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A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces

Duncan, A. B. and Elliott, C. M. and Pavliotis, G. A. and Stuart, A. M. (2015) A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces. Journal of Nonlinear Science, 25 (2). pp. 389-449. ISSN 0938-8974. https://resolver.caltech.edu/CaltechAUTHORS:20160715-172927058

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Abstract

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 DD 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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00332-015-9237-xDOIArticle
http://link.springer.com/article/10.1007%2Fs00332-015-9237-xPublisherArticle
https://arxiv.org/abs/1311.1007arXivDiscussion Paper
http://rdcu.be/uFztPublisherFree ReadCube access
Additional Information:© 2015 Springer. Received: 2 November 2013 / Accepted: 22 January 2015.
Subject Keywords:Homogenization, Laplace–Beltrami, Lateral diffusion, Multiscale analysis, Helfrich elastic membrane, Effective diffusion tensor
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ116
Issue or Number:2
Classification Code:35Q92 · 60H30 · 35B27
Record Number:CaltechAUTHORS:20160715-172927058
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160715-172927058
Official Citation:Duncan, A.B., Elliott, C.M., Pavliotis, G.A. et al. J Nonlinear Sci (2015) 25: 389. doi:10.1007/s00332-015-9237-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69078
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:18 Jul 2016 18:48
Last Modified:03 Oct 2019 10:18

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