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

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of Akron

2017-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63476

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/