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A multiscale analysis of diffusions on rapidly varying surfaces

journal contribution
posted on 2023-06-09, 06:42 authored by A M Duncan, C M Elliott, G A Pavliotis, A M Stuart
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission, and other phenomena such as exo- and endocytosis, signal transduction, chemotaxis, and cell growth. In many cases, the surfaces can possess spatial inhomogeneities and/or be rapidly changing shape. Using a generalization of the model for a thermally excited Helfrich elastic membrane, we consider the problem of lateral diffusion on quasi-planar surfaces, possessing both spatial and temporal fluctuations. Using results from homogenization theory, we show that, under the assumption of scale separation between the characteristic length and timescales of the membrane fluctuations and the characteristic scale of the diffusing particle, the lateral diffusion process can be well approximated by a Brownian motion on the plane with constant diffusion tensor D that depends on a highly nonlinear way on the detailed properties of the surface. The effective diffusion tensor will depend on the relative scales of the spatial and temporal fluctuations, and for different scaling regimes, we prove the existence of a macroscopic limit in each case.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Nonlinear Science

ISSN

0938-8974

Publisher

Springer Verlag

Issue

2

Volume

25

Page range

389-449

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Probability and Statistics Research Group Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2017-06-15

First Compliant Deposit (FCD) Date

2017-06-15

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