Negative velocity fluctuations of pulled reaction fronts

TL;DR

This paper develops a WKB theoretical framework to analyze the probability and behavior of reaction fronts propagating into unstable states under shot noise, focusing on negative velocity fluctuations and their implications.

Contribution

It introduces a WKB approach for the microscopic A->2A, 2A->A, and random walk models to quantify rare negative velocity fluctuations of reaction fronts.

Findings

Quantifies the probability of slow or reversed front motion due to noise.

Provides a theoretical method to predict front arrest or reversal events.

Enhances understanding of stochastic effects in reaction-diffusion systems.

Abstract

The position of a reaction front, propagating into an unstable state, fluctuates because of the shot noise. What is the probability that the fluctuating front moves considerably slower than its deterministic counterpart? Can the noise arrest the front motion for some time, or even make it move in the wrong direction? We present a WKB theory that assumes many particles in the front region and answers these questions for the microscopic model A->2A, 2A->A and random walk.