This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching the decay...
This paper is devoted to the practical computation of the
magnetic potential induced by a distribution of magnetization in
the theory of micromagnetics. The problem turns out to be a coupling of
an interior and an exterior problem. The aim of this work is to describe
a complete method that mixes the approaches of Ying [12] and Goldstein
[6] which consists in constructing a mesh for the exterior
domain composed of homothetic layers. It has the advantage of being well
suited for catching the...
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.
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.
We study a two-dimensional model for micromagnetics, which consists in an energy functional over -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....
We present a phase field approach to wetting problems, related to
the minimization of capillary energy. We discuss in detail both
the -convergence results on which our numerical algorithm
are based, and numerical implementation. Two possible choices of
boundary conditions, needed to recover Young's law for the contact
angle, are presented. We also consider an extension of the
classical theory of capillarity, in which the introduction of a
dissipation mechanism can explain and predict the hysteresis...
We study a two-dimensional model for micromagnetics, which consists in an energy functional over
-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the...
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...
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...
Download Results (CSV)