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arXiv · 2208.01586

Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections

Giacomo Canevari·Apala Majumdar·Bianca Stroffolini·Yiwei Wang
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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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Giacomo Canevari, Apala Majumdar, Bianca Stroffolini, Yiwei Wang. 2022-08-02. Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections. https://arxiv.org/abs/2208.01586

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