Nonlinear Bias and the Convective Fisher Equation

TL;DR

This paper models 1D interface dynamics with fluctuations using Monte Carlo simulations, revealing asymmetries and velocity differences consistent with the Fisher equation, but lacking a mean-field transition.

Contribution

It introduces a stochastic simulation approach to study nonlinear bias effects in the convective Fisher equation, highlighting differences from mean-field predictions.

Findings

Asymmetry in interface profiles moving in opposite directions

Velocity differences observed in simulations

No mean-field transition detected in Monte Carlo results

Abstract

We combine random walks, growth and decay, and convection, in a Monte Carlo simulation to model 1D interface dynamics with fluctuations. The continuum limit corresponds to the deterministic Fisher equation with convection. We find qualitatively the same type of asymmetry, as well as velocity difference, for interface profiles moving in opposite directions. However a transition apparent in the mean-field (continuum) limit is not found in the Monte Carlo simulation.