Stinner, Björn (2009) On a surface finite element method for biomembranes with lipid decomposition. In: EPSRC Symposium Capstone Conference, University of Warwick, Coventry, 30 Jun-03 Jul 2009 (Unpublished)

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Abstract

Bilayers consisting of lipids molecules are the basic component of cell membranes. Vesicles formed from such biomembranes show a variety of interesting shapes that can be explained by its elastic bending energy. Due to inhomogeneities the lipids may separate and form different phases on the membrane which results in an energy contribution from the phase interfaces. We have been numerically studying equilibrium shapes, i.e., local energy minima by relaxing suitable initial shapes. A suitable (kind of) gradient flow dynamics has been defined for this purpose where the inter-membrane domains are described using the phase field methodology. The governing equations consist of pde on the membrane surface describing the phase separation coupled to a geometric evolution law for the membrane. The discretisation is based on representing the membrane by a triangulated surface on which quadratic parametric FEs are defined. The convergence as grid parameter and diffuse interface thickness tend to zero has been numerically investigated. Further issues are the sharp interface limit of the phase-field approach and adaptive mesh refinement.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Official Date:	3 July 2009
Dates:	Date Event 3 July 2009 Completion
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Conference Paper Type:	Paper
Title of Event:	EPSRC Symposium Capstone Conference
Type of Event:	Conference
Location of Event:	University of Warwick, Coventry
Date(s) of Event:	30 Jun-03 Jul 2009

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