Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids

TL;DR

This paper develops a hybrid algorithm to analyze critical points of Landau-de Gennes free energy in 3D cuboids, revealing complex solution landscapes and new metastable states relevant for nematic liquid crystals.

Contribution

It introduces a method to construct 3D critical points from 2D data and studies how geometry influences solution landscapes in nematic systems.

Findings

Discovery of multi-layer 3D critical points

Identification of novel energy pathways and metastable states

Demonstration of geometry's effect on solution landscapes

Abstract

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 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 3D 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 tailor-made static and dynamic properties of confined nematic liquid crystal systems in 3D.