Front propagation in A$\to$2A, A$\to$3A process in 1d: velocity, diffusion and velocity correlations

TL;DR

This paper investigates the velocity, diffusion, and correlations of propagating fronts in a one-dimensional reaction-diffusion process involving A particles transforming into 2A or 3A, using approximate methods validated by simulations.

Contribution

It introduces a leading particle approach to compute front velocity and analyzes velocity correlations, providing new insights into front dynamics in reaction-diffusion systems.

Findings

Front velocity varies as a power law of _t in certain parameter ranges.

Velocity correlations significantly influence front diffusion estimates.

Exact analysis shows uncorrelated random walk behavior when _t=D.

Abstract

We study front propagation in the reaction diffusion process $\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one dimensional (1d) lattice with hard core interaction between the particles. Using the leading particle picture, velocity of the front in the system is computed using different approximate methods, which is in good agreement with the simulation results. It is observed that in certain ranges of parameters, the front velocity varies as a power law of $\epsilon_t$, which is well captured by our approximate schemes. We also observe that the front dynamics exhibits temporal velocity correlations and these must be taken care of in order to find the exact estimates for the front diffusion coefficient. This correlation changes sign depending upon the sign of $\epsilon_t-D$, where $D$ is the bare diffusion coefficient of $A$ particles. For $\epsilon_t=D$, the leading particle and thus the front moves like an uncorrelated random walker, which is explained through an exact analysis.