Transition of Defect Patterns from 2D to 3D in Liquid Crystals (Communications in Computational Physics, 2018)
Defects arise when nematic liquid crystals are under topological constraintsat the boundary. Recently the study of defects has drawn a lot of attention becauseof the growing theoretical and practical significance. In this paper, we investigate therelationship between two-dimensional defects and three-dimensional defects withinnematic liquid crystals confined in a shell. A highly accurate spectral method is usedto 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 breakto reconfigure the disclination lines. We study this three-dimensional reconfigurationof disclination lines in detail under different boundary conditions. In particular, wefind that the temperature plays an important role in deciding whether the transitionbetween two-dimensional defects and three-dimensional defects is continuous or discontinuousfor the shell with planar anchoring condition on both inner and outer surfaces.We also discuss the characterization of defects in two- and three-dimensionalspaces within the tensor model.