Simulations of stochastic reaction-diffusion systems

Abstract

Direct simulation of a discrete stochastic model of reaction-diffusion provides a means of studying the fluctuations which occur when populations are finite. This paper introduces the mathematical model along with the computational model which implements it, and shows the relationship to some standard random methods for PDE simulation. Two examples are then given. First, the stochastic phase-field model is introduced. This attempt to study the influence of randomness in liquid-solid interface problems leads easily to meaningful extensions of the standard PDE model. Second, some experiments with a model threshold reaction problem are described. These illustrate many of the effects of the stochastic model which the PDE idealization does not address. In particular, varying the population scale in the model leads to a variety of new observations and conjectures.