A Nonlocal Contour Dynamics Model for Chemical Front Motion

TL;DR

This paper introduces a nonlocal contour dynamics model to describe chemical front motion in reaction-diffusion systems, capturing complex pattern formation like labyrinthine structures through interface motion analysis.

Contribution

It derives a novel nonlocal equation of motion for reaction fronts, providing a new theoretical framework for understanding pattern formation in chemical systems.

Findings

High concentration domains can evolve into labyrinthine patterns.

Nearby fronts exhibit repulsive interactions.

Model aligns with observed chemical pattern phenomena.

Abstract

Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered from the point of view of interface motion. A dissipative nonlocal equation of motion for the boundary between high and low concentrations of the slow species is derived heuristically. Under these dynamics, a compact domain of high concentration may develop into a space-filling labyrinthine structure in which nearby fronts repel. Similar patterns have been observed recently by Lee, McCormick, Ouyang, and Swinney in a reacting chemical system.