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Transition of Defect Patterns from 2D to 3D in Liquid Crystals

Published online by Cambridge University Press:  07 February 2017

Yang Qu*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Ying Wei*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Pingwen Zhang*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
*
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
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Abstract

Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention because of the growing theoretical and practical significance. In this paper, we investigate the relationship between two-dimensional defects and three-dimensional defects within nematic liquid crystals confined in a shell. A highly accurate spectral method is used to solve the Landau-de Gennes model to get the detailed static structures of defects. Interestingly, the solution is radial-invariant when the thickness of the shell is sufficiently small. As the shell thickness increases, the solution undergoes symmetry break to reconfigure the disclination lines. We study this three-dimensional reconfiguration of disclination lines in detail under different boundary conditions. In particular, we find that the temperature plays an important role in deciding whether the transition between two-dimensional defects and three-dimensional defects is continuous or discontinuous for the shell with planar anchoring condition on both inner and outer surfaces. We also discuss the characterization of defects in two- and three-dimensional spaces within the tensor model.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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References

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