Two site self consistent method for front propagation in reaction-diffusion system

TL;DR

This paper introduces a simple two-site self-consistent method to analytically estimate front velocities in reaction-diffusion systems, demonstrating excellent agreement with simulations and potential applicability to other similar processes.

Contribution

The paper presents a novel, simple analytical approach (TSSCM) for estimating front velocities in reaction-diffusion systems, improving understanding and computational efficiency.

Findings

Excellent agreement between TSSCM estimates and simulations.

Method applicable across all parameter regimes.

Potential for extension to other reaction-diffusion processes.

Abstract

We study front propagation in the reaction diffusion process $A\leftrightarrow2A$ on one dimensional lattice with hard core interaction between the particles. We propose a two site self consistent method (TSSCM) to make analytic estimates for the front velocity and are in excellent agreement with the simulation results for all parameter regimes. We expect that the simplicity of the method will allow one to use this technique for estimating the front velocity in other reaction diffusion processes as well.