English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the effects of elastic anisotropy on the Landau-de Gennes criticalpoints for nematic liquid crystals, in a square domain. The elastic anisotropyis captured by a parameter, $L_2$, and the critical points are described bythree degrees of freedom. We analytically construct a symmetric critical pointfor all admissible values of $L_2$, which is necessarily globally stable forsmall domains i.e., when the square edge length, $\lambda$, is small enough. Weperform 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 $L_2$, andprove associated stability results that corroborate the stabilising effects of$L_2$ for reduced Landau-de Gennes critical points. We complement our analysiswith numerically computed bifurcation diagrams for different values of $L_2$,which illustrate the interplay of elastic anisotropy and geometry for nematicsolution landscapes, at low temperatures.

Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model