Related papers: Hydrodynamic Limit For An Active Exclusion Process
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…
This article analyzes the formulation of space-time continuous hyperbolic hydrodynamic models for systems of interacting particles moving on a lattice, by connecting their local stochastic lattice dynamics to the formulation of an…
Active matter has been widely studied in recent years because of its rich phenomenology, whose mathematical understanding is still partial. We present some results, based on [8, 17] linking microscopic lattice gases to their macroscopic…
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…
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in…
This is a short survey on recent results obtained by the authors on dynamical phase transitions of interacting particle systems. We consider particle systems with exclusion dynamics, but it is conjectured that our results should hold for a…
In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive…
The accumulation of self-propelled particles on repulsive barriers is a widely observed feature in active matter. Despite being implicated in a broad range of biological processes, from biofilm formation to cytoskeletal movement, wetting of…
We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The hydrodynamic limit leads to an integro-differential equation for the density of particles with a given orientation. Volume…
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…
Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each…
Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology,…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
We consider an interacting particle system which models the sterile insect technique. It is the superposition of a generalized contact process with exchanges of particles on a finite cylinder with open boundaries (see Kuoch et al., 2017).…
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 quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the…
We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…
We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability…
In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with…
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…