More compact invariant manifolds appearing in the non-linear coupling of oscillators

Near partially elliptic rest points of generic families of vector fields or transformations, many types of normally hyperbolic invariant compact manifolds can appear, diffeomorphic to intersections of quadrics. To cite this article: M. Chaperon et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Numerical and theoretical study of a Dual Mesh Method using finite volume schemes for two phase flow problems in porous media

Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates for different test-cases. Received March 21, 1997 / Revised version received October 13, 1997     

X-ray fluorescent and EXAFS studies of the electronic and spatial structure of dialkyl sulfides and their PdCl2 complexes in extraction systems

SK_α, SK_β, ClK_β, ClK_β, and PdL_β2 X-ray fluorescent and PdK EXAFS spectra were obtained for some organic solutions of dialkyl sulfide complexes with palladium chloride. Solvent effects on the electronic and spatial structure of complexes in solution are discussed. In the benzene solution of [PdCl₂2(C₆H₁₃)₂S], complex molecules interact with solvent molecules along a coordinate that is perpendicular to the plane of the complex molecule. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurmal Strukturnoi Khimii, Vol. 35, No. 4, pp. 105c111, July–August, 1994. Translated by L. Smolina     

Modulation of Particle Concentrations in the Interference Laser Radiation Field

Spatial redistribution of microparticles in a suspension on exposure to the interference laser field depending on the parameters of the particles and the field characteristics has been analyzed theoretically. Results of experimental investigations are presented that illustrate the capture of an ensemble of polymeric small spheres and also of the lymphocytes of human blood and other microparticles in a liquid in the interference radiation bands of the He–Ne laser.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Mlcrolasers based on silica microspheres

Light can be confined efficiently in the high-Q, small-volume whispering-gallery-modes observed in silica microspheres. By coupling these microspheres to eroded optical fibers and fiber tips, direct mapping of the whispering-gallery modes has been achieved and the mode numbers have been assessed. The properties of these modes have allowed us to obtain laser action with very low thresholds in Nd-doped silica microspheres. Further projects in the field of non-linear optics and cavity quantum electrodynamics are described.     

Unexpected end‐groups of poly(acrylic acid) prepared by RAFT polymerization

Low‐molecular‐weight poly(acrylic acid) (PAA) was synthesized by reversible addition fragmentation chain transfer polymerization with a trithiocarbonate as chain‐transfer agent (CTA). With a combination of NMR spectroscopy and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, the PAA end‐groups of the polymer were analyzed before and after neutralization by sodium hydroxide. The polymer prior to neutralization is made up of the expected trithiocarbonate chain‐ends and of the H‐terminated chains issued from a reaction of transfer to solvent. After neutralization, the trithiocarbonates are transformed into thiols, disulfides, thiolactones, and additional H‐terminated chains. By quantifying the different end‐groups, it was possible to demonstrate that fragmentation is the rate limiting step in the transfer reaction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5439–5462, 2004     

A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems

Summary The reconstruction from a shaded image of a Lambertian and not self-shadowing surface illuminated by a single distant pointwise light source may be written as a first-order Hamilton-Jacobi equation.In this paper, we continue the investigation begun in E. Rouy and A. Tourin into the uniqueness of the solution of this equation; the approach is based on the viscosity solutions theory and the dynamic programming principle.More precisely, we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve. We prove a general comparison result for a piecewise Lipschitz continuous Hamiltonian and illustrate it by numerical experiments.     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Explicit construction of elements of the ring S(n,r) of invariants of n-ary forms of degree r

Translated from Matematicheskie Zametki, Vol. 51, No. 2, pp. 139–143, February, 1992.