Two-dimensional ferronematics, canonical harmonic maps and minimal connections
Canevari, Giacomo and Majumdar, Apala and Stroffolini, Bianca and Wang, Yiwei (2023) Two-dimensional ferronematics, canonical harmonic maps and minimal connections. Preprint / Working Paper. arXiv, Ithaca, NY. (In Press) (https://doi.org/10.48550/arXiv.2208.01586)
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Abstract
We study a variational model for ferronematics in two-dimensional domains, in the "super-dilute" regime. The free energy functional consists of a reduced Landau-de Gennes energy for the nematic order parameter, a Ginzburg-Landau type energy for the spontaneous magnetisation, and a coupling term that favours the co-alignment of the nematic director and the magnetisation. In a suitable asymptotic regime, we prove that the nematic order parameter converges to a canonical harmonic map with non-orientable point defects, while the magnetisation converges to a singular vector field, with line defects that connect the non-orientable point defects in pairs, along a minimal connection.
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Item type: Monograph(Preprint / Working Paper) ID code: 82768 Dates: DateEvent13 October 2023Published13 October 2023Accepted2 August 2022SubmittedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 13 Oct 2022 16:22 Last modified: 27 Mar 2024 01:28 URI: https://strathprints.strath.ac.uk/id/eprint/82768