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Small deformations of Helfrich energy minimising surfaces with applications to biomembranes
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Elliott, Charles M., Fritz, Hans and Hobbs, Graham (2017) Small deformations of Helfrich energy minimising surfaces with applications to biomembranes. Mathematical Models and Methods in Applied Sciences, 27 (8). pp. 1547-1586. doi:10.1142/s0218202517500269
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Official URL: http://doi.org/10.1142/s0218202517500269
Abstract
In this paper we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Surfaces, Differential equations, Elliptic, Lagrange equations | ||||||
| Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||
| ISSN: | 0218-2025 | ||||||
| Official Date: | 12 June 2017 | ||||||
| Dates: |
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| Volume: | 27 | ||||||
| Number: | 8 | ||||||
| Page Range: | pp. 1547-1586 | ||||||
| DOI: | 10.1142/s0218202517500269 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Open Access Version: |
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