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On the sharp interface limit of a phase field model for near-spherical two phase biomembranes
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Elliott, Charles M., Hatcher, L. and Stinner, Björn (2022) On the sharp interface limit of a phase field model for near-spherical two phase biomembranes. Interfaces and Free Boundaries, 24 (2). pp. 263-286. doi:10.4171/IFB/473 ISSN 1463-9963.
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Official URL: https://doi.org/10.4171/IFB/473
Abstract
We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is motivated by lipid raft formation. We introduce a reduced diffuse interface energy depending only on the membrane composition and derive the Γ−limit. We demonstrate that the Euler-Lagrange equations for the limiting functional and the sharp interface energy coincide. Finally, we consider a system of gradient flow equations with conserved Allen-Cahn dynamics for the phase field model. Performing a formal asymptotic analysis we obtain a system of gradient flow equations for the sharp interface energy coupling geodesic curvature flow for the phase interface to a fouth order PDE free boundary problem for the surface deformation.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Membranes (Biology), Membranes (Biology) -- Mathematical models, Perturbation (Mathematics), Curvature | ||||||||||||
| Journal or Publication Title: | Interfaces and Free Boundaries | ||||||||||||
| Publisher: | EMS Press | ||||||||||||
| ISSN: | 1463-9963 | ||||||||||||
| Official Date: | 14 May 2022 | ||||||||||||
| Dates: |
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| Volume: | 24 | ||||||||||||
| Number: | 2 | ||||||||||||
| Page Range: | pp. 263-286 | ||||||||||||
| DOI: | 10.4171/IFB/473 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Copyright Holders: | © 2021 EMS Press | ||||||||||||
| Date of first compliant deposit: | 27 October 2021 | ||||||||||||
| Date of first compliant Open Access: | 27 October 2021 | ||||||||||||
| RIOXX Funder/Project Grant: |
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