Does Atkinson-Wilcox Expansion Converges for any Convex Domain?

2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far field pattern of the radiating field. In this work we give a simple characterization of the strictly convex domains, such that a reasonable generalization of the AtkinsonWilcox expansion converges uniformly in the corresponding exterior domain. All these strictly convex domains are spheres

Theory of thermoelasticity

The development of the theory of thermoelasticity, which examines the interactions between the deformation of elastic media and the thermal field, is traced and the fundamental problems of the theory are presented. Results of recent studies on the subject are presented. Emphasis is primarily on media with generalized anisotropy, or isotropy media. Thermomechanical problems and mathematical formulations and resolutions are included

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers

On the Scattering of an Acoustic Plane Wave by a Soft Prolate Spheroid

This thesis solves the scattering problem in which an acoustic plane wave of propagation number K1 is scattered by a soft prolate spheroid. The interior field of the scatterer is characterized by a propagation number K2, while the field radiated by the scatterer is characterized by the propagation number K3. The three fields and their normal derivatives satisfy boundary conditions at the surface of the scatterer. These boundary conditions involve six complex parameters depending on the propagation numbers. The scattered wave also satisfies the Sommerfeld radiation condition at infinity. Through analytical methods, series representations are constructed for the interior field and scattered field for an arbitrary sphere and a prolate spheroid. In addition, results for the reciprocity relations and Energy theorem are derived. Application to detection of whales and submarines are discussed, as well as classification of fish, squid and zoo plankton. In general Ref[ ] is used for reference and the work is done in three dimensions

The Full Anisotropic Adaptive Fourier Modal Method and its Application to Periodic and Aperiodic Photonic Nanostructures

The thesis introduces the Fourier Modal Method as simulation tool for periodic photonic nanostructures, and extends the method towards the simulation of aperiodic structures using real and complex coordinate transformations. As exemplary cases, the method is applied for the characterization of a woodpile photonic crystal with the first complete photonic bandgap in the visible spectrum, and to the transmission properties of a long period fiber grating

Gratings: Theory and Numeric Applications, Second Revisited Edition

International audienceThe second Edition of the Book contains 13 chapters, written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers.In comparison with the First Edition, we have added two more chapters (ch.12 and ch.13), and revised four other chapters (ch.6, ch.7, ch.10, and ch.11