Two-dimensional ferronematics, canonical harmonic maps and minimal connections

Giacomo Canevari, Apala Majumdar, Bianca Stroffolini, Yiwei Wang

Research output: Working paper

27 Downloads (Pure)

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.
Original languageEnglish
Place of PublicationIthaca, NY
Number of pages56
DOIs
Publication statusAccepted/In press - 13 Oct 2023

Keywords

  • Ginzburg-Landau functional
  • Modica-Mortola functional
  • canonical harmonic maps
  • non-orientable singularities
  • minimal connections

Fingerprint

Dive into the research topics of 'Two-dimensional ferronematics, canonical harmonic maps and minimal connections'. Together they form a unique fingerprint.

Cite this