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Title: Kinks in a model for two-phase lipid bilayer membranes
Author: Helmers, Michael
ISNI:       0000 0004 2724 1584
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
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In the spontaneous curvature model for two-phase lipid bilayer membranes the shape of vesicles is governed by a combination of an elastic bending energy and an interface energy that penalises the size of phase boundaries. Each lipid phase induces a preferred curvature to the membrane surface, and these curvatures as well as phase boundaries may lead to the development of kinks. In a rotationally symmetric setting we introduce a family of energies for smooth surfaces and phase fields for the lipid components and study convergence to a sharp-interface limit, which depends on the choice of the bending parameters of the phase field model. We prove that, if kinks are excluded, our energies $Gamma$-converge to the commonly used sharp-interface spontaneous curvature energy with the additional assumption of $C^1$-regularity across interfaces. For a choice of parameters such that kinks may appear, we obtain a limit that coincides with the $Gamma$-limit on all reasonable membranes and extends the classical model by assigning a bending energy also to kinks. We illustrate the theoretical result by some numerical examples.
Supervisor: Niethammer, Barbara Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Calculus of variations and optimal control ; Statistical mechanics,structure of matter (mathematics) ; Biology and other natural sciences (mathematics)