Surface, size and topological effects for some nematic equilibria on rectangular domains

Fang, Lidong and Majumdar, Apala and Zhang, Lei (2020) Surface, size and topological effects for some nematic equilibria on rectangular domains. Mathematics and Mechanics of Solids, 25 (5). pp. 1101-1123. ISSN 1081-2865 (https://doi.org/10.1177/1081286520902507)

[thumbnail of Fang-etal-MMS-2020-Surface-size-and-topological-effects-for-some-nematic-equilibria]
Preview
 Text. Filename: Fang_etal_MMS_2020_Surface_size_and_topological_effects_for_some_nematic_equilibria.pdf
Accepted Author Manuscript
Download (2MB)| Preview

Abstract

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, ϵ, which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the ϵ→ 0 limit relevant for macroscopic domains and the ϵ→∞ limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the ϵ→∞ limit, whereas we observe fractional point defects in the ϵ→ 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of ϵ and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

  • Item type:Article
    ID code:73006
    Dates:
    Date
    Event
    1 May 2020
    Published
    26 February 2020
    Published Online
    6 January 2020
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:02 Jul 2020 12:00
    Last modified:09 Apr 2024 01:37
    URI:https://strathprints.strath.ac.uk/id/eprint/73006
CORE (COnnecting REpositories)