TY - JOUR
T1 - Transition of Defect Patterns from 2D to 3D in Liquid Crystals
AU - Yang Qu, Ying Wei & Pingwen Zhang
JO - Communications in Computational Physics
VL - 3
SP - 890
EP - 904
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0034
UR - https://global-sci.org/intro/article_detail/cicp/11264.html
KW - 
AB - <p style="text-align: justify;">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.</p>