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Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary field of study. Such behaviors are often modeled by active matter, in which each individual is…

Mathematical Physics · Physics 2021-08-31 Clément Erignoux

We consider one-dimensional, locally finite interacting particle systems with two conservation laws. The models have a family of stationary measures with product structure and we assume the existence of a uniform bound on the inverse of the…

Probability · Mathematics 2007-05-23 Benedek Valko

We study the hydrodynamic and the hydrostatic behavior of the Simple Symmetric Exclusion Process with \emph{slow boundary}. The term \emph{slow boundary} means that particles can be born or die at the boundary sites, at a rate proportional…

Probability · Mathematics 2017-03-23 Rangel Baldasso , Otávio Menezes , Adriana Neumann , Rafael R. Souza

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 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

We study the asymptotic behaviour of the symmetric zero-range process in the finite lattice $\{1,\ldots, N-1\}$ with slow boundary, in which particles are created at site $1$ or annihilated at site $N\!-\!1$ with a rate proportional to…

Probability · Mathematics 2021-06-14 Susana Frómeta , Ricardo Misturini , Adriana Neumann

We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile described by a variational formula. The…

Probability · Mathematics 2007-05-23 Timo Seppalainen

We study the following class of scalar hyperbolic conservation laws with discontinuous fluxes: \partial_t\rho+\partial_xF(x,\rho)=0. The main feature of such a conservation law is the discontinuity of the flux function in the space variable…

Analysis of PDEs · Mathematics 2007-10-02 Gui-Qiang Chen , Nadine Even , Christian Klingenberg

We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…

Statistical Mechanics · Physics 2024-04-30 Arvind Ayyer

We consider a class of generalized long-range exclusion processes evolving either on $\mathbb Z$ or on a finite lattice with an open boundary. The jump rates are given in terms of a general kernel depending on both the departure and…

Probability · Mathematics 2024-10-24 Patrícia Gonçalves , Julian Kern , Lu Xu

We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…

Probability · Mathematics 2018-02-28 Sunder Sethuraman , Doron Shahar

We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…

Statistical Mechanics · Physics 2007-05-23 A. Brzank , G. M. Schütz

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

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse…

Statistical Mechanics · Physics 2021-01-27 Paolo Glorioso , Luca V. Delacrétaz , Xiao Chen , Rahul M. Nandkishore , Andrew Lucas

We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we…

Probability · Mathematics 2023-12-04 Chiara Franceschini , Patrícia Gonçalves , Federico Sau

We study the hydrodynamic limits of the simple exclusion processes and the zero range processes on crystal lattices. For a periodic realization of crystal lattice, we derive the hydrodynamic limit for the exclusion processes and the zero…

Probability · Mathematics 2020-04-21 Zehao Guan

Consider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random…

Probability · Mathematics 2007-09-05 A. Faggionato , M. Jara , C. Landim

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. For any given environment satisfying…

Probability · Mathematics 2019-11-11 Christophe Bahadoran , T. Mountford , K. Ravishankar , E Saada

The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place…

Probability · Mathematics 2009-11-10 Jozsef Fritz , Balint Toth

We consider continuous-time random walks on a random locally finite subset of $\mathbb{R}^d$ with random symmetric jump probability rates. The jump range can be unbounded. We assume some second--moment conditions and that the above…

Probability · Mathematics 2022-06-03 Alessandra Faggionato