Elastic energy for reflection-symmetric topologies

Details Elastic energy for reflection-symmetric topologies Elastic energy for reflection-symmetric topologies

2005-07-20

arxiv.org/abs/math-ph/0507055v1

J. Phys. A: Math. Gen. 39 (2006) 2673-2687

Physics

Mathematical Physics

21 pages

Scientific paper

10.1088/0305-4470/39/11/008

Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with reflection-symmetric topologies, we derive a new lower bound for the one-constant elastic energy. For certain topologies, called conformal and anticonformal, the lower bound agrees with a previous result. For the remaining topologies, called nonconformal, the new bound is an improvement. For nonconformal topologies we derive an upper bound, which differs from the lower bound by a factor depending only on the aspect ratios of the prism.

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