A reduced Landau-de Gennes study for nematic equilibria in three-dimensional prisms

Han, Yucen and Shi, Baoming and Zhang, Lei and Majumdar, Apala (2023) A reduced Landau-de Gennes study for nematic equilibria in three-dimensional prisms. IMA Journal of Applied Mathematics, 88 (5). pp. 645-676. ISSN 1464-3634 (https://doi.org/10.1093/imamat/hxad031)

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Abstract

We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal crosssection 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.

ORCID iDs

Han, Yucen, Shi, Baoming, Zhang, Lei and Majumdar, Apala

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Item metadata

Item type:	Article
ID code:	87094
Dates:	Date Event 1 December 2023 Published 8 November 2023 Published Online 24 October 2023 Accepted
Subjects:	Science > Mathematics
Department:	Faculty of Science > Mathematics and Statistics
Depositing user:	Pure Administrator
Date deposited:	27 Oct 2023 13:45
Last modified:	11 Nov 2024 14:07
URI:	https://strathprints.strath.ac.uk/id/eprint/87094

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