Related papers: Spatial-segregation limit for exclusion processes …
We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of…
We study condensation and evaporation of particles which repel each other, using a simple set of rules on a square lattice. Different results are obtained for a mobile and an immobile surface layer.A two point limit cycle is observed for…
Dynamical properties of a few ultra-cold fermions confined in a double-well potential is studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest neighbor interactions. We consider two kinds of inter-particle interactions. In one case, the particle-hole symmetry…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical…
We study the existence and the exponential ergodicity of a general interacting particle system, whose components are driven by independent diffusion processes with values in an open subset of $\mathds{R}^d$, $d\geq 1$. The interaction…
Chemically-active droplets exhibit complex avoiding trajectories. While heterogeneity is inevitable in active matter experiments, it is mostly overlooked in their modelling. Exploiting its geometric simplicity, we fully-resolve the head-on…
Bacteria regulate their motility through a variety of mechanisms, including quorum sensing (QS) and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter…
We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
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…
Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of…
We study the hydrodynamic limit for a periodic $1$-dimensional exclusion process with a dynamical constraint, which prevents a particle at site $x$ from jumping to site $x\pm1$ unless site $x\mp1$ is occupied. This process with degenerate…