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. (C) 2015 Elsevier B.V. All rights reserved.

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

Canevari, Giacomo;
2016-01-01

Abstract

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. (C) 2015 Elsevier B.V. All rights reserved.
Nematic liquid crystals; Landau-de Gennes theory; Radial-hedgehog; Minimizing configurations; Stable configurations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1010164
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