### 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 language | English |
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Pages (from-to) | 2673-2687 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 11 |

DOIs | |

Publication status | Published - 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