violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

random close packing in a granular model we introduce a two dimensional lattice model of granular matter using a combination of proof and simulation we demonstrate an order disorder phase transition in the model to which we associate the granular phenomenon of random close packing we use peierls contours to prove that the model is sensitive to boundary conditions at high density and markov chain monte carlo simulation to show it is insensitive at low density

geometrical families of mechanically stable granular packings we enumerate and classify nearly all of the possible mechanically stable ms packings of bidipserse mixtures of frictionless disks in small sheared systems we find that ms packings form continuous geometrical families where each family is defined by its particular network of particle contacts we also monitor the dynamics of ms packings along geometrical families by applying quasistatic simple shear strain at zero pressure for small numbers of particles nl16 we find that the dynamics is deterministic and highly contracting that is if the system is initialized in a ms packing at a given shear strain it will quickly lock into a periodic orbit at subsequent shear strain and therefore sample only a very small fraction of the possible ms packings in steady state in studies with ng16 we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space we argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of ms packing geometrical families visited in steady state this work is part of our long term research program to develop a master equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems

local theory of the statistics of sphere packings abstract we describe a theory for the statistics of random packings of spheres in terms of the distributions of local voronoi cells in the packing several sum rules are shown to apply to the voronoi cells generated from a packing of spheres the theory is implemented numerically by applying these sum rules to randomly generated cells and we compare predictions for the packing fraction and the distribution of cell shapes in sphere packings with known results

statistical mechanics of maximal independent sets the graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory a maximal independent set is defined by the set of occupied nodes that satisfy some packing and covering constraints it is known that finding minimum and maximum density maximal independent sets are hard optimization problems in this paper we use cavity method of statistical physics and monte carlo simulations to study the corresponding constraint satisfaction problem on random graphs we obtain the entropy of maximal independent sets within the replica symmetric and one step replica symmetry breaking frameworks shedding light on the metric structure of the landscape of solutions and suggesting a class of possible algorithms this is of particular relevance for the application to the study of strategic interactions in social and economic networks where maximal independent sets correspond to pure nash equilibria of a graphical game of public goods allocation

granular contact force density of states and entropy in a modified edwards ensemble a method has been found to analyze edwards granular contact force probability functional for a special case as a result the granular contact force probability density functions are obtained from first principles for this case the results are in excellent agreement with the experimental and simulation data the derivation assumes edwards flat measure a density of states dos that is uniform within the metastable regions of phase space the enabling assumption supported by physical arguments and empirical evidence is that correlating information is not significantly recursive through loops in the packing maximizing a state counting entropy results in a transport equation that can be solved numerically for the present this has been done using the mean structure approximation projecting the dos across all angular coordinates to more clearly identify its predominant nonuniformities these features are 1 the grain factor psi related to grain stability and strong correlation between the contact forces on the same grain and 2 the structure factor upsilon related to newton s third law and strong correlation between neighboring grains

homogeneity of infinite dimensional isoparametric submanifolds a subsets of a riemannian manifoldn is called extrinsically homogeneous ifs is an orbit of a subgroup of the isometry group ofn in th thorbergsson proved the remarkable result that every complete connected full irreducible isoparametric submanifold of a flnite dimensional euclidean space of rank at least 3 is extrinsically homogeneous this result combined with results of pt1 and da flnally classifled irreducible isoparametric submanifolds of a flnite dimensional euclidean space of rank at least 3 while thorbergsson s proof used tits buildings a simpler proof without using tits buildings was given by olmos cf o2 the main purpose of this paper is to extend thorbergsson s result to the inflnite dimensional case the study of inflnite dimensional isoparametric submanifolds of a hilbert space always assumed to be separable was initiated by terng t2 besides its intrinsic interest the theory of inflnite dimensional isoparametric submanifolds is a very useful tool in studying the submanifold geometry of compact symmetric spaces cf tt as well as hl and ew although much progress has been made especially many basic properties of flnite dimensional isoparametric submanifolds having been successfully extended to the inflnite dimensional case cf t2 t5 and hl the classiflcation of inflnite dimensional isoparametric submanifolds is far from being solved to this end the understanding of the homogeneity of inflnite dimensional isoparametric submanifolds will certainly play a very important role as it does in the flnite dimensional case examples of non homogeneous inflnite dimensional isoparametric hypersurfaces have been found by terng and thorbergsson cf tt in this paper we will prove the following theorem which solves a long standing open problem cf t3 t4 tt theorem a let m be a complete connected irreducible isoparametric submanifold in a hilbert space v assume that the set of all the curvature normals of m at some point is not contained in any a ne line then m is extrinsically homogeneous in the hilbert space v remark in this theorem the dimension of m and thus v could be either flnite or inflnite without loss of generality we may assume that m is full i e

estimation of extreme depth based quantile regions consider the extreme quantile region induced by the halfspace depth function hd of the form q fx 2 rd hd x p g such that pq p for a given very small p 0 this region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result a simulation study clearly demonstrates the good performance of our estimator we use the procedure for risk management by applying it to stock market returns

exclusion processes with degenerate rates convergence to equilibrium and tagged particle stochastic lattice gases with degenerate rates namely conservative particle systems where the exchange rates vanish for some configurations have been introduced as simplified models for glassy dynamics we introduce two particular models and consider them in a finite volume of size l in contact with particle reservoirs at the boundary we prove that as for non degenerate rates the inverse of the spectral gap and the logarithmic sobolev constant grow as l2 it is also shown how one can obtain via a scaling limit from the logarithmic sobolev inequality the exponential decay of a lyapunov functional for a degenerate parabolic differential equation porous media equation we analyze finally the tagged particle displacement for the stationary process in infinite volume in dimension larger than two we prove that in the diffusive scaling limit it converges to a brownian motion with non degenerate diffusion coefficient

submanifold geometry in symmetric spaces the classical local invariants of a submanifold in a space form are the first fundamental form the shape operators and the induced normal connection and they determine the submanifold up to ambient isometry one of the main topics in differential geometry is to study the relation between the local invariants and the global geometry and topology of submanifolds many remarkable results have been developed for submanifolds in space forms whose local invariants satisfy certain natural conditions the study of focal points of a submanifold in an arbitrary riemannian manifold arises from the morse theory of the energy functional on the space of paths in the riemannian manifold joining a fixed point to the submanifold the morse index theorem relates the geometry of a submanifold to the topology of this path space the focal structure is intimately related to the local invariants of the submanifold in the case of space forms one can go backwards and reconstruct the local invariants from the focal structure so it is not too surprising that most of the structure theory of submanifolds can be reformulated in terms of their focal structure what is perhaps surprising is a fact that became increasingly evident to the authors from their individual and joint research over the past decade while extending the theory of submanifolds to ambient spaces more general than space forms proves quite difficult if one tries to use the same approach as for the space forms at least for symmetric spaces it has proved possible to develop an elegant theory based on focal structure that reduces to the classical theory in the case of space forms this paper is an extended report on this theory and the authors believe that the methods developed herein provide important tools for a continuing study of the submanifold geometry in symmetric spaces first we set up some notations let n g be a riemannian manifold m an immersed submanifold of n and m the normal bundle of m the end point map m n of m is the restriction of the exponential map exp to m if v m x is a singular point of and the dimension of the kernel of d v is m then v is called a multiplicity m focal normal and exp v is called a multiplicity m focal point of m with respect to m in n the focal data m is defined to be the set of all pairs v m such that v is a multiplicity m focal normal of m the focal variety v m is the set of all pairs v m with v m m the main purpose of our paper is to study the global geometry and topology

ensemble theory for force networks in hyperstatic granular matter an ensemble approach for force networks in static granular packings is developed the framework is based on the separation of packing and force scales together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle in this paper we will give a general formulation of this force network ensemble and derive the general expression for the force distribution psfd for small regular packings these probability densities are obtained in closed form while for larger packings we present a systematic numerical analysis since technically the problem can be written as a noninvertible matrix problem where the matrix is determined by the contact geometry we study what happens if we perturb the packing matrix or replace it by a random matrix the resulting psfd s differ significantly from those of normal packings which touches upon the deep question of how network statistics is related to the underlying network structure overall the ensemble formulation opens up a different perspective on force networks that is analytically accessible and which may find applications beyond granular matter

nonparametric imputation by data depth abstractwe present single imputation method for missing values which borrows the idea of data depth a measure of centrality defined for an arbitrary point of a space with respect to a probability d

edwards measure and the steady state regime of a model with kinetic constraints under tapping we study the tapping dynamics of a one dimensional ising model with symmetric kinetic constraints we define and test a variant of the edwards hypothesis that one may build a thermodynamics for the steady state by using a flat measure over the metastable states with several macroscopic quantities fixed various types of tapping are compared and the accuracy of this measure becomes quickly excellent when the number of quantities fixed on average increases independent of the way the system is excited we attribute the validity of the naive flat measure at weak tapping to the spatial separation of density defects

higher order corrections to the effective potential close to the jamming transition in the perceptron model in view of the results achieved in a previously related work a altieri s franz and g parisi j stat mech 2016 093301 10 1088 1742 5468 2016 09 093301 regarding a plefka like expansion of the free energy up to the second order in the perceptron model we improve the computation here focusing on the role of third order corrections the perceptron model is a simple example of constraint satisfaction problem falling in the same universality class as hard spheres near jamming and hence allowing us to get exact results in high dimensions for more complex settings our method enables to define an effective potential or thouless anderson palmer free energy namely a coarse grained functional which depends on the generalized forces and the effective gaps between particles the analysis of the third order corrections to the effective potential reveals that albeit irrelevant in a mean field framework in the thermodynamic limit they might instead play a fundamental role in considering finite size effects we also study the typical behavior of generalized forces and we show that two kinds of corrections can occur the first contribution arises since the system is analyzed at a finite distance from jamming while the second one is due to finite size corrections we nevertheless show that third order corrections in the perturbative expansion vanish in the jamming limit both for the potential and the generalized forces in agreement with the isostaticity argument proposed by wyart and coworkers finally we analyze the relevant scaling solutions emerging close to the jamming line which define a crossover regime connecting the control parameters of the model to an effective temperature

theory of powders starting from the observations that powders have a large number of particles and reproducible properties we show how statistical mechanics applies to powders the volume of the powder plays the role of the energy in conventional statistical mechanics with the hypothesis that all states of a specified volume are equally probable we introduce a variable x the compactivity which is analogous to the temperature in thermodynamics some simple models are considered which demonstrate how the problems involved can be tackled using the concept of compactivity there is an increasing interest in applying the methods of statistical mechanics and of transport theory to systems which are neither atomistic nor in equilibrium but which still fulfil a remaining tenet of statistical physics which is that systems can be completely defined by a very small number of parameters and can be constructed in a reproducible way powders fall into this category if a powder consists for example of uniform cubes of salt and is poured into a container falling at low density uniformly from a great height one expects a salt powder of a certain density repeating the preparation reproduces the same density a treatment such as shaking the powder by a definite routine produces a new density and the identical routine applied to another sample of the initial powder will result in the same final density clearly a maxwell demon could arrange the little cubes of nacl to make a material of different properties to that of our experiment but if such demonics are ignored and we restrict ourselves to extensive operations such as stirring shaking compressing all actions which do not act on grains individually then well defined states of the powder result in this paper we will set up a framework for describing the state of the powder basing our development on anologies with statistical mechanics some attempts have been made to apply information theory ideas directly to powders

simple strong glass forming models mean field solution with activation we introduce simple models inspired by previous models for froths and covalent glasses with trivial equilibrium properties but dynamical behaviour characteristic of strong glass forming systems these models are also a generalization of backgammon or urn models to a non constant number of particles where entropic barriers are replaced by energy barriers allowing for the existence of activated processes we formulate a mean field version of the models which keeps most of the features of the finite dimensional ones and solve analytically the out of equilibrium dynamics in the low temperature regime where activation plays an essential role

bridging centrality and extremity refining empirical data depth using extreme value statistics abstract data depth measures the centrality of a point with respect to a given distribution or data cloud it provides a natural center outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme in particular the halfspace depth is shown to have many desirable properties and broad applicability however the empirical halfspace depth is zero outside the convex hull of the data this property has rendered the empirical halfspace depth useless outside the data cloud and limited its utility in applications where the extreme outlying probability mass is the focal point such as in classification problems and control charts with very small false alarm rates to address this issue we apply extreme value statistics to refine the empirical halfspace depth in the tail this provides an important linkage between data depth which is useful for inference on centrality and extreme value statistics which is useful for inference on extremity the refined empirical halfspace depth can thus extend all its utilities beyond the data cloud and hence broaden greatly its applicability the refined estimator is shown to have substantially improved upon the empirical estimator in theory and simulations the benefit of this improvement is also demonstrated through the applications in classification and statistical process control

asymptotic dynamics of self driven vehicles in a closed boundary we study the asymptotic dynamics of self driven vehicles in a loop using a car following model with the consideration of volume exclusions in particular we derive the dynamical steady states for the single cluster case and obtain the corresponding fundamental diagrams exhibiting two branches representative of entering and leaving the jam respectively by simulations we find that the speed average over all vehicles eventually reaches the same value regardless of final clustering states the autocorrelation functions for overall speed average and single vehicle speed are studied each revealing a unique time scale we also discuss the role of noises in vehicular accelerations based on our observations we give trial definitions about the degree of chaoticity for general self driven many body systems

polar coordinates induced by actions of compact lie groups let g be a connected lie subgroup of the real orthogonal group 0 n for the action of g on r we construct linear subspaces a that intersect all orbits we determine for which g there exists such an a meeting all the g orbits orthogo nally groups that act transitively on spheres are obvious examples with few exceptions all possible g arise as the isotropy subgroups of riemannian symmetric spaces introduction let g be a compact lie group acting on a real vectorspace v and let k be a g invariant inner product on v having a linear cross section a c v of

topological crossovers in the forced folding of self avoiding matter abstract we study the scaling properties of forced folding of thin materials of different geometry the scaling relations implying the topological crossovers from the folding of three dimensional plates to the folding of two dimensional sheets and further to the packing of one dimensional strings are derived for elastic and plastic manifolds these topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry elasto plastic materials such as paper sheets during the fast folding under increasing confinement force are expected to obey the scaling force diameter relation derived for elastic manifolds however in experiments with paper strips of different geometry we observed the crossover from packing of one dimensional strings to folding two dimensional sheets only because the fractal dimension of the set of folded elasto plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn

on edwards theory of powders abstract we briefly review a statistical mechanics approach for the description of granular materials following the original ideas developed by edwards we show that edwards assumptions works very well for a class of lattice models and we discuss some recent analytic results obtained in such a framework on their phase diagram jamming transition and mixing segregation properties

fundamental problems in statistical physics of jammed packings abstract for packed i e jammed hard and rough objects kinetic energy is a minor and ignorable quantity as is elastic strain hence in the static case the stress equations need supplementing by missing equations depending solely on configurations a different pathway of analysis is the calculation of the probability distribution of interparticle forces this paper presents the mini review of recently obtained results in this field and poses a number of fundamental problems which are yet to be solved

control charts for multivariate processes abstract this article uses the concept of data depth to introduce several new control charts for monitoring processes of multivariate quality measurements for any dimension of the measurements these charts are in the form of two dimensional graphs that can be visualized and interpreted just as easily as the well known univariate x x and cusum charts moreover they have several significant advantages first they can detect simultaneously the location shift and scale increase of the process unlike the existing methods which can detect only the location shift second their construction is completely nonparametric in particular it does not require the assumption of normality for the quality distribution which is needed in standard approaches such as the 2 and hotelling s t 2 charts thus these new charts generalize the principle of control charts to multivariate settings and apply to a much broader class of quality distributions

nonequilibrium temperatures in steady state systems with conserved energy we study a class of nonequilibrium lattice models describing local redistributions of a globally conserved quantity which is interpreted as an energy a particular subclass can be solved exactly allowing us to define a statistical temperature t th along the same lines as in the equilibrium micro canonical ensemble we compute the response function and find that when the fluctuation dissipation relation is linear the slope t fd 1 of this relation differs from the inverse temperature t th 1 we argue that t th is physically more relevant than t fd since in the steady state regime it takes equal values in two subsystems of a large isolated system finally a numerical renormalization group procedure suggests that all models within the class behave similarly at a coarse grained level leading to a parameter that describes the deviation from equilibrium quantitative predictions concerning this parameter are obtained within a mean field framework

edwards measures for powders and glasses can one construct a thermodynamics for compact slowly moving powders and grains a few years ago edwards proposed a possible step in this direction raising the fascinating perspective that such systems have a statistical mechanics of their own different from that of maxwell boltzmann and gibbs allowing us to have some information while still ignoring dynamic details recent developments in the theory of glasses have come to confirm these ideas within mean field in order to go beyond we explicitly generate edwards measure in a 3d model comparison of the results with the irreversible compaction data shows very good agreement the present framework immediately suggests new experimental checks

perturbative theory of the packing of mixtures and of non spherical particles abstract we present a simple theory for the packing of irregular particles and mixtures considered as a perturbation of a packing of monodisperse spheres using the perturbation theory we extract the different geometrical effects which effect the packing density and discuss why packings of irregular particles are generally less dense than packings of monodisperse spheres whereas packings of mixtures of particles of different sizes are generally denser than monodisperse sphere packings

transmission of stress in granular materials as a problem of statistical mechanics abstract we consider the problem of stress transmission in granular materials we formulate the simplest statically determinate problem of stress transmission through a static granular material this is the case when grains are rigid and have an average coordination number of z d 1 under this condition the system of newton s equations of interparticle force and torque balance is complete this means that there exists a complete set of equations for the macroscopic stress tensor ij r i e the d where d is the dimension of the problem equations of force balance j ij r g i r have to be supported by d d 1 2 equations these equations have their origin in newton s laws of interparticle force and torque balance and incorporate tensorial geometrical characteristics of the packing we conjecture that in order to have a coherent and self consistent continuum theory of stress transmission in static granular media it is necessary to link the averaging procedure to the concept of compactivity we emphasize that although real granular materials have many features ignored within the proposed framework it is essential for making progress to derive equations of stress transmission for the simplest model as opposed to guessing and postulating

a model for the packing of irregularly shaped grains in this paper we will attempt to address the problem of the packing properties of granular materials composed of irregularly shaped grains using configurational statistical mechanics in particular we will develop a model for a system of irregular grains based upon perturbing a packing of mono or poly disperse spheres in the mono disperse case we will show that the system packs less densely than a packing of perfect spheres except when local correlations between configurations of grains are taken into account the opposite is found to be true for a perturbation expansion based upon poly disperse spheres finally we will show that for a bi disperse packing of spheres phase segregation occurs for any size ratio and discuss whether this is to be expected

protocol independent granular temperature supported by numerical simulations a possible approach to the statistical description of granular assemblies starts from edwards s assumption that all blocked states occupying the same volume are equally probable edwards and oakeshott physica a 157 1080 1989 we performed computer simulations using two dimensional polygonal particles excited periodically according to two different protocols excitation by pulses of negative gravity and excitation by rotating gravity the first protocol exhibits a nonmonotonous dependency of the mean volume fraction on the pulse strength the overlapping histogram method is used in order to test whether the volume distribution is described by a boltzmann like distribution and to calculate the inverse compactivity as well as the logarithm of the partition sum we find that the mean volume is a unique function of the measured granular temperature independently of the protocol and of the branch in g and that all determined quantities are in agreement with edwards s theory

applications of the statistical mechanics of inherent states to granular media abstract we review the results of a statistical mechanics approach to granular materials and its extension to non thermal systems in their inherent states we introduce a tapping dynamics based on a dynamics used for real granular matter which allows to visit the space of the inherent states it is assumed that under stationarity or quasi stationarity the distribution among the inherent states satisfies the principle of maximum entropy this leads to a distribution characterised by a configurational temperature related to edwards compactivity the prediction from such an approach are checked on a standard hamiltonian lattice model and in the present unifying framework it is possible to explain a variety of properties of granular materials ranging from their logarithmic compaction to typical memory phenomena

a statistical mechanics approach to the inherent states of granular media abstract we consider a statistical mechanics approach to granular systems by following the original ideas developed by edwards we use the concept of inherent states defined as the stable configurations in the potential energy landscape introduced in the context of glasses under simplifying assumptions the equilibrium inherent states can be characterized by a configurational temperature 1 we link to edwards compactivity and address the problem of its experimental measure we also discuss the possibility to describe the time dependent distribution probability in the inherent states with an appropriate master equation

new kinds of entropy two new entropies are offered in this paper neither belongs to the traditional conservative statistical mechanics the first recognizes that the discovery that there are states of granular or glassy systems which can be restricted by an appropriate experimental pathway implies that an entropy can be defined for them by deriving an appropriate boltzmann equation in which the pathway to the steady state has an increasing entropy until the state characterized by a compactivity x v s is reached the second problem is to consider a state where energy flows in and flows out leaving a steady state e g a steady turbulent flow time dependent correlation functions are well defined and hence a probability of the history of the system is defined there are many ad hocstudies of such systems we ask whether such systems will possess an entropy defined by the usual plogpbut now pis the probability of the entire history of the system and the integral is over all histories

structural characterization and statistical properties of two dimensional granular systems a recently developed method is used for the analysis of structures of planar disordered granular assemblies within this method the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization the second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure our third aim is to quantify the statistics of basic volumes used for the entropic analysis we report the following results 1 quadrons are more useful than grains as basic quasiparticles for the entropic formalism 2 both grain and quadron volume distributions show nontrivial peaks and shoulders these can be understood only in the context of the quadrons in terms of particular conditional distributions 3 increasing friction increases the mean cell size as expected but does not affect the conditional distributions which is explained on a fundamental level we conclude that grain size and shape distributions determine the conditional distributions while their relative weights are dominated by friction and by the pack formation process this separates sharply the different roles that friction and grain shape distributions play 4 the analysis of the quadron volumes shows that gamma distributions which are accepted to describe foamlike structures well are too simplistic for general granular systems 5 a range of quantitative results is obtained for the density of states of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated the structural characteristics of granular systems are compared with numerically generated foamlike dirichlet voronoi constructions

fluctuation dissipation ratio for compacting granular media in this paper we investigate the possibility of a dynamical definition of an effective temperature for compacting granular media in the framework of the fluctuation dissipation fd relations we have studied two paradigmatic models for the compaction of granular media which consider particles diffusing on a lattice with either geometrical tetris model or dynamical kob andersen model constraints idealized compaction without gravity has been implemented for the tetris model and compaction with a preferential direction imposed by gravity has been studied for both models in the ideal case of an homogeneous compaction the obtained fd ratio is clearly shown to be in agreement with the prediction of edwards measure at various densities similar results are obtained with gravity only when the homogeneity of the bulk is imposed in this case the fd ratio obtained dynamically for horizontal displacements and mobility and from edwards measure coincide finally we propose experimental tests for the validity of the edwards construction through the comparison of various types of dynamical measurements

tapping thermodynamics of the one dimensional ising model we analyse the steady state regime of a one dimensional ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media the idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure the agreement between the two averages is excellent in all the cases examined showing that a static approach is capable of predicting certain measurable properties of the steady state regime

principal component analysis of persistent homology rank functions with case studies of spatial point patterns sphere packing and colloids abstract persistent homology while ostensibly measuring changes in topology captures multiscale geometrical information it is a natural tool for the analysis of point patterns in this paper we explore the statistical power of the persistent homology rank functions for a point pattern x we construct a filtration of spaces by taking the union of balls of radius a centred on points in x x a x x b x a the rank function k x a b r 2 a b r is then defined by k x a b rank h k x a h k x b where is the induced map on homology from the inclusion map on spaces we consider the rank functions as lying in a hilbert space and show that under reasonable conditions the rank functions from multiple simulations or experiments will lie in an affine subspace this enables us to perform functional principal component analysis which we apply to experimental data from colloids at different effective temperatures and to sphere packings with different volume fractions we also investigate the potential of rank functions in providing a test of complete spatial randomness of 2d point patterns using the distances to an empirically computed mean rank function of binomial point patterns in the unit square

statistical theory of correlations in random packings of hard particles a random packing of hard particles represents a fundamental model for granular matter despite its importance analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory here we take inspiration from liquid theories for the n particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up a progressive expansion into a shell of particles converges in the large layer limit under a kirkwood like approximation of higher order correlations we apply the formalism to hard disks and predict the density of two dimensional random close packing rcp rcp 0 85 0 01 and random loose packing rlp rlp 0 67 0 01 our theory also predicts a phase diagram and angular correlation functions that are in good agreement with experimental and numerical data

stationary probability distribution in granular media abstract we discuss recent developments in the formulation of a statistical mechanics approach to non thermal systems such as granular media we review a few important numerical results on the assessment of edwards theory and in particular we apply these ideas to study a mean field model of a hard sphere binary mixture under gravity which can be fully analytically investigated as a consequence we derive the rich phase diagram and predict the features of segregation patterns of the mixture

breakdown properties of location estimates based on halfspace depth and projected outlyingness we describe multivariate generalizations of the median trimmed mean and w estimates the estimates are based on a geometric construction related to projection pursuit they are both affine equivariant coordinate free and have high breakdown point the generalization of the median has a breakdown point of at least 1 d 1 in dimension d and the breakdown point can be as high as 1 3 under symmetry in contrast various estimators based on rejecting apparent outliers and taking the mean of the remaining observations have breakdown points not larger than 1 d 1 in dimension d

quasi equilibrium interpretation of ageing dynamics we develop an interpretation of the off equilibrium dynamical solution of mean field glassy models in terms of quasi equilibrium concepts we show that the relaxation of the thermo remanent magnetization follows a generalized version of the onsager regression postulate of induced fluctuations we then find the rationale for the equality between the fluctuation dissipation ratio and the rate of growth of the configurational entropy close to the asymptotic state found empirically in mean field solutions