Pattern Formation in Landau-de Gennes Theory
Ho-Man Tai, Yong Yu
TL;DR
This paper investigates the formation of defect patterns in liquid crystal droplets using Landau-de Gennes theory, confirming numerical results through rigorous mathematical construction of specific solutions.
Contribution
It provides a rigorous mathematical construction of biaxial-ring and split-core-segment solutions, confirming previous numerical findings in the Landau-de Gennes framework.
Findings
Construction of biaxial-ring solutions
Construction of split-core-segment solutions
Confirmation of numerical results by Gartland-Mkaddem
Abstract
We study the spherical droplet problem in 3D-Landau de Gennes theory with finite temperature. By rigorously constructing the biaxial-ring solutions and split-core-segment solutions, we theoretically confirm the numerical results of Gartland-Mkaddem in [14]. The structures of disclinations are also addressed.
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Taxonomy
TopicsLiquid Crystal Research Advancements · Theoretical and Computational Physics · Nonlinear Dynamics and Pattern Formation