Some properties of the nematic radial hedgehog in Landau-de Gennes' theory

TL;DR

This paper investigates the properties of a nematic radial hedgehog defect within the Landau-de Gennes theory, establishing monotonicity of the scalar order parameter and proving the uniqueness of the minimizer below a critical temperature.

Contribution

It demonstrates the monotonicity of the scalar order parameter and proves the uniqueness of the hedgehog solution under certain temperature conditions in the Landau-de Gennes framework.

Findings

Scalar order parameter is monotonic

Uniqueness of the minimizing hedgehog below T*

Analysis within Landau-de Gennes theory

Abstract

In the Landau-de Gennes theoretical framework of a $Q -tensor description of nematic liquid crystals, we consider a radial hedgehog defect with strong anchoring conditions in a ball $B \subset \mathbb{R}^3$ . We show that the scalar order parameter is monotonic, and we prove uniqueness of the minimizing hedgehog below the spinodal temperature $T^\ast$ .