“Models for liquid crystals on surfaces”
Venerdì 25 Febbraio 2022, ore 12:00 - Sala Riunioni 702 - Axel Voigt (Institute of Scientific Computing Technische Universität Dresden - Germany)
While continuous models for liquid crystals are well established in 2D and 3D, their formulation on curved surfaces introduces new phenomena. We consider models for polar and nematic liquid crystals on curved surfaces, where we ensure a tangential alignment of the director field. This leads to a strong coupling of the unknowns with topological and geometrical properties of the surface. Numerical investigations by surface finite elements for the resulting vector- and tensor-valued surface partial differential equations are used to explore these couplings. If in addition the surface is allowed to relax, this leads to unexpected equilibrium shapes. They are determined by the texture of the liquid crystal and strongly depend on the assumptions made in the derivation of the surface models.