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Small deformations of Helfrich energy minimising surfaces with applications to biomembranes

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 (08), pp. 1547-1586.

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Other 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 ...

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Item type:Article
Date:2017
Institutions:Mathematics
Identification Number:
ValueType
10.1142/S0218202517500269DOI
Keywords:MEMBRANES; PROTRUSIONS; CURVATURE; DYNAMICS; VESICLES; WILLMORE; THEOREM; DRIVEN; FLOW; Surface deformations; Helfrich energy; point forces; PDEs on surfaces; existence and uniqueness of weak solutions; discretisation; surface finite element method
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:39417
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