Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus

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

Research output: Contribution to journalArticle

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 - 2017

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Ring or annulus
Aspect Ratio
Aspect ratio
Asymptotic analysis
Defects
Dimensionless
Asymptotic Analysis
Dependent
Nematic liquid crystals
Isotropy
Local Stability
Nematic Liquid Crystal
Unstable
Temperature
Prediction
Model
Range of data

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Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus. / Lewis, A.H.; Aarts, D.G.A.L.; Howell, P.D.; Majumdar, Apala.

In: SIAM Journal on Applied Mathematics, Vol. 77, No. 6, 2017, p. 1851–1875.

Research output: Contribution to journalArticle

Lewis, A.H. ; Aarts, D.G.A.L. ; Howell, P.D. ; Majumdar, Apala. / Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus. In: SIAM Journal on Applied Mathematics. 2017 ; Vol. 77, No. 6. pp. 1851–1875.
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