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2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Mouhcine Tilioua (2011)

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke (2006)

ESAIM: Control, Optimisation and Calculus of Variations

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ -convergence theorem and show compactness up to translation in all L p and the optimal Orlicz space for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher (1994) for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.

A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke (2005)

ESAIM: Control, Optimisation and Calculus of Variations

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all Lp and the optimal Orlicz space for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher (1994) for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.

Dynamics of systems with Preisach memory near equilibria

Stephen McCarthy, Dmitrii Rachinskii (2014)

Mathematica Bohemica

We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...

Energetics and switching of quasi-uniform states in small ferromagnetic particles

François Alouges, Sergio Conti, Antonio DeSimone, Yvo Pokern (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We...

Energetics and switching of quasi-uniform states in small ferromagnetic particles

François Alouges, Sergio Conti, Antonio DeSimone, Yvo Pokern (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and...

Geometric structure of magnetic walls

Myriam Lecumberry (2005)

Journées Équations aux dérivées partielles

After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.

Homogenization of ferromagnetic multilayers in the presence of surface energies

Kévin Santugini-Repiquet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is...

Homogenization of micromagnetics large bodies

Giovanni Pisante (2004)

ESAIM: Control, Optimisation and Calculus of Variations

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies ε ( m ) = Ω φ x , x ε , m ( x ) d x - Ω h e ( x ) · m ( x ) d x + 1 2 3 | u ( x ) | 2 d x of a large ferromagnetic body is obtained.

Homogenization of micromagnetics large bodies

Giovanni Pisante (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies ε ( m ) = Ω φ x , x ε , m ( x ) d x - Ω h e ( x ) · m ( x ) d x + 1 2 3 | u ( x ) | 2 d x of a large ferromagnetic body is obtained.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2009)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

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