Nematic equilibria on a two-dimensional annulus

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

Research output: Contribution to journalArticle

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Abstract

We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.
Original languageEnglish
Pages (from-to)438-466
Number of pages29
JournalStudies in Applied Mathematics
Volume138
Issue number4
Early online date16 Jan 2017
DOIs
Publication statusPublished - 31 May 2017

Fingerprint

Ring or annulus
Defects
Sector
Anisotropy
Preferred numbers
Stability criteria
Stability Criteria
Aspect Ratio
Tangent line
Aspect ratio
Quantify
Diagram
Perturbation
Configuration
Invariant
Geometry
Demonstrate

Keywords

  • nematic equilibria
  • two‐dimensional annulus
  • tangent anchoring
  • Oseen–Frank theoretical framework

Cite this

Lewis, A. H. ; Aarts, D. G. A. L. ; Howell, P. D. ; Majumdar, A. / Nematic equilibria on a two-dimensional annulus. In: Studies in Applied Mathematics. 2017 ; Vol. 138, No. 4. pp. 438-466.
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Nematic equilibria on a two-dimensional annulus. / Lewis, A. H.; Aarts, D. G. A. L.; Howell, P. D.; Majumdar, A.

In: Studies in Applied Mathematics, Vol. 138, No. 4, 31.05.2017, p. 438-466.

Research output: Contribution to journalArticle

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T1 - Nematic equilibria on a two-dimensional annulus

AU - Lewis, A. H.

AU - Aarts, D. G. A. L.

AU - Howell, P. D.

AU - Majumdar, A.

PY - 2017/5/31

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AB - We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen–Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defect-free state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.

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