Multistability for a reduced nematic liquid crystal model in the exterior of 2D polygons

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Abstract

We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with K edges, in a reduced Landau-de Gennes framework. This complements our previous work on the 'interior problem' for nematic equilibria confined inside regular polygons (SIAM Journal on Applied Mathematics, 80(4):1678-1703, 2020). The two essential dimensionless model parameters are λ-the ratio of the edge length of polygon hole to the nematic correlation length, and an additional degree of freedom, ϒ*-the nematic director at infinity. In the λ → 0 limit, the limiting profile has two interior point defects outside a generic polygon hole, except for a triangle and a square. For a square hole, the limiting profile has either no interior defects or two line defects depending on ϒ*, and for a triangular hole, there is a unique interior point defect outside the hole. In the λ → ∞ limit, there are at least (K 2) stable states and the multistability is enhanced by ϒ*, compared to the interior problem. Our work offers new insights into how to tune the existence, location, and dimensionality of defects.
Original languageEnglish
Article number24
Number of pages34
JournalJournal of Nonlinear Science
Volume33
DOIs
Publication statusPublished - 5 Jan 2023

Keywords

  • liquid crystal model
  • multistability
  • 2D polygons
  • nematic liquid crystal
  • f partially ordered materials
  • viscoelastic anisotropic materials

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