## Abstract

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing, test configurations constructed from local conformal solutions of the Euler-Lagrange equation. The ratio of the upper and lower bounds depends only on the aspect ratios of the prism. As the aspect ratios are varied, the minimum-energy conformal state undergoes a sharp transition from being smooth to having singularities on the edges.

Translated title of the contribution | Elastic energy of liquid crystals in convex polyhedra |
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Original language | English |

Pages (from-to) | L573 - L580 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 (44) |

DOIs | |

Publication status | Published - Nov 2004 |