On the non existence of monotone linear schema for some linear parabolic equations

In this Note, we present a result concerning the non existence of linear monotone schema with fixed stencil on regular meshes for some linear parabolic equation in two dimensions. The parabolic equations of interest arise from non isotropic diffusion modelling. A corollary is that no linear monotone 9 points-schemes can be designed for the one-dimensional heat equation emerged in the plane with an arbitrary direction of diffusion. Some applications of this result are provided: for the Fokker–Planck–Lorentz model for electrons in the context of plasma physics; all linear monotone scheme for the one-dimensional hyperbolic heat equation treated as a two-dimensional problem are not consistent in the diffusion limit for an arbitrary direction of propagation. We also examine the case of the Landau equation. To cite this article: C. Buet, S. Cordier, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Equisingular Deformations of Sandwiched Singularities

We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Champ de vitesse dans un échangeur à vortex en régime turbulentHeat exchanger velocity field with turbulent inlet condition

We consider the isothermal flow through a cylindrical flat chamber, a model of some particular heat exchanger, for which LDV measurements and a numerical simulation have been performed. Experimental results show the establishment of an important vortex zone, the secondary flow extending all along the chamber radius. This observation leads to an expected significant increase of the fluid mixing. Results issued from the numerical simulation appear to be in close agreement with experimental data. Nevertheless, the k–ε model used here must be improved to obtain a better approach near the vortex centre. To cite this article: S. Petitot et al., C. R. Mecanique 330 (2002) 593–599.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

Einfluß der Dilatation einer ebenen Phasengrenzfläche auf den Stoffdurchgang

The common methods for calculating the mass transfer across liquid-liquid interfaces in technical applications take into account the mass transfer resistances within the bulk phases. The transfer resistance of the interface and a possible coupling between the momentum and the mass transport is not taken into account. In the present paper a survey is given of theoretical approaches which can describe this coupling and the additional mass transfer resistance. A theory is proposed by Hampe which can be used to explain the coupling between momentum and mass transport employing thermodynamics of irreversible processes. On the basis of this work, the influence of the dilatation of a flat interface on the mass transfer is deduced. It is also concluded from this theory that the diffusion coefficients within the bulk phases are coupled near the thermodynamic equilibrium.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.     

Dielectronic Recombination of Very Heavy Lithiumlike Ions

Hyperfine Interactions - An overview of measurements of dielectronic recombination (DR) with the heaviest lithiumlike ions is presented. The experiments have been carried out at the heavy ion...