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.

  • 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:18 Apr 2024 11:40
    URI:https://strathprints.strath.ac.uk/id/eprint/87094
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