Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elastic anisotropy of nematic liquid crystals in the two-dimensional
  Landau-de Gennes model   We study the effects of elastic anisotropy on the Landau-de Gennes critical
points for nematic liquid crystals, in a square domain. The elastic anisotropy
is captured by a parameter, $L_2$, and the critical points are described by
three degrees of freedom. We analytically construct a symmetric critical point
for all admissible values of $L_2$, which is necessarily globally stable for
small domains i.e., when the square edge length, $\lambda$, is small enough. We
perform asymptotic analyses and numerical studies to discover at least $5$
classes of these symmetric critical points - the $WORS$, $Ring^{\pm}$,
$Constant$ and $pWORS$ solutions, of which the $WORS$, $Ring^+$ and $Constant$
solutions can be stable. Furthermore, we demonstrate that the novel $Constant$
solution is energetically preferable for large $\lambda$ and large $L_2$, and
prove associated stability results that corroborate the stabilising effects of
$L_2$ for reduced Landau-de Gennes critical points. We complement our analysis
with numerically computed bifurcation diagrams for different values of $L_2$,
which illustrate the interplay of elastic anisotropy and geometry for nematic
solution landscapes, at low temperatures.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat