The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory

Abstract

We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by $\lambda$, and the well height denoted by $\epsilon$. The WORS are distinctive equilibria reported in [10] for square domains, without taking the third dimension into account, which have two mutually perpendicular defect lines running along the square diagonals, intersecting at the square centre. We prove the existence of WORS on three-dimensional wells for arbitrary well heights, with (i) natural boundary conditions and (ii) realistic surface energies on the top and bottom well surfaces, along with Dirichlet conditions on the lateral surfaces. Moreover, the WORS is globally stable for $\lambda$ small enough in both cases and unstable as $\lambda$ increases. We numerically compute novel mixed 3D solutions for large $\lambda$ and $\epsilon$ followed by a numerical investigation of the effects of surface anchoring on the WORS, exemplifying the relevance of the WORS solution in a 3D context.

References in corpus (5)

• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• Introduction to Q-tensor theory
• Instability of point defects in a two-dimensional nematic liquid crystal model
• Dimension reduction for the Landau-de Gennes model on curved nematic thin films
• Bifurcation analysis in a frustrated nematic cell

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• Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids
• Modeling and Computation of Liquid Crystals
• Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model
• Pattern Formation for Nematic Liquid Crystals-Modelling, Analysis, and Applications
• Solution Landscapes in the Landau-de Gennes Theory on Rectangles