Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transition of defect patterns from 2D to 3D in liquid crystals   Defects arise when nematic liquid crystals are under topological constraints
at the boundary. Recently the study of defects has drawn a lot of attention. In
this paper, we investigate the relationship between two-dimensional defects and
three-dimensional defects within nematic liquid crystals confined in a shell
under the Landau-de Gennes model. We use a highly accurate spectral method to
numerically 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 increase,
the solution undergo symmetry break to reconfigure the disclination lines. We
study this three-dimensional reconfiguration of disclination lines in detail
under different boundary conditions. We also discuss the topological charge of
defects in two- and three-dimensional spaces within the tensor model.

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The categories of this paper are: hep-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
2
The categories of this paper are: math