Seminario EDP UAM-ICMAT
Homogenisation of nonlocal exchange energies in micromagnetics
Ponente: Leon Happ (UAM)Fecha: viernes 30 de enero de 2026 - 13:45Lugar: Aula Gris 1, ICMAT
Resumen:
In my talk I will present a recent joint work with Rossella Giorgio and Hidde Schönberger, where we conduct the joint homogenisation and localisation of a nonlocal version of the micromagnetic energy functional including symmetric and antisymmetric exchange energies. The common local symmetric exchange term, which resembles the well-known Dirichlet energy, naturally admits a nonlocal representation in the spirit of Bourgain, Brezis and Mironescu. It was proved first by Ponce that this nonlocal formulation indeed Gamma-converges to its local counterpart under sufficient conditions on the localising kernels. Recently, this result has been extended by Davoli, Di Fratta and Giorgio to the case where an additional antisymmetric exchange term representing the chiral Dzyaloshinskii-Moriya interaction (DMI) is considered. We take this as a motivation to study the variational multiscale behaviour of this nonlocal functional in the highly heterogeneous framework and undertake its homogenisation in the regime where the scale of the inhomogeneities and the horizon of the nonlocal interactions are comparable. We develop a version of nonlocal two-scale convergence to perform the
homogenisation procedure. By adapting to the S^2-constraint - a hallmark of micromag netics -, we extend the relatively young research direction of nonlocal homogenisation to the setting of manifold constraints.
