Liquid crystal defects in the Landau-de Gennes theory in two dimensions - beyond the one-constant approximation

Georgy Kitavtsev, Jonathan Robbins, Valeriy Slastikov, A. Zarnescu

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)
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Abstract

We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general k-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case k = 2. In this case we identify three types of radial pro files: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parameters.

We also numerically study the stability properties of the critical points of the Landau-de Gennes energy and capture the intricate dependence of various qualitative features of these solutions on the elastic constants and the physical regimes of the liquid crystal system.
Original languageEnglish
Article number2769
JournalMathematical Models and Methods in Applied Sciences
Volume26
Issue number14
Early online date21 Dec 2016
DOIs
Publication statusPublished - 30 Dec 2016

Keywords

  • Liquid crystals
  • Q-tensors
  • k-radially symmetric solutions
  • minimisers

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