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

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