exact mean field solutions of the asymmetric random average process we consider the asymmetric random average process arap with continuous mass variables and parallel discrete time dynamics studied recently by krug garcia and rajesh majumdar both j statist phys 99 2000 the model is defined by an arbitrary state independent fraction density function r with support on the unit interval we examine the exactness of mean field steady state mass distributions in dependence of and identify as a conjecture based on high order calculations the class of density functions yielding product measure solutions additionally the exact form of the associated mass distributions p m is derived using these results we show examplary the exactness of the mean field ansatz for monomial fraction densities r n 1 rn 2 with n 2 for verification we calculate the mass distributions p m explicitly and prove directly that product measure holds furthermore we show that even in cases where the steady state is not given by a product measure very accurate approximants can be found in the class

packing geometry and statistics of force networks in granular media the relation between packing geometry and force network statistics is studied for granular media based on simulations of two dimensional packings of hertzian spheres we develop a geometrical framework relating the distribution of interparticle forces p f to the weight distribution p w which is measured in experiments we apply this framework to reinterpret recent experimental data on strongly deformed packings and suggest that the observed changes of p w are dominated by changes in contact network while p f remains relatively unaltered we furthermore investigate the role of packing disorder in the context of the q model and address the question of how force fluctuations build up as a function of the distance beneath the top surface

jamming at zero temperature and zero applied stress the epitome of disorder we have studied how two and three dimensional systems made up of particles interacting with finite range repulsive potentials jam i e develop a yield stress in a disordered state at zero temperature and zero applied stress at low packing fractions phi the system is not jammed and each particle can move without impediment from its neighbors for each configuration there is a unique jamming threshold phi c at which particles can no longer avoid each other and the bulk and shear moduli simultaneously become nonzero the distribution of phi c values becomes narrower as the system size increases so that essentially all configurations jam at the same packing fraction in the thermodynamic limit this packing fraction corresponds to the previously measured value for random close packing in fact our results provide a well defined meaning for random close packing in terms of the fraction of all phase space with inherent structures that jam the jamming threshold point j occurring at zero temperature and applied stress and at the random close packing density has properties reminiscent of an ordinary critical point as point j is approached from higher packing fractions power law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure shear modulus and excess number of overlapping neighbors moreover near point j certain quantities no longer self average suggesting the existence of a length scale that diverges at j however point j also differs from an ordinary critical point the scaling exponents do not depend on dimension but do depend on the interparticle potential finally as point j is approached from high packing fractions the density of vibrational states develops a large excess of low frequency modes indeed at point j the density of states is a constant all the way down to zero frequency all of these results suggest that point j is a point of maximal disorder and may control behavior in its vicinity perhaps even at the glass transition

on minimax robust detection of stationary gaussian signals in white gaussian noise the problem of detecting a wide sense stationary gaussian signal process embedded in white gaussian noise in which the power spectral density of the signal process exhibits uncertainty is investigated the performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a neyman pearson criterion with a fixed false alarm probability as the length of the observation interval grows without bound a stochastic suppression condition is identified for the uncertainty set of spectral density functions and it is established that under the stochastic suppression condition the resulting minimax problem possesses a saddle point which is achievable by the likelihood ratio tests matched to a so called suppressing power spectral density in the uncertainty set no convexity condition on the uncertainty set is required to establish this result

robust matched filters the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered two general aspects of this problem are treated first maximin robust designs are characterized for a general hilbert space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty these results are seen to generalize earlier results for specific matched filtering problems the second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion channel distortion is modeled by considering an unknown received signal which may differ in l 2 norm from the transmitted or nominal signal by no more than a fixed amount the effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion general expressions are developed for the determination of the robust filter and its performance and numerical results are presented for the case of baseband detection in gauss markov noise

nonequilibrium statistical mechanics of dividing cell populations we present and study a model for the nonequilibrium statistical mechanics of protein distributions in a proliferating cell population our model describes how the total protein variation is shaped by two processes variation in protein production internal to the cells and variation in division and inheritance at the population level it enables us to assess the contribution of each of these components separately we find that even if production is deterministic cell division can generate a large variation in protein distribution in this limit we solve exactly a special case and draw an analogy between protein distribution along cell generations and stress distribution in layers of granular material at the other limit of extremely noisy protein production we find that the population structure restrains variation and that the details of division do not affect the tail of the distribution

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

force and weight distributions in granular media effects of contact geometry the influence of the local contact network on interparticle forces and effective particle weights is studied in simulations of two dimensional packings of frictionless hertzian spheres the weight distribution p w changes qualitatively when approaching a boundary and differs for regular and irregular packings while the interparticle force distribution p f is robust we provide examples where p w at the boundary which is the quantity probed experimentally deviates substantially from p f in the bulk discrepancies between the p w s predicted by the q model and measured in experiments are due to differences in the contact geometry

jamming graphs a local approach to global mechanical rigidity we revisit the concept of minimal rigidity as applied to frictionless repulsive soft sphere packings in two dimensions with the introduction of the jamming graph minimal rigidity is a purely combinatorial property encoded via laman s theorem in two dimensions it constrains the global average coordination number of the graph for example however minimal rigidity does not address the geometry of local mechanical stability the jamming graph contains both properties of global mechanical stability at the onset of jamming and local mechanical stability we demonstrate how jamming graphs can be constructed using local moves via the henneberg construction such that these graphs fall under the jurisdiction of correlated percolation we then probe how jamming graphs destabilize or become unjammed by deleting a bond and computing the resulting rigid cluster distribution we also study how the system restabilizes with the addition of new contacts and how a jamming graph with extra redundant contacts destabilizes the latter endeavor allows us to probe a disk packing in the rigid phase and uncover a potentially new diverging length scale associated with the random deletion of contacts as compared to the study of cut out or frozen in subsystems

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

force distributions in three dimensional compressible granular packs we present an experimental investigation of the probability distribution of normal contact forces p f at the bottom boundary of static three dimensional packings of compressible granular materials we find that the degree of deformation of individual grains plays a large role in determining the form of this distribution for small amounts of deformation we find a small peak in p f below the mean force with an exponential tail for forces larger than the mean force as the degree of deformation is increased the peak at the mean force grows in height and the slope of the exponential tail increases

entropy maximization in the force network ensemble for granular solids a long standing issue in the area of granular media is the tail of the force distribution in particular whether this is exponential gaussian or even some other form here we resolve the issue for the case of the force network ensemble in two dimensions we demonstrate that conservation of the total area of a reciprocal tiling a direct consequence of local force balance is crucial for predicting the local stress distribution maximizing entropy while conserving the tiling area and total pressure leads to a distribution of local pressures with a generically gaussian tail that is in excellent agreement with numerics both with and without friction and for two different contact networks

cluster cluster aggregation as an analogue of a turbulent cascade kolmogorov phenomenology scaling laws and the breakdown of self similarity abstract we present a detailed study of the statistical properties of a system of diffusing aggregating particles in the presence of a steady source of monomers we emphasize the case of low spatial dimensions where strong diffusive fluctuations invalidate the mean field description provided by standard smoluchowski kinetic theory the presence of a source of monomers allows the system to reach a statistically stationary state at large times this state is characterized by a constant flux of mass directed from small to large masses it therefore admits a phenomenological description based on the assumption of self similarity and constant mass flux analogous to the kolmogorov s 1941 theory of turbulence unlike turbulence the aggregation problem is analytically tractable using powerful methods of statistical field theory we explain in detail how these methods should be adapted to study the far from equilibrium flux dominated states characteristic of turbulent systems we consider multipoint correlation functions of the mass density by an exact evaluation of the scaling exponents for the one and two point correlation functions we show that the assumption of self similiarity breaks down at large masses for spatial dimensions d 2 we calculate non rigorously the exponents of the higher order correlation functions as an expansion where 2 d we show that the mass distribution exhibits non trivial multiscaling an analogy can be drawn with the case of hydrodynamic turbulence the physical origin of this multiscaling is traced to the presence of strong correlations between particles participating in large mass aggregation events these correlations stem from the recurrence of diffusion processes in d 2 the analytic methods developed here will have more general applicability beyond the study of this specific problem

on minimax robustness a general approach and applications the minimax approach to the design of systems that are robust with respect to modeling uncertainties is studied using a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary the existence and characterization of minimax robust solutions that form saddle points are discussed through various methods that take into account several common features of the games encountered in applications in particular it is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust the efficacy of the methods proposed for a general game is tested in the problems of matched filtering wiener filtering quadratic detection and output energy filtering in which uncertainties in their respective signal and noise models are assumed to exist these problems are analyzed in a common hilbert space framework and they serve to point out the advantages and limitations of the proposed techniques

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

contact forces in anisotropic frictional granular materials the probability density functions pdfs of contact forces in anisotropic cohesionless and frictional granular materials are studied numerically and theoretically using discrete element simulations of biaxial deformation of a large two dimensional assembly consisting of 200 000 disks it is observed that the pdfs for the normal and tangential components of the contact forces depend significantly on contact orientation the pdfs exhibit exponential decay and the pdf for the tangential component of the contact forces is not always symmetrical with respect to zero tangential force the shape of the pdf for the normal component of the contact forces changes with shear strain a qualitative explanation for this change is given that is related to the biaxial deformation mechanism in which the disrupted contacts are predominantly oriented in the direction of the minor principle stress a maximum entropy method is employed to study these pdfs theoretically using a prescribed stress tensor as constraint it is found that the theoretical results correspond qualitatively to many of the results obtained from the discrete element simulations discrepancies between theory and simulations are attributed to the fact that the kinematics have not been taken into account in the theory

conserved mass models and particle systems in one dimension in this paper we study analytically a simple one dimensional model of mass transport we introduce a parameter p that interpolates between continuous time dynamics p 0 limit and discrete parallel update dynamics p 1 for each p we study the model with i both continuous and discrete masses and ii both symmetric and asymmetric transport of masses in the asymmetric continuous mass model the two limits p 1 and p 0 reduce respectively to the q model of force fluctuations in bead packs s n coppersmith et al phys rev e 53 4673 1996 and the recently studied asymmetric random average process j krug and j garcia cond mat 9909034 we calculate the steady state mass distribution function p m assuming product measure and show that it has an algebraic tail for small m p m m where the exponent depends continuously on p for the asymmetric case we find p 1 p 2 p for 0 p 1 and 1 1 and for the symmetric case p 2 p 2 8 5p p 2 for all 0 p 1 we discuss the conditions under which the product measure ansatz is exact we also calculate exactly the steady state mass mass correlation function and show that while it decouples in the asymmetric model in the symmetric case it has a nontrivial spatial oscillation with an amplitude decaying exponentially with distance

matrix product approach for the asymmetric random average process we consider the asymmetric random average process which is a one dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables first the explicit functional representations so called beta densities of all local interactions leading to steady states of product measure form are rigorously derived this also completes an outstanding proof given in a previous publication then we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz due to continuous state variables we obtain a matrix algebra in the form of a functional equation which can be solved exactly

micro mechanical analysis of deformation characteristics of three dimensional granular materials the deformation characteristics of idealized granular materials have been studied from the micro mechanical viewpoint using bagi s three dimensional micro mechanical formulation for the strain tensor bagi k 1996 mechanics of materials 22 165 177 this formulation is based on the delaunay tessellation of space into tetrahedra the set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles bagi s formulation expresses the continuum macro scale strain as an average over all edges of their relative displacements between two successive states and the complementary area vectors this latter vector is a geometrical quantity determined from the set of edges i e from the structure of the particle packing results from discrete element method simulations of isotropic and triaxial loading of a three dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary area vectors of edges subdivided into physical and virtual contacts and of the relative displacements of edges the investigated statistics are probability density functions and averages over groups of edges with the same orientation it is shown that these averages can be represented by second order fourier series in edge orientation edge orientations are distributed isotropically contrary to contact orientations the average lengths of the branch vectors and the normal component of the complementary area vectors are distributed isotropically with respect to the edge orientation and their average values are related to each other and to the volume fraction of the assembly the other two components of the complementary area vector are zero on average the total deformation of the assembly as given by the average of the relative displacements of the edges of the delaunay tessellation follows the uniform strain prediction however neither the deformation of the physical contact network nor of the virtual contact network has this property the average relative displacement of physical edges in the normal direction determined by the branch vector is smaller than that according to the uniform strain assumption while that of virtual contacts is larger this is caused by the high interparticle stiffness that hinders compression the reverse observation holds for the tangential component of the relative displacement vector the contribution of the deformation of the empty space between physical contacts to the continuum macro scale strain tensor is therefore very important for the understanding and the prediction of the macro scale deformation of granular materials

an implicit particle in cell method for granular materials an implicit in time method for granular materials is described the method combines the material point method a first order contact algorithm and a newton krylov equation solver to give improved energy conservation stabilization of the finite grid instability and the correct description of collisions between grains

failure tolerance of load bearing hierarchical networks we investigate the statistics and dynamics of failure in a two dimensional load bearing network with branching hierarchical structure and its variants the variants strengthen the original lattice by using connectivity strategies which add new sites to the maximal cluster in top to bottom or bottom to top versions we study the load bearing capacity and the failure tolerance of all versions as well as that of the strongest realization of the original lattice the v lattice the average number of failures as a function of the test load shows power law behavior with power 5 2 for the v lattice but sigmoidal behavior for all other versions thus the v lattice turns out to be the critical case of the load bearing lattices the distribution of failures is gaussian for the original lattice the v lattice and the bottom to top strategy but is non gaussian for the top to bottom one the bottom to top strategy leads to stable and strong lattices and can resist failure even when tested with weights which greatly exceed the capacity of its backbone we also examine the behavior of asymmetric lattices and discover that the mean failure rates are minimized if the probability of connection p is symmetric with respect to both neighbors our results can be of relevance in the context of realistic networks

simple models for granular force networks abstract a remarkable feature of static granular matter is the distribution of force along intricate networks even regular inter particle contact networks produce wildly inhomogeneous force networks where certain chains of particles carry forces far larger than the mean although the full information of each inter particle contact requires analysis of the stress tensor potentially including friction and elasticity there is a rich tradition of approximating these interactions with simple scalar models that focus on the geometry of the system in this paper we briefly review past theoretical approaches to understanding the geometry of force networks we then investigate the structure of experimentally derived granular force networks using a simple algorithm to obtain corresponding graphs we compare our observations with the results of geometric models including random bond percolation which show similar spatial distributions without enforcing vector force balance our findings suggest that some aspects of the mean geometry of granular force networks may be captured by these simple descriptions

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

transmission of packets on a hierarchical network statistics and explosive percolation we analyze an idealized model for the transmission or flow of particles or discrete packets of information in a weight bearing branching hierarchical two dimensional network and its variants the capacities add hierarchically down the clusters each node can accommodate a limited number of packets depending on its capacity and the packets hop from node to node following the links between the nodes the statistical properties of this system are given by the maxwell boltzmann distribution we obtain analytical expressions for the mean occupation numbers as functions of capacity for different network topologies the analytical results are shown to be in agreement with the numerical simulations the traffic flow in these models can be represented by the site percolation problem it is seen that the percolation transitions in the 2d model and in its variant lattices are continuous transitions whereas the transition is found to be explosive discontinuous for the v lattice the critical case of the 2d lattice the scaling behavior of the second order percolation case is studied in detail we discuss the implications of our analysis

distribution of local fluxes in diluted porous media we study the distributions of channel openings local fluxes and velocities in a two dimensional random medium of nonoverlapping disks we present theoretical arguments supported by numerical data of high precision and find scaling laws as functions of the porosity for the channel openings we observe a crossover to a highly correlated regime at small porosities the distribution of velocities through these channels scales with the square of the porosity the fluxes turn out to be the convolution of velocity and channel width corrected by a geometrical factor furthermore while the distribution of velocities follows a gaussian form the fluxes are distributed according to a stretched exponential with exponent 1 2 finally our scaling analysis allows us to express the tortuosity and pore shape factors from the kozeny carman equation as direct average properties from microscopic quantities related to the geometry as well as the flow through the disordered porous medium

the automatic robustness of minimum distance functionals on montre que les estimateurs de distance minimale forment une classe d estimateurs automatiquement robustes dans le meme sens que l estimateur du maximum de vraisemblance

optimal filtering in stochastic discrete time systems with unknown inputs in this note we derive a recursive filtering algorithm for the linear discrete time dynamic system with indeterminate stochastic inputs the algorithm is based on the minimax optimal method of parameter estimation in the linear regression model with parameters of two different types unknown and stochastic with partially known characteristics

forces on bins the effect of random friction the q model of coppersmith et al phys rev e 53 4673 1996 has renewed interest in understanding the forces generated along the walls and at the bottom of a silo filled with a granular material fluctuations in the mean stress have been characterized for the q model and related to experimental work on stress chains the classical engineering approach to bin loads follows from janssen s analysis z ver dtsch ing 39 1045 1895 predicting a saturation of stress as a function of depth in a tall silo in this paper we reexamine the janssen theory introducing randomness into the important parameters in the theory the janssen analysis relies on assumptions not met in practice for this reason we numerically solve the partial differential equations governing the equilibrium of forces in a bin again including randomness in parameters we show that the most important of these parameters is a coefficient of friction at the wall of the bin this random friction model combines some features of fluctuations as seen in experiments with a classical continuum mechanics approach to describing granular materials

robust wiener kolmogorov theory a minimax formulation is considered for the problem of designing robust linear causal estimators of linear functions of discrete time wide sense stationary signals when knowledge of the signal and or noise spectra is inexact the solution is given under mild regularity conditions in terms of a least favorable pair of spectra thus reducing the minimax problem to a direct maximization problem which in many cases can be solved easily it is noted that this design method leads in particular to robust n step predictors robust causal filters and robust n lag smoothers the method of design is illustrated by a thorough development of the special case of one step noiseless prediction further solutions are given explicitly for the problem of robust causal filtering of an uncertain signal in white noise and numerical examples are given for this case which illustrate the effectiveness of this design

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

probability density functions of contact forces for cohesionless frictional granular materials a theory is developed for the probability density functions of contact forces for cohesionless frictional granular materials in quasi static equilibrium this theory is based on a maximum information entropy principle with an expression for information entropy that is appropriate for granular materials entropy is maximized under the constraints of a prescribed stress and that the normal component of the contact force is compressive and that the tangential component of the contact force is limited by coulomb friction the theory results in a dependence of the probability density function for the tangential contact forces on the friction coefficient the theoretical predictions are compared with results from discrete element simulations on isotropic two dimensional assemblies under hydrostatic stress good qualitative agreement is found for means and standard deviations of contact forces and the shape of the probability density functions while the quantitative agreement is fairly good discrepancies between theory and simulations such as the difference in shape of the probability density function for the normal force and the observed dependence on elastic properties of the exponential decay rate of tangential forces are attributed to the fact that the method does not take into account any kinematics which are essential in relation to elastic effects

model for force fluctuations in bead packs we study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials we present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile we compare our results for the force distribution function for this model including exact results for certain contact angle probability distributions with numerical simulations of force distributions in random sphere packings this model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings our model is closely related to some that have been studied in the context of self organized criticality we present evidence that in the force distribution context critical power law force distributions occur only when a parameter hidden in other interpretations is tuned our numerical mean field and exact results all indicate that for almost all contact distributions the distribution of forces decays exponentially at large forces

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

stress distribution in static two dimensional granular model media in the absence of friction we present simulations of static model sandpiles in two dimensions 2d and focus on the stress distribution in such arrays made of discrete particles we use the simplest possible model i e spherical particles with a linear spring and a linear dashpot active on contact and without any frictional forces our model is able to reproduce several recent theoretical predictions for different boundary conditions we examine the contact network and the stresses in the array and at the bottom of the pile in some cases we observe a dip i e the relative minimum in pressure under the center of the pile we connect the dip to arching and we relate arching to the structure of the contact network finally we find that small polydispersity is sufficient to cause a so called stress network i e strong fluctuations in stress from these data we determine the probability distribution for the vertical stress at the bottom and relate it to theoretical and other numerical work

anomalous force diffusion in nearly ordered packings of frictionless discs we derive analytic expressions for force propagation in packings of frictionless discs with a narrow distribution of disc sizes by expanding to first order about the known ordered solution the distribution of contact forces p f is found to be narrow at the upper surface and broadens at a rate that varies with depth being superdiffusive near the surface until crossing over to a subdiffusive regime near the fixed base furthermore the response to an isolated load propagates along the edge of a cone as in the ordered case but fluctuates under ensemble averaging by an amount that depends purely on height not on the lateral position finally we comment on ways in which the analytical framework presented here could be extended to a wider range of granular packings

stress propagation in sand abstract we describe a new continuum approach to the modelling of stress propagation in static granular media focussing on the conical sandpile created from a point source we argue that the stress continuity equations should be closed by means of scale free local constitutive relations between different components of the stress tensor encoding the construction history of the pile this history determines the organization of the grains and thereby the local relationship between stresses our preferred model fixed principle axes fpa assumes that the eigendirections but not the eigenvalues of the stress tensor are determined forever when a material element is first buried stresses propagate along a nested set of arch like structures within the medium the results are in good quantitative agreement with published experimental data the fpa model is one of a larger class called oriented stress linearity osl models in which the direction of the characteristics for stress propagation are fixed at burial we speculate on the connection between these characteristics and the stress paths observed microscopically

distribution of repetitions of ancestors in genealogical trees we calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non overlapping generations each ancestor at generation g in the past has a weight w which is up to a normalization the number of times this ancestor appears in the genealogical tree of an individual at present the distribution pg w of these weights reaches a stationary shape p1 w for large g i e for a large number of generations back in the past for small w p1 w is a power law p1 w w with a non trivial exponent which can be computed exactly using a standard procedure of the renormalization group approach some extensions of the model are discussed and the eect of these variants on the shape of p1 w are analysed c 2000 elsevier science b v all rights reserved

on the robustness of the adaptive lasso to model misspecification penalization methods have been shown to yield both consistent variable selection and oracle parameter estimation under correct model specification in this article we study such methods under model misspecification where the assumed form of the regression function is incorrect including generalized linear models for uncensored outcomes and the proportional hazards model for censored responses estimation with the adaptive least absolute shrinkage and selection operator lasso penalty is proven to achieve sparse estimation of regression coefficients under misspecification the resulting estimators are selection consistent asymptotically normal and oracle where the selection is based on the limiting values of the parameter estimators obtained using the misspecified model without penalization we further derive conditions under which the penalized estimators from the misspecified model may yield selection consistency under the true model the robustness is explored numerically via simulation and an application to the wisconsin epidemiological study of diabetic retinopathy

an exactly solvable dissipative transport model we introduce a class of one dimensional lattice models in which a quantity which may be thought of as an energy is either transported from one site to a neighbouring one or locally dissipated transport is controlled by a continuous bias parameter q which allows us to study symmetric as well as asymmetric cases we derive sufficient conditions for the factorization of the n body stationary distribution and give an explicit solution for the latter before briefly discussing physically relevant situations

stress in frictionless granular material adaptive network simulations we present a minimalistic approach to simulations of force transmission through granular systems we start from a configuration containing cohesive tensile contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces the procedure works by sequentially removing and adding individual contacts between adjacent beads while the bead positions are not modified in a series of two dimensional realizations the resulting force networks are shown to satisfy a linear constraint among the three components of average stress as anticipated by recent theories the coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about 0 6 of the normal loading the spatial distribution of contact forces shows strong concentration along force chains the probability of contact forces of magnitude f shows an exponential falloff with f the response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally

on distribution of contact forces in random granular packings abstract in an earlier paper ngan phys rev e 68 2003 011301 proposed a statistical mechanics based theory to predict the mathematical form of the probability force distribution of contact forces in stressed granular packings however the wrong choice of the mean force constraint in that work leads to unsatisfactory prediction in the 3d situation although the 2d prediction is very accurate the present work shows that a different mean strain constraint chosen for the force distribution can yield the correct prediction when compared to computer simulation results in both 2d and 3d furthermore new simulation results are used to verify the interpretation that the shape of the force distribution measured by a parameter in the predicted force distribution is a structure sensitive term

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

spatial correlations in polydisperse frictionless two dimensional packings we investigate next nearest neighbor correlations of the contact number in simulations of polydisperse frictionless packings in two dimensions we find that disks with few contacting neighbors are predominantly in contact with disks that have many neighbors and vice versa at all packing fractions this counterintuitive result can be explained by drawing a direct analogy to the aboav weaire law in cellular structures we find an empirical one parameter relation similar to the aboav weaire law that satisfies an exact sum rule constraint surprisingly there are no correlations in the radii between neighboring particles despite correlations between contact number and radius

memory in two dimensional heap experiments the measurement of force distributions in sandpiles provides a useful way to test concepts and models of the way forces propagate within noncohesive granular materials recent theory j p bouchaud m e cates and p claudin j phys i 5 639 1995 m e cates j p wittmer j p bouchaud and p claudin phil trans roy soc 356 2535 1998 by bouchaud et al implies that the internal structure of a heap and therefore the force pathway is a strong function of the construction history in general it is difficult to obtain information that could test this idea from three dimensional granular experiments except at boundaries however two dimensional systems such as those used here can yield information on forces and particle arrangements in the interior of a sample we obtain position and force information through the use of photoelastic particles these experiments show that the history of the heap formation has a dramatic effect on the arrangement of particles texture and a weaker but clear effect on the forces within the sample specifically heaps prepared by pouring from a point source show strong anisotropy in the contact angle distribution depending on additional details they show a stress dip near the center heaps formed from a broad source show relatively little contact angle anisotropy and no indication of a stress dip

an rkhs approach to robust l sup 2 estimation and signal detection the application of rkhs reproducing kernel hilbert space theory to the problems of robust signal detection and estimation is investigated it is shown that this approach provides a general and unified framework in which to analyze the problems of l sup 2 estimation matched filtering and quadratic detection in the presence of uncertainties regarding the second order structure of the random processes involved

asymptotic behavior of a stationary silo with absorbing walls we study the nearest neighbors one dimensional uniform q model of force fluctuations in bead packs 1 a stochastic model to simulate the stress of granular media in two dimensional silos the vertical coordinate plays the role of time and the horizontal coordinate the role of space the process is a discrete time markov process with state space 1 n at each layer time the weight supported by each grain is a random variable of mean one its own weight plus the sum of random fractions of the weights supported by the nearest neighboring grains at the previous layer the fraction of the weight given to the right neighbor of the successive layer is a uniform random variable in 0 1 independent of everything the remaining weight is given to the left neighbor in the boundaries a uniform fraction of the weight leans on the wall of the silo this corresponds to absorbing boundary conditions for this model we show that there exists a unique invariant measure the mean weight at site i under the invariant measure is i n 1 i we prove that its variance is frac 1 2 i n 1 i 2 o n3 and the covariances between grains i j are of order o n3 moreover as n the law under the invariant measure of the weights divided by n2 around site integer part of rn r 0 1 converges to a product of gamma distributions with parameters 2 and 2 r 1 r 1 sum of two exponentials of mean r 1 r 2 liu et al 2 proved that for a silo with infinitely many weightless grains any product of gamma distributions with parameters 2 and 2 with 0 are invariant our result shows that as the silo grows the model selects exactly one of these gamma s at each macroscopic place

on robust wiener signal estimation a minimax formulation is considered for the problem of designing robust linear causal estimators of continuous time signals in noise it is shown that the minimax estimation problem can generally be reduced to finding a least favorable pair of spectra in particular robust predictors filters and finite lag smoothers are shown to be just the optimal predictors filters and smoothers respectively for a least favorable pair this result can often greatly simplify the design of robust estimators

bootstrapping lasso estimators in this article we consider bootstrapping the lasso estimator of the regression parameter in a multiple linear regression model it is known that the standard bootstrap method fails to be consistent here we propose a modified bootstrap method and show that it provides valid approximation to the distribution of the lasso estimator for all possible values of the unknown regression parameter vector including the case where some of the components are zero further we establish consistency of the modified bootstrap method for estimating the asymptotic bias and variance of the lasso estimator we also show that the residual bootstrap can be used to consistently estimate the distribution and variance of the adaptive lasso estimator using the former result we formulate a novel data based method for choosing the optimal penalizing parameter for the lasso using the modified bootstrap a numerical study is performed to investigate the finite sample performance of the modified bootstrap the methodology prop

statistical properties of genealogical trees we analyze the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and nonoverlapping generations by reconstructing the genealogy of an individual from the population evolution we measure the distribution of ancestors appearing more than once in a given tree after a transient time the probability of repetition follows up to a rescaling a stationary distribution which we calculate both numerically and analytically this distribution exhibits a universal shape with a nontrivial power law which can be understood by an exact though simple renormalization calculation some real data on human genealogy illustrate the problem which is relevant to the study of the real degree of diversity in closed interbreeding communities

average stresses and force fluctuations in noncohesive granular materials a lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress the model is similar in spirit to the scalar q model of coppersmith et al phys rev e 53 4673 1996 but ensures balance of all components of forces and torques at each site the geometric randomness in real granular materials is modeled by choosing random variables at each site consistent with the assumption of cohesionless grains configurations of the model can be generated rapidly allowing the statistical study of relatively large systems for a two dimensional 2d system with rough walls the model generates configurations consistent with continuum theories for the average stresses unlike the q model without requiring the assumption of a constitutive relation for a 2d system with periodic boundary conditions the model generates single grain force distributions similar to those obtained from the q model with a singular distribution of q s

scheidegger s rivers takayasu s aggregates and continued fractions abstract a discrete model of 1 1 dimensional aggregation equivalent to scheidegger s 1967 river model is tackled with continued fractions an exact expression for the power law distribution of aggregate masses is found

factorized steady states in mass transport models on an arbitrary graph we study a general mass transport model on an arbitrary graph consisting of l nodes each carrying a continuous mass the graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass chosen from a site dependent distribution is transported between the nodes at each time step the dynamics conserves the total mass and the system eventually reaches a steady state this general model includes as special cases various previously studied models such as the zero range process and the asymmetric random average process we derive a general condition on the stochastic mass transport rules valid for arbitrary graph and for both parallel and random sequential dynamics that is sufficient to guarantee that the steady state is factorizable we demonstrate how this condition can be achieved in several examples we show that our generalized result contains as a special case the recent results derived by greenblatt and lebowitz for d dimensional hypercubic lattices with random sequential dynamics

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

mechanical analog of temperature for the description of force distribution in static granular packings it is shown that in a stressed granular packing the effect of the applied pressure and structural randomness on the contact force distribution can be described accurately by a variational principle of minimizing energy subject to the constraint of keeping entropy at a fixed value the constraint on entropy may be regarded as a measure of the degree of retained disorderness in the system this procedure leads to the introduction of a parameter known as the mechanical temperature similar to the role of the conventional thermal temperature in a thermal system the mechanical temperature can be viewed as a parameter controlling the mixity between energy minimization and entropy maximization in the equilibrium condition

the compaction of aggregates of non spherical linear viscous particles an approximate discrete element model is used to study the compaction of aggregates of non spherical linear viscous particles the numerical model is developed in which each particle is treated individually with the appropriate constitutive relations kinematic conditions contact constraints and elimination of overlap satisfied for every particle in the aggregate mesh update algorithms are generated based on mixed triangular and quadrilateral element system the algorithms are used to detect contact generate mesh modify concave elements and prevent locking the method could be used in a variety of problems that can be represented using granular media such as asphalt polymers aluminum snow food product and others a series of numerical simulations are shown to demonstrate the efficiency and accuracy of the model

statistics of the elastic behaviour of granular materials the elastic behaviour of isotropic assemblies of granular materials consisting of two dimensional bonded and non rotating particles is studied from the micromechanical viewpoint discrete element simulations have been performed of assemblies of 50 000 particles with various coordination numbers average number of contacts per particle and various ratios of tangential to normal stiffness statistics such as mean standard deviation and probability distribution function have been computed for geometrical quantities and contact displacements under compressive and shearing loading a linear relation is observed between the average number of contacts of a particle and its circumference average displacements do not conform to generalised uniform strain as is often assumed the probability density functions for normal and tangential displacements are nearly gaussian none of the considered energies satisfy an equipartition of energy between normal and tangential modes

fractional diffusion model for force distribution in static granular media we present the results of a numerical and an experimental investigation of the probability distribution of normal contact forces in static packs of particles with two different hardnesses force distributions are computed and compared with existing models and experimental data it is found that the probability distribution function of normal contact forces p f is well described by a semiempirical model derived from a fractional diffusion equation this model reproduces most of the features common to force distributions observed in experimental and numerical studies including the finite value for p f as the forces tend to zero the results indicate that the fractional model fits well both the numerical and experimental data over a wide range of particle deformations in contrast to the existing models these results provide an insight into the physics of granular media and complement previous findings

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

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

exact tracer diffusion coefficient in the asymmetric random average process we study tracer diffusion in the continuous time asymmetric random average process which is an interacting particle system on generalizing the hammersley process from the equations of motion for the particle position correlations we obtain the exact tracer diffusion coefficient which is in agreement with a recent heuristic result by krug and garcia

the stress transmission universality classes of periodic granular arrays the transmission of stress is analysed for static periodic arrays of rigid grains with perfect and zero friction for minimal coordination number which is sensitive to friction sphericity and dimensionality the stress distribution is soluble without reference to the corresponding displacement fields in non degenerate cases the constitutive equations are found to be simple linear in the stress components the corresponding coefficients depend crucially upon geometrical disorder of the grain contacts

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

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

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

heterogeneity of colloidal particle networks analyzed by means of minkowski functionals the heterogeneity and large scale connectivity of colloidal particle networks which are generated by brownian dynamics simulations is examined this is achieved by employing integral geometric measures in the form of the minkowski functionals or quermassintegrals it is found that these measures in conjunction with the parallel body technique amount to a powerful tool to characterize the structure going beyond the information contained in the pair correlation function the development of heterogeneities during network formation as well as their dependence on the volume fraction and the interaction potential is studied in particular it is found that slow coagulation enhances the heterogeneity of the network compared to fast coagulation

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

a solution of the filtering and smoothing problems for uncertain stochastic linear dynamic systems the authors present new filtering algorithms for uncertain stochastic dynamic systems which are optimal in the sense of a minimax stochastic criterion these algorithms allow us to estimate the state vector of dynamic systems given incomplete a priori information about the system characteristics and using observations of the state and input signals the filtering algorithm is used to construct an optimal two filter smoothing algorithm for pure uncertain dynamic systems these algorithms are numerically tested results are compared with the results of kalman filtering and smoothing in the case of complete information about the input signal characteristics

memories in sand experimental tests of construction history on stress distributions under sandpiles we report experiments on piles of cohesionless granular materials showing the effect of construction history on static stress distributions stresses under piles are monitored by sensitive capacitive techniques the piles are formed either by pouring granular material from a funnel with a small outlet localized source or from a large sieve homogeneous rain localized sources yield stress profiles with a clear stress dip near the center of the pile the homogeneous rain profiles have no stress dip we show that the stress profiles scale linearly with the pile height experiments on wedge shaped piles show similar but weaker effects

force density function relationships in 2 d granular media an integral transform relationship is developed to convert between two important probability density functions distributions used in the study of contact forces in granular physics developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the cartesian probability density and another the force magnitude probability density also the transforms identify which functional forms are relevant to describing the probability density observed in nature and so the modified bessel function of the second kind has been identified as the relevant form for the cartesian probability density corresponding to exponential forms in the force magnitude distribution furthermore it is shown that this transform pair supplies a mathematical framework sufficient for describing the evolution of the force magnitude distribution under shearing apart from the choice of several coefficients whose