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Symmetry and pattern formation for a planar layer of nematic liquid crystal

Symmetry and pattern formation for a planar layer of nematic liquid crystal
Symmetry and pattern formation for a planar layer of nematic liquid crystal
Using equivariant bifurcation theory, and on the basis of symmetry considerations independent of the model, we classify square and hexagonally periodic patterns that typically arise when a homeotropic or planar isotropic nematic state becomes unstable, perhaps as a consequence of an applied magnetic or electric field. We relate this to a Landau–de Gennes model for the free energy, and derive dispersion relations in sufficient generality to illustrate the role of up/down symmetry in determining which patterns can arise as a stable bifurcation branch from either initial state.
0022-2488
4201-4219
Chillingworth, David
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
Golubitsky, Martin
0d621907-d42e-44ee-8192-aa87a167d43e
Chillingworth, David
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
Golubitsky, Martin
0d621907-d42e-44ee-8192-aa87a167d43e

Chillingworth, David and Golubitsky, Martin (2003) Symmetry and pattern formation for a planar layer of nematic liquid crystal. Journal of Mathematical Physics, 44 (9), 4201-4219. (doi:10.1063/1.1598620).

Record type: Article

Abstract

Using equivariant bifurcation theory, and on the basis of symmetry considerations independent of the model, we classify square and hexagonally periodic patterns that typically arise when a homeotropic or planar isotropic nematic state becomes unstable, perhaps as a consequence of an applied magnetic or electric field. We relate this to a Landau–de Gennes model for the free energy, and derive dispersion relations in sufficient generality to illustrate the role of up/down symmetry in determining which patterns can arise as a stable bifurcation branch from either initial state.

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Published date: 2003

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Local EPrints ID: 29797
URI: http://eprints.soton.ac.uk/id/eprint/29797
ISSN: 0022-2488
PURE UUID: c1a421b7-a9b7-4938-b7a3-3d66b5dc17a3

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Date deposited: 12 May 2006
Last modified: 08 Jan 2022 01:05

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Author: Martin Golubitsky

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