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Accumulation time of diffusion in a 2D singularly perturbed domain
File(s)
diffR.pdf (3.24 MB)
Accepted version
Author(s)
Bressloff, PC
Type
Journal Article
Abstract
A general problem of current interest is the analysis of diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One major application is to intracellular diffusion, where the holes could represent organelles or biochemical substrates. In this paper, we use a combination of matched asymptotic analysis and Green’s function methods to calculate the so-called accumulation time for relaxation to steady state. The standard measure of the relaxation rate is in terms of the principal non-zero eigenvalue of the negative Laplacian. However, this global measure does not account for possible differences in the relaxation rate at different spatial locations, is independent of the initial conditions, and relies on the assumption that the eigenvalues have sufficiently large spectral gaps. As previously established for diffusion-based morphogen gradient formation, the accumulation time provides a better measure of the relaxation process.
Date Issued
2022-03
Date Acceptance
2022-01-31
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, 478 (2259)
URI
URL
DOI
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
478
Issue
2259
Copyright Statement
© 2022 The Author(s)

Published by the Royal Society under the terms of the
Creative Commons Attribution License http://creativecommons.org/licenses/
by/4.0/, which permits unrestricted use, provided the original author and
source are credited.
License URL
Identifier
http://dx.doi.org/10.1098/rspa.2021.0847
Publication Status
Published
Date Publish Online
2022-03-02