Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

TL;DR

This paper investigates the behavior of reaction fronts in a lattice-based reaction-diffusion system, deriving simple formulas for front speed and diffusion that match simulations, considering the system's discrete nature.

Contribution

It provides analytical expressions for front propagation speed and diffusion in a lattice reaction system, accounting for discrete particles and sites, validated by simulations.

Findings

Derived explicit formulas for front speed and diffusion coefficient.

Analytical results agree well with simulation data.

System behavior characterized across the full parameter space.

Abstract

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.