Wednesday, July 3, 2013

1307.0295 (Xavier Lamy)

Spontaneous breaking of uniaxial symmetry in nematics    [PDF]

Xavier Lamy
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. For an arbitrary form of the bulk energy density, we show that energy minimizers among uniaxially symmetric configurations are usually not equilibrium configurations. A more precise result is obtained in the case of configurations with translational invariance in at least one direction. Namely, uniaxial configurations must have a uniform director field. In the case of a hybrid nematic cell, or of a capillary with radial anchoring, our result implies that biaxial escape always occurs, and that it does so not only in the core of a defect: uniaxial order is destroyed in the whole cell.
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