Showing papers by "University of Paris published in 1976"

Kolmogorov entropy and numerical experiments

Abstract: Numerical investigations of dynamical systems allow one to give estimates of the rate of divergence of nearby trajectories, by means of a quantity which is usually assumed to be related to the Kolmogorov (or metric) entropy. In this paper it is shown first, on the basis of mathematical results of Oseledec and Piesin, how such a relation can be made precise. Then, as an example, a numerical study of the Kolmogorov entropy for the H\'enon-Heiles model is reported.

Strong MHD helical turbulence and the nonlinear dynamo effect

Abstract: To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971~~)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number. Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘AlfvBn effect ’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of largescale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a - power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are - 2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field willgrow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frisch et aZ. (1975), results from a competition between the helicity and Alfvh effects and yields an inertial range with approximately - 1 and - 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale Zinj and the rate k (per unit mass), the time of build-up of magnetic energy with scale L 9 Zinl is t % L( prp;nj)-k 21 FLM 77

Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions

Abstract: A study of the dynamics of a discrete two-dimensional system of classical particles is presented. In this model, dynamics and computations may be done exactly, by definition. The equilibrium state is investigated and the Navier-Stokes hydrodynamical equations are derived. Two hydrodynamical modes exist in the model: the sound waves and a kind of vorticity diffusion. In the Navier-Stokes equations one obtains a transport coefficient which is given by a Green-Kubo formula. The related time correlation function has been calculated in a numerical simulation up to a time of the order of 50 mean free flights. After a short time of exponential decay this time correlation behaves like ${t}^{\ensuremath{-}S}$, the exponent being compared to theoretical predictions.

The motor end-plate specific form of acetylcholinesterase: appearance during embryogenesis and re-innervation of rat muscle.

Abstract: – We have solubilized three active molecular forms of AChE from rat muscle and have confirmed the presence of one of these forms (EP form, apparent sedimentation coefficient: 16 s) uniquely at the motor end-plate regions of several skeletal muscles. This form was never detected in smooth muscle extracts. In sternocleidomastoidian muscle it disappeared after denervation and reappeared after re-innervation in the region where nerve and muscle had come in contact. During the embryonic development of hind leg muscles the EP form appeared on the 14th or 15th day of gestation. The EP form of muscle AchE appears to be an excellent biochemical marker of the neuromuscular junction.

Observation of a narrow charged state at 1876 MeV/c2 Decaying to an exotic combination of Kππ

Abstract: We report evidence for the production of a new narrow charged state in e/sup +/e/sup -/ annihilation at a center-of-mass energy of 4.03 GeV. This state, which has a mass of 1876 +- 15 MeV/c/sup 2/, is observed in the exotic channel Kminus-or-plus..pi../sup plus-or-minus/..pi.. +- , but not in the nonexotic channel Kminus-or-plus..pi../sup +/..pi../sup -/. It is produced primarily in association with a system of mass 2.01 +- 0.02 GeV/c/sup 2/. These characteristics are just those expected of a charged charmed meson. (AIP)

Custom as a Source of International Law

Abstract: The attitude of international lawyers towards customary international law is somewhat similar; they invoke rules of customary international law every day, but they have great difficulty in agreeing on a definition of customary international law. This chapter deals with the relationship between treaties and custom. In the North Sea Continental Shelf cases the International Court treated the Truman Proclamation and similar claims by other States as State practice which had given rise to a rule of customary law. Anthony D'Amato argues that claims and other statements by States are likely to conflict with one another, and that physical acts do not suffer from this defect. Assertions made in abstracto concerning the content of existing law are sometimes found in resolutions passed by the representatives of States at the meetings of international organizations. In the Nottebokm case the International Court relied partly on the fact that national laws provide for naturalization only when there is a genuine link.

Proposed experiment to test the nonseparability of quantum mechanics

Abstract: As a criterion between quantum mechanics and local hidden-variable theories, the so-called Einstein-Podolsky-Rosen paradox is mainly tested in the form of the statistical correlation between polarizations of photons issuing from a cascade transition. It has been stated more than once that an improved form of the test would make use of polarizers, the orientation of which would change randomly in a time comparable with the time of flight of the two photons; the Bell locality assumption could then be replaced by a weaker assumption also considered by Bell: The Einstein principle of separability. However, to our knowledge, no workable experimental scheme has yet been proposed, and we believe the one described in this paper to be a workable one. After explaining the difference between the Bell locality assumption and the Einstein principle of separability, we briefly discuss the theoretical implications of the modified experiment. The overall scheme of the apparatus we are proposing is described, and the generalized Bell inequalities, modified for our case, are derived. As in previous experiments, supplementary assumptions are made in order to derive experimentally testable inequalities. Finally, we describe the device we intend to use to carry out the proposed scheme.

Remarks on the Korteweg-de Vries equation

Abstract: We show for the Korteweg-de Vries equation an existence uniqueness theorem in Sobolev spaces of arbitrary fractional orders≧2, provided the initial data is given in the same space.

Image d'une somme d'operateurs monotones et applications

Abstract: LetA andB be monotone (multivalued) operators in a Hilbert spaceH. The paper deals with the relations between the rangeR(A+B) ofA+B and the algebraic sum of the ranges ofA andB, R(A)+R(B).

Infrared absorption spectra of carbon monoxide in rare gas matrices

Abstract: Medium and high resolution infrared spectra of CO trapped in solid Ne, Ar, Kr and Xe are presented. Spectra of low optical density samples are identical to those previously observed but a different assignment is proposed. Monomeric absorption is clearly identified by double doping experiments and by sample deposition through a nitrogen cold trap. In addition other broad weak bands are observed on the spectra of high optical density samples. These bands are assigned to combinations between internal vibration, libration and lattice vibrations. The barrier hindering rotation due to site distortion is estimated to 30–50 cm −1 . Librational motion is strongly perturbed by coupling with lattice motion. Carbon monoxide is also an efficient probe to study the dynamical properties of rare gas lattices.

TOTAL MINERAL DISSOLVED TRANSPORT BY WORLD MAJOR RIVERS / Transport en sels dissous des plus grands fleuves mondiaux

Abstract: World variations of dissolved transport Td [t km−2 year−1] and major ion content S [mg 1.−1] with runoff q [1. s−1 km−2] and solid transport Ts [t km−2 year−1] are examined on the basis of 40 of the world's biggest rivers (basin area A >400 00 km2 or discharge Q > 5 000 m3 s−1). For each river estimates of A, Q, S, Td and Ts are given and two subsamples are considered according to the size of the rivers. For each subsample it is found that S is inversely related to q, Td is directly related to q and to Ts. The ratio Ts/Td is highly variable but generally increases when Ts increases. Climate dominates S variation and relief Td variation; wide scatterings of S and Td are due to the other factor. On a world scale relief is the main factor controlling variations of Td with Ts. The direct relationship between Td and Ts confirms the work of Alekin and Brazhnikova in the Soviet Union, while the inverse relationship found by Judson and Ritter in the conterminous USA seems to be a minor trend due to the i...

Étude des couches minces et des surfaces par réflexion rasante, spéculaire ou diffuse, de rayons X

Abstract: 2014 The Fresnel formulae applied to optical surfaces, assumed to be perfectly plane and homogeneous, do not correctly explain the specular reflection curves obtained with bulk specimens or thin films. Considerations on various scattering processes (either elastic or inelastic) show that only elastic scattering, due to surface roughness or structural inhomogeneity, must play a role in the analysis of the reflection curves. In this paper some roughness models are presented and their validity range is given for both specular and diffuse reflection. Theoretical curves derived from these models are compared with experiments carried out on bulk specimen of titanium, silicon and germanium using the copper or chromium K03B11 radiations. REVUE DE PHYSIQUE APPLIQUÉE TOME 11, JANVIER 1976, PAGE

Theory of photochemical reactions.

Abstract: Although the great number of electronic states available to an excited molecule might seem to preclude a coherent picture of photochemical reaction mechanisms, it is possible to bring out some basic features common to a great many reactions. The electronic states of the primary diradical intermediates, surface crossings, topicity, and avoided surface crossings have been shown to be essential components of the electronic theory of photochemical reactions. Diradicals have four important electronic states. Knowing these states, and making a simple electron count, it is possible to draw state correlation diagrams. Some diagrams show a typical surface crossing of the ground singlet state with the lowest (singlet, triplet) pair of excited states, with clear-cut consequences of quantum yields under various conditions. In other reactions the surfaces stay apart. The critical discriminating feature that determines the type of correlation diagram is the topicity. Photochemical reactions can be classified according to topicity, which is useful in interpreting their mechanisms (53). Avoided surface crossings can also be classified into different types. Figure 7, which illustrates the interplay of a covalent and an ionic surface responsible for photochemical electron transfer, is a typical multidimensional representation of a photochemical reaction. The chemical behavior of the excited zwitterionic states of common intermediates, such as twisted ethylene or diallyl, reflects the quantum mechanical nature of photochemical processes. In these states, for perfectly symmetric systems, charge oscillates back and forth between two symmetry-equivalent sites. Slight geometric perturbations can create a sudden polarization of the excited molecule, with localization of almost a full charge at one end of the molecule. A photon is transformed into an electrical signal thanks to an appropriate molecular distortion. Nature may have used this simple process in the N-retinylidene visual chromophore to trigger an electrical response to vision.

Molecular-weight determination of animal-cell RNA by electrophoresis in formamide under fully denaturing conditions on exponential polyacrylamide gels.

Abstract: A method for electrophoretic analysis of RNA under fully denaturing conditions on exponential gradient polyacrylamide gels is described. Full denaturation, and strand separation of DNA - RNA hybrids and double-stranded RNA is obtained in dry formamide only if electrophoresis is carried out at 45 degrees and 55 degrees C, respectively. In such conditions, the effects of secondary structure of RNA, important in aqueous medium, are suppressed and a linear correlation is obtained between the logarithm of the molecular weight of an RNA and its final position in the gel over the entire molecular weight range of 10(4) - 10(7). Based on absolute molecular weight standards, obtained from sequenced rRNA of Escherichia coli and tRNA and extrapolating to higher molecular weights the size of animal cell was reexamined. Precursor tRNA from HeLa cells migrates according to a molecular weight of 4.1 x 10(6). Nascent precursor mRNA has molecular weights of up to 5 x 10(6) in the case of duck erythroblasts and of up to 10(7) in HeLa cells. This seems to represent the largest size of non-viral animal-cell RNA molecules.