Analysis of Nematic Liquid Crystals with Disclination Lines

Details Analysis of Nematic Liquid Crystals with Disclination Lines Analysis of Nematic Liquid Crystals with Disclination Lines

2011-06-24

arxiv.org/abs/1106.5031v1

Mathematics

Analysis of PDEs

40 pages, 1 figure

Scientific paper

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.

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