Kalender Department Mathematik

Tue, 15.01.2019, 16:30
Particles in Membranes
Kolloquium

Referent: Prof. Dr. Ralf Kornhuber, Freie Universität Berlin
Veranstalter: Nicolas Neuss
Raum: HS 13

The interplay of curvature and particles diffusing in biological membranes is responsible for organizing and shaping the membrane and gives rise to a variety of cellular functions. Hybrid models combining a continuum representation of the membrane with discrete, highly coarse grained descriptions of particles  have a long history in physics, while mathematical analysis is still in its infancy. We present a hierarchy of variational formulations of existing hybrid models, where the coupling of particles and membrane is formulated in terms of  linear constraints to the minimization of the Canham–Helfrich energy of the membrane. Utilizing concepts from shape calculus, we derive a numerically feasible representation of  the derivative of the minimal Canham–Helfrich energy for given particle positions with respect to the particle positions. This representation is applied in numerical investigations of the clustering behavior of BAR domains and paves the way to Langevin dynamics of particles in membranes.