Numerics for Liquid Crystals with Variable Degree of Orientation. Issue 1753 (16th February 2015)

• Record Type: Journal Article
• Authors: Nochetto, Ricardo H.; Walker, Shawn W.; Zhang, Wujun
• Editors: Calderer, C.; Lipton, R.; Margetis, D.; Otto, F.
• Is Part Of: MRS proceedings. Issue 1753:(2015)
• Publication Date: 2015-02-16
• Subjects: simulation, -- liquid crystal, -- fluid; Electrical engineering -- Congresses; Physics -- Congresses; Materials -- Research -- Congresses; Materials science -- Congresses; 620.11
• DOI: 10.1557/opl.2015.159
• Languages: English
• ISSNs: 0272-9172

Abstract

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 fieldn 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 forn, 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.