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A Coordinate Free Formulation of Effective Diffusion on Channels - MaRDI portal

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A Coordinate Free Formulation of Effective Diffusion on Channels

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Publication:6346973

arXiv2008.05436MaRDI QIDQ6346973

Author name not available (Why is that?)

Publication date: 12 August 2020

Abstract: We study diffusion processes in regions generated by sliding a cross section by the phase flow of vector filed on curved spaces of arbitrary dimension. We do this by studying the effective diffusion coefficient D that arises when trying to reduce the n-dimensional diffusion equation to a 1-dimensional diffusion equation by means of a projection method. We use the mathematical language of exterior calculus to derive a coordinate free formula for this coefficient in both infinite and finite transversal diffusion rate cases. The use of these techniques leads to a formula for D which provides a deeper understanding of effective diffusion than when using a coordinate dependent approach.












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