反射对称拓扑的弹性能
Elastic energy for reflection-symmetric topologies
摘要：
多面体域中的向列相液晶是液晶显示器的原型，可以用切向边界条件下的单位矢量场来描述。这里我们考虑矩形棱柱的情况。对于具有反射对称拓扑结构的构型，我们导出了一个新的一常数弹性能的下界。对于某些拓扑，称为共形和反共形，下界同意以前的结果。对于其余的拓扑，称为非共形，新的界限是一个改进。对于非共形拓扑结构，我们推导出一个上限，它不同于下限的一个因素，只取决于纵横比的棱镜。
英文摘要：
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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