Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand
Diffraction par un convexe.
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to the Bragg part of the diffraction spectrum. The corresponding intensity function on this Bragg part is computed. We deduce the diffraction spectrum of weighted Delone sets on beta-lattices in the split case for the weight, when beta is the golden mean.
Diffusion électromagnétique à basse fréquence par un réseau de cylindres diélectriques. Étude numérique
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...
Electromagnetic Scattering from a Spheroid Imbedded in a Dielectric half-space: An Integral Equation Analytic Approach
Energy Functionals in Scattering Theory
Étude de la diffraction dans les instruments d'optique; son influence sur les observations astronomiques
Étude sur les vibrations rectilignes et sur la diffraction, dans les milieux isotropes et dans l'éther des cristaux.
Expansion for the superheating field in a semi-infinite film in the weak- limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak- limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers...
Expansion for the superheating field in a semi-infinite film in the weak-κ limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion...
Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.
We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L∞ norm.
Fonctionnelle quadratique et équations intégrales pour les problèmes d'onde harmonique en domaine extérieur
Generalized Backscattering and the Lax-Phillips Transform
2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle w = Sq in terms of the incoming angle with S orthogonal and Id-S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact support. As a corollary we show that the...
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
High frequency approximation of integral equations modeling scattering phenomena
High frequency asymptotic solutions of the reduced wave equation on infinite regions with nonconvex boundaries.
Initial Dirichlet problem for half-plane diffraction: Global formulae for its generalized eigenfunctions, explicit solution by the Cagniard-de Hoop method.
Integral equations via saddle point problem for 2D electromagnetic problems