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, [Formula: see text] , and the critical points are described by 3 d.f. We analytically construct a symmetric critical point for all admissible values of [Formula: see text] , which is necessarily globally stable for small domains, i.e. when the square edge length, [Formula: see text] , is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the [Formula: see text] , [Formula: see text] , [Formula: see text] and [Formula: see text] solutions, of which the [Formula: see text] , [Formula: see text] and [Formula: see text] solutions can be stable. Furthermore, we demonstrate that the novel [Formula: see text] solution is energetically preferable for large [Formula: see text] and large [Formula: see text] , and prove associated stability results that corroborate the stabilizing effects of [Formula: see text] for reduced Landau–de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of [Formula: see text] , which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.