Effective diffusion on riemannian fiber bundles

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.

15 pages, 3 Figures. Some corrections added

References in corpus (3)

• Curvature Dependent Diffusion Flow on Surface with Thickness
• Diffusion in a Curved Tube
• Projecting diffusion along the normal bundle of a plane curve

Cited by in corpus (1)

• Effective diffusion in the region between two surfaces