central limit theorems for infinite series of queues and applications to simple exclusion we prove that a tagged particle in asymmetric simple exclusion satisfies a central limit theorem when properly rescaled to obtain this result we derive several results of positive or negative correlation for occupation times of a server in a series of queues which imply various central limit theorems

nonequilibrium phase transition in a non integrable zero range process the present work is an endeavour to determine analytically features of the stationary measure of a non integrable zero range process and to investigate the possible existence of phase transitions for such a nonequilibrium model the rates defining the model do not satisfy the constraints necessary for the stationary measure to be a product measure even in the absence of a drive detailed balance with respect to this measure is violated analytical and numerical investigations on the complete graph demonstrate the existence of a first order phase transition between a fluid phase and a condensed phase where a single site has macroscopic occupation the transition is sudden from an imbalanced fluid where both species have densities larger than the critical density to a critical neutral fluid and an imbalanced condensate

a stochastic burgers equation from a class of microscopic interactions we consider a class of nearest neighbor weakly asymmetric mass conservative particle systems evolving on mathbb z which includes zero range and types of exclusion processes starting from a perturbation of a stationary state when the weak asymmetry is of order o n gamma for 1 2 gamma leq1 we show that the scaling limit of the fluctuation field as seen across process characteristics is a generalized ornstein uhlenbeck process however at the critical weak asymmetry when gamma 1 2 we show that all limit points satisfy a martingale formulation which may be interpreted in terms of a stochastic burgers equation derived from taking the gradient of the kpz equation the proofs make use of a sharp boltzmann gibbs estimate which improves on earlier bounds

nonequilibrium fluctuations for a tagged particle in mean zero one dimensional zero range processes we prove a non equilibrium functional central limit theorem for the position of a tagged particle in mean zero one dimensional zero range process the asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation

diffraction of elastic waves by a penny shaped crack consider an infinite elastic solid containing a penny shaped crack we suppose that time harmonic elastic waves are incident on the crack and are required to determine the scattered displacement field u i in this paper we describe a new method for solving the corresponding linear boundary value problem for u i which we denote by s we begin by defining an elastic double layer we prove that any solution of s can be represented by an elastic double layer whose density satisfies certain conditions we then introduce various green functions and define a new crack green function g ij that is discontinuous across the crack next we use g ij to derive a fredholm integral equation of the second kind for the discontinuity in u i across the crack we prove that this equation always has a unique solution hence we are able to prove that the original boundary value problem s always possesses a unique solution and that this solution has an integral representation as an elastic double layer whose density solves an integral equation of the second kind

random walk of second class particles in product shock measures we consider shock measures in a class of conserving stochastic particle systems on these shock measures have a product structure with a step like density profile and include a second class particle at the shock position we show for the asymmetric simple exclusion process for the exponential bricklayers process and for a generalized zero range process that under certain conditions these shocks and therefore the second class particles perform a simple random walk some previous results including random walks of product shock measures and stationary shock measures seen from a second class particle are direct consequences of our more general theorem multiple shocks can also be handled easily in this framework similar shock structure is also found in a nonconserving model the branching coalescing random walk where the role of the second class particle is played by the rightmost or leftmost particle

hydrodynamical limit for spatially heterogeneous simple exclusion processes we prove hydrodynamical limit for spatially heterogeneous asymmetric simple exclusion processes on z d the jump rate of particles depends on the macroscopic position x through some nonnegative smooth velocity profile x hydrodynamics are described by the entropy solution to a spatially heterogeneous conservation law of the form

guaranteed convergence method of analysis of the scattering by an arbitrarily oriented zero thickness pec disk buried in a lossy half space in this paper a guaranteed convergence method for the accurate and efficient analysis of the electromagnetic scattering by an arbitrarily oriented zero thickness perfectly electrically conducting pec disk buried in a lossy half space is presented an electric field integral equation efie in the vector hankel transform domain is obtained by expanding the unknown surface current density in cylindrical harmonics a convergence of exponential type is achieved by means of galerkin s method with expansion functions reconstructing the expected physical behavior of the bm n th harmonic at the center and the edge of the disk the obtained coefficient matrix can be quickly computed since its elements can be reviewed as the sum of single integrals efficiently evaluable by means of an analytical acceleration technique and double integrals of exponentially decaying functions

hitting times for independent random walks on ℤd we consider a system of asymmetric independent random walks on z d denoted by t t e r stationary under the product poisson measure v p of marginal density p 0 we fix a pattern a an increasing local event and denote by the hitting time of a by using a loss network representation of our system at small density we obtain a coupling between the laws of t conditioned on r t for all times t when d 3 this provides bounds on the rate of convergence of the law of t conditioned on r t toward its limiting probability measure as t tends to infinity we also treat the case where the initial measure is close to v without being product

fluctuations for stationary q tasep we consider the q totally asymmetric simple exclusion process q tasep in the stationary regime and study the fluctuation of the position of a particle we first observe that the problem can be studied as a limiting case of an n particle q tasep with a random initial condition and with particle dependent hopping rate then we explain how this n particle q tasep can be encoded in a dynamics on a two sided gelfand tsetlin cone described by a two sided q whittaker process and present a fredholm determinant formula for the q laplace transform of the position of a particle two main ingredients in its derivation is the ramanujan s bilateral summation formula and the cauchy determinant identity for the theta function with an extra parameter based on this we establish that the position of a particle obeys the universal stationary kpz distribution the baik rains distribution in the long time limit

quenched convergence and strong local equilibrium for asymmetric zero range process with site disorder we study asymmetric zero range processes on z with nearest neighbour jumps and site disorder the jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles we prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities and dynamic local loss of mass at supercritical hydrodynamic densities our results do not assume starting from local gibbs states as byproducts of these results we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin in particular we relax the weak convexity assumption of 7 8 for the escape of mass property 1 msc 2010 subject classification 60k35 82c22

on the solutions of a class of dual integral equations occurring in diffraction problems it is shown that there exists a category of two dimensional diffraction problems which can be put into a standard form of dual integral equations these diffraction problems include diffraction of electromagnetic waves by a finite strip a finite slit the diffraction of scalar or vector elastic waves by a rigid strip or crack etc a general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions the sufficient conditions for a given dual integral equations to be solvable in this manner are also determined hence the method forms a complement to the weiner hopf method to illustrate the method solutions are obtained for a bench mark problem the diffraction of light by a finite perfectly conducting strip or equivalently the diffraction of sh waves by a crack comparison with results obtained by others for low intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies both the near field and the far field are obtained the latter is shown to correspond to the fraunhoffer diffraction pattern for high frequency it is also shown that for the equivalent crack problem the stress intensity factor sif fluctuates rapidly with changes in the angle of incidence for high frequencies thus making the sif especially sensitive to angle of incidence at high frequencies

lower current large deviations for zero range processes on a ring we study lower large deviations for the current of totally asymmetric zero range processes on a ring with concave current density relation we use an approach by jensen and varadhan which has previously been applied to exclusion processes to realize current fluctuations by travelling wave density profiles corresponding to non entropic weak solutions of the hyperbolic scaling limit of the process we further establish a dynamic transition where large deviations of the current below a certain value are no longer typically attained by non entropic weak solutions but by condensed profiles where a non zero fraction of all the particles accumulates on a single fixed lattice site this leads to a general characterization of the rate function which is illustrated by providing detailed results for four generic examples of jump rates including constant rates decreasing rates unbounded sublinear rates and asymptotically linear rates our results on the dynamic transition are supported by numerical simulations using a cloning algorithm

on the 162 8 80 codes constructions of 162 8 80 and 159 8 78 codes are given this solves the open problems of finding the minimum length of binary codes of dimension s and minimum distances 78 and 80 respectively

matrix product representation of the stationary state of the open zero range process many one dimensional lattice particle models with open boundaries like the paradigmatic asymmetric simple exclusion process asep have their stationary states represented in the form of a matrix product with matrices that do not explicitly depend on the lattice site in contrast the stationary state of the open 1d zero range process zrp takes an inhomogeneous factorized form with site dependent probability weights we show that in spite of the absence of correlations the stationary state of the open zrp can also be represented in a matrix product form where the matrices are site independent non commuting and determined from algebraic relations resulting from the master equation we recover the known distribution of the open zrp in two different ways first using an explicit representation of the matrices and boundary vectors second from the sole knowledge of the algebraic relations satisfied by these matrices and vectors finally an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden markov chains

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

microscopic shape of shocks in a domain growth model considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities e g the inviscid burgers equation for the simple exclusion process the physical solutions of these partial differential equations develop discontinuities called shocks the microscopic structure of these shocks is of much interest and far from being well understood we introduce a domain growth model in which we find a stationary in time product measure for the model as seen from a defect tracer or second class particle traveling with the shock we also show that under some natural assumptions valid for a wider class of domain growth models no other model has stationary product measure as seen from the moving defect tracer

microscopic position and structure of a shock in ca 184 we consider the time evolution of the cellular automaton ca 184 with random initial conditions we derive a partial differential equation that describes the macroscopic time evolution of the coarse grained local density and we study some solutions of this equation in particular shock solutions and rarefaction type solutions for initial step profiles in order to elucidate the emergence of the large scale hydrodynamic behaviour we define a microscopic position of a shock and find its mean velocity its diffusion coefficient and the microscopic structure of the shock as seen from this position

tm scattering by perfectly conducting polygonal cross section cylinders a new surface current density expansion retaining up to the second order edge behavior in the analysis of scattering by perfectly conducting cylinders with polygonal cross section by means of surface integral operator formulations fast convergence can be achieved by expanding the surface current density on each side with basis functions factorizing the correct behavior of the fields on the wedges usually the factorized edge behavior is chosen to be coincident with the first order behavior prescribed by meixner s theory however it could not be the correct one and consequently the convergence of the method becomes increasingly slow as the theoretical behavior differs from the real one this phenomenon is particularly notable when one or more of the predicted singularities unexpectedly disappear to overcome this problem in this work the analysis of tm scattering is made by introducing a new expansion devised so that only the first two terms are responsible for the reconstruction of the singularities while the remaining part of the expansion factorizes the second order edge behavior actually the proposed expansion outperforms the one introduced by the authors in a previous work factorizing the first order edge behavior even when this is the correct one

euler hydrodynamics of one dimensional attractive particle systems we consider attractive irreducible conservative particle systems on z without necessarily nearest neighbor jumps or explicit invariant measures we prove that for such systems the hydrodynamic limit under euler time scaling exists and is given by the entropy solution to some scalar conservation law with lipschitz continuous flux our approach is a generalization of bahadoran et al stochastic process appl 99 2002 1 30 from which we relax the assumption that the process has explicit invariant measures

on a 145 32 binary cyclic code we discovered that a 145 32 binary cyclic code generated by the product of an irreducible polynomial of degree 28 with exponent 145 and the polynomial x sup 4 x sup 3 x sup 2 x 1 has a minimum distance of 44

some new results on the minimum length of binary linear codes of dimension nine let n k d be the smallest integer n for which a binary linear code of length n dimension k and minimum distance d exists using the residual code technique the macwilliams identities and the weight distribution of appropriate reed muller codes we prove that n 9 64 133 n 9 120 spl ges 244 n 9 124 252 and n 9 184 371 we also show that puncturing a known 322 9 160 code yields length optimal codes with parameters 319 9 158 315 9 156 and 312 9 154

hydrodynamic limit for particle systems with nonconstant speed parameter we establish the hydrodynamic limit for a class of particle systems on d with nonconstant speed parameter assuming that the speed parameter is continuously differentiable in the spatial variable if the particle system is on the one dimensional lattice and totally asymmetric we derive the hydrodynamic equation for continuous speed parameters we obtain nontrivial upper and lower bounds when either the speed parameter is discontinuous or there is a blockage at a fixed site

te scattering by arbitrarily connected conducting strips the scattering by an arbitrary collection of perfectly conducting connected strips is analyzed for te incidence the studied configurations include both closed and open polygonal cross section cylinders as well as more complicated structures in which more than two strips are connected at a point the proposed method is very efficient as few expansion functions are needed in a galerkin scheme this is achieved by means of expansion functions factorizing the correct edge singularity of the electromagnetic field and ensuring the continuity of the current at connecting points

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

scattering by polygonal cross section dielectric cylinders at oblique incidence we analyze the scattering by polygonal cross section lossless dielectric cylinders illuminated by an obliquely incident plane wave the problem is formulated in terms of a system of surface integral equations opportunely devised so as to be valid for objects with edges and incident angles including the total reflection limit angle by means of galerkin s method in the spectral domain with analytically fourier transformable expansion functions factorizing the correct edge behaviors and continuity conditions of the unknowns convergence of exponential type is achieved and the coefficients of the scattering matrix are reduced to single integrals that can be efficiently evaluated numerical results for both near field and far field parameters are presented showing the quick convergence of the method even when applied to composite cylindrical objects

on the dirichlet problem for asymmetric zero range process on increasing domains in order to obtain hitting time estimates for the asymmetric zero range process azrp on d in dimensions d 3 we characterize the principal eigenvalue of the generator of the azrp with dirichlet boundary on special domains we obtain a donsker varadhan variational representation and show that the corresponding eigenfunction is unique in a natural class of functions

multiple shocks in bricklayers model in bricklayers model which is a generalization of the misanthrope processes we show that a nontrivial class of product distributions is closed under the time evolution of the process this class also includes measures fitting to shock data of the limiting pde in particular we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting in an attractive way via their jump rates our results are related to those of belitsky and schutz 4 on the simple exclusion process although we do not use quantum formalism as they do the structures we find are described from a fixed position similar ones were found in balazs 2 valak as seen from the random position of the second class particle

hydrodynamical limit for space inhomogeneous one dimensional totally asymmetric zero range processes we consider totally asymmetric attractive zero range processes with bounded jump rates on z in order to obtain a lower bound for the large deviations from the hydrodynamical limit of the empirical measure we perturb the process in two ways we first choose a finite number of sites and slow down the jump rate at these sites we prove a hydrodynamical limit for this perturbed process and show the appearance of dirac measures on the sites where the rates are slowed down the second type of perturbation consists of choosing a finite number of particles and making them jump at a slower rate in these cases the hydrodynamical limit is described by nonentropy weak solutions of quasilinear first order hyperbolic equations these two results prove that the large deviations for asymmetric processes with bounded jump rates are of order at least e cn all these results can be translated to the context of totally asymmetric simple exclusion processes where a finite number of particles or a finite number of holes jump at a slower rate

cluster growth and dynamic scaling in a two lane driven diffusive system using high precision monte carlo simulations and a mean field theory we explore coarsening phenomena in a simple driven diffusive system the model is reminiscent of vehicular traffic on a two lane ring road at sufficiently high density the system develops jams clusters which coarsen with time a key parameter is the passing probability for small values of the growing clusters display dynamic scaling with a growth exponent of 2 3 for larger values of the growth exponent must be adjusted suggesting the ordered jammed state is not a genuine phase but rather a finite size effect

time domain boundary element analysis of elastic wave interaction with a crack the mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous isotropic linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face the integral equation relates the unknown crack opening displacement which depends on time and position to the incident wave field the integral equation has been solved numerically by a time stepping method in conjunction with a boundary element discretization of the crack surface for normal incidence of a longitudinal step stress wave on a penny shaped crack results as functions of time have been obtained for the crack opening displacement the elastodynamic mode i stress intensity factor and the scattered far field

derivation of the hydrodynamical equation for the zero range interaction process small volume is so large compared with the distances between molecules that it contains an infinite number of them which are in equilibrium with given characteristics density temperature of course these parameters vary with x say p x t x if we look at the system after a time t the system will be still locally in equilibrium with other local characteristics p x t t x t varying slowly in time although each particle individually moves very rapidly we want to derive the equation of evolution of these macroscopical parameters however it is surprising that this derivation is almost never based on the analysis of the movement of the particles but rather on conservation laws the limiting procedure that we describe below has been used by various authors 2 8 in efforts to give rigorous treatment of the program alluded to above consider a system of infinitely many particles in rd or xd moving according

new constructions of codes meeting the griesmer bound for any binary linear n k d code the grfesmer bound says that n geq sum i 0 k 1 lceil d 2 i rceil we investigate codes that meet this bound with equality we give new descriptions of sum i 0 k 1 lceil d 2 i rceil k d codes that have earlier been constructed by solomon and stiffler belov and helleseth and van tilborg finally we show how to construct several new families of such codes with parameters not obtainable by any previous known constructions

asymptotic results on infinite tandem queueing networks we consider an infinite tandem queueing network consisting of gi 1 stations with i i d service times we investigate the asymptotic behavior of t n k the inter arrival times between customers n and n 1 at station k and that of w n k the waiting time of customer n at station k we establish a duality property by which w n k and the idle times y n k play symmetrical roles this duality structure interesting by itself is also instrumental in proving some of the ergodic results we consider two versions of the model the quadrant and the half plane in the quadrant version the sequences of boundary conditions w 0 k k and t n 0 n are given in the half plane version the sequence t n 0 n is given under appropriate assumptions on the boundary conditions and on the services we obtain ergodic results for both versions of the model for the quadrant version we prove the existence of temporally ergodic evolutions and of spatially ergodic ones furthermore the process t n k n converges weakly with k to a limiting distribution which is invariant for the queueing operator in the more difficult half plane problem the aim is to obtain evolutions which are both temporally and spatially ergodic we prove that 1 n k 1 nw 0 k converges almost surely and in l1 to a finite constant this constitutes a first step in trying to prove that t n k n converges weakly with k to an invariant limiting distribution

spectral gap for zero range dynamics we give a lower bound on the spectral gap for symmetric zero range processes under some conditions on the rate function we show that the gap shrinks as n 2 independent of the density for the dynamics localized on a cube of size n d we follow the method outlined by lu and yau where a similar spectral gap is proved for kawasaki dynamics

how to initialize a second class particle we identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior respectively including zero range misanthrope and many other models the initial condition is a step profile which in some classical cases of asymmetric models gives rise to a rarefaction fan scenario we also point out a model with nonconcave nonconvex hydrodynamics where the rescaled second class particle distribution has both continuous and discrete counterparts the results follow from a substantial generalization of ferrari and kipnis arguments ann inst h poincare 31 1995 143 154 for the totally asymmetric simple exclusion process the main novelty is the introduction of a signed coupling measure as initial data which nevertheless results in a proper probability initial distribution for the site of the second class particle and makes the extension possible we also reveal in full generality a very interesting invariance property of the one site marginal distribution of the process underneath the second class particle which in particular proves the intrinsicality of our choice for the initial distribution finally we give a lower estimate on the probability of survival of a second class particle antiparticle pair

discontinuous condensation transition and nonequivalence of ensembles in a zero range process we study a zero range process where the jump rates do not only depend on the local particle configuration but also on the size of the system rigorous results on the equivalence of ensembles are presented characterizing the occurrence of a condensation transition in contrast to previous results the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases this leads to a richer phase diagram including nonequivalence of ensembles in certain phase regions the paper is motivated by results from granular clustering where these features have been observed experimentally

a remark on the hydrodynamics of the zero range processes the nonequilibrium stationary hydrodynamical properties of the symmetric nearest neighbor zero range processes are studied local equilibrium and fourier s law are proven to hold and the bulk diffusion coefficient and the equal time covariance of the limiting nonequilibrium stationary density fluctuations field are computed the result fits with those already known and confirms some conjectures derived from a time dependent macroscopic analysis the very simple proof is based on a result already published but may be not so well known in this context

a central limit theorem for reversible exclusion and zero range particle systems we give easily verifiable conditions under which a functional central limit theorem holds for additive functionals of symmetric simple exclusion and symmetric zero range processes also a reversible exclusion model with speed change is considered let t be the configuration of the process at time t and let f be a function on the state space the question is for which functions f does l 2 0 t f s ds converge to a brownian motion a general but often intractable answer is given by kipnis and varadhan in this article we determine what conditions beyond a mean zero condition on f are required for the diffusive limit above specifically we characterize the h l space in an applicable way our method of proof relies primarily on a sharp estimate on the spectral gap of the process and weak regularity properties for the invariant measures

the initial drift of a 2d droplet at zero temperature we consider the 2d stochastic ising model evolving according to the glauber dynamics at zero temperature we compute the initial drift for droplets which are suitable approximations of smooth domains a specific spatial average of the derivative at time 0 of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient we compute the explicit value of this coefficient

existence of the zero range process and a deposition model with superlinear growth rates we give a construction of the zero range and bricklayers processes in the totally asymmetric attractive case the novelty is that we allow jump rates to grow exponentially earlier constructions have permitted at most linearly growing rates we also show the invariance and extremality of a natural family of i i d product measures indexed by particle density extremality is proved with an approach that is simpler than existing ergodicity proofs

large deviations of interacting particle systems in infinite volume we prove a large deviation theorem from the hydrodynamical limit for the empirical measure of ginzburg landau and zero range processes in infinite volume starting from deterministic initial configurations in the ginzburg landau case the main tool is the study of the evolution of the h 1 norm and in the zero range case the attractiveness which allows couplings

invariant measures for a two species asymmetric process we consider a process of two classes of particles jumping on a one dimensional lattice the marginal system of the first class of particles is the one dimensional totally asymmetric simple exclusion process when classes are disregarded the process is also the totally asymmetric simple exclusion process the existence of a unique invariant measure with product marginals with density and for the first and first plus second class particles respectively was shown by ferrari kipnis and saada recently derrida janowsky lebowitz and speer have computed this invariant measure for finite boxes and performed the infinite volume limit based on this computation we give a complete description of the measure and derive some of its properties in particular we show that the invariant measure for the simple exclusion process as seen from a second class particle with asymptotic densities and is equivalent to the product measure with densities to the left of the origin and to the right of the origin

a new method of solution of hallen s problem a wide class of electromagnetic scattering problems can be expressed as a system of dual integral equations this kind of integral equation occurring in boundary value problems wherein there is one equation for a certain region and another for the dual domain is usual in diffraction problems considerable attention has been drawn by many researchers in the field of optics acoustics scattering of elastic waves accelerator physics and antenna theory wiener hopf techniques enable us to solve such kinds of integral equations when the two regions are contiguous and semi infinite unfortunately wiener hopf techniques do not apply if one of the regions is finite this is the case for realistic scatterers such as irises antennas and drift tubes in accelerators in this article a general method for solving such dual integral equations is discussed and applied to a particular case hallen s equation of cylindrical antennas this method consists of a transformation of the dual integral equations into a fre

boundary driven zero range processes in random media the stationary states of boundary driven zero range processes in random media with quenched disorder are examined and the motion of a tagged particle is analyzed for symmetric transition rates also known as the random barrier model the stationary state is found to be trivial in absence of boundary drive out of equilibrium two further cases are distinguished according to the tail of the disorder distribution for strong disorder the fugacity profiles are found to be governed by the paths of normalized stable subordinators the expectations of integrated functions of the tagged particle position are calculated for three types of routes

optimal linear codes of dimension 4 over f sub 5 let n sub q k d be the smallest integer n for which there exists a linear code of length n dimension k and minimum distance d over a field of q elements in this correspondence we determine n sub 5 4 d for all but 22 values of d

optimum codes of dimension 3 and 4 over gf 4 n sub q k d the length of a q ary optimum code for given k and d for q 4 and k 3 4 is discussed the problem is completely solved for k 3 and the exact value of n sub 4 4 d is determined for all but 52 values of d

hydrodynamics and hydrostatics for a class of asymmetric particle systems with open boundaries we consider attractive particle systems in mathbb z d with product invariant measures we prove that when particles are restricted to a subset of mathbb z d with birth and death dynamics at the boundaries the hydrodynamic limit is given by the unique entropy solution of a conservation law with boundary conditions in the sense of bardos et al comm part diff equ 4 1017 1034 1979 for the hydrostatic limit between parallel hyperplanes we prove a multidimensional version of the phase diagram conjectured in popkov and schutz europhys lett 48 257 263 1999 and show that it is robust with respect to perturbations of the boundaries

a new class of codes meeting the griesmer bound an infinite sequence of k dimensional binary linear block codes is constructed with parameters n 2 k 2 k 2 15 d 2 k 1 2 k 3 8 k geq 7 for k geq 8 these codes are unique while there are five nonisomorphic codes for k 7 by shortening these codes in an appropriate way one finds codes meeting the griesmer bound for 2 k 1 2 k 3 15 leq d leq 2 k 1 2 k 3 8 k geq 7

stationary stochastic higher spin six vertex model and q whittaker measure in this paper we consider the higher spin six vertex model on the lattice mathbb z ge 2 times mathbb z ge 1 we first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space time limit for the stationary higher spin six vertex model in particular along the characteristic line we recover baik rains fluctuations with size of characteristic exponent 1 3 we also consider some of the main degenerations of the higher spin six vertex model and we adapt our analysis to the relevant cases of the q hahn particle process and of the exponential jump model

asymmetric attractive particle systems on z hydrodynamic limit for monotone initial profiles we extend previous results on the preservation of local equilibrium for one dimensional asymmetric attractive particle systems the hydrodynamic behavior is studied for general monotone initial profiles

new code parameters from reed solomon subfield codes we determine the dimensions of subfield codes of reed solomon codes and construct certain extensions and lengthenings of these codes we start from the duals using the language of orthogonal arrays as a first result this allows us to obtain a fair number of improvements in the list of binary ternary and quaternary linear codes with largest known minimal distance

new minimum distance bounds for certain binary linear codes let an n k d code denote a binary linear code of length n dimension k and minimum distance at least d define d n k as the maximum value of d for which there exists a binary linear n k d code t verhoeff 1989 has provided an updated table of bounds on d n k for 1

diffraction by three semi infinite planes an explicit solution to the scattering of a plane wave by three parallel equidistant semi infinite planes is derived the solution involves a wiener hopf factorization of a 2 2 matrix various properties of the scattered field are obtained

new bounds on binary linear codes of dimension eight corresp let n k d be the smallest integer n such that a binary linear code of length n dimension k and minimum distance at least d exists new results are given that improve the best previously known bounds on n 8 d

quasi stationary measures for conservative dynamics in the infinite lattice we study quasi stationary measures for conservative particle systems in the in finite lattice existence of quasi stationary measures is established for a fairly general class of reversible systems for the special cases of a system of independent random walks and the symmetric simple exclusion process it is shown that qualitative features of quasi stationary measures change drastically with dimension

internal dla and the stefan problem generalized internal diffusion limited aggregation is a stochastic growth model on the lattice in which a finite number of sites act as poisson sources of particles which then perform symmetric random walks with an attractive zero range interaction until they reach the first site which has been visited by fewer than alpha particles at which point they stop sites on which particles are frozen constitute the occupied set we prove that in appropriate regimes the particle density has a hydrodynamic limit which is the one phase stefan problem this is then used to study the asymptotic behavior of the occupied set in two dimensions when the walks are independent with one source at the origin and alpha 1 we obtain in particular that the occupied set is asymptotically a disc of radius k sqrt t where k is the solution of exp k 2 4 pi k 2 settling a conjecture of lawler bramson and griffeath

the nonexistence of certain binary linear codes some of the upper bounds given by t verhoeff 1987 are improved by proving the nonexistence of codes with certain parameters necessary preliminary results are stated the results give rise to upper bounds on d n k for many further values of n k by using simple standard techniques the further bounds would automatically follow from theorems by using verhoeff s computerized updating program but the authors state them here because several of them are required in the proofs of subsequent theorems

product measure steady states of generalized zero range processes we establish necessary and sufficient conditions for the existence of factorizable steady states of the generalized zero range process on a periodic or infinite lattice this process allows transitions from a site i to a site i q involving a bounded number of multiple particles with rates depending on the content of the site i the direction q of movement and the number of particles moving we also show the sufficiency of a similar condition for the continuous time mass transport process where the mass at each site and the amount transferred in each transition are continuous variables we conjecture that this is also a necessary condition

limit shapes for gibbs ensembles of partitions we explicitly compute limit shapes for several grand canonical gibbs ensembles of partitions of integers these ensembles appear in models of aggregation and are also related to invariant measures of zero range and coagulation fragmentation processes we show that all possible limit shapes for these ensembles fall into several distinct classes determined by the asymptotics of the internal energies of aggregates

metastability in a condensing zero range process in the thermodynamic limit zero range processes with decreasing jump rates are known to exhibit condensation where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value we study such a process on a one dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed super critical particle density we show that the process exhibits metastability with respect to the condensate location i e the suitably accelerated process of the rescaled location converges to a limiting markov process on the unit torus this process has stationary independent increments and the rates are characterized by the scaling limit of capacities of a single random walker on the lattice our result extends previous work for fixed lattices and diverging density in beltran and landim probab theory relat fields 152 3 4 781 807 2012 and we follow the martingale approach developed there and in subsequent publications besides additional technical difficulties in estimating error bounds for transition rates the thermodynamic limit requires new estimates for equilibration towards a suitably defined distribution in metastable wells corresponding to a typical set of configurations with a particular condensate location the total exit rates from individual wells turn out to diverge in the limit which requires an intermediate regularization step using the symmetries of the process and the regularity of the limit generator another important novel contribution is a coupling construction to provide a uniform bound on the exit rates from metastable wells which is of a general nature and can be adapted to other models

relaxation to equilibrium of conservative dynamics i zero range processes under mild assumptions we prove that for any local function u the decay rate to equilibrium in the variance sense of zero range dynamics on the d dimensional integer lattice is c u t d 2 o t d 2 the constant c u is computed explicitly

dynamics of the condensate in zero range processes for stochastic processes leading to condensation the condensate once it is formed performs an ergodic stationary state motion over the system we analyse this motion and especially its characteristic time for zero range processes the characteristic time is found to grow with the system size much faster than the diffusive time scale but not exponentially fast this holds both in the mean field geometry and on finite dimensional lattices in the generic situation where the critical mass distribution follows a power law the characteristic time grows as a power of the system size

driven tracer particle in one dimensional symmetric simple exclusion consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interaction we investigate the behavior of a tagged particle under the action of an external constant driving force we prove that the diffusively rescaled position of the test particle ex e 2t t 0 converges in probability as e 0 to a deterministic function v t the function v depends on the initial distribution of the random environment through a non linear parabolic equation this law of large numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional symmetric zero range process with an asymmetry at the origin an einstein relation is satisfied asymptotically when the external force is small

the diffraction of stress waves by a plane finite crack in two dimensions uniqueness and existence in this paper we consider the two dimensional problem of the diffraction of stress waves by a finite plane crack in a homogeneous isotropic elastic solid we prove that provided the elastic displacement is bounded this problem has at most one solution also by introducing a new class of green functions we are able to give a constructive proof of existence the solution is given in terms of the solution of any one of a class of fredholm integral equations of the second kind

processus des misanthropes we consider a system of identical interacting particles moving on the lattice d the rate at which a particle at the site x jumps to the site y is p y x b x y where p is an irreducible probability on d and b x y is an increasing resp decreasing function of the number x resp y of particles at site x resp y we study the convergence of the system to equilibrium and describe the invariant measures

existence of hydrodynamics for the totally asymmetric simple k exclusion process in a totally asymmetric simple k exclusion process particles take nearest neighbor steps to the right on the lattice z under the constraint that each site contain at most k particles we prove that such processes satisfy hydrodynamic limits under euler scaling and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function our technique requires no knowledge of the invariant measures of the process which is essential because the equilibria of asymmetric k exclusion are unknown but we cannot calculate the flux function precisely the proof proceeds via a coupling with a growth model on the two dimensional lattice in addition to the basic k exclusion with constant exponential jump rates we treat the site disordered case where each site has its own jump rate randomly chosen but frozen for all time the hydrodynamic limit under site disorder is new even for the simple exclusion process the case k 1 our proof makes no use of the markov property so at the end of the paper we indicate how to treat the case with arbitrary waiting times

new optimal binary linear codes of dimensions 9 and 10 eighteen new codes are presented which improve the bounds on maximum minimum distance for binary linear codes they are rate m r pm r spl ges 1 degenerate quasi cyclic qc codes based on the known upper bounds six of these new codes are optimal in addition five two weight qc codes of dimension 8 are given

diffraction of elastic waves by a penny shaped crack analytical and numerical results the diffraction of time harmonic stress waves by a penny shaped crack in an infinite elastic solid is an important problem in fracture mechanics and in the theory of the ultrasonic inspection of materials martin proc r soc lond a 378 263 1981 has proved that the corresponding linear boundary value problem has precisely one solution and that this solution can be constructed by solving a two dimensional fredholm integral equation of the second kind however this integral equation has a complicated matrix kernel and the components of its vector solution are coupled the main purpose of the present paper is to show how martin s integral equation can be explicitly solved in terms of a sequence of functions each of which satisfies a very simple scalar integral equation of the second kind this simplification may be made for any incident wave for an incident plane wave further simplifications are possible we show that the solution at an arbitrary angle of incidence can be derived from the solution at a particular angle of incidence namely grazing incidence the resulting computational procedure is especially attractive if only the stressintensity factors or the far field displacements are required finally we present some numerical results for the scattering of a p wave at normal incidence and an sv wave at oblique incidence and compare these with those of other authors

the smallest length of eight dimensional binary linear codes with prescribed minimum distance let n 8 d be the smallest integer n for which a binary linear code of length n dimension 8 and minimum distance d exists we prove that n 8 18 42 n 8 26 58 n 8 28 61 n 8 30 65 n 8 34 74 n 8 36 77 n 8 38 81 n 8 42 89 and n 8 60 124 after these results all values of n 8 d are known

q zero range has random walking shocks but no other surprises in the zero range world we check all nearest neighbour 1 dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature we find the totally asymmetric version of the celebrated q zero range process as the only new example besides an already known model of doubly infinite occupation numbers and exponentially increasing jump rates we also examine the interaction of shocks which appears somewhat more involved for q zero range than in the already known cases

recurrence and density decay for diffusion limited annihilating systems we study an infinite system of moving particles where each particle is of type a or b particles perform independent random walks at rates d a 0 and d b geqslant 0 and the interaction is given by mutual annihilation a b rightarrow emptyset the initial condition is i i d with finite first moment we show that this system is site recurrent that is each site is visited infinitely many times we also generalize a lower bound on the density decay of bramson and lebowitz by considering a construction that handles different jump rates

absorbing state phase transition for driven dissipative stochastic dynamics on ℤ we study the long time behavior of conservative interacting particle systems in the activated random walk model for reaction diffusion systems and the stochastic sandpile we prove that both systems undergo an absorbing state phase transition

an isotropic elastic medium containing a cylindrical borehole with a rigid plug abstract an analytical and numerical analysis is made of an isotropic elastic medium containing a cylindrical borehole of infinite length in which is located a tightly fitting rigid plug of finite length both the pulling of the plug and the occurrence of a radial misfit are considered the boundary conditions are mixed with zero radial and shear stresses at the bore surface outside the plug region and displacements given across the plug surface using integral representations for a love auxiliary function the crucial step is the analytical incorporation of the square root singularity at boundary condition junctions this is done by using neumann bessel function series representations of the integrand kernels of boundary condition stresses such that discontinuous weber schafheitlin integrals can be used to satisfy these conditions exactly displacement conditions are solved in terms of integrals of products of bessel functions the solutions provide expressions for the far field behaviour of a kelvin point load solution for the plug pull case and a combined centre of expansion plus double force for radial misfit numerical results show good convergence of the method and the correct singular behaviours of borehole surface stresses

condensation in stochastic particle systems with stationary product measures we study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities we review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit this leads to strengthened results on weak convergence for subcritical systems and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions extending previous results which focused on attractive and finite systems we use relative entropy techniques which provide simple proofs making use of general versions of local limit theorems for independent random variables

time harmonic body force loading of a mode i penny shaped crack abstract the present paper is concerned with the problem of determining dynamic sif of a penny shaped crack in an infinite elastic medium which is subjected to the action of time harmonic axial body forces placed symmetrically with respect to the crack plane the solution of the problem is obtained by superposition of the solutions of two simpler problems the first of these problems is related to the unperturbed crackless space under the prescribed axial body forces while the second problem consists in finding the dynamic sif of the penny shaped crack whose faces are directly acted upon by some axial stresses the form of these axial stresses is determined from the solution of the first problem fourier and hankel transforms have been used to solve the first problem next by means of the hankel transform the second problem has been reduced to a pair of dual integral equations which have been subsequently transformed into a fredholm integral equation of the second kind via an auxiliary function the integral equation has been solved numerically in order to determine the variations of the dynamic stress intensity factor at the rim of the penny shaped crack for some particular body force loading cases