Front Propagation up a Reaction Rate Gradient

TL;DR

This paper investigates how reaction rate gradients influence front propagation in reaction-diffusion systems, using reaction-diffusion equations with a cutoff to model fluctuations, and derives an analytic expression for front velocity dependence on density.

Contribution

It introduces an analytic approximation for front velocity in systems with reaction rate gradients, highlighting the impact of diffusion implementation on velocity divergence.

Findings

Front velocity diverges as density increases.

Diffusion implementation affects the divergence behavior.

Analytic approximation matches numerical results at large densities.

Abstract

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fl uctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the front velocity depe ndence on bulk particle density, showing that the velocity indeed diverge s in the infinite density limit. The form in which diffusion is impleme nted, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.