Mesoscopic Models of Reaction-Diffusion Processes with Exclusion Mechanism

Abstract

We study a class of Markov jump processes describing reaction-diffusion phenomena in a dynamic medium. The model consists basically of a bounded domain divided into cells, each of them being the collection of a given number of sites. These sites are in one of two possible phases of the medium, being either empty, or occupied by particles. The cells are considered as homogenous, the spatial structure of the sites being ignored. The model describes chemical reactions and interactions with the medium, while the individual particles can also perform jumps between neighbouring cells. We consider an exclusion mechanism which prohibits adsorption or jump of particles in a saturated cell. We analyze the macroscopic behaviour of this class of processes in the limit when the cell size tends to 0 and the number of sites per cell tends to infinity, giving conditions for convergence towards the solution of a deterministic reaction-diffusion system.