日時: 2013年11月28日(木)16:20-17:20
場所: 京都教育大学 A棟4階 1A413教室
講演者: Pierluigi Colli 氏 (Department of Mathematics, The University of Pavia)
題目: A phase field model for the Willmore flow with constraints applying to the evolution of membranes
Biological cell membranes define the border between the interior of the cell and its surrounding medium and can be roughly described as a bilayer in which several kinds of lipids are assembled and through which proteins diffuse. The size of the cell (a few microns) is typically much larger than the thickness of the membrane (a few nanometers) and a possible approach to model the geometric properties of the latter is to assume the membrane to be a two-dimensional embedded surface in the three-dimensional space with a shape at equilibrium being determined by the Canham-Helfrich elastic bending energy. In a simplified setting, this energy reduces to the Willmore functional which is a well-known object in differential geometry. Two natural geometric constraints come along with cell membranes: the inextensibility of the membrane fixes the total area while a volume constraint follows from its permeability properties.
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