Stana, R. and Lythe, G. orcid.org/0000-0001-7966-5571 (2022) Diffusion in a disk with inclusion: Evaluating Green’s functions. PLOS ONE, 17 (4). e0265935. ISSN 1932-6203
Abstract
We give exact Green’s functions in two space dimensions. We work in a scaled domain that is a circle of unit radius with a smaller circular “inclusion”, of radius a, removed, without restriction on the size or position of the inclusion. We consider the two cases where one of the two boundaries is absorbing and the other is reflecting. Given a particle with diffusivity D, in a circle with radius R, the mean time to reach the absorbing boundary is a function of the initial condition, given by the integral of Green’s function over the domain. We scale to a circle of unit radius, then transform to bipolar coordinates. We show the equivalence of two different series expansions, and obtain closed expressions that are not series expansions.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Stana, Lythe. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Jan 2025 10:57 |
Last Modified: | 07 Jan 2025 10:57 |
Status: | Published |
Publisher: | Public Library of Science |
Identification Number: | 10.1371/journal.pone.0265935 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221430 |