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Related papers: Hydrodynamic Limit of a Boundary-Driven Elastic Ex…

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In this paper, we prove the hydrodynamic limit for the ergodic dynamics of the Facilitated Exclusion Process with closed boundaries in the symmetric, asymmetric and weakly asymmetric regimes. For this, we couple it with a Simple Exclusion…

Probability · Mathematics 2025-02-04 Hugo Da Cunha , Lu Xu

Starting from a microscopic model of self-propelled hard spheres we use tools of non-equilibrium statistical mechanics and the kinetic theory of hard spheres to derive a Smoluchowski equation for interacting Active Brownian particles. We…

Statistical Mechanics · Physics 2017-04-05 Benjamin Hancock , Aparna Baskaran

We construct a nearest-neighbour interacting particle system of exclusion type, which illustrates a transition from slow to fast diffusion. More precisely, the hydrodynamic limit of this microscopic system in the diffusive space-time…

Probability · Mathematics 2023-01-18 Patricia Gonçalves , Gabriel Nahum , Marielle Simon

In this article, we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists in a superposition of several dynamics: the exclusion rule, that dictates that no more than a particle per site with a…

Probability · Mathematics 2024-09-06 Oslenne Araújo , Patrícia Gonçalves , Alexandre B. Simas

We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe the limiting soliton flow, we introduce a…

Mathematical Physics · Physics 2026-04-15 David A. Croydon , Makiko Sasada

We consider an interacting unbounded spin system, with conservation of the mean spin. We derive quantitative rates of convergence to the hydrodynamic limit provided the single-site potential is a bounded perturbation of a strictly convex…

Probability · Mathematics 2014-05-15 Max Fathi , Georg Menz

We describe the hydrodynamic behavior of the $k$-step exclusion process. Since the flux appearing in the hydrodynamic equation for this particle system is neither convex nor concave, the set of possible solutions include in addition to…

Probability · Mathematics 2010-11-10 Herve Guiol , Krishnamurthi Ravishankar , Ellen Saada

We introduce and analyse a two-sided branching-selection particle system which generalises the well-known $N$-particle branching Brownian motion ($N$-BBM) model, which we call the $(N,p)$-BBM, where either the leftmost or rightmost particle…

Probability · Mathematics 2026-04-24 Jacob Mercer

In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…

Analysis of PDEs · Mathematics 2026-05-19 Yong Wang , Hang Xiong , Hongyao Zhang

We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity…

Probability · Mathematics 2025-12-24 Mario Ayala , D. R. Michiel Renger

We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size $n$. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We…

Probability · Mathematics 2022-08-05 Lu Xu

This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of…

Analysis of PDEs · Mathematics 2025-01-06 Vincent Duchêne , Roberta Bianchini

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that…

Probability · Mathematics 2025-08-28 Oslenne Araújo , Patrícia Gonçalves , Adriana Neumann , Maria Chiara Ricciuti

The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of…

Probability · Mathematics 2025-01-28 Deyue Li

We study the non-equilibrium statistical mechanics of a system of freely moving particles, in which binary encounters lead either to an elastic collision or to the disappearance of the pair. Such a system of {\em ballistic annihilation}…

Statistical Mechanics · Physics 2009-11-13 M. I. Garcia de Soria , P. Maynar , G. Schehr , A. Barrat , E. Trizac

We consider attractive particle systems in $\Z^d$ with product invariant measures. We prove that when particles are restricted to a subset of $\Z^d$, with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the…

Probability · Mathematics 2011-09-05 Christophe Bahadoran

We consider an interacting particle system in the interval $[1,N]$ with reservoirs at the boundaries. While the dynamics in the channel is the simple symmetric exclusion process, the reservoirs are also particle systems which interact with…

Probability · Mathematics 2018-12-05 Thu Dang Thien Nguyen

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

Probability · Mathematics 2016-08-11 Miklós Z. Rácz , Mykhaylo Shkolnikov

We study the symmetric Dyson exclusion process (SDEP) - a lattice gas with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of…

Statistical Mechanics · Physics 2026-05-20 Ali Zahra , Jerome Dubail , Gunter M. Schütz

We introduce and study analytically and numerically a simple model of inter-agent competition, where underachievement is strongly discouraged. We consider $N\gg 1$ particles performing independent Brownian motions on the line. Two particles…

Statistical Mechanics · Physics 2025-03-03 P. L. Krapivsky , Ohad Vilk , Baruch Meerson