Nematic liquid crystals in a polyheadral 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.
|Translated title of the contribution||Elastic energy for reflection-symmetric topologies|
|Pages (from-to)||2673 - 2687|
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 17 Mar 2006|
Bibliographical notePublisher: IOP Publishing Ltd
Other identifier: IDS number 032LP