Elastic energy for reflection-symmetric topologies

Apala Majumdar, J. M. Robbins, M. Zyskin

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)2673-2687
Number of pages15
JournalJournal of Physics A: Mathematical and General
Volume39
Issue number11
DOIs
Publication statusPublished - 1 Mar 2006

Keywords

  • elastic energy
  • reflection-symmetric topologies
  • liquid crystal displays

Cite this

Majumdar, A., Robbins, J. M., & Zyskin, M. (2006). Elastic energy for reflection-symmetric topologies. Journal of Physics A: Mathematical and General, 39(11), 2673-2687. https://doi.org/10.1088/0305-4470/39/11/008