Diffusion in the Presence of Cells with Semi-permeable Membranes

We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of the domain than to enter the interior of its complement, with...

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Bibliographic Details
Published in:Journal of statistical physics 2020-03, Vol.178 (6), p.1417-1441
Main Authors: Freidlin, M., Koralov, L.
Format: Article
Language:English
Subjects:
Boundaries
Domains
Mathematical and Computational Physics
Parameters
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Trapping
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Summary:We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of the domain than to enter the interior of its complement, with a small parameter controlling the trapping mechanism. We describe the limiting behavior of the processes. In particular, if the parameters controlling the boundary behavior have different orders of magnitude for different domains or if the domains are nested, metastable distributions between the trapping regions are described.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-020-02510-6