Revisiting the two-dimensional defect-free azimuthal nematic equilibrium on an annulus

A. H. Lewis, D. G. A. L. Aarts, P. D. Howell, A. Majumdar

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Abstract

We study the azimuthal defect-free nematic state on a two-dimensional annulus within a simplified and reduced two-dimensional Landau--de Gennes model for nematic liquid crystals. We perform a detailed asymptotic analysis of the instabilities of the defect-free state in terms of a dimensionless material and temperature-dependent variable and the annular aspect ratio. The asymptotic analysis is accompanied by a rigorous local stability result, again in terms of a dimensionless material and temperature-dependent parameter and annular aspect ratio. In contrast to Oseen--Frank predictions, the defect-free state can be unstable in this model, with elastic isotropy and strong anchoring, for a range of macroscopically relevant annular aspect ratios.
Original languageEnglish
Pages (from-to)1851–1875
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume77
Issue number6
DOIs
Publication statusPublished - 2 Nov 2017

Keywords

  • Landau–de Gennes
  • azimuthal state
  • stability
  • asymptotics

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