D. Chillingworth and M. Golubitsky
Symmetry and pattern formation for a planar layer of nematic liquid crystal
Journal of Mathematical Physics.
44 (9) (2003) 4201-4219.
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.