Effective diffusion on riemannian fiber bundles

TL;DR

This paper develops equations to model effective diffusion on Riemannian fiber bundles by projecting the diffusion equation onto the base manifold, generalizing previous models for curved channels and interfaces.

Contribution

It introduces a general framework for effective diffusion on Riemannian fiber bundles, extending prior work on diffusion in curved structures.

Findings

Derived equations for diffusion on fiber bundles

Generalized previous models to a broader geometric setting

Provides a mathematical framework for diffusion in complex structures

Abstract

The purpose of this paper is to provide equations to model the evolution of effective diffusion over a Riemannian fiber bundle (under the hypothesis of infinite diffusion rate along compact fibers). These equations are obtained by projecting the diffusion equation onto the base manifold of the fiber bundle. The projection (or dimensional reduction) is achieved by integrating the diffusion equation along fibers of the bundle. This work generalizes an put into a general framework previous work on effective diffusion over channels and the interfaces between curved surfaces.