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

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• 作者：G. Di Fratta ; J. M. Robbins ; V. Slastikov ; A. Zarnescu
• 关键词：Nonlinear elliptic PDE system ; Singular ODE system ; Stability ; Vortex ; Liquid crystal defects
• 刊名：Journal of Nonlinear Science
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：26
• 期：1
• 页码：121-140
• 全文大小：1,259 KB
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• 作者单位：G. Di Fratta (1)
  J. M. Robbins (1)
  V. Slastikov (1)
  A. Zarnescu (2) (3)
  
  1. School of Mathematics, University of Bristol, Bristol, UK
  2. Department of Mathematics, University of Sussex, Falmer, UK
  3. Institute of Mathematics “Simion Stoilow”, Bucharest, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Mathematical and Computational Physics
  Mechanics
  Applied Mathematics and Computational Methods of Engineering
  Economic Theory
  
• 出版者：Springer New York
• ISSN：1432-1467

文摘

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, \(b^2\) small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case \(b^2=0\), we investigate in greater detail the regime of vanishing elastic constant \(L \rightarrow 0\), where we obtain three explicit point defect profiles, including the global minimiser. Keywords Nonlinear elliptic PDE system Singular ODE system Stability Vortex Liquid crystal defects