Solution landscape of a reduced Landau–de Gennes model on a hexagon

Abstract

We investigate the solution landscape of a reduced Landau–de Gennes model for nematic liquid crystals (NLCs) on a two-dimensional hexagon at a fixed temperature, as a function of λ—the edge length. This is a generic example for reduced approaches on regular polygons. We apply the high-index optimization-based shrinking dimer method to systematically construct the solution landscape consisting of multiple solutions, with different defect configurations, and relationships between them. We report a new stable T state with index-0 that has an interior −1/2 defect; new classes of high-index saddle points with multiple interior defects referred to as H-class and TD-class saddle points; changes in the Morse index of saddle points as λ 2 increases and novel pathways mediated by high-index saddle points that can control and steer dynamical pathways on the solution landscape. The range of topological degrees, locations and multiplicity of defects offered by these saddle points can be used to navigate the complex solution landscapes of NLCs and other related soft matter systems.