Numerics for liquid crystals with variable degree of orientation

Document Type

Conference Proceeding

Publication Date

1-1-2015

Abstract

We consider the simplest one-constant model, put forward by J. Eriksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field n and its degree of orientation s, where the pair (n, s) minimizes a sum of Frank-like energies and a double well potential. In particular, the Euler-Lagrange equations for the minimizer contain a degenerate elliptic equation for n, which allows for line and plane defects to have finite energy. Using a special discretization of the liquid crystal energy, and a strictly monotone energy decreasing gradient flow scheme, we present a simulation of a plane-defect in three dimensions to illustrate our method.

Publication Source (Journal or Book title)

Materials Research Society Symposium Proceedings

First Page

66

Last Page

71

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