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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. (2020) Domain formation via phase separation for spherical biomembranes with small deformations. European Journal of Applied Mathematics . doi:10.1017/S0956792520000297 (In Press)
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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 | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Journal or Publication Title: | European Journal of Applied Mathematics | ||||||||
| Publisher: | Cambridge University Press | ||||||||
| ISSN: | 0956-7925 | ||||||||
| Official Date: | 2020 | ||||||||
| Dates: |
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| Date of first compliant deposit: | 13 August 2020 | ||||||||
| DOI: | 10.1017/S0956792520000297 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | In Press | ||||||||
| Publisher Statement: | 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 | ||||||||
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