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Pré-Publication, Document De Travail Année : 2015

Radial symmetry on three-dimensional shells in the Landau-de Gennes theory

Résumé

We study the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We prove that the radial-hedgehog solution is the unique minimizer of the Landau-de Gennes energy in two separate regimes: (i) for thin shells when the temperature is below the critical nematic supercooling temperature and (ii) for a fixed shell width at sufficiently low temperatures. In case (i), we provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution.
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Dates et versions

hal-01157765 , version 1 (28-05-2015)

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  • HAL Id : hal-01157765 , version 1

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Apala Majumdar, Giacomo Canevari, Mythily Ramaswamy. Radial symmetry on three-dimensional shells in the Landau-de Gennes theory. 2015. ⟨hal-01157765⟩
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