Hopping Conduction and Bacteria: Transport in Disordered Reaction-Diffusion Systems

TL;DR

This paper investigates transport mechanisms in disordered reaction-diffusion systems with localized growth zones, revealing that at low oasis density, transport occurs via rare hopping events influenced by discreteness effects.

Contribution

It introduces a model of transport in disordered reaction-diffusion systems with spatially restricted growth, emphasizing the role of rare hopping events at low oasis density.

Findings

Transport is mediated through rare hopping events in low oasis density regimes.

An approximate expression for the average traversal time between two oases is derived.

Discreteness effects are crucial in modeling transport in these systems.

Abstract

We report some basic results regarding transport in disordered reaction-diffusion systems with birth (A->2A), death (A->0), and binary competition (2A->A) processes. We consider a model in which the growth process is only allowed to take place in certain areas--"oases"--while the rest of space--the "desert"--is hostile to growth. In the limit of low oasis density, transport is mediated through rare "hopping" events, necessitating the inclusion of discreteness effects in the model. By first considering transport between two oases, we are able to derive an approximate expression for the average time taken for a population to traverse a disordered medium.