Luca Lussardi - Ricercatore, Politecnico di Torino - A MULTIPLE SCALES MODEL FOR BIOMEMBRANES AND VARIATIONAL LIMITS
Biomembranes are remarkable structures with both fluid-like and solid-like properties: the main constituents are amphiphilic lipids, which have a head part that attracts water and a tail part that repels it. As a consequence, such lipids organise themselves in micelle and bilayer structures, where the head parts shield the lipid tails from the contact with water. In a recent paper by Peletier and Röger (2009), a mesoscale model was introduced in the form of energy for idealised and rescaled head and tails densities. The energy has two contributions; one penalises the proximity of tail to polar (head or water) particles, and the second implements the head-tail connection as an energetic penalisation. The thickness of the structure is minimal, and a full Gamma-convergence result has been proved in the 2D case. The Gamma-limit turns out to be the Euler elastic functional for curves in the plane. The 3D case is much harder, and there are only partial results. In this seminar, Prof. Lussardi will present the mesoscopic model proposed by Peletier and Röger. He will briefly explain how the deduction of the 2D-macroscopic model by Gamma-convergence works and then he will provide some details on the 3D-case. The analysis of such a case requires in-depth tools from geometric measure theory, like currents and varifolds, to have weak notions of surfaces suitable for Calculus of Variations and for which a suitable notion of curvatures exists. This research project is in collaboration with Mark Peletier and Matthias Röger
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