Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids

Abstract We investigate critical points of a Landau–de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. develop hybrid saddle dynamics-based algorithm to efficiently compute solution landscapes these 3D systems. Our main results concern (a) the construction LdG from database two-dimensional (2D) and (b) studies effects cross-section size cuboid height on landscapes. In doing so, we discover multiple-layer constructed by stacking 2D top each other, novel pathways between distinct minima mediated metastable escaped solutions, all which can be tuned for tailor-made static dynamic properties confined liquid crystal systems 3D.