2021/09/21 by Baoming Shi, Shi, Baoming, Yucen Han +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Liquid Crystal Research Advancements #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Plant Reproductive Biology #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.2109.10318
openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length λ and aspect ratio b. First, we analytically prove that, for any b with a small enough λ or for a large enough b with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying λ and b, and report a novel X state, which emerges from saddle-node bifurcation and serves as the parent state in such a solution landscape. Various new classes are then found among these solution landscapes, including the X class, the S class, and the L class. By tracking the Morse indices of individual solutions, we present bifurcation diagrams for nematic equilibria, thus illustrating the emergence mechanism of critical points and several effects of geometrical anisotropy on confined defect patterns.