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On a surface phase field model for two-phase biological membranes
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Stinner, Björn (2010) On a surface phase field model for two-phase biological membranes. In: 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Dresden, Germany, 25-28 May 2010 (Unpublished)
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Official URL: http://tu-dresden.de/die_tu_dresden/fakultaeten/fa...
Abstract
Vesicles formed by lipid bilayers (biomembranes) show a variety of interesting shapes that can be explained by their elastic energy. Due to inhomogeneities the lipids may separate and form different phases which results in an energy contribution from the phase interfaces. In order to compute equilibrium shapes a gradient flow dynamics has been defined where the membrane is represented by an evolving hypersurface and intra-membrane domains are described using the phase field method. The governing equations consist of a geometric evolution law of Willmore flow type coupled to a surface Allen-Cahn equation. The field variables are the positions of material points of the surface, the mean curvature vector, and the surface phase field function. Using asymptotic expansions the sharp interface limit of the stationary equations has been computed and results in a free boundary problem on the membrane surface which is unknown as well but given as the solution to a geometric equation. Numerical investigations with a method based on surface finite elements support the formal result.
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Official Date: | 26 May 2010 | ||||
Dates: |
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Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications | ||||
Type of Event: | Conference | ||||
Location of Event: | Dresden, Germany | ||||
Date(s) of Event: | 25-28 May 2010 | ||||
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