### Abstract

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 |
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Original language | English |

Pages (from-to) | 2673 - 2687 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 (11) |

Publication status | Published - 17 Mar 2006 |

### Bibliographical note

Publisher: IOP Publishing LtdOther identifier: IDS number 032LP

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## Cite this

Majumdar, A., Robbins, JM., & Zyskin, M. (2006). Elastic energy for reflection-symmetric topologies.

*Journal of Physics A: Mathematical and General*,*39 (11)*, 2673 - 2687.