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

doi:10.1137/17m1124656

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

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	1851-1875
Number of pages	25
Journal	SIAM Journal on Applied Mathematics
Volume	77
Issue number	6
DOIs	https://doi.org/10.1137/17m1124656
State	Published - Jan 2017
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-04-06
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is partly based on work supported by award KUK-C1-013-04 from the King Abdullah University of Science and Technology (KAUST). The first author's work was supported by the Engineering and Physical Sciences Research Council (EPSRC) studentship. The fourth author's work was supported by an EPSRC Career Acceleration Fellowship EP/J001686/1 and EP/J001686/2, an OCIAM Visiting Fellowship, a UK Fluids Short Research Visit grant, and the Keble Advanced Studies Centre.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Applied Mathematics

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10.1137/17m1124656

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title = "Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus",

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.",

author = "Lewis, {A. H.} and Aarts, {D. G. A. L.} and Howell, {P. D.} and A. Majumdar",

note = "KAUST Repository Item: Exported on 2021-04-06 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is partly based on work supported by award KUK-C1-013-04 from the King Abdullah University of Science and Technology (KAUST). The first author's work was supported by the Engineering and Physical Sciences Research Council (EPSRC) studentship. The fourth author's work was supported by an EPSRC Career Acceleration Fellowship EP/J001686/1 and EP/J001686/2, an OCIAM Visiting Fellowship, a UK Fluids Short Research Visit grant, and the Keble Advanced Studies Centre. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2017",

month = jan,

doi = "10.1137/17m1124656",

language = "English (US)",

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pages = "1851--1875",

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publisher = "Society for Industrial and Applied Mathematics Publications",

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AU - Lewis, A. H.

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

AU - Howell, P. D.

AU - Majumdar, A.

N1 - KAUST Repository Item: Exported on 2021-04-06 Acknowledged KAUST grant number(s): KUK-C1-013-04 Acknowledgements: This publication is partly based on work supported by award KUK-C1-013-04 from the King Abdullah University of Science and Technology (KAUST). The first author's work was supported by the Engineering and Physical Sciences Research Council (EPSRC) studentship. The fourth author's work was supported by an EPSRC Career Acceleration Fellowship EP/J001686/1 and EP/J001686/2, an OCIAM Visiting Fellowship, a UK Fluids Short Research Visit grant, and the Keble Advanced Studies Centre. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2017/1

Y1 - 2017/1

N2 - 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.

AB - 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.

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JF - SIAM Journal on Applied Mathematics

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ER -

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

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