Elastic energy of liquid crystals in convex polyhedra

A Majumdar, JM Robbins, M Zyskin

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)


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 contributionElastic energy of liquid crystals in convex polyhedra
Original languageEnglish
Pages (from-to)L573 - L580
Number of pages8
JournalJournal of Physics A: Mathematical and General
Volume37 (44)
Publication statusPublished - Nov 2004

Bibliographical note

Publisher: IOP Publishing td


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