Hopping Transport in Hostile Reaction-Diffusion Systems

TL;DR

This paper studies how particles move in a disordered reaction-diffusion system with growth, competition, and death, analyzing transport properties and first passage times relevant to biological populations and hopping conduction.

Contribution

It introduces a model combining reaction-diffusion dynamics with disordered environments and derives analytical results for transport and first passage times.

Findings

First passage time distribution for high growth rates

Estimated crossing times in large disordered systems

Connection to hopping conduction in semiconductors

Abstract

We investigate transport in a disordered reaction-diffusion (RD) model consisting of particles which are allowed to diffuse, compete with one another (2A->A), give birth in small areas called "oases" (A->2A), and die in the "desert" outside the oases (A->0). This model has previously been used to study bacterial populations in the lab and is related to a model of plankton populations in the oceans. We first consider the nature of transport between two oases: in the limit of high growth rate, this is effectively a first passage process, and we are able to determine the first passage time probability density function in the limit of large oasis separation. This result is then used along with the theory of hopping conduction in doped semiconductors to estimate the time taken by a population to cross a large system.