Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Une formule de Landau–Zener pour un croisement non dégénéré et involutif de codimension 3Landau–Zener formula for non-degenerate involutive codimension 3 crossings

In this Note, we study a 2×2 system of evolution equations with some codimension 3 crossing. We derive two conditions of non-degeneracy. We focus on one of them and reduce our system to some Landau–Zener's type system. Using this reduction, we describe the energy transfer at the crossing by Landau–Zener formula for 2-scales semi-classical measures. To cite this article: C. Fermanian Kammerer, P. Gérard, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 915–920.     

On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

Temperature Stresses in a Piecewise-Homogeneous Cylindrical Shell Caused by the Presence of a Longitudinal Crack

By using the method of generalized conjugation problems, we propose a numerical scheme for investigation of the redistribution of temperature stresses in a piecewise-homogeneous cylindrical shell caused by a longitudinal crack. This scheme is based on systems of integral equations (some of them are singular) to determine the unknown jumps of integral characteristics of the disturbed temperature field and displacements and their derivatives on the line of a crack and on the interface as well as the derivatives of these integral characteristics with respect to the longitudinal coordinate at the interface.     

MODEL COMPARISON FOR ACOUSTIC SCATTERING BY A SPHERICAL AIR BUBBLE IN WATER

The oscillation of a bubble has many vibrational modes, contributing to different portions in acoustic scattering. Without approximations a priori, an hydrodynamic approach is applied to investigate acoustic scattering by a bubble in water, taking into account the heat exchange and viscosity. The scattering function is derived for a wide range of frequencies. Examples are shown to illustrate the thermal and viscous effects on sound scattering. Comparison is made with three existing models. While these models are known not to be applicable for high frequencies, it is shown here that even in the low-frequency region, there are also noticeable discrepancies between the exact solution and the three existing models with regard to the scattering properties such as the scattering cross-section, and the quality factor of resonant peaks. By numerical simulation, we claim that the discrepancies may be due to the incomplete consideration of the thermal exchange process in the previous models. The approach presented here is valid for any other fluid enclosure in liquids.