M 511 oder M 643

Biological vesicles are the basic tools used by living cells for organizing and transporting substances. The membrane of such a vesicle has unusual mechanic properties. It resists bending like a solid but can also be seen as a two-dimensional fluid because its components can move freely within the plane of the membrane. We describe here a 3D nonlinear elastic model for membranes with positive thickness. To reflect the solid-fluid nature of the membrane, the stored energy function of the model is highly anisotropic and degenerate. This model is highly anisotropic and degenerate to account for the solid-fluid nature of the membrane. We then perform a Gamma limit analysis of this model in the thin membrane regime. At the limit, we recover the theory of Helfrich: the vesicle membrane is described as an oriented surface and its free energy is given by a second order geometric functional depending on its mean curvature. More specifically, this energy is a variation of the Willmore functional.

Prof. Dr. Benoît Merlet

Université Paris Nord, École Polytechnique