M. Golubitsky and D. Chillingworth
Bifurcation and planar pattern formation for a liquid crystal
In: Conference on Bifurcations, Symmetry and Patterns.
(J. Buescu, S. Castro, A. Dias and I. Labouriau, eds.)
Birkhauser, Basel, 2003, 55-66.
We consider the Landau - de Gennes model for the free energy of a
liquid crystal, and discuss the geometry of its equilibrium set
(critical points) for spatially uniform states in the absence of
external fields. Using equivariant bifurcation theory we classify
(on the basis of symmetry considerations independent of the model)
square and hexagonally periodic patterns that can arise when a
homeotropic nematic state becomes unstable, perhaps as a consequence
of an applied magnetic or electric field.