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

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).

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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