Nematic liquid crystals in a rectangular confinement : solution landscape, and bifurcation

Shi, Baoming and Han, Yucen and Zhang, Lei (2022) Nematic liquid crystals in a rectangular confinement : solution landscape, and bifurcation. SIAM Journal on Applied Mathematics, 82 (5). pp. 1808-1828. ISSN 0036-1399 (https://doi.org/10.1137/21m1447404)

[thumbnail of Shi-etal-AM-2022-Nematic-liquid-crystals-in-a-rectangular-confinement]
Preview
 Text. Filename: Shi_etal_AM_2022_Nematic_liquid_crystals_in_a_rectangular_confinement.pdf
Accepted Author Manuscript
License: Creative Commons Attribution 4.0 logo
Download (11MB)| Preview

Abstract

We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau–de Gennes framework in terms of two geometry-dependent variables: half short edge length λ and aspect ratio b . First, we analytically prove that, for any b with a small enough λ or for a large enough b with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying λ and b , and report a novel X state, which emerges from saddle-node bifurcation and serves as the parent state in such a solution landscape. Various new classes are then found among these solution landscapes, including the X class, the S class, and the L class. By tracking the Morse indices of individual solutions, we present bifurcation diagrams for nematic equilibria, thus illustrating the emergence mechanism of critical points and several effects of geometrical anisotropy on confined defect patterns.

  • Item type:Article
    ID code:82979
    Dates:
    Date
    Event
    31 December 2022
    Published
    18 October 2022
    Published Online
    27 June 2022
    Accepted
    20 September 2021
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:28 Oct 2022 13:09
    Last modified:17 Apr 2024 00:50
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/82979
CORE (COnnecting REpositories)