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SUMMARY:Homogenization of nonlocal exchange energies in micromagnetics - L
 eon Happ (Technische Universität Wien)
DTSTART:20250822T100000Z
DTEND:20250822T104500Z
UID:TALK234775@talks.cam.ac.uk
DESCRIPTION:In this talk\,&nbsp\;I will present a recent joint work with R
 ossella Giorgio and Hidde Sch\\"onberger\, where we conduct the joint homo
 genization and localization of a nonlocal version of the micromagnetic fun
 ctional including symmetric and antisymmetric exchange energies.&nbsp\;\nT
 he common local symmetric exchange term\, which resembles the well-known D
 irichlet energy\, naturally admits a nonlocal representation in the spirit
  of Bourgain\, Brezis and Mironescu. It was proven first by Ponce that thi
 s nonlocal formulation indeed \\(\\Gamma\\)-converges to its local counter
 part under sufficient conditions on the localizing kernels. Recently\, thi
 s result has been extended by Davoli\, Di Fratta and Giorgio to the case w
 here an additional antisymmetric exchange term representing the chiral Dzy
 aloshinskii-Moriya interaction (DMI) is considered. We take this as a moti
 vation to study the variational multiscale behavior of this nonlocal funct
 ional in the highly heterogeneous framework and undertake its homogenizati
 on in the regime where the scale of the inhomogeneities and the horizon of
  the nonlocal interactions are comparable. We develop a version of nonloca
 l two-scale convergence to perform the homogenization procedure. By adapti
 ng to the \\(\\mathbb{S}^2\\)-constraint -- a hallmark of micromagnetics -
 -\, we extend the relatively young research direction of nonlocal homogeni
 zation to the setting of manifold constraints.
LOCATION:Seminar Room 1\, Newton Institute
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