram of @xmath13 the _ hook length _ of this cell is @xmath20 and the _ content _ is @xmath21 . it is well known that the generating function for partitions that have at most @xmath22 parts is @xmath23 , where @xmath24 . more definitions on partitions can be found , for example , in @xcite or @xcite . an _ overpartition _ is a partition where the last occurrence of an integer can be overlined @xcite . last occurrences in an overpartition are in one to one correspondence with corners of the ferrers diagram and overlined parts can be represented by marking the corresponding corners . the generating function for overpartitions that have at most @xmath22 parts is @xmath25 . let @xmath13 be a partition . a _ plane partition _ of shape @xmath13 is a filling of cells of the ferrers diagram of @xmath13 with positive integers that form a nonincreasing sequence along each row and each column . we denote the shape of a plane partition @xmath5 by @xmath26 and the sum of all entries by @xmath27 , called the weight of @xmath5 . it is well known , under the name of macmahon s formula , that the generating function for plane partitions is @xmath28 one way to prove this is to construct a bijection between plane partitions and pairs of semi - standard young tableaux of the same shape and to use the rsk correspondence between these young tableaux and certain matrices @xcite . recall that a plane overpartition is a plane partition where in each row the last occurrence of an integer can be overlined or not and in each column the first occurrence of an integer can be overlined or not and all the others are overlined . this definition implies that the entries strictly decrease along diagonals , i.e. all connected components are also border components . therefore , a plane overpartition is a diagonally strict plane partition where some entries are overlined . more precisely , it is easy to check that inside a border component only one entry can be chosen to be overlined or not and this entry is the upper right entry . plane overpartitions are therefore in bijection with diagonally strict plane partitions where each border component can be overlined or not ( or weighted by 2 ) . recently , those weighted diagonally strict plane partitions were studied in @xcite . the first result obtained was the shifted macmahon s formula that says that the generating function for plane overpartitions is indeed equation . this was obtained as a limiting case of the generating function formula for plane overpartitions which fit into an @xmath29 box , i.e. whose shapes are contained in the rectangular shape with @xmath30 rows and @xmath31 columns . @xcite[osnovna ] the generating function for plane overpartitions which fit in an @xmath29 box is @xmath32 this theorem was proved in @xcite using schur @xmath33 and @xmath34 symmetric functions and a suitable fock space . in @xcite the theorem was proved in a bijective way where an rsk type algorithm ( due to sagan @xcite , see also chapter xiii of @xcite ) was used to construct a bijection between plane overpartitions and matrices of nonnegative integers where positive entries can be overlined . in section 2 , we give a mostly combinatorial proof of the generalized macmahon formula @xcite . namely , we prove : @xcite @xmath35 [ mirjana ] in the above formula , @xmath36 is the set of plane partitions with at most @xmath30 rows and @xmath31 columns . when we set @xmath37 , only the border components of level @xmath38 have a non zero weight and we get back theorem [ osnovna ] . the main result of section 3 is a hook content formula for the generating function for plane overpartitions of a given shape . more generally , we give a weighted generating function where overlined parts are weighted by some parameter @xmath39 . let @xmath40 be the set of all plane overpartitions of shape @xmath13 . the number of overlined parts of a plane overpartition @xmath5 is denoted by @xmath41 . for example , @xmath42 is a plane overpartition of shape @xmath43 , with @xmath44 and @xmath45 . [ t1 ] let @xmath13 be a partition . the weighted generating function for plane overpartitions of shape @xmath13 is @xmath46 we prove this theorem using using a correspondence between plane overpartitions and sets of nonintersecting paths that use three kinds of steps . ( the work of brenti used similar paths to compute super schur functions @xcite . ) another way to prove this result is to show that plane overpartitions of shape @xmath13 are in bijection with super semistandard tableaux of shape @xmath13 . this is presented in a remark in section [ nonint ] . we also give the weighted generating function formula for plane overpartitions `` bounded '' by @xmath13 , where by that we mean plane overpartitions such that the @xmath18 row of the plane overpartition is an overpartition that has at most @xmath47 parts and at least @xmath48 parts . let @xmath49 be the set of all such plane overpartitions . [ t2 ] let @xmath13 be a partition . the weighted generating function for plane overpartitions such that the @xmath18 row of the plane overpartition is an overpartition that has at most @xmath47 parts and at least @xmath48 parts is @xmath50 note that it is enough to assign weights to overlined ( or nonoverlined ) parts only because generating functions where overlined and nonoverlined parts are weighted by @xmath39 and @xmath51 , respectively , follow trivially from the above formulas . the number of nonintersecting paths is given by a determinantal formula ( lemma 1 of @xcite ) . this result was anticipated by lindstrm @xcite and karlin and mcgregor @xcite , but gessel and viennot were first to use it for enumerative purpose of various classes of plane partitions @xcite . applying the result and evaluating the determinants we obtain hook content formulas . we use a simple involution to show that the stanley hook content formula ( theorem 7.21.2 of @xcite ) follows from our formula . from the symmetric function point of view , these formulas are given by schur functions in a difference of two alphabets , as explained in section 3 . the end of section 3 is devoted to _ reverse _ plane overpartitions . a reverse plane partition of shape @xmath13 is a filling of cells of the ferrers diagram of @xmath13 with nonnegative integers that form a nondecreasing sequence along each row and each column . a reverse plane overpartition is a reverse plane partition where ( 1 ) only positive entries can be overlined , ( 2 ) in each row the last occurrence of an integer can be overlined or not and ( 3 ) in each column the first occurrence of a positive integer can be overlined or not and all others ( if positive ) are overlined . an example of a reverse plane overpartition is @xmath52 it was proved by gansner @xcite that the generating function for reverse plane partitions of a given shape @xmath13 is @xmath53 let @xmath54 be the set of all reverse plane overpartitions of shape @xmath13 . the generating function for reverse plane overpartitions is given by the following hook formula . let @xmath13 be a partition . the generating function for reverse plane overpartitions of shape @xmath13 is @xmath55 [ reverse ] we construct a bijection between reverse plane overpartitions of a given shape and sets of nonintersecting paths whose endpoints are not fixed . using results of @xcite we obtain a pfaffian formula for the generating function for reverse plane partitions of a given shape . subsequently , we evaluate the pfaffian and obtain a proof of the hook formula . when @xmath13 is the partition with @xmath30 parts equal to @xmath31 , this result is the generating function formula for plane overpartitions fitting in an @xmath29 , box namely theorem [ osnovna ] . in section 4 we make a connection between plane overpartitions and domino tilings . we give some basic properties of this correspondence , such as how a removal of a box or an overline changes the corresponding tiling . this correspondence connects a measure on strict plane partitions studied in @xcite to a measure on domino tilings . this connection was expected by similarities in correlation kernels , limit shapes and some other features of these measures , but the connection was not established before . in section 5 we propose a bijection between matrices and pairs of plane overpartitions based on ideas of berele and remmel @xcite . we give another stronger version of the shifted macmahon s formula , as we give a weighted generating function for plane overpartitions with bounded entries . let @xmath56 be the set of all plane overpartitions with the largest entry at most @xmath22 . [ boundedparts ] the weighted generating functions for plane overpartitions where the largest entry is at most @xmath22 is @xmath57 in section 6 we study interlacing sequences and cylindric partitions . we say that a sequence of partitions @xmath58 is _ interlacing _ if @xmath59 or @xmath60 is a horizontal strip , i.e. a skew shape having at most one cell in each column . let @xmath61 be a sequence of 0 s and 1 s . we say that an interlacing sequence @xmath58 has _ profile _ @xmath62 if when @xmath63 , respectively @xmath64 , then @xmath59 , respectively @xmath65 is a horizontal strip . interlacing sequences are generalizations of plane partitions . indeed plane partitions are interlacing sequences with profile @xmath66 . [ htp ! ] we now define the _ diagram _ of an interlacing sequence . see figure [ fig1 ] . we start with a square grid ; we denote the two directions defined by the grid lines with 0 and 1 . a profile @xmath61 is represented by a path of length @xmath67 on this grid where the path consists of grid edges whose directions are given by @xmath68 . this path forms the ( upper ) border of the diagram . excluding the endpoints of the path we draw the diagonal rays ( which form @xmath69 angles with grid lines ) starting at the vertices of the path and we index them ( from left to right ) with integers from @xmath38 to @xmath70 . a diagram is a connected subset of boxes of a square grid whose ( upper ) border is given by the profile path and along the @xmath18 diagonal ray there are @xmath71 boxes . the filling numbers on the @xmath18 diagonal ray are parts of @xmath72 with the largest part at the top . observe that by the definition of interlacing sequences we obtain monotone sequences of numbers in the direction of grid lines . a ( skew ) plane partition and cylindric partition are examples of interlacing sequences . a plane partition can be written as @xmath73 with profile @xmath74 and @xmath72s are diagonals of the plane partition . a skew plane partition is an interlacing sequence @xmath75 with a profile @xmath76 . a cylindric partition is an interlacing sequence @xmath77 where @xmath78 , and @xmath70 is called the period of @xmath79 . a cylindric partition can be represented by the _ cylindric diagram _ that is obtained from the ordinary diagram by identification of the first and last diagonal . a _ connected component _ of an interlacing sequence @xmath79 is the set of rookwise connected boxes of its diagram that are filled with a same number . we denote the number of connected components of @xmath79 with @xmath80 . for the example from figure [ fig1 ] we have @xmath81 and its connected components are shown in figure [ fig1 ] ( bold lines represent boundaries of these components ) . if a box @xmath6 belongs to a connected component @xmath7 then we define its _ level _ @xmath82 as the smallest positive integer such that @xmath83 does not belong to @xmath7 . in other words , a level represents the distance from the `` rim '' , distance being measured diagonally . a _ border component _ is a rookwise connected subset of a connected component where all boxes have the same level . we also say that this border component is of this level . for the example from figure [ fig1 ] , border components and their levels are shown in figure [ fig2 ] ( different levels are represented by different colors ) . [ htp ! ] let @xmath84 be a sequence of nonnegative integers where @xmath85 is the number of @xmath10level border components of @xmath79 . we set @xmath86 for the example above @xmath87 . for a cylindric partition @xmath5 , we define _ cylindric connected components _ and _ cylindric border components _ in the same way but connectedness is understood on the cylinder , i.e. boxes are connected if they are rookwise connected in the cylindric diagram . we define @xmath88 where @xmath89 is the number of cylindric border components of level @xmath10 . in section 6 we give a generating function formula for skew plane partitions . let @xmath90 be the set of all skew plane partitions @xmath91 with profile @xmath92 , where @xmath93 and @xmath94 . ( generalized macmahon s formula for skew plane partitions ; hall - littlewood case ) @xmath95 [ skew ] note that as profiles are words in @xmath96 , a profile @xmath97 encodes the border of a ferrers diagram @xmath13 . skew plane partitions of profile @xmath62 are in one to one correspondence with reverse plane partitions of shape @xmath13 . moreover , one can check that @xmath98 therefore the theorem of gansner ( equation ) is theorem [ skew ] with @xmath99 and our theorem [ reverse ] on reverse plane overpartitions is theorem [ skew ] with @xmath37 . this theorem is also a generalization of results of vuleti @xcite . in @xcite a 2parameter generalization of macmahon s formula related to macdonald symmetric functions was given and the formula is especially simple in the hall - littlewood case . in the hall - littlewood case , this is a generating function formula for plane partitions weighted by @xmath100 . theorem [ skew ] can be naturally generalized to the macdonald case , but we do not pursue this here . let @xmath101 be the set of all cylindric partitions with period @xmath70 and profile @xmath102 . the main result of section 6 is : ( generalized macmahon s formula for cylindric partitions ; hall - littlewood case)[uvodcyl ] @xmath103 where @xmath104 is the smallest positive integer such that @xmath105 . the case @xmath99 is due to borodin and represents a generating function formula for cylindric partitions . cylindric partitions were introduced and enumerated by gessel and krattenthaler @xcite . the result of borodin could be also proven using theorem 5 of @xcite and the @xmath106-extension of bailey s @xmath107 summation due to gustafson ( equation ( 7.9 ) in @xcite ) @xcite . again theorem [ uvodcyl ] can be naturally generalized to the macdonald case . the trace generating function of those cylindric partitions could also be easily derived from our proof , as done by okada @xcite for the reverse plane partitions case . + the paper is organized as follows . in section 2 we give a mostly combinatorial proof of the generalized macmahon formula . in section 3 we use nonintersecting paths and obtain the hook length formulas for plane overpartitions and reverse plane partitions of a given shape . in section 4 we make the connection between tilings and plane overpartitions . in section 5 we construct a bijection between matrices and pairs of plane overpartitions and obtain a generating function formula for plane overpartitions with bounded part size . in section 6 we give the hook formula for reverse plane partitions contained in a given shape and the 1parameter generalization of the generating function formula for cylindric partitions . section 7 contains some concluding remarks . + * acknowledgment . * the authors want to thank alexei borodin , the advisor of the third author , for help and guidance and cdric boutillier , dominique gouyou - beauchamps , richard kenyon and jeremy lovejoy for useful discussions . the authors also want to thank one of the anonymous referee for his long list of constructive comments .

generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths , rsk type algorithms and symmetric functions . we extend some of the generating functions to cylindric partitions . also , we show that plane overpartitions correspond to certain domino tilings and we give some basic properties of this correspondence .

generating functions for plane overpartitions are obtained using various methods such as nonintersecting paths , rsk type algorithms and symmetric functions . we extend some of the generating functions to cylindric partitions . also , we show that plane overpartitions correspond to certain domino tilings and we give some basic properties of this correspondence .

1005.1675

c

all of the evidence presented in this paper points to grb 090417b being a dark burst because of localized extinction in the host galaxy . the host galaxy has a redshift of @xmath39 , and is clearly seen at optical and ultraviolet wavelengths . therefore lyman-@xmath11 absorption can not account for the missing optical afterglow . the @xmath1-ray light curve and spectrum during the first @xmath304 ks obey the conventional closure relationships and are consistent with synchrotron radiation from a relativistic fireball expanding into an external medium ( although the structure of that medium can not be determined with the available data ) . optical afterglows have been detected for many grbs with similar @xmath1-ray properties , so it unlikely that the lack of an optical detection is due to unusual physics during the afterglow phase of the burst . optical observations of grb 090417b started 378 s after the bat trigger , and follow - up observations were made from several observatories for several days after the burst . these observations went deep enough to have detected an optical afterglow if one had been present with a luminosity similar to that of other optical afterglows . therefore , the dark nature of grb 090417b can not be explained by a lack of observations . the dust hypothesis , however , can explain this dark burst . the @xmath1-ray spectrum is consistent with an column density of @xmath305 @xmath47 , which corresponds to an extinction of @xmath162 mag along the line of site in the host galaxy , assuming a milky way extinction law as explained in [ section : xrt_data ] . this value is in agreement with the minimum extinction , as explained in [ section : dark ] , that is needed to obscure the expected bright optical afterglow ( @xmath306 mag ) . an extremely high extinction ( @xmath30740 mag ) is also predicted by the dust scattering model , which is consistent with the @xmath1-ray data . such a large amount of dust along the line of sight to the grb naturally explains the lack of any detection at ultraviolet , optical , or near - infrared wavelengths while allowing a conventional @xmath1-ray afterglow to be observed . it is also consistent with the result of @xcite who found large mean extinctions for the putative host galaxies of several grbs . our result , that the extinction along the line of sight in the host grb 090417b is likely to be at least ten magnitudes in the uvot @xmath106 band , provides strong evidence that local dust concentrations in the host galaxy are responsible for at least some low - redshift dark bursts . unlike many grb host galaxies the dust in the host galaxy of grb 090417b appears to follow a milky way extinction law . in addition the host appears to be an @xmath227 galaxy with a star - formation rate that exceed @xmath308 @xmath309 yr@xmath30 . in other words , the host appears to have dust properties , and a luminosity that are similar to those of the milky way , and a star - formation rate that is consistent with what is seen in other grb host galaxies . grb 090417b is one of the few dark grbs where the association with a host galaxy is secure . in most cases associations between a grb and a galaxy have been made based on the probability of the nearest observed galaxy lying as close to the centre of the @xmath1-ray error circle as it does . there are a few exceptions , such as grb 000210 , grb 050713a and xrf 050416a . the host galaxy of grb 000210 was identified from the locations of its radio and @xmath1-ray afterglow . @xcite found a probability of a chance alignment of the galaxy and the burst of @xmath310 and conclude that if this is the host then the dark nature of grb 000210 is likely due to dust either at the location of the progenitor or along the line of sight . xrf 050416a occurred at a low redshift ( @xmath311 @xcite ) . although technically dark an optical afterglow was detected and was consistent with the standard fireball model ( e.g. , * ? ? ? * ; * ? ? ? the presence of an optical afterglow and the low line - of - sight extinction suggests that this burst should not be considered to be a dark grb . the line - of - sight extinction for xrf 050416a is @xmath23 mag @xcite , which is consistent with what is seen for most optically detected grb afterglows . @xcite note that grb 050713a also only barely qualifies as a dark burst under the @xcite definition . the internal line - of - sight extinction for this burst is unknown . however , an optical afterglow was seen @xcite , so it is unlikely that the extinction was large . the latter two of these bursts are technically dark based on the spectral slope between the @xmath1-ray and optical regimes ( @xmath15 ) criteria of @xcite . however , in these cases optical or infrared afterglows were detected , suggesting that these grbs were borderline cases of dark bursts . further evidence that dust is responsible for grb 090417b being dark comes from the late - time softening of the @xmath1-ray spectrum . this softening is consistent with what is predicted from the dust scattering model @xcite , and requires approximately 1540 mag of extinction at optical wavelengths . the effects of dust scattering do not become apparent in the @xmath1-ray spectrum until @xmath312 s after the burst . since @xmath1-ray spectra are usually extracted from early - time data ( when there are a large number of photons ) it is possible that the softening seen for grb 090417b has been present in the late - time @xmath1-ray spectra of other dark bursts , but has not been seen due to low count rates . for example , the standard catalogue of _ swift_/xrt spectral fits @xcite uses data taken within @xmath313 ks of the bat trigger , well before a softening due to dust scattering is expected to appear . @xcite point out that the host galaxies of dark grbs are not unusually reddened relative to the hosts of optically bright grbs . their analysis assumes that their statistical association of bursts with the nearest detected galaxy on the sky reveals the true hosts of these bursts . it is uncertain if this is valid for all of the grbs in their sample . however , it is likely that at least some ( if not all ) of these galaxies actually did host the associated grbs . although some of the hosts of dark grbs have been found to be unusually dusty compared to the hosts of optically - bright grbs ( e.g. , grb 030115 @xcite ) , there is no evidence that the hosts of dark grbs have systematically higher mean extinctions than the hosts of optically bright grbs . however , the mean extinction of the host is probably not the factor that determines if a particular burst is dark or not since any extinction due to material that is not along the line of sight to the burst will not affect our observations of the afterglow . what is important in making a burst optically dark or bright is the extinction along the line of sight . this extinction can be due to dust at the location of the grb , although it has been suggested that the ultraviolet and @xmath1-ray emission from grbs can destroy circumburst dust out to a few tens of pc from the progenitor @xcite . one way to get a dusty environment around a grb progenitor is the stellar wind from a wolf - rayet progenitor . collisions between wind - driven shells of material ejected during various stages of the wolf - rayet star s evolution can trigger the formation of large amounts of dust ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the radius of a wolf - rayet wind bubble is consistent with with the distance from the progenitor that we find for the dust along the line of sight to grb 090417b ( tens of pc ) . alternately , the extinction could be due to unrelated dust in the host that just happens to lie along the line of sight , such as a dusty star - forming region or a giant molecular cloud . giant molecular clouds have diameters of approximately 100 pc @xcite , but often contain dense cores where star formation occurs . a chance alignment of one of these cores along the line of sight to grb 090417b could account for the high extinction inferred from the x - ray data . for grb 090417b the late - time evolution of the @xmath1-ray spectrum can be explained if there is a sheet of dust at a distance of @xmath314 pc from the burst . this suggests that grb 090417b may have been dark because of either a dusty environment within 3080 pc of the progenitor ( e.g. * ? ? ? * ; * ? ? ? * ) , or a chance alignment of the progenitor with a region of high extinction in the host galaxy . the galactic extinction model of @xcite suggests that roughly 25% of the sight lines through the milky way have @xmath315 mag . the modelling of @xcite suggests that most sightline through a galaxy like the milky way , as seen from within the galaxy , have @xmath316 mag . however , their work does not include clumpiness in the dust distribution , which would lead to a larger fraction of sightlines having higher extinctions . this suggests that a non - negligible ( albeit uncertain ) fraction of grbs may be located along a sightline with more than approximately one magnitude of extinction in their hosts . when high - redshift dark bursts are accounted for the fraction of dark bursts is roughly comparable of the estimated fraction of highly extincted sightlines , which suggests that obscuration by dust along the line of sight may be responsible for some dark grbs .

this is one of the few cases where a host galaxy has been clearly identified for a dark gamma - ray burst and thus an ideal candidate for studying the origin of dark bursts . our results suggest that this dust sheet imparts an extinction of mag , which is sufficient to explain the missing optical flux . grb 090417b is an example of a gamma - ray burst that is dark due to the localized dust structure in its host galaxy .

grb 090417b was an unusually long burst with a duration of at least 2130 s and a multi - peaked light curve at energies of 15150 kev . it was optically dark and has been associated with a bright star - forming galaxy at a redshift of 0.345 that is broadly similar to the milky way . this is one of the few cases where a host galaxy has been clearly identified for a dark gamma - ray burst and thus an ideal candidate for studying the origin of dark bursts . we find that the dark nature of grb 090417b can not be explained by high redshift , incomplete observations , or unusual physics in the production of the afterglow . assuming the standard relativistic fireball model for the afterglow we find that the optical flux is at least 2.5 mag fainter than predicted by the-ray flux . the _ swift_/xrt-ray data are consistent with the afterglow being obscured by a dense , localized sheet of dust approximately 3080 pc from the burst along the line of sight . our results suggest that this dust sheet imparts an extinction of mag , which is sufficient to explain the missing optical flux . grb 090417b is an example of a gamma - ray burst that is dark due to the localized dust structure in its host galaxy .

1308.3807

i

a common bifurcation to instability , one that occurs in so - called natural hamiltonian systems that have hamiltonians composed of the sum of kinetic and potential energy terms , happens when under a parameter change the potential energy function changes from positive to negative curvature . in such a bifurcation , pairs of pure imaginary eigenvalues corresponding to real oscillation frequencies collide at zero and transition to pure imaginary , corresponding to growth and decay . this behavior , which can occur in general hamiltonian systems and is termed the steady state ( ss ) bifurcation , is depicted in the complex frequency @xmath0 plane in fig . alternatively , the hamiltonian hopf ( hh ) bifurcation is the generic bifurcation that occurs in hamiltonian systems when pairs of nonzero eigenvalues collide in the so - called kren collision @xcite between eigenmodes of positive and negative signature , as depicted in fig . [ hbif]b . such bifurcations occur in a variety of mechanical systems @xcite ; however , hh bifurcations also occur in infinite - dimensional systems with discrete spectra . in fact , one of the earliest such bifurcations was identified in the field of plasma physics @xcite for streaming instabilities , where signature was associated with the sign of the dielectric energy , and this idea made its way into fluid mechanics @xcite . streaming instabilities were interpreted in the noncanonical hamiltonian context in @xcite , where signature was related to the sign of the oscillation energy in the stable hamiltonian normal form @xcite ( see [ stabnf ] below ) . the purpose of this chapter and its companion @xcite is to describe hamiltonian bifurcations in the noncanonical hamiltonian formalism ( see @xcite ) , which is the natural form for a large class of matter models including those that describe fluids and plasmas . particular emphasis is on the continuum hamiltonian hopf ( chh ) bifurcation , which is terminology we introduce for particular bifurcations that arise in hamiltonian systems when there exists a continuous spectrum . there also exist a continuum steady state ( css ) bifurcation , but this will only be mentioned in passing . a difficulty presents itself when attempting to generalize kren s theorem , which states that a necessary condition for the bifurcation to instability is that the colliding eigenvalues of the hh bifurcation have opposite signature , to systems with continuous spectra . this difficult arises because ` eigenfunctions ' associated with the continuous spectrum are not normalizable , in the usual sense , and consequently obstacles have to be overcome to define signature for the continuous spectrum . this was done first in the context of the vlasov equation in @xcite and for fluid shear flow in @xcite . given this definition of signature , it become possible in @xcite to define the chh , a meaningful generalization of the hh bifurcation . in the present chapter we motivate and explore aspects of the chh , which are picked up in our companion chapter @xcite . to this end we describe in secs . [ sec : discrete ] and [ sec : theories ] large classes of hamiltonian systems that possess discrete and continuous spectra when linearized about equilibria . these classes are noncanonically hamiltonian , as is the case in general for matter models in terms eulerian variables . for a general field variable @xmath1 that represents the state of such a system , a noncanonical hamiltonian dynamical system has the form _ t=\ { , h}= , where @xmath2 $ ] is the hamiltonian functional and @xmath3 the poisson bracket defined by \{f , g}=d [ ] . [ genpb ] in general one may consider a @xmath4 multicomponent theory , i.e. , @xmath5 , with @xmath6 being an operator that makes ( [ genpb ] ) a lie algebra realization on functionals ( observables ) . because the operator @xmath6 need not have the canonical form , may depend on @xmath1 , and may possess degeneracy this structure was referred to in @xcite as noncanonical . because of the degeneracy , the poisson bracket of ( [ genpb ] ) possesses casimir invariants @xmath7 $ ] that satisfy \{c , f}0 f. we refer the reader to @xcite for further details . in sec . [ sec : discrete ] we consider a class of 1 + 1 multi - fluid theories , that possess discrete spectra when linearized about homogeneous equilibria . the linearization procedure along with techniques for canonization and diagonalization , i.e. , transformation to conventional canonical form and transformation to the stable normal form , respectively , are developed . then , specific examples are considered that display both ss and hh bifurcations . in sec . [ sec : theories ] we consider a class of 2 + 1 theories . the class is described and the chh bifurcation for the particular case of the vlasov - poisson system is discussed . relationship to the results of sec . [ sec : discrete ] is shown by introducing the waterbag model , which is one way of discretizing the continuous spectrum , and motivates our definition of the chh bifurcation . finally , in sec . [ sec : conclu1 ] , we summarize and introduce the material that will be treated in @xcite .

hamiltonian bifurcations in the context of noncanonical hamiltonian matter models are described . first , a large class of 1 + 1 hamiltonian multi - fluid models is considered . next , using these 1 + 1 examples as a guide , a large class of 2 + 1 hamiltonian systems is introduced , and hamiltonian bifurcations with continuous spectra are examined . it is shown how to attach a signature to such continuous spectra , which facilitates the description of the continuous hamiltonian hopf bifurcation . this chapter lays the groundwork for kren - like theorems associated with the chh bifurcation that are more rigorously discussed in our companion chapter .

hamiltonian bifurcations in the context of noncanonical hamiltonian matter models are described . first , a large class of 1 + 1 hamiltonian multi - fluid models is considered . these models have linear dynamics with discrete spectra , when linearized about homogeneous equilibria , and these spectra have counterparts to the steady state and hamiltonian hopf bifurcations when equilibrium parameters are varied . examples of fluid sound waves and plasma and gravitational streaming are treated in detail . next , using these 1 + 1 examples as a guide , a large class of 2 + 1 hamiltonian systems is introduced , and hamiltonian bifurcations with continuous spectra are examined . it is shown how to attach a signature to such continuous spectra , which facilitates the description of the continuous hamiltonian hopf bifurcation . this chapter lays the groundwork for kren - like theorems associated with the chh bifurcation that are more rigorously discussed in our companion chapter .

1311.1711

i

high resolution imaging , in particular in biology and materials science , is mostly done using scanning electron microscopy ( sem ) . the ease of use and the widespread availability has made this the number one method for imaging in the aforementioned fields . structuring and manipulation of nano sized features is traditionally the domain of focused ion beams . here , mainly liquid metal ion sources ( lmis ) using gallium are used however , other techniques such as various types of gfis,@xcite alloy lmis,@xcite magneto optical trap sources ( motis)@xcite and multicusp plasma sources@xcite are runners up . good reviews discussing these two techniques can be found in refs . [ ] and [ ] for sem and fib , respectively . helium ion microscopy presents a technique that unites many of the advantages of sem and fib in a single tool . more importantly , it also overcomes some of the deficiencies of sem and fib . in particular , the possibility to image biological and in general insulating samples without coating at highest resolution is important for many scientific questions currently discussed in materials science and biology . another important charged particle beam technique namely transmission electron microscopy ( tem)depends on very thin samples free of defects from the preparation . the unique nano sized beam of the him makes it possible to not only mill and pattern smallest features but also do this with minimal damage to the crystal lattice . in the following we will give an outline of the working principle and signal generation in helium ion microscopy , followed by two sections highlighting specific imaging applications and examples of materials modification . the initial idea of a scanning ion microscope has been put forward by knoll and ruska already in 1932.@xcite the working principle of a helium ion microscope can be divided into three different stages . 1 . helium ionization and acceleration 2 . beam formation and control 3 . sample interaction in this introduction we will only briefly touch points 1 and 2 . instead , we will focus on the physics that is important to understand the application of the technique to imaging and nanofabrication . the first is made possible by using a newly developed gas field ion source ( gfis ) . gfis have been investigated for a long time@xcite for their use in microscopes.@xcite the idea is based on the initial design of a field ion microscope by e. mller.@xcite however , only recently a stable ion source with a high brightness and small virtual source size has been realized by ward , notte and economou for use in a microscope.@xcite it is based on an emitter whose apex has been shaped into a three sided pyramid ( see fig . [ fig : him - source ] ) . work is done currently to understand and optimize the supertip formation process in order to maximise the achievable current.@xcite using scanning field ion microscopy ( sfim ) the apex of the tip can be monitored and shaped using high fields that can ultimately remove weakly bound atoms from the apex . in this way the configuration of the tip apex can be controlled at the atomic level . although monomers are possible , trimers are more stable . figure [ fig : him - source](b ) shows a sfim image of the tip . the trimer in the center and the edge of the first two shelves below the trimer are visible . the combination of a pyramidally shaped tip and the carefully shaped apex concentrates the electric field , so that subsequent helium ionization predominantly happens at the top most atoms of the pyramid . using apertures in the beam path allows to select current originating from ionization events on a single apex atom . typical source parameters are listed in table [ tab : column - param ] . .typical helium ion source parameters@xcite [ cols="<,^ , < " , ] the second point is technologically demanding and requires a high degree of knowledge on the design and implementation of the involved electrostatic lenses , quadrupoles , octopoles , etc . for more details the reader is refereed to numerous monographs available on charged particle optics such as [ ] . the critical source parameters important for the ion optical performance of the column are given in table [ tab : column - param ] . the energy spread of 1ev is an upper bound . earlier measurements indicate that the values could in fact be lower by a factor of two to four.@xcite one of the important consequences of the parameters listed in table [ tab : column - param ] is the image side beam convergence angle @xmath0 . typical values for @xmath0 are well below 1mrad . this small beam divergence results in a large depth of field @xmath1 here , @xmath2 denotes the minimum feature that can be resolved in the image . assuming identical resolutions the him will have a superior depth of field as compared to low voltage sem with typical @xmath0 values of 8mrad.@xcite once the focused ion beam strikes the sample , the interaction of the accelerated particles with the substrate atoms and electrons will give rise to a large number of different signals . we will cover the available signals in the following section . before we do so , we will briefly discuss the processes that occur during ion / sample interaction and that are important for the achievable resolution in charged particle beam imaging . besides the small beam diameter , the shape and size of the actual interaction volume between the impinging particle and the sample plays an important role to reach ultimate resolution . figure [ fig : charged - part - beams ] compares monte carlo ( mc ) simulation results for different charged particle beams . from the figure it is evident that the interaction volume relevant for secondary electron ( se ) generation of the focused he beam is smaller than for the other two.@xcite for the case of a ga beam the large cross section of ga with in this case si leads to substantial scattering in the near surface region relevant for the se signal generation . for a low energy electron beam needed to simultaneously optimize resolution and surface sensitivity in sem electron electron scattering in the sample widens the beam dramatically in the first few nanometers deteriorating the achievable resolution . scattering also occurs in him . in the case of a 30kev he beam scattering occurs with the nuclei of the sample atoms . however , due to the low mass of helium , scattering is not very efficient in the first few nanometers of sample material . this results in minimal beam divergence inside the sample . consequently the collected se originate from a cylinder with a minimal volume . the somewhat lower energy of the se in him@xcite and the lower characteristic escape depth for se in him for light elements@xcite enhances this difference between sem and him even further . next we will discuss available particles and correoponding signals . we will in particular highlight their benefits and drawbacks when used for imaging and what kind of physical quantities can be accessed using them . the sequence in which they are discussed is determined by their abundance in the tool . this also corresponds to the ease of use and how widespread the technique is available in the current instrument base . an initial overview of some of the different contrast mechanisms is given by bell.@xcite secondary electron ( se ) emission generated by ions can be split into two parts . in the logical order we will first discuss se generation followed by the transport of electrons through the material . the latter is important as the generated electrons still need to reach and subsequently leave the surface into the vacuum so they can be detected . as has been proposed by bethe@xcite the rate of secondary electron generation @xmath3 ( electrons per incoming ion ) is proportional to the stopping power of the incident particle @xmath4 in ev / . @xmath5 here , @xmath6 denotes a scaling constant . it is assumed that at least in the relevant near surface region , atomic collisions do not play an important role and @xmath4 depends only on the electronic stopping power . the generated se1 are mostly excited by the incoming ions via kinetic emission ( ke).@xcite two types of secondary electrons of type 2 ( se2 ) exist in ion beam imaging . type 2 electrons can be generated either by recoiling target atoms or from other ses of type 1 . the second type of se2 generation ( se generated by se ) does not play an important role in him . this becomes clear when looking at the maximum energy of the se , which is taken to be equal to the energy loss of the impinging he for a head on collision@xcite @xmath7 here , @xmath8 is the electron mass , @xmath9 the ion velocity , and @xmath10 denotes the fermi velocity . the cross section for such a collision is highest if the ion velocity@xmath11 m/s for a primary energy of 35kev matches the fermi velocity of the electrons in the material . for gold and 35kev he this yields a maximum se energy of 45ev . however , this energy is approximately equal to or even below the effective energy needed for se generation by electrons in many materials.@xcite thus the size of the electron electron collision cascade is restricted . however , kinetic excitation of electrons is also possible by recoil atoms , provided they are fast enough so that their speed still matches the fermi velocity of the target material . electrons produced by recoiling target atoms are usually called se2 . ramachandra et al.@xcite calculated the ratio between se2 and se1 as function of energy and material . the conclusion that can be drawn from their calculation is that for higher primary energies a smaller se2/se1 ratio can be achieved for most materials and consequently a higher resolution is possible . the other process for electron emission is potential emission ( pe ) via auger neutralization . however , only for very low energies below 5kev pe becomes dominant@xcite over ke . once secondary electrons have been generated they still need to escape from the solid . this process can be described as a diffusion process . the characteristic length scale of this diffusion process the effective diffusion length of secondary electrons @xmath12is of the order of 1 nm for nearly all materials.@xcite this leads to the fact that only the first few nanometers of the material add to the emitted ses . measurements of the effective se yield in him show variations between 1 for carbon and values as high as 8 for platinum.@xcite the number and energy distribution of these ion induced secondary electrons differs from what is found in a sem . a sharper maximum at lower energies is usually found@xcite in him . in fig . [ fig : se - yield](a ) a comparison of calculated se yields in sem , ga fib and him is presented . the calculations done by ohya et al . still overestimate peak position as well as peak width.@xcite these differences between actual measurement results of se yields in a him and calculations are attributed to se generation mechanisms not considered in the calculations . indications exist that bulk plasmon excitations can play an important role@xcite for se generation in him . an actual measurement of se yield as a function of se energy and the work function dependence of the distribution maximum is presented in fig . [ fig : se - yield](b ) . . ( b ) experimentally obtained se yield for three different metals . the dependence of the peak position on work function is shown as an inset . reproduced with permission from proc . spie , vol . 8036 , 80360o-180360o-10 ( @xcite ) . copyright ( 2011 ) spie . ] a consequence of the particular energy distribution of se in him and the small se generation volume is an enhanced surface sensitivity . this has been shown in a recent comparative study of him and sem imaging performance on carbon coated gold nano rods.@xcite only at very low acceleration voltages is sem able to visualize the thin carbon layer covering the gold particles . however , low voltage sem suffers from carbon deposition in the imaged area making detailed studies challenging . an example of the high sensitivity of him with respect to the material work function is the visualization of different half unit cell surface termination in ti@xmath13sic@xmath14.@xcite depending on the position of the cleavage plane the surface is either terminated by si ( half unit cell ) or ti ( full unit cell ) . the difference in the chemistry of the top surface layer of atoms results in different se yields for the two terminations . as a result they can be discriminated in him . a software package called _ ionise _ developed by p. rack and coworkers is available that allows the calculation of the expected se yield for a large number of materials.@xcite although good agreement has been achieved between simulation and experiment , only a limited number of analytical applications based on se yield are known.@xcite sample topography in him is made visible in a similar way as in sem . the dependence of the se yield on the specimen tilt with respect to the incoming beam can be described the following secant law @xmath15 however , experimental studies showed that the actually measured se yield at the detector deviates from the expected secant behaviour.@xcite the deviations lead to a more linear response curve , which in turn should reduce the strong edge effect known from sem . nevertheless , a very strong edge effect has been observed in thin layers.@xcite in summary , the achievable high resolution and surface sensitivity in him is based on the fact that the ses originate from a cylinder at the beam penetration point with a diameter of approximately 1nm given by the beam diameter and a length of less than 3nm determined by @xmath12 . this small probe volume helps to achieve very high image resolution in him . it should be noted that obtaining such high resolution images has become substantially easier since the introduction of uhv him.@xcite at small fields of views usually high fluences are reached as a consequence of the large pixel density . in an uhv him implantation and sputtering can still negatively affect the sample during imaging . carbon deposition on the other hand can be excluded.@xcite the removal of hydrocarbons from the sample chamber vacuum prevents the formation of carbon deposits in the imaged area . as a consequence some exceptional imaging results could be achieved ( see fig . [ fig : bio](b ) ) . what backscattered electrons are to the sem , backscattered helium ( bshe ) atoms and ions are to him . this rather bold statement is true in several ways , as will be highlighted in the next paragraphs . two different ways to utilize bshe are available in current him . first , and most commonly used , is a microchannel plate ( mcp ) detector to acquire qualitative element distribution maps . second , a silicon drift detector can be used to obtain spectroscopic information from microscopic areas . the latter allows quantitative element identification based on the same principles as rutherford backscattering spectroscopy ( rbs ) . while se images usually are rich in morphological contrast , bshe images obtained with the mcp are poor in topography and rich in elemental contrast . in contrast to the se images , the information in these images originates from the bulk of the sample . to measure them the mcp is inserted below the pole piece in the primary beam path . while a center hole allows the primary beam to reach the sample , this geometry maximizes the solid angle , and thus the collection efficiency of the detector . the obtained contrast can be understood by examining the rutherford scattering cross section @xmath16 where @xmath17 is the elementary charge , and @xmath18 and @xmath19 denote the atomic number of impinging and target particle , respectively . assuming that the target atom is at rest , @xmath20 is the energy of the impinging particle , @xmath21 is an arbitrary element of solid angle , and @xmath22 is the scattering angle . for fixed @xmath18helium for this review and a given energy , a dependence on @xmath23 leads to a strong contrast between different elements . a more detailed analysis of the scattering cross section shows that a dependence that is related to the structure of the periodic table of elements also exists . this is a result of the change in screening along the rows of the periodic table . in fig . [ fig : bshe - yield ] , experimentally obtained bshe yields for various elements are presented . . the row structure of the periodic table can clearly be seen on top of a general increase in bshe yield for heavy elements . data courtesy of carl zeiss ag . ] the dependence of the yield on the structure of the periodic table is clearly present . at this point it is important to realize that a high sensitivity is needed from the detector that is used . under standard imaging conditions in him , typically 500 or less ions are used per pixel . assuming a high backscatter yield of 20% and taking into account the detector solid angle , no more than 50 ions will reach the detector . a large fraction of these backscattered he particles are also neutral@xcite due a charge transfer process which occurs once they enter the sample . however , this would represent an ideal case for a heavy element bulk target . in practice these numbers can be substantially smaller and not a single ion should be lost in the detector.@xcite one should realize that contrary to the electrons discussed in the previous section , bshe represent a bulk signal . depending on the atomic number sampling depth , between a few tens of nanometers and a few hundred nanometers can be achieved . as can be seen from equ . ( [ equ : cross - section ] ) , the backscatter efficiency can be increased by lowering the acceleration voltage . as a side effect , this will also reduce the range of the helium and thus the sampling depth . in addition to the qualitative element distribution , also quantitative information on the elemental composition can be obtained . for a binary collision when momentum and energy are conserved the kinetic energy of the backscattered helium @xmath24 depends on the on the ratio of the masses of the impinging ( @xmath25 ) and target ( @xmath26 ) particle . measuring the energy loss at a fixed angle allows the mass of the collision partner , as well as its position relative to the sample surface , to be determined . at high kev or low mev energies this is known as rutherford backscatter spectroscopy ( rbs ) . this method is known to deliver high sensitivity and excellent depth - resolution . the nature of the involved square function makes the method very sensitive to differences between light elements . a silicon drift detector with a resolution of approximately 4kv can be used for this purpose . however , due to the relatively low primary energy of only 35kev , the measured peaks are not as well defined as in classical rbs . nevertheless , the nature of him allows such spectra from areas of only several m@xmath27 to be obtained.@xcite the technique has been successfully applied to measure zro@xmath14 layer thicknesses on si substrates with monolayer sensitivity@xcite and for thickness measurements of cobalt / nickel nano rings.@xcite the achievable resolution is not only limited by the detector . as a result of the already low primary energy , the backscattered particles have a high probability to undergo multiple scattering events . this occurs for the impinging , as well the backscattered helium particle . consequently , a statistical broadening of the exit energies of the bshe exists . it has been shown by simulations that even for an ideal combination , such as a 75 nm thick heavy hafnium oxide film on silicon , an intrinsic uncertainty of 14% exists for the depth resolution of hf . given the current detector resolution this value is further increased to 60%.@xcite compositional characterization will have even larger errors due to a severe peak overlap.@xcite figure [ fig : hfo ] presents an experimentally obtained spectrum from hafnium oxide . the simnra@xcite calculated fits to obtain elemental composition and layer thickness have been added for different real and ideal detector resolutions . an increase of detector resolution to 1kv would substantially improve the quality of the obtained spectra and consequently of the fit accuracy . these curves should be taken to be an indication of what could be possible and not an exact representation of the achievable resolution . one also needs to keep in mind that the majority of the backscattered particles are neutral,@xcite complicating any post scattering treatment . the yield of both signals secondary electrons as well as back scattered helium also depends on the crystalline orientation of the sample with respect to the beam . this allows for two additional contrast mechanisms in him . the well known channeling contrast@xcite can be exploited to obtain the crystal orientation of samples with a large lateral resolution.@xcite this technique makes use of calculations of the blocked area fraction , which yields results similar to stereographic projections of channeling minima or laue back reflection patterns . one of the surprising results is that despite the very small wavelength of he ions , scanning transmission ion microscopy ( stim ) is possible . both dark field and bright field images could be recorded in which thickness fringes and line defects could be identified.@xcite generally speaking , ionoluminescence ( il ) is a phenomenon of light emission due to the optical transitions of an electronic system which has been excited by ion irradiation . three main stages can be distinguished in the luminescence process:@xcite 1 . energy absorption and excitation of the electronic system ; 2 . system relaxation and energy transfer to the emission centers ; 3 . transition of the system into the ground state by photon emission . during sample bombardment with he@xmath28 ions , light can be obtained from the excited backscattered neutral he,@xcite excited sputtered atoms and molecular complexes,@xcite or from the sample material itself.@xcite for the case where emission originates from excited species which have left the sample , the spectrum consists of discrete doppler broadened lines . these lines corresponds to the optical transitions within atomic ( or molecular ) orbitals . this light is usually observed at a distance up to a few millimeters from the target surface.@xcite in the case of organic samples , ionoluminescence reveals the electronic structure of the organic compounds.@xcite for the investigation of material properties we are mainly interested in the luminescence from the sample itself . the physics of the emission processes is usually described by considering the sample s electronic band structure , or by using configuration coordinate diagrams.@xcite according to its origin , there are two general types of luminescence : _ extrinsic _ and _ intrinsic_.@xcite in the case of extrinsic luminescence , the light generation is related to the presence of impurity atoms or ions ( so called _ activators _ ) in the sample material . depending on their electronic structure , activators can be divided in the following groups : 1 . transition metal ions with d@xmath29 electronic configuration ( e.g. ti@xmath30 , cr@xmath30 , mn@xmath31 ) ; 2 . ions with s@xmath32-configuration ( e.g. tl@xmath28 , pb@xmath31 , sb@xmath30 ) ; 3 . earth elements ( ree@xmath33 ) ; 4 . actinides ( e.g. uo@xmath34 , cm@xmath30 ) . sometimes the presence of a certain impurity ( _ sensitizer _ ) is needed for the luminescence of an activator ( for example ce@xmath30 for activation of tb@xmath30 ions @xcite ) . as opposed to sensitizers , _ quenchers _ suppress light emission from an activator . for example , fe@xmath31 ions act as quenchers for emission from mn@xmath31 in apatite.@xcite at high activator concentrations self quenching may occur due to resonant absorption processes . intrinsic luminescence on the other hand , is emission from the sample material itself . two cases can be distinguished . first , optical transitions from delocalized states , or in other words the recombination of free electrons from the conduction band with holes in the valence band . this can include direct and indirect transitions . the radiative recombination of free excitons also falls in this category . second , optical transitions from localized states can also be attributed to intrinsic luminescence . this includes the following processes : recombination of excitons trapped at defect sites ( so called self trapped excitons@xcite ) , emission from excited defects known as color centers ( e.g. nitrogen vacancy centers in diamond@xcite ) , and transitions of charge carriers from delocalized into localized states . the shape and width of the emission peaks and bands strongly depends on electron phonon interactions and thermal effects . a strong electron phonon interaction leads to a stokes shift and peak broadening . as a result , it is desirable to perform ionoluminescence measurements at cryogenic temperatures , which has not been done to date in him . since ionoluminescence is in many aspects similar to the cathodoluminescence ( cl ) phenomenon often observed in scanning electron microscopy ( sem ) , databases of cl studies can be employed for the interpretation of il spectra . ionoluminescence studies are significantly complicated by the fact that an ion beam not only induces light emission , but also directly influences the optical properties of the target due to defect creation . ion irradiation can lead to target coloration ( e.g. in alkali halides@xcite ) and enhanced emission , but also quench the luminescence ( e.g. semiconductor materials@xcite ) . however , the use of him to observe il phenomena allows these processes to be followed in situ with a high lateral resolution .

helium ion microcopy ( him ) based on gas field ion sources ( gfis ) represents a new ultra high resolution microscopy and nano fabrication technique . it is an enabling technology that not only provides imagery of conducting as well as uncoated insulating nano structures but also allows to create these features . the latter can be achieved using resists or material removal due to sputtering .

helium ion microcopy ( him ) based on gas field ion sources ( gfis ) represents a new ultra high resolution microscopy and nano fabrication technique . it is an enabling technology that not only provides imagery of conducting as well as uncoated insulating nano structures but also allows to create these features . the latter can be achieved using resists or material removal due to sputtering . the close to free form sculpting of structures over several length scales has been made possible by the extension of the method to other gases such as neon . a brief introduction of the underlying physics as well as a broad review of the applicability of the method is presented in this review .

1311.1711

i

in the past half decade helium ion microscopy has proven to be an interesting alternative to its direct and well established competitors : scanning electron microscopy and gallium focused ion beam . however , the authors strongly believe , and hope to have demonstrated above , that him is more than a replacement for sem and fib . it excels over sem and fib in particular for * high resolution imaging of uncoated biological samples * imaging of insulating samples * a high surface sensitivity * imaging of ultra thin layers * materials modification with unprecedented resolution * direct write lithography * resist patterning at the same time new applications and techniques are constantly being developed and refined . in particular , analytical additions are needed and are currently being developed . while ionoluminescence has its special applications , additions such as secondary ion mass spectroscopy@xcite still need to prove their applicability in real materials science problems . however , although spectroscopy is currently still in its infancy , the extension of the technique to other gases such as neon , and potentially even heavier ones , guarantees an exciting future of the technique in particular for nano fabrication applications . 141ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1116/1.2101792 [ * * , ( ) ] link:\doibase 10.1016/j.ultramic.2004.11.020 [ * * , ( ) ] link:\doibase 10.1021/nl801472n [ * * , ( ) ] link:\doibase 10.1116/1.1526694 [ * * , ( ) ] @noop _ _ , ed . ( , , ) link:\doibase 10.1116/1.2955728 [ * * , ( ) ] link:\doibase 10.1007/bf01342199 [ * * , ( ) ] link:\doibase 10.1063/1.326679 [ * * , ( ) ] link:\doibase 10.1116/1.584328 [ * * , ( ) ] link:\doibase 10.1143/jjap.31.l291 [ * * , ( ) ] http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=432639&tool=pmcentrez&rendertype=abstract [ * * , ( ) ] link:\doibase 10.1116/1.568497 [ * * , ( ) ] link:\doibase 10.1016/0167 - 9317(85)90022-x [ * * , ( ) ] link:\doibase 10.1116/1.584014 [ * * , ( ) ] link:\doibase 10.1007/bf01329651 [ * * , ( ) ] link:\doibase 10.1016/0169 - 4332(95)00351 - 7 [ * * , ( ) ] link:\doibase 10.1116/1.2357967 [ * * , ( ) ] link:\doibase 10.1007/s00339 - 004 - 2869 - 6 [ * * , ( ) ] link:\doibase 10.1016/j.ultramic.2013.03.013 [ * * , ( ) ] link:\doibase 10.1016/j.ultramic.2012.07.026 [ * * , ( ) ] link:\doibase 10.1063/1.4726112 [ * * , ( ) ] link:\doibase 10.1063/1.3702209 [ * * , ( ) ] link:\doibase 10.1016/j.ultramic.2012.11.005 [ * * , ( ) ] link:\doibase 10.1007/978 - 1 - 4615 - 0765 - 9 [ _ _ ] ( , , ) link:\doibase 10.1007/978 - 3 - 540 - 85916 - 1 [ _ _ ] , , vol . ( , , ) link:\doibase 10.1016/0169 - 4332(93)90301-q [ * * , ( ) ] link:\doibase 10.1016/j.phpro.2008.07.088 [ * * , ( ) ] in link:\doibase 10.1063/1.2799423 [ _ _ ] , vol . , ( , ) pp . in link:\doibase 10.1117/12.886347 [ _ _ ] , vol . , ( , , ) pp . link:\doibase 10.1016/j.ultramic.2009.01.013 [ * * , ( ) ] link:\doibase 10.1017/s1431927609090138 [ * * , ( ) ] link:\doibase 10.1116/1.3258634 [ * * , ( ) ] link:\doibase 10.1103/physrev.59.913 [ * * , ( ) ] link:\doibase 10.1016/j.nimb.2007.12.058 [ * * , ( ) ] in link:\doibase 10.1007/978 - 1 - 4615 - 2840 - 1_4 [ _ _ ] , , ( , , ) pp . link:\doibase 10.1002/sia.2107 [ * * , ( ) ] link:\doibase 10.1103/physrevb.24.4412 [ * * , ( ) ] link:\doibase 10.1016/j.nimb.2008.11.003 [ * * , ( ) ] link:\doibase 10.1134/s1027451010050186 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.84.378 [ * * , ( ) ] link:\doibase 10.1016/j.ultramic.2013.07.010 [ * * , ( ) ] , link:\doibase 10.1016/j.scriptamat.2011.03.013 [ * * , ( ) ] link:\doibase 10.1166/jnn.2012.4260 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/24/33/335702 [ * * , ( ) ] link:\doibase 10.1017/s1431927611005514 [ * * , ( ) ] link:\doibase 10.3762/bjnano.3.57 [ * * , ( ) ] link:\doibase 10.1116/1.3502667 [ * * , ( ) ] link:\doibase 10.1116/1.3271254 [ * * , ( ) ] in @noop _ _ ( , , ) in link:\doibase 10.1063/1.59188 [ _ _ ] ( , ) pp . link:\doibase 10.1103/physreva.39.3836 [ * * , ( ) ] link:\doibase 10.1017/s1431927610093682 [ * * , ( ) ] in link:\doibase 10.1007/978 - 3 - 642 - 67112 - 8_5 [ _ _ ] ( , , ) chap . , pp . in link:\doibase 10.1007/978 - 3 - 540 - 87529 - 1_1 [ _ _ ] , , ( , , ) chap . , pp . link:\doibase 10.1016/0031 - 8914(73)90154 - 7 [ * * , ( ) ] link:\doibase 10.1103/physreva.12.876 [ * * , ( ) ] link:\doibase 10.1016/0029 - 554x(65)90154 - 0 [ * * , ( ) ] link:\doibase 10.1016/0029 - 554x(78)90916 - 3 [ * * , ( ) ] link:\doibase 10.1021/ac50009a001 [ * * , ( ) ] in link:\doibase 10.1007/978 - 1 - 4615 - 5361 - 8_5 [ _ _ ] , ( , ) pp . link:\doibase 10.1016/s0168 - 583x(97)00182 - 1 [ * * , ( ) ] in @noop _ _ , ( , , ) ed . , pp . link:\doibase 10.1149/1.2408364 [ * * , ( ) ] link:\doibase 10.1306/d4267ab9 - 2b26 - 11d7 - 8648000102c1865d [ * * , ( ) ] link:\doibase 10.1016/0022 - 3697(90)90144 - 5 [ * * , ( ) ] link:\doibase 10.1016/j.physrep.2013.02.001 [ * * , ( ) ] in link:\doibase 10.1007/bfb0104335 [ _ _ ] , , vol . , ( , , ) link:\doibase 10.1017/s1431927612013463 [ * * , ( ) ] link:\doibase 10.1088/0957 - 0233/22/2/024004 [ * * , ( ) ] link:\doibase 10.1002/sca.20267 [ * * , ( ) ] in http://www.microscopy.org/mandm/2010/jiang.pdf[__ ] ( , ) link:\doibase 10.1038/srep03514 [ * * , ( ) ] link:\doibase 10.1016/s0022 - 5320(67)80038 - 8 [ * * , ( ) ] link:\doibase 10.1016/j.microrel.2012.06.130 [ * * , ( ) ] link:\doibase 10.1016/j.surfcoat.2006.01.075 [ * * , ( ) ] link:\doibase 10.1016/j.nimb.2011.10.070 [ * * , ( ) ] link:\doibase 10.1143/jjap.37.l398 [ * * , ( ) ] link:\doibase 10.1063/1.1337646 [ * * , ( ) ] @noop ( ) link:\doibase 10.1103/physrevb.14.2583 [ * * , ( ) ] link:\doibase 10.1080/00337577908234484 [ * * , ( ) ] link:\doibase 10.1017/s1431927612005922 [ * * , ( ) ] link:\doibase 10.1016/j.nimb.2009.03.069 [ * * , ( ) ] link:\doibase 10.1016/s0168 - 583x(01)00465 - 7 [ * * , ( ) ] link:\doibase 10.1016/j.nimb.2012.12.052 [ * * , ( ) ] link:\doibase 10.1021/nn900744z [ * * , ( ) ] , in http://meetings.aps.org/link/baps.2010.mar.h21.7[__ ] , vol . ( , , ) link:\doibase 10.1021/nn401992q [ * * , ( ) ] link:\doibase 10.1021/nl801457b [ * * , ( ) ] http://www.worldcat.org/isbn/096542071 http://books.google.com/books?vid=isbn096542071 http://www.amazon.com/gp/search?keywords=096542071&index=books&linkcode=qs http://www.librarything.com/isbn/096542071 http://www.worldcat.org/oclc/191686602[__ ] ( , ) link:\doibase 10.1103/physrevlett.109.265505 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/22/17/175306 [ * * , ( ) ] link:\doibase 10.1063/1.4726053 [ * * , ( ) ] link:\doibase 10.1103/physrevb.81.153401 [ * * , ( ) ] link:\doibase 10.1016/j.progsurf.2012.05.001 [ * * , ( ) ] link:\doibase 10.1063/1.4792511 [ * * , ( ) ] link:\doibase 10.1021/nl202269n [ * * , ( ) ] link:\doibase 10.1002/app.1990.070391003 [ * * , ( ) ] link:\doibase 10.3762/bjnano.3.58 [ * * , ( ) ] link:\doibase 10.1021/la204437r [ * * , ( ) ] link:\doibase 10.1016/j.susc.2012.02.007 [ * * , ( ) ] link:\doibase 10.1209/0295 - 5075/85/46001 [ * * , ( ) ] link:\doibase 10.1093/oxfordjournals.jmicro.a023780 [ * * , ( ) ] link:\doibase 10.1002/sca.20268 [ * * , ( ) ] link:\doibase 10.1016/j.nima.2010.12.220 [ * * , ( ) ] link:\doibase 10.1017/s1551929512000715 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/24/17/175302 [ * * , ( ) ] link:\doibase 10.1116/1.568515 [ * * , ( ) ] link:\doibase 10.1002/sia.740010103 [ * * , ( ) ] link:\doibase 10.1016/0168 - 583x(93)90781-z [ * * , ( ) ] link:\doibase 10.1116/1.3250204 [ * * , ( ) ] in link:\doibase 10.1117/12.862438 [ _ _ ] , vol . , ( ) p. link:\doibase 10.1007/978 - 3 - 7091 - 0424 - 8 [ _ _ ] , edited by and ( , , ) pp . link:\doibase 10.1002/sca.21009 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/21/45/455302 [ * * , ( ) ] link:\doibase 10.1017/s1551929511000307 [ * * , ( ) ] in link:\doibase 10.1007/978 - 3 - 7091 - 0424 - 8_11 [ _ _ ] , ( , , ) pp . link:\doibase 10.1116/1.3237095 [ * * , ( ) ] link:\doibase 10.1116/1.4800983 [ * * , ( ) ] link:\doibase 10.1116/1.3517536 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/19/41/415704 [ * * , ( ) ] link:\doibase 10.1016/0168 - 583x(87)90004 - 8 [ * * , ( ) ] link:\doibase 10.1016/0370 - 1573(81)90106-x [ * * , ( ) ] and , eds . , link:\doibase 10.1007/978 - 3 - 540 - 44502 - 9 [ _ _ ] , , vol . ( , , ) link:\doibase 10.1088/0022 - 3727/46/19/195501 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/22/28/285310 [ * * , ( ) ] link:\doibase 10.1063/1.1947391 [ * * , ( ) ] link:\doibase 10.1038/35084037 [ * * , ( ) ] link:\doibase 10.3762/bjnano.4.53 [ * * , ( ) ] link:\doibase 10.3762/bjnano.3.67 [ * * , ( ) ] link:\doibase 10.1002/sca.21003 [ * * , ( ) ] link:\doibase 10.1116/1.3511509 [ * * , ( ) ] link:\doibase 10.1016/j.mee.2010.11.041 [ * * , ( ) ] link:\doibase 10.1016/j.carbon.2009.12.057 [ * * , ( ) ] link:\doibase 10.1088/0957 - 4484/23/39/395302 [ * * , ( ) ] link:\doibase 10.1116/1.3237101 [ * * , ( ) ] link:\doibase 10.1016/0001 - 6160(87)90034 - 4 [ * * , ( ) ] link:\doibase 10.1103/physrevb.38.1087 [ * * , ( ) ] link:\doibase 10.1063/1.4739240 [ * * , ( ) ] link:\doibase 10.1002/sca.20262 [ * * , ( ) ] link:\doibase 10.1016/j.nima.2010.12.123 [ * * , ( ) ]

the close to free form sculpting of structures over several length scales has been made possible by the extension of the method to other gases such as neon . a brief introduction of the underlying physics as well as a broad review of the applicability of the method is presented in this review .

helium ion microcopy ( him ) based on gas field ion sources ( gfis ) represents a new ultra high resolution microscopy and nano fabrication technique . it is an enabling technology that not only provides imagery of conducting as well as uncoated insulating nano structures but also allows to create these features . the latter can be achieved using resists or material removal due to sputtering . the close to free form sculpting of structures over several length scales has been made possible by the extension of the method to other gases such as neon . a brief introduction of the underlying physics as well as a broad review of the applicability of the method is presented in this review .

1011.3272

i

space - time codes ( stc ) in multi - input multi - output ( mimo ) systems have been extensively studied for their ability to provide transmit diversity gain and spatial multiplexing gain @xcite . space - time trellis codes ( sttc ) @xcite and space - time block codes ( stbc ) @xcite are able to provide diversity gain and have code rate limited by 1 . on the other hand , bell labs layered space - time ( blast ) system @xcite , high - rate linear dispersion ( ld ) codes @xcite , golden code @xcite , perfect codes @xcite , ps - sr code@xcite , etc . , have code rate @xmath0 and are able to provide multiplexing gain ( the latter four have diversity gain too ) . to achieve higher code rates with low joint - decoding complexity , many stbc with code rate @xmath1 have been designed to be group - decodable ( quasi - orthogonal ) @xcite . in contrast , there were much fewer designs of group - decodable stbc with code rate @xmath0 ( high - rate stbc ) . in @xcite , square 2-group - decodable stbc of code rate 1.25 for 4 transmit antennas were obtained by computer search ; in @xcite , 2-group - decodable stbc of code rate @xmath2 for @xmath3 ( @xmath4 ) transmit antennas were constructed . in @xcite , it was also shown that the group - decodable code structure is beneficial to diversity - embedded ( de ) space - time codes as it avoids interference between the different diversity layers in the de codes and helps to guarantee the designed diversity levels . in this paper , group - decodable high - rate stbc with arbitrary number of transmit antennas and code lengths is considered , then systematic methods to construct them with full symbol - wise diversity are presented . their maximum achievable code rate and decoding complexity are analyzed . specific code examples are constructed and simulated . the rest of this paper is organized as follows . high - rate stbc with code rate @xmath0 will be abbreviated as stbc . in section ii , the system model is described and group - decodable stbc is defined . unbalanced 2-group - decodable stbc and balanced 2-group - decodable stbc are constructed systematically in section iii and section iv , respectively . comparisons of the decoding complexity and ber performance are shown in section v. finally , this paper is concluded in section vi . in this paper , bold lower case and upper case letters denote vectors and matrices ( sets ) , respectively ; @xmath5 and @xmath6 denote the real and the complex number field , respectively ; @xmath7 and @xmath8 stand for the real and the imaginary part of a complex vector or matrix , respectively ; @xmath9^*$ ] , @xmath9^t$ ] , @xmath9^h$ ] and @xmath10 denote the complex conjugate , the transpose , the complex conjugate transpose and the frobenius norm of a matrix , respectively ; @xmath11 and @xmath12 represent dimension of a vector / matrix space and rank of a matrix , respectively ; @xmath13 denotes an identity matrix .

high - rate space - time block codes ( stbc with code rate ) in multi - input multi - output ( mimo ) systems are able to provide both spatial multiplexing gain and diversity gain , but have high maximum likelihood ( ml ) decoding complexity . since group - decodable ( quasi - orthogonal ) code structure can reduce the decoding complexity , we present in this paper systematic methods to construct group - decodable high - rate stbc with full symbol - wise diversity gain for arbitrary transmit antenna number and code length . we show that the proposed group - decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number , and the slope of this near - linear dependence increases with the code length . comparisons with existing low - rate and high - rate codes ( such as orthogonal stbc and algebraic stbc ) are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes . space - time block codes ( stbc ) , group - decodable code structure , code construction .

high - rate space - time block codes ( stbc with code rate ) in multi - input multi - output ( mimo ) systems are able to provide both spatial multiplexing gain and diversity gain , but have high maximum likelihood ( ml ) decoding complexity . since group - decodable ( quasi - orthogonal ) code structure can reduce the decoding complexity , we present in this paper systematic methods to construct group - decodable high - rate stbc with full symbol - wise diversity gain for arbitrary transmit antenna number and code length . we show that the proposed group - decodable stbc can achieve high code rate that increases almost linearly with the transmit antenna number , and the slope of this near - linear dependence increases with the code length . comparisons with existing low - rate and high - rate codes ( such as orthogonal stbc and algebraic stbc ) are conducted to show the decoding complexity reduction and good code performance achieved by the proposed codes . space - time block codes ( stbc ) , group - decodable code structure , code construction .

astro-ph0112180

i

deuterium is thought to be produced in significant amount only during primordial big bang nucleosynthesis ( bbn ) , and to be thoroughly destroyed in stellar interiors . deuterium is thus a key element in cosmology and in galactic chemical evolution ( see e.g. audouze & tinsley 1976 ; gautier & owen 1983 ; vidal madjar & gry 1984 ; boesgaard & steigman 1985 ; olive _ et al . _ 1990 ; pagel 1992 ; vangioni - flam & cass 1994 ; vangioni - flam _ _ 1995 ; prantzos 1996 ; scully _ et al . _ 1997 ; cass & vangioni - flam 1998 ; tosi _ et al . _ 1998 ) . indeed , its primordial abundance is the best tracer of the baryonic density parameter of the universe , @xmath11 , and the decrease in its abundance during galactic evolution traces the cosmic star formation rate at various epochs . the first ( indirect ) measurement of the deuterium abundance was carried out using @xmath12he in the solar wind , giving the presolar value d / h@xmath13 ( geiss & reeves 1972 ) . the first measurements of the d / h ratio in the interstellar medium ( ism ) were reported shortly thereafter by rogerson & york ( 1973 ) , and their value ( d / h)@xmath14 has remained a landmark average value for the interstellar d / h ratio . finally direct measurements of the primordial ( d / h ) ratio in low - metallicity material at high redshift have been successfully carried out these past few years ( e.g. , burles 2001 for a review , and references therein ) . the values derived cluster around ( d / h)@xmath15 although with significant dispersion , which may or may not be real . quite similarly the measurements of the ( d / h ) ratio in the galactic ism towards hot stars with the _ copernicus _ satellite lead to many evaluations of d / h ( see e.g. york and rogerson 1976 ; vidal madjar _ et al . _ 1977 ; laurent _ et al . _ 1979 ; ferlet _ et al . _ 1980 ; york 1983 ; allen _ et al . _ 1992 ) which also show dispersion around the above york & rogerson ( 1973 ) value . this dispersion has been recently confirmed by imaps observations ( jenkins _ et al . _ 1999 ; sonneborn _ et al . _ 2000 ) , indicating that the d / h ratio may vary by a factor @xmath16 in the solar neighborhood , i.e. , within a few hundred parsecs . in this paper we present a new determination of the d / h ratio on the line of sight to the nearby da white dwarf ( wd ) g191-b2b based on observations obtained with the far ultraviolet spectroscopic explorer ( _ fuse _ , moos _ et al . _ 2000 ; sahnow _ et al . _ 2000 ) . this paper is one of a series in this volume describing the first results of the _ fuse _ ( d / h ) program in the local ism ( lism ) . this program and its results are summarized in the overview paper by moos et al . ( 2002 ) . observing white dwarfs has many advantages over hot and cool stars for studying the d / h ratio , as explained in vidal - madjar _ et al . _ ( 1998 ) : these targets can be chosen close to the sun , in order to avoid a complex line of sight structure , and in the high temperature range , so that the interstellar absorption is superimposed on a smooth stellar continuum . the risk of contamination by low column density h i fluffs possibly present in the hot star winds ( gry , lamers & vidal madjar 1984 ) is negligible for wds , and their hot continuum offers the possibility of observing the numerous uv lines of n i and especially o i , which is a very useful tracer of h i and d i. the ( d / h ) ratio has already been measured toward four white dwarfs , using the hst : g191-b2b ( lemoine _ et al . _ 1996 ; vidal madjar _ et al . _ 1998 ; sahu _ et al . _ 1999 ) , hz43a ( landsman _ et al . _ 1996 ) , sirius b ( hbrard _ et al . _ 1999 ) and feige 24 ( vennes _ et al . for hz43a , sirius b and feige 24 the average d / h values obtained are compatible with the local ism ( lism ) d / h determination ( linsky 1998 ) made within the local interstellar cloud ( the lic in which the sun is embedded ) , although in the case of sirius b this compatibility is marginal . in the case of g191-b2b , it was found that the line of sight comprises one neutral region corresponding to the lic , and two more ionized absorbing components ( lemoine _ et al . _ 1996 ; vidal - madjar _ et al . the average ( d / h ) ratio ( defined as the ratio of the total column densities of d i and h i ) was found to be ( d / h)@xmath17 ( vidal madjar _ et al . _ 1998 ) , significantly different from the value measured toward capella ( d / h)@xmath18 ( linsky 1998 ) . the ( d / h ) ratio measured toward g191-b2b has been contested by sahu et al . ( 1999 ) , who used stis data and concluded to the presence of two interstellar components only , and to a d / h ratio compatible with that observed toward capella . the disagreement resides in the evaluation of the total d i column density ( vidal - madjar 2000 ; sahu 2000 ) , and arises presumably because the lyman @xmath1 d line is saturated and the column density is thus sensitive to the line profile . the number of components assumed on the line of sight may also introduce differences between the analyses of these groups ( see vidal - madjar 2001 for a detailed discussion ) . in the present work we re - examine these issues , making use of high quality _ fuse _ and stis observations of g191-b2b . we first measure the @xmath0(d i ) , @xmath0(o i ) and @xmath0(n i ) column densities using the unsaturated lines of these elements in the _ fuse _ datasets , notably lyman @xmath2 and lyman @xmath3for d i ( section 2 ) . we then analyze the recent high quality stis observations in section 3 , and provide explicit evidence for the presence of three absorbing components ( at least ) on the line of sight . we also provide a refined estimate of the total h i column density . all throughout this work , considerable effort has been put on quantifying possible systematic uncertainties related to fixed - pattern noise , detector artifacts , background uncertainties , wavelength calibration and modeling of the stellar continua , as well as to the velocity structure of the line of sight . in particular , we argue in section 3.3 that previous estimates of the total @xmath0(h i ) are subject to a large systematic uncertainty related to the possible presence of additional weak [ @xmath0(h i)@xmath19@xmath20 hot ( @xmath21k ) components . this effect may have a large impact on our understanding of the observed variations of the ( d / h ) ratio in the ism , as it may affect other lines of sight , and is the subject of a companion paper ( vidal - madjar & ferlet 2002 ) . we provide a summary of our results and a short discussion in section 4 ; an overall discussion of the _ fuse _ results is given by moos _

high - resolution spectra of the hot white dwarf g191-b2b , covering the wavelength region 9051187 , were obtained with the far ultraviolet spectroscopic explorer ( _ fuse _ ) . this data was used in conjunction with existing high - resolution hubble space telescope stis observations to evaluate the total h i , d i , o i and n i column densities along the line of sight .

high - resolution spectra of the hot white dwarf g191-b2b , covering the wavelength region 9051187 , were obtained with the far ultraviolet spectroscopic explorer ( _ fuse _ ) . this data was used in conjunction with existing high - resolution hubble space telescope stis observations to evaluate the total h i , d i , o i and n i column densities along the line of sight . previous determinations of(d i ) based upon ghrs and stis observations were controversial due to the saturated strength of the d i lyman line . in the present analysis the column density of d i has been measured using only the unsaturated lyman and lyman lines observed by _ fuse_. a careful inspection of possible systematic uncertainties tied to the modeling of the stellar continuum or to the uncertainties in the _ fuse _ instrumental characteristics has been performed . the column densities derived are :d i ,o i , andn i quoted with uncertainties . the measurement of the h i column density by profile fitting of the lyman line has been found to be unsecure . if additional weak hot interstellar components are added to the three detected clouds along the line of sight , the h i column density can be reduced quite significantly , even though the signal - to - noise ratio and spectral resolution at lyman are excellent . the new estimate of(h i ) toward g191-b2b reads :h i ( uncertainty ) , so that the average ( d / h ) ratio on the line of sight is : ( d / h) ( uncertainty ) .

astro-ph0112180

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we have measured the total column densities of d i , n i and o i toward g191-b2b using unsaturated absorption lines of these elements in high quality _ fuse _ spectra . after a careful examination of the possible systematic uncertainties tied to the choice of the stellar continuum and to the instrumental configuration , we have derived the following column densities with @xmath8 uncertainties : we have also analyzed new high signal - to - noise ratio high resolution stis observations of g191-b2b and provided concrete evidence for the presence of at least three interstellar absorbing components on the line of sight by analyzing the interstellar absorption lines of n i , o i , si ii , si iii , s iii and fe ii present in the stis bandpass . we have also measured the total hydrogen column density on the line of sight using the velocity structure derived from the above metals . we have performed an exhaustive study of systematic effects on the value of @xmath0(h i ) . in particular we have discovered a new major source of uncertainty on @xmath0(h i ) tied to the possible presence of additional weak hot absorbers whose combined absorption profile can contribute significantly to the wings of the blended lyman @xmath1 profile . the column density of these absorbers is small compared to the other main components , and they would not be detected in any other species than h i , but their contribution to the lyman @xmath1 absorption profile can reduce significantly the total h i column density measured from the profile fitting . in order to constrain their impact , we have analyzed simultaneously lyman @xmath1 and the higher order lyman lines , and concluded that the best value of @xmath0(h i ) toward g191-b2b is : we emphasize that this uncertainty is a systematic uncertainty which had gone unnoticed before . therefore the above result supersedes previous estimates of @xmath0(h i ) toward g191-b2b obtained from the profile fitting of lyman @xmath1 . a detailed analysis of this uncertainty and its consequences on @xmath0(h i ) determinations toward other stars is discussed in a companion paper ( vidal - madjar & ferlet 2002 ) . we thus derive the following neutral abundance ratios toward g191-b2b , with @xmath8 uncertainties : most of the uncertainty in the above result results from the systematic uncertainty on the @xmath0(h i ) determination . this clearly shows the importance of measuring accurate ( d / o ) and ( d / n ) ratios in the interstellar medium instead of abundances relative to hydrogen , as emphasized by timmes _ interestingly if one uses the recent measurement of @xmath0(h i ) from the modeling of the atmosphere of g191-b2b and the fit of the euve spectrum , @xmath86(h i)@xmath99 ( @xmath8 ) , one finds @xmath100 ( @xmath8 ) . at this stage , however , due to the uncertainty inherent to the modeling of the white dwarf atmosphere , it is probably more conservative to use the interstellar determination for @xmath0(h i ) , and therefore the previous value of the ( d / h ) ratio . the above new value for the ( d / h ) ratio agree with the range of values measured by linsky ( 1998 ) toward a dozen stars of the lism and with the values previously derived toward g191-b2b . however the discrepancy between previous estimates of the ( d / h ) ratio toward g191-b2b and the lism average d / h ratio has disappeared due to a revision of the uncertainty on the estimation of the total h i content . a detailed interpretation of this ( d / h ) value and of the accompanying ( d / o ) and ( d / n ) ratios and their implications is provided in a companion paper by moos _ ( 2002 ) . rccccc 1025.4440 & d i & 0.264 @xmath102 & 0.190 @xmath103 & + 1025.4429 & d i & 0.527 @xmath102 & 0.190 @xmath103 & + 972.2725 & d i & 0.967 @xmath104 & 0.813 @xmath105 & + 972.2721 & d i & 0.193 @xmath102 & 0.813 @xmath105 & + 949.4848 & d i & 0.465 @xmath104 & 0.421 @xmath105 & weak + 949.4846 & d i & 0.929 @xmath104 & 0.421 @xmath105 & weak + 1134.9803 & n i & 0.435 @xmath102 & 0.150 @xmath103 & + 1134.4149 & n i & 0.297 @xmath102 & 0.154 @xmath103 & + 1134.1653 & n i & 0.152 @xmath102 & 0.158 @xmath103 & + 954.1042 & n i & 0.676 @xmath104 & 0.330 @xmath105 & blend + 953.9699 & n i & 0.348 @xmath102 & 0.170 @xmath103 & + 953.6549 & n i & 0.250 @xmath102 & 0.183 @xmath103 & + 953.4152 & n i & 0.132 @xmath102 & 0.193 @xmath103 & + 1039.2303 & o i & 0.920 @xmath104 & 0.947 @xmath105 & + 1026.4757 & o i & 0.246 @xmath104 & 0.111 @xmath105 & weak + 1026.4744 & o i & 0.187 @xmath106 & 0.118 @xmath107 & weak + 1025.7633 & o i & 0.201 @xmath106 & 0.212 @xmath107 & blend + 1025.7626 & o i & 0.302 @xmath104 & 0.191 @xmath105 & blend + 1025.7616 & o i & 0.169 @xmath102 & 0.765 @xmath105 & blend + 988.7734 & o i & 0.465 @xmath102 & 0.226 @xmath103 & strong + 988.6549 & o i & 0.830 @xmath104 & 0.566 @xmath105 & blend + 988.5778 & o i & 0.553 @xmath106 & 0.629 @xmath107 & weak + 976.4481 & o i & 0.331 @xmath104 & 0.386 @xmath105 & + 971.7382 & o i & 0.116 @xmath102 & 0.585 @xmath105 & strong + 971.7376 & o i & 0.207 @xmath104 & 0.146 @xmath105 & blend + 950.8846 & o i & 0.158 @xmath104 & 0.194 @xmath105 & + 948.6855 & o i & 0.631 @xmath104 & 0.100 @xmath103 & + 936.6295 & o i & 0.365 @xmath104 & 0.100 @xmath103 & + 929.5168 & o i & 0.229 @xmath104 & 0.100 @xmath103 & + 925.4460 & o i & 0.354 @xmath106 & 0.459 @xmath107 & weak + 924.9500 & o i & 0.154 @xmath104 & 0.100 @xmath103 & + 921.8570 & o i & 0.100 @xmath104 & 0.562 @xmath107 & weak + cccc hst ghrs - ech . & 14.84@xmath108 & 13.90@xmath109 & vidal madjar _ et al . _ 1998 + lwrs+mdrs & 14.79@xmath108 & 13.82@xmath36 & this work + mdrs & 14.84@xmath110 & 13.89@xmath111 & this work + hirs & 14.88@xmath111 & 13.84@xmath36 & this work + -all & 14.86@xmath36 & 13.87@xmath36 & this work + cll hst ghrs - ech . & 13.43@xmath109 & vidal madjar _ et al . _ 1998 + hst stis - ech.#1 & 13.55@xmath112 & sahu _ et al . _ 1999 + hst ghrs - ech . & 13.40@xmath108 & sahu _ et al . _ 1999 + lwrs+mdrs & 13.41@xmath113 & d i , no h i , this work + mdrs & 13.41@xmath114 & d i & h i , this work + hirs & 13.36@xmath110 & d i & h i ( fig . [ aas_fig2 ] ) , this work + hirs & 13.38@xmath111 & d i & h i , double lsf , this work + hirs & 13.42@xmath110 & d i , no h i , this work + all & 13.40@xmath36 & this work + lcccc 18.315@xmath115 & euve & & & dupuis _ et al . _ 1995 + 18.32 & euve & & & lanz _ et al . _ 1996 + 18.36@xmath108 & ghrs - g160 m & 3 & free & lemoine _ et al . _ 1996 + 18.38@xmath109 & ghrs - ech . & 3 & free & vidal madjar _ et al . _ 1998 + 18.30@xmath114 & euve & & & barstow & hubeny 1998 + 18.31@xmath116 & stis - ech . # 1 & 2 & fixed & sahu _ et al . _ 1999 + 18.34@xmath109 & ghrs - ech . & 2 & fixed & sahu _ et al . _ 1999 + lllllccc 1334.5320 & c ii & 0.128 & 0.288 @xmath103 & 316 + 1200.7098 & n i & 0.0430 & 0.398 @xmath103 & 350 , 351 + 1200.2233 & n i & 0.0862 & 0.399 @xmath103 & 350 , 351 + 1199.5496 & n i & 0.130 & 0.401 @xmath103 & 351 + 1242.8040 & n v & 0.500 & 0.336 @xmath103 & 339 + 1302.1685 & o i & 0.0519 & 0.340 @xmath103 & 323 + 1304.3702 & si ii & 0.0917 & 0.107 @xmath117 & 323 + 1193.2897 & si ii & 0.585 & 0.409 @xmath117 & 352 , 353 + 1190.4158 & si ii & 0.293 & 0.410 @xmath117 & 353 , 354 + 1206.5000 & si iii & 1.67 & 0.255 @xmath117 & 349 + 1259.5190 & s ii & 0.0166 & 0.465 @xmath105 & 334 + 1190.2030 & s iii & 0.0231 & 0.651 @xmath105 & 353 , 354 + 2382.7651 & fe ii & 0.320 & 0.313 @xmath103 & 324 + 2586.6499 & fe ii & 0.0691 & 0.272 @xmath103 & 298 , 299 + 2600.1729 & fe ii & 0.239 & 0.270 @xmath103 & 297 + lllcllc n i & 395.0/314 & 382.3/311 & 1.7% & 323.2/309 & 309.1/306 & 0.3% + o i & 214.3/61 & 193.1/58 & 11% & 113.9/60 & 101.4/57 & 8.3% + si ii & 772.0/468 & 651.4/465 & @xmath118% & 678.6/463 & 553.6/460 & @xmath118% + si iii & 210.6/152 & 192.8/149 & 0.4% & 185.2/150 & 170.8/147 & 0.75% + fe ii & 277.6/142 & 141.8/139 & @xmath118% & 227.9/139 & 123.3/136 & @xmath118% + all & 2677.8/1270 & 1908.8/1259 & @xmath118% & 2076.7/1250 & 1442.5/1239 & @xmath118% + cccccc 1 & 7.7 & 11.2 & 19.4 & 18.32 & 2469.9 + 2 & 7.7 & 11.3 & 19.4 & 18.37 & 2470.1 + 3 & 7.7 & 11.7 & 19.4 & 18.32 & 2006.8 + 4 & 7.7 & 11.6 & 19.4 & 18.37 & 2001.8 + 5 & 7.7 & 11.6 & 19.4 & 18.33 & 1987.3 +

previous determinations of(d i ) based upon ghrs and stis observations were controversial due to the saturated strength of the d i lyman line . in the present analysis the column density of d i has been measured using only the unsaturated lyman and lyman lines observed by _ fuse_. a careful inspection of possible systematic uncertainties tied to the modeling of the stellar continuum or to the uncertainties in the _ fuse _ instrumental characteristics has been performed . the column densities derived are :d i ,o i , andn i quoted with uncertainties . the new estimate of(h i ) toward g191-b2b reads :h i ( uncertainty ) , so that the average ( d / h ) ratio on the line of sight is : ( d / h) ( uncertainty ) .

high - resolution spectra of the hot white dwarf g191-b2b , covering the wavelength region 9051187 , were obtained with the far ultraviolet spectroscopic explorer ( _ fuse _ ) . this data was used in conjunction with existing high - resolution hubble space telescope stis observations to evaluate the total h i , d i , o i and n i column densities along the line of sight . previous determinations of(d i ) based upon ghrs and stis observations were controversial due to the saturated strength of the d i lyman line . in the present analysis the column density of d i has been measured using only the unsaturated lyman and lyman lines observed by _ fuse_. a careful inspection of possible systematic uncertainties tied to the modeling of the stellar continuum or to the uncertainties in the _ fuse _ instrumental characteristics has been performed . the column densities derived are :d i ,o i , andn i quoted with uncertainties . the measurement of the h i column density by profile fitting of the lyman line has been found to be unsecure . if additional weak hot interstellar components are added to the three detected clouds along the line of sight , the h i column density can be reduced quite significantly , even though the signal - to - noise ratio and spectral resolution at lyman are excellent . the new estimate of(h i ) toward g191-b2b reads :h i ( uncertainty ) , so that the average ( d / h ) ratio on the line of sight is : ( d / h) ( uncertainty ) .

astro-ph0007238

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there are two principal conclusions of the imaps d / h program . first , the atomic d / h ratio in the ism , averaged over path lengths of 250 to 500 pc , exhibits significant spatial variability . differences in the atomic d / h ratio on long pathlengths in the ism have been suspected for many years ( vidal - madjar et al . 1978 ; vidal - madjar & gry 1984 ) , but not until now have data of sufficient quality been available to evaluate and reduce statistical and systematic errors to levels where these differences are unequivocal . second , we find no support for the simple picture that variations in d / h anticorrelate with those of n / h , i.e. , one measure of how much the gas has been processed through stellar interiors . figure [ dnfig ] shows the relationship between d / h and n / h for the three sightlines studied by imaps plus the white dwarf g191@xmath137b2b ( vidal - madjar et al . 1998 ; sahu et al . we point out that some elements are systematically removed from the gas phase as they are incorporated into interstellar dust ( savage & sembach 1996 ) , but the abundance of n does not seem to be appreciably altered by this effect ( meyer et al . . beyond the effects from depletions onto dust , spatial variations in interstellar gas abundances can arise as a natural consequence of galactic chemical evolution and the changing influences of different stellar populations . the lack of an anticorrelation between n / h and d / h depicted in fig . [ dnfig ] indicates that the variability of d / h is not just a consequence of different mixing ratios of material with differing levels of stellar processing , as we might anticipate , for instance , from the variable addition of metal - poor , infalling gas from the galactic halo ( meyer et al . we may need to go further and draw a distinction between contributions from stars that simply destroy deuterium and those that both destroy deuterium and enrich the medium with additional nitrogen . that is , we could envision some stars cycling material only through their shallow layers that are only hot enough to burn deuterium , while others eject material from much deeper layers where the synthesis of heavier elements has taken place . this additional level of complexity could explain the behavior that we observed . global models of galactic chemical evolution ( audouze & tinsley 1974 ; tosi 1988a , b ; dearborn , steigman & tosi 1996 ; scully et al . 1996 ; tosi et al . 1998 ) describe the destruction of d during stellar formation , evolution , and eventual mass loss . these models predict variations in d / h , n , and o abundances that are manifested as abundance gradients on a scale of @xmath1381 kpc . however , the predicted trends in galactic abundances may not accurately represent what is observable in the diffuse ism . tenorio - tagle ( 1996 ) showed that the chemical enrichment of the diffuse ism by ob associations , including supernovae from massive stars , is a slow process . following a supernova explosion , chemically enriched ejecta remain clumpy and not well mixed with the diffuse ism it encounters until it is incorporated into new star forming regions . this is a result of very long time scales for diffusion between different parcels of gas in the warm ( @xmath139k ) and cold ( @xmath140k ) phases of the ism . the diffusion time scale for enriched gas to thoroughly mix with the warm diffuse ism can be very long ( @xmath141 yr - tenorio - tagle 1996 ) . on the spatial scale sampled by the imaps observations , different sight lines may encounter regions with very different dynamical and chemical histories . differential galactic rotation and random cloud motions are expected to stir the diffuse ism and chemically enriched parcels of gas , but these parcels retain their distinct chemical properties until they are disrupted through photoevaporation , most likely by the formation of new massive stars . tenorio - tagle finds that diffusion is efficient only for the hot phase of the ism ( @xmath142 yr ) , which accounts for a very small fraction of the total diffuse ism . only after the enriched gas and diffuse gas are highly ionized would the chemically enriched gas from the earlier generation of stars quickly diffuse into the ambient ism . thus , the time scale for mixing interstellar gases with different processing histories can be much longer than the chemical evolution time scale . however , it is possible that interstellar turbulence and its secondary phenomena may accelerate the mixing rate . since the distribution of star forming regions ( ob associations ) shows large inhomogeneities on scales @xmath143 kpc , their corresponding chemical enrichment of the ism may be expected to be nonuniform as well . this is perhaps revealed indirectly by variations in region abundances ( peimbert 1999 ) and solar - type stars at similar galactocentric radii ( edvardsson , et al . 1993 ) . several processes unrelated to stellar nucleosynthesis may , under the right circumstances , alter the atomic d / h ratio of some parcels of interstellar gas ( see lemoine et al . 1999 for a review ) . d may be incorporated into hd ( watson 1973 ) , but the fraction of molecular gas on our sight lines is very low ( see 1 ) . differential radiation pressure on d and h ( vidal - madjar et al . 1978 ; bruston et al . 1981 ) may lead to a separation of d in some clouds near strong radiation fields . adsorption of d onto dust grains ( jura 1982 ) may deplete d from the gas phase . bauschlicher ( 1998 ) found that reactions of h and d with polycyclic aromatic hydrocarbon ( pah ) cations might systematically provide some d enrichment in pahs . a very different perspective has been offered by mullan & linsky ( 1999 ) , who suggested that significant quantities of d may be formed in stellar flares from m dwarf stars and ejected into interstellar space . some or all of these processes could be at work in the diffuse ism and alter the atomic d / h ratio on individual sight lines , independent of the degree of chemical enrichment from stellar evolution . however , they have not yet been demonstrated to be quantitatively significant . observational and theoretical tests of the efficiency and applicability of these processes are needed to better understand the mechanisms affecting the d / h ratio in the diffuse ism . while the d / h ratios derived from imaps spectra are in the general range expected from galactic chemical evolution models , a factor of three variation in the mean d / h ratio on path lengths of several hundred pc is unexpected . the apparent lack of an anti - correlation of the d / h abundance ratio with the metallicity of the gas and its variability on smaller than expected scales suggests that other processes in the galaxy may be masking more general chemical evolution trends . this may pose a problem for deriving a `` primordial '' d / h by extrapolating back from d / h measurements in the milky way to extragalactic absorbers at higher and higher redshifts , or to even to evaluate `` primordial '' d / h directly from high redshift observations , until we understand the reasons for these differences . the spatial variations found in this study underline the importance of high - quality d / h determinations . d / h measurements in more distant regions of the galaxy are needed to determine whether the properties of the gas within 500 pc of the sun are representative of the galactic disk . observations with the fuse satellite should probe such more distant environments and hopefully answer some of these questions . the value of d / h for is larger than that usually considered typical for the milky way . this robust result establishes a new lower limit to the primordial d / h ratio . within the framework of standard big bang nucleosynthesis ( walker et al . 1991 ) , the large value of d / h found toward is equivalent to a cosmic baryon density of @xmath3 . this error simply reflects the uncertainty in the d / h ratio toward reported in this paper . we regard this value of @xmath144 as an upper limit since no correction has been applied for the destruction of deuterium in stars . this upper limit on @xmath145 is consistent with the preferred values of @xmath145 derived from recent analyses of the boomerang and maxima cosmic microwave background measurements ( e.g. , lange et al . 2000 ; tegmark & zaldarriaga 2000 ; hu et al . however , any lowering of this upper limit on @xmath145 to correct for astration will lead to a marginal disagreement with simple inflation models ( see figure 4 in tegmark & zaldarriaga 2000 ) and requires adjustments of other cosmological parameters . alternatively , the @xmath145 upper limit from d / h may be taken as a prior assumption for the constraint of other cosmological parameters using the cmb data ( e.g. , see hu et al . 2000 ) . we wish to thank the us and german space agencies , nasa and dara , for their joint support of the mission that made these observations possible . the successful execution of our observations was the product of efforts over many years by engineering teams at princeton university observatory , ball aerospace systems group , and daimler - benz aerospace . important contributions to the success of imaps also came from the efforts of d. a. content and r. a. keski - kuha and other members of the optics branch of the nasa goddard space flight center and from o. h. siegmund and s. r. jelinsky at the berkeley space sciences laboratory . we also thank bruce draine for insightful discussions on atomic interactions with dust grains and pahs . this work was supported in part by nasa grant nag5 - 616 to princeton university . the data were obtained from the national space science data center at nasa - goddard . anders , e. , & grevesse , n. 1989 , geochim . acta , 53 , 197 audouze , j. , & tinsley , b. 1974 , apj , 192 , 487 bauschlicher , c. w. 1998 , apj , 509 , l125 bevington , p. r. , & robinson , d. k. 1992 , data reduction and error analysis for the physical sciences , 2nd ed . 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evidently , the atomic d / h ratio in the ism , averaged over path lengths of 250 to 500 pc , exhibits significant spatial variability . furthermore , the observed spatial variations in d / h do not appear to be anticorrelated with n / h , one measure of heavy element abundances . we briefly discuss some hypotheses to explain the d / h spatial variability . within the framework of standard big bang nucleosynthesis , the large value of d / h found toward is equivalent to a cosmic baryon density of , which we regard as an upper limit since there is no correction for the destruction of deuterium in stars .

high resolution far ultraviolet spectra of the early - type stars and were obtained to measure the interstellar deuterium abundances in these directions . the observations were made with the interstellar medium absorption profile spectrograph ( imaps ) during the _ orfeus - spas ii _ mission in 1996 . imaps spectra cover the wavelength range 9301150 with . the interstellar features are resolved and cleanly separated from interstellar in the and profiles of both sight lines , and also in the profile of . the profiles were modeled using a velocity template derived from several lines in the imaps spectra recorded at higher signal - to - noise . to find the best column density , we minimized for model profiles that included not only the as a free parameter , but also the effects of several potential sources of systematic error which were allowed to vary as free parameters . column densities were measured by analyzing absorption profiles in a large number of high dispersion spectra for each of these stars and applying this same -minimization technique . ultimately we found that d / h for and for , values that contrast markedly with d / h derived in 1 for ( the stated errors are 90% confidence limits ) . evidently , the atomic d / h ratio in the ism , averaged over path lengths of 250 to 500 pc , exhibits significant spatial variability . furthermore , the observed spatial variations in d / h do not appear to be anticorrelated with n / h , one measure of heavy element abundances . we briefly discuss some hypotheses to explain the d / h spatial variability . within the framework of standard big bang nucleosynthesis , the large value of d / h found toward is equivalent to a cosmic baryon density of , which we regard as an upper limit since there is no correction for the destruction of deuterium in stars . 1paper i # 110^#1 3 cm^-3 2h

1512.05352

i

the diffusion of charged particles in a turbulent magnetic field plays a pivotal role in the understanding of the origin of cosmic rays , more than a century since their discovery , over a broad range of particle energy , from the interplanetary solar energetic particles ( * ? ? ? * hereafter sep ) to the pev cosmic rays likely produced at individual supernova remnant shocks @xcite . in a volume of space ( for instance interplanetary region close to the sun , or interstellar medium stirred by supernova explosion ) threaded by a strong statistically uniform average magnetic field @xmath4 with a small fluctuation @xmath5 , the particle diffusion parallel to the average field has been originally modeled in @xcite . the discrepancy later found @xcite between the mean - free path of some sep events and the prediction of the quasi - linear theory ( hereafter qlt ) spurred intense theoretical work . @xcite has shown that including the measured , despite noisy , steepening of the power spectrum at high wavenumber for selected events approaches the predicted mean free path to the measurements . @xcite concluded that the geometry of the magnetic fluctuations in the solar wind must be different from the simple picture of qlt . perpendicular diffusion is usually regarded as negligible compared to the parallel diffusion . nevertheless , the interpretation of a number of heliospheric measurements and numerical simulations of energetic particles suggests a significant contribution arising from perpendicular transport . time - intensity profiles of energetic protons at spacecraft separated by more than @xmath6 in longitude at @xmath0 au provide evidence of a significant motion across the parker spiral magnetic field lines @xcite . whether the motion across the spiral is due to a pure field line meandering or , in addition to that , to the departure of protons from the actual local field lines , called here cross - field diffusion , is among the purposes of this investigation . from the @xmath7-ray variability in the solar flares observed by rhessi @xcite it has been argued that perpendicular chaotic motion of a few tens of @xmath8 electrons in flaring loops was observed in a non - diffusive phase . test - particle simulations @xcite show that even in a weak three - dimensional isotropic turbulence charged particles decorrelate from magnetic field lines on a time scale comparable to the gyroperiod . these results pinpoint to a propagation regime wherein early - time perpendicular transport can not be neglected . it is well known that the transport of charged particles in turbulence depends on the anisotropy of the power spectrum @xcite . anisotropic turbulence in the solar wind was first found by @xcite as elongation of turbulence fluctuations along the magnetic field , and confirmed by several studies later on ( * ? ? ? high - heliolatitude _ ulysses _ measurements @xcite provided a new insight : the power spectrum of the local magnetic field in the solar wind is consistent with the anisotropic incompressible mhd - scale turbulence conjectured by @xcite ( hereafter gs95 ) . such an interpretation was confirmed over a frequency interval comparable with the presumably `` entire '' inertial range of the fast solar wind turbulence @xcite . a scrutiny of the power spectrum dependence on the angle of the flow to the magnetic field and on the wave - vector anisotropy @xcite confirmed an approximate consistency with gs95 . @xcite argue that the disagreement in the outer length - scale predicted by gs95 , inferred to be @xmath9 times larger than measured , might be explained with unbalance between alfvn modes propagating in opposite directions , in contrast with the balance assumed in gs95 . however , the gs95 model does not account for the difference in power - law exponents of the power spectrum of velocity and magnetic fluctuations in the inertial range measured , e.g. , by wind throughout the solar cycle 23 @xcite . numerical simulations of mhd turbulence have pointed out that the anisotropy increases at small scales @xcite and the turbulent eddies become more elongated along the direction of the local magnetic field @xcite . in this paper i investigate the time - dependent perpendicular transport within the mhd - scale turbulence gs95 . @xcite pioneered the study of pitch - angle scattering in the gs95 turbulence within the qlt limit @xcite , finding a scattering frequency more than ten orders of magnitude smaller than the isotropic turbulence over @xmath10 decades of particle kinetic energy . extension to a regime immune to qlt divergence at small pitch - angle @xcite confirmed such a scattering inefficiency @xcite . since in the gs95 anisotropic turbulence the wave - vectors of the mhd - scale fluctuations are predominantly perpendicular to the local average field , one could expect a small ratio of the perpendicular to the parallel average displacement as compared to the 3d isotropic case . note that test - particle simulations by @xcite found that the ratio of perpendicular to parallel diffusion coefficient in a synthesised scale - dependent anisotropic turbulence devised to reproduce gs95 is a few percent , comparable to the isotropic turbulence . diffusion perpendicular to the mean magnetic field has been long known to be dominated by the meandering of the magnetic field lines @xcite . the rate of separation of turbulent field lines along the direction of the mean field was found in @xcite , by solving a fokker - planck equation , to be very fast in the 3d isotropic power - spectrum turbulence , resulting in a significant perpendicular transport solely due to field - line meandering . @xcite , arguing that field lines diverge exponentially along the mean field direction , found that even if the particle does not undergo significant pitch - angle scattering ( `` collisionless '' case ) , the jump from a field line to another warrants a strong perpendicular diffusion due to the exponential divergence . @xcite showed that an exponential divergence of field - lines reduces the electron thermal conductivity in the galaxy clusters medium . @xcite used a variety of methods , including fokker - planck equation for a static gs95 mhd turbulence and a numerical monte - carlo model , and found a field - line separation growing as a power - law . such theoretical analyses omitted gradient / curvature drift motion of the guiding - center ; this assumption is justified for the thermal electrons in the galaxy clusters medium . the present paper investigates the limits of neglecting the gradient / curvature drift in the solar wind turbulent plasma . in this paper i use the decomposition of the instantaneous perpendicular average square displacement of a charged particle in a magnetic turbulence in two distinct contributions : meandering of magnetic field lines and gradient / curvature drift of the particle guiding - center from the local field line . those have been analytically calculated for the slab- and the 3d isotropic turbulence in ( * ? ? ? * hereafter fj11 ) and the latter numerically confirmed for the 3d isotropic turbulence @xcite . the gradient / curvature drift is usually neglected in theoretical analysis or interpretation of numerical simulations as the cross - field motion is assumed to be dominated by jumps between field lines once the particle has travelled a certain distance away from the original field line . in this paper i calculate gradient / curvature drift and field line contributions to the perpendicular transport for the gs95 anisotropic turbulence and investigate the departure of particles from the field lines as a function of time . benchmark parameters are tailored to solar wind energetic particles events . this paper is organized as follows : in sect . [ anisotropy ] the power spectra of alfvn polarisation modes relevant to perpendicular transport in gs95 turbulence are described ; in sect . [ coeff_diff ] the calculation of the instantaneous transport coefficients , due to gradient / curvature drift and to magnetic field line random walk , is outlined ( details are in the appendices ) and compared with the previous finding of an exponential divergence of field lines ; in sect . [ discussion ] the two contributions to the perpendicular transport are compared and the role of gradient / curvature drift average displacement in the sep longitudinal spread is estimated ; sect . [ conclusion ] contains the conclusions .

the particle motion away from the turbulent local field line is assessed as gradient / curvature drift of the guiding - center and compared with the magnetic field line random walk . at inertial scales however , for higher energies ( mev protons ) within the range of multi - spacecraft measurements , the longitudinal spread originating from transport due to gradient / curvature drift reaches up to .

i derive analytically the temporal dependence of the perpendicular transport coefficient of a charged particle in the three - dimensional anisotropic turbulence conjectured by goldreich - sridhar by implementing multi - spacecraft constraints on the turbulence power spectrum . the particle motion away from the turbulent local field line is assessed as gradient / curvature drift of the guiding - center and compared with the magnetic field line random walk . at inertial scales much smaller than the turbulence outer scale , particles decorrelate from field lines in a free - streaming motion , with no diffusion . in the solar wind at au , for energy sufficiently small ( kev protons ) , the perpendicular average displacement due to field line tangling generally dominates over two decades of turbulent scales . however , for higher energies ( mev protons ) within the range of multi - spacecraft measurements , the longitudinal spread originating from transport due to gradient / curvature drift reaches up to . this result highlights the role of the perpendicular transport in the interpretation of interplanetary and interstellar data .

1012.0553

c

i have reviewed a number of qcd topics where conventional wisdom relevant to hadronic physics at the lhc has been challenged . for example , the initial - state and final - state interactions of the quarks and gluons entering perturbative qcd hard - scattering subprocesses lead to the breakdown of traditional concepts of factorization and universality at leading twist . these soft - gluon rescattering , which are associated with the wilson line of the propagating partons , lead to bjorken - scaling single - spin asymmetries , diffractive deep inelastic scattering , the breakdown of the lam - tung leading twist relation in drell - yan reactions , as well as nuclear shadowing . furthermore , the gribov - glauber theory applied to the antishadowing domain predicts that nuclear structure functions are not universal , but instead depend on the flavor quantum numbers of each quark and antiquark , thus explaining the anomalous nuclear dependence recently observed in deep - inelastic neutrino scattering . surprisingly , isolated hadrons can be produced at large transverse momentum at a significant rate at the lhc directly within a hard higher - twist qcd subprocess , rather than from jet fragmentation . direct " processes can explain the observed deviations from perturbative qcd predictions in measurements of inclusive hadron cross sections at fixed @xmath0 , as well as the baryon anomaly " , the anomalously large proton - to - pion ratio seen in high centrality heavy - ion collisions . the intrinsic charm contribution to the proton structure function at high @xmath1 can explain the anomalously large rate for high @xmath2 photon plus charm jet events observed by d0 at the tevatron . intrinsic charm and bottom distributions also imply anomalously large production of charm and bottom jets at high @xmath2 at the lhc , as well as a novel mechanism for higgs and @xmath3 production at high @xmath4 the correspondence between theories in a warped anti - de sitter space and light - front quantization in physical space - time is very powerful , and leads to much insight into qcd dynamics , including a nonperturbative qcd running coupling and a remarkably accurate relativistic lf schrodinger equation which reproduces much of light - quark spectroscopy and dynamics , using a soft - wall model of with a positive sign dilaton . other novel features of qcd have also been discussed , including the consequences of confinement for quark and gluon condensates and the implications for the qcd contribution to the cosmological constant . i have also emphasized that setting the renormalization scale of the qcd coupling using the scheme - independent blm method will greatly improve the precision of qcd predictions , and thus greatly increase the sensitivity of searches for new physics at the lhc . invited talk , presented at the 5th workshop on high @xmath203 physics at the lhc held at the instituto de ciencias nucleares of the universidad national automata de mexico in mexico city , september 27-october 1 , 2010 . i am grateful to the organizers for their invitation to this meeting , and i thank all of my collaborators whose work has been cited in this report . this research was supported by the department of energy , contract de ac0276sf00515 . slac - 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i review a number of topics where conventional wisdom relevant to hadron physics at the lhc has been challenged . for example , the initial - state and final - state interactions of the quarks and gluons entering perturbative qcd hard - scattering subprocesses lead to the breakdown of traditional concepts of factorization and universality for transverse - momentum - dependent observables at leading twist . these soft - gluon rescattering effects produce bjorken - scaling single - spin asymmetries , the breakdown of the lam - tung leading - twist relation in drell - yan reactions , as well as diffractive deep inelastic scattering , the antishadowing of nuclear structure functions is predicted to depend on the flavor quantum numbers of each quark and antiquark , thus explaining the anomalous nuclear dependence observed in deep - inelastic neutrino scattering . isolated hadrons can be produced at large transverse momentum directly within a hard higher - twist qcd subprocess , rather than from jet fragmentation , even at the lhc . direct " processes can explain the observed deviations from pqcd predictions of the power - law fall - off of inclusive hadron cross sections at fixed , as well as the baryon anomaly " , the anomalously large proton - to - pion ratio seen in high - centrality heavy - ion collisions at rhic . the intrinsic charm contribution to the proton structure function at high can explain the large rate for high photon plus charm - jet events observed by d0 at the tevatron . the intrinsic charm and bottom distributions imply a large production rate for charm and bottom jets at high at the lhc , as well as a novel mechanism for higgs and production at high the light - front wavefunctions derived in ads / qcd can be used to calculate jet hadronization at the amplitude level . the elimination of the renormalization scale ambiguity for the qcd coupling using the scheme - independent blm method will improve the precision of qcd predictions and thus increase the sensitivity of searches for new physics at the lhc . the implications of in - hadron condensates " for the qcd contribution to the cosmological constant are also discussed .

i review a number of topics where conventional wisdom relevant to hadron physics at the lhc has been challenged . for example , the initial - state and final - state interactions of the quarks and gluons entering perturbative qcd hard - scattering subprocesses lead to the breakdown of traditional concepts of factorization and universality for transverse - momentum - dependent observables at leading twist . these soft - gluon rescattering effects produce bjorken - scaling single - spin asymmetries , the breakdown of the lam - tung leading - twist relation in drell - yan reactions , as well as diffractive deep inelastic scattering , the antishadowing of nuclear structure functions is predicted to depend on the flavor quantum numbers of each quark and antiquark , thus explaining the anomalous nuclear dependence observed in deep - inelastic neutrino scattering . isolated hadrons can be produced at large transverse momentum directly within a hard higher - twist qcd subprocess , rather than from jet fragmentation , even at the lhc . such direct " processes can explain the observed deviations from pqcd predictions of the power - law fall - off of inclusive hadron cross sections at fixed , as well as the baryon anomaly " , the anomalously large proton - to - pion ratio seen in high - centrality heavy - ion collisions at rhic . the intrinsic charm contribution to the proton structure function at high can explain the large rate for high photon plus charm - jet events observed by d0 at the tevatron . the intrinsic charm and bottom distributions imply a large production rate for charm and bottom jets at high at the lhc , as well as a novel mechanism for higgs and production at high the light - front wavefunctions derived in ads / qcd can be used to calculate jet hadronization at the amplitude level . the elimination of the renormalization scale ambiguity for the qcd coupling using the scheme - independent blm method will improve the precision of qcd predictions and thus increase the sensitivity of searches for new physics at the lhc . the implications of in - hadron condensates " for the qcd contribution to the cosmological constant are also discussed . = 1

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i

landau s fermi - liquid ( fl ) theory@xcite can describe electronic properties of some correlated electron systems at low temperatures@xcite . in this theory , low - energy excitations are described by quasiparticles ( qps ) , i.e. electrons in a self - consistent field of surrounding electrons due to electron correlation . also , the interactions between qps , described by the landau parameters , are independent of temperature . due to these two properties , the temperature dependences of physical quantities in low-@xmath4 region are governed by the temperature dependence of the fermi distribution function , and the corrections due to electron correlation , the mass enhancement and the fl correction , are independent of temperature . as a result , thermodynamic or magnetic or transport quantities show the same temperature dependences as those of the free electron system in low-@xmath4 region , and the difference is the coefficient due to the mass enhancement or the fl correction or both . for example , the specific heat is proportional to @xmath4 , and the coefficient is renormalized by the mass enhancement ; the spin susceptibility is independent of temperature , and the coefficient is renormalized by the mass enhancement and the fl correction . the original landau phenomenological theory@xcite can be justified by microscopic perturbation theory with several imposed conditions@xcite . one of the basic assumptions , the one - to - one correspondence , becomes valid if the qp damping is much smaller than temperature considered ( i.e. , the qp lifetime , the inverse of the qp damping , is very long ) . actually , the single - particle spectral function near the fermi level becomes delta - function - type in the coherent limit [ i.e. , @xmath5 for all fermi momenta ] , @xmath6^{2}+\gamma_{\alpha}^{\ast}(\boldk)^{2 } } \rightarrow z_{\alpha}(\boldk)\delta(\epsilon-\xi_{\alpha}^{\ast}(\boldk)).\label{eq : akw - fl}\end{aligned}\ ] ] here we consider only the coherent part , @xmath7 , where the self - energy is approximated as @xmath8 ; @xmath9 is @xmath10 , @xmath11 is the qp band index , @xmath12 is the qp energy , which is of the order of @xmath4 , @xmath13^{-1}$ ] is the inverse of the mass enhancement factor , and @xmath14 is the qp damping . since the delta - function - type spectral function is obtained for an exact eigenstate , the fl becomes an approximate eigenstate for momenta near the fermi level if the qp dampings at these momenta are much smaller than @xmath4 . in the fl theory the qp damping becomes small rapidly compared with decreasing temperature as a result of its @xmath15 dependence@xcite . in addition , the other basic assumption about the landau parameters becomes valid if the reducible four - point vertex functions and mass enhancement factor are independent of temperature@xcite . note , first , that the landau parameter is proportional to the product of the reducible four - point vertex function and the square root of the four mass enhancement factors@xcite ; second , that the four - point vertex function describes the multiple scattering of an electron and a hole@xcite ; third , that all reducible diagrams can be split into two parts by removing a pair of the single - particle green s functions , while all irreducible diagrams can not be done by using that removing@xcite . in contrast to successful description@xcite in the paramagnetic ( pm ) phase of sr@xmath0ruo@xmath1 , landau s fl theory fails in describing electronic properties of other pm ruthenates near a magnetic quantum - critical point ( qcp ) . for example , in sr@xmath0ru@xmath2ti@xmath3o@xmath1 , located near an antiferromagnetic ( af ) qcp@xcite , the spin susceptibility shows the curie - weiss - like temperature dependence and the inplane resistivity , @xmath16 , shows the @xmath4-linear dependence@xcite , deviating from the fl - type @xmath15 dependence ; the characteristic wave vectors of this af qcp@xcite , @xmath17 and its symmetrically equivalent ones , are the same as the wave vectors of the most strongly enhanced spin fluctuation in sr@xmath0ruo@xmath1@xcite . also , in ca@xmath18sr@xmath19ruo@xmath1 around @xmath20 , located near a ferromagnetic qcp@xcite , the curie - weiss - like temperature dependence of the spin susceptibility and @xmath21 dependence of @xmath16 are observed@xcite . since such non - fl - like behaviors are observed in other systems near a magnetic qcp@xcite or a mott transition@xcite , where many - body effects generally become very important , these experimental facts@xcite indicate the necessity of both considering how the basic assumptions of landau s fl theory are violated and discussing many - body effects beyond landau s fl theory in a more elaborate theory . so far , there are two candidates for the origin of such non - fl - like behaviors . one is bad metal@xcite due to local correlation enhanced near a mott transition . if the low - energy excitations can be satisfactorily described by using only low - order taylor series of the self - energy in terms of frequency , the coherent part of the single - particle green s function plays dominant roles in discussing electronic properties . however , if there are some non - negligible contributions from the higher - order taylor series , the incoherent part also becomes important . such case is realized in a pm metallic phase near the mott transition due to the formation of the upper and lower hubbard peaks , arising from enhanced local correlation@xcite . since perturbation theory can treat the coherent part appropriately and its treatment of the incoherent part is insufficient@xcite , perturbation theory is unsuitable in the latter case . instead , the latter case can be well described in dynamical - mean - field theory ( dmft ) since the dmft can take account of the frequency dependence of the self - energy nonperturbatively@xcite . actually , several non - fl - like behaviors are obtained in the dmft near the mott transition as a result of the @xmath4-linear unrenormalized qp damping and the temperature - dependent mass enhancement factor@xcite . [ in this paper , i define the unrenormalized qp damping as the qp damping divided by the inverse of the mass enhancement factor . ] these results indicate the importance of nonperturbative effects of local correlation near the mott transition . note that hund s metal@xcite is classified as the bad metal since the non - fl - like behaviors in the hund s metal arise from local spin fluctuation enhanced near a mott transition , although there is a crucial difference between the hund s rule coupling dependence of the critical value of the intraorbital coulomb interaction for the mott transition at half - filling and non - half - filling@xcite . the other is nearly magnetic metal@xcite due to spatial correlation enhanced near a magnetic qcp . if a system is located far away from a magnetic qcp , all scattering processes are independent of temperature . however , if the system approaches the qcp , several characteristic scattering processes of the qcp show the strong temperature - dependent enhancement@xcite . for example , in case near a stripe - type af qcp the scattering processes mediated by af spin fluctuations with @xmath22 and its symmetrically equivalent ones are strongly enhanced as decreasing temperature@xcite . such strong temperature - dependent enhancement leads to the strong temperature dependence of the reducible four - point vertex function whose momentum is characterized by the qcp . thus , the basic assumption of landau s fl theory about the landau parameters is violated only for the characteristic momenta of spin fluctuation enhanced near the qcp@xcite . also , the basic assumption about the qp damping is violated for the characteristic momenta due to the formation of hot spot , arising from enhanced spin fluctuation@xcite ; at the hot spot , the qp damping does not become much smaller than temperature considered . for example , in case near the stripe - type af qcp , the qp dampings at the momenta connected by the nesting vector @xmath22 and its symmetrically equivalent ones are more strongly enhanced than those at the other momenta due to the enhancement of the corresponding af spin fluctuations@xcite . these two violations suggest the necessity of discussing electronic properties near a magnetic qcp in the microscopic perturbation theory beyond landau s fl theory . actually , fluctuation - exchange ( flex ) approximation reproduces several non - fl - like behaviors due to the hot - spot structure of the qp damping or the curie - weiss - like temperature dependence of spin fluctuations or both@xcite . as explained in sect . 2.3 , this approximation can take account of spatial correlation beyond a mean - field theory and describe electronic properties of a metallic phase at low temperatures for moderately strong electron correlation satisfactorily@xcite . in contrast to case near the mott transition , the dmft is inappropriate to describe electronic properties near a magnetic qcp since the dmft neglects spatial correlation completely@xcite . these results indicate powerfulness of the microscopic perturbation theory and the importance of temperature - dependent spatial correlation near a magnetic qcp . with the backgrounds explained above , i studied electronic structure and magnetic and transport properties@xcite of ruthenates near and away from the af qcp in the flex approximation with current vertex corrections ( cvcs ) arising from the self - energy and maki - thompson ( mt)@xcite term for the @xmath23-orbital hubbard model on a square lattice and succeeded in reproducing several experimental results of sr@xmath0ru@xmath2ti@xmath3o@xmath1@xcite and sr@xmath0ruo@xmath1@xcite . thus , the non - fl - like behaviors@xcite in sr@xmath0ru@xmath2ti@xmath3o@xmath1 can be understood as the nearly magnetic meal near the af qcp . moreover , since the results away from the af qcp about the orbital dependence of the mass enhancement are in better agreement with the experiment@xcite in sr@xmath0ruo@xmath1 than those of the dmft@xcite , electronic properties of ruthenates at low temperatures except a few cases@xcite near the mott transition may be better described in the microscopic perturbation theory than in the dmft . in this paper , i review part of the above previous study@xcite and show some new results . in sect . 2 , i explain the microscopic theory@xcite used for analyzing @xmath16 of some quasi - two - dimensional ( quasi-@xmath24d ) pm ruthenates . in sect . 3 , i show the results about many - body effects on @xmath16 of the ruthenates near and away from the af qcp in the flex approximation with the cvcs arising from the self - energy and mt term and compare these results with the results obtained in other cases where the cvcs are more simplified . in sect . 4 , i summarize the results and draw some conclusions . due to the limit of space , i do not consider the aslamasov - larkin ( al ) cvc@xcite , which is the other cvc in the flex approximation ; its detailed derivation and effects are going to be discussed elsewhere@xcite .

i review many - body effects on the resistivity of a multiorbital system beyond landau s fermi - liquid ( fl ) theory . landau s fl theory succeeds in describing electronic properties of some correlated electron systems at low temperatures . however , the behaviors deviating from the temperature dependence in the fl , non - fl - like behaviors , emerge near a magnetic quantum - critical point . to improve this situation , i formulate the resistivity of a multiorbital hubbard model using the extended liashberg theory and adopt this method to the inplane resistivity of quasi - two - dimensional paramagnetic ruthenates in combination with the fluctuation - exchange approximation including the current vertex corrections arising from the self - energy and maki - thompson term .

i review many - body effects on the resistivity of a multiorbital system beyond landau s fermi - liquid ( fl ) theory . landau s fl theory succeeds in describing electronic properties of some correlated electron systems at low temperatures . however , the behaviors deviating from the temperature dependence in the fl , non - fl - like behaviors , emerge near a magnetic quantum - critical point . these indicate the importance of many - body effects beyond landau s fl theory . those effects in multiorbital systems have been little understood , although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems . to improve this situation , i formulate the resistivity of a multiorbital hubbard model using the extended liashberg theory and adopt this method to the inplane resistivity of quasi - two - dimensional paramagnetic ruthenates in combination with the fluctuation - exchange approximation including the current vertex corrections arising from the self - energy and maki - thompson term . the results away from and near the antiferromagnetic quantum - critical point reproduce the temperature dependence observed in srruo and srrutio , respectively . i highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems .

1503.06937

c

in summary , i reviewed many - body effects@xcite of @xmath16 of the quasi-@xmath24d pm ruthenates away from and near the af qcp in the flex approximation with the cvcs arising from the self - energy and mt term or with the cvc arising from the self - energy or without all the cvcs . the temperature dependence of @xmath16 away from and near the af qcp qualitatively agree with experiments of sr@xmath0ruo@xmath1@xcite and sr@xmath0ru@xmath2ti@xmath3o@xmath1@xcite , respectively : in case away from the af qcp , the crossover between the @xmath4-linear and the @xmath15 dependence at about @xmath218 ev and the @xmath15 dependence at low temperatures are obtained ; in case near the af qcp , the @xmath4-linear dependence even at low temperatures is obtained . here the main effect of the ti substitution on the temperature dependence of @xmath16 is assumed to be pushing the system nearer the af qcp than sr@xmath0ruo@xmath1 . the obtained results reveal some important aspects of many - body effects on the resistivity of correlated electron systems . first , the overestimation of the value of @xmath16 in the relaxation - time approximation and the back - flow - like effect of the mt cvc on the value of @xmath16 are ubiquitous . it is also ubiquitous that the power of the temperature dependence of the resistivity is determined almost by the temperature dependence of the momentum- and orbital - dependent unrenormalized qp damping . the similar results have been obtained in a single - orbital hubbard model on a square lattice@xcite . moreover , the @xmath4-linear resistivity near the af qcp is similar to that obtained in those previous studies@xcite . however , i emphasize that the criticality of the resistivity , the power of its temperature dependence , does not always connect with the criticality of spin fluctuation enhanced near a magnetic qcp in multiorbital systems , while these are always the same in single - orbital systems . this characteristic property comes from the facts that the orbital whose unrenormalized qp damping is small mainly contributes to the resistivity , and that the main orbital of the characteristic spin fluctuation of a magnetic qcp has the large unrenormalized qp damping . since the momentum , the temperature , and the orbital dependence of the damping of a qp ( i.e. , the unrenormalized qp damping or the qp damping ) are overlooked in landau s fl theory and such momentum dependence is overlooked in the dmft@xcite , the obtained results highlight their importance in discussing the resistivity of correlated electron systems . i close this paper with several remarks about the remaining issues . first , it is necessary to study the transport properties of other ruthenates@xcite using the method i used and discuss the similarities and differences . in particular , the study for a quasi-@xmath24d ruthenate@xcite near a ferromagnetic qcp is highly desirable to understand the similarities and differences between many - body effects and role of each @xmath23 orbital near the af and the ferromagnetic qcp . furthermore , it is important to analyze the transport properties of @xmath35d ruthenates@xcite since comparison of the results in quasi-@xmath24d and @xmath35d ruthenates leads to a deep understanding of the dimensionality . other remaining issues are the applications to other correlated electron systems such as transition - metal oxides@xcite , organic conductors@xcite , cecoin@xmath230@xcite , and upt@xmath38@xcite since these studies are important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems . then , it is intriguing to study the transport properties in a superconducting phase by extending the present method@xcite in a pm phase since in some cases@xcite the cvcs arising from not only spin fluctuations but also superconducting fluctuations play important roles . furthermore , another remaining issue is to clarify the role of each @xmath23 orbital in the thermal transport@xcite in the superconducting phase of sr@xmath0ruo@xmath1 on the basis of the method where the orbital dependence of the damping of a qp is satisfactorily considered . this is because the combination of my result@xcite and several previous studies@xcite suggest the existence of the difference between the main orbitals of the inplane transport and the superconductivity ; if this is correct , we should pay attention to the effects of the orbital - dependent damping of a qp on the thermal transport@xcite for correct understanding of the experimental results .

these indicate the importance of many - body effects beyond landau s fl theory . those effects in multiorbital systems have been little understood , although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems . i highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems .

i review many - body effects on the resistivity of a multiorbital system beyond landau s fermi - liquid ( fl ) theory . landau s fl theory succeeds in describing electronic properties of some correlated electron systems at low temperatures . however , the behaviors deviating from the temperature dependence in the fl , non - fl - like behaviors , emerge near a magnetic quantum - critical point . these indicate the importance of many - body effects beyond landau s fl theory . those effects in multiorbital systems have been little understood , although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multiorbital systems . to improve this situation , i formulate the resistivity of a multiorbital hubbard model using the extended liashberg theory and adopt this method to the inplane resistivity of quasi - two - dimensional paramagnetic ruthenates in combination with the fluctuation - exchange approximation including the current vertex corrections arising from the self - energy and maki - thompson term . the results away from and near the antiferromagnetic quantum - critical point reproduce the temperature dependence observed in srruo and srrutio , respectively . i highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems .

0901.4103

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the band theory of electrons predicts that any crystal with an odd number of electrons per unit cell must be a metal . however , strong electron - electron interactions can invalidate this conclusion , and such crystals can also be insulators , known as mott insulators . i will use this term here more broadly : often the mott insulator has a secondary instability to spin or charge ordering which increases the size of the unit cell , so that the ultimate ground state of the insulator does have an even number of electrons per unit cell ( many examples of such instabilities will be discussed below ) . i will continue to refer to such insulators as mott insulators because electron - electron interactions are crucial to understanding their broken symmetries and excitation spectrum . in contrast , describing the ordering by using the instabilities of a metallic state with an odd number of electrons per unit cell leads to a rather poor understanding of the insulator and of the energy scales characterizing its excitations . a canonical model used to study mott insulators is the single - band hubbard model @xmath0 where @xmath1 annihilates an electron with spin @xmath2 on the sites , @xmath3 , of a regular lattice , and @xmath4 is the number operators for these electrons . for small @xmath5 , the ground state of @xmath6 is a metal ( on most lattices ) which can be described in the traditional framework of band and fermi liquid theory . for strong repulsion between the electrons with @xmath7 , and with the chemical potential @xmath8 adjusted so that there is one electron per unit cell , charge fluctuations are strongly suppressed on each site , and the ground state is a mott insulator . the low energy excitations of the mott insulator are described by an effective hamiltonian which is projected onto the subspace of states with exactly one electron per site . these states are described by the spin orientation of each electron , and the effective hamiltonian is a heisenberg quantum spin model @xmath9 where @xmath10 is the antiferromagnetic exchange interaction , @xmath11 is the spin @xmath12 operator on site @xmath3 , and the ellipses refer to multiple spin - exchange terms which are generated at higher orders in the expansion in @xmath13 . one of the purposes of this article is to survey theoretical advances in understanding the ground states of @xmath14 on a variety of lattices in two spatial dimensions . a number of experimental realizations ( some newly discovered ) will also be surveyed and critically compared with theory . more broadly , the study of models like @xmath6 and @xmath14 will lead us to a number of exotic phases , both insulating and conducting , which require modern concepts from gauge theory and ` topological ' order for their complete characterization . our unifying strategy here will be to access these exotic states across a quantum phase transition from a conventional state . we will begin by characterizing the ` order ' in a conventional state , and then turn up the strength of quantum fluctuations leading to a quantum ` disordering ' transition to an exotic state . this approach will lead to 4 broad classes of exotic states , discussed in the sections below : + ( _ i _ ) . we begin with an insulator with antiferromagnetic long - range order , well described by @xmath14 . quantum fluctuations of the antiferromagnetism lead to states with full su(2 ) spin rotation symmetry , and an energy gap to spin excitations . in section [ sec : lgw ] we consider a simple , and now well - understood model : the coupled dimer antiferromagnet . in this case , well - developed methods from the theory of finite temperature phase transitions can be extended to successfully describe its ground states and quantum phase transition . in section [ sec : tri ] , we will introduce a recent experimental example of a triangular lattice antiferromagnet , and develop a theory for the non - magnetic insulating states in which the quantum interference effects play a more fundamental role , and new theoretical ideas are required . + ( _ ii _ ) . we begin with the fermi liquid state of @xmath6 , characterized by a fermi surface ( in some cases , fermi points ) of charge @xmath15 , spin @xmath12 quasiparticles . now we postulate a continuous mott transition to an insulator in which the spin and charge of the quasiparticles separate , and a ` ghost ' fermi surface survives in the insulator , with the fermi surface excitations carrying @xmath12 spin , but no charge ; these are fermionic spinons . the current status of such exotic states will be reviewed in section [ sec : mott ] . + ( _ iii _ ) . as discussed in section [ sec : ffl ] , the heavy fermion state of rare - earth intermetallics is described by the kondo - heisenberg model describing the exchange coupling of local moments to itinerant conducting electrons . the kondo effect tightly entangles the local spins and the itinerant electrons , leading to a ` large fermi surface ' state , which encloses a volume determined by the total electron density , including both the local and itinerant electrons . for sufficiently strong exchange between the spins , the kondo screening can break down , and the local moments and itinerant electrons disentangle , leading to a ` fractionalized fermi liquid ' . in the simplest models , the itinerant electrons form a small , metallic fermi surface of conventional electronic quasiparticles , while the local moments form a spinon fermi surface . + ( _ iv _ ) . we begin with a metallic fermi liquid state , in the presence of spin density wave order . this order will generally break up the fermi surface into electron and hole pockets . section [ sec : acl ] will describe a quantum transition in which the spin density wave order becomes short range , but ghost fermi pockets survive in the resulting ` algebraic charge liquid ' . in the latter state , the fermi surface excitations carry charge @xmath15 but no spin . such a state has been used recently to develop a theory of the enigmatic underdoped region of the cuprates . the concluding section [ sec : exp ] will survey recent experiments on mott insulators on a number of frustrated lattices , and compare observations with numerical studies and the theoretical proposals .

i survey theoretical advances in our understanding of the quantum phases and phase transitions of mott insulators , and of allied conducting systems obtained by doping charge carriers . a number of new experimental examples of mott insulators have appeared in recent years , and i critically compare their observed properties with the theoretical expectations .

i survey theoretical advances in our understanding of the quantum phases and phase transitions of mott insulators , and of allied conducting systems obtained by doping charge carriers . a number of new experimental examples of mott insulators have appeared in recent years , and i critically compare their observed properties with the theoretical expectations . rapporteur talk at the 24th solvay conference on physics , + _ quantum theory of condensed matter _ , brussels , oct 11 - 13 , 2008

1311.6553

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there are three well - known large - scale star forming regions ( w3/w4/w5 @xcite ) in the cas ob6 association . w5 ( also called the ic 1848 h ii region ) is the eastern part of the molecular cloud complex and consists of two components w5 west and w5 east @xcite . there are four known o stars , hd 17505 , hd 17520 , hd 237019 and bd + 60 586 in w5 west , while one visible o star hd 18326 is at the center of w5 east . all but hd 237019 are surrounded by many low - mass stars in clusters . these o stars are thought to be the ionizing sources of the h ii region . the simple morphology of each h ii region helps us to study the influence of strong uv radiation from massive stars on the surrounding materials and the triggering mechanisms for star formation @xcite . hence , w5 is an ideal laboratory to study star formation processes with feed back from high - mass stars . the initial mass function ( imf ) of this star forming region is also an interesting scientific issue . in this context , our target of interest is the ic 1848 cluster ( hereafter ic 1848 ) , also known as ocl 364 , situated in the center of w5 west , containing the brightest star hd 17505 , which is a multiple system consisting of an o6.5iii , two o7.5v , and an o8.5v stars @xcite . many investigators ( @xcite and therein ) provided radio maps at various frequencies to investigate the large - scale structures and the physical properties of the w3/w4/w5 complex . since active star formation takes place in these regions , investigators have a continuing interest in the processes involved . @xcite and @xcite studied star formation in w5 a ( or ic 1848 a ) , which is a bright - rimmed molecular cloud to the eastern end of w5 . @xcite discussed many interesting observational aspects associated with the triggered star formation in w5 . a census of embedded stellar sources in the w3/w4/w5 region have been published by @xcite . the authors identified 19 clusters , with about half the stars in 5 rich clusters . @xcite identified several young stellar objects ( ysos ) using the iras point source catalog and found that the young stars are mainly distributed around the edge of the h ii region . the authors argued from a comparison of evolutionary time scales that there is a distinct difference in the star formation history of the ionizing stars and the young stars on the border of expanding h ii regions . because of the presence of clumps evaporating away from the ionising sources and the shorter time scale for star formation under the assumed expanding velocities , they also suggested that radiatively driven implosion - star formation triggered by the strong uv radiation from young ob stars @xcite - may be the dominant triggering mechanism in w5 . _ spitzer_/irac and mips imaging data , @xcite provided photometric data for more than 17,000 point sources and yso classifications . the identified ysos made it possible to study the clustering properties of these ysos and to discuss plausible triggering mechanisms required to explain the distinct generations within w5 . the high resolution irac and mips images revealed several isolated cometary globules and elephant trunk structures with polycyclic aromatic hydrocarbon ( pah ) emission . later @xcite studied the disk evolution of intermediate - mass stars . cometary globules , bright - rimmed clouds , and h ii region outflows are suggested as evidence of triggered star formation , and many studies have investigated the physical properties of these objects @xcite . several photometric studies @xcite involving ic 1848 have been made in the optical bands . these studies provided useful photometric data and fundamental parameters , such as reddening , distance , and age for ic 1848 . however , most analyses assumed a normal reddening law ( @xmath13 ) , and the multiplicity of early - type stars was not fully taken into account . furthermore , the limiting magnitudes were not deep enough to study the pre - main sequence ( pms ) stars fainter than @xmath14 mag in the young clusters or associations in the perseus arm . recently , a deep @xmath15 photometric study for ic 1848 w5 east has been made by @xcite with archival data . the authors presented the imf for stars in the mass range from @xmath16 to @xmath17 , as well as their fundamental parameters . however , no deep optical photometric study has been made for ic 1848-w5 west . since the results of @xcite provided very good membership criteria for the pms stars with accretion disks , the age distribution and mass accretion rates of pms stars , the star formation history within the region , and the imf down to the @xmath18 regime can be studied . in addition , the two micron all sky survey ( 2mass ) @xcite and _ spitzer_/irac data @xcite make it possible to test carefully the reddening law in a wide wavelength range . the previously published distance to ic 1848 , derived using various methods , is in the range 1.7 to 2.4 kpc . the photometric surveys mentioned above provided distances of 1.7 kpc @xcite , @xmath19 kpc @xcite , @xmath5 kpc @xcite , and 2.3 kpc @xcite . some studies have implicitly assumed that the distance to ic 1848 is the same as that to w3 or w4 ( or ic 1805 ) ( 1.9 2.4 kpc ) . @xcite independently derived a distance of 2.3 kpc using their galactic rotation model . early studies have relied on this distance . recently , @xcite derived a distance of @xmath20 kpc for a w3oh maser using its vlbi parallax . @xcite preferred to use a distance of 1.89 kpc to match the observed and theoretical stellar radii . since distance is a critical parameter in converting observational quantities to reliable physical parameters , we need to revisit its determination . the sejong open cluster survey ( sos ) project is dedicated to provide homogeneous photometric data down to @xmath21 mag for many open clusters . the overview of the project can be found in @xcite ( paper 0 ) . the young open cluster ngc 2353 was studied as part of this project @xcite . this paper on ic 1848 is the third in the series . the observations and comparisons with previous photometry are described in section 2 . in section 3 , we discuss the reddening law in the direction of ic 1848 and present fundamental parameters estimated from the photometric diagrams . the imf of ic 1848 and the mass accretion rates of pms stars with uv excesses are presented in section 4 and 5 , respectively . finally , we summarize the results from this study in section 6 . @xmath22 , j2000 ) . squares outline the observed regions.,scaledwidth=45.0% ]

h photometry and the list of young stellar objects identified by koenig et al . permitted us to select a large number of pms stars comprising 196 h emission stars , 35 h emission candidates , 5 class i , 368 class ii , and 24 transition disk candidates . from the hertzsprung - russell diagram using stellar evolution models the imf was derived from stars with mass larger than , and the slope is slightly steeper ( ) than the salpeter / kroupa imf . finally , we estimated the mass accretion rate of pms stars with a uv excess .

ic 1848 is one of the young open clusters in the giant star forming cas ob6 association . several interesting aspects relating to star formation processes in giant star forming regions attracted us to study the initial mass function ( imf ) , star formation mode , and properties of pre - main sequence stars ( pms ) . a and h photometric study of the young open cluster ic 1848 was conducted as part of the sejong open cluster survey " ( sos ) . we have selected 105 early - type members from photometric diagrams . their mean reddening is mag . using the published photometric data with near- and mid - infrared archival data we confirmed the normal reddening law ( ) toward the cluster ( ic 1848 ) . a careful zero - age main sequence fitting gives a distance modulus of mag , equivalent to kpc . h photometry and the list of young stellar objects identified by koenig et al . permitted us to select a large number of pms stars comprising 196 h emission stars , 35 h emission candidates , 5 class i , 368 class ii , and 24 transition disk candidates . from the hertzsprung - russell diagram using stellar evolution models , we estimate an age of 5 myr from several evolved stars and 3 myr from the pms stars . the imf was derived from stars with mass larger than , and the slope is slightly steeper ( ) than the salpeter / kroupa imf . finally , we estimated the mass accretion rate of pms stars with a uv excess . the mean mass accretion rate is about in the mass range of to , whereas intermediate - mass stars ( ) exhibit a much higher accretion rate of . [ firstpage ] open clusters and associations : individual ( ic 1848 ) circumstellar matter stars : luminosity function , mass function accretion , accretion disks

1606.03642

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inspection of bridges , tunnels , wind turbines , and other large civil engineering structures for defects is a time - consuming , costly , and potentially dangerous task . in the future , _ smart coating _ technology , or _ smart paint _ , could do the job more efficiently and without putting people in danger . the idea behind smart coating is to form a thin layer of a specific substance on an object which then makes it possible to measure a condition of the surface ( such as temperature or cracks ) at any location , without direct access to the location . the concept of smart coating already occurs in nature , such as proteins closing wounds , antibodies surrounding bacteria , or ants surrounding food to transport it to their nest . these diverse examples suggest a broad range of applications of smart coating technology in the future , including repairing cracks or monitoring tension on bridges , repairing space craft , fixing leaks in a nuclear reactor , or stopping internal bleeding . we continue the study of coating problems in the context of self - organizing programmable matter consisting of simple computational elements , called particles , that can establish and release bonds and can actively move in a self - organized way using the geometric version of the amoebot model presented in @xcite . in doing so , we proceed to investigate the runtime analysis of our universal coating algorithm , introduced in @xcite . we first show that coating problems do not only have a ( trivial ) linear lower bound on the runtime , but that there is also a linear lower bound on the competitive gap between the runtime of fully local coating algorithms and coating algorithms that rely on global information . we then investigate the worst - case time complexity of our universal coating algorithm and show that it terminates within a linear number of rounds with high probability ( w.h.p . ) , where @xmath0 is the number of particles in the system and @xmath1 is a constant . ] , which implies that our algorithm is optimal in terms of worst - case runtime and also in a competitive sense . moreover , our simulation results show that in practice the competitive ratio of our algorithm is often better than linear . in the _ geometric amoebot model _ , we consider the graph @xmath2 , where @xmath3 is the infinite regular triangular grid graph . each vertex in @xmath4 is a position that can be occupied by at most one particle ( see figure [ fig : graph_handover](a ) ) . each particle occupies either a single node or a pair of adjacent nodes in @xmath2 . any structure a particle system can form can be represented as a subgraph of @xmath2 . two particles occupying adjacent nodes are _ connected _ by a _ bond _ , and we refer to such particles as _ neighbors_. the bonds do not only ensure that the particles form a connected structure but they are also used for exchanging information as explained below . particles move by executing a series of _ expansions _ and _ contractions_. a particle which occupies one node is _ contracted _ and can expand to an unoccupied adjacent node to occupy two nodes . if it occupies two nodes it is _ expanded _ and can contract to occupy a single node . in figure [ fig : graph_handover](b ) , we illustrate a set of expanded and contracted particles on the underlying graph @xmath2 . for an expanded particle , we denote the node the particle last expanded into as the _ head _ of the particle and the other occupied node as its _ tail_. for a contracted particle , the single node occupied by the particle is both its head and its tail . , where nodes of @xmath2 are shown as black circles . ( b ) shows five particles on @xmath2 ; the underlying graph @xmath2 is depicted as a gray mesh ; a contracted particle is depicted as a single black circle and an expanded particle is depicted as two black circles connected by an edge . ( c ) depicts the resulting configuration after a handover was performed by particles @xmath5 and @xmath6 in ( b ) . ] [ fig : graph_handover ] to stay connected as they move , neighboring particles coordinate their motion in a _ handover _ , which can occur in two ways . a contracted particle @xmath5 can initiate a handover by expanding into a node occupied by an expanded neighbor @xmath6 , `` pushing '' @xmath6 and forcing it to contract . alternatively , an expanded particle @xmath6 can initiate a handover by contracting `` pulling '' a contracted neighbor @xmath5 to the node it is vacating , thereby forcing @xmath5 to expand . figures [ fig : graph_handover](b ) and [ fig : graph_handover](c ) illustrate two particles labeled @xmath5 and @xmath6 performing a handover . particles are _ anonymous _ but each has a collection of uniquely labeled _ ports _ corresponding to the edges incident to the nodes the particle occupies . bonds between adjacent particles are formed through ports that face each other . the particles are assumed to have a common _ chirality _ , meaning they share the same notion of _ clockwise ( cw ) direction_. this allows each particle @xmath5 to label its ports counting in the clockwise direction ; without loss of generality , we assume each particle labels its head and tail ports from @xmath7 to @xmath8 . however , particles may have different offsets of the labelings , so they do not share a common sense of orientation . each particle hosts a local memory of constant size for which any neighboring particle has read and write access . with this mechanism particles can communicate by writing into each other s memory . the _ configuration _ @xmath9 of the system at the beginning of time @xmath10 consists of the nodes in @xmath2 occupied by the object and the set of particles , and for each particle @xmath5 , @xmath9 contains the current state of @xmath5 , including whether it is expanded or contracted , its port labeling , and the contents of its local memory . following the standard asynchronous model of computation @xcite , we assume that the system progresses through atomic _ activations _ of individual particles . at each ( atomic ) activation a particle can perform at most one movement and an arbitrary bounded amount of computation involving its local memory and the shared memories of its neighbors . a classical result under this model is that for any asynchronous execution of atomic particle activations , we can organize these activations sequentially still producing the same end configuration @xcite . we count ( asynchronous ) time in terms of the number of activations . a _ round _ is over once each particle has been activated at least once . we assume the activation sequence to be _ fair _ , i.e. , for each particle @xmath5 and any point in time @xmath10 , @xmath5 will eventually be activated at some time @xmath11 . in the _ universal coating problem _ we consider an instance @xmath12 where @xmath13 represents the particle system and @xmath14 represents the fixed object to be coated . let @xmath15 be the number of particles in the system , @xmath16 be the set of nodes occupied by @xmath13 , and @xmath17 be the set of nodes occupied by @xmath14 ( when clear from the context , we may omit the @xmath18 notation ) . for any two nodes @xmath19 , the _ distance _ @xmath20 between @xmath21 and @xmath22 is the length of the shortest path in @xmath2 from @xmath21 to @xmath22 . the distance @xmath23 between a @xmath24 and @xmath25 is defined as @xmath26 . define _ layer @xmath27 _ to be the set of nodes that have a distance @xmath27 to the object , and let @xmath28 be the number of nodes in layer @xmath27 . an instance is _ valid _ if the following properties hold : 1 . the particles are all contracted and are initially in the _ idle _ state . the subgraphs of @xmath2 induced by @xmath17 and @xmath29 , respectively , are connected , i.e. , there is a single object and the particle system is connected to the object . the subgraph of @xmath2 induced by @xmath30 is connected , i.e. , the object @xmath14 has no holes . does contain holes , we consider the subset of particles in each connected region of @xmath30 separately . ] @xmath30 is @xmath31-connected , i.e. , @xmath14 can not form _ tunnels _ of width less than @xmath31 . note that a width of at least @xmath32 is needed to guarantee that the object can be evenly coated . the coating of narrow tunnels requires specific technical mechanisms that complicate the protocol without contributing to the basic idea of coating , so we ignore such cases in favor of simplicity . a configuration @xmath9 is _ legal _ if and only if all particles are contracted and @xmath33 meaning that all particles are as close to the object as possible or _ coat @xmath14 as evenly as possible_. a configuration @xmath9 is said to be _ stable _ if no particle in @xmath9 ever performs a state change or movement . an algorithm _ solves _ the universal coating problem if , starting from any valid instance , it reaches a _ stable legal configuration _ in a finite number of rounds . many approaches have been proposed with potential applications in smart coating ; these can be categorized as active and passive systems . in passive systems , particles move based only on their structural properties and interactions with their environment , or have only limited computational ability and lack control of their motion . examples include dna self - assembly systems ( see , e.g. , the surveys in @xcite ) , population protocols @xcite , and slime molds @xcite . our focus is on active systems , in which computational particles control their actions and motions to complete specific tasks . coating has been extensively studied in the area of _ swarm robotics _ , but not commonly treated as a stand - alone problem ; it is instead examined as part of _ collective transport _ ( e.g. , @xcite ) or _ collective perception _ ( e.g. , see respective section of @xcite ) . some research focuses on coating objects as an independent task under the name of _ target surrounding _ or _ boundary coverage_. the techniques used in this context include stochastic robot behaviors @xcite , rule - based control mechanisms @xcite and potential field - based approaches @xcite . while the analytic techniques developed in swarm robotics are somewhat relevant to this work , those systems have more computational power and movement capabilities than those studied in this work . michail and spirakis recently proposed a model @xcite for network construction inspired by population protocols @xcite . the population protocol model is related to self - organizing particle systems but is different in that agents ( corresponding to our particles ) can move freely in space and establish connections at any time . it would , however , be possible to adapt their approach to study coating problems under the population protocol model . in @xcite we presented our universal coating algorithm and proved its correctness . we also showed it to be worst - case work - optimal , where work is measured in terms of number of particle movements . in this paper we continue the analysis of the _ universal coating algorithm _ introduced in @xcite . as our main contribution in this paper , we investigate the runtime of our algorithm and prove that our algorithm terminates within a _ linear number of rounds _ with high probability . we also present a matching linear lower bound for local - control coating algorithms that holds with high probability . we use this lower bound to show a _ linear lower bound on the competitive gap _ between fully local coating algorithms and coating algorithms that rely on global information , which implies that our algorithm is also optimal in a competitive sense . we then present some simulation results demonstrating that in practice the competitive ratio of our algorithm is often much better than linear . in section [ sec : algo ] , we again present the algorithm introduced in @xcite . we present a comprehensive formal runtime analysis of our algorithm , by first presenting some lower bounds on the competitive ratio of any local - control algorithm in section [ sec : performance ] , and then proving that our algorithm has a runtime of @xmath34 rounds w.h.p . in section [ sec : wcruntime ] , which matches our lower bounds .

imagine coating buildings and bridges with smart particles ( also coined smart paint ) that monitor structural integrity and sense and report on traffic and wind loads , leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time . in this paper , we study the problem of uniformly coating objects of arbitrary shape in the context of _ self - organizing programmable matter _ , i.e. , the programmable matter consists of simple computational elements called particles that can establish and release bonds and can actively move in a self - organized way . we continue the study of our universal coating algorithm by focusing on its runtime analysis , showing that our algorithm terminates within a _ linear number of rounds _ with high probability . we also present a matching linear lower bound that holds with high probability . we use this lower bound to show a _ linear lower bound on the competitive gap _ between fully local coating algorithms and coating algorithms that rely on global information , which implies that our algorithm is also optimal in a competitive sense . simulation results show that the competitive ratio of our algorithm may be better than linear in practice .

imagine coating buildings and bridges with smart particles ( also coined smart paint ) that monitor structural integrity and sense and report on traffic and wind loads , leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time . in this paper , we study the problem of uniformly coating objects of arbitrary shape in the context of _ self - organizing programmable matter _ , i.e. , the programmable matter consists of simple computational elements called particles that can establish and release bonds and can actively move in a self - organized way . particles are anonymous , have constant - size memory and utilize only local interactions in order to coat an object . we continue the study of our universal coating algorithm by focusing on its runtime analysis , showing that our algorithm terminates within a _ linear number of rounds _ with high probability . we also present a matching linear lower bound that holds with high probability . we use this lower bound to show a _ linear lower bound on the competitive gap _ between fully local coating algorithms and coating algorithms that rely on global information , which implies that our algorithm is also optimal in a competitive sense . simulation results show that the competitive ratio of our algorithm may be better than linear in practice .

1301.4518

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in this paper , the diagram monoids @xmath0 and one of its submonoids @xmath1 are first introduced in order to get an understanding of the diagram monoids @xmath2 and @xmath3,which are submonoids of @xmath1 . presentations of the latter two are provided in this paper , as well as references to papers in which presentations for the former two are provided . we then introduce the well known temperley - lieb algebra , @xmath4 . with these diagram monoids and the temperley - lieb algebra , we can give a presentation of the motzkin monoid , @xmath5 . in particular , we show that any diagram in @xmath5 can be decomposed into a product of the form @xmath6 , where @xmath7 , @xmath8 , and @xmath9 . ( note there is a particular form called standard " form mainly involving the placement of empty vertices . ) this is particularly important because of the inductive nature of our proof . + we start with a word in @xmath6 form , append a generator , @xmath10 , to the end of the word , and then try to get it back into @xmath6 form . we apply the relations of @xmath5 to first get @xmath11 into the form @xmath12 ( which we call @xmath13 form ) , where @xmath14 , and @xmath8 . from this @xmath13 form , we then get to minimal @xmath6 form , which is done by taking a diagram in @xmath13 form , and moving all the empty vertices to the right . this is done using five lemmas ( hop , burrow , slide , wallslide , and fuse wire ) , and also putting an order on @xmath1 . from here , we concern ourselves with the case that the edges in @xmath15 in minimal @xmath6 form have endpoints that are empty vertices of @xmath16 or @xmath17 . we show that we can put words of this form into standard @xmath6 form ( where standard @xmath6 form is as defined in section 4.3.1 ) . + the preceding inductive proof tells us that the number of distinct words is equal to the number of standard words , and thus equal to the number of diagrams in @xmath5 , giving us a presentation of @xmath5 . we define the _ rook monoid _ , denoted @xmath0 , as the set of one - to - one functions from a subset of @xmath18 to a subset of @xmath18 . these functions can be written as diagrams : a graph on two rows of @xmath19 vertices , each labeled from @xmath20 to @xmath19 from left to right . on the graph we connect vertices on the top line to vertices on the bottom line . take for example the following diagram in @xmath21 : + @xmath22 the rook monoid is a _ monoid _ under the operation of function composition , where the functions go from the top row of vertices to the bottom . to perform function composition with two diagrams @xmath23 , @xmath24 , we place @xmath23 above @xmath24 and identify the vertices in the bottom row of @xmath23 with the corresponding vertices in the top row of @xmath24 . in terms of functions , if we consider @xmath23 as the function @xmath25 , and @xmath24 as the function @xmath26 , then the product @xmath27 is thought of as the composition @xmath28 , where if @xmath29 is in the range of @xmath25 , and in the domain of @xmath26 , we get that the pre - image of @xmath29 , say @xmath30 , in @xmath25 is in the domain of @xmath28 , and the image of @xmath29 , say @xmath31 , in @xmath26 is in the range of @xmath28 . in particular , @xmath30 is in the domain of @xmath28 if and only if there exists @xmath29 in the domain of @xmath26 such that @xmath32 . this @xmath30 then corresponds to the value @xmath31 in the range of @xmath28 such that @xmath33 . note that in the diagram form we then draw an edge from @xmath30 on top to @xmath31 on bottom . for example , + if @xmath23= units < 0.3cm,0.15 cm > x from 1 to 6 , y from 0 to 3 = 0.3pt at 1 -1 at 1 2 at 2 -1 at 2 2 at 3 -1 at 3 2 at 4 -1 at 4 2 at 5 -1 at 5 2 1 -1 1 2 / 3 -1 2 2 / 5 -1 3 2 / 2 -1 4 2 / 4 -1 5 2 / and @xmath24= units < 0.3cm,0.15 cm > x from 1 to 6 , y from 0 to 3 = 0.3pt at 1 -1 at 1 2 at 2 -1 at 2 2 at 3 -1 at 3 2 at 4 -1 at 4 2 at 5 -1 at 5 2 1 -1 1 2 / 2 -1 3 2 / 3 -1 5 2 / 4 -1 4 2 / units < 0.3cm,0.15 cm > x from 1 to 12 , y from 0 to 3 = 0.3pt at 1 -3.5 at 1 -.5 at 1 1 at 1 4 at 2 -3.5 at 2 -.5 at 2 1 at 2 4 at 3 -3.5 at 3 -.5 at 3 1 at 3 4 at 4 -3.5 at 4 -.5 at 4 1 at 4 4 at 5 -3.5 at 5 -.5 at 5 1 at 5 4 at -4 .5 at 8 2 at 8 -1 at 9 2 at 9 -1 at 10 2 at 10 -1 at 11 2 at 11 -1 at 12 2 at 12 -1 at 6.5 .5 1 1 1 4 / 2 1 4 4 / 2 4 3 1 / 3 4 5 1 / 4 4 2 1 / 5 4 4 1 / 1 -.5 1 -3.5 / 2 -3.5 3 -.5 / 3 -3.5 5 -.5 / 4 -3.5 4 -.5 / 8 2 8 -1 / 9 2 9 -1 / 10 2 10 -1 / 12 2 11 -1 / another way to think about the rook monoid , @xmath0 , is as the set of @xmath34 matrices which have entries in the set @xmath35 , with the property that there is at most one @xmath20 in each row and each column . take for example , @xmath36 , which consists of the matrices : @xmath37 note that the elements in @xmath0 are in a one - to - one correspondence with the possible ways in which one can place non - attacking rooks on a @xmath34 chess board . we define the _ rank _ of a diagram as the number of edges it has , or the number of @xmath20s in the corresponding matrix . + if we desire a rook matrix of rank @xmath38 , we choose @xmath38 columns and @xmath38 rows in a total of @xmath39 ways . we then can choose to place the @xmath20s in the @xmath38 chosen rows / columns in a total of @xmath40 ways ( such that no row or column has two or more nonzero entries ) . summing over all the possible ranks up to and including @xmath19 gives rise to the order of @xmath0 : @xmath41 the relationship between diagrams and matrices is given in a very natural way . we connect the vertex in the @xmath42 position in the top row of a diagram to the @xmath43 position in the bottom row if and only if the corresponding matrix has a 1 in the ( @xmath44,@xmath45)-position . take for example the following matrix - diagram correspondence in @xmath21 : @xmath46 note that matrix multiplication is equivalent to diagram multiplication by stacking : @xmath47 is equivalent to @xmath48 a presentation of the rook monoid is provided on page 339 in @xcite . the _ planar rook monoid _ , @xmath1 , is the set of order - preserving one - to - one functions from a subset of @xmath49 to a subset of @xmath49 . these order - preserving functions correspond to those diagrams that can be drawn with edges that do not cross . for example , the set @xmath50 consists of the following diagrams : @xmath50 = @xmath51 @xmath52 @xmath53 @xmath54 @xmath55 @xmath56 for a diagram @xmath57 , we define @xmath58 and @xmath59 to be the sets containing the indices of the vertices of @xmath57 which are incident to an edge on top and on bottom respectively . for example , if @xmath57 = @xmath60 , then @xmath61(@xmath57 ) = \{1,2,3,5 } and @xmath62(@xmath57 ) = \{@xmath63,@xmath64,@xmath65,@xmath66 } + where we label the top vertices from 1 to @xmath19 and the bottom vertices from @xmath63 to @xmath67 . for a planar rook diagram @xmath57 , there is only one way to connect the vertices by edges , thus these sets @xmath61(@xmath57 ) and @xmath62(@xmath57 ) uniquely determine @xmath57 . + notice that the product of two planar rook diagrams is planar ( seen easily through diagram multiplication ) , thus @xmath1 is a submonoid of @xmath0 . to obtain the order of @xmath1 , as in @xmath0 , we choose @xmath38 columns , and @xmath38 rows in @xmath39 , however as stated above this choosing determines a unique diagram , thus the total number of planar rook diagrams is : @xmath68 let @xmath69 be the element of @xmath1 such that @xmath70\setminus\{i+1\}$ ] and @xmath71\setminus\{i\}=\{1,2,\ldots , i-1,i+i,\ldots , n\}$ ] , as shown below : @xmath72 let @xmath73 be the element of @xmath1 such that @xmath74\setminus\{i\}$ ] and @xmath75\setminus\{i+1\}$ ] as shown below : @xmath76 as proven in @xcite , every planar rook diagram can be written as a product of @xmath69 s and @xmath73 s . the following relations hold for all @xmath44 such that the terms in the relation are defined : 1 . @xmath77 2 . \a ) @xmath78 + b ) @xmath79 3 . \a ) @xmath80 + b ) @xmath81 4 . \a ) @xmath82 + b ) @xmath83 + c ) @xmath84 + d ) @xmath85 5 . @xmath86 6 . if @xmath87 , then @xmath88 these relations can easily be verified by drawing the diagram products they refer to . furthermore , as proven in @xcite , these relations suffice to completely characterize @xmath1 .

in 2010 , tom halverson and georgia benkart introduced the motzkin algebra , a generalization of the temperley - lieb algebra , whose elements are diagrams that can be multiplied by stacking one on top of the other . halverson and benkart gave a diagrammatic algorithm for decomposing any motzkin diagram into diagrams of three subalgebras : the right planar rook algebra , the temperley - lieb algebra , and the left planar rook algebra .

in 2010 , tom halverson and georgia benkart introduced the motzkin algebra , a generalization of the temperley - lieb algebra , whose elements are diagrams that can be multiplied by stacking one on top of the other . halverson and benkart gave a diagrammatic algorithm for decomposing any motzkin diagram into diagrams of three subalgebras : the right planar rook algebra , the temperley - lieb algebra , and the left planar rook algebra . we first explore the right and left planar rook monoids , by finding presentations for these monoids by generators and relations , using a counting argument to prove that our relations suffice . we then turn to the newly - developed motzkin monoid , where we describe halverson s decomposition algorithm algebraically , find a presentation by generators and relations , and use a counting argument but with a much more sophisticated algorithm .

1301.3094

i

electrons in a bernal - stacked graphene bilayerbilayerreview , castrojphys behave as a chiral two - dimensional gas of massive dirac fermions ( c2deg)@xcite . the chiral nature of the electrons lead to transport and optical properties that are different from those of conventional semiconductor 2deg s or of the 2deg in monolayer graphene . in particular , in the absence of coulomb interaction , the landau level ( ll ) spectrum is given by @xmath8 where the landau level index @xmath9 and the effective cyclotron frequency @xmath10 where @xmath11 is the magnetic field and @xmath12 the effective mass of the electrons . each landau level is four - time degenerate when counting valley and spin degrees of freedom with the exception of landau level @xmath5 which is eight - time degenerate . indeed , an electronic state in landau level @xmath5 is specified by its guiding - center @xmath1 ( in the landau gauge ) , spin @xmath13 valley @xmath14 and orbital @xmath15 indices@xcite . ( in landau level @xmath16 valley and layer degrees of freedom are equivalent . ) when the coulomb interaction is negligible with respect to the disorder broadening at low temperature and when the small zeeman splitting is neglected , the eight states in @xmath5 are degenerate and the hall conductivity has plateaus at @xmath17 where @xmath18@xcite . in recent transport experimentsfeldman , martin , bao , dean , zhao , velasco , freitag , weitz , it was shown that in sufficiently pure sample , when disorder is low or when the magnetic field is large enough , the coulomb interaction completely lifts the degeneracy of the @xmath5 octet and lead to the formation of seven new plateaus in the hall conductivity i.e. @xmath19 where @xmath20 .$ ] these plateaus were attributed to the formation of broken - symmetry many - body ground states . these states can alternatively be described as quantum hall ferromagnets ( qhf s ) where the spin and/or valley pseudospins and/or orbital pseudospins are spontaneously and collectively aligned in space@xcite . in bilayer graphene , a top - bottom gates voltage imbalance can be applied to create a potential difference @xmath6 ( which we call the `` bias '' hereafter ) between the two layers . in dual - gated bilayer graphene , @xmath21 and the total density of electrons in the bilayer can be controlled independently . this allows the phase diagram of the c2deg to be studied as a function of @xmath7 magnetic field and temperature . such study has been done by weitz et al.@xcite in high - quality bilayer graphene suspended between a top gate electrode and the substrate . the measurements show a series of phase transitions between different qhf states as @xmath21 is increased at given filling factor and magnetic field . special attention has been given to the filling factor @xmath22 where the precise nature of the ground state when @xmath23 near zero bias is still debated@xcite . all experiments were done at relatively small magnetic field @xmath24 t with the exception of the experiments reported in ref . where @xmath11 reached @xmath25 t. various aspects of the qhf states in bilayer graphene ( in particular the nature and the evolution of the ground state of the c2deg near charge neutrality as @xmath23 ) have been studied theoretically by a number of authorsnandkishore , gorbarnu0,gorbarnutot , gorbarconductivity , shizuya2012,shizuyadipole , shizuyacyclotron , shizuyamodes01,sari . in the work of gorbar et al.@xcite and shizuyashizuya2012 , the phase diagram of the c2deg as a function of bias for @xmath26 is presented . gorbar et al . have considered the effect of both static@xcite and dynamical screenings@xcite of the coulomb interaction . the modified gap equation captures the linear scaling of the transport gaps with the magnetic field which is seen in all the experiments at low magnetic field . the transport gaps are also strongly reduced with respect to the unscreened case and become more comparable to those observed experimentally . the dynamical screening was found to reproduce the offset in the behavior of the gap with magnetic field in the spin - polarized qhf state near zero bias which is seen in the experiments@xcite . shizuya points out that the filled levels @xmath27 can not be considered as completely inert . instead , they lead to a correction @xmath28 of the energy of the orbital levels @xmath15 that can change the ordering of these states in a way that depend on their occupation . a negative capacitance effect is also found that suppress rotation of the valley pseudospins . the work that we present in this paper extends our previous study of the phase diagram of the c2deg at zero biasbarlasprl1,barlasprl2,coteorbital , coteorbital2 and complements the study of gorbar et al . and shizuya . we give a comprehensive account of the phase diagram of the c2deg in bilayer graphene at all integer filling factors @xmath29 $ ] in landau level @xmath5 as a function of an applied bias @xmath6 at a fixed magnetic field . our analysis is based on an effective two - band model@xcite which describes the low - energy physics near the valleys @xmath30 . we explicitly take into account as symmetry - breaking terms the zeeman splitting @xmath31 and the bias @xmath32 . in the effective two - band model , the bias @xmath6 lifts the degeneracy between the orbital levels @xmath33 and @xmath34 by a small amount @xmath35 where @xmath36 with @xmath37 the interlayer hopping between carbon atoms that are part of a dimer . we also include in our model the interlayer next nearest - neighbor hopping term @xmath38 between carbons atoms in the same sublattices . this term causes a small asymmetry in the electronic band structure and was neglected in previous studies@xcite . it combines with the correction @xmath39 to give an energy difference @xmath40 between the @xmath34 and @xmath33 orbital levels where @xmath41 is the intralayer hopping energy between nearest - neighbors . this correction is thus finite at zero bias and breaks the orbital degeneracy . our phase diagram is not electron - hole symmetric around @xmath22 and the sequence of phase transitions is different for each filling factor . in our analysis , we treat the electron interaction in the hartree - fock approximation ( hfa ) and compute the collective excitations and electromagnetic absorption of the different phases of the c2deg in the generalized random - phase approximation ( grpa ) . we include in our study both uniform and non - uniform states and allow for the possibility of any type of coherent ( or qhf ) state . by coherent state , we mean a state where the average value @xmath42 for @xmath43 and/or @xmath44 and/or @xmath45 where @xmath46 creates an electron in a state with quantum numbers @xmath47 in our phase diagram which is summarized on fig . 5 , the layer - coherent states occur at very small bias because of the small interlayer distance @xmath48 nm in bilayer graphene . as the bias is increased , we find around a critical bias corresponding to the regions where the hall conductivity ceases to be quantized in the experiments@xcite a state with both layer and spin coherence . the orbital coherent states occur at a much larger bias corresponding to the situation where level @xmath34 gets lower in energy than level @xmath33 in valley @xmath49 ( see fig . figniveaux ) . in - between these coherent states are various incoherent states , some of which have been studied before@xcite . interestingly , we find that the application of an electric field in the plane of the layers can produce a new state where all three coherences ( layer , orbital and spin ) are present . in such a state , it is possible to control the degree of _ spin _ polarization by changing the strength of the external in - plane _ electric _ field . we also present a study the properties of the different ground states in the phase diagram . for all filling factors , we show how the transport gaps evolve with bias . in most cases , this evolution is qualitatively similar to that obtained with screening corrections@xcite . we compute all the intra - ll collective excitations in the various phases showing that all coherent states but the orbital state are characterized by a linearly - dispersing gapless ( in the long - wavelength limit ) goldstone mode . this mode becomes gapped after the transition to an adjacent incoherent state . in the orbital phase , the orbital - pseudospin goldstone mode dispersion is anisotropic and this mode becomes unstable at a finite wave vector indicating a transition to a charge - density - wave statecoteorbital , coteorbital2 . we identify the number of spin - waves and orbital modes in each phase . these later modes are active in optical absorption . the inter - ll and some intra - ll magnetoexcitons have been computed recentlysari , shizuyadipole , shizuyacyclotron , shizuyamodes01 and we comment on the difference with our results and how the presence of the inter - ll magnetoexcitons in the spectrum may complicate the detection of the intra - ll excitations . the main results of our paper are summarized in fig . 5 ( phase diagram ) , fig . 8 ( transport gaps ) and fig . 9,10 ( collective mode dispersions ) . this paper is organized in the following way . section ii introduces the two - band model of bilayer graphene with the resulting ll spectrum in finite magnetic field . section iii summarizes the hartree - fock and generalized random - phase approximations that we use to take into account the coulomb interaction and gives the formalism for the calculation of the electromagnetic absorption . our numerical results for the phase diagram , transport gaps , collective excitations and optical absorption are presented in sec . iv . in sec . v , we show how the application of an in - plane electric field allow to control the spin polarization in some phases . we conclude in sec . vi .

in a bernal - stacked graphene bilayer , an electronic state in landau level is described by its guiding - center index ( in the landau gauge ) and by its valley , spin , and orbital indices and when coulomb interaction is taken into account , the chiral two - dimensional electron gas ( c2deg ) in this system can support a variety of quantum hall ferromagnetic ( qhf ) ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space . in this work , we give a comprehensive account of the phase diagram of the c2deg at integer filling factors $ ] in landau level when an electrical potential difference between the two layers is varied . we consider states with or without layer , spin , or orbital coherence . for each phase we also study the effect of an external in - plane electric field on a coherent state that has both valley and spin coherence and show that it is possible , in such a state , to control the spin polarization by varying the strength of the external in - plane electric field .

in a bernal - stacked graphene bilayer , an electronic state in landau level is described by its guiding - center index ( in the landau gauge ) and by its valley , spin , and orbital indices and when coulomb interaction is taken into account , the chiral two - dimensional electron gas ( c2deg ) in this system can support a variety of quantum hall ferromagnetic ( qhf ) ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space . in this work , we give a comprehensive account of the phase diagram of the c2deg at integer filling factors $ ] in landau level when an electrical potential difference between the two layers is varied . we consider states with or without layer , spin , or orbital coherence . for each phase , we discuss the behavior of the transport gap as a function of the spectrum of collective excitations and the optical absorption due to orbital pseudospin - wave modes . we also study the effect of an external in - plane electric field on a coherent state that has both valley and spin coherence and show that it is possible , in such a state , to control the spin polarization by varying the strength of the external in - plane electric field .

nucl-th9412011

i

the purpose of this paper is to study the @xmath15 ( @xmath16 stands for @xmath16(1232 ) , @xmath17 stands for either the @xmath18 or the @xmath19 ) reactions for kaon productions in heavy ion collisions . one of the main goals of intermediate energy heavy ion physics is to determine the equation of state ( eos ) of nuclear matter . theoretical studies show that the kaons produced in heavy ion collisions are sensitive to the eos @xcite@xcite . to calculate the kaon production in heavy ion collisions one needs two ingredients @xcite@xcite : \1 . a transport theory to describe the evolution of the heavy ion colliding systems . the elementary cross sections of kaon production in the @xmath20 and @xmath21 collisions ( here @xmath22 stands for either a nucleon @xmath23 or a @xmath24 ) . therefore , in order to obtain a definite conclusion about the eos one needs the reliable elementary cross sections for the kaon production as well as the dynamical transport models . one usually uses transport models such as buu / vuu @xcite and qmd @xcite to simulate the dynamical evolution of projectile and target systems . in these models collision terms and the nuclear mean field are included . by including the nuclear mean field one hopes to determine the eos . in the collision terms , the following reactions are included as main processes : @xmath25 @xmath26 @xmath27 @xmath28 @xmath29 @xmath30 then , kaons can be produced mainly through the following reactions : @xmath31 and @xmath32 the lorentz - invariant differential multiplicity for kaons for a given impact parameter @xmath33 in heavy ion collisions is connected with the elementary cross section by @xmath34 \frac{d\omega } { 4\pi } \nonumber \\ & & + \sum _ { \pi b_{coll } } e '' \frac{d^3\sigma _ { \pi b\rightarrow y k } ( \sqrt { s_{\pi b}})}{d^3 p''}/ \sigma _ { \pi b}^{tot}(\sqrt { s_{\pi b } } ) , \label{basic1}\end{aligned}\ ] ] where the primed and the double - primed quantities are in the center - of - momentum ( c.m . ) frames of the two colliding baryons ( @xmath20 ) and pion - baryon ( @xmath21 ) , respectively . the unprimed quantities are in the c.m . frame of the two nuclei . @xmath35 and @xmath36 are the total cross sections for two baryons @xmath37 and the pion - nucleon system ( @xmath38 ) as functions of c.m . energy @xmath39 and @xmath40 , respectively . the factor @xmath41 $ ] stands for the pauli blocking correction for the final nucleon @xmath23 in the @xmath42 reaction due to the surrounding nuclear medium . the lorentz - invariant differential kaon - production cross section in heavy ion collisions is then given by : @xmath43 from eq.([basic1 ] ) we see that the elementary cross sections are directly related to the kaon yields in heavy ion collisions . thus , it is important to have good elementary kaon - production cross sections . however , most elementary cross sections needed in studying heavy ion collisions are not well known experimentally . therefore one has to use the available experimental data as far as possible . in the case when no experimental data are available one has to rely on symmetry considerations and theoretical models to extrapolate the available experimental data . the elementary kaon - production cross section in @xmath20 collisions used in eq.([basic1 ] ) are usually taken from randrup and ko@xcite . in their works , the @xmath44and @xmath45 total cross sections are obtained from @xmath46 cross section by symmetry consideration in isospin space , and the @xmath16 is treated as spin-@xmath47 ( not @xmath48 ) and isospin-@xmath48 particle . moreover , the coupling constants relevant to the @xmath16 are assumed to be the same as for the nucleon @xmath23 . the elementary @xmath49-production cross section in @xmath21 collisions needed in eq.([basic1 ] ) are usually taken from cugnon and lombard s parametrization@xcite . in this parametrization the isospin averaged cross sections are obtained from only three available experimental data assuming proton and neutron @xmath50 symmetry . this symmetry is , in principle , valid for the light nuclei , and not appropriate for collisions between heavy nuclei with a large neutron excess , i.e. @xmath51 . furthermore the parametrization for the reaction @xmath1 is not given , hence the contribution of this channel to kaon production in the heavy ion collision is unclear . by using the elementary cross section of randrup and ko , one finds that @xmath52 gives the main contribution to the total kaon yield in heavy ion collisions@xcite . however , the elementary cross section for this channel is experimentally unknown . thus a more sophisticated study of this channel is still necessary . in order to determine the cross section for the reaction @xmath52 , one needs at first to study the reaction @xmath53 according to randrup and ko s model@xcite@xcite . since in heavy ion collisions many pions are produced , and the threshold of @xmath54 is lower than in @xmath42 , the reaction @xmath55 seems to be important as a secondary process besides the @xmath42 channel for kaon production . according to a study of the giessen group , the @xmath56 process is dominant for kaon production in proton - nucleus reactions@xcite . recently , in the simulation codes of buu and qmd the isospin dependence has been considered . one distinguishes the members of the nucleon isospin - doublet(@xmath57 and @xmath58 ) , of the pion isospin - triplet(@xmath59 , @xmath60 and @xmath61 ) and of the delta isospin - quartet ( @xmath62 , @xmath63 , @xmath64 , and @xmath65)@xcite@xcite . this enables us to calculate the kaon production in an isospin dependent way , hence one needs information on all the possible isospin channels for kaon production . this means that the isospin - averaged elementary cross sections of @xmath66 and @xmath67 can not be used for this purpose . for an isospin - dependent description of kaon production , one needs all the isospin channels . however , the cross sections for some isospin channels are not available in experiment . therefore one needs a theoretical model to evaluate all the unknown isospin channels . on the other hand , in order to study medium effects for kaon production , a dynamical model for the elementary cross sections is needed , since one can not simply obtain the in - medium cross sections from a parametrization of experimental data of the corresponding cross sections in free space . as a first step , we concentrate on the @xmath68 reactions . once we know this cross sections we can calculate the second term in eq.([basic1 ] ) . this channel is also the basis to study @xmath69 , since the parameters of the @xmath68 reactions are ingredients for calculating the reaction @xmath69 in the present model . in this paper , we present results for all @xmath15 reactions using a resonance model . part of this work has been briefly reported in @xcite . by a resonance model we mean that the @xmath70 reactions happen via intermediate resonance states , which decay both into @xmath71 and @xmath72 . the coupling constants in the meson - baryon - resonances can be determined from the relevant branching ratios of the resonances . the cross sections of @xmath70 are obtained coherently from the square of the sum of all resonance amplitudes . besides these @xmath11-channel resonances which give peaks in the total cross sections , the @xmath12-channel @xmath13-exchange is also included . it provides a smooth background .

in a resonance model the reactions and are studied . for the reactions and , parametrizations of the calculated total cross sections for all different isospin channels are given for the use of kaon productions in heavy ion collisions . the differential cross sections are also studied .

in a resonance model the reactions and are studied . for the reactions and , the resonances , and are included as intermediate states . for the reactions , the resonances , and are considered , while for the reactions the intermediate resonances are and . besides these resonances in the-channel , the-channel-exchanges are also taken into account as a smooth background . the relevant coupling constants for the meson - baryon vertices are obtained ( except for ) from the experimental decay branching ratios of the relevant resonances . all isospin channels of the and cross sections are calculated . by comparing the calculated results with the available experimental data , we find that the total cross sections of the reactions can be explained by the resonance model . the cross sections , for which no experimental data are available , are predicted theoretically . parametrizations of the calculated total cross sections for all different isospin channels are given for the use of kaon productions in heavy ion collisions . the differential cross sections are also studied . = 2.5em

1606.02443

i

recently hawking , perry , and strominger ( hps ) @xcite @xcite proposed an interesting scenario that may resolve the information loss problem @xcite . they suggest that quantum information about collapsing matter is stored in an infinite number of conserved noether currents having asymptotic symmetries , including supertranslation on a horizon . this is expected to maintain the unitarity of quantum gravity , and all of the information may be accessible in the region outside of the horizon . by incorporating superrotation symmetry on a horizon , this symmetry - based scenario may also provide a possibility of revealing the statistical mechanical origin of the bekenstein hawking entropy @xmath0 , as already pointed out in previous papers @xcite and @xcite by one of the authors of this paper . the nonvanishing holographic charges of these asymptotic symmetries can yield a huge number of different physical states with the same adm energy and angular momentum . the degeneracy is so large that it may account for the order of @xmath0 @xcite . in holographic charge arguments , the physical degrees of freedom emerge from would - be gauge degrees of freedom of the general covariance . this can be grasped easily by recalling the poincar covariance as a simple example . in fact , the lorentz transformation is a subgroup of the poincar group and generates an infinite number of physical states with different values of the momentum . the poincar transformation is a subgroup of general coordinate transformations . because general relativistic theories have the general covariance as the gauge symmetry , the poincar transformation can be regarded as a would - be gauge transformation , which actually causes a transition between physical states . on a horizon , a similar mechanism works , and an infinite - dimensional asymptotic symmetry appears . in the spirit of brown and henneaux @xcite , strominger first suggested in @xcite that a three - dimensional black hole entropy is derived using a virasoro algebra as an asymptotic symmetry at spatial infinity . carlip @xcite proposed an asymptotic virasoro symmetry on a black hole horizon and argued that the black hole entropy is derived using the cardy formula with a macroscopically large central charge . however , the original argument of carlip encountered various types of criticism @xcite@xcite@xcite@xcite@xcite and remains controversial . the existence of supertranslation and superrotation as a consistent asymptotic symmetry on a stationary horizon of a four - dimensional schwarzschild black hole was first reported in a paper @xcite by one of the authors of the present paper . subsequently , it was explicitly demonstrated that falling matter really excites charged states of the asymptotic symmetry in a three - dimensional black hole spacetime @xcite . it is not known yet whether a gravitational wave excites charged states of supertranslation and superrotation on a horizon . hps recently revisited supertranslation and superrotation on the horizon @xcite @xcite by using a different coordinate system from that in @xcite and @xcite . using a coordinate system , hps introduced asymptotic metrics near a horizon as @xmath1 where the horizon is located at @xmath2 and uppercase roman letters run over spatial coordinates on the horizon . based on the above form , hps argue that stationary black holes do not carry classical supertranslation hair because the holographic charge vanishes in the classical level @xcite . it is worth noting that the coordinate system in eq . ( [ 001 ] ) covers both regions inside of the horizon and outside of the horizon , and can be physically implemented by free - falling block - numbered clocks distributed in the space near the horizon , as depicted in the left panel of figure 1 . because of the clock free motion , it is very natural from the viewpoint of equivalence principle that nonzero holographic charges on the horizon can not be observed . apart from hps s setup , if we adopt a rindler - type coordinate system in which an asymptotic near - horizon metric is given by@xmath3 where @xmath4 is rindler acceleration and the horizon is located at @xmath5 , we indeed have nonvanishing classical holographic charges on the horizon even for stationary black holes @xcite . the coordinate system in eq . ( [ 002 ] ) is implemented by accelerating block - numbered clocks distributed in the space near the horizon , as depicted in the right panel of figure 1 . the appearance of the charges @xmath6 $ ] in the accelerated coordinate system is reminiscent of that of a thermal bath in the unruh effect @xcite . $ ] on the horizon vanish for stationary black holes . ( right ) a coordinate system implemented by accelerating block - numbered clocks distributed in the space near the horizon . in this coordinate system , non - zero classical holographic charges @xmath6 $ ] appear on the horizon as soft black hole hair even for stationary black holes . the appearance of the charges in the accelerated coordinate system is reminiscent of that of a thermal bath in the unruh effect . , height=207 ] as in the black hole complementarity scenario @xcite , the hps scenario requires some mechanism to avoid the no - cloning paradox . if all of the information about collapsing matter is stored in the conserved charges on the horizon , we may make a precise copy of the quantum information of the matter inside of the horizon by using the charge information . although this naively seems to contradict the no - cloning theorem of quantum mechanics @xcite , hps have not yet provided any plausible resolution of this paradox . let us consider the gravitational collapse depicted in the left panel of figure 2 . in this scenario , information about the collapsing matter is imprinted in the holographic charge states of asymptotic symmetries on the horizon . if we throw additional matter into the black hole , as depicted in the right panel of figure 2 , a new horizon appears and encloses the old horizon . then new holographic charge states have to carry all of the information about the original collapsing matter and additional matter . naively , this appears strange . the new holographic charges must remember quantum information about the behavior of the original collapsing matter before the additional matter arrived . thus , we potentially have duplicate quantum information about the collapsing matter on the two different horizons . this challenges the no - cloning theorem again . this situation remains unchanged even if we take a large mass limit on the black hole . in this limit , the near - horizon geometry is merely a minkowski spacetime , and each horizon coincides with one of the rindler horizons . the situation is depicted in figure 3 . thus , even if a linearized theory of quantum gravity is considered in a minkowski background with rindler horizons , the no - cloning problem should be resolved properly . this implies that the investigation of holographic charges on rindler horizons is valuable . to analyze the above problems of asymptotic rindler spacetimes , we construct a general theory of gravitational holographic charges for a ( 1 + 3)-dimensional linearized gravity field in section 2 of this paper . although matter crossing a rindler horizon generates horizon deformation and a time - dependent coordinate shift , that is , gravitational memory , the charges of supertranslation and superrotation on the horizon can be defined during and after its passage through the horizon . in particular , it is verified that the charges become time - independent after matter absorption by the horizon . it should be emphasized that the time independence of the charge is very nontrivial for a general coordinate transformation . for instance , a noether current for an infinitesimal coordinate transformation @xmath7 is given in einstein gravitational theory by @xmath8 and is locally conserved : @xmath9 . the charge @xmath10 is defined by the integration of @xmath11 in a bulk region @xmath12 as@xmath13 even though @xmath9 holds , the time independence of @xmath10 is not generally ensured . this is because the surface integral of the flux @xmath14 does not disappear for many @xmath15 even if we have no gravitational wave and matter on the surface . from the local balance relation of conserved currents , @xmath16 @xmath10 can vary in time because the right - hand side of the above equation is generally nonzero . thus , for a surface of interest such as a horizon , the time independence of the holographic charges has to be checked independently by confirming that @xmath9 . in section 2 , we show the time independence of the holographic charges on rindler horizons . a general formula for conserved holographic charges after the horizon absorbs the matter is provided . it is also proven that holographic states on the horizon can not store any information about absorbed perturbative gravitational waves . to show the memory effect of horizons , a measure of the classical gravitational memory @xmath17 on a future horizon at @xmath18 with a rindler wedge located at @xmath19 is introduced by time integration of the holographic charges . it differs from the standard gravitational memory that appears in @xcite @xcite @xcite @xcite @xcite and provides a more profound insight because it consists of conserved charges . in section 3 , we introduce a quantum gravitational memory operator @xmath20 for a rindler horizon and propose a possible resolution of the no - cloning paradox from the viewpoint of quantum measurement contextuality . the energy - momentum tensor of quantum matter inside of a horizon does not commute with @xmath21 on the horizon . this also leads to noncommutativity between holographic charges of different horizons . thus , a measurement of @xmath21 on a horizon affects other @xmath22 and quantum states of matter inside of the horizon . they are not independent observables , and the reality of @xmath21 is subject to the contextuality of quantum measurement . on the basis of this fact , we propose a conjecture that the holographic charge reality is conditioned to measurements by appropriate physical detectors . then no cloning paradox arises , at least in the first order of perturbative quantum gravity . in a method similar to that of unruh dewitt particle detectors @xcite @xcite for unruh radiation in a rindler spacetime , physical detectors accumulating information for evaluation of a quantum metric near the horizon may observe the holographic charges as a reality . owing to gravitational interaction between infalling matter and the metric detectors distributed in the space , the detectors share quantum entanglement with the matter inside of the horizon . if we place no detector to measure the quantum metric near the horizon , the absorbed matter is not decohered by the measurement . all of the quantum information about the infalling matter remains carried by the matter itself . hence , the holographic noether charges are not physical objects that share quantum entanglement with the matter inside but merely a gauge freedom of general covariance in this case . therefore , even in quantum theory , the horizon can not be regarded as a real holographic screen spanning the space in the absence of measurement devices . this conjecture avoids the no - cloning paradox and also supports a conservative conjecture for the information loss problem in @xcite , @xcite and @xcite , which is quite different from that in the firewall conjecture @xcite . in this paper , the natural units are adopted : @xmath23 .

in a rindler - type coordinate system spanned in a region outside of a black hole horizon , we have nonvanishing classical holographic charges as soft hairs on the horizon for stationary black holes . taking a large black hole mass limit , the spacetimes with the charges are described by asymptotic rindler metrics . we construct a general theory of gravitational holographic charges for a ( 1 + 3)-dimensional linearized gravity field in the minkowski background with rindler horizons . although matter crossing a rindler horizon causes horizon deformation and a time - dependent coordinate shift , that is , gravitational memory , the supertranslation and superrotation charges on the horizon can be defined during and after its passage through the horizon . it is generally proven that holographic states on the horizon can not store any information about absorbed perturbative gravitational waves . + + + _ graduate school of science , tohoku university , + sendai 980 - 8578 , japan _ +

in a rindler - type coordinate system spanned in a region outside of a black hole horizon , we have nonvanishing classical holographic charges as soft hairs on the horizon for stationary black holes . taking a large black hole mass limit , the spacetimes with the charges are described by asymptotic rindler metrics . we construct a general theory of gravitational holographic charges for a ( 1 + 3)-dimensional linearized gravity field in the minkowski background with rindler horizons . although matter crossing a rindler horizon causes horizon deformation and a time - dependent coordinate shift , that is , gravitational memory , the supertranslation and superrotation charges on the horizon can be defined during and after its passage through the horizon . it is generally proven that holographic states on the horizon can not store any information about absorbed perturbative gravitational waves . however , matter crossing the horizon really excites holographic states . by using gravitational memory operators , which consist of the holographic charge operators , we suggest a resolution of the no - cloning paradox of quantum information between matter falling into the horizon and holographic charges on the horizon from the viewpoint of the contextuality of quantum measurement . + + + _ graduate school of science , tohoku university , + sendai 980 - 8578 , japan _ +

1402.2201

i

an atom s core level binding energies depend on its chemical species . this fact has been exploited for decades in order to determine the proportion of different species within a given sample via core level spectroscopy - which provides the distribution of core electron binding energies within a sample . an atom s binding energies also depend on its environment , i.e. , the species of its surrounding atoms . for instance , in a cu metal all atoms have the same environment , and hence the binding energies for a given cu core level type , e.g. 2p@xmath0 , will be the same for all atoms . by contrast , in a cupd alloy exhibiting substitutional disorder the cu atoms exhibit a variety of environments , and hence also a variety of 2p@xmath0 binding energies . such a dispersion in the binding energies has been observed in many alloy systems @xcite , and in theory can be used to deduce information about specific environments within a sample , including the concentration profile on the atomic scale . the viability of achieving this via high kinetic energy photoelectron spectroscopy ( hike ) has recently been demonstrated @xcite . this is promising because hike , unlike other widely - used techniques , is both bulk - sensitive and non - destructive . such environment - resolved spectroscopy would prove useful to the many research areas involving alloys in which segregation plays a crucial role , e.g. metal embrittlement @xcite , and nanocatalyst design @xcite . however , success in this endeavor hinges upon a solid understanding of the relationship between an atom s environment , its electronic structure , and its core level binding energies in alloys . the central quantity with regards to environment - resolved spectroscopy in alloys is the ( alloy - metal ) core level shift ( cls ) , which for a core level bound to an @xmath1 site @xmath2 is defined as @xmath3 where @xmath4 is the binding energy of the core level , and @xmath5 is the binding energy of the core level belonging to the type under consideration in a pure @xmath1 metal . note that this is a site - dependent quantity ; one must determine @xmath6 for all @xmath1 sites in the system under consideration in order to determine the @xmath1 cls distribution . this is problematic for systems exhibiting substitutional disorder on account of their lack of periodicity - which is a prerequisite for treatment within the conventional theoretical framework exploited by most _ ab initio _ methods . one way around this problem is to approximate the system under consideration as periodic , but with a large unit cell , i.e. , a supercell . in this _ supercell approximation _ one determines @xmath6 for all @xmath1 sites , and hopes that the range of environments exhibited by these sites is representative of the ` true ' ( non - periodic ) system , and hence will result in an accurate representation of the true @xmath1 cls distribution . random alloys - the archetype of disordered alloys in which there are no correlations between the species of sites - are the most tractable system exhibiting substitutional disorder to treat theoretically , and have been the focus of both experimental @xcite and theoretical @xcite attempts to understand the distribution of clss in alloys . in this context the dispersion of @xmath1 clss is known as ` disorder broadening ' on account of the increased width of , for example , the cu cls distribution for a cupd random alloy relative to that for a cu metal . sophisticated _ ab initio _ models utilizing the supercell approximation have provided insight into disorder broadening in these systems @xcite . however , most systems of practical interest can not be idealized as random alloys , and unfortunately the complexity of these systems is such that a description of their disorder broadenings using _ ab initio _ models is intractable within the supercell approximation . accurate methods do exist which do not resort to the supercell approximation . _ ab initio _ methods rooted in the coherent potential approximation ( cpa)@xcite have been shown to provide excellent agreement with experiment @xcite . furthermore , they can treat complex systems @xcite . however , cpa - based approaches can not provide detailed information regarding the disorder broadening in complex systems - nor even random alloys . while phenomenological models have been developed which can provide such information @xcite , their accuracy has been questioned @xcite . one criticism is that these models do not take into account ` final state effects ' associated with changes in the valence electron density after photoemission . it has even been claimed that the complexity of the relationship between clss and environment in alloys precludes an accurate alternative to _ ab initio _ methods @xcite . here we present an accurate phenomenological model for clss in alloys which relates @xmath6 - including the final state contribution - to the environment of site @xmath2 . the model , like previous approaches , is charge - transfer based , and provides a simple framework for rationalizing the disorder broadening phenomenon . the layout of this work is as follows . in sec . [ sec : model ] we review the theory which underpins the model , and derive expressions for clss which apply to a wide range of alloy systems . we then apply the model to the problem of characterizing the interface quality of metallic multilayers . this problem has received significant attention on account of its importance to nanotechnology @xcite , and can be restated as follows : what is the degree of ` interface roughening ' @xmath7 in a given sample ? [ fig : figure_cu5ni5](a ) provides an illustration of the multilayer system [ ni@xmath8/cu@xmath8 ] with various @xmath7 - where the square brackets signify that the system at @xmath10 consists of a 10 monolayer stack ni@xmath8/cu@xmath8 repeated throughout all space . in this regard , sec . [ sec : comp_details ] contains details of our calculations , and our results are presented in sec . [ sec : results ] . finally , in sec . [ sec : summary ] we summarize our main findings , and discuss the limitations of the model , and intentions for future work . note that throughout this work we use hartree atomic units unless otherwise stated . to transform energies within hartree atomic units to ev the former quantity should be multiplied by a factor 27.2114 . /cu@xmath8 ] at various @xmath7 ( a ) , and the corresponding model spectra ( b ) . in ( b ) , each red bar corresponds to a different value of @xmath11 : the ordinate of the bar is the cls corresponding to @xmath11 according to eqn . , and its height reflects the frequency of cu sites with that value of @xmath11 . the bars corresponding to @xmath12 , 6 , and 12 are indicated . the dotted curves in ( b ) are spectra for @xmath10.,scaledwidth=50.0% ]

in alloys exhibiting substitutional disorder , the variety of atomic environments manifests itself as a ` disorder broadening ' in their core level binding energy spectra . disorder broadening can be measured experimentally , and in principle can be used to deduce information about specific atomic environments within a sample . we describe such a model . several counterintuitive aspects of the disorder broadening phenomenon are uncovered , an understanding of which is essential for the correct interpretation of experimental results . a ` disorder narrowing ' is even possible .

in alloys exhibiting substitutional disorder , the variety of atomic environments manifests itself as a ` disorder broadening ' in their core level binding energy spectra . disorder broadening can be measured experimentally , and in principle can be used to deduce information about specific atomic environments within a sample . however , progress in this endeavor is hampered by the lack of a model for this phenomenon which can treat complex systems . in this work we describe such a model . the model is used to elucidate the relationship between charge transfer , atomic environment , and disorder broadening in complex systems , with a focus on the problem of characterizing the interface quality of cuni multilayers . we also validate the model against the results of _ ab initio _ electronic structure calculations . several counterintuitive aspects of the disorder broadening phenomenon are uncovered , an understanding of which is essential for the correct interpretation of experimental results . for instance , it is shown that systems with inhomogeneous concentration profiles can exhibit disorder broadenings significantly larger than random alloys . furthermore in some systems a ` disorder narrowing ' is even possible .

1402.2201

i

above we have presented a model for core level shifts in alloys , and have used it to add insight into the relationship between atomic environment , charge transfer and disorder broadening in complex systems . our key result is that the mapping between the distribution of atomic environments and core level spectra is often counterintuitive . for instance , systems with inhomogeneous concentration profiles can exhibit significantly larger disorder broadenings than is possible in random alloys , and even a ` disorder narrowing ' in some cases . for the correct interpretation of experimental spectra for complex systems , it is crucially important to understand such phenomena . the model can be easily adapted to treat other core level spectroscopies , the most prominent of which is auger electron spectroscopy . hence we expect that it should find widespread use as a framework in which to interpret experimental results . however , it is by no means a panacea . recall that the model is underpinned by the nra - cefm - which itself is a particular case of the cefm . implicit in the nra - cefm are a number of approximations which may be problematic . one is the _ spherical approximation _ - that only the monopole moments of the charge distribution in each site are considered for the purposes of evaluating the madelung energy . one must go beyond this approximation in order to obtain a quantitatively accurate description of the electron density within disordered alloys @xcite . this is especially true for regions near surfaces . a generalization of the cefm has been described in ref . which does not rely upon the spherical approximation . while the nra - cefm could be generalized in an analogous manner , it is not clear whether this would be fruitful . the strength of the nra - cefm over the ` general ' cefm is its simplicity , with which comes a small loss in accuracy relative to the cefm . it is not clear whether the gain in accuracy achieved by generalizing the nra - cefm to go beyond the spherical approximation is worth the resulting loss in simplicity . another potentially problematic approximation implicit in the nra - cefm is that the nuclei of the system under consideration form an undistorted crystal lattice . the breakdown of this approximation can have far - reaching consequences . the addition of distortions to the crystal lattice of cuau results in a reversal of the average relationship between a site s cls and its number of unlike nearest neighbors @xcite . the reasons for this are not known , and warrant further investigation . the nra - cefm , suitably modified to treat lattice distortions , may add insight into this phenomenon , though it would be optimistic to expect that anything more than a qualitative understanding could be achieved . it should be borne in mind that the aforementioned approximations , while implicit in the nra - cefm , are also utilized in many _ ab initio _ calculations , and are not expected to preclude the model from making _ at least _ qualitatively accurate predictions . a more problematic limitation of the model is that its free parameters are not known _ a priori _ : they must be obtained from _ ab initio _ calculations or by other means . fortunately these parameters are highly transferable between systems ; for details see refs . . in the future we intend to calculate these parameters for a wide range of alloys . this would enable the model to be readily applied to many systems .

the model is used to elucidate the relationship between charge transfer , atomic environment , and disorder broadening in complex systems , with a focus on the problem of characterizing the interface quality of cuni multilayers . for instance , it is shown that systems with inhomogeneous concentration profiles can exhibit disorder broadenings significantly larger than random alloys . furthermore in some systems

in alloys exhibiting substitutional disorder , the variety of atomic environments manifests itself as a ` disorder broadening ' in their core level binding energy spectra . disorder broadening can be measured experimentally , and in principle can be used to deduce information about specific atomic environments within a sample . however , progress in this endeavor is hampered by the lack of a model for this phenomenon which can treat complex systems . in this work we describe such a model . the model is used to elucidate the relationship between charge transfer , atomic environment , and disorder broadening in complex systems , with a focus on the problem of characterizing the interface quality of cuni multilayers . we also validate the model against the results of _ ab initio _ electronic structure calculations . several counterintuitive aspects of the disorder broadening phenomenon are uncovered , an understanding of which is essential for the correct interpretation of experimental results . for instance , it is shown that systems with inhomogeneous concentration profiles can exhibit disorder broadenings significantly larger than random alloys . furthermore in some systems a ` disorder narrowing ' is even possible .

1102.0412

r

of the 25 galaxies in this study , only five have radio sources that are dominated by thermal emission , four have sources that are dominated by non - thermal emission , six have radio sources that are ambiguous within the uncertainty limits , and sixteen have no detected radio sources ( figures 1 to 9 ; tables 3 and 4 ) . to measure the flux densities , we used the aips++ viewer program to create identical polygonal apertures around each of our sources at 3 and 6 cm for the atca data and at 1.3 and 3.6 cm for the vla data . by using identical convolution kernels and apertures , we are able to maximize the accuracy of the relative photometry . errors in the flux densities were determined by adding in quadrature the uncertainties due to the absolute flux calibration , variation from the sky background , and changes in the size and shape of the aperture . for the purposes of determining the uncertainties in the spectral index @xmath10 , the final term in the uncertainty due to variation in aperture is neglected as identical apertures are used at both frequencies . see tables [ fluxtable_vla ] and [ fluxtable_atca ] for integrated and peak flux densities as well as spectral indices of each source . massive , short - lived stars drive the thermal free - free emission we observe at radio wavelengths ; hence , an understanding of the photo - ionization rate for each of our candidate udhii regions enables us to predict the number of massive stars in a cluster . lyman continuum photons ionize these hii regions ; thus , with knowledge of the radio luminosities , we can predict a lower bound on the lyman continuum flux @xcite , @xmath28 a number of possible issues must be kept in mind when interpreting the @xmath29 values and radio flux densities . first , the application of this equation assumes the emission is purely thermal and optically thin . contamination from non - thermal emission within the synthesized beams is also a possible issue at the spatial resolutions used here , and would inflate the resulting @xmath29 values . to partially mitigate these issues , it is advantageous to use flux densities obtained at the highest radio frequency available for two reasons : ( 1 ) the higher frequency emission suffers from less self - absorption and is therefore more likely to be optically thin , and ( 2 ) the higher the frequency , the less likely it is to contain a significant amount of non - thermal contaminating flux . second , an electron temperature must also be assumed , and we adopt a `` typical '' hii region temperature of @xmath30 k ; the uncertainty in @xmath29 due to this assumption is @xmath31% . finally , the actual @xmath29 values could be higher than observed if a significant fraction of the ionization radiation is either absorbed by dust within the hii region or suffers from significant leakage through a porous ism . thus , when these conditions are met , the @xmath29 values quoted here should be interpreted as lower limits . the inferred values for @xmath29 of each of the identified thermal sources are shown in table [ derivedproperties ] . assuming each of these thermal sources contains an embedded star cluster , we also estimate the number of o7.5 v stars , each having a lyman continuum flux @xmath32 s@xmath33 @xcite , required to produce the observed free - free , thermal radio flux ( see table [ derivedproperties ] ) . we used the stellar synthesis code starburst99 @xcite in combination with @xmath29 to estimate the total stellar masses of the natal clusters . following @xcite , we assume each cluster has a metallicity @xmath34 and a salpeter imf from 1 to 100 m@xmath35 . assuming the @xmath29 values scale directly with the cluster mass and that the clusters are @xmath36 myr old , we infer stellar masses for the radio detected star - forming regions ranging between @xmath37 m@xmath35 and @xmath38 m@xmath35 ( see table [ derivedproperties ] ) . the most massive of these star - forming regions also appear to be slightly spatially extended at the resolution of these observations and likely include a number of star clusters that are not resolved . in order to determine the sizes of the detected sources in table [ derivedproperties ] , we initially fit a gaussian profile to each source , from which the synthesized beam was deconvolved in order to estimate the actual source sizes . the major limitation of this method is that it requires the source to be roughly gaussian , which is not true for many sources presented here , some of which appear to have quite complex structure . nevertheless , this method will , at a minimum , provide information about whether or not a source is extended at the resolution of the observation . using this method , we infer the physical sizes of the star forming regions based upon the distances in table [ detectionlimits ] and deconvolved angular sizes in tables [ fluxtable_vla ] and [ fluxtable_atca ] , with resulting sizes ranging between @xmath39 pc to a few @xmath40 pc . these sizes are much larger than one would expect for an individual cluster ( a few pc ) ; thus we conclude that most of the radio - detected star - forming regions presented here are likely to be groups of individual clusters , which may well be at slighltly different evolutionary states . furthermore , these large inferred sizes allow for a complex origin for the observed emission and potential non - thermal contamination ; there is ample room within these large regions for a large number of ultracompact hii regions , evolved hii regions , snr , and other objects . higher spatial resolution observations are clearly required in order to disentangle the components of the complex sources and facilitate more precise size measurements . in order to provide a comparison for the relative fluxes of non - thermal and thermal sources , we calculate the expected flux densities and detection thresholds for the galactic supernova remnant cas a , an uchii region complex w49a at the distance of the galaxies in this sample . cas a is the canonical `` young '' core collapse snr in the galaxy , with the highest luminosity and youngest age of any such remnant in the milky way @xcite . likewise , w49a is a benchmark star - forming region in the galaxy , with @xmath41 individual thermal radio sources and @xmath42 s@xmath33 ( e.g. * ? ? ? the expected signal - to - noise for analogs to cas a and w49a in our sample galaxies at 3.6 cm are shown in table [ detectionlimits ] . for example , if cas a would have been a @xmath43 detection in a given galaxy , we would be unlikely to identify an individual supernova remnant . if w49a would have been a detection @xmath44 in a given galaxy and yet no thermal sources are detected , such a detection limit would suggest no current star formation above this limit in that galaxy . given our detection limits for objects similar to cas a and w49a , there are a few striking non - detections that merit further investigation . for example , in the galaxy mrk 1479 ( @xmath45 mpc , * ? ? ? * ; * ? ? ? * ) , cas a and w49a would have exhibed detections at the level of @xmath46 and @xmath47 , respectively ; yet no radio sources are detected . the lack of such natal clusters could suggest that the current star formation rate in mrk 1479 is below that of the milky way . however , the inclusion of mrk 1479 in both the markarian catalog of ultraviolet bright galaxies and vorontsov - velyaminov ( vv ) catalog of interacting galaxies suggests that it must have recently been undergoing vigorous star formation . thus , the lack of detected thermal radio sources in this case supports the hypothesis that the natal stage of a cluster s evolution is extremely short .

, we find that of the 25 galaxies in this sample only five have radio sources with spectral indices that are only consistent with a thermal origin ; four have radio sources that are only consistent with a non - thermal origin ; six have radio sources whose nature is ambiguous due to uncertainties in the spectral index ; and sixteen have no detected radio sources . for those sources that appear to be dominated by thermal emission , we infer the ionizing flux of the star clusters and the number of equivalent o7.5 v stars that are required to produce the observed radio flux densities . the dearth of current massive cluster formation in these galaxies suggests that either their current star formation intensities have fallen to near or below that of the milky way and/or that the evolutionary state that gives rise to thermal radio emission is short - lived .

in order to investigate the relationship between the local environment and the properties of natal star clusters , we obtained radio observations of 25 star - forming galaxies within 20 mpc using the very large array ( vla ) and the australia telescope compact array ( atca ) . natal star - forming regions can be identified by their characteristic thermal radio emission , which is manifest in their spectral index at centimeter wavelengths . the host galaxies in our sample were selected based upon their likelihood of harboring young star formation . in star - forming regions , the ionizing flux of massive embedded stars powers the dominant thermal free - free emission of those sources , resulting in a spectral index of ( where ) , which we compute . with the current sensitivity , we find that of the 25 galaxies in this sample only five have radio sources with spectral indices that are only consistent with a thermal origin ; four have radio sources that are only consistent with a non - thermal origin ; six have radio sources whose nature is ambiguous due to uncertainties in the spectral index ; and sixteen have no detected radio sources . for those sources that appear to be dominated by thermal emission , we infer the ionizing flux of the star clusters and the number of equivalent o7.5 v stars that are required to produce the observed radio flux densities . the most radio - luminous clusters that we detect have an equivalent of o7.5 v stars , and the smallest only have an equivalent of o7.5 v stars ; thus these star - forming regions span the range of large ob - associations to moderate `` super star clusters '' ( sscs ) . with the current detection limits , we also place upper limits on the masses of clusters that could have recently formed ; for a number of galaxies we can conclusively rule out the presence of natal clusters significantly more massive than the galactic star - forming region w49a ( m ) . the dearth of current massive cluster formation in these galaxies suggests that either their current star formation intensities have fallen to near or below that of the milky way and/or that the evolutionary state that gives rise to thermal radio emission is short - lived .

1102.0412

c

in this radio study of 25 galaxies selected based upon their optical signposts of star formation , we expected to detect a number of thermal radio sources originating from massive nascent star clusters . however , we only detect definite thermal - dominated radio sources in five of the sample galaxies , with an additional six galaxies hosting radio sources whose origins are ambiguous within uncertainties . using the benchmark galactic star - forming region w49a , we put these non - detections in context ; in several galaxies , w49a would have been a @xmath48 detection . for example , mrk 1479 is a notable case of a uv galaxy , included in both the vv and markarian catalogs , with no evidence of thermal radio emission coming from an object similar to w49a at a @xmath49 level . for the five galaxies with detected thermal radio sources , the inferred properties of the nascent clusters range from large ob - associations to moderate super star clusters extending both above and below the mass of w49a . one hypothesis to explain the dearth of natal clusters in this sample is that the timescale a star - forming region spends in a stage that is detectable in radio is extremely brief . @xcite suggest that sscs may spend as little as @xmath50 to @xmath51 myr in the embedded phase when they are detectable with thermal radio emission . compared to galaxy evolution timescales , the time interval for star formation is very short . our results are consistent with this hypothesis , however a more complete statistical sample is needed to better constrain the timescales . such a larger and complete sample would allow us to compare the number of clusters in different evolutionary stages and track the emergence process . while this study was intended to identify candidate natal star - forming regions in nearby galaxies , follow - up efforts are imperative . in particular , this work would benefit from higher spatial resolution observations than those presented here . such observations will be critical for disentangling thermal and non - thermal sources in close proximity . in addition , higher frequency radio observations will provide much stronger constraints on the the spectral energy distributions of the thermal radio sources . in particular , high spatial resolution observations at @xmath52 ghz will be useful for better understanding the relationship between between cluster properties and the local environment in which they are formed . a. a. would like to acknowledge the national science foundation ( nsf ) for supporting his research through its research experiences for undergraduates ( reu ) program . k. e. j. gratefully acknowledges support for this paper provided by nsf through career award 0548103 and the david and lucile packard foundation through a packard fellowship . _ facilities : _ ,

the most radio - luminous clusters that we detect have an equivalent of o7.5 v stars , and the smallest only have an equivalent of o7.5 v stars ; thus these star - forming regions span the range of large ob - associations to moderate `` super star clusters '' ( sscs ) . with the current detection limits , we also place upper limits on the masses of clusters that could have recently formed ; for a number of galaxies we can conclusively rule out the presence of natal clusters significantly more massive than the galactic star - forming region w49a ( m ) .

in order to investigate the relationship between the local environment and the properties of natal star clusters , we obtained radio observations of 25 star - forming galaxies within 20 mpc using the very large array ( vla ) and the australia telescope compact array ( atca ) . natal star - forming regions can be identified by their characteristic thermal radio emission , which is manifest in their spectral index at centimeter wavelengths . the host galaxies in our sample were selected based upon their likelihood of harboring young star formation . in star - forming regions , the ionizing flux of massive embedded stars powers the dominant thermal free - free emission of those sources , resulting in a spectral index of ( where ) , which we compute . with the current sensitivity , we find that of the 25 galaxies in this sample only five have radio sources with spectral indices that are only consistent with a thermal origin ; four have radio sources that are only consistent with a non - thermal origin ; six have radio sources whose nature is ambiguous due to uncertainties in the spectral index ; and sixteen have no detected radio sources . for those sources that appear to be dominated by thermal emission , we infer the ionizing flux of the star clusters and the number of equivalent o7.5 v stars that are required to produce the observed radio flux densities . the most radio - luminous clusters that we detect have an equivalent of o7.5 v stars , and the smallest only have an equivalent of o7.5 v stars ; thus these star - forming regions span the range of large ob - associations to moderate `` super star clusters '' ( sscs ) . with the current detection limits , we also place upper limits on the masses of clusters that could have recently formed ; for a number of galaxies we can conclusively rule out the presence of natal clusters significantly more massive than the galactic star - forming region w49a ( m ) . the dearth of current massive cluster formation in these galaxies suggests that either their current star formation intensities have fallen to near or below that of the milky way and/or that the evolutionary state that gives rise to thermal radio emission is short - lived .

astro-ph9608139

i

in this paper and paper i , we have sought to develop a systematic theory of gravitational microlensing . we focused on microlensing by a planar distribution of point masses in paper i. in this paper we have studied gravitational microlensing by a three - dimensional distribution of point masses , focusing on the nature of the critical curves , the caustics , the illumination pattern , and especially the macroimage magnification distribution @xmath4 . in the process , we have explained many of the differences between two- and three - dimensional microlensing that have been seen in previous numerical simulations . in 3 we studied the lensing properties of three - dimensional lens distributions by considering in detail multiplane configurations with two , three , and four point masses . the lensing properties of a three - dimensional lens distribution is fundamentally different from that of a planar distribution in that a light ray could have arrived in the vicinity of a lens either having suffered only weak deflections along the way from the source , or after having been strongly deflected one or more times by the intervening lens . the latter situation can not arise in a purely planar distribution of lenses , and it gives rise to secondary caustics and critical lines that have no analogues in the planar case . in addition , in the case of more than two point masses , the caustic topology is no longer simply related to the critical curve topology because caustics corresponding to different critical lines may overlap each other . for @xmath1 point masses that are widely separated in lagrangian space , there are @xmath3 primary critical curves ( i.e. , critical curves that have not suffered any strong deflections ) and @xmath2 critical curves in total . features in the `` normalized '' differential cross - section , @xmath74 , that are associated with the secondary caustics are relatively weak and at low magnifications . significant features occuring at moderate to high magnifications are invariably associated with the primary caustics . in 4 we derived a semi - analytic expression for the caustic - induced feature at the high magnification end of @xmath4 for a low optical depth lens distribution . in the low optical depth limit , we showed that the multiplane lens equation near a point mass is formally equivalent to the single plane equation of a point mass perturbed by shear . consequently , the ( primary ) caustic has the familiar astroid shape , and the differential cross - section exhibits the same scaling behavior found in paper i ( i.e. , @xmath308 depends on magnification @xmath72 and the effective shear @xmath309 through the combination @xmath310 ) . by modeling the illumination pattern as a superposition of the patterns due to individual `` point mass plus weak shear '' lenses , we found that the caustic - induced feature in the macroimage magnification distribution @xmath4 can be written as a weighted sum of the semi - analytic feature derived in paper i for a planar lens distribution ( eq.[[eq32 ] ] ) . the resulting semi - analytic caustic - induced feature is similar to the feature in the planar case , but it is shifted to higher magnification . in the moderate to high @xmath72 regime , our semi - analytic @xmath4 agrees remarkably well with the magnification distribution obtained from numerical simulations by rauch ( 1991 ) , even for optical depth as high as @xmath311 . this is very different from the two - dimensional case studied in paper i. in the two - dimensional case , we have found that the caustic - induced feature in @xmath4 tends to be more pronounced than the low optical depth result , even for optical depth as low as @xmath5 . we argued that this particular difference between two- and three - dimensional microlensing is due to the fact that for a given value of optical depth , the fraction of point masses whose ( primary ) caustics are not simple astroids is significantly higher in the planar case than in the three - dimensional case . finally , we discussed briefly the deviations of the numerical @xmath4 from the semi - analytic distribution at low magnification . we thank k. rauch for providing us with the results of rauch ( 1991 ) . we also thank s. mao and k. rauch for helpful discussions . a.b . and l.k acknowledge the hospitality shown to them at cita during their visits in 1995 . this work was supported in part by nserc ( canada ) , the ciar cosmology program , cita , the institute for astronomy ( l.k . ) , the dudley observatory ( a.b . ) , and a cita national fellowship ( m.h.l . ) .

in paper i we studied the theory of gravitational microlensing for a planar distribution of point masses . in this second paper , we extend the analysis to a three - dimensional lens distribution . first we study the lensing properties of three - dimensional lens distributions by considering in detail the critical curves , the caustics , the illumination patterns , and the magnification cross - sections of multiplane configurations with two , three , and four point masses . for point masses that are widely separated in lagrangian space , we find that there are critical curves in total , but that only of these produce prominent caustic - induced features at the high magnification end of . in the case of a low optical depth random distribution of point masses , we show that the multiplane lens equation near a point mass can be reduced to the single plane equation of a point mass perturbed by weak shear . this allows us to calculate the caustic - induced feature in the macroimage magnification distribution as a weighted sum of the semi - analytic feature derived in paper i for a planar lens distribution . the resulting semi - analytic caustic - induced feature is similar to the feature in the planar case , but it does not have any simple scaling properties , and it is shifted to higher magnification . the semi - analytic distribution is compared to the results of previous numerical simulations for optical depth , and they are in better agreement than a similar comparison in the planar case . we explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors . for ,

in paper i we studied the theory of gravitational microlensing for a planar distribution of point masses . in this second paper , we extend the analysis to a three - dimensional lens distribution . first we study the lensing properties of three - dimensional lens distributions by considering in detail the critical curves , the caustics , the illumination patterns , and the magnification cross - sections of multiplane configurations with two , three , and four point masses . for point masses that are widely separated in lagrangian space , we find that there are critical curves in total , but that only of these produce prominent caustic - induced features at the high magnification end of . in the case of a low optical depth random distribution of point masses , we show that the multiplane lens equation near a point mass can be reduced to the single plane equation of a point mass perturbed by weak shear . this allows us to calculate the caustic - induced feature in the macroimage magnification distribution as a weighted sum of the semi - analytic feature derived in paper i for a planar lens distribution . the resulting semi - analytic caustic - induced feature is similar to the feature in the planar case , but it does not have any simple scaling properties , and it is shifted to higher magnification . the semi - analytic distribution is compared to the results of previous numerical simulations for optical depth , and they are in better agreement than a similar comparison in the planar case . we explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors . for , the fraction is , much less than the for the planar case . = cmmib10 scaled 1200 = cmmib10 = cmbsy10 scaled 1200 = cmbsy10 = = = = = = = `` 710b = ' ' 710c = `` 710d = ' ' 710e = `` 710f = ' ' 7110 = `` 7111 = ' ' 7112 = `` 7113 = ' ' 7114 = `` 7115 = ' ' 7116 = `` 7117 = ' ' 7118 = `` 7119 = ' ' 711a = `` 711b = ' ' 711c = `` 711d = ' ' 711e = `` 711f = ' ' 7120 = `` 7121 = ' ' 7122 = `` 7123 = ' ' 7124 = `` 7125 = ' ' 7126 = `` 7127 = ' ' 7272 = " 7201 # 1#1 # 1

1507.06125

i

quantum simulation offers a means to probe many - body physics that can not be simulated efficiently by classical computers , using controllable quantum systems to physically realize a desired many - body hamiltonian@xcite . in the analog approach to quantum simulation exemplified by cold atoms in optical lattices@xcite , the simulator s hamiltonian maps to the desired hamiltonian . compared to digital quantum simulation , realized via complex sequences of gate operations@xcite , analog quantum simulation is usually carried out with simpler building blocks . for example , the heisenberg and hubbard hamiltonians of great interest in many - body physics are directly synthesized by cold atoms in optical lattices@xcite . although of immense interest and proposed long ago@xcite , analog simulation of fermionic hubbard systems has proven to be very challenging@xcite . the anticipated regime of the intensely debated spin liquid , unconventional superconductivity , and pseudogap@xcite has yet to be accessed even for cold atoms . here , the required low temperature @xmath0 is problematic due to the weak tunnel - coupling @xmath1 of cold atoms@xcite . moreover , experimentally resolving individual lattice sites , crucial elsewhere in bose - hubbard simulation@xcite , remains very challenging in quantum simulation of the hubbard model . here , we perform atomic resolution measurements resolving spin - spin interactions of individual dopants , realizing an analog quantum simulation of a two - site hubbard system . we demonstrate the much desired combination of low effective temperatures , single - site spatial resolution , and non - perturbative interaction strengths of great importance in condensed matter@xcite . the dopants physical hamiltonian @xmath2 , determined at the time of fabrication@xcite , maps to an effective hubbard hamiltonian @xmath3 , where @xmath4 is the on - site coulomb repulsion , @xmath5 ( @xmath6 ) creates ( destroys ) a fermion at lattice site @xmath7 with spin @xmath8 , @xmath9 is the number operator , and h.c . is the hermitian conjugate . here , it is desirable to achieve non - perturbative ( intermediate ) interaction strengths @xmath10 associated with quantum fluctuations and emergent phenomena@xcite , _ i.e. _ , beyond perturbative heisenberg interactions ( large @xmath10 ) realized in photon - based@xcite and ion - based@xcite simulations , and magnetic ions on metal surfaces@xcite . we focus on the system ground state , prepared by relaxation upon cooling@xcite , rather than system dynamics . = tunnel rate to tip , @xmath11 tunnel rate from reservoir ) the inter - acceptor coupling @xmath1 obeys @xmath12 . @xmath13 measures the interacting states quasi - particle wavefunction ( qpwf ) , contains interference processes from which we obtain two - body wavefunction amplitudes , and determine the entanglement entropy and effective hubbard interactions . b. acceptor pair ( double - protrusion ) in topography at @xmath14 v and @xmath15 pa ( top ) , and spectrally and spatially resolved @xmath13 taken at a bias @xmath16 v where topography is flat apart from atomic corrugation ( bottom ) . valence band ( vb ) , 2-hole ground state and 2-hole excited states are indicated . c. effective energy diagram of sequential hole tunneling through 2-hole ground and excited state of coupled acceptors . ] because the states of our artificial hubbard system are coupled and interacting , tunneling spectroscopy locally probes the spectral function . the spectral function is of key interest in many - body physics because it provides rich information on interactions@xcite , and is highly sought after in future `` cold - atom tunneling microscope '' experiments@xcite . for our few - body system , the local spectral function describes the quasi - particle wavefunction ( qpwf)@xcite and the discrete coupled - spin spectrum of the dopants . we find that interference of atomic orbitals directly contained in the qpwf allows us to quantify the electron - electron correlations and the entanglement entropy . the entanglement entropy is a fundamental concept for correlated many - body phases@xcite that has thus far evaded measurement for fermions . in the counterintuitive regime of our experiments , entanglement entropy increases as the valence bond is stretched , as coulomb interactions overcome quantum tunneling . in our system , the entanglement entropy is directly related to the hubbard interactions @xmath10 , and we find that @xmath10 is tunable with dopant separation , increasing from @xmath17 for @xmath18 , where @xmath19 nm is the effective bohr radius . this range , of interest to simulate unconventional superconductivity and spin liquids@xcite , is realized here due to the large bohr radii of the hydrogenic states . the semiconductor host allows for electrostatic control of the chemical potential@xcite , desirable to dynamically control filling - factor@xcite but not possible for ions on metal surfaces@xcite .

in quantum simulation , many - body phenomena are probed in controllable quantum systems . recently , simulation of bose - hubbard hamiltonians using cold atoms revealed previously hidden local correlations . however , fermionic many - body hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms . to date we simulate a two - site hubbard hamiltonian at low effective temperatures with single - site resolution using subsurface dopants in silicon . we measure quasiparticle tunneling maps of spin - resolved states with atomic resolution , finding interference processes from which the entanglement entropy and hubbard interactions are quantified . we find separation - tunable hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants , establishing dopants as a platform for quantum simulation of the hubbard model .

in quantum simulation , many - body phenomena are probed in controllable quantum systems . recently , simulation of bose - hubbard hamiltonians using cold atoms revealed previously hidden local correlations . however , fermionic many - body hubbard phenomena such as unconventional superconductivity and spin liquids are more difficult to simulate using cold atoms . to date the required single - site measurements and cooling remain problematic , while only ensemble measurements have been achieved . here we simulate a two - site hubbard hamiltonian at low effective temperatures with single - site resolution using subsurface dopants in silicon . we measure quasiparticle tunneling maps of spin - resolved states with atomic resolution , finding interference processes from which the entanglement entropy and hubbard interactions are quantified . entanglement , determined by spin and orbital degrees of freedom , increases with increasing covalent bond length . we find separation - tunable hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants , establishing dopants as a platform for quantum simulation of the hubbard model .

1207.5653

i

sometimes , especially in applications dealing with signal processing and biology , theory provides us with some additional information allowing us to restrict the parameter space to a finite number of points ; in these cases , we speak of _ discrete parameter models_. statistical inference when the parameter space is reduced to a lattice was first considered by hammersley @xcite in a seminal paper . however , since the author was motivated by the measurement of the mean weight of insulin , he focused mainly on the case of a gaussian distribution with known variance and unknown integer mean ( see @xcite , page 192 ) ; this case was further developed by khan @xcite . the poisson case also met some attention in the literature and was dealt with by hammersley ( @xcite , page 199 ) and others @xcite . previous works have shown that the rate of convergence of @xmath0-estimators is often exponential [ @xcite , @xcite ] . general treatments of admissibility and related topics are in @xcite ( see also the book @xcite ) ; special cases have been dealt with in @xcite ( page 424 , for the case of a translation integral parameter and of integral data under the quadratic loss ) , @xcite ( for the case of the gaussian distribution ) and @xcite ( for the case of the discrete uniform distribution ) . other papers dealing with optimality in discrete parameter spaces are @xcite . optimality of estimation under a discrete parameter space was also considered by vajda @xcite in a nonorthodox setting inspired by rnyi s theory of random search . other aspects that have been studied are bayesian encompassing @xcite , construction of confidence intervals ( @xcite , pages 224225 ) , comparison of statistical experiments ( @xcite , @xcite , section 2.2 ) , sufficiency and minimal sufficiency @xcite and best prediction @xcite . moreover , in the estimation of complex statistical models ( see @xcite , @xcite , chapter 4 ) and in the calculation of efficiency rates ( see @xcite ) , approximating a general parameter space by a sequence of finite sets has proved to be a valuable tool . a few papers showed the practical importance of discrete parameter models in signal processing , automatic control and information theory and derived some bounds on the performance of the estimators ( see @xcite ) . more recently , the topic has received new interest in the information theory literature ( see @xcite , and the review paper @xcite ) , in stochastic integer programming ( see @xcite ) , and in geodesy ( see , e.g. , @xcite , section 5 ) . however , no general formula for the convergence rate has ever been obtained , no optimality proof under generic conditions has been provided and no general discussion of efficiency and superefficiency in discrete parameter models has appeared in the literature . in the present paper , we provide a full answer to these problems in the case of discrete parameter models for samples of i.i.d . ( independent and identically distributed ) random variables . therefore , after introducing some examples of discrete parameter models in section [ sect - examples ] , in section [ sect - m - estimators ] we investigate the properties of a class of @xmath0-estimators . in particular , in section [ sect - consistencyofmleandbe ] , we derive some conditions for strong consistency ; then , in section [ sect - asymptoticdistributionofthemle ] , we calculate an asymptotic approximation of the distribution of the estimator and we establish its convergence rate . these results are specialized to the case of the maximum likelihood estimator ( ) and extended to bayes estimators in section [ sect - mleandbayesestimators ] . in section [ sect - optimalityandefficiencyofthemle ] , we derive upper bounds for the convergence rate in the standard and in the minimax contexts , and we discuss the relations between information inequalities , efficiency and superefficiency . in particular , we prove that estimators of discrete parameters have uncommon efficiency properties . indeed , under the zero one loss function , no estimator is efficient in the class of consistent estimators for any value of @xmath1 ( @xmath2 being here the true value of the parameter ) and no estimator attains the information inequality we derive . but the still has some appealing properties since it is minimax efficient and attains the minimax information inequality bound .

in some estimation problems , especially in applications dealing with information theory , signal processing and biology , theory provides us with additional information allowing us to restrict the parameter space to a finite number of points . in this case , we speak of discrete parameter models . even though the problem is quite old and has interesting connections with testing and model selection , asymptotic theory for these models has hardly ever been studied . therefore , we discuss consistency , asymptotic distribution theory , information inequalities and their relations with efficiency and superefficiency for a general class of-estimators . .

in some estimation problems , especially in applications dealing with information theory , signal processing and biology , theory provides us with additional information allowing us to restrict the parameter space to a finite number of points . in this case , we speak of discrete parameter models . even though the problem is quite old and has interesting connections with testing and model selection , asymptotic theory for these models has hardly ever been studied . therefore , we discuss consistency , asymptotic distribution theory , information inequalities and their relations with efficiency and superefficiency for a general class of-estimators . .

1105.1294

i

quantum theory is described via feynman path integral ( fpi ) . the integrand in fpi has the form of @xmath3 , where @xmath4 is the imaginary unit and @xmath5 is the action . the action is usually taken to be real . however , if we assume that the integrand is more fundamental than the action in quantum theory , then we can consider a theory where the action is taken to be complex , by speculating that since the integrand is complex , the action can be also complex . based on this assumption and other related works in some backward causation developments inspired by general relativity@xcite@xcite and the non - locality explanation of fine - tuning problems@xcite@xcite , the complex action theory ( cat ) has been studied intensively by one of the authors ( h.b.n ) and ninomiya@xcite@xcite . compared to the usual real action theory ( rat ) , the imaginary part of the action is thought to give some falsifiable predictions . indeed , many interesting suggestions have been made for higgs mass@xcite , quantum mechanical philosophy@xcite , some fine - tuning problems@xcite , black holes@xcite , de broglie - bohm particle and a cut - off in loop diagrams@xcite . in ref . we have studied the time - development of some state by a non - hermitian diagonalizable bounded hamiltonian @xmath6 , and shown that we can effectively obtain a hermitian hamiltonian after a long time development by introducing a proper inner product . if the hermitian hamiltonian is given in a local form , a conserved probability current density can be constructed with two kinds of wave functions . we note that the non - hermitian hamiltonian is a generic one , so it does not belong to a class of the pt symmetric non - hermitian hamiltonians , which has been intensively studied recently@xcite@xcite . for reviews see refs . . in ref . , we have proposed the replacement of hermitian operators of coordinate and momentum @xmath7 and @xmath8 and their eigenstates @xmath9 and @xmath10 with non - hermitian operators @xmath11 and @xmath12 , and @xmath13 and @xmath14 with complex eigenvalues @xmath2 and @xmath1 , so that we can deal with complex @xmath2 and @xmath1 obtained at the saddle point . introducing a philosophy to keep the analyticity in parameter variables of fpi and defining a modified set of complex conjugate , real and imaginary parts , hermitian conjugates and bras , we have explicitly constructed them for complex @xmath2 and @xmath1 by squeezing the coherent states of harmonic oscillators . in addition , extending the study of ref . to the complex coordinate formalism , we have investigated a system defined by a diagonalizable non - hermitian bounded hamiltonian , and shown that a hermitian hamiltonian is effectively obtained after a long time development also in the complex coordinate formalism . in addition , as other works related to complex saddle point paths , in refs . @xcite@xcite the complete set of solutions of the differential equations following from the schwinger action principle has been obtained by generalizing the path integral to include sums over various inequivalent contours of integration in the complex plane . in ref . complex langevin equations have been studied . in refs . and a method to examine the complexified solution set has been investigated . the cat has been studied intensively as mentioned above , but there remain many things to be studied . for instance , in the above studies it has been supposed and taken as a matter of course that the momentum and hamiltonian in the cat have the same forms as those in the rat , and it has not been examined explicitly so far . in the rat , we first write the lagrangian @xmath15 in terms of a coordinate @xmath2 and its time derivative @xmath16 , and then define the momentum @xmath1 by the relation @xmath17 . next , we define the hamiltonian @xmath18 via the legendre transformation as @xmath19 . by replacing @xmath2 and @xmath1 with their corresponding operators in the classical hamiltonian @xmath6 , we obtain the quantum hamiltonian . this is a well - known story in the rat , but what happens in the cat ? once we allow the action to be complex , various quantities known in the rat can drastically change , and we can encounter various exotic situations . hence we have to be careful about them . indeed , the momentum relation @xmath17 in the cat is not so trivial . we write @xmath20 as @xmath21 . if we quantum mechanically have in mind that our formalism corresponds to the deformation of the contour of originally real @xmath2 and @xmath1 , then using functional integral fpi and imagining to choose the @xmath22-integrals along the real axis we would intuitively think that both @xmath22 and @xmath23 could be chosen real and thus @xmath16 would be real . this is seemingly a discrepancy for the equation @xmath24 with @xmath25 complex , and also for its naive operator interpretation by expecting that the operators corresponding to these dynamical variables are still hermitian . in fact this seeming discrepancy partly motivated us to construct the complex coordinate formalism in ref . . it is the main subject of the present paper to formulate in such a way that we can quantum mechanically assign at least some meaning to the relation @xmath17 . normally in quantum mechanics @xmath23 has no definite value . rather in fpi the system at time @xmath26 is given in a superposition of essentially all @xmath23-values . to see whether the momentum relation holds in the cat or not , we analyze it explicitly by writing it in the form of the operator acting on appropriate states with a number @xmath0 put as replacement for @xmath23 . see eq.([phat_p_xi2 ] ) . we shall show in this paper that the relation @xmath17 is true in the classical sense along the time development of the saddle points in the integral @xmath27 in @xmath28 . indeed we put forward this saddle point interpretation of @xmath17 as eq.([pjmqj ] ) . since with complex mass @xmath25 the saddle point or classical path will typically be complex , there is nothing strange in @xmath17 of eq.([pjmqj ] ) conceived as a saddle point relation . from the above point of view , in this paper we explicitly examine how the momentum and hamiltonian are defined in the cat based on the complex coordinate formalism of ref . . we replace hermitian operators of coordinate and momentum @xmath7 and @xmath8 and their eigenstates @xmath9 and @xmath10 with non - hermitian operators @xmath11 and @xmath12 , and @xmath13 and @xmath14 with complex eigenvalues @xmath2 and @xmath1 , and utilize the new devices such as a modified set of complex conjugate , hermitian conjugates and bras to realize the philosophy of keeping the analyticity in parameter variables of fpi . in the usual way of deriving and understanding the functional integral , a functional integral corresponding to finite time interval say @xmath29 $ ] with endpoints fixed to specific @xmath30 and @xmath31 values is expressed as @xmath32 , where @xmath33 is a priori taken over real @xmath34 s . we claim that this interpretation is possible even for complex @xmath31 and @xmath30 by following the formalism of ref . . we can deform formally the infinitely many contours as long as the action @xmath5 is an analytical function of all the @xmath34 s . in this way going to complex contours only with restriction to go from @xmath35 to @xmath36 is rather trivial . we , however , stress that after the deformation of the contour in a different way for each moment @xmath37 the contours still start at @xmath35 and ends at @xmath38 , but in between of course they are usually complex . that is to say , appropriate contours are chosen at each time @xmath37 . the present paper has also a role of showing an explicit application of the formalism of ref . . starting from the lagrangian @xmath39 in fpi , we derive the momentum relation by considering an eigenvalue problem of the momentum operator , which includes a parameter @xmath0 . we attempt to split up a wave function @xmath40 into various @xmath0-components , and investigate the time - development of the @xmath0-parametrized wave function in fpi . this study elucidates that the momentum in the cat has the same form as that in the rat . in addition we also derive the hamiltonian @xmath6 in fpi starting from the lagrangian @xmath39 in the cat . next in an opposite way we try to check whether we can reproduce the lagrangian starting from the hamiltonian , and show that the lagrangian is derived from the hamiltonian . this result confirms that the hamiltonian in the cat has the same form as that in the rat . it leads us to the momentum relation again via the saddle point for @xmath1 . we also give the third derivation of the momentum relation via the saddle point for @xmath2 . this paper is organized as follows . in section 2 we briefly review the complex coordinate formalism of ref . . introducing the philosophy of keeping the analyticity in parameter variables of fpi and the new devices to realize it such as a modified set of bra , complex conjugates , hermitian conjugate and hermiticity , we construct non - hermitian operators of coordinate and momentum @xmath11 and @xmath12 , and the hermitian conjugates of their eigenstates @xmath41 and @xmath42 with complex eigenvalues @xmath2 and @xmath1 . in section 3 we derive the momentum relation by solving an eigenvalue problem of the momentum operator and considering the time - development of the wave function solution in fpi . we also derive the free hamiltonian starting from the free lagrangian in fpi . next starting from the lagrangian with a potential term in fpi , we derive the momentum relation and the hamiltonian with the potential term . in section 4 oppositely by using the hamiltonian @xmath6 we derive the lagrangian @xmath39 in fpi . also , we again obtain the momentum relation via the saddle point for @xmath1 . this study reveals that the momentum and hamiltonian in the cat have the same forms as those in the rat . section 5 is devoted to conclusion and outlook . in appendix [ via_saddle_q ] we explain the third derivation of the momentum relation via the saddle point for @xmath2 .

in the complex action theory ( cat ) we explicitly examine how the momentum and hamiltonian are defined from the feynman path integral ( fpi ) point of view based on the complex coordinate formalism of our foregoing paper . after reviewing the formalism briefly , , we derive the momentum and hamiltonian . we also show the third derivation of the momentum relation via the saddle point for .

in the complex action theory ( cat ) we explicitly examine how the momentum and hamiltonian are defined from the feynman path integral ( fpi ) point of view based on the complex coordinate formalism of our foregoing paper . after reviewing the formalism briefly , we describe in fpi with a lagrangian the time development of a-parametrized wave function , which is a solution to an eigenvalue problem of a momentum operator . solving this eigenvalue problem , we derive the momentum and hamiltonian . oppositely , starting from the hamiltonian we derive the lagrangian in fpi , and we are led to the momentum relation again via the saddle point for . this study confirms that the momentum and hamiltonian in the cat have the same forms as those in the real action theory . we also show the third derivation of the momentum relation via the saddle point for .

1105.1294

i

in the complex action theory ( cat ) even a coordinate @xmath2 and a momentum @xmath1 can be complex in general . in ref . , to handle the complex @xmath2 and @xmath1 , we have proposed the replacement of hermitian operators of coordinate and momentum @xmath7 and @xmath8 and their eigenstates @xmath43 and @xmath10 with non - hermitian operators @xmath11 and @xmath12 , and @xmath13 and @xmath14 with complex eigenvalues @xmath2 and @xmath1 . we have introduced a philosophy of keeping the analyticity in parameter variables of feynman path integral ( fpi ) , and defined modified bras @xmath73 and @xmath296 , a modified complex conjugate @xmath60 , and a modified hermitian conjugate @xmath297 to realize the philosophy , by means of which we have explicitly constructed @xmath11 , @xmath12 , and the hermitian conjugates of their eigenstates @xmath41 and @xmath42 by utilizing the coherent states of harmonic oscillators . here @xmath298 denotes a set of parameters which we keep the analyticity in . in this paper , based on the complex coordinate formalism of ref . , we have explicitly examined how the momentum and hamiltonian are defined in the cat from the fpi point of view . in section 2 we have briefly reviewed the complex coordinate formalism of ref . . first we have explained that the delta function can be used also for complex parameters when it satisfies some condition , and introduced the new devices to realize the philosophy of keeping the analyticity in parameter variables of fpi . the philosophy allows us to deform the path of fpi . then we have briefly shown the construction of non - hermitian operators @xmath11 and @xmath12 , and the hermitian conjugates of their eigenstates @xmath41 and @xmath42 with complex eigenvalues @xmath2 and @xmath1 by utilizing the coherent states of harmonic oscillators . in section [ derivation_hamiltonian ] based on the philosophy and using the new devices explained in section [ fundamental ] we have described in fpi with a lagrangian the time development of a @xmath0-parametrized wave function , which is a solution to an eigenvalue problem of a momentum operator . solving the eigenvalue problem and considering the time - development of the wave function solution in fpi we have derived the momentum relation @xmath17 . furthermore we have also studied the form of the hamiltonian in the cat . we have derived the hamiltonian starting from the lagrangian in fpi , first in a free theory case , and then in a potential case . in section [ derivation_lagrangian ] , oppositely starting from the hamiltonian , we have derived the lagrangian in a potential case via fpi , and also the momentum relation again via the saddle point for @xmath1 . these explicit studies have confirmed that both of the momentum and hamiltonian in the cat have the same forms as those in the real action theory ( rat ) . in appendix [ via_saddle_q ] we have explained the third derivation of the momentum relation via the saddle point for @xmath2 . now the momentum and hamiltonian in the cat have been identified clearly , based on the complex coordinate formalism of ref . . as a next step what should we study to develop the cat ? one direction is to study a future - included theory , that is to say , a theory including not only a past time but also a future time as an integration interval of time , which we have not considered in this paper , in the complex coordinate formalism . it is interesting to study such a future - included theory by considering a kind of wave function of universe including the future information , which was discussed in ref . . in addition , it is also important to study an expectation value in the cat . we shall attempt to discuss how the expectation value is defined in the cat generally , and also clarify its relation to the modified hermiticity . furthermore , it is also intriguing to investigate in detail the possible misestimation of the past state by extrapolating back in time with the hermitian hamiltonian . as pointed out in ref . , the misestimation by a historian living in the late time can occur in some fundamental theory which is described by a non - hermitian hamiltonian . we will study them and report the progress in the future .

we describe in fpi with a lagrangian the time development of a-parametrized wave function , which is a solution to an eigenvalue problem of a momentum operator . solving this eigenvalue problem oppositely , starting from the hamiltonian we derive the lagrangian in fpi , and we are led to the momentum relation again via the saddle point for . this study confirms that the momentum and hamiltonian in the cat have the same forms as those in the real action theory .

in the complex action theory ( cat ) we explicitly examine how the momentum and hamiltonian are defined from the feynman path integral ( fpi ) point of view based on the complex coordinate formalism of our foregoing paper . after reviewing the formalism briefly , we describe in fpi with a lagrangian the time development of a-parametrized wave function , which is a solution to an eigenvalue problem of a momentum operator . solving this eigenvalue problem , we derive the momentum and hamiltonian . oppositely , starting from the hamiltonian we derive the lagrangian in fpi , and we are led to the momentum relation again via the saddle point for . this study confirms that the momentum and hamiltonian in the cat have the same forms as those in the real action theory . we also show the third derivation of the momentum relation via the saddle point for .

1610.05378

i

multilayer networks @xcite are emerging as a powerful paradigm for describing complex systems characterized by the coexistence of different types of interactions . multilayer networks represent an appropriate descriptive model for real networked systems in disparate contexts , such as social @xcite , technological @xcite and biological systems @xcite . for example , global infrastructures are formed by several interdependent networks , such as power grids , water supply networks , and communication systems , and studying their properties require to account for the presence of such interdependencies @xcite . cell function and/or malfunction ( yielding diseases ) can not be understood if the information on the different nature of the interactions forming the interactome ( protein - protein interactions , signaling , regulation ) are not integrated in a general multilayer scenario @xcite . similarly , the complexity of the brain is encoded in the different nature of the interactions existing at the functional and the structural levels @xcite . a multilayer networks is composed of a set of networks forming its layers @xcite . nodes can be connected within and across layers . it has been shown that multilayer networks are much more fragile than isolated networks just because of the presence of interdependencies among the layers of the system @xcite . in particular , the fragility of the system increases as the number of layers increases @xcite . such a feature has an intuitive explanation . in the standard percolation model for multilayer networks , the probability that a node is damaged equals to the probability that at least one of its interdependent nodes is damaged . as the number of layers increases , the probability of individual failures grows thus making the system more fragile . this scenario leads , however , to the conundrum : if the fragility of a system is increased by the number of layers of interactions , why are there so many real systems that display multiple layers of interactions ? further , the addition of new layers of interactions in a preexisting multilayer network has generally a cost , so it does nt seem reasonable to spend resources just to make the system less robust . the purpose of the current paper is to provide a potential explanation by introducing a new model for percolation in networks composed of multiple interacting layers . in the model , we will assume that a node is damaged only if all its interdependent nodes are simultaneously damaged . the model is perfectly equivalent to the standard one when the number of layer equals two . additional layers , however , provide the system with redundant interdependencies , generating backup mechanisms against the failure of the system , and thus making it more robust . the robustness of multilayer networks in presence of redundant interdependencies is here investigated using a message - passing theory @xcite ( also known as the cavity method ) . we build on recent advances obtained in standard interdependent percolation theory @xcite to propose a theory that is valid for multilayer networks with link overlap @xcite as long as the multilayer network is locally tree - like . this limitation is common to all message - passing approaches for studying critical phenomena on networks . corrections have been recently proposed @xcite on single networks to improve the performace of message - passing theory and similar approximations valid for loopy multilayer networks might be envisaged in the future .

, the addition of a new layer of interdependent nodes to a preexisting multilayer network will never improve its robustness . whereas such a model seems appropriate to understand the effect of interdependencies in the simplest scenario of a network composed of only two layers , it may seem not reasonable for real systems where multiple network layers interact one with the other . the model reduces to the standard percolation model for multilayer networks when the number of layers equals two . for larger number of layers

in the standard model of percolation on multilayer networks , a node is functioning only if its copies in all layers are simultaneously functioning . according to this model , a multilayer network becomes more and more fragile as the number of layers increases . in this respect , the addition of a new layer of interdependent nodes to a preexisting multilayer network will never improve its robustness . whereas such a model seems appropriate to understand the effect of interdependencies in the simplest scenario of a network composed of only two layers , it may seem not reasonable for real systems where multiple network layers interact one with the other . it seems in fact unrealistic that a real system , such a living organism , evolved , through the development of multiple layers of interactions , towards a fragile structure . in this paper , we introduce a model of percolation where the condition that makes a node functional is that the node is functioning in at least two of the layers of the network . the model reduces to the standard percolation model for multilayer networks when the number of layers equals two . for larger number of layers , however , the model describes a scenario where the addition of new layers boosts the robustness of the system by creating redundant interdependencies among layers . we prove this fact thanks to the development of a message - passing theory able to characterize the model in both synthetic and real - world multilayer graphs .

1011.3200

c

in this article , we study the @xmath273 form - factors @xmath20 , @xmath21 , @xmath22 , @xmath274 , @xmath25 , @xmath26 and @xmath27 with the @xmath3-meson light - cone qcd sum rules . in calculations , we observe that the dominating contributions come from the two - particle @xmath3-meson light - cone distribution amplitude @xmath4 , its line - shapes have significant impacts on the values of the form - factors , we can search for the ideal values of the parameter @xmath66 . in the @xmath3-meson light - cone sum rules for the @xmath275 form - factors , the dominating contributions @xmath188 , while in the @xmath3-meson light - cone sum rules for the @xmath7 form - factors , the dominating contributions @xmath276 . if we take the value @xmath277 as in the @xmath3-meson light - cone qcd sum rules for the @xmath275 form - factors , the central values of the present predictions are at least ( or almost ) twice as large as the existing theoretical estimations , and the @xmath128 deviates greatly from the value extracted from the radiative decays @xmath160 and @xmath278 , the non - factorizable contributions are neglected in the extraction . on the other hand , if we take the value @xmath244 , the present predictions are compatible with other theoretical estimations . in calculations , we observe that the main uncertainty comes from the parameter @xmath66 ( or @xmath82 ) , which determines the line - shapes of the two - particle and three - particle @xmath3-meson light - cone distribution amplitudes , it is of great importance to refine this parameter . we can extract the values of those form - factors from the experimental data on the radiative and semi - leptonic decays at the kek - b and the lhcb in the future , and obtain severe constraints on the parameter @xmath66 .

in this article , we study the , , form - factors with the light - cone qcd sum rules , where the-meson light - cone distribution amplitudes are used . in calculations , we observe that the line - shapes of the-meson light - cone distribution amplitude have significant impacts on the values of the form - factors , and expect to obtain severe constraints on the parameters of the-meson light - cone distribution amplitudes from the experimental data in the future .

in this article , we study the , , form - factors with the light - cone qcd sum rules , where the-meson light - cone distribution amplitudes are used . in calculations , we observe that the line - shapes of the-meson light - cone distribution amplitude have significant impacts on the values of the form - factors , and expect to obtain severe constraints on the parameters of the-meson light - cone distribution amplitudes from the experimental data in the future . + zhi - gang wang + department of physics , north china electric power university , baoding 071003 , p. r. china pacs numbers : 12.38.lg ; 13.20.he * key words : * meson , light - cone qcd sum rules

1210.5862

i

there is now a substantial literature focusing on the geometrical and analytical properties of self - similar fractals , which are commonly described as the unique non - empty compact subset @xmath0 satisfying @xmath1 , where @xmath2 is a finite collection of contractions on an underlying complete metric space @xmath3 . the existence and uniqueness of @xmath4 is guaranteed by an extension of the usual contraction principle for complete metric spaces ( @xcite , theorem 1.1.4 , for example ) . a fundamental problem in this area is to calculate the hausdorff dimension , @xmath5 say , of the self - similar fractal @xmath4 , and in a wide class of examples it is now known ( @xcite , corollary 1.5.9 ) that @xmath5 is the unique positive @xmath6 solving @xmath7 , where @xmath8 are the contraction ratios of @xmath2 . additionally , various stochastic versions of this result have been investigated . for example , when the underlying metric space @xmath3 is finite dimensional euclidean space , in @xcite a random self - similar set @xmath4 satisfying @xmath9 , where @xmath10 is a random ( finite or countable ) collection of scaling factors and @xmath11 are independent copies ( up to translation ) of @xmath4 , independent of @xmath10 , is constructed and ( assuming @xmath4 is non - empty and @xmath12 fulfils a non - overlapping condition ) the hausdorff dimension of @xmath4 is shown to be @xmath13-a.s . equal to the unique positive @xmath6 solving @xmath14 which obviously reduces to the deterministic equation when @xmath15 , @xmath13-a.s . note that we are assuming that all the random variables are defined on an underlying probability space with probability measure @xmath13 , and @xmath16 is the expectation under @xmath13 . a similar result was proved independently in @xcite . the aim of this article is to obtain similar hausdorff dimension results to those discussed above for a class of random self - similar trees that do not fit into the usual framework for random self - similar sets . first though , it is necessary to deal with questions concerning their construction . our starting point , rather than to define a random set directly , is to consider a fixed fractal subset of @xmath17 and build a random metric upon it . more precisely , for @xmath18 , set @xmath19 for some constant @xmath20 , and define @xmath21 to be the unique non - empty compact set satisfying @xmath22 , where we now define @xmath23 . the set @xmath21 , shown in figure [ ssd ] , is easily checked to be a _ dendrite _ , by which we mean that it is an arc - wise connected topological space containing no subset homeomorphic to the circle . although the euclidean metric is important for its construction , we are only interested in @xmath21 as a topological space . indeed , the hausdorff dimension of @xmath21 with respect to the intrinsic random metric we construct upon it can be strictly larger than 2 . ( -265,50)@xmath24 ( 0,50)@xmath25 heuristically , we build a random metric on @xmath21 by first supposing that the distance between the `` edge '' from @xmath24 to @xmath25 is of length 1 . we then replace this by three randomly scaled copies of the edge with new lengths given by @xmath10 , see figure [ edgerep ] , and continue inductively to replace edges independently of each other by triples of scaled edges , with the relevant scaling factors having the same distribution as @xmath10 . as the number of inductive steps increases our discrete approximations eventually fill out a dense subset of @xmath21 , and ( under certain distributional conditions on the scaling factors ) calculating the `` limiting distance '' between points yields a metric @xmath26 on @xmath21 such that @xmath27 is a compact metric space , and the topology induced by @xmath26 on @xmath21 is the same as the original ( euclidean ) one , @xmath13-a.s . see section [ ssdsec ] for full details . ( 10,2.75 ) ( .5,.25)(3.5,0.25 ) ( 0,.25)@xmath24 ( 4,.25)@xmath25 ( 2,0)@xmath28 ( 4.5,.75)(5.5,.75 ) ( 6.5,.25)(9.5,.25 ) ( 8.0,.25)(8,1.75 ) ( 6,0.25)@xmath24 ( 10,0.25)@xmath25 ( 8,2)@xmath29 ( 7.25,0)@xmath30 ( 8.75,0)@xmath31 ( 8.5,1)@xmath32 importantly , we do not assume that @xmath33 , @xmath13-a.s . , and , as a result of this , the distance in @xmath27 between @xmath24 and @xmath25 depends , in general , on all of the steps in the inductive procedure . for reasons related to the construction of the metric @xmath26 as a so - called resistance metric , we call this limiting distance between @xmath24 and @xmath25 , @xmath34 say , a resistance perturbation . similarly , the distance between @xmath24 and @xmath35 in @xmath27 is not simply @xmath30 , but equal to @xmath36 , where @xmath37 is the resistance perturbation associated with this `` edge '' of @xmath21 and has the same distribution as @xmath34 . the fact that @xmath21 is a dendrite means that we can characterise these resistance perturbations in a convenient way that allows us to deduce their distributional properties and perform calculations with them . in section [ dimension ] , we provide conditions on @xmath10 that allow us to deduce the hausdorff dimension of @xmath27 . proving that the @xmath6 defined by ( [ alpha ] ) is an upper bound for the hausdorff dimension it straightforward , and requires no further conditions than those used for the construction of @xmath27 . on the other hand , when obtaining a lower bound for the dimension of a fractal defined in a recursive fashion , it is often a problem when parts of the fractal become small too quickly , and this is the case here . for the proof in @xcite of the result described above , the underlying euclidean geometry of the random sets being considered is critical , but since our fractal trees are not embedded into any fixed metric space there is no easy translation of this argument to our setting . another common assumption for proving a hausdorff dimension lower bound and related results is that the scaling factors are bounded uniformly away from zero @xcite , @xcite . we show in theorem [ lowerboundbounded ] one application of this condition in our setting . more interestingly , though , is that knowledge of the geometry of the trees in consideration allows us to avoid a uniform lower bound ; in fact , we shall require only that clusters of small scaling factors are not too large . we construct a random graph approximation to @xmath21 and use a percolation argument upon this to show that this is the case when the scaling factors are independent and their distributions satisfy a simple polynomial tail bound at 0 , see theorem [ hausdorfflower2 ] . let us complete the discussion of our results related to random self - similar dendrites by outlining a pair of examples . firstly , one choice of random scaling factors that does not fit into any previously studied set - up but satisfies conditions that allow us to calculate the hausdorff dimension of the fractal @xmath27 is if we suppose @xmath10 are independent identically - distributed @xmath38 random variables . it is easy to check that the hausdorff dimension is 2 in this case . note in particular that @xmath39 , @xmath13-a.s . ; consequently there are indeed non - trivial resistance perturbations in this case . secondly , although we can not calculate the hausdorff dimension using the techniques of this article , when @xmath10 are the square - roots of a dirichlet @xmath40 triple , the construction of @xmath27 is of interest in its own right . the reason for this is explained in detail in @xcite , where it is proved that in this case @xmath27 is a version of the continuum random tree of aldous , which is an important random dendrite with connections to many other stochastic tree - like objects @xcite . the family of random scaling factors that we use to construct the random metric space @xmath27 form what is known as a multiplicative cascade , which is a probabilistic structure that has been studied extensively , see @xcite , @xcite , @xcite , @xcite . much of this previous work has concentrated on investigating properties of an associated tree - martingale limit ( see section [ multcasc ] for a definition ) , and we add to this body of knowledge by proving a tail bound at 0 for this random variable ( proposition [ lefttailprop ] ) . we also define the height of a ( generalised ) multiplicative cascade , and derive a simple condition that yields the finiteness of this quantity and its moments , see corollary [ heightupperbound ] and theorem [ heighttheorem ] . finally , let us remark that , although only one particular self - similar fractal dendrite is considered in this article , at the expense of some additional notation relatively minor refinements of the proofs used here allow the results we obtain to be extended to any post - critically finite self - similar fractal dendrite ( see @xcite for a definition of a post - critically finite self - similar fractal ) . a treatment of the general case appears in @xcite .

in this article a collection of random self - similar fractal dendrites is constructed , and their hausdorff dimension is calculated . previous results determining this quantity for random self - similar structures have relied on geometric properties of an underlying metric space or the scaling factors being bounded uniformly away from zero . however , using a percolative argument , and taking advantage of the tree - like structure of the sets considered here , it is shown that conditions such as these are not necessary . the scaling factors of the recursively defined structures in consideration form what is known as a multiplicative cascade , and results about the height of this random object are also obtained .

in this article a collection of random self - similar fractal dendrites is constructed , and their hausdorff dimension is calculated . previous results determining this quantity for random self - similar structures have relied on geometric properties of an underlying metric space or the scaling factors being bounded uniformly away from zero . however , using a percolative argument , and taking advantage of the tree - like structure of the sets considered here , it is shown that conditions such as these are not necessary . the scaling factors of the recursively defined structures in consideration form what is known as a multiplicative cascade , and results about the height of this random object are also obtained .

math0609557

i

in 1998 , goresky , kottwitz and macpherson @xcite established the gkm theory , which gives a direct link between equivariant topology and combinatorics ( or more precisely , a link between gkm manifolds and gkm graphs ) . the most essential properties of a gkm manifold @xmath5 , such as the equivariant cohomology and betti numbers of @xmath5 , can thus be explicitly expressed in terms of its corresponding gkm graph . a lot of work on this subject has been carried out since then ( @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite ) . for example , a series of papers by guillemin and zara showed that much geometrical and topological information of a gkm manifold can be read out from the corresponding gkm graph . in the gkm theory , the action group is a torus . alternately , when the action group is chosen to be a mod 2-torus , there is an analogous theory , namely the mod 2 gkm theory ( see @xcite or @xcite ) , which has successfully been applied to find the lower bound of the number of fixed points and to study the equivariant cobordism classification and the smith problem in @xcite . .2 cm the work of this article is mainly motivated by the gkm theory . however , we shall carry out our work in the mod 2 category . thus , let us first recall some basic facts about the mod 2 gkm theory , which inspired us to study colored regular graphs . suppose that @xmath6 ( a mod 2-torus of rank @xmath7 ) , which is also an @xmath3-dimensional linear space over @xmath8 . let @xmath9 be the universal principal @xmath10-bundle , where @xmath11 is the classifying space of @xmath10 . it is well - known that @xmath12 and @xmath13\ ] ] is a @xmath8-polynomial ring over @xmath14 , where the @xmath15 s are one - dimensional generators . .2 cm now suppose that @xmath5 is a closed manifold with an effective @xmath10-action such that the fixed point set @xmath16 is finite , which implies @xmath17 ( see @xcite ) . then the _ borel construction _ @xmath18 is defined as the orbit space of the induced diagonal action @xmath19 on @xmath20 , i.e. , @xmath21 so that the equivariant cohomology of @xmath5 is @xmath22 as shown in @xcite , to the @xmath10-manifold @xmath5 , one can always assign a regular graph @xmath23 with a label @xmath24 @xmath25 for each edge @xmath26 in @xmath23 . the gkm theory points out that when the @xmath10-manifold @xmath5 satisfies certain conditions , its equivariant cohomology is a free module over @xmath27 and can be explicitly read out from @xmath28 : @xmath29~|~f(v)\equiv f(w)\mod\alpha(e)~\text { for } e\in e_v\cap e_w\}\ ] ] where @xmath30 denotes the vertex set of @xmath23 and @xmath31 denotes the set of all edges in @xmath23 that are adjacent to @xmath32 . .2 cm in the extreme case where @xmath33 , the associated graph @xmath23 with @xmath16 as its vertex set can be derived as follows . .2 cm every real irreducible representation of @xmath10 is one - dimensional , so it must be a homomorphism @xmath34 . moreover , for each @xmath35 , @xmath36 since @xmath37 is an involution . therefore , by identifying the multiplicative group @xmath38 with @xmath8 , one can identify the set of all real irreducible representations of @xmath10 with @xmath25 . notice that @xmath39 is also an @xmath3-dimensional linear space over @xmath8 . .2 cm now choose a point @xmath40 , and choose a linear identification @xmath41 . then the induced tangent representation at @xmath32 can be expressed as an @xmath3-dimensional real representation @xmath42 , which can be further split into @xmath7 real irreducible representations @xmath43 clearly the set @xmath44 is independent of the choice of @xmath45 . since @xmath10 acts effectively on @xmath5 , @xmath46 are linearly independent in @xmath25 , so they form a basis of @xmath25 . .2 cm for each @xmath47 , the subgroup @xmath48 is of codimension one in @xmath10 , and the @xmath49-dimensional component of the fixed set of @xmath50 acting on @xmath5 is a circle @xmath51 ( c.f . @xcite or @xcite ) . since @xmath52 , the @xmath10-action on @xmath5 induces an involution on @xmath51 , so @xmath51 contains only two fixed points @xmath32 and @xmath53 in @xmath16 . let us label @xmath51 by @xmath47 and choose an orientation on @xmath51 . then one gets two _ oriented _ edges with endpoints @xmath54 and with the same `` label '' @xmath47 . since the labeled oriented edges always appear in pairs with reversing orientations , one can merge each pair into an _ unoriented _ edge , so that each @xmath51 determines one edge with two @xmath10-fixed points as its endpoints ( i.e. , a @xmath49-valent graph ) . then , our desired graph @xmath23 is the union of all these @xmath49-valent graphs such that the vertex set of @xmath23 consists of all fixed points of @xmath16 . @xmath23 is called the _ moment graph _ and the `` labelling map '' @xmath55 is called the _ axial function _ , where @xmath56 denotes the set of all unoriented edges . .2 cm it is obvious that in this simple case , the moment graph @xmath23 is a regular @xmath3-valent graph , and the axial function @xmath57 satisfies the following two conditions : 1 . for each vertex @xmath32 in @xmath23 , if @xmath58 are all edges adjacent to @xmath32 , then @xmath59 linearly span @xmath25 , so they are all nontrivial and distinct ; 2 . for each edge @xmath26 in @xmath23 , let @xmath60 and @xmath61 denote the two endpoints of @xmath26 . if @xmath62 and @xmath63 are the sets of edges adjacent to @xmath32 and @xmath53 respectively , then @xmath64 ( because they form irreducible decompositions of two equivalent tangent representations of @xmath65 at @xmath32 and @xmath53 respectively ) . it is not difficult to verify that this is equivalent to @xmath66 .2 cm conversely , given a finite connected regular graph @xmath23 together with some axial function @xmath67 satisfying the previous two conditions , a natural question is : _ what information on the topology of manifolds can we extract from the pair @xmath68 _ ? this seems to be an open - ended question . recently , some interesting and beautiful work on this subject has been done by some mathematicians . for example , in @xcite guillemin and zara obtained some purely combinatorial analogues of the main results in the gkm theory . in addition , they also obtained a realization theorem for abstract gkm - graphs : for an abstract gkm graph @xmath68 , there exists a complex manifold @xmath5 and a gkm action of the torus @xmath69 on @xmath5 such that @xmath68 is its gkm graph . note that the constructed complex manifold @xmath5 is not compact , not equivariantly formal , and admits no canonical compactification . .2 cm this article will deal with the problem from a different viewpoint , in the mod @xmath70 category . we shall introduce a `` skeletal expansion technique '' for any given abstract @xmath10-colored finite connected regular @xmath3-valent graphs @xmath71 , where @xmath67 satisfies the above two conditions . specifically , we shall give a canonical way to inductively attach cells on @xmath23 to form a cell complex @xmath72 such that the @xmath49-skeleton of @xmath72 is just @xmath23 . we will call this technique the _ skeletal expansion _ , and we shall use it to carry out our work as follows . .2 cm first , we determine under what conditions this procedure of cell - gluing can be performed to the end until one obtains a closed manifold ( see theorem [ th : manifold ] ) . we further show that every closed combinatorial @xmath1-manifold can be obtained in this way ( see theorem [ th : colorable ] ) . .2 cm next , we consider the realization problem : can we always construct a @xmath10-action on an @xmath3-dimensional closed manifold such that its moment graph is exactly the given @xmath10-colored regular @xmath3-valent graph @xmath71 ? to do this , our strategy is first to try to construct the orbit space of an action from @xmath71 . then by the work of davis and januszkiewicz @xcite on the reconstruction of small covers ( which is stated briefly below ) , we shall use the obtained orbit space to construct the desired @xmath10-action . we shall show that under certain conditions , any abstract @xmath10-colored finite connected regular @xmath3-valent graph @xmath71 is realizable as the moment graph of an @xmath3-dimensional closed @xmath10-manifold ( see theorem [ realization ] ) . .2 cm an _ @xmath3-dimensional convex polytope _ @xmath73 is just an @xmath3-dimensional compact manifold which is the intersection of a finite set of half - spaces in @xmath74 . it naturally becomes a cell decomposition of @xmath75 and has a minimum set of defining half - spaces , each of which corresponds to an @xmath1-dimensional face of @xmath76 . denote the set of all these codimension one faces by @xmath77 . if every vertex is surrounded by exactly @xmath7 faces in @xmath77 , then @xmath76 is called a _ simple _ convex polytope . clearly , the @xmath49-skeleton of each @xmath3-dimensional simple convex polytope is a regular @xmath3-valent graph @xmath78 . .2 cm if @xmath76 is an @xmath3-dimensional simple convex polytope , a _ characteristic function _ is a map @xmath79 such that the @xmath7 faces in @xmath77 adjacent to each vertex are sent to @xmath7 linearly independent vectors in @xmath10 . each such @xmath80 is dual to an axial function @xmath81 , such that for each edge @xmath82 and those faces @xmath83 containing @xmath26 , @xmath84 . it is easy to see that both @xmath85 and @xmath86 are determined by each other . .2 cm an @xmath3-dimensional closed manifold @xmath5 is called a _ small cover _ over @xmath76 if it admits an effective and locally standard @xmath10-action such that the orbit space @xmath87 . in @xcite , davis and januszkiewicz observed that for each simple convex polytope @xmath76 and each characteristic function @xmath80 , there is a canonical way to construct a small cover @xmath88 over @xmath76 , and every small cover over @xmath76 can be reconstructed in this way . moreover , @xmath78 is exactly the moment graph for @xmath88 and @xmath86 is the corresponding axial function . .2 cm in the case of small covers , reconstructing the orbit spaces and @xmath10-manifolds from moment graphs is simple . in fact , the orbit space @xmath89 of a small cover @xmath5 is bounded by @xmath90 with a very nice regular cell decomposition corresponding to @xmath91 , and this cell complex is topologically dual to a triangulation of @xmath90 . the skeletal expansion of the moment graph @xmath68 of @xmath5 will exactly reproduce the pre - defined cell decomposition on @xmath92 , so that this can lead us to recover the orbit space @xmath76 and its characteristic function @xmath85 , and thus @xmath5 can be reconstructed . more generally , if @xmath5 is not a small cover , the problem of reconstructing the @xmath10-manifold @xmath5 and its orbit space compatible with the moment graph becomes much more complicated . we remark that if the orbit space @xmath89 is a compact @xmath3-manifold with boundary such that the pre - image of each component of the boundary of @xmath89 contains a fixed point , then the skeletal expansion of the moment graph @xmath68 will produce a cell decomposition of the boundary of @xmath89 . .2 cm * acknowledgements . * the authors would like to thank m. masuda , f. luo and x. r. zhang for very helpful discussions leading to the results in dimensions two and three . the authors also would like to thank the referee , who gave many valuable suggestions and comments .

in this article we describe a canonical way to expand a certain kind of-colored regular graphs into closed-manifolds by adding cells determined by the edge - colorings inductively . we show that every closed combinatorial-manifold can be obtained in this way . when , we give simple equivalent conditions for a colored graph to admit an expansion .

in this article we describe a canonical way to expand a certain kind of-colored regular graphs into closed-manifolds by adding cells determined by the edge - colorings inductively . we show that every closed combinatorial-manifold can be obtained in this way . when , we give simple equivalent conditions for a colored graph to admit an expansion . in addition , we show that if a-colored regular graph admits an-skeletal expansion , then it is realizable as the moment graph of an-dimensional closed-manifold .

hep-ph9804224

i

we consider the production of a real photon or of a lepton pair in a quark - gluon plasma . the plasma is assumed to be in equilibrium at temperature @xmath1 . the theoretical framework used in the calculation is that of thermal field theory improved by the hard loop resummation @xcite of braaten and pisarski : in this approach one distinguishes hard momenta , of order @xmath1 , from soft momenta , of order @xmath2 , where @xmath3 is the quantum chromodynamics ( qcd ) coupling constant assumed to be small ( @xmath4 ) . after resummation of hard thermal loops , one is led to an effective field theory from which observables can be evaluated perturbatively . the production rates of real or virtual photons have already been evaluated , at the one loop level , in the effective theory @xcite . concerning soft virtual photons , it was found that the rate of production is considerably modified and enhanced compared to the result of the bare theory . besides the usual quark - antiquark annihilation process , there appear many production mechanisms , in particular processes where the photon is radiated off a ( hard ) quark in a scattering process where the quark is backward scattered in the plasma via soft quark exchange . this is to be contrasted to the result obtained in a semi - classical approximation @xcite where the photon is radiated off fast quarks in scattering processes mediated by a gluon exchange : we call such processes bremsstrahlung emission of a photon . in this study we reconcile the two approaches and show that the bremsstrahlung processes favored by the semi - classical approximation appear at the two - loop level in the effective theory and that , in fact , they contribute at the same order in @xmath2 as the processes in the one - loop effective theory . such a result should not be a surprise . consider the case of a soft virtual photon . the rate of production is related to the imaginary part of the vacuum polarization diagram @xcite . in the one - loop approximation of the effective field theory , it involves only effective fermion propagators and effective vertices @xcite . a dominant contribution to the rate arises when the internal fermion momentum is soft and , therefore , all effective propagators and effective vertices have the same order of magnitude as their bare counterparts . a close examination of the final result shows , however , that it has a logarithmic sensitivity to scales of order @xmath1 ( see section [ bpycomp ] ) : this means that such a diagram also receives a dominant contribution from hard fermion momenta . when the momentum becomes large , the hard thermal loop ( htl ) corrections to propagators and vertices are suppressed by , at least , a factor @xmath3 with respect to their bare counterparts . this suppression factor @xmath3 can easily be compensated by the larger phase space available to a hard fermion ( @xmath5 ) compared to soft fermion ( @xmath6 ) , thereby leading to a contribution of the same order of magnitude from the soft region and the hard region of phase - space . now , when an observable is sensitive to the thermal corrections of hard vertices and propagators , it is obvious that all such corrections should be taken into account for the calculation to be complete . some of these thermal corrections are naturally included in the lowest order of the effective theory via the resummation of hard thermal loops . but , even if the htl approximation is correct for soft external particles , it does not account for all thermal corrections to hard vertices and hard propagators . for instance , neglecting the external momenta as one does in the calculation of the hard thermal loops is no longer justified when these momenta are not soft . besides , equally important may be the contribution arising from soft gluons in the loop giving the htl when the external momenta are hard , due to the bose enhancement of the soft gluon term . within the effective theory , both types of additional thermal corrections to a hard propagator or vertex are taken into account by considering a one - loop correction to this propagator or vertex . in the calculation of the virtual photon production rate in the effective theory , soft gluon exchange appears in two - loop diagrams . it will be seen that the bremsstrahlung production mechanism is precisely given by these diagrams when the exchanged gluon is space - like . the evaluation of these diagrams is discussed below . these contributions are clearly not included in the effective one - loop diagram . this is obvious when looking at the corresponding physical processes and it manifests itself in the result by the calculated rate being proportional to the square of the thermal gluon mass @xmath7 , in contrast to the one - loop result where only the thermal quark mass appears @xcite . another important contribution of the two - loop diagrams is associated with time - like gluon exchanges : physically this represents qcd compton scattering and quark - antiquark annihilation to produce a gluon and a photon . to evaluate this properly requires care since the two - loop diagrams with a hard time - like gluon exchanged are already part of the one - loop diagram with effective propagators and vertices . taking into account the contribution of the appropriate counterterms in the effective lagrangian will prevent double - counting and allow the correct evaluation of the soft , time - like , gluon contribution . the case of soft real photon production follows essentially the same pattern , except for the crucial fact that , the external line in the vacuum polarization diagram being massless , collinear divergences appear when evaluating the two - loop diagrams : the quasi - overlap of two such divergences , associated with the fermion propagators , leads to an enhancement factor of @xmath8 @xcite . the paradoxical result then follows that the one - loop contribution is relatively suppressed by a factor @xmath9 compared to the two - loop one ! the latter is entirely dominated by the bremsstrahlung process since the kinematical constraints require the gluon to be space like for the enhancement factor to occur . the compton and annihilation mechanisms are sub - dominant . the case of a hard real photon , of momentum of @xmath10 , shares features with both cases above . the one - loop approximation has a logarithmic sensitivity to the hard fermion momentum in the loop @xcite . the two - loop bremsstrahlung has a @xmath11 collinear enhancement , as in the real soft photon case , which however is compensated by a factor @xmath12 , where @xmath13 is the photon momentum , leaving the bremsstrahlung contribution at the same order in @xmath2 as the one - loop contribution . in the following we are concerned mainly with the bremsstrahlung part of the two - loop diagrams , and leave the discussion of the compton and annihilation processes and their interplay with the counterterms of the effective theory to future work . we do not discuss the production of soft real photons since this has already been studied in detail in @xcite . in the next section we derive the general expression for the ( real or virtual ) photon production rate at the two loop level . then we consider the case of soft virtual photons produced at rest in the plasma and derive the leading behavior analytically . we compare to the one - loop results and show that the bremsstrahlung contribution is numerically dominant although both contributions are technically of the same order in @xmath3 . the semi - classical approach is then discussed and it is shown that even though the approximations inherent in the semi - classical approach are not really justified in the case of soft photon production in a quark - gluon plasma , it leads to a result quite comparable to that obtained in thermal field theory . turning to the case of hard real photons , it is shown that the bremsstrahlung mechanism is of the same order as the already calculated one - loop result . carrying out a more detailed comparison with the latter approach , it is found that the bremsstrahlung process dominates over the one - loop result for photon momentum of @xmath10 but is relatively suppressed by a logarithmic factor for hard enough photons . for very hard energies , we find that the photon production is in fact dominated by a new process consisting of a @xmath14 annihilation where the quark or antiquark undergoes a scattering in the medium . we summarize all the thermal field theory results concerning real and virtual photon production in a concluding section . the role of counterterms in the application of the effective theory up to two - loops is discussed in a first appendix where the problem is also illustrated in a simple example . in a second appendix , the importance of phase space factors in thermal calculations is emphasized and the difference with the zero temperature phase space is made clear .

in this paper , we extend the study of bremsstrahlung photon production in a quark - gluon plasma to the cases of soft static photons and hard real photons . the rate of real or virtual photon production in the plasma is appreciably increased compared to the one - loop predictions . 1 physics department and winnipeg institute for theoretical physics , + university of winnipeg , winnipeg , manitoba r3b 2e9 , canada lapth678/98 , win98 - 05 , hep - ph/9804224

in this paper , we extend the study of bremsstrahlung photon production in a quark - gluon plasma to the cases of soft static photons and hard real photons . the general framework of this study is the effective perturbative expansion based on the resummation of hard thermal loops . despite the fact that bremsstrahlung only comes at two loops , we find that in both cases it generates contributions of the same order of magnitude as those already calculated by several other groups at one loop . furthermore , a new process contained in the two - loop diagrams dominate the emission of a very hard real photon . in all cases , the rate of real or virtual photon production in the plasma is appreciably increased compared to the one - loop predictions . 1 . laboratoire de physique thorique lapth , + bp110 , f-74941 , annecy le vieux cedex , france 2 . physics department and winnipeg institute for theoretical physics , + university of winnipeg , winnipeg , manitoba r3b 2e9 , canada lapth678/98 , win98 - 05 , hep - ph/9804224

0902.0552

i

the rapid development and wide application of computer techniques permits to collect and store a huge amount data , where the number of measured variables is usually large . such high dimensional data occur in many modern scientific fields , such as micro - array data in biology , stock market analysis in finance and wireless communication networks . traditional estimation or test tools are no more valid , or perform badly for such high - dimensional data , since they typically assume a large sample size @xmath2 with respect to the number of variables @xmath0 . a better approach in this high - dimensional data setting would be based on asymptotic theory which has both @xmath2 and @xmath0 approaching infinity . to illustrate this purpose , let us mention the case of hotelling s @xmath3-test . the failure of @xmath3-test for high - dimensional data has been mentioned as early as by @xcite . as a remedy , dempster proposed a so - called non - exact test . however , the theoretical justification of dempster s test arises much later in @xcite inspired by modern random matrix theory ( rmt ) . these authors have found necessary correction for the @xmath3-test to compensate effects due to high dimension . in this paper , we consider two lr tests concerning covariance matrices . we first give a theoretical explanation for the fail of these tests in high - dimensional data context . next , with the aid of random matrix theory , we provide necessary corrections to these lr tests to cope with the high dimensional effects . first , we consider the problem of one - sample covariance hypothesis test . suppose that @xmath4 follows a @xmath0-dimensional gaussian distribution @xmath5 and we want to test @xmath6 where @xmath7 denotes the @xmath0-dimensional identity matrix . note that testing @xmath8 with an arbitrary covariance matrix @xmath9 can always be reduced to the above null hypothesis by the transformation @xmath10 . let @xmath11 be a sample from @xmath4 , where we assume @xmath12 . the sample covariance matrix is @xmath13 and set @xmath14 the likelihood ratio test statistic is @xmath15 keeping @xmath0 fixed while letting @xmath16 , then the classical theory depicts that @xmath17 converges to the @xmath18 distribution under @xmath19 . however , as it will be shown , this classical approximation leads to a test size much higher than the nominal test level in the case of high - dimensional data , because @xmath17 approaches infinity for large @xmath0 . as seen from table 1 in [ sec : test1 ] , for dimension and sample sizes @xmath20 , the realized size of the test is 22.5% instead of the nominal 5% level . the result is even worse for the case @xmath21 , with a 100% test size . based on a recent clt for linear spectral statistics ( lss ) of large - dimensional sample covariance matrices @xcite , we construct a corrected version of @xmath17 in [ sec : test1 ] . as shown by the simulation results of [ sec : simul1 ] , the corrected test performs much better in case of high dimensions . moreover , it also performs correctly for moderate dimensions like @xmath22 or 20 . for dimension and sample sizes @xmath23 cited above , the sizes of the corrected test are 5.9% and 5.2% , respectively , both close to the 5% nominal level . the second test problem we consider is about the equality between two high - dimensional covariance matrices . let @xmath24 and @xmath25 @xmath26 be observations from two @xmath0-dimensional normal populations @xmath27 , respectively . we wish to test the null hypothesis @xmath28 the related sample covariance matrices are @xmath29 where @xmath30 , @xmath31 are the respective sample means . let @xmath32 where @xmath33 and @xmath34 denote @xmath35 the likelihood ratio test statistic is @xmath36 and when @xmath37 , we get @xmath38 under @xmath39 . of cause , in this limit scheme , the data dimension @xmath0 is held fixed . however , employing this @xmath1 limit distribution for dimensions like 30 or 40 , increases dramatically the size of the test . for instance , simulations in [ sec : simul2 ] show that , for dimension and sample sizes @xmath40 , the test size equals 21.2% instead of the nominal 5% level . the result is worse for the case of @xmath41 , leading to a 49.5% test size . the reason for this fail of classical lr test is the following . modern rmt indicates that when both dimension and sample size are large , the likelihood ratio statistic @xmath42 drifts to infinity almost surely . therefore , the classical @xmath1 approximation leads to many false rejections of @xmath19 in case of high - dimensional data . based on recent clt for linear spectral statistics of @xmath43-matrices from rmt , we propose a correction to this lr test in [ sec : test2 ] . although this corrected test is constructed under the asymptotic scheme @xmath44 , @xmath45 , @xmath46 , simulations demonstrate an overall correct behavior including small or moderate dimensions @xmath0 . for example , for the above cited dimension and sample sizes @xmath47 , the sizes of the corrected test equal 5.6% and 5.2% , respectively , both close to the nominal 5% level . related works include @xcite , @xcite and @xcite . these authors propose several procedures in the high - dimensional setting for testing that i ) a covariance matrix is an identity matrix , proportional to an identity matrix ( spherecity ) and is a diagonal matrix or ii ) several covariance matrices are equal . these procedures have the following common feature : their construction involves some well - chosen distance function between the null and the alternative hypotheses and rely on the first two spectral moments , namely the statistics tr@xmath48 and tr@xmath49 from sample covariance matrices @xmath48 . therefore , the procedures proposed by these authors are different from the likelihood - based procedures we consider here . another important difference concerns the gaussian assumption on the random variables used in all these references . actually , for testing the equality between two covariance matrices , the correction proposed in this paper applies equally for non - gaussian and high - dimensional data leading to a valid pseudo - likelihood test . the rest of the paper is organized as following . preliminary and useful rmt results are recalled in [ sec : useful ] . in [ sec : test1 ] and [ sec : test2 ] , we introduce our results for the two tests above . proofs and technical derivations are postponed to the last section .

in this paper , we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from gaussian populations when the dimension is large compared to the sample size . next , using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random f - matrices , we propose necessary corrections for these lr tests to cope with high - dimensional effects . simulations demonstrate that the corrected lr tests yield a realized size close to nominal level for both moderate ( around 20 ) and high dimension , while the traditional lr tests with approximation fails . another contribution from the paper is that for testing the equality between two covariance matrices , the proposed correction applies equally for non - gaussian populations yielding a valid pseudo - likelihood ratio test .

in this paper , we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from gaussian populations when the dimension is large compared to the sample size . next , using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random f - matrices , we propose necessary corrections for these lr tests to cope with high - dimensional effects . the asymptotic distributions of these corrected tests under the null are given . simulations demonstrate that the corrected lr tests yield a realized size close to nominal level for both moderate ( around 20 ) and high dimension , while the traditional lr tests with approximation fails . another contribution from the paper is that for testing the equality between two covariance matrices , the proposed correction applies equally for non - gaussian populations yielding a valid pseudo - likelihood ratio test .

1512.08906

c

in this paper , we investigated thermal fluctuations of the granular gas driven by gaussian thermostat on the basis of the two - point kinetic theory . in particular , we considered the inelastic variable hard sphere ( ivhs ) as the component of the granular gas . spherically symmetric moment @xmath25 , which is calculated using the dsmc method , is more similar to @xmath25 , which is analytically obtained by neglecting @xmath26 in the collisional term of @xmath25 , than @xmath25 , which is analytically obtained by including @xmath26 in the collisional term of @xmath25 in cases of the ihs and ivhs with @xmath7 . @xmath26 , which is calculated using the dsmc method , is similar to @xmath26 , which is analytically obtained , in the range of @xmath73 in the case of the ihs and in the range of @xmath75 in the case of ivhs with @xmath7 , whereas @xmath26 , which is analytically obtained for the ims , diverges at @xmath231 . correlations of thermal fluctuations of the pressure deviator and two times of the heat flux at the same time were evaluated using two parameters @xmath183 and @xmath184 . @xmath183 , which is calculated using the dsmc method , is similar to @xmath183 in eq . ( 44 ) in the range of @xmath67 in cases of the ihs and ivhs , whereas @xmath183 , which is calculated using the dsmc method , is similar to @xmath183 in eq . ( 44 ) in the range of @xmath76 in the case of the ims . meanwhile , @xmath184 in eq . ( 45 ) is similar to @xmath184 , which is calculated using the dsmc method , in the range of @xmath67 in the case of the ihs and in the range of @xmath73 in cases of the ivhs with @xmath7 and ims . the use of @xmath232 and @xmath233 in eqs . ( 44 ) and ( 45 ) improved similarities between @xmath183 , which is calculated using the dsmc method , and @xmath183 in eq . ( 44 ) with @xmath25 in eq . ( 6 ) or @xmath184 , which is calculated using the dsmc method , and @xmath184 in eq . ( 45 ) with @xmath25 and @xmath26 in eqs . ( 6 ) and ( 7 ) . time correlations of thermal fluctuations of the pressure deviator and two times of the heat flux were evaluated using two parameters , namely , @xmath198 and @xmath199 . @xmath198 , which is calculated using the dsmc method , is similar to @xmath198 in eq . ( 46 ) in cases of the ihs , ivhs with @xmath7 and ims . @xmath199 , which is calculated using the dsmc method , is slightly smaller than @xmath199 in eq . ( 47 ) , when @xmath194 for the ihs and ivhs with @xmath7 or @xmath194 and @xmath196 for the ims . the viscosity coefficient , which is calculated using the dsmc method , is quite similar to the viscosity coefficient , which is analytically obtained by the kinetic theory , in cases of the ihs , ivhs with @xmath7 and ims . the thermal conductivity , which is calculated using the dsmc method , does not fit the thermal conductivity , which is obtained by the kinetic theory , in ranges of @xmath70 and @xmath223 in the case of the ihs . the thermal conductivity , which is calculated using the dsmc method , does not fit the thermal conductivity , which is obtained by the kinetic theory , in the range of @xmath3 in cases of the ivhs with @xmath7 and ims . the diffusive thermal conductivity , which is calculated using the dsmc method , is similar to the diffusive thermal conductivity , which is obtained by the kinetic theory , in the range of @xmath74 in cases of the ihs , ivhs with @xmath7 and ims . finally , differences between the thermal conductivity and diffusive thermal conductivity at @xmath194 , which are calculated using the dsmc method and those obtained by the kinetic theory , increases , as @xmath8 decreases .

in this paper , we investigate thermal fluctuations of the granular gas , which is driven by gaussian thermostat , on the basis of two - point kinetic theory . in particular , we consider thermal fluctuations of the inelastic variable sphere , which was proposed by yano [ j. phys .

in this paper , we investigate thermal fluctuations of the granular gas , which is driven by gaussian thermostat , on the basis of two - point kinetic theory . in particular , we consider thermal fluctuations of the inelastic variable sphere , which was proposed by yano [ j. phys . a , 46 ( 37 ) , 375502 ( 2013 ) ] . time correlations of thermal fluctuations of the pressure deviator and two times of the heat flux are calculated on the basis of the two - point kinetic theory and compared with their numerical results , which are calculated using the direct simulation monte carlo ( dsmc ) method . finally , we compare transport coefficients , which are calculated on the basis of the kinetic theory , with those calculated using the dsmc method .

1610.03288

i

let @xmath1 be a compact , connected surface , and let @xmath7 be a finite ( possibly empty ) subset of @xmath1 of cardinality @xmath8 . let @xmath9 denote the group of homeomorphisms of @xmath1 for the operation of composition that leave @xmath10 invariant . if @xmath1 is orientable , let @xmath11 denote the set of elements of @xmath9 that preserve orientation . note that @xmath11 is a subgroup of @xmath9 of index two . we define the _ mapping class group @xmath12 of @xmath1 relative to @xmath10 _ by : @xmath13 if @xmath1 is orientable ( resp . non orientable ) , the group @xmath12 is thus the set of isotopy classes of @xmath11 ( resp . @xmath9 ) , the isotopies being relative to the set @xmath10 . if @xmath14 ( resp . @xmath9 ) then we let @xmath15 $ ] denote its mapping class in @xmath12 . up to isomorphism , @xmath12 only depends on the cardinality @xmath3 of the subset @xmath10 , and we shall often denote this group by @xmath16 . if @xmath10 is empty , then we omit it from the notation , and shall just write @xmath17 , @xmath18 , @xmath19 etc . the mapping class group may also be defined in other categories ( pl category , smooth category ) , the groups obtained being isomorphic @xcite . the mapping class group has been widely studied from different points of view see @xcite for example . if @xmath20 , there is a surjective homomorphism @xmath21 defined by @xmath22 for all @xmath23 and @xmath24 , where @xmath25 is the symmetric group on @xmath3 letters . this homomorphism induces a surjective homomorphism from @xmath12 to @xmath25 that we also denote by @xmath26 , and its kernel is called the _ pure mapping class group of @xmath1 relative to @xmath10 _ , denoted by @xmath27 . so we have a short exact sequence : @xmath28 and if @xmath23 then @xmath15\in pmcg(s;x)$ ] if and only if @xmath29 fixes @xmath10 pointwise . mapping class groups are closely related to surface braid groups . if @xmath20 , the _ @xmath3^th^ ordered configuration space _ @xmath30 of @xmath1 is the set of all ordered @xmath3-tuples of distinct points of @xmath1 that we may consider as a subspace of the @xmath3-fold product of @xmath1 with itself . the group @xmath31 acts freely on @xmath30 by permuting coordinates , and the associated quotient is the _ @xmath3^th^ unordered configuration space _ of @xmath1 , denoted by @xmath32 . the fundamental group @xmath33 ( resp . @xmath34 ) , denoted by @xmath35 ( resp . @xmath36 ) is the _ braid group _ . _ pure braid group _ ) of @xmath1 on @xmath3 strings @xcite , and @xmath35 and @xmath36 are related by a short exact sequence similar to that of ( [ eq : sigmamcg ] ) . it is well known that @xmath37 ( resp . @xmath38 ) is isomorphic to _ artin s braid group _ _ artin s pure braid group _ ) on @xmath3 strings . if @xmath39 is a @xmath40-fold covering map , where @xmath41 , then for all @xmath42 , there is a continuous map : @xmath43 defined by @xmath44 for all @xmath45 , and the induced homomorphism @xmath46 on the level of fundamental groups is injective @xcite . taking @xmath47 to be the standard @xmath6-fold ( universal ) covering , where @xmath48 is the @xmath6-sphere and @xmath49 is the real projective plane , this result was then applied in @xcite to classify the isomorphism classes of the finite subgroups of @xmath50 , and to show that @xmath50 and @xmath51 are linear groups for all @xmath20 . if @xmath52 ( resp . @xmath53 ) , let @xmath54 ( resp . @xmath55 ) be a compact , connected orientable ( resp . non - orientable ) surface of genus @xmath56 without boundary . in the non - orientable case , @xmath56 is the number of projective planes in a connected sum decomposition . if @xmath53 and @xmath8 , the orientable double covering @xmath57 induces a homomorphism @xmath58 , where the @xmath5-point subset of marked points in @xmath1 is equal to the inverse image by @xmath59 of a @xmath3-point subset of @xmath0 . one of the main aims of this paper is to generalise the injectivity result of @xcite to this homomorphism . if @xmath60 and @xmath61 , it was shown in @xcite that there exists an injective homomorphism @xmath62 , and that via @xmath63 , @xmath64 may be identified with the subgroup of @xmath65 that consists of isotopy classes of symmetric homeomorphisms . in section [ sec : embeddings ] , we show that a similar result holds for all @xmath8 , namely that the homomorphism @xmath66 induced by @xmath59 is injective , and that via @xmath66 , @xmath67 may be identified with the subgroup of @xmath68 that consists of isotopy classes of symmetric homeomorphisms . [ th : braidmcg ] let @xmath69 , let @xmath55 be a compact , connected , non - orientable surface of genus @xmath56 without boundary , and let @xmath1 be its orientable double covering . then the homomorphism @xmath70 induced by the covering @xmath71 is injective . further , if @xmath61 then we have a commutative diagram of the following form : @xmath72{d}{\varphi_{k\ # } } & mcg(n;k)\arrow{r}{\tau_{k}}\arrow[hook]{d}{\phi_k } & mcg(n)\arrow[hook]{d}{\phi } \arrow{r } & 1\\ 1\arrow{r } & b_{2k}(s)\arrow{r } & mcg(s;2k ) \arrow{r}{{\widetilde{\tau}}_{k } } & mcg(s ) \arrow{r } & 1 , \end{tikzcd}\ ] ] where @xmath73 and @xmath74 are the homomorphisms induced by forgetting the markings on the sets of marked points . note that in contrast with @xcite , theorem [ th : braidmcg ] holds for all @xmath53 , not just for @xmath61 . as we recall in remark [ rem : notinjective ] , the result of @xcite does not hold if @xmath75 . the proof of this exceptional case @xmath75 in theorem [ th : braidmcg ] will turn out to be the most difficult , in part due to the non injectivity of @xmath76 . in section [ sec : vcd ] , we compute the cohomological dimension of the braid groups of all compact surfaces without boundary different from @xmath48 and @xmath49 , and we give an upper bound for the virtual cohomological dimension of the mapping class group @xmath77 for all @xmath78 and @xmath42 . recall that the _ virtual cohomological dimension _ @xmath79 of a group @xmath80 is a generalisation of the cohomological dimension @xmath81 of @xmath80 , and is defined to be the cohomological dimension of any torsion - free finite index subgroup of @xmath80 @xcite . in particular , if @xmath80 is a braid or mapping class group of finite ( virtual ) cohomological dimension then the corresponding pure braid or mapping class group has the same ( virtual ) cohomological dimension . in ( * theorem 5 ) , it was shown that if @xmath82 ( resp . @xmath83 ) then @xmath84 ( resp . @xmath85 ) . these results are generalised in the following theorem , the proof being a little more straightforward due to the fact that the braid groups of @xmath86 and @xmath87 are torsion free if @xmath53 . [ th : cdbraid ] let @xmath88 . then : @xmath89 we then turn our attention to the mapping class groups . if @xmath90 , j. harer proved that ( * ? ? ? * theorem 4.1 ) : @xmath91 using the embedding of @xmath92 in @xmath65 given in @xcite , g. hope and u. tillmann showed that if @xmath61 then @xmath93 ( * ? ? ? * corollary 2.2 ) . using ( * ? ? ? * theorem 5 ) , it was shown in ( * ? ? ? * corollary 6 ) that if @xmath82 ( resp . @xmath83 ) then @xmath94 ( resp . @xmath95 ) . in the case of @xmath48 , we thus recover the results of harer . in the second part of section [ sec : vcd ] , we generalise some of these results to non - orientable surfaces with marked points . [ prop : vcdmap ] let @xmath96 . the mapping class groups @xmath97 and @xmath98 have the same ( finite ) virtual cohomological dimension . further : a. @xmath99 . b. if @xmath61 then @xmath100 . this paper is organised as follows . in section [ sec : odc ] , we recall some definitions and results about orientation - true mappings and the orientable double covering of non - orientable surfaces , we describe how we lift an element of @xmath101 to one of @xmath18 in a continuous manner , and we show how this correspondence induces a homomorphism from the mapping class group of a non - orientable surface to that of its orientable double covering ( proposition [ prop : hopetillmann ] ) . in section [ sec : embeddings ] , we prove theorem [ th : braidmcg ] using long exact sequences of fibrations involving the groups that appear in equation ( [ eq : mcgtop ] ) and the corresponding braid groups @xcite . in most cases , using @xcite , we obtain commutative diagrams of short exact sequences , and the conclusion is obtained in a straightforward manner . the situation is however much more complicated in the case where @xmath0 is the klein bottle and @xmath1 is the @xmath6-torus @xmath102 , due partly to the fact that the exact sequences that appear in the associated commutative diagrams are no longer short exact . this case requires a detailed analysis , notably in the case @xmath103 . in section [ sec : vcd ] , we prove theorem [ th : cdbraid ] and proposition [ prop : vcdmap ] . finally , in an appendix , we provide presentations of @xmath104 and @xmath105 that we use in the proof of theorem [ th : braidmcg ] . the first - named author was partially supported by fapesp - fundao de amparo a pesquisa do estado de so paulo , projeto temtico topologia algbrica , geomtrica 2012/24454 - 8 . he and the second - named author would like to thank the ` rseau franco - brsilien en mathmatiques ' for financial support for their respective visits to the laboratoire de mathmatiques nicolas oresme umr cnrs 6139 , universit de caen normandie , from the 2^nd^ to the 15^th^ of september 2016 , and to the instituto de matemtica e estatstica , universidade de so paulo , from the 9^th^ of july to the 1^st^ of august 2016 . the third - named author was supported by the consejo nacional de ciencia y tecnologa to visit the laboratoire de mathmatiques nicolas oresme umr cnrs 6139 , universit de caen normandie , from the 1^st^ of february 2014 to the 31^st^ of january 2015 . during that period , he was also partially supported by the laboratorio internacional solomon lefschetz ( laisla ) .

in this paper , we make use of the relations between the braid and mapping class groups of a compact , connected , non - orientable surface without boundary and those of its orientable double covering to study embeddings of these groups and their ( virtual ) cohomological dimensions . we first generalise results of to show that the mapping class group of relative to a-point subset embeds in the mapping class group of relative to a-point subset . we then compute the cohomological dimension of the braid groups of all compact , connected aspherical surfaces without boundary , which generalises results of . finally , if the genus of is greater than or equal to , we give upper bounds for the virtual cohomological dimension of . [ multiblock footnote omitted ] [ multiblock footnote omitted ] [ multiblock footnote omitted ]

in this paper , we make use of the relations between the braid and mapping class groups of a compact , connected , non - orientable surface without boundary and those of its orientable double covering to study embeddings of these groups and their ( virtual ) cohomological dimensions . we first generalise results of to show that the mapping class group of relative to a-point subset embeds in the mapping class group of relative to a-point subset . we then compute the cohomological dimension of the braid groups of all compact , connected aspherical surfaces without boundary , which generalises results of . finally , if the genus of is greater than or equal to , we give upper bounds for the virtual cohomological dimension of . [ multiblock footnote omitted ] [ multiblock footnote omitted ] [ multiblock footnote omitted ]

1212.5159

r

the total gas mass and stellar mass in our bcd sample both range from @xmath252 to @xmath253 @xmath254 . figure 2 shows the distribution of total gas mass as a function of stellar mass for e - type and i - type bcds . the solid line is a reference line for the case when the two qualities are the same . we find that , almost all i - type bcds lie above the @xmath255 line , whereas more than half of the e - type bcds just below this line , indicating that i - type bcds tend to have larger gas masses than e - type bcds at a given stellar mass . for i - type bcds , except for the apparent merging system , mrk 108 , whose gas content is extraordinarily high , the gas mass well correlates with the stellar mass , namely galaxies with a larger stellar mass also contains higher gas masses . the e - type bcds seem to have a similar @xmath256 relation when @xmath257 @xmath254 . while at the high - mass end ( @xmath258 ) , galaxies tend to have lower gas contents comparing to the lower mass counterparts . as a comparison , in figure 2 we also plot the data for field dis which are adopted from lee el al . ( 2003 ) . in this plot , field dis seem to distribute similarly to bcds as a whole , but the @xmath256 relation of field dis has a smaller dispersion than that of bcds . ratio , and the cross in the bottom right gives the typical error bar of the bcd sample.,scaledwidth=48.0% ] since we are interested in the potential for connections / differences between different types of dwarfs , it is informative to consider the gas fraction of a galaxy . in figure 3 we plot the number distribution of gas fraction , @xmath259 , in e- and i - type bcds , and field dis . as mentioned above , i - type bcds are generally more gas - rich than e - type bcds . the separation between these types of bcds is more striking in figure 3 . the @xmath260 for e - type bcds shows a wide distribution and ranges from @xmath261 to @xmath262 , and has a median value of @xmath263 . however , the distribution of @xmath260 for i - type bcds is much narrower , and looks similar to that for field dis . i - type bcds concentrate between @xmath264 ( 14 out of 17 ) , while relatively more field dis have @xmath265 . the median values of @xmath260 are @xmath266 and @xmath267 , for i - type bcds and field dis , respectively . to quantify the significance of the difference or similarity of the gas content among these different types of galaxies , we perform a nonparametric statistical test , the kolmogorov - smirnov ( k - s ) test . the k - s test for the i - type sample against the e - type sample rejects the null hypothesis ( that these two data sets can be derived from a same parent population ) at a @xmath268 significance level . on the other hand , the k - s tests give probabilities of @xmath269 , @xmath270 and @xmath271 , for the dis vs i- and e - type bcds , all bcds as a whole , data sets , respectively . therefore , we conclude that the gas fraction distributions of i- and e - type bcds are much different , whereas the gas fraction distributions of dis and bcds seem to be indistinguishable . nevertheless , we caution that such analysis is possibly limited by the small numbers of the samples . we show the gas fraction of different types of galaxies plotted against their stellar mass in figure 4 . at the low - mass end ( @xmath272 ) , in general , the gas mass is roughly independent on the stellar mass ( i.e. proportional to the baryonic mass ) . at higher masses , however , the relation exhibits a break and becomes considerably steeper since the gas has been more efficiently converted to stars in higher stellar mass galaxies . from figure 4 we can see that most bcds and field dis distributes similarly in the @xmath259-@xmath231 plot . however , at a given stellar mass , the gas fractions for e - type bcds have a larger span and a lower mean value than those for i - type bcds and field dis , which confirms that e - type bcds are generally more gas - poor . star - forming dwarf galaxies are observed to be well mixed chemically throughout their high surface brightness components ( kobulnicky & skillman 1996 , 1997 ) , having no significant gradients or inhomogeneities in oxygen abundances measured from hii regions located at different galactocentric radii ( e.g. lee & skillman 2004 ) . in figure 5 we show the metallicity distributions for e- and i - type bcds and dis . it seems that all of these different types of dwarfs show a double - peaked distribution of metallicity . however , e - type bcds have a larger median oxygen abundance ( @xmath273 ) than i - type bcds and dis ( both @xmath274 ) . in the following we explore the chemical evolution for bcds by investigating in detail the correlations between their oxygen abundance and gas mass , baryonic mass , and gas fraction . ) as a function of stellar mass for bcds and dis . the cross in the bottom right gives the typical error bar of the bcd sample . more massive systems have lower gas fractions.,scaledwidth=48.0% ] figure 6 shows the metallicity as a function of the total gas mass . albeit with large scatters , a galaxy with a greater gas mass is generally more abundant in metals . if we look into different types of galaxies , the scatter will reduce much . a unweighted least - squares linear fit , using a geometrical mean functional relationship ( isobe et al . 1990 ) , to the two bcd subsamples , gives , @xmath275 @xmath276 for e- and i - type bcds respectively . the fitted trends are shown as ( purple ) solid and ( blue ) dashed lines in figure 6 , and the rms deviations of the data from the relationships are 0.35 and 0.34 dex in ( o / h ) , for e- and i - type bcds , respectively . while for the di sample , we obtain the following @xmath277 relation @xmath278 with a rms scatter of 0.26 dex in ( o / h ) , and is shown with the ( red ) dot - dashed line in figure 6 . although the slopes of the @xmath279 relations for i- and e - type bcds are almost the same , and there are larger scatters in these relations , it is clear that e - type bcds have higher mean oxygen abundance than i - type ones at a given gas mass , suggesting that they are depleted in gas relative to i - type bcds of comparable metallicity . field dis have a shallower @xmath279 relation than bcds , but are mixed with bcds in the plot . combining this difference with the fact that i - type bcds are more gas - rich than e - type bcds ( see section 3.2 ) , it might indicate a possible difference in potential for the progenitors and/or evolutionary phases of e- and i - type bcds . figure 7 plots the oxygen abundance as a function of the total baryonic mass . for e - type bcds , unlike figure 6 , this figure shows a much better correlation between metallicity and baryonic mass . a geometric linear fit to the e - type sample ( 36 members ) gives the following relation @xmath280 with a rms scatter of 0.25 dex in ( o / h ) . the fitted relation is plotted with a solid line . , with the cross showing the typical error bar of the bcd sample . , scaledwidth=48.0% ] we also do the same fits to the i - type bcd and di samples , which give @xmath281 and @xmath282 with rms scatters of 0.31 dex and 0.22 dex in ( o / h ) , for the i - type bcds and dis , respectively . the dashed and dot - dashed lines superposed in figure 7 are the respective fitting results for i - type bcds and dis . these results show that the baryonic mass - metallicity relations for i- and e - type bcds have similar slopes , which are a bit steeper than that of field dis . however , e - type bcds appear to lie at a higher oxygen abundance comparing with i - type ones at a given baryonic mass , which again seems to suggest that e- and i - type bcds might be at different evolutionary phases and/or have different progenitors . in fact , bcds also have steeper _ l - z _ and mass - metallicity ( _ m - z _ ) relations than dis ( zgg10 ; zahid et al . kunth & stlin ( 2000 ) show that there exist offsets between the @xmath2 band _ l - z _ relations of bcds , dis and des / dsphs , in the sense that at a given @xmath2 luminosity it becomes relatively more metal - deficient following the des / dsphs , dis and bcds sequence . this offset persists even only comparing the metallicities of the old populations in dis and des / dsphs ( grebel et al . woo et al . ( 2008 ) find the same phenomenon in the _ m - z _ relations of dis and des / dsphs . in the current work , however , we find that dis distribute in between the two types of bcds in the baryonic - metallicity relation . therefore , the evolutionary connections , if exist , between des , dis , and bcds may be complicated . the relation between metallicity and gas fraction can be used to check different chemical evolution models . the closed - box model predicts a linear correlation between the logarithm of the inverse gas fraction @xmath283 and the oxygen abundance by number , @xmath284 , namely ( e.g. lee et al . 2003 ) @xmath285 where @xmath286 is the yield of oxygen and we have assumed that the fraction of gas in the form of hydrogen is @xmath287 ( solar value ) . a comparison of the observed oxygen abundances to those predicted by closed - box models ( thick solid line ) is shown in figure 8 , which indicates that few of the galaxies in these bcd and di samples agree with a closed - box chemical evolution . the vast majority of galaxies appear to have oxygen abundances less than that expected by closed - box models ( with a salpeter imf ) , which imply varying imf , and/or gas inflows / outflows in these galaxies . it is also interesting to find that i - type bcds and dis occupy a similar region in this plot , whereas e - type bcds extend to the most metal - rich and gas - poor region . this indicates that ( 1 ) these galaxies follow a similar chemical evolution path ( e.g. experiencing similar gas flows ) , but at different phase ( e.g. e - type bcds are more evolved than dis and i - type bcds ) ; or ( 2 ) e - type bcds experience different gas flows from dis and i - type bcds ( see below ) . the effects of inflows and/or outflows have been described by many authors ( e.g. , edmunds 1990 ; dalcanton 2007 ; erb 2008 ; matteucci 2008 ; spitoni et al . in particular , dalcanton ( 2007 ) shows that inflows are very efficient in reducing the effective yield , @xmath288 , for gas - poor galaxies while outflows are more effective in changing @xmath288 in gas - rich galaxies . erb ( 2008 ) and matteucci ( 2008 ) introduce a model in which galaxies have inflows / outflows proportional to the star formation rate ( sfr ) . this model adopts the instance recycling and mixing approximations , and the infalling gas is assumed to have no metal , while the enriched outflows is considered to have the same metallicity as the interstellar medium ( ism ) . in this model , we can change two free parameters , the amount of outflow @xmath289 and inflow @xmath290 in unit of the sfr of the galaxy , to reproduce the observed oxygen abundance . two more parameters can be varied , if necessary , i.e. , the true yield @xmath291 ( i.e. imf ) and the fraction @xmath292 of mass still locked in stars . in figure 8 we also plot the predicted metallicity - gas fraction relations from this model using different parameters . we adopt @xmath286 as 1 and @xmath293 of the true oxygen yield predicted by the closed - box model with a salpeter imf(@xmath294 ; meynet & maeder 2002 ) , and vary @xmath289 and @xmath290 to reproduce the dependence of oxygen abundance on the inverse gas fraction . the parameter @xmath292 is a slowly decreasing function of time , as more stars leave the main sequence , but can vary in quite a small range . it is expected to be @xmath295 at @xmath296 yr and @xmath297 at @xmath298 yr ( bruzual & charlot 2003 ) for sub - solar metallicity galaxies with a salpeter imf . given the age of these galaxies ( see , e.g. zgg11 ) , we have used @xmath299 , in despite of that the results are not very sensitive to the chosen value . for a salpeter imf , as shown in figure 8 , the pure inflow model ( black dotted lines ) with a variable rate can not explain the observed metallicity - gas fraction relation , ( especially for e - type bcds ) , which is consistent with the finding in spitoni et al . small inflow rate predicts a higher metallicity than the observed one , whereas high inflow rate can not reach the gas - poor region . pure outflow model ( thin solid lines ) or the combination of outflow and inflow models ( dashed and dot - dashed lines ) can reproduce the observed distribution , but the pure outflow model may need very high flow rate . the best solution could be a combination of gas flows and a variable imf . ; meynet & maeder 2002 ) . the thin solid ( dashed ) lines are pure outflow ( inflow ) models , with an effective yield 1 ( black ) and @xmath293 ( blue ) of the true yield . the rest ( noncontinuous ) lines show the results of applying the model in erb ( 2008 ) with values of @xmath289 , @xmath290 and @xmath286 in the labels . the labeled galaxy , mrk 108 , which is an apparent merging system , appears to be interpreted by none of these models.,scaledwidth=48.0% ]

the results of correlations among the oxygen abundance , stellar mass , gas mass , baryonic mass , and gas fraction are present both for e- and i - type bcds , which are classified according to loose & thuan ( 1985 ) and show elliptical and irregular outer haloes , respectively . , we suggest that e - type bcds , at least a part of them , and i - type ones might be likely at different evolutionary phases and/or having different progenitors . our investigation of the correlation between oxygen abundance and gas fraction shows that bcds appear to have not evolved as isolated systems , but to have experienced some gas flows and/or mergers .

in this paper , we report our studies on the gaseous and chemical properties of a relatively large sample ( 53 members ) of blue compact dwarf galaxies ( bcds ) . the results of correlations among the oxygen abundance , stellar mass , gas mass , baryonic mass , and gas fraction are present both for e- and i - type bcds , which are classified according to loose & thuan ( 1985 ) and show elliptical and irregular outer haloes , respectively . these correlations of i - type bcds show similar slopes to those of e - type ones . however , in general , e - type bcds are more gas - poor and metal - rich than i - type ones at a given baryonic mass . based on these results , we suggest that e - type bcds , at least a part of them , and i - type ones might be likely at different evolutionary phases and/or having different progenitors . our investigation of the correlation between oxygen abundance and gas fraction shows that bcds appear to have not evolved as isolated systems , but to have experienced some gas flows and/or mergers .

1212.5159

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in this section we will mainly discuss the possible evolutionary connections between bcds , des and dis . there have been several evolutionary scenarios , both from observational and theoretical aspects , between bcds , des , and dis ( see papaderos et al . 1996 for a review ) . however , the question of whether there is an evolutionary connection between these three types of dwarf galaxies have not been achieved a solid answer yet . as mentioned in section 1 , some apparently contrary results are present in previous studies on the basis of observational measurements . for the bcds in our sample , metallicity correlates with gas mass and total baryonic mass , in the sense that more massive systems are more abundant in metals . for these two correlations , i - type bcds show similar slopes to e - type ones . however , i - type bcds are generally more metal - poor and gas - rich than e - type ones at a given gas / baryonic mass . although field dis seem to have a shallower slope relative to bcds , they are well mixed with bcds in the distributions of @xmath279 and @xmath300 plots . moreover , in the plot of metallicity - gas fraction relation , i - type bcds generally occupy a region differing from e - type ones . our results may shed some light on the evolutionary connection between the three types of dwarf galaxies . i- and e - type bcds might be at different evolutionary phases and/or have different progenitors . for example , if some e - type bcds are formed from des ( e.g. silk et al . 1987 ) , whereas i - type ones are formed from dis , then this part of e - type bcds should be more evolved than i - type ones . this scenario is also supported by the fact that many e - type bcds show structural properties compatible with des ( papaderos et al . 1996 ; gil de paz & madore 2005 ) . in addition , field dis show chemical and gaseous properties in between i- and e - type bcds , which suggests that they could be connected to both types of bcds ( e.g. thuan 1985 ; davies & phillipps 1988 ) . as discussed in papaderos et al . ( 1996 ) , the interchanges between dis , bcds and des need gas outflows / inflows to get involved , which is very consistent with our result that most bcds should have experienced gas flows during their lives . indeed , observations have provided ( direct ) evidence for gas flows in bcds ( e.g. , papaderos et al . 1994 ; martin 1996 , 1999 ; martin et al . 2001 ; elson et al . 2009 ; van eymeren et al . 2009 ; lpez - schez et al . 2010 ) . using x - ray data , papaderos et al . ( 1994 ) estimate a galactic wind flowing at a velocity of @xmath301 km s@xmath218 for the bcd vii zw 403 , whereas the estimated escape velocity for this galaxy is only 50 km s@xmath218 . martin et al . ( 2001 ) have shown that the galactic wind in ngc 1569 carries away almost all the oxygen produced in the current starburst . more recently , elson et al . ( 2009 ) present their hi observations for ngc 2915 , and find a gas component clearly lagging in velocity relative to the main gas disk of the galaxy . this might be evidence for gas accretion from inter - galactic space onto the outer galaxy disk . van eymeren et al . ( 2009 ) report their detailed kinematic studies on the neutral ( hi ) and ionized ( h@xmath292 ) gas components in a nearby bcd , ngc 4861 . the authors find that both in hi and h@xmath292 the galaxy shows several outflows . using multi - wavelength data , another work by this group ( lpez - schez et al . 2010 ) have studied the environment of a sample of nearby bcds , and shown that all bcds present evident interacting features in their hi component despite the environment in which they reside . in particular , ic 4870 , which has an elliptical outer component , is accreting hi clouds .

these correlations of i - type bcds show similar slopes to those of e - type ones . however , in general , e - type bcds are more gas - poor and metal - rich than i - type ones at a given baryonic mass . based on these results

in this paper , we report our studies on the gaseous and chemical properties of a relatively large sample ( 53 members ) of blue compact dwarf galaxies ( bcds ) . the results of correlations among the oxygen abundance , stellar mass , gas mass , baryonic mass , and gas fraction are present both for e- and i - type bcds , which are classified according to loose & thuan ( 1985 ) and show elliptical and irregular outer haloes , respectively . these correlations of i - type bcds show similar slopes to those of e - type ones . however , in general , e - type bcds are more gas - poor and metal - rich than i - type ones at a given baryonic mass . based on these results , we suggest that e - type bcds , at least a part of them , and i - type ones might be likely at different evolutionary phases and/or having different progenitors . our investigation of the correlation between oxygen abundance and gas fraction shows that bcds appear to have not evolved as isolated systems , but to have experienced some gas flows and/or mergers .

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several applications where wireless body area networks ( wban ) are deployed around the human body , reliable and low delay communication is of paramount importance because of the critical nature of the collected data ( e.g. heart rate , blood pressure ) . energy consumption is also key for the prolonged operation of the devices attached to the human body . for their communication needs these wbans usually employ radio frequency ( rf ) technologies that operate in the industrial , scientific and medical ( ism ) radio band . one of the dominant solutions is the ieee 802.15.4 standard that is engineered specifically for low power devices @xcite . however , it is also possible to use the widely popular wireless lan ( wlan ) standard ieee 802.11 @xcite because of the readily available access point ( ap ) infrastructure . regardless of the specific wireless communication technology , when multiple sensors are deployed in the human body , a wban in a star topology is usually created so that all the on - body nodes communicate with a gateway for forwarding the collected data . [ fig : dual - rf - bcc - principle ] ( left ) depicts the organization of a wban in a star topology that is employed by practical systems @xcite . although rf is the only practical mechanism to forward data in this scenario , still several significant problems remain . rf signals suffer considerably from body shadowing in a highly variable way with respect to human body @xcite . this makes communication between on - body nodes , and also off - body , very unreliable . this inherent unreliability of rf communication around the human body is a critical problem for several real - life applications . we discuss two emerging application scenarios here to motivate our system design . one example is vital sign monitoring where multiple nodes need to be deployed in several different places of the human body @xcite . traffic is usually flowing in the uplink direction , i.e. from the wban nodes to the gateway . consider for example a human that has a node on the torso and one on the wrist for monitoring the heart rate . if this human is a patient lying in bed , then the rf link of the sensor on the torso might be completely blocked . however , it is possible that the node on the wrist can communicate perfectly with the gateway . or it can happen the other way around as fig . [ fig : dual - rf - bcc - principle](a ) indicates . since humans usually move frequently , any sensor can be potentially blocked and the data may not be communicated on - time to the gateway ( or it can be lost completely ) . besides health monitoring , the other important application is real - time media entertainment . with the rising popularity of wearable devices , it is even possible that high data rate video streams need to be forwarded from the human body ( uplink ) . one specific application example with downlink traffic , is audio streaming from a wifi access point ( ap ) to on - body earphones without wires @xcite . in these two examples rf connectivity between the ap and the earphones / glasses might be unreliable leading to problems in the audio / video transmission . therefore , the optimal node on the body must be found and act as a relay in order to transmit the data to and from the wifi ap . this node can be for example a smartphone . to address the problems identified in the aforementioned scenarios , in this paper we propose a novel wban architecture , a network layer ( nwk ) protocol that exploits the proposed architecture , and an optimization framework supported by an analytical performance model of the system . in our architecture that is depicted in fig . [ fig : dual - rf - bcc - principle](b ) , all the wban nodes on the human body are equipped with both rf and body - coupled communication ( bcc ) transceivers . when the rf link of a node is unreliable the node uses the bcc link for forwarding its data through the human body to a node with a better rf link . the rationale of this design choice is based on the extremely power - efficient bcc technology that can be used instead of rf communication . prototype bcc transceivers use simple baseband communication and have a very small form factor ( 1mm@xmath0 dye in @xcite ) . thus , the proposed wban architecture with two transceivers on board a wban node is an economically and technically viable option for real - life applications . * contributions . * the contributions of this paper are : * first , we propose a new cooperative wban architecture that employs two communication technologies namely bcc and rf . this architecture is orchestrated by a novel nwk relay selection protocol that identifies the optimal relay for forwarding the data off the body . the proposed scheme is unlike any existing relay selection protocols since two different communication technologies are used . * second , for each medium access control ( mac ) protocol of the rf and bcc subnetworks we develop accurate expressions of the delay and energy consumption as a function of specific protocol parameters . our novel contributions here include first the performance modeling of a nwk that concurrently uses two wireless mac / phy technologies . second , our model is a cross - technology model , i.e. it quantifies the impact of a specific parameter setting for one mac on the second and on the complete system . * third , we propose the use of the analytical performance models for further optimization of the duty cycling of the bcc transceivers and the retransmission strategy of the rf transceivers so that energy consumption and delay are minimized . * benefits . * the _ first _ advantage is that devices with a blocked rf link can use the services of the remaining nodes for forwarding their data to a gateway and improve thus the reliability of the data delivery . this idea is demonstrated with the help of fig . [ fig : dual - rf - bcc - principle](b ) while we have also outlined this generic architecture in @xcite . this is accomplished with c1 . _ second _ , rf transmissions are reduced to the absolute minimum since wban nodes do not communicate with each other through the rf link . the benefit is that the rf link is carrying a reduced load and the interference to surrounding rf devices is also minimized @xcite . this is accomplished with c1 . third _ advantage is that a node with an rf link that is not completely blocked , but operates inefficiently ( higher number of required retransmissions that increase delay and energy consumption ) , can communicate with other nodes through bcc and select another node for data forwarding . this is accomplished with c2 and c3 . our performance evaluation focuses on highlighting these benefits . performance is evaluated both through simulations and also through the use of real rf traces . results with ieee 802.15.4 rf traces interestingly support even more the need for our system in real scenarios due to the severity of human body shadowing . * paper organization . * the rest of this paper is organized as follows . related work is presented in section [ section : related - works ] . in section [ section : system - architecture ] we provide an overview of the system architecture and in section [ section : relay - selection ] we delve into the details of the relay selection and packet forwarding algorithm . section [ section : modeling - approach ] presents the motivation and an overview of our performance modeling approach . in section [ section : rf - radio - model ] we present the performance model of the rf network while in section [ section : bcc - model ] we present the analytical model of the bcc network . the mac protocol optimization that further exploits the previous analysis is described in section [ section : optimization ] . the performance of our system is evaluated with simulations and real measurements in section [ section : experiments ] . finally , in section [ section : conclusions ] we conclude this paper .

one network is formed between on - body nodes , and is realized with capacitive body - coupled communication ( bcc ) , while an ieee 802.15.4 radio frequency ( rf ) network is used for forwarding data to the gateway . wban nodes that have blocked rf links due to body shadowing forward their data through the bcc link to a node that acts as a relay and has an active rf connection . for this architecture we design a network layer protocol that manages the two communication technologies and is responsible for relay selection and data forwarding .

in this paper we are concerned with the problem of data forwarding from a wireless body area network ( wban ) to a gateway when body shadowing affects the ability of wban nodes to communicate with the gateway . to solve this problem we present a new wban architecture that uses two communication technologies . one network is formed between on - body nodes , and is realized with capacitive body - coupled communication ( bcc ) , while an ieee 802.15.4 radio frequency ( rf ) network is used for forwarding data to the gateway . wban nodes that have blocked rf links due to body shadowing forward their data through the bcc link to a node that acts as a relay and has an active rf connection . for this architecture we design a network layer protocol that manages the two communication technologies and is responsible for relay selection and data forwarding . next , we develop analytical performance models of the medium access control ( mac ) protocols of the two independent communication links in order to be used for driving the decisions of the previous algorithms . finally , the analytical models are used for further optimizing energy and delay efficiency . we test our system under different configurations first by performing simulations and next by using real rf traces . wireless body area network ( wban ) , body sensor network ( bsn ) , ieee 802.15.4 , body shadowing , medium access control ( mac ) , capacitive body - coupled communication , cooperative communications , relay , performance analysis , delay , energy , optimization .

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in this paper we deal with the problem of optimizing data delivery from a wban to a gateway . the problem is challenging because communication between on - body and off - body nodes is very unreliable @xcite . the most promising way to attack the problem is through cooperation between wban nodes @xcite . with cooperation the nodes that aid in forwarding the data of other nodes are the _ relays_. there is a plethora of works that focus on selecting the optimal relay in the general case of wireless sensor networks ( wsn ) by considering different optimization objectives , while fewer works have focused in wbans . _ the majority of research works investigated cooperation in wsns / wbans with the objective to minimize power consumption . _ in @xcite the authors consider relay selection in wsns for minimizing the power consumption of individual nodes . they evaluate the impact of the sensor wake up schedules on the consumed power , and then they propose incentive mechanisms for participating in the cooperative network . this is an optimization approach that perceives the nodes as independent competing entities that may help each other for relaying data to a gateway . a number of authors investigated the impact of cooperation on the power consumption and lifetime of the complete wban introducing thus a more holistic approach @xcite . in these two works the cooperating nodes communicate with each other through the rf links opportunistically when they can not reach the gateway . however , a particular node may still not be able to reach another on - body node . to combat these intermittent problems , another parameter that was also investigated together with relay selection was power control . power control effectively means topology control in the wban @xcite , i.e. we can allocate more power to nodes that need it so that they can reach the rest of the network or the gateway . even though this approach ensures optimal power allocation for given channel conditions , power may be wasted in nodes with poor rf links . in the category of research efforts that target power minimization we can not identify solutions that eliminate the problem of a completely blocked rf link , but rather state - of - art solutions that allocate optimally the system resources to combat the rf inefficiencies . this is still unacceptable in scenarios where data from a specific node must be transmitted in real - time to the gateway . another significant number of research efforts focused on the problem of reliable communication and was motivated from experimental results . in @xcite the authors first focus on obtaining an experimental characterization of the channel . from the obtained results , the use of statically assigned relay nodes in specific body locations was proposed . nevertheless , specific on - body nodes may still fail or be occluded due to body shadowing . another aspect that affects the wban performance is the mobility of the user . mobility models for wbans driven from experiments were studied in @xcite . in this work the authors study the problem of user mobility and posture changes and how they affect wban performance . the solution is a multi - hop protocol that is aided by a single relay . in contrast to all the previous works that look into each specific node as a potential relay , there is an option to use multiple wban nodes for improving the reliability and/or energy / power . this class of protocols , that also targets generalized wireless cooperative networks , proposes the creation of _ clusters _ across groups of nodes in order to improve the diversity gain in the rf link by simultaneously transmitting the same information over different wireless paths @xcite . nevertheless , there is the major problem of node synchronization in this case . in cooperative schemes that involve many nodes we can also add recent works that apply advanced techniques like network coding @xcite . despite the architectural and protocol differences , all the previously described schemes share one common characteristic which is the use of a single rf communication technology . to alleviate the problems of a single technology two different ones can be used . the number of works in this area is quite limited . a communication protocol that uses two technologies was presented in @xcite . in that work the authors proposed the use of two different rf bands namely the 433mhz and 2.4ghz . the 433mhz band is used for data aggregation whereas the 2.4ghz band is used for data forwarding to the gateway . since the range of the 433mhz band is limited to approximately 2 meters around the node it is possible to improve the reliability and energy consumption by reducing the number of nodes competing for the same channel . still , both links use rf for on - body communications and two independent rf bands are required . _ thus , all the techniques we discussed in the last three paragraphs can not address completely the rf reliability problem because of the fundamental problems of the wireless channel . _ finally , we should mention that none of the previous works employed an in - depth analysis of the impact of the mac protocol parameters on energy / delay / reliability of the complete cooperative network . we could only trace a limited number of works for non - cooperative systems that use analytical protocol performance models for further optimization . these approaches use the mac model of ieee 802.15.4 for power minimization at an individual node @xcite . when compared to all the related works , our approach is significantly different . it focuses on using simultaneously the most reliable and most efficient rf link ( in terms of delay / energy ) for data forwarding since these two aspects are intertwined . our solution consists of a new wban architecture and a novel cooperative protocol design that is supported by an analytical performance model . with our system even when at least one node has an active rf link the data from every wban node will reach the gateway . to the best of our knowledge no other wban system can guarantee that .

in this paper we are concerned with the problem of data forwarding from a wireless body area network ( wban ) to a gateway when body shadowing affects the ability of wban nodes to communicate with the gateway . to solve this problem we present a new wban architecture that uses two communication technologies .

in this paper we are concerned with the problem of data forwarding from a wireless body area network ( wban ) to a gateway when body shadowing affects the ability of wban nodes to communicate with the gateway . to solve this problem we present a new wban architecture that uses two communication technologies . one network is formed between on - body nodes , and is realized with capacitive body - coupled communication ( bcc ) , while an ieee 802.15.4 radio frequency ( rf ) network is used for forwarding data to the gateway . wban nodes that have blocked rf links due to body shadowing forward their data through the bcc link to a node that acts as a relay and has an active rf connection . for this architecture we design a network layer protocol that manages the two communication technologies and is responsible for relay selection and data forwarding . next , we develop analytical performance models of the medium access control ( mac ) protocols of the two independent communication links in order to be used for driving the decisions of the previous algorithms . finally , the analytical models are used for further optimizing energy and delay efficiency . we test our system under different configurations first by performing simulations and next by using real rf traces . wireless body area network ( wban ) , body sensor network ( bsn ) , ieee 802.15.4 , body shadowing , medium access control ( mac ) , capacitive body - coupled communication , cooperative communications , relay , performance analysis , delay , energy , optimization .

1105.5437

i

new strong interactions are a natural possibility for the dynamics underlying electroweak symmetry breaking . in analogy with the ads / cft correspondence @xcite , such dynamics are expected to have a weakly - coupled dual description in terms of a compactified five - dimensional gauge theory . in the dual five - dimensional description , the ordinary electroweak gauge - bosons are understood as the lightest kaluza - klein " resonances of the five - dimensional gauge theory , whose light masses arise either through the boundary conditions imposed on the five - dimensional gauge fields , as in the case of higgsless models @xcite , or through the vacuum expectation value of a composite scalar higgs @xcite . in both higgsless @xcite and composite higgs models @xcite , the observed mass - eigenstate fermions result from mixing between two kinds of gauge - eigenstate fermions : a set with quantum numbers resembling those of standard model fermions and a new set of vector fermions @xcite . the first set are elementary ( non - composite ) fermion fields that are only weakly coupled to the new strong dynamics , and they correspond to brane - localized " states that are largely confined to the ultraviolet boundary of the compactified space . in contrast , the new vector fermions are kaluza - klein resonances arising from the bulk fields `` of the compactified five - dimensional theory , and in the dual four - dimensional theory they correspond to a tower of composite states arising from the underlying strong dynamics . the fermions observed in experiment correspond to the lighter mass eigenstates resulting from this mixing , and they are mostly composed of elementary fields with a smaller admixture of vector states ; we will refer to these as ' ' ordinary fermions " . the heavier partner mass eigenstates , which have not yet been observed , are predominantly composed of the composite , vectorial states ; we will refer to these as heavy vector fermions " . their mass scale @xmath4 is typically in the @xmath5 gev range . the composition of the lighter mass eigenstates will affect their properties . consider , for instance , an elementary brane - localized fermion @xmath6 , whose left - handed component is a member of the weak doublet @xmath7 , and whose right - handed component is an electroweak singlet . we will denote by @xmath8 and @xmath9 , respectively , the degree of mixing of the weak doublet @xmath7 and weak singlet @xmath10 fields with the new vector fermions @xmath11 bearing the same lorentz and electroweak quantum numbers . then , as suggested by fig . [ fig : mass - fig ] , the mass of the lighter ordinary fermion " mass eigenstate resulting from the mixing will be of order @xmath12 . it is then clear that in order for the light flavors of the ordinary fermions to receive their appropriate masses @xmath8 and/or @xmath9 must be quite small , whereas for the top quark neither @xmath8 nor @xmath9 can be too small if @xmath13 is to have its observed value . hence , from the four - dimensional point of view , the light ordinary fermions will be essentially elementary , while the top - quark must be substantially composite . and composite vector fermions @xmath11 , and a yukawa coupling between @xmath14 and @xmath10 is mediated by scalar @xmath15 . as discussed in the text , the mass of the lighter mass eigenstate will depend on the dirac mass @xmath4 of the vector fermions , and the mixing factors @xmath16.,width=377,height=151 ] in these models , the hierarchy of ordinary fermion masses is then transferred to a hierarchy of the values of the mixing factors @xmath17 . in models with a warped extra - dimension , a possible explanation for such a hierarchy , results from the combination of the exponential factor in the ads@xmath18 metric , along with different fermion profiles in the bulk @xcite . we will assume that the strong electroweak breaking dynamics incorporates either minimal @xcite or next - to - minimal @xcite flavor violation , and therefore that non - sm contributions of these strong dynamics to flavor - changing neutral currents are sufficiently suppressed to avoid conflict with experiment . fermion compositeness can yield significant corrections to low - energy observables ; some are beneficial and others are problematic . in higgsless models , for example , the presence of vector fermions with sm quantum numbers can cancel contributions to the @xmath19 parameter arising from the extended gauge sector @xcite . additional effects are expected to arise predominantly from the top sector , where the mixing factors @xmath20 are largest . two electroweak quantities are particularly sensitive to effects in the top - sector : the @xmath2 coupling , @xmath21 , and the deviation in the ratio of the @xmath22- and @xmath23-boson masses from that predicted in the sm , also known as the electroweak @xmath0 parameter @xcite . potential contributions to both parameters can be understood in terms of the ( approximate ) global symmetry structure of the new strong dynamics . just as in the sm , contributions to @xmath0 can be suppressed if the symmetry breaking sector has an approximate @xmath24 symmetry which , via electroweak symmetry breaking , breaks to a diagonal custodial @xmath25 symmetry @xcite . furthermore , as shown by agashe _ et . al . _ @xcite , corrections to the @xmath2 coupling can be suppressed if custodial symmetry is extended to include a left - right parity symmetry @xmath26 whose action consists in exchanging @xmath27 and @xmath28 charges and making @xmath29 an eigenstate of @xmath26 . in this case , the required overall symmetry structure is @xmath30 . due to the mass splitting between the top- and bottom - quark , neither the conventional @xmath25 nor the extended @xmath31 symmetry can be exact , even in the limit of zero hypercharge . @xmath25 requires that the top and bottom quarks form a doublet , and hence @xmath32 in the symmetry limit . @xmath31 symmetry requires that the top and bottom quark masses both equal that of an additional exotic quark of charge + 5/3 , with which they form a triplet @xcite . in the sm , the dimension - four top - quark yukawa coupling @xmath33 breaks @xmath25 weakly , and is responsible for transmitting electroweak symmetry breaking to the top - quark sector . therefore , the leading sm corrections to both @xmath0 and @xmath21 are proportional to @xmath34 . in models in which the top - quark is composite , _ i.e. _ has a large vector fermion component , the vector fermions can be members of custodial singlets , doublets , or triplets . however , unlike in the sm and simple generalizations thereof @xcite , both positive and negative corrections to @xmath0 and @xmath21 can be generated . this is both dangerous and interesting . it is dangerous because the sm predictions for @xmath0 and @xmath21 are in agreement with experiment . it is interesting because the agreement is not perfect : the sm prediction for @xmath21 is about @xmath35 below the measured value ( with weak dependence on the higgs mass ) @xcite , whereas the sm prediction for @xmath0 is in full agreement with experiment for a light higgs ( @xmath36 gev ) but is @xmath35 below for a heavy higgs ( @xmath37 gev ) @xcite . moreover , the measured left - handed and right - handed @xmath38 couplings have a strong and positive correlation , and the sm predictions are both approximately @xmath35 below their expectation values . in this paper we consider the effect of top compositeness on @xmath0 and @xmath21 , and discuss the patterns of top compositeness that can yield phenomenologically viable models . to begin , we examine the low - energy operators induced @xcite when the heavy vector fermion states are integrated out " at tree - level , and correlate the phenomenological properties of these operators with the custodial quantum numbers of these fermions . in sections iii and iv , we construct simple models that illustrate these effects by extending the sm via the addition of one weak - charged vector fermion multiplet mixing with the left - handed elementary top - bottom doublet , and/or one weak - singlet fector fermion mixing with the elementary right - handed top . these models may be considered as highly deconstructed versions @xcite of full five - dimensional duals @xcite to various underlying strongly - interacting composite higgs theories : deconstructions that de - scope the theory to include only one non - standard kaluza - klein fermion level . taken together , the simple models discussed illustrate the various ways in which the third - generation fermion masses arise in any strongly - interacting composite higgs theory with a weakly coupled five - dimensional dual . finally , in section [ sec : conclusions ] we compare our results to previous calculations in five - dimensional models , note what happens if the right - handed top is mixes with a triplet state , and present our conclusions .

in this paper we consider the effects of top quark compositeness on the electroweak parameters and and the coupling . these models may also be viewed as highly - deconstructed versions of five - dimensional gauge theories dual to various strongly - interacting composite higgs theories . we comment on how our results relate to extra - dimensional models previously considered , and we demonstrate that one pattern of breaking is phenomenologically favored .

in this paper we consider the effects of top quark compositeness on the electroweak parameters and and the coupling . we do so by using an effective field theory analysis to identify several promising patterns of mixing between sm - like and vector fermions , and then analyzing simple extensions of the standard model that realize those patterns . these models illustrate four ways in which an extended symmetry , which controls the size of radiative corrections to the observables discussed , may be broken . these models may also be viewed as highly - deconstructed versions of five - dimensional gauge theories dual to various strongly - interacting composite higgs theories . we comment on how our results relate to extra - dimensional models previously considered , and we demonstrate that one pattern of breaking is phenomenologically favored .

1210.3884

i

in the papers @xcite , treschev developed a new averaging method called continuous averaging . it is a powerful tool to derive sharp constants in the exponentially small splitting problems in hamiltonian systems with one and a half degrees of freedom . but the technicality becomes very heavy when we use the method to study hamiltonian systems of more degrees of freedom . for this reason , the method has not been applied to other problems yet . in this paper , we use the continuous averaging to give a new proof of the nekhoroshev theorem . we consider the following analytic nearly integrable hamiltonian system : @xmath0 the phase space is @xmath1 we complexify the variables and extend the domain of @xmath2 to a @xmath3 neighborhood and that of @xmath4 to a @xmath5 neighborhood of the original domains respectively . the extended phase space to the complex domain is @xmath6 where @xmath5 is the width of analyticity in @xmath4 and @xmath3 is that of the slow variables @xmath7 . as stated in @xcite , nekhoroshev theorem ensures that when the unperturbed hamiltonian @xmath8 is quasi - convex , by which we mean that the set @xmath9 is strictly convex , the following general estimate holds for sufficiently small @xmath10:@xmath11 for some constants @xmath12 independent of @xmath13 , where @xmath14 is the action variable component of any orbit associated to hamiltonian ( [ eq : main ] ) with initial condition in the set @xmath15 . there are many works studying the stability exponents @xmath16 and @xmath17 ( c.f.@xcite ) . their approaches are based on a careful study of the geometric and number theoretical aspects of resonances . instead , in this paper we try to sharpen the estimates in the analytic part of the proof using continuous averaging to obtain an improved normal form ( see theorem [ thm : main ] ) . then we apply the normal form to lochak s argument to get the nekhoroshev theorem ( see theorem [ thm : global ] ) where all the stability constants are estimated explicitly . in this paper , we only work on the case @xmath18 . but the normal form theorem can be easily applied to other prescribed @xmath16 and @xmath17 to get the corresponding @xmath19 . the method of lochak is called the simultaneous diophantine approximation , which turns out to be an important alternative to the classical approach via small divisor techniques , as explained in @xcite . its main idea is to do the averaging in a vicinity of a periodic orbit . so it is essentially an averaging procedure for systems with one fast angle . in general , we can kill the dependence on the fast angle up to exponential smallness . this makes the simultaneous diophantine approximation suitable to prove the nekhoroshev theorem . the work @xcite can be considered as a development of the continuous averaging to the small divisor case . in this paper , it is the first time that the continuous averaging has been developed to the simultaneous diophantine approximation . we point out the relation between continuous averaging and some important pdes . the idea of the continuous averaging is to study the averaging procedure using pde instead of iterations . the pde has the form @xmath20 , where @xmath21 is the hilbert transform of @xmath22 in some special cases ( see section 3 for more details ) . this type of equation has been studied ( c.f . @xcite ) as a simplified model for quasi - geostrophic equation ( c.f . @xcite ) , incompressible euler equation , etc . it would be interesting if we could apply some pde techniques to our problem . to state our theorems , we need the following definitions . 1 . we use @xmath23 to denote the @xmath24 norms for a vector in @xmath25 or @xmath26 . without causing confusion , we also use @xmath27 to denote the absolute value of a function whose range is in @xmath28 or @xmath29 . 2 . for a function @xmath30 , the @xmath31 is defined as:@xmath32 if we have the fourier expansion @xmath33 , and the other variables @xmath34 . 3 . @xmath35 . [ def : norm ] we also use the following definition to characterize the convexity of the unperturbed part @xmath36 . consider a hamiltonian @xmath36 defined on @xmath37 . then , we define the associated constants @xmath38 to characterize the convexity of @xmath36 . @xmath39 [ def : convex ] now we state a simplified version of our main theorem . the complete version is stated in the next section . [ thm : simple ] consider a hamiltonian system @xmath40 satisfying inequalities ( [ eq : ineq ] ) in definition [ def : convex ] and @xmath41 . for every orbit @xmath42 with initial condition @xmath43 and @xmath44 , we have the following estimates provided @xmath10 is small enough . @xmath45 for@xmath46 where @xmath47 satisfies * @xmath48 , * @xmath49 . + the norm @xmath50 is taken over @xmath51 . this theorem gives the estimate of the stability constant @xmath19 in . for a given system , we need to optimize @xmath52 under the constraints in the theorem . we see that the decomposition of @xmath5 can be qualitatively written as @xmath53 where the constants @xmath54 and @xmath55 . though not solved explicitly , we expect our estimate here improves the previous results @xcite since the continuous averaging method gives us an improved normal form theorem ( see theorem [ thm : main ] ) . a possible application of the result is to the 3-body problem in order to get long time stabilities . this direction is already pioneered in @xcite . but the mass ratio of jupiter to the sun obtained in @xcite is too small to be satisfactory . on the other hand , in @xcite , the authors construct diffusing orbits for restricted planar 3-body problem . the diffusion time there is polynomial w.r.t . @xmath56 . the paper is organized as follows . first we give a complete statement of the main theorem and compare it with previous results in section [ section : complete ] . then we state a normal form theorem [ thm : main ] about averaging in a vicinity of periodic orbits in section [ section : normal ] . this is the main result that we obtain using continuous averaging , which improves the corresponding one in @xcite . then we give a brief introduction to the continuous averaging method in section [ section : ca ] . after that we give a proof of theorem [ thm : main ] in section [ section : main ] . this section is a higher dimensional generalization of the case studied in section [ section : ca ] . we try to draw analogy between the two sections . with the normal form theorem , we first show local stability result of nekhoroshev theorem in section [ section : local ] , and then global stability in section [ section : global ] . here local stability means the stability result in a neighborhood of a periodic orbit and global stability means stability for all initial conditions . finally , we have two appendices [ section : appendix ] and [ section : majorant ] . the first one contains some technical estimates for the continuous averaging . the second one is some basics of majorant estimates .

in this paper we develop the _ continuous averaging _ method of treschev to work on the simultaneous diophantine approximation and apply the result to give a new proof of the nekhoroshev theorem . we obtain a sharp normal form theorem and an explicit estimate of the stability constants appearing in the nekhoroshev theorem .

in this paper we develop the _ continuous averaging _ method of treschev to work on the simultaneous diophantine approximation and apply the result to give a new proof of the nekhoroshev theorem . we obtain a sharp normal form theorem and an explicit estimate of the stability constants appearing in the nekhoroshev theorem .