Constant-angle surfaces in liquid crystals

Abstract

We discuss some properties of surfaces in whose unit normal vector has constant angle with an assigned direction field. The constant-angle condition can be rewritten as a Hamilton–Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and examine some properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog). We also show how our results may be used to study the shape of disclination cores.

Acknowledgments

P.C. was supported by the Italian M.I.U.R. research grant ‘Modelli matematici per la scienza dei materiali’ (2005).

Notes

† In complex coordinates the conformal (holomorphic) transformation is (w_g+ig)), with w_g the harmonic conjugate of g