Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations

Abstract

A stochastic algorithm for simulation of fluctuation-induced reaction-diffusion kinetics is presented and further developed following our previous study [J. Math. Chem. (2015), DOI 10.1007/s10910-014-0446-6] where this method was used to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. This model is based on the spatially inhomogeneous, nonlinear Smoluchowski equations with random initial distribution density. Here we focus on the spatial distribution of the reactants, and study the segregation effect which we have found under certain reaction conditions. In addition, to extend simulations on large samples we implemented the method in the cellular-automata framework interpreted as a stochastic interacting particles system in discrete but randomly progressed time instances. We have suggested a first passage time technique to characterize the clustering of electrons and holes, which seems to be quite convenient and informative instrument also in more general processes when there is a need to analyze the segregation phenomena.