series expansion for a stochastic sandpile using operator algebra we extend the series for the activity density in a one dimensional stochastic sandpile with fixed particle density p the first terms of which were obtained via perturbation theory dickman and vidigal 2002 j phys a math gen 35 7269 the expansion is in powers of the time the coefficients are polynomials in p we devise an algorithm for evaluating expectations of operator products and extend the series to constructing pade approximants to a suitably transformed series we obtain predictions for the activity that compare well against simulations in the supercritical regime

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

numerical study of the langevin theory for fixed energy sandpiles the recently proposed langevin equation aimed to capture the relevant critical features of stochastic sandpiles and other self organizing systems is studied numerically the equation is similar to the reggeon field theory describing generic systems with absorbing states but it is coupled linearly to a second conserved and static nondiffusive field it has been claimed to represent a different universality class including different discrete models the manna as well as other sandpiles reaction diffusion systems etc in order to integrate the equation and surpass the difficulties associated with its singular noise we follow a numerical technique introduced by dickman our results coincide remarkably well with those of discrete models claimed to belong to this universality class in one two and three dimensions this provides a strong backing for the langevin theory of stochastic sandpiles and to the very existence of this meagerly understood universality class

a spectral analysis of the decoupling algorithm for semiconductor simulation the location in the complex plane of the eigenvalues of the derivatives of the partial nonlinear maps which constitute the fixed point mapping t defining gummel s method for decoupling the steady state semiconductor equations is examined for the general n dimensional case in particular it is proven that the size of these eigenvalues is unconditionally smaller than 1 it is shown that for up to three dimensional models all the derivatives are suitably compact this implies that the spectral radii of these mappings are equal to the size of the largest eigenvalue for the current continuity equations this implies an essential improvement over earlier contraction mapping results furthermore the precise location of the eigenvalues of the derivatives of the maps defined through the current continuity equations for the general one dimensional case is found for a special one dimensional case it is proven that the size of the eigenvalues of the total mapping t defining gummel s method is unconditionally smal

integration of langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions efficient and accurate integration of stochastic partial differential equations with multiplicative noise can be obtained through a split step scheme which separates the integration of the deterministic part from that of the stochastic part the latter being performed by sampling exactly the solution of the associated fokker planck equation we demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which langevin equations have been proposed this provides precise estimates of the associated scaling exponents clarifying the classification of these nonequilibrium problems and confirms or refutes some existing theories

the mean field scaling function of the universality class of absorbing phase transitions with a conserved field we consider two mean field like models which belong to the universality class of absorbing phase transitions with a conserved field in both cases we analytically derive the order parameter as a function of the control parameter and of an external field conjugated to the order parameter this allows us to calculate the universal scaling function of the mean field behaviour the obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models showing that four is the upper critical dimension of this particular universality class

scaling behavior of the conserved transfer threshold process we analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process we determined the steady state scaling behavior of the order parameter as a function of both the control parameter and an external field conjugated to the order parameter the external field is realized as a spontaneous creation of active particles which drives the system away from criticality the obtained results yield that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field

o t 2 h 4 finite difference scheme for decoupled system of two quasilinear parabolic equations abstract let lh be the five point finite difference operator which has o h2 local truncation error at the points h and 1 h next to the ends of interval 0 1 and o h4 at the interior mesh points 2h 3h 1 2h the operator generates the pentadiagonal coherent matrix which is not of positive type and not diagonally dominant however the matrix satisfies the maximum principle the operator lh has been used in a number of publications to solve elliptic and parabolic equations in the paper lh is applied to approximate the second derivatives uxx and vxx in the two diffusion equations pu t au xx t x u v and qvt bvxx g t x u v it is proved that the obtained semi discrete scheme is o h4 globally convergent for approximation of the derivatives with respect to t the o 2 trapezoidal rule is used the fully discrete scheme obtained in this way constitutes a system of algebraic equations associated with a pentadiagonal matrix to solve this system of equations an implicit iterative method based on an algorithm for pentadiagonal matrices is proposed numerical results illustrating the method are presented

completeness of the trajectories of particles coupled to a general force field we analyze the extendability of the solutions to a certain second order differential equation on a riemannian manifold m g which is defined by a general class of forces both prescribed on m or depending on the velocity the results include the general time dependent anholonomic case and further refinements for autonomous systems or forces derived from a potential are obtained these extend classical results for lagrangian and hamiltonian systems several examples show the optimality of the assumptions as well as the utility of the results including an application to relativistic pp waves

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

universality in sandpile models a classification of sandpile models into universality classes is presented on the basis of extensive numerical simulations in which we measure an extended set of exponents the manna two state model s s manna j phys a 24 l363 1991 is found to belong to a universality class of random neighbor models which is distinct from the universality class of the original model of bak tang and wiesenfeld p bak c tang and k wiesenfeld phys rev lett 59 381 1987 directed models are found to belong to a universality class which includes the directed model introduced and solved by dhar and ramaswamy d dhar and r ramaswamy phys rev lett 63 1659 1989

abelian manna model in three dimensions and below the abelian manna model of self organized criticality is studied on various three dimensional and fractal lattices the exponents for avalanche size duration and area distribution of the model are obtained by using a high accuracy moment analysis together with earlier results on lower dimensional lattices the present results reinforce the notion of universality below the upper critical dimension and allow us to determine the coefficients of an e expansion by rescaling the critical exponents by the lattice dimension and incorporating the random walker dimension a remarkable relation is observed satisfied by both regular and fractal lattices

how to simulate the quasistationary state for a large class of processes with an absorbing state statistical properties of the surviving sample attain time independent values in the quasistationary qs regime we propose a practical simulation method for studying quasistationary properties based on the equation of motion governing the qs distribution in applications to the contact process the method is shown to reproduce exact results for the process on a complete graph and known scaling behavior to high precision at the critical point our method is about an order of magnitude more efficient than conventional simulation

oslo model hyperuniformity and the quenched edwards wilkinson model we present simulations of the one dimensional oslo rice pile model in which the critical height at each site is randomly reset after each toppling we use the fact that the stationary state of this sand pile model is hyperuniform to reach system of sizes 10 7 most previous simulations were seriously flawed by important finite size corrections we find that all critical exponents have values consistent with simple rationals 4 3 for the correlation length exponent d 9 4 for the fractal dimension of avalanche clusters and z 10 7 for the dynamical exponent in addition we relate the hyperuniformity exponent to the correlation length exponent finally we discuss the relationship with the quenched edwards wilkinson model where we find in particular that the local roughness exponent is loc 1

conserved lattice gas model with infinitely many absorbing states in one dimension the conserved lattice gas model with infinitely many absorbing states is studied on a chain and on a ladder in both one dimensional lattices it exhibits a phase transition from an absorbing phase to an active state the model defined on a chain is solved exactly and shows a critical behavior with classical critical exponents however the model defined on a ladder shows a critical behavior obtained from numerical simulation that places the model in the same universality class as the manna model

quasistationary analysis of the contact process on annealed scale free networks we present an analysis of the quasistationary qs state of the contact process cp on annealed scale free networks using a mapping of the cp dynamics in a one step process and analyzing numerically and analytically the corresponding master equation the relevant qs quantities determined via the master equation exhibit an excellent agreement with direct qs stochastic simulations of the cp the high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions corrections that mask the correct finite size scaling obtained analytically by applying an exact heterogeneous mean field approach our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real quenched complex networks

hierarchical electrochemical modeling and simulation of bio hybrid interfaces abstract in this article we propose and investigate a hierarchy of mathematical models based on partial differential equations pde and ordinary differential equations ode for the simulation of the biophysical phenomena occurring in the electrolyte fluid that connects a biological component a single cell or a system of cells and a solid state device a single silicon transistor or an array of transistors the three members of the hierarchy ordered by decreasing complexity are i a 3d poisson nernst planck pnp pde system for ion concentrations and electric potential ii a 2d reduced pnp system for the same dependent variables as in i iii a 2d area contact pde system for electric potential coupled with a system of odes for ion concentrations the backward euler method is adopted for temporal semi discretization and a fixed point iteration based on gummel s map is used to decouple system equations spatial discretization is performed using piecewise linear triangular finite elements stabilized via edge based exponential fitting extensively conducted simulation results are in excellent agreement with existing analytical solutions of the pnp problem in radial coordinates and experimental and simulated data using simplified lumped parameter models

generalized pseudo riemannian geometry generalized tensor analysis in the sense of colombeau s construction is employed to introduce a nonlinear distributional pseudo riemannian geometry in particular after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo riemannian metric generalized connection and generalized curvature tensor we prove a fundamental lemma of pseudo riemannian geometry in this setting and define the notion of geodesics of a generalized metric finally we present applications of the resulting theory to general relativity

moment analysis of the probability distribution of different sandpile models we reconsider the moment analysis of the bak tang wiesenfeld and the stochastic sandpile model introduced by manna j phys a 24 l363 1991 in two and three dimensions in contrast to recently performed investigations our analysis reveals that the models are characterized by different scaling behavior i e they belong to different universality classes

numerical analysis of a langevin equation for systems with infinite absorbing states one dimensional systems with an infinite number of absorbing states exhibit a phase transition that is not fully understood yet their static critical exponents are universal and belong in the reggeon field theory or directed percolation universality class however exponents associated with the spreading of a localized seed appear to be nonuniversal depending on the nature of the initial condition we investigate this problem by integrating numerically a non markovian langevin equation proposed recently to describe such phase transitions we find that the static critical exponents are universal as expected on the other hand the langevin equation reproduces the nonuniversal behavior observed in microscopic models for exponents associated with the spreading of an initially localized seed and satisfies the generalized hyperscaling relation proposed for those systems

scaling behavior of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension we analyze numerically the critical behavior of an absorbing phase transition in a conserved lattice gas in an external field the external field is realized as a spontaneous creation of active particles that drives the system away from criticality nevertheless the order parameter obeys certain scaling laws for sufficiently small external fields these scaling laws are investigated and the corresponding exponents are determined in various dimensions d 2 3 4 5 at the so called upper critical dimension d mathrm c 4 one has to modify the usual scaling laws by logarithmic corrections

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

simple sandpile model of active absorbing state transitions we study a simple sandpile model of active absorbing state transitions in which a particle can hop out of a site only if the number of particles at that site is above a certain threshold we show that the active phase has product measure whereas nontrivial correlations are found numerically in the absorbing phase it is argued that the system relaxes to the latter phase slower than exponentially the critical behavior of this model is found to be different from that of the other known universality classes

steady state of stochastic sandpile models we study the steady state of the abelian sandpile models with stochastic toppling rules the particle addition operators commute with each other but in general these operators need not be diagonalizable we use their abelian algebra to determine their eigenvalues and the jordan block structure these are then used to determine the probability of different configurations in the steady state we illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example for systems of size 12 and also study the density profile in the steady state

effects of pair correlation on mean field theory of btw sand pile model we extend the mean field calculation of btw sand pile model to one that includes the correlation between pairs of nearest neighbors specifically we derive dynamical equations of both one site and two site densities and solve the equations order by order starting with the mean field solution the investigation provides analytical results for both stationary and dynamic states of the sand pile near the critical point which are valid in the regime where h e2 1h e2 1 h incoming rate of sand grains e bulk dissipation rate of sand grainse bulk dissipation rate of sand grains in the stationary case we evaluate the pair correlation and the correction to the mean field single site densities due to the correlation the correction is found to be of the same order as the mean field solution in the dynamic case the initial state deviates from the stationary state by a small fluctuation which subsequently decays exponentially with the time constant being reduced from the corresponding mean field value again the correction to the time constant in this case is found comparable to the mean field value itself

n site approximations and coherent anomaly method analysis for a stochastic sandpile n site cluster approximations for a stochastic sandpile in one dimension are developed a height restriction is imposed to limit the number of states each site can harbor at most two particles height z i l 2 this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded on the basis of results for nl 11 sites the critical particle density as ensuremath zeta c 0 930 1 is estimated in good agreement with simulations a coherent anomaly analysis yields estimates for the order parameter exponent ensuremath beta 0 41 1 and the relaxation time exponent ensuremath nu ensuremath simeq 2 5

critical behavior of a one dimensional fixed energy stochastic sandpile we study a one dimensional fixed energy version that is with no input or loss of particles of manna s stochastic sandpile model the system has a continuous transition to an absorbing state at a critical value of the particle density and exhibits the hallmarks of an absorbing state phase transition including finite size scaling critical exponents are obtained from extensive simulations which treat stationary and transient properties and an associated interface representation these exponents characterize the universality class of an absorbing state phase transition with a static conserved density in one dimension they differ from those expected at a linear interface depinning transition in a medium with point disorder and from those of directed percolation

universality split in absorbing phase transition with conserved field on fractal lattices the universality split in absorbing phase transition between the conserved lattice gas clg model and the conserved threshold transfer process cttp is investigated on a checkerboard fractal and on a sierpinski gasket the critical exponents theta beta nu and z which are associated with respectively the density of active particles in time the order parameter the temporal correlation length and the dynamics of active particles are elaborately measured for two models on selected fractal lattices the exponents for the clg model are found to be distinctly different from those of the cttp model on a checkerboard fractal whereas the two models exhibit the same critical behavior on a sierpinski gasket indicating that the universality split between the two models occurs only on a checkerboard fractal such a universality split is attributed from the dominant hopping mechanisms caused by the intrinsic properties of the underlying fractal lattice

absorbing state phase transitions exact solutions of small systems i derive precise results for absorbing state phase transitions using exact numerically determined quasistationary qs probability distributions for small systems analysis of the contact process on rings of 23 or fewer sites yields critical properties control parameter order parameter ratios and critical exponents z and ensuremath beta ensuremath nu ensuremath perp with an accuracy of 0 06 or better precise results are also obtained for the pair contact process the qs distribution yields insights on the statistical entropy of these models preliminary application to a model in the stochastic sandpile class is also described

self organized critical directed percolation abstract we introduce and study a dynamic transport model exhibiting self organized criticality the novel concepts of our model are the probabilistic propagation of activity and unbiased random repartition of energy among the active site and its nearest neighbors for space dimensionality d 2 we argue that the model is related to d 1 dimensional directed percolation with time interpreted as the preferred direction

sandpiles with height restrictions we study stochastic sandpile models with a height restriction in one and two dimensions a site can topple if it has a height of two as in manna s model but in contrast to previously studied sandpiles here the height or number of particles per site cannot exceed two this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded two toppling rules are considered in one the particles are redistributed independently while the other involves some cooperativity we study the fixedenergy system no input or loss of particles using cluster approximations and extensive simulations and find that it exhibits a continuous phase transition to an absorbing state at a critical value z c of the particle density the critical exponents agree with those of the unrestricted manna sandpile

path integral representation for a stochastic sandpile we introduce an operator description for a stochastic sandpile model with a conserved particle density and develop a path integral representation for its evolution the resulting exact expression for the effective action highlights certain interesting features of the model for example it is nominally massless and the dynamics is via cooperative diffusion using the path integral formalism we construct a diagrammatic perturbation theory yielding a series expansion for the activity density in powers of time

absorbing phase transition in conserved lattice gas model on fractal lattices we study the continuous phase transition of the conserved lattice gas clg model from an active phase into an absorbing phase on two fractal lattices i e on a checkerboard fractal and on a sierpinski gasket in the clg model a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty we estimate critical exponents theta beta nu and nu perpendicular characterizing respectively the density of active particles in time the order parameter the temporal and spatial correlation lengths near the critical point and the results are confirmed by off critical scaling and finite size scaling the order parameter exponent beta on a checkerboard fractal appears to lie between the one dimensional 1d value and two dimensional 2d value of the clg model while that on a sierpinski gasket lies between the 1d and 2d values of the conserved threshold transfer process such a difference is manifested based on the intrinsic properties of the underlying fractal lattices

smoothness of time functions and the metric splitting of globally hyperbolic spacetimes the folk questions in lorentzian geometry which concerns the smoothness of time functions and slicings by cauchy hypersurfaces are solved by giving simple proofs of a any globally hyperbolic spacetime m g admits a smooth time function open image in new window whose levels are spacelike cauchy hyperfurfaces and thus also a smooth global splitting open image in new window if a spacetime m admits a continuous time function t then it admits a smooth time function open image in new window with timelike gradient open image in new window on all m

how self organized criticality works a unified mean field picture we present a unified dynamical mean field theory based on the single site approximation to the master equation for stochastic self organized critical models in particular we analyze in detail the properties of sandpile and forest fire ff models in analogy with other nonequilibrium critical phenomena we identify an order parameter with the density of active sites and control parameters with the driving rates depending on the values of the control parameters the system is shown to reach a subcritical absorbing or supercritical active stationary state criticality is analyzed in terms of the singularities of the zero field susceptibility in the limit of vanishing control parameters the stationary state displays scaling characteristics of self organized criticality soc we show that this limit corresponds to the breakdown of space time locality in the dynamical rules of the models we define a complete set of critical exponents describing the scaling of order parameter response functions susceptibility and correlation length in the subcritical and supercritical states in the subcritical state the response of the system to small perturbations takes place in avalanches we analyze their scaling behavior in relation with branching processes in sandpile models because of conservation laws a critical exponents subset displays mean field values ensuremath nu frac 1 2 and ensuremath gamma 1 in any dimensions we treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects we present numerical simulations that confirm our results in the case of the forest fire model our approach can distinguish between different regimes soc ff and deterministic ff studied in the literature and determine the full spectrum of critical exponents

sticky grains do not change the universality class of isotropic sandpiles we revisit the sandpile model with sticky grains introduced by mohanty and dhar phys rev lett 89 104303 2002 whose scaling properties were claimed to be generically in the universality class of directed percolation for both isotropic and directed models while for directed models this conclusion is unquestionable for isotropic models we present strong evidence that the asymptotic scaling in the self organized regime in which a stationary critical state exists in the limit of slow driving and vanishing dissipation rate is like other stochastic sandpiles generically in the manna universality class this conclusion is drawn from extensive monte carlo simulations and is strengthened by the analysis of the langevin equations proposed by the same authors to account for this problem argued to converge upon coarse graining to the well established set of langevin equations for the manna class

critical density of the abelian manna model via a multitype branching process a multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the abelian manna model this branching process incorporates partially the spatiotemporal correlations of the activity which are essential for the dynamics in particular in low dimensions an analytical expression for the critical density in arbitrary dimensions is derived which significantly improves the results over mean field theories as confirmed by comparison to the literature on numerical estimates from simulations the method can easily be extended to lattices and dynamics other than those studied in the present work

equivalence between the abelian sandpile model and the q 0 limit of the potts model abstract we establish an equivalence between the undirected abelian sandpile model and the q 0 limit of the q state potts model the equivalence is valid for arbitrary finite graphs two dimensional abelian sandpile models thus correspond to a conformal field theory with central charge c 2 the equivalence also gives a monte carlo algorithm to generate random spanning trees we study the growth process of the spread of fire under the burning algorithm in the background of a random recurrent configuration of the abelian sandpile model the average number of sites burnt upto time t varies at ta in two dimensions our numerically determined value of a agrees with the theoretical prediction a 8 5 we relate this exponent to the conventional exponents characterizing the distributions of avalanche sizes

finite size scaling analysis of the critical behavior of a general epidemic process in 2d abstract we investigate the critical behavior of a stochastic lattice model describing a general epidemic process by means of a monte carlo procedure we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization a finite size scaling analysis is employed to determine the critical point as well as some critical exponents we show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class we also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters

numerical study of a field theory for directed percolation a numerical method is devised for the study of stochastic partial differential equations describing directed percolation the contact process and other models with a continuous transition to an absorbing state owing to the heightened sensitivity to fluctuations attending multiplicative noise in the vicinity of an absorbing state a useful method requires discretization of the field variable as well as of space and time when applied to the field theory for directed percolation in 1 1 dimensions the method yields critical exponents which compare well against accepted values

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

universal finite size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field we analyze numerically three different models exhibiting an absorbing phase transition we focus on the finite size scaling as well as the dynamical scaling behavior an accurate determination of several critical exponents allows one to validate certain hyperscaling relations using these hyperscaling relations it is possible to express the avalanche exponents of a self organized critical system in terms of the ordinary exponents of a continuous absorbing phase transition

the globally hyperbolic metric splitting for non smooth wave type space times abstract we investigate a generalization of the so called metric splitting of globally hyperbolic space times to non smooth lorentzian manifolds and show the existence of this metric splitting for a class of wave type space times the approach used is based on smooth approximations of non smooth space times by families or sequences of globally hyperbolic space times in the same setting we indicate as an application the extension of a previous result on the cauchy problem for the wave equation

approach to criticality in sandpiles a popular theory of self organized criticality predicts that the stationary density of the abelian sandpile model equals the threshold density of the corresponding fixed energy sandpile we recently announced that this density conjecture is false when the underlying graph is any of z2 the complete graph kn the cayley tree the ladder graph the bracelet graph or the flower graph in this paper we substantiate this claim by rigorous proof and extensive simulations we show that driven dissipative sandpiles continue to evolve even after a constant fraction of the sand has been lost at the sink nevertheless we do find and prove a relationship between the two models the threshold density of the fixed energy sandpile is the point at which the driven dissipative sandpile begins to lose a macroscopic amount of sand to the sink

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

some results and a conjecture for manna s stochastic sandpile model we present some analytical results for the stochastic sandpile model studied earlier by manna in this model the operators corresponding to particle addition at different sites commute the eigenvalues of operators satisfy a system of coupled polynomial equations for an l l square we construct a nontrivial toppling invariant and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues for periodic boundary conditions in one direction one more toppling invariant can be constructed we show that there are many forbidden subconfigurations and only an exponentially small fraction of all stable configurations are recurrent we obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration and conjecture a formula for its exact value for finite size rectangles

tricritical directed percolation we consider a modification of the contact process incorporating higher order reaction terms the original contact process exhibits a non equilibrium phase transition belonging to the universality class of directed percolation the incorporated higher order reaction terms lead to a non trivial phase diagram in particular a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions the corresponding tricritical scaling behavior is analyzed in detail i e we determine the critical exponents various universal scaling functions as well as universal amplitude combinations

a finite element approximation theory for the drift diffusion semiconductor model two sided estimates are derived for the approximation of solutions to the drift diffusion steady state semiconductor device system which are identified with fixed points of gummel s solution map the approximations are defined in terms of fixed points of numerical finite element discretization maps by use of a calculus developed by krasnosel skii and his coworkers it is possible both to locate approximations near fixed points in an a priori manner as well as fixed points near approximations in an a posteriors manner these results thus establish a nonlinear approximation theory in the energy norm with rate keyed to what is possible in a standard linear theory this analysis provides a convergence theory for typical computational approaches in current use for semiconductor simulation

bak tang wiesenfeld sandpile model around the upper critical dimension we consider the bak tang wiesenfeld sandpile model phys rev lett 59 381 1987 phys rev a 38 364 1988 on square lattices in different dimensions dl 6 a finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents the dynamical exponent and the dimension of the avalanches above the upper critical dimension d u 4 the exponents equal the known mean field values an analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension

critical behaviour of an interacting surface reaction model the authors investigate the kinetics of a generalized monomer monomer surface reaction model in which there is a variable excluded volume interaction between same species particles as and bs for no interaction this system reduces to the monomer monomer model for which there is a first order transition between a and b saturated phases as a function of the excluded volume interaction the first order transition line for weak interaction terminates at a tricritical point where two second order transitions meet these transitions which appear to be in the reggeon field theory universality class separate the a saturated reactive and b saturated phases series expansions and various time dependent monte carlo simulations are used to estimate the critical parameters and exponents associated with these transitions

asymptotic behavior of the order parameter in a stochastic sandpile we derive the first four terms in a series for the order paramater the stationary activity density in the supercritical regime of a one dimensional stochastic sandpile in the two dimensional case the first three terms are reported this is done by reorganizing the pertubation theory derived using a path integral formalism dickman and vidigal j phys a 35 7269 2002 to obtain an expansion for stationary properties since the process has a strictly conserved particle density p the fourier mode n 1 k 0 p when n and so is not a random variable isolating this mode we obtain a new effective action leading to an expansion for in the parameter 1 1 4p this requires enumeration and numerical evaluation of more than 200 000 diagrams for which task we develop a computational algorithm predictions derived from this series are in good accord with simulation results we also discuss the nature of correlation functions and one site reduced distributions in the small high density limit

critical exponents for the restricted sandpile i report large scale monte carlo studies of a one dimensional height restricted stochastic sandpile using the quasistationary simulation method results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems but are consistent with recent predictions derived from a langevin equation for stochastic sandpiles ramasco phys rev e 69 045105 r 2004 this suggests that apparent violations of universality in one dimensional sandpiles are due to strong corrections to scaling and finite size effects

universality of the local persistence exponent for models in the directed ising class in one dimension we investigate local persistence in five different models and their variants in the directed ising di universality class in one dimension these models have right left symmetry we study grassberger s models a and b we also study branching and annihilating random walks with two offspring the nonequilibrium kinetic ising model and the interacting monomer dimer model grassberger s models are updated in parallel this is not the case in other models we find that the local persistence exponent in all these models is unity or very close to it a change in the mode of the update does not change the exponent unless the universality class changes in general persistence exponents are not universal thus it is of interest that the persistence exponent in a range of models in the di class is the same excellent scaling behavior of finite size scaling is obtained using exponents in the di class in all models we also study off critical scaling in some models and di exponents yield excellent scaling behavior we further study graded persistence which shows similar behavior however for a logistic map with delay which also has the transition in the di class there is no transition from nonzero to zero persistence at the critical point thus the accompanying transition in persistence and universality of the persistence exponent hold when the underlying model has right left symmetry