Nematic liquid crystals on curved surfaces - a thin film limit

Abstract

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of 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 Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.

20 pages, 4 figures

References in corpus (3)

• Topology and Dynamics of Active Nematic Vesicles
• Topological Defects in Spherical Nematics
• Solving the incompressible surface Navier-Stokes equation by surface finite elements

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• Cooling a spherical nematic shell
• Active smectics on a sphere
• Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals