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

Giacomo Canevari, Mythily Ramaswamy, Apala Majumdar

Research output: Contribution to journalArticle

7 Citations (Scopus)

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
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Landau-de Gennes theory
  • Minimizing configurations
  • Nematic liquid crystals
  • Radial-hedgehog
  • Stable configurations

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