Trois formulations d'un modèle de plasma quasi-neutre avec courant non nul

In this Note, we propose three formulations of a model describing a quasi-neutral plasma with non-vanishing current. In order to study and compare the numerical efficiency of each formulation, two test-problems are implemented in one dimension. The first is a periodic perturbation of a uniform stationary plasma. The second is a case of plasma expansion in vacuum between two electrodes. To cite this article: P. Crispel et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Genericity of the Morse-Smale Property for Damped Wave Equations

We prove that for damped hyperbolic equations the Morse-Smale property (hyperbolicity of equilibria and transversal intersection of stable and unstable manifolds) is generic. More precisely, we prove that in an appropriate functional space of nonlinear terms in the equation, the set of functions for which the latter has the Morse-Smale property is residual, i.e., it is a countable intersection of open dense sets. The result extends a similar result proved in [1] for reaction diffusion equations. However, because of the absence of knowledge about nodal sets of polutions new ideas were needed in the proof.     

Lagrangian skeletons,periodic geodesic flows and symplectic cuttings

In this paper, we investigate symplectic manifolds endowed with a Morse–Bott function with only two critical submanifolds, one of which is Lagrangian while the other one is symplectic.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Scanning tunnelling microscopic images of the surface ordering of the liquid crystal 4-n-octyl-4'-cyanobiphenyl

Images of the surface ordering of 4-n-octyl-4'-cyanobiphenyl, a room temperature smectic liquid crystal deposited upon graphite, have been obtained by scanning tunnelling microscopy. The microscope was operated in air using the constant-current mode. Under certain tunnelling conditions it has been possible to resolve both the aliphatic and aromatic parts of the molecule, and to observe individual benzene rings. Two previously unreported conformations have been observed: an overlapping bilayer structure with spacing 3.7 nm, and a monolayer structure with spacing 2.4 nm. The latter structure may represent the first visual evidence for a surface polar ordered structure.     

High-order harmonic generation with a strong laser field and an attosecond-pulse train: The Dirac-Delta comb and monochromatic limits

In recent publications, it has been shown that high-order harmonic generation can be manipulated by employing a time delayed attosecond-pulse train superposed to a strong, near-infrared laser field. It is an open question, however, which is the most adequate way to approximate the attosecond-pulse train in a semianalytic framework. Employing the strong-field approximation and saddle-point methods, we make a detailed assessment of the spectra obtained by modeling the attosecond-pulse train by either a monochromatic wave or a Dirac-Delta comb. These are the two extreme limits of a real train, which is composed by a finite set of harmonics. Specifically, in the monochromatic limit, we find the downhill and uphill sets of orbits reported in the literature, and analyze their influence on the high-harmonic spectra. We show that, in principle, the downhill trajectories lead to stronger harmonics, and pronounced enhancements in the low plateau region. These features are analyzed in terms of quantum interference effects between pairs of quantum orbits, and compared to those obtained in the Dirac-Delta limit.     

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     

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