Eigenframe discontinuities of the Q-tensor model

TL;DR

This paper investigates the defect structures in the Q-tensor model of liquid crystals, revealing that the defect set is 1-rectifiable and classifying eigenvector behavior near singularities, thus advancing understanding of disclination structures.

Contribution

It provides a rigorous analysis of eigenframe discontinuities in the Q-tensor model, generalizing previous results on ring disclinations and characterizing defect sets.

Findings

Defect set is 1-rectifiable

Classified asymptotic profile of eigenvector near singularities

Extended understanding of ring disclinations in Q-tensor models

Abstract

In this paper, we study the defect structure of minimizer of a Landau-de Gennes energy functional in three-dimensional domains, subject to constraint $|Q|=1$. The set of defects is identified by discontinuities in both the eigenframe and the leading eigenvector. Through a blow-up analysis, we prove that the defect set is 1-rectifiable and classify the asymptotic profile of the leading eigenvector near singularities. This generalizes some previous results on the structure of ring disclinations in the $Q$-tensor model.