Stana, R, Lythe, G orcid.org/0000-0001-7966-5571 and Molina-Paris, C (2021) Diffusion in a Disk with a Circular Inclusion. SIAM Journal on Applied Mathematics, 81 (3). pp. 1287-1302. ISSN 0036-1399
Abstract
We consider diffusion in a disk, representing a cell with a circular interior compartment. Using bipolar coordinates, we perform exact calculations, not restricted by the size or location of the intracellular compartment. We find Green functions, hitting densities and mean times to move from the compartment to the cellular surface and vice versa. For molecules with diffusivity $D$, mean times are proportional to $R^2/D$, where $R$ is the radius of the cell. We find explicit expressions for the dependence on $a^2$ (the fraction of the cell occupied by the intracellular compartment) and on the displacement of the compartment from the center of the cell. We consider distributions of initial conditions that are (i) uniform on the nuclear surface, (ii) uniform on the cellular surface, or (iii) given by the hitting density of particles diffusing from the nuclear to the cellular surface.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021, Society for Industrial and Applied Mathematics. This is an author produced version of an article published in SIAM Journal on Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | diffusion, Green's function, mean times |
Dates: |
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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: | 12 Jan 2021 09:59 |
Last Modified: | 22 Jul 2021 17:37 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/20M1351394 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:169758 |