Stationary solutions of discrete Landau–de Gennes theory: 3 [formula omitted] 3 Q-tensor case

Abstract

We study equilibria of a discrete Landau–de Gennes energy functional for nematic liquid crystals in the small intersite coupling regime. We consider the 3 × 3 Q−tensor case in finite lattices and graphs and show necessary and sufficient conditions for the continuation of equilibria of the decoupled discrete Landau–de Gennes system. The main tools are continuation and symmetry arguments. The theory connects the Landau–de Gennes equilibria to equilibria of a generalized discrete Oseen–Frank energy and also implies that the gradient flow of the decoupled Landau–de Gennes energy has normally hyperbolic invariant submanifolds.