Courbure scalaire et géométrie conforme

We present a study of the scalar curvature problems in conformal geometry. We deal with the Nirenberg and Yamabe problems, the prescribed scalar curvature problem, the Yamabe equivariant problem, and the questions connected with the multiplicity of metrics having the same scalar curvature. The problems of the best constants in the Sobolev imbedding theorem and the positive mass theorem (which is highly physical and connected with general relativity) are first treated. The mathematics of these two subjects will appear throughout the text.

Résumé

On présente une étude des problèmes de courbure scalaire en géométrie conforme. Sont ainsi traités: les problèmes de Nirenberg et Yamabe, le problème de la courbure scalaire prescrite, le problème de Yamabe équivariant et les questions relatives à la multiplicité des métriques ayant une même courbure scalaire. Les problèmes de meilleures constantes dans les inclusions de Sobolev et le théorème de la masse positive (qui est hautement physique et lié à la relativité générale) sont d'abord présentés. Les mathématiques de ces deux sujets apparaitront tout au long du texte.     

Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact

We show that the classical Marsden-Weinstein Reduction theorem for Hamiltonian systems with symmetries is still true for contact manifolds and cosympletic manifolds (i.e. canonical manifolds in the sense of A. Lichnerowicz).

In fact, we precise the notion of transitive almost contact structure, which enables us to consider the cosymplectic geometry as a limit of the contact geometry when a certain parameter goes to zero. This point of view unifies both theories.

However, we have to give two distinct proofs for the contact Reduction theorem and the cosymplectic one.     

Étude géométrique du monopole magnétique

Le mouvement d'une particule chargée soumise au champ d'un monopole magnétique est étudié dans un cadre géométrique.

Le formalisme sans corde de Wu et de Yang permet d'interprêter géométriquement la symmétrie de rotation mais s'avére insuffisant pour traiter les symétries cachées découvertes récemment par Jackiw. Cette tache est accomplie par la quantification géométrique de Souriau et de Kostant. La relation des deux constructions est expliquée en détail.     

Estimation du nombre d'echantillons et du domaine spectral necessaires pour determiner une forme moyenne par une technique de superposition

An average form can be extracted from a set of forms, assuming that they are all obtained by a common process. Considering this set as a representative sample of a statistic population allows the determination of the minimal required number of forms and also the useful spectral domain.     

Les nouvelles générations de détecteurs infrarouge à base de HgCdTeNew generations of infrared detectors based on HgCdTe

The technology of very high performance cooled infrared detectors made with HgCdTe has progressed continuously for ten years and reached today an industrial maturity that allows the production of large size arrays at a more and more reasonable cost. At the same time, new prototypes of more complex sensors have appeared (megapixel arrays, multicolour arrays, high definition long linear arrays, …) that show the strong potentialities of this very high performance technology. This paper presents the technology developed in France and gives the state of the art of products available in industry; it then focuses on some very recent realizations of advanced prototypes made at LETI (dualband arrays, megapixel arrays, …). To cite this article: G. Destefanis, C. R. Physique 4 (2003).     

Étude par spectrométrie auger et par spectrométrie de masse de la chimisorption de l'oxyde de carbone sur le molybdène polycristallin

A combination of Auger spectrometry and mass spectrometry was employed to study CO chemisorption on polycrystalline Mo surfaces at room temperature. We observed five adsorption states and calculated the binding parameters (E,n₀,τ₀) for the three important states. The results obtained by the two methods are in accord but we pointed out the occurence of electronic desorption in Auger experiments. Contamination effects by C atoms in such studies were investigated by repeated cycles of adsorption-desorption and a characteristic evolution of flash desorption peaks was observed. The results are discussed in this point of view enhancing the importance of a control of the adsorption surface cleanness by a method of great sensibility like Auger spectrometry.     

Electromigration du cuivre de l'argent et de l'or dans l'aluminum

By electromigration experiments we have measured the apparent effective valences of copper, silver and gold in aluminium. These data, used together with complementary calculations, allow us to calculate in each case the cross-terms between ssolute and solvent fluxes. The values thus obtained are qualitatively in good agreement with direct calculations.     

Variation du travail de sortie du W (100) par adsorption d'oxyge`ne,de ce´sium et co-adsorption d'oxyge`ne et de ce´sium

The work-function determination by the Kelvin method is used to study the adsorption of oxygen, cesium and co-adsorption of oxygen and cesium on a (100) tungsten surface, at room temperature. The work-function change of the clean surface with the oxygen exposure is used to estimate the sticking coefficient and the dipole moment of adsorbed oxygen. During cesium deposition on the clean surface, a minimum at 1.58 eV and a plateau at 1.80 eV are obtained. Starting from the minimum obtained with cesium, oxygen adsorption leads to a decrease of the work function down to 1.17 eV, when cesium adsorption on a previously oxygenated surface gives a 1.12 eV minimum and an increase of the plateau up to 2.20 eV. This last variation is shown to be consistent with the observed increase of the dipole moment of cesium adsorbed on a partially oxygenated surface, which accounts also for the lowering of the work function minimum.     

Étude de l'adsorption par ellipsométrie: adsorption du Xe/(0001) graphite

The adsorption isotherms of xenon on the perfectly homogeneous (0001) face of graphite are known with great accuracy through classical volumetric measurements, LEED and Auger diffusion. Ellipsometric measurements have led to the same results. The formation of five successive monolayers and two phase transitions in the first monolayer have been shown. The ellipsometric signal Δ which is related to the formation of one monolayer varies linearly with the layer number, with only a slight discrepancy for n= 4.5. In the first monolayer the ellipsometric signal Δ varies linearly with the coverage ratio θ, 0 < 9 < 1. The detection sensibility corresponds to $\text{1}\text{100th}$ of a monolayer.     

Etude du rendement photoelectrique du magnesium et de l'aluminium en ultravide entre 6 et 12 eV a l'aide du rayonnement synchrotron d'orsay

The photoelectric yields of magnesium and aluminum are studied in the far UV by making use of conventional radiation sources and the radiation emitted by the collision ring at Orsay. The films are prepared in ultra high vacuum and studied in situ. The results are in good agreement with the calculated photoelectric yield curves making evident the surface effects in this spectral region.     

Niveaux d'énergie et spectres de rayons X du rutile

The electronic levels of the complex TiO^?8₆ in the D_2h symmetry are determined according to an extended L. C. A. O. method. The results can explain the X-ray spectra of TiO₂. The absoption L_III and K rays are related to transitions from the 2p_3/2 and 1 s levels to the conduction band levels since the emission L_III and K components are explained by the transitions from the valence band levels to the 2p_3/2 and 1 s states. Interband transitions are related to the components of the optical reflexion spectrum of TiO₂ for the energies 0–20 eV. A comparaison is made with the electronic band structures of SnO₂, TiO₂ and BaTiO₃. At the center of the Brillouin zone, we obtain a forbidden gap of 3,01 eV, the corresponding widths of the valence and conduction band are 4,8 and 2,9 eV.     

Etude simulée et comparative de différents systèmes optiques en vue d'améliorer l'injection dans les fibres multimodes

Sans résumé     

Etude de l'autodiffusion dans la phase cubique centree de l'europium et du gadolinium

The self-diffusion coefficient follows a relation of the form : D = (1,0_?0.4^+0.7)exp (?shape=case>34400RT±700)

$\text{cm}{}^2\text{sec}$

for b.c.c. europium D = (1,0_?0.3^+0.5) × 10^?2 exp(?

$\text{32700 ±4000}\text{RT}\text{)}$

$\text{cm}{}^2\text{sec}$

for β-b.c.c. gadolinium.Whereas europium has normal self-diffusion parameters, β-b.c.c. gadolinium must be set in the class of the anomalous b.c.c. rare-earth metals.From these results we conclude that there exists no evident connexion between the instability of the 4f shell and the activation energies anomalously low in the b.c.c. phases of the rare-earth metals.     

Asymétrie du temps: Polarisation et pouvoir d'analyse dans les réactions nucléaires

Measurements of the proton polarization in the reactions ⁷Li(³He, $\text{p}$)⁹Be and ⁹Be(³He, $\text{p}$)¹¹B and of the analyzing powers of the inverse reactions, initiated by polarized protons at the same c.m. energies, show significant differences which imply the failure of the polarization-analyzing-power theorem and, prima facie, of time-reversal invariance in these reactions. The reaction ²H(³He, $\text{p}$)⁴He and its inverse have also been investigated and show some smaller differences. A discussion of the instrumental asymmetries is presented.     

Émission d'électrons auger caractéristiques du néon et du sodium,observée lors de collisions de ces ions avec différentes cibles solides

The Ne and Na Auger emission observed from collisions of these ionized gases with different solid targets, in an energy range from 5 to 50 keV, has been investigated. The Auger electron distributions were analyzed. Moreover, for the Ne⁺-Mg and Na⁺-Mg collisions, the Auger yield variation as a function of various parameters which influence the implantation, was studied. The experimental Auger yields ρ_A were compared to the calculated ones in a model which takes into account the stationnary concentration profiles of implanted atoms inside the target. For the Ne, the experimental results are in good agreement with the proposed model but this model is inadequate to explain the Na ρ_A variations as a function of ionic energy and incidence angle, at the room temperature.     

Coadsorption de l'oxygène et du monoxyde de carbone sur des surfaces de rhénium

Temperature programmed desorption ($\text{2.65}\text{K}\text{sec}$) has been used to study carbon monoxide and mixed layers of carbon monoxide and oxygen on rhenium ribbons, strongly oriented parallel to the (0001) plane. Four binding states, populated in decreasing energy have been detected. Interpretation of the results on β states agrees qualitatively with King's model postulating dissociation of carbon monoxide molecules and a repulsive interaction energy between carbon and oxygen atoms. However, in the coadsorbed layers studies, it is shown that all the oxygen atoms do not play a part in the recombination process, during desorption, and that when oxygen is adsorbed after carbon monoxide, a displacement reaction occurs, due to apparent transfer from β states towards molecular α states. Optimization of the results on pure carbon monoxide layers leads to an interactional energy ω, equal to 3 $\text{kcal}\text{mole}$, and is only possible if is assumed that β states are formed on alternatively filled and empty rows.     

Représentation d''une particule quantique de spin 1/2 par le produit de Moyal et une super-variété symplectique plate

The aim of this paper is to show that it is possible to represent a quantum particle with a spin with the help of a star product and a flat supermanifold. We extend to the supermanifolds the Schouten bracket, the exterior differentiation, the Lie derivative. These notions allow us to define the Poisson bracket and the symplectic supermanifolds. It is easy to define the Moyal product: the Grassman algebra of the superfunctions becomes a Clifford algebra. We suppose that the observables of a quantum particle with a spin are superfunctions defined on a flat supermanifold. The study of these star algebras proves the existence of a spectral resolution for some particular elements. Consequently the equation of motion for an observable admits stationary solutions. The examples considered show that the spin splits a given state into two other ones.     

Décomposition du fibré des spineurs d''une variété spin Kähler-quanternionenienne sous l''action de la 4-forme fondamentale

On a spin quaternionic-Kähler manifold M^4m, we give the spectral decomposition of the spin bundle the action of the fundamental 4-form Ω. Moreover, we compute the eigenvalues of Ω which, in the compact case, play an essential role in the problem of estimating the eigenvalues of the Dirac operator. The proof is based on the decomposition of the spin representation into irreducible components under the action of the group Sp(1) × Sp(m). We show that this algebraic results induces a Whitney decomposition of the spin bundle which, when restricted to the fibres, is the spectral decomposition under the action of Ω.