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Singularities of eddy current problems

Martin Costabel, Monique Dauge, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace...

Singularities of Maxwell interface problems

Martin Costabel, Monique Dauge, Serge Nicaise (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate time harmonic Maxwell equations in heterogeneous media, where the permeability μ and the permittivity ε are piecewise constant. The associated boundary value problem can be interpreted as a transmission problem. In a very natural way the interfaces can have edges and corners. We give a detailed description of the edge and corner singularities of the electromagnetic fields.

Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche, Serge Nicaise (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in L p ( Ω ) 2 . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space W 2 , p ( Ω ) 2 and an explicit singular one.

Some initial boundary problems in electrodynamics for canonical domains in quaternions

Erhard V. Meister, L. Meister (2001)

Mathematica Bohemica

The initial boundary-transmission problems for electromagnetic fields in homogeneous and anisotropic media for canonical semi-infinite domains, like halfspaces, wedges and the exterior of half- and quarter-plane obstacles are formulated with the use of complex quaternions. The time-harmonic case was studied by A. Passow in his Darmstadt thesis 1998 in which he treated also the case of an homogeneous and isotropic layer in free space and above an ideally conducting plane. For thin layers and free...

Some new results in multiphase geometrical optics

Olof Runborg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical optics for the scalar wave equation as a kinetic transport equation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated system of moment equations, closed by an assumption on the form of the density function in the kinetic equation. We consider two different closure assumptions based on delta...

Stabilité des solitons de l’équation de Landau-Lifshitz à anisotropie planaire

André de Laire, Philippe Gravejat (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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 of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Currently displaying 201 – 220 of 280