Recent developments in the modeling, analysis, and numerics of ferromagnetism

M Kruzik, A Prohl - SIAM review, 2006 - SIAM
Micromagnetics is a continuum variational theory describing magnetization patterns in
ferromagnetic media. Its multiscale nature due to different inherent spatiotemporal physical …

A reduced theory for thin‐film micromagnetics

A DeSimone, RV Kohn, S Müller… - Communications on Pure …, 2002 - Wiley Online Library
Micromagnetics is a nonlocal, nonconvex variational problem. Its minimizer represents the
ground‐state magnetization pattern of a ferromagnetic body under a specified external field …

Another thin-film limit of micromagnetics

RV Kohn, VV Slastikov - Archive for rational mechanics and analysis, 2005 - Springer
We consider the variational problem of micromagnetics for soft, relatively small thin films with
no applied magnetic field. In terms of the film thickness t, the diameter l and the magnetic …

Energy-driven pattern formation

RV Kohn - International Congress of Mathematicians, 2007 - ems.press
Many physical systems can be modelled by nonconvex variational problems regularized by
higher-order terms. Examples include martensitic phase transformation, micromagnetics …

Optimal Besov differentiability for entropy solutions of the eikonal equation

F Ghiraldin, X Lamy - Communications on Pure and Applied …, 2020 - Wiley Online Library
Optimal Besov Differentiability for Entropy Solutions of the Eikonal Equation Page 1 Optimal
Besov Differentiability for Entropy Solutions of the Eikonal Equation FRANCESCO GHIRALDIN …

2-d stability of the Néel wall

A DeSimone, H Knüpfer, F Otto - Calculus of Variations and Partial …, 2006 - Springer
We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-
d unit-length vector field. More precisely we are interested in transition layers which connect …

Stability of static walls for a three-dimensional model of ferromagnetic material

G Carbou - Journal de mathématiques pures et appliquées, 2010 - Elsevier
In this paper we consider a three-dimensional model of ferromagnetic material. We deal with
the static domain wall configuration calculated by Walker. We prove the stability of this …

Stability for static walls in ferromagnetic nanowires

G Carbou, S Labbé - … and Continuous Dynamical Systems-Series B, 2006 - hal.science
The goal of this article is to analyse the time asymptotic stability of one dimensional Bloch
wall in ferromagnetic materials. The equation involved in modelling such materials is the …

Compactness, kinetic formulation, and entropies for a problem related to micromagnetics

T Riviere, S Serfaty - 2003 - Taylor & Francis
We carry on the study of (Rivière T, Serfaty S. Limiting domain wall energy for a problem
related to micromagnetics. Comm Pure Appl Math 2001; 54 (3): 294–338.) on the …

Stabilization of walls for nano-wires of finite length

G Carbou, S Labbé - ESAIM: Control, Optimisation and Calculus of …, 2012 - cambridge.org
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length.
First we justify the model by Γ-convergence arguments. Furthermore we prove the existence …