Constant-angle surfaces in liquid crystals

Paolo Cermelli (1) , Antonio J. Di Scala (2)

1 Mathematics
2 DIMAT - Department of Mathematics [Torino]

We discuss some properties of surfaces in $\rr^3$ whose unit normal vector has constant angle with an assigned direction field. The constant angle condition can be rewritten as an 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.

Mots clés: Physical Sciences

Paolo Cermelli, Antonio J. Di Scala. Constant-angle surfaces in liquid crystals. Philosophical Magazine, 2007, 87 (12), pp.1871-1888. ⟨10.1080/14786430601110364⟩. ⟨hal-00513811⟩