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arXiv · 2211.07536

A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms

Yucen Han·Baoming Shi·Lei Zhang·Apala Majumdar
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Abstract

We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.

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Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar. 2022-11-03. A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms. https://arxiv.org/abs/2211.07536

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