Elastic energy for reflection-symmetric topologies

TL;DR

This paper derives new bounds for the elastic energy of nematic liquid crystals in rectangular prisms with reflection-symmetric topologies, improving understanding of their energy landscape and stability.

Contribution

It introduces a new lower bound for elastic energy in reflection-symmetric topologies, especially for nonconformal cases, and compares it with existing bounds.

Findings

New lower bound for nonconformal topologies

Agreement of bounds for conformal and anticonformal topologies

Upper bound depending on prism aspect ratios

Abstract

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.