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Paquin-Lefebvre F, Holcman D. Modelling and asymptotic analysis of the concentration difference in a nanoregion between an influx andoutflux diffusion acrossnarrow windows. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady state, we compute asymptotically the distribution of concentration between the different windows. The solution is obtained by solving Laplace’s equation using Green’s function techniques and second-order asymptotic analysis, and depends on the influx amplitude, the diffusion properties, as well as the geometrical organization of all the windows, such as their distances and the mean curvature. We explore the range of validity of the present asymptotic expansions using numerical simulations of the mixed boundary value problem. Finally, we introduce a length scale to estimate how deep inside a domain a local diffusion current can spread.
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Affiliation(s)
- F. Paquin-Lefebvre
- Applied Mathematics and Computational Biology, IBENS, Ecole Normale Supérieure, 75005 Paris, France
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- Applied Mathematics and Computational Biology, IBENS, Ecole Normale Supérieure, 75005 Paris, France
- Department of Applied Mathematics and Theoretical Physics, and Churchill College, University of Cambridge, Cambridge CB3 0DS, UK
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