Micromagnetics of curved thin films

G Di Fratta - Zeitschrift für angewandte Mathematik und Physik, 2020 - Springer
In this paper, we aim at a reduced 2 d-model describing the observable states of the
magnetization in curved thin films. Under some technical assumptions on the geometry of …

Micromagnetics of thin films in the presence of Dzyaloshinskii–Moriya interaction

E Davoli, G Di Fratta, D Praetorius… - … Models and Methods in …, 2022 - World Scientific
In this paper, we study the thin-film limit of the micromagnetic energy functional in the
presence of bulk Dzyaloshinskii–Moriya interaction (DMI). Our analysis includes both a …

Linearized von Kármán theory for incompressible magnetoelastic plates

M Bresciani - Mathematical Models and Methods in Applied …, 2021 - World Scientific
We study the asymptotic behavior, in the sense of Γ-convergence, of a thin incompressible
magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von Kármán …

Stochastic homogenization of the Landau–Lifshitz–Gilbert equation

F Alouges, A De Bouard, B Merlet, L Nicolas - Stochastics and Partial …, 2021 - Springer
Following the ideas of Zhikov and Piatnitski (Izv Math 70 (1): 19–67, 2006), and more
precisely the stochastic two-scale convergence, this paper establishes a homogenization …

Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions

E Davoli, L D'Elia, J Ingmanns - Journal of Nonlinear Science, 2024 - Springer
We perform a stochastic homogenization analysis for composite materials exhibiting a
random microstructure. Under the assumptions of stationarity and ergodicity, we …

The mathematics of thin structures

JF Babadjian, G Di Fratta, I Fonseca, G Francfort… - Quarterly of Applied …, 2023 - ams.org
This article offers various mathematical contributions to the behavior of thin films. The
common thread is to view thin film behavior as the variational limit of a three-dimensional …

Homogenization of chiral magnetic materials: A mathematical evidence of Dzyaloshinskii's predictions on helical structures

E Davoli, G Di Fratta - Journal of Nonlinear Science, 2020 - Springer
In this paper, we investigate the influence of the bulk Dzyaloshinskii–Moriya interaction on
the magnetic properties of composite ferromagnetic materials with highly oscillating …

Homogenization of nondilute suspension of viscous fluid with magnetic particles

T Dang, Y Gorb, SJ Bolanos - SIAM Journal on Applied Mathematics, 2021 - SIAM
This paper seeks to carry out the rigorous homogenization of a particulate flow consisting of
a nondilute suspension of a viscous Newtonian fluid with magnetizable particles. The fluid is …

Homogenization of the Landau-Lifshitz equation

L Leitenmaier, O Runborg - arXiv preprint arXiv:2012.12567, 2020 - arxiv.org
In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly
oscillatory material coefficient with period $\varepsilon $ modeling a ferromagnetic …

Reduced theory of symmetric and antisymmetric exchange interactions in nanowires

G Di Fratta, FN Rybakov, V Slastikov - arXiv preprint arXiv …, 2024 - esaim-cocv.org
We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a
wire generated by a regular simple curve γ and defined in the space of S2-valued functions …