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)
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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: https://orcid.org/0000-0003-4802-6720 and Zhang, Lei;-
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Item type: Article ID code: 73006 Dates: DateEvent1 May 2020Published26 February 2020Published Online6 January 2020AcceptedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 02 Jul 2020 12:00 Last modified: 16 Sep 2024 00:50 URI: https://strathprints.strath.ac.uk/id/eprint/73006