TY - GEN

T1 - Numerics for liquid crystals with variable degree of orientation

AU - Nochetto, Ricardo H.

AU - Walker, Shawn W.

AU - Zhang, Wujun

N1 - Publisher Copyright: © 2015 Materials Research Society.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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U2 - 10.1557/opl.2015.159

DO - 10.1557/opl.2015.159

M3 - Conference contribution

T3 - Materials Research Society Symposium Proceedings

SP - 66

EP - 71

BT - Mathematical and Computational Aspects of Materials Science

A2 - Otto, F.

A2 - Margetis, D.

A2 - Calderer, C.

A2 - Lipton, R.

PB - Materials Research Society

T2 - 2014 MRS Fall Meeting

Y2 - 30 November 2014 through 5 December 2014

ER -