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

2019/11/25 by Zhiyuan Geng, Wei Wang, Geng, Zhiyuan +1
Materials Science · Mathematics · #35A15 #35J50 #82D30 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Liquid Crystal Research Advancements #Material Dynamics and Properties

paper · doi:10.48550/arxiv.1911.11258

openalex publication_date 2019/11/25 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

Abstract

We study radial symmetric point defects with degree \frac k2 in 2D disk or ℝ² 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 ℝ². 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.

Citations

• Liquid crystals with variable degree of orientation
• The Physics of Liquid Crystals
• Regularity of Minimizers of a Tensor-valued Variational Obstacle Problem in Three Dimensions

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