Affiliation:
1. Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XQ, UK
2. Beijing International Center for Mathematical Research, Center for Quantitative Biology, Peking University, Beijing 100871, People’s Republic of China
Abstract
We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter,
L
2
, and the critical points are described by 3 d.f. 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,
λ
, is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the
WORS
,
Ring
±
,
C
o
n
s
t
a
n
t
and
p
W
O
R
S
solutions, of which the
WORS
,
Ring
+
and
C
o
n
s
t
a
n
t
solutions can be stable. Furthermore, we demonstrate that the novel
C
o
n
s
t
a
n
t
solution is energetically preferable for large
λ
and large
L
2
, and prove associated stability results that corroborate the stabilizing 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.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
4 articles.
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