Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

G. Di Fratta*, J. M. Robbins, V. Slastikov, A. Zarnescu

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
349 Downloads (Pure)

Abstract

We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b2 = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.

Original languageEnglish
Pages (from-to)121-140
Number of pages20
JournalJournal of Nonlinear Science
Volume26
Issue number1
Early online date25 Aug 2015
DOIs
Publication statusPublished - Feb 2016

Keywords

  • Liquid crystal defects
  • Nonlinear elliptic PDE system
  • Singular ODE system
  • Stability
  • Vortex

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