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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 StuartLateral 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.
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Publication status
- Published
File Version
- Published version
Journal
Journal of Nonlinear ScienceISSN
0938-8974Publisher
Springer VerlagExternal DOI
Issue
2Volume
25Page range
389-449Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2017-06-15First Compliant Deposit (FCD) Date
2017-06-15Usage metrics
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