Related papers: Directed Fixed Energy Sandpile Model
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We propose a framework employing stochastic differential equations to facilitate the long-term stability analysis of power grids with intermittent wind power generations. This framework takes into account the discrete dynamics which play a…
We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…
Directed sandpile models with different toppling rules are studied by means of numerical simulations in two dimensions, with the purpose of determining the different universality classes. It is concluded that the random-threshold directed…
The degree of predictability of large avalanche events in the directed sandpile model is studied. A waiting time based prediction strategy which exploits the local anticorrelation of large events is discussed. With this strategy we show…
We present calculations of forces for two dimensional static sandpile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces.…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We study the Sinai model for the diffusion of a particle in a one dimensional quenched random energy landscape. We consider the particular case of discrete energy landscapes made of random +/- 1 jumps on the semi infinite line Z+ with a…
We extend a previously studied lattice model of particles with infinite repulsions to the case of finite energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are…
A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr [Nature 399, 241 (1999)] and reproduces some of the experimentally observed features. Avalanches of…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…
We review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution we derive the phase diagram for this model and elucidate scaling…
Energy-based learning is a powerful framework for generative modelling, but its training is inherently non-convex, leading potentially to sensitivity to initialisation, poor local optima, and unstable gradient dynamics. We present a…