Two-dimensional ferronematics, canonical harmonic maps and minimal connections
Canevari, Giacomo and Majumdar, Apala and Stroffolini, Bianca and Wang, Yiwei (2022) Two-dimensional ferronematics, canonical harmonic maps and minimal connections. Other. arXiv, Ithaca, NY. (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.
ORCID iDs
Canevari, Giacomo, Majumdar, Apala
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Item type: Monograph(Other) ID code: 82768 Dates: DateEvent2 August 2022Published2 August 2022SubmittedKeywords: Ginzburg-Landau functional, Modica-Mortola functional, canonical harmonic maps, non-orientable singularities, minimal connections, Mathematics, Mathematics(all) Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 13 Oct 2022 16:22 Last modified: 25 May 2023 11:15 URI: https://strathprints.strath.ac.uk/id/eprint/82768