TY - JOUR

T1 - Elastic energy of liquid crystals in convex polyhedra

AU - Majumdar, A.

AU - Robbins, J. M.

AU - Zyskin, M.

PY - 2004/10/20

Y1 - 2004/10/20

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1088/0305-4470/37/44/L05

U2 - 10.1088/0305-4470/37/44/L05

DO - 10.1088/0305-4470/37/44/L05

M3 - Article

VL - 37

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 44

M1 - L573

ER -