A Density-Dependent Diffusion Model of an Interacting System of Brownian Particles

TL;DR

This paper develops computational methods to analyze how particle density influences diffusion in one-dimensional interacting Brownian systems, with applications to biological and physical processes.

Contribution

It introduces new computational techniques for studying density-dependent diffusion in one-dimensional particle systems, extending previous work to include complex interactions.

Findings

Diffusion rate depends on average particle density.

Techniques enable analysis of various physical systems with density-dependent diffusion.

Large-scale simulations confirm the density dependence of diffusion rates.

Abstract

Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing computational techniques to analyze the density-dependent diffusion behavior of one-dimensional interacting particle systems, which have been used to model numerous microscopic processes [17-19], and we apply our techniques to an interacting system of Brownian particles, with hard-core interactions and nearest-neighbor adhesion, known as single-file dynamics. Through large-scale numerical simulations that exploit Monte-Carlo techniques and high-performance computing resources, we show that the diffusion rate in such systems depends on the average particle density. Extensions to the techniques we present here enable researchers to examine the density-dependent diffusion behavior of many physical systems in nature that undergo one-dimensional diffusion associated with a change in the particle density; such as ion transport processes, channeling in zeolites, etc.