Surface, size and topological effects for some nematic equilibria on rectangular domains

Lidong Fang, Apala Majumdar, Lei Zhang

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We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, ϵ, which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the ϵ→ 0 limit relevant for macroscopic domains and the ϵ→∞ limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the ϵ→∞ limit, whereas we observe fractional point defects in the ϵ→ 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of ϵ and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.
Original languageEnglish
Pages (from-to)1101-1123
Number of pages23
JournalMathematics and Mechanics of Solids
Issue number5
Early online date26 Feb 2020
Publication statusPublished - 1 May 2020


  • nematic liquid crystals
  • Landau-de Gennes model
  • bifurcation diagram
  • asymptotic limit
  • well order reconstruction solution


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