Interfacial Velocity Corrections due to Multiplicative Noise

TL;DR

This paper investigates how finite particle number fluctuations influence the velocity of reaction fronts, using stochastic differential equations to analyze a specific reaction system and confirming a recent heuristic velocity correction.

Contribution

It introduces a stochastic differential equation approach to quantify velocity corrections due to fluctuations in reaction front propagation.

Findings

Velocity correction scales as 1/ln^2(N)

Results align with recent heuristic predictions

Provides a quantitative framework for fluctuation effects

Abstract

The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading edge which perforce has low density, it is interesting to study the role that finite particle number fluctuations have on this picture. Here, we use the well-known mapping of discrete Markov processes to stochastic differential equations and focus on the front velocity in the simple $A+A \stackrel{\leftarrow}{\to} A$ system. Our results are consistent with a recent (heuristic) proposal that $v_{MS} - v \sim {1\over \ln^2 {N}}$.