论文信息 - An operator-splitting method for a liquid crystal model

An operator-splitting method for a liquid crystal model

Abstract In this paper an operator-splitting method is applied to find the micro-structure of a liquid crystal model with a simplified Oseen–Frank energy functional. Both projection and penalty methods are used to deal with the constant length constraint. The methods are implemented to compute director fields of liquid crystal slabs of various shapes and with various boundary data. The computational results verify researcher expectations. Some new singularity patterns are observed as well.

[1] David Kinderlehrer,et al. Existence and partial regularity of static liquid crystal configurations , 1986 .

[2] Yoshikazu Giga,et al. On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg–Landau type energy for gradient fields , 1997, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[3] F. C. Frank,et al. I. Liquid crystals. On the theory of liquid crystals , 1958 .

[4] Robert V. Kohn,et al. Singular Perturbation and the Energy of Folds , 2000, J. Nonlinear Sci..

[5] Yoshikazu Giga,et al. A mathematical problem related to the physical theory of liquid crystal configurations , 1987 .

[6] P. D. Gennes,et al. An analogy between superconductors and smectics A , 1972 .

[7] F. Lin. Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena , 1989 .

[8] David Kinderlehrer,et al. Mathematical Questions of Liquid Crystal Theory , 1987 .

[9] Xing-Bin Pan,et al. Asymptotics of minimizers of variational problems involving curl functional , 2000 .

[10] R. Glowinski,et al. Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics , 1987 .

[11] H. Brezis,et al. Ginzburg-Landau Vortices , 1994 .

[12] P. Gennes,et al. The physics of liquid crystals , 1974 .

[13] W. L. Mcmillan. Measurement of Smectic-A- Phase Order-Parameter Fluctuations in the Nematic Phase of p-n-Octyloxybenzylidene-p'- Toluidine , 1973 .