Point defects in 2-D liquid crystals with singular potential: profiles and stability

TL;DR

This paper investigates the existence and stability of radial symmetric point defects in 2D liquid crystals modeled with a singular bulk energy, revealing stability for certain defect degrees and instability for others.

Contribution

It establishes the existence of defect profiles and characterizes their stability in a 2D liquid crystal model with singular potential, using analytical methods.

Findings

Existence of radial symmetric defect solutions in 2D.

Stability for defect degree |k|=1.

Instability for defect degree |k|>1.

Abstract

We study radial symmetric point defects with degree $\frac {k}{2}$ in 2D disk or $\mathbb{R}^2$ in $Q$-tensor framework with singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the profiles of radial symmetric point defects with degree $\frac k2$ in 2D disk or $\mathbb{R}^2$. Then we prove that the solution is stable for $|k|=1$ and unstable for $|k|>1$. Some identities are derived and used throughout the proof of existence and stability/instability.