Vortices in two-dimensional nematics

We study a two-dimensional model describing spatial variations of orientational ordering in nematic liquid crystals. In particular, we show that the spatially extended Onsager-Maier-Saupe free energy may be decomposed into Landau-de Gennes-type and relative entropy-type contributions. We then prove that in the high concentration limit the states of the system display characteristic vortex-like patterns and derive an asymptotic expansion for the free energy of the system.

Keywords

Liquid crystals, nematics, spatial patterns, vortices

2010 Mathematics Subject Classification

82B21, 82B26, 82D30

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Published 1 January 2009