Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

TL;DR

This paper tests a recent theoretical prediction for the fluctuations of reaction front positions in noisy, stochastic simulations, and examines velocity shifts caused by small noise in a one-dimensional lattice model.

Contribution

It provides empirical validation of the theory for front diffusion coefficients and explores noise-induced velocity shifts in stochastic reaction-diffusion systems.

Findings

The theory accurately predicts the front diffusion coefficient in stochastic simulations.

Small noise causes a systematic shift in the front velocity from deterministic predictions.

Simulation results support the theoretical framework for reaction front fluctuations.

Abstract

The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.