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.     

Wechselnde Bindungen in einem Zweikörpersystem mit trockener Reibung

Übersicht Betrachtet wird ein zwangserregtes Zweikörpersystem mit wechselnden Bindungen infolge trockener Reibung. Stationäre Bewegungen werden als Grenzfall instationärer Einschwingvorgänge berechnet. Abhängig von den Systemparametern ergeben sich drei typische Bewegungsformen. Ihnen entsprechen dauernde Haftzustände, wechselnde Haft-Gleitzustände oder dauernde Gleitzustände an der Berührfläche beider Körper.

---

Intermittant constraints in a two-body-system with dry friction

Summary An externally excited two-body-system with intermittant constraints due to dry friction is considered. Stationary motions are calculated as limit cases of instationary transients. Depending on the parameters of the system, three typical modes are of interest. These correspond to permanent sticking, slipstick behaviour, or to permanent slipping in the contact surface of the bodies, respectively.

     

Studies aimed at the synthesis of morphine V an economic approach to (±)-reticuline from 3,4-dihydropapaverine

Regioselective demethylation of 3,4-dihydropapaveraldine ($\text{2}$a) at 7 and 3' positions affords a properly substituted diphenolic key intermidiate ($\text{2}$d) for the synthesis of reticuline and N-norreticuline.     

Analysis of tunable diode-laser spectra of Q(J,0) lines in CH3F near 1475 cm using a multispectrum fitting technique

We have analyzed the methyl fluoride ^RQ(J,0)Q branch lines located near 1475 cm⁻¹ using a simultaneous multi-spectrum fitting technique. In this analysis we have used previously recorded diode-laser data in which we collected many data points covering only one or two Q branch lines in a particular run. The analysis consists of simultaneously fitting 57 spectra collected with numerous pressure and path length conditions for all absorption lines. The data are concatenated to create one continuous spectrum of the Q branch. We have determined the intensity and self-broadened widths at 296 K for 23 ^RQ(J,0) lines.     

Lattice vibrations of armchair carbon nanotubes: phonons,soliton deformations and lattice discreteness effects

Small and large-amplitude elastic deformations of the armchair structure of single-walled carbon nanotubes are investigated with emphasis on the cylindrical geometry. As starting model, we consider a discrete one-dimensional lattice of atoms interacting via a Lennard-Jones type two-body potential. In an expansion scheme using cylindrical coordinates where radial displacements are assumed negligible compared to the angular motions, a sine-lattice Hamiltonian is derived. In the limit of small-amplitude angular displacements, the dispersion spectrum of acoustic phonons is derived and the associate characteristic frequency is given as a function of parameters of the model. In the large-amplitude regime, lattice vibrations give rise to kink-type deformations which move undergoing lattice dispersion and lattice discreteness effects. The dispersion law of the kink motion is obtained and shown to lower the effect of lattice discreteness, giving rise to a vanishing Peierls stress for kink sizes of the order of a few lattice spacings. Implications of the coupling of two armchair structures on the stability of vibrational modes of an individual armchair nanotube are also discussed. A gap of forbidden modes is predicted in the phonon spectrum while the energy needed to create a kink deformation in individual nanotubes is shifted in the presence of a wall-to-wall interaction.Received: 2 August 2004, Published online: 14 December 2004PACS: 81.07.De Nanotubes - 62.30. + d Mechanical and elastic waves-vibrations - 63.22. + m Phonons in low-dimensional nanoscale materials - 63.20.Ry Anharmonic lattices modes     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

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).     

Polariton gap solitary waves in semiconductor microcavities

We study nonlinear dynamics of optical pulse propagation in the spectral region inside the polariton gap. It is shown that the Kerr nonlinearity can lead to formation of solitary waves in this region of frequencies.