Expanding impulsive gravitational waves

We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.Comment: 11 pages, LaTeX, To appear in Class. Quantum Gra

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Diffusion and activation of ultrashallow B implants in silicon on insulator: End-of-range defect dissolution and the buried Si∕SiO2 interface

The fabrication of preamorphized p-type ultrashallow junctions in silicon-on-insulator (SOI) has been investigated. Electrical and structural measurements after annealing show that boron deactivation and transient enhanced diffusion are reduced in SOI compared to bulk wafers. The reduction is strongest when the end-of-range defects of the preamorphizing implant are located deep within the silicon overlayer of the SOI silicon substrate. Results reveal a very substantial increase in the dissolution rate of the end-of-range defect band. A key player in this effect is the buried Si/SiO2 interface, which acts as an efficient sink for interstitials competing with the silicon surface.</p

UNE MÉTHODE NUMÉRIQUE DE RÉSOLUTION DES ÉQUATIONS DE L'ACOUSTIQUE DANS UN MILIEU À CARACTÉRISTIQUES C∞ PAR MORCEAUX

Nous présentons une méthode numérique pour la résolution des systèmes d'équations de l'acoustique linéaire et faiblement non linéaire valable même lorsque le milieu comporte des dioptres avec points singuliers (arête d'un dièdre, sommet d'un cône). L'intérêt de notre méthode est qu'elle fonctionne sans aucune connaissance préalable des conditions de passage.We present a numerical method for the solution of the systems of equations of linear and weakly nonlinear acoustics valid even when the medium involves dioptra with singular points (edge of a diedra, top of a cone). The basic feature of our method is that no previous knowledge of the transmission conditions is needed