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BIRS Workshop Lecture Videos

Dimension Reduction for the Landau-de Gennes Model In Thin Nematic Films Golovaty, Dmitry


I will present a recent Gamma-convergence result that describes the behavior of the Landau-de Gennes (LdG) model for a nematic liquid crystalline film in the limit of vanishing thickness. The film is assumed to be attached to a fixed surface. In the LdG theory, an equilibrium liquid crystal configuration is specified by a tensor-valued order parameter field - a nematic Q-tensor - that minimizes an energy consisting of the bulk potential, elastic, and surface (weak anchoring) energy contributions. In the asymptotic regime of vanishing thickness, the anchoring energy plays a greater role and it is essential to understand its influence on the structure of the minimizers of the derived limiting surface energy. I will outline a general convergence result and then discuss the limiting problem in several parameter regimes. This is a joint work with Alberto Montero and Peter Sternberg.

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