Diffusion in the presence of a local attracting factor: Theory and some interdisciplinary applications

TL;DR

This paper develops a theoretical model for diffusion influenced by a local attractiveness factor, deriving explicit equations for drift and diffusion, with applications to chemotaxis and social dynamics.

Contribution

It introduces a new analytical framework for diffusion with heterogeneous attraction, providing explicit formulas for velocity and diffusion coefficients.

Findings

Derived explicit expressions for drift and diffusion in heterogeneous environments

Applied the model to chemotactic diffusion processes

Extended the framework to social dynamics scenarios

Abstract

We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in the study of various diffusion problems. The corresponding drift-diffusion equation and the explicit expressions for the velocity field and the diffusion coefficient are obtained and discussed. We consider some examples of applications of the results obtained to chemotactic diffusion processes and social dynamics.