Hybrid method for simulating front propagation in reaction-diffusion systems

TL;DR

This paper introduces a hybrid simulation method to study front propagation in reaction-diffusion systems, highlighting how microscopic fluctuations influence macroscopic front dynamics.

Contribution

A novel hybrid simulation scheme that enables large-scale analysis of microscopic fluctuations in reaction-diffusion front propagation.

Findings

Microscopic fluctuations significantly affect front speed and shape.

The hybrid method effectively captures fluctuation effects at large particle numbers.

Macroscopic relaxation dynamics are influenced by microscopic particle interactions.

Abstract

We study the propagation of pulled fronts in the $A <-> \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we concentrate on the corrections to the deterministic behavior due to the number of particles per site $\Omega$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\Omega$ which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.