Showing papers by "École Polytechnique published in 1975"

Martingales with values in uniformly convex spaces

Abstract: Using the techniques of martingale inequalities in the case of Banach space valued martingales, we give a new proof of a theorem of Enflo: every super-reflexive space admits an equivalent uniformly convex norm. Letr be a number in ]2, ∞[; we prove moreover that if a Banach spaceX is uniformly convex (resp. ifδ x(ɛ)/ɛ r whenɛ → 0) thenX admits for someq<∞ (resp. for someq

Internal kink modes in toroidal plasmas with circular cross sections

Abstract: The stability criterion of the internal kink mode is given in toroidal geometry for plasmas with circular cross sections Contrary to known results in cylindrical geometry, the internal kink mode can be stable if the pressure gradient is sufficiently low

Complex Formation in Reactive and Inelastic Scattering: Statistical Adiabatic Channel Model of Unimolecular Processes III

Abstract: The statistical adiabatic channel model developed previously [25] for unimolecular dissociation reactions is extended to describe bimolecular collisions proceeding via a strongly bound intermediate complex. As examples three cases are considered, in which the intermediate complex corresponds to a known stable molecule: O + O2 O3*, O + NO NO2* and Cl + NO ClNO*. Using known molecular properties and the experimental high pressure recombination rate constants, the specific dissociation rate constants k(E,J), state to state inelastic scattering cross sections σ(v,j v',j') and center of mass translational energy distributions are calculated with the same simple potential model. Rate constants kvv, for vibrational relaxation are computed and found to be in good agreement with experimental results available for the O + O2 vibrational relaxation. The dependence of cross sections and final state distributions as a function of initial state is illustrated in some detail. Even within the statistical model, there is found to be a marked memory of initial conditions. The range of validity of statistical models is discussed. Das in einer vorgehenden Arbeit [25] fur unimolekulare Dissoziationsreaktionen entwickelte statistische Modell adiabatischer Reaktionskanale wird hier erweitert auf bimolekulare Reaktionen, die uber einen gebundenen Zwischenkomplex verlaufen. Drei Beispiele werden behandelt, in denen der Zwischenkomplex einem bekannten stabilen Molekul entspricht: O + O2 O3*, O + NO NO2* und Cl + NO ClNO*. Mit Hilfe bekannter Molekularkonstanten und der Hochdruckrekombinationskonstanten wird ein einfaches Potentialmodell festgelegt, das es dann ohne weitere Parameter ermoglicht, spezifische Zerfallskonstanten der Zwischenkomplexe, k(E,J), inelastische Streuquerschnitte σ(v,j v',j') und damit auch die Translationsenergieverteilungen nach dem Stos zu berechnen. Weiterhin werden Geschwindigkeitskonstanten fur Schwingungsrelaxation (kvv) berechnet, die in guter Ubereinstimmung mit experimentellen Werten fur das O + O2-System stehen. Es werden an Beispielen die Abhangigkeit der Endzustandsverteilungen vom Anfangsquantenzustand der Systeme erlautert. Auch mit den statistischen Annahmen wird ein bemerkenswertes “Gedachtnis” an den Ausgangszustand gefunden. Es werden Kriterien fur den Gultigkeitsbereich statistischer Theorien diskutiert.

Decay properties and borel summability for the Schwinger functions inP(Φ)2 theories

Abstract: For the truncated Schwinger functions of theP(Φ)2 field theories, we show strong decrease in the separation of points. This shows uniqueness of theories withP of degree four. We also extend the domain of analyticity in the coupling constant. For theories withP of degree four, the combination of these two results gives Borel summability.

Normal Modes in the Ion-Beam-Plasma System

Abstract: Two types of dispersion relations are experimentally shown to exist in an ion-beam-plasma system. For beam velocities close to the ion-sound speed, two normal modes, one unstable, are seen. For larger beam velocities, the interferometer output exhibits beating between the three predicted stable normal modes, which are the "fast" and "slow" ion-beam modes and the plasma ion-acoustic wave.

The low-energy absorption edge in 2H-MoS2 and 2H-MoSe2

Abstract: The optical transmission of thick samples of 2H-MoS2 and 2H-MoSe2 has been measured below the A exciton energy for each material. The absorption coefficients have been calculated, and the low absorption starting at 1·1–1·2 eV has been attributed to an indirect d-d transition for both materials. There appears to be considerable d-p valence band overlap giving rise to further higher absorption before the strong A, B excitons, which have been associated with direct transitions from a p-like valence band. An energy band scheme has been sketched on the basis of these interpretations.

Spin-dependent Hall effect in semiconductors

Abstract: We recall the theory of the spin-dependent Hall effect in semiconductors and give an elementary presentation, stressing the physical aspects of the problem. The spin-dependent Hall effect arises from the spin-orbit interaction in the crystal, via the admixture of $p$ states into the conduction-band Bloch functions. A remarkable consequence of this admixture is the existence of the so-called periodic part of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}$, which can be interpreted as a transverse displacement of the spin-polarized electron. This transverse displacement yields a first contribution to the spin-dependent Hall effect; the displacement contribution corresponds to a side jump of the electron upon scattering and gives a transverse conductivity independent of the scattering process. A second contribution to the spin-dependent Hall effect is the skew scattering, due to a left-right asymmetry of the scattering cross section. Next, we report the experimental study of the spin-dependent Hall effect in $n$-type indium antimonide. The spin-dependent Hall effect is unambiguously separated from the much larger ordinary Hall effect by using a spin-resonance method. The study of the effect on a series of samples of various doping levels evidences the presence of the two contributions. In the weakly doped samples, only the displacement contribution remains, and the measurements agree, without any adjustable parameter, with the theoretical predictions for the transverse mobility ${\ensuremath{\mu}}_{yx}^{D}=\ensuremath{-}160$ ${\mathrm{cm}}^{2}$/V sec. For higher concentrations, the skew scattering becomes notable, cancelling the displacement contribution and changing the sign of the over-all effect. The contribution of multiple scattering to this process appears to be dominant; a semiempirical calculation is given, which agrees with experiment within a factor of 2. Finally, we report the study of the spin-dependent Hall effect in highly doped $n$-type germanium. The necessary extensions of the theory are presented. The study of the effect as a function of temperature in a sample with ${N}_{D}\ensuremath{\approx}3.1\ifmmode\times\else\texttimes\fi{}{10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ reveals a behavior quite similar to that observed in the case of InSb. At low temperature, the displacement contribution is observed alone and is found to be in good agreement with theory (${\ensuremath{\mu}}_{yx}^{D}=\ensuremath{-}0.20$ ${\mathrm{cm}}^{2}$/V sec) without any adjustable parameter. At higher temperature, the skew scattering increases and changes the sign of the observed effect. A model with two kinds of carriers is shown to account for the observed temperature dependence.

Relativistic nonlinear plasma waves in a magnetic field

Abstract: Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.

Unimolecular Processes IV: Product State Distributions after Dissociation

Abstract: The statistical adiabatic channel model is used to calculate the distribution of internal states and center of mass translational energies of fragments in unimolecular dissociation. The reactions ClNO Cl + NO and NO2 NO + O are considered as examples. The influence of molecular parameters and dynamical constraints is illustrated. Mechanisms providing randomness in photodissociation and unimolecular decomposition are discussed as well as the relation between dissociation rates and statistical scattering. The statistical calculations for NO2 decomposition are in good agreement with the experimental center of mass translational energy distributions from photofragment spectroscopy. Die Besetzung von Quantenzustanden der Produkte im unimolekularen Zerfall und die Verteilung der Translationsenergie der Fragmente im Schwerpunktssystem wird nach dem statistischen Modell adiabatischer Reaktionskanale berechnet. Als Beispiele werden die Reaktionen ClNO Cl + NO und NO2 NO + O untersucht. Der Einflus von Molekulkonstanten und einschrankender dynamischer Bedingungen wird erlautert. Mechanismen, die statistisches Verhalten im unimolekularen Zerfall allgemein und besonders auch in der Photodissoziation erzeugen, werden im Zusammenhang mit den Bedingungen fur statistische Streuung diskutiert. Die statistischen Berechnungen zum Zerfall von NO2 stehen im Einklang mit experimentellen Translationsenergieverteilungen aus der Photofragmentspektroskopie.

Long-time behaviour of a two-level system in interaction with an electromagnetic field

Abstract: We present an exactly solvable model describing the interaction between a two-level system and the electromagnetic field. For long interaction times we evidence some purely quantum-mechanical effects, such as the destruction of coherence of radiation and the Gaussian envelope of the transition probability.

Spin relaxation of conduction electrons in n -type indium antimonide at low temperature

Abstract: We present a theory of the spin relaxation time of the conduction electrons in indium antimonide at liquid-helium temperature; earlier work on the subject is reviewed and discussed. The theory is compared with our measurements and the experimental data available in the literature: The relevant mechanism in highly doped samples ($n\ensuremath{\gtrsim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) is shown to be scattering by ionized impurities. The spin-flip matrix element arises from the admixture of different spin states in the Bloch functions of the conduction band (Elliott process). Good agreement with experiment is obtained with no adjustable parameter. In the less-doped samples ($n\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) the currently invoked relaxation mechanism (modulation of the $g$ factor or of the hyperfine interactions by the motion of the electrons) is shown to be ineffective. The impurity Elliott process is reconsidered; the effect of disorder is included by using a model of quasimacroscopic fluctuations of the electron density, which qualitatively accounts for the observed linewidths.

Sur les exposants de Lojasiewicz

Abstract: Dans une premiere partie, on demontre les inegalites de Łojasiewicz a l'aide de la theorie des ensembles sous-analytiques de Hironaka, et on montre que les exposants de Łojasiewicz sont toujours rationnels (theoreme 1).

Resonant exciton in GaSe

Abstract: Experimental evidence is given for the occurrence in $\mathrm{Ga}{\mathrm{S}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ ($0\ensuremath{\le}x\ensuremath{\le}0.2$) of a resonance between the free exciton associated with the direct band gap on the one hand and states near the indirect-conduction-band minimum on the other hand. This evidence includes the temperature dependence of the luminescence spectrum of $\mathrm{Ga}{\mathrm{S}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ for excitation energies lying above and below the exciton ground state, the excitation spectra of two characteristic luminescence lines, and the shape of the absorption line of the free exciton. The experimental results are in excellent agreement with a model of recombination kinetics proposed earlier for GaSe as well as with Fano's theory of the line shape of resonant states.

Reducing energy consumption through trajectory optimization for a metro network

Abstract: The techniques of optimal control and optimization are applied to a practical problem of reducing energy consumed by the Montreal Metro (subway) system The problem considered is the determination of tunnel trajectories in the "equivalent" vertical plane when trains traveling in both directions must follow the same trajectory The problem is first formulated as a control problem with control and state constraints Then, under certain simplifying assumptions, an heuristic method employing a direct search algorithm is presented and used in the trajectory optimization The trajectories are optimized to reduce the sum of the energy consumed by the trains traveling in both directions on the trajectory The results show an average reduction of 773 percent in energy consumption as compared with existing trajectories The trajectories found using the method presented here will be followed in future tunnel construction

Scattering theory with dissipative interactions and time delay

Abstract: The general formalism of scattering theory with dissipative interactions is presented from the time-dependent viewpoint. A definition of time delay is proposed in this framework, generalizing that given for simple scattering systems. The time delay is expressed by a formula which reduces to that of Eisenbud and Wigner when there is no absorption.

Raman scattering : measurements of depolarization ratios and order parameters in an oriented nematic mesophase

Abstract: A recent Raman investigation technique [1,2] has been used to study the evolution, with respect to temperature, of two depolarization ratios and deduce the behaviour of the order parameters and in the nematic liquid crystal p-heptyl- p'-nitrile-biphenyl without recourse to a non-nematic probe. Results show that while values can be accounted for within the frame of existing mean-field theories, values are somewhat lower than what could be predicted by these theories.

On a particular conference scheduling problem

Abstract: In this paper we present some results related to the conference problem: a set of meetings (each one of them involving two persons) has to be scheduled within a time period of k days. The problem consists of finding a schedule that is as uniform as possible for each person. A graph theoretical model is described and some applications in the area of scheduling are mentioned.