Elastic anisotropy in the reduced Landau-de Gennes model

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, lambda, is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points-the WORS, Ring & PLUSMN;, 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 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.

Automated summary

This study investigates the effects of elastic anisotropy on Landau-de Gennes critical points in nematic liquid crystals on a square domain. Various symmetric critical points are discovered and the stabilizing effects of L-2 are proven. Numerical bifurcation diagrams illustrate the interplay of elastic anisotropy and geometry in nematic solution landscapes.