MODEL FOR HETEROGENEOUS DIFFUSION

Abstract

A revertible kinetic equation for Brownian particles is introduced when the turning frequency and the collision kernel are spatially heterogeneous. We derive an anisotropic diffusion equation by taking the singular limit of the kinetic equation and then balancing out its curvature effect. We see that an extra information such as the turning frequency or waiting time is also needed together with the diffusivity to model a diffusion phenomenon correctly if the environment is spatially heterogeneous. A thought experiment is introduced to test the validity of diffusion laws. We observe that diffusion models with diffusivity alone fail the test and the anisotropic model driven in the paper passes the test.