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

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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)

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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.

ORCID iDs

Fang, Lidong, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Zhang, Lei;
  • 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:11 Nov 2024 12:45
    URI:https://strathprints.strath.ac.uk/id/eprint/73006
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