I³MS - Voigt Seminar

We consider a thin film limit of a Frank-Oseen and a Landau-de Gennes model. In the limiting process we observe a continuous transition where the normal and tangential parts of the director field and the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Frank-Oseen and surface Landau-de Gennes model, we consider an $L^2$-gradient flow. The resulting vector- and tensor-valued surface partial differential equations are numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties and the topology of the surface. We will explain the 

numerical approaches in detail and discuss various model extensions.