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A class of two-species ({\it three-states}) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the…

Statistical Mechanics · Physics 2009-10-31 Mauro Mobilia , Pierre-Antoine Bares

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…

Probability · Mathematics 2009-12-14 Lorenzo Bertini , Claudio Landim , Mustapha Mourragui

We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with…

Probability · Mathematics 2021-04-27 Kohei Hayashi

We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary…

Statistical Mechanics · Physics 2018-02-16 Arvind Ayyer , Caley Finn , Dipankar Roy

The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…

Analysis of PDEs · Mathematics 2017-03-21 Judith Berendsen , Martin Burger , Jan-Frederik Pietschmann

We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…

Probability · Mathematics 2009-08-14 Glauco Valle

In this paper, we give the moderate deviation principle from the hydrodynamic limit of the simple exclusion process on $1$-dimensional torus starting from a nonequilibrium state, which extends the result given in Gao and Quastel (2003)…

Probability · Mathematics 2023-05-16 Xiaofeng Xue

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the…

Probability · Mathematics 2024-07-16 Lu Xu , Linjie Zhao

We prove a hydrodynamic limit for the totally asymmetric simple exclusion process with spatially inhomogeneous jump rates given by a speed function that may admit discontinuities. The limiting density profiles are described with a…

Probability · Mathematics 2011-10-18 Nicos Georgiou , Rohini Kumar , Timo Seppalainen

We study a minimal model to understand the formation of clusters on surfaces in the presence of surface defects. We consider reaction diffusion model in which atoms undergoes reactions at the defect centers to form clusters. Volume…

Materials Science · Physics 2015-06-12 Trilochan Bagarti , Anupam Roy , K. Kundu , B. N. Dev

We consider a two-species chemotaxis model in $\R^d(d \ge 3)$ featuring nonlinear porous medium-type diffusion and nonlocal attractive power-law interaction. Here, the nonlinear diffusion is chosen to be $1/m_1+1/m_2=(d+2)/d$ in such a way…

Analysis of PDEs · Mathematics 2025-11-11 Shen Bian

We consider a class of multidimensional conservation laws with vanishing nonlinear diffusion and dispersion terms. Under a condition on the relative size of the diffusion and dispersion coefficients, we establish that the…

Analysis of PDEs · Mathematics 2008-10-13 Joaquim M. Correia , Philippe G. LeFloch

A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…

Statistical Mechanics · Physics 2017-01-10 Urna Basu

We study reaction-diffusion processes with concentration-dependent diffusivity. First, we determine the decay of the concentration in the single-species and two-species diffusion-controlled annihilation processes. We then consider two…

Statistical Mechanics · Physics 2013-05-30 P. L. Krapivsky

We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Specifically, we examine periodic Riesz interactions indexed by…

Probability · Mathematics 2024-08-20 Elias Hess-Childs

In this short note, we review a recently developed method for analysing multi-component driven diffusive systems with open boundaries. The approach generalises the extremal-current principle known for single-component models and is based on…

Mathematical Physics · Physics 2025-12-12 Ali Zahra

We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in…

Probability · Mathematics 2026-02-09 Hugo Da Cunha , Clément Erignoux , Marielle Simon

Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously…

Mathematical Physics · Physics 2012-08-09 Benjamin D. Goddard , Grigorios A. Pavliotis , Serafim Kalliadasis

Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a domain of sub-critical densities. We prove the hydrodynamic…

Mathematical Physics · Physics 2017-08-02 Nicolas Dirr , Marios G. Stamatakis , Johannes Zimmer

We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a…

Probability · Mathematics 2024-06-10 Tomasz Komorowski , Stefano Olla , Marielle Simon