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Numerics for Liquid Crystals with Variable Degree of Orientation

Published online by Cambridge University Press:  16 February 2015

Ricardo H. Nochetto ,
Shawn W. Walker  and
Wujun Zhang
Ricardo H. Nochetto
Affiliation:
Department of Mathematics, University of Maryland
Shawn W. Walker
Affiliation:
Department of Mathematics, Louisiana State University
Wujun Zhang
Affiliation:
Department of Mathematics, University of Maryland
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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.

Keywords

simulationliquid crystalfluid
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1753: Symposium NN – Mathematical and Computational Aspects of Materials Science , 2015 , mrsf14-1753-nn06-11
Copyright
Copyright © Materials Research Society 2015 

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