Multistability for nematic liquid crystals in cuboids with degenerate planar boundary conditions

Shi, Baoming and Han, Yucen and Majumdar, Apala and Zhang, Lei (2024) Multistability for nematic liquid crystals in cuboids with degenerate planar boundary conditions. SIAM Journal on Applied Mathematics, 84 (2). pp. 756-781. ISSN 0036-1399 (https://doi.org/10.1137/23m1604606)

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Abstract

We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau–de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, λ, and the parameter h, which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on h and λ, and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of λ and h.

  • Item type:Article
    ID code:89181
    Dates:
    Date
    Event
    30 April 2024
    Published
    26 April 2024
    Published Online
    23 January 2024
    Accepted
    25 September 2023
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:09 May 2024 12:07
    Last modified:19 Jun 2024 01:25
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/89181
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