Numerics for Liquid Crystals with Variable Degree of Orientation
Keyword(s):
AbstractWe 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.
2020 ◽
Vol 54
(4)
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pp. 1181-1220
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1991 ◽
Vol 114
(4)
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pp. 335-347
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1991 ◽
Vol 113
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pp. 97-120
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2017 ◽
Vol 55
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pp. 1357-1386
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1991 ◽
Vol 44
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pp. 453-468
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