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

Giacomo Canevari, Mythily Ramaswamy, Apala Majumdar

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)18-34
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume314
Early online date9 Oct 2015
DOIs
Publication statusPublished - 1 Jan 2016

Fingerprint

Radial Symmetry
Radial Solutions
Shell
Three-dimensional
symmetry
Supercooling
Spherical Shell
Thin Shells
Nematic liquid crystals
Minimality
spherical shells
Nematic Liquid Crystal
supercooling
Minimizer
Temperature
liquid crystals
Boundary conditions
boundary conditions
temperature
Geometry

Keywords

  • Landau-de Gennes theory
  • minimizing configurations
  • nematic liquid crystals
  • radial-hedgehog
  • stable configurations

Cite this

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Radial symmetry on three-dimensional shells in the Landau-de Gennes theory. / Canevari, Giacomo; Ramaswamy, Mythily; Majumdar, Apala.

In: Physica D: Nonlinear Phenomena, Vol. 314, 01.01.2016, p. 18-34.

Research output: Contribution to journalArticle

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AU - Canevari, Giacomo

AU - Ramaswamy, Mythily

AU - Majumdar, Apala

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AB - 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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