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Domain formation via phase separation for spherical biomembranes with small deformations
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Elliott, Charles M. and Hatcher, L. (2021) Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics, 32 (6). pp. 1127-1152. doi:10.1017/S0956792520000297 ISSN 0956-7925.
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Official URL: https://doi.org/10.1017/S0956792520000297
Abstract
We derive and analyse an energy to model lipid raft formation on biological membranes involving a coupling between the local mean curvature and the local composition. We apply a perturbation method recently introduced by Fritz, Hobbs and the rst author to describe the geometry of the surface as a graph over an undeformed Helfrich energy minimising surface. The result is a surface Cahn-Hilliard functional coupled with a small deformation energy. We show that suitable minimisers of this energy exist and consider a gradient ow with conserved Allen-Cahn dynamics, for which existence and uniqueness results are proven. Finally, numerical simulations show that for the long time behaviour raft-like structures can emerge and stabilise, and their parameter dependence is further explored.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QH Natural history |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Membranes (Biology) -- Mathematical models, Lipid membranes -- Mathematical models, Curvature | |||||||||
| Journal or Publication Title: | European Journal of Applied Mathematics | |||||||||
| Publisher: | Cambridge University Press | |||||||||
| ISSN: | 0956-7925 | |||||||||
| Official Date: | December 2021 | |||||||||
| Dates: |
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| Volume: | 32 | |||||||||
| Number: | 6 | |||||||||
| Page Range: | pp. 1127-1152 | |||||||||
| DOI: | 10.1017/S0956792520000297 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in European Journal of Applied Mathematics http://doi.org/10.1017/S0956792520000297. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © copyright holder. | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Copyright Holders: | © The Author(s), 2020. Published by Cambridge University Press | |||||||||
| Date of first compliant deposit: | 13 August 2020 | |||||||||
| Date of first compliant Open Access: | 18 March 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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