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A boundary integral equation for Calderón's inverse conductivity problem.

Kari Astala, Lassi Päivärinta (2006)

Collectanea Mathematica

Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel walls. Néel...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields. This...

A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP

Christophe Besse, Brigitte Bidégaray-Fesquet, Antoine Bourgeade, Pierre Degond, Olivier Saut (2004)

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

This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell’s equations for the wave field coupled with a version of Bloch’s equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material....

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