Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottementFinite element method with Lagrange multipliers for contact problems with friction

In this Note, we propose a finite element method with Lagrange multipliers in order to approximate contact problems with friction. The discretized normal and tangential constraints at the candidate contact interface are expressed by using continuous piecewise linear Lagrange multipliers in the saddle-point formulation. An optimal error estimate is established and several numerical studies corresponding to this choice of the discretized normal and tangential constraints are achieved. To cite this article: L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.     

Possible spectroscopic manifestation of the angular group induced bond alteration (AGIBA) effect in toluene

The most obvious consequence of the concept of aromaticity is the common confidence that in aromatic compounds, bond lengths do not alternate and are between typical to the single and double ones. However, in 1994, performing crystal structure investigations of substituted pyridines and their salts, Krygowski and co‐workers have discovered a very surprising angular group induced bond alteration (AGIBA) effect: It appears that some angular substituents, like methoxy or nitrozo groups, can induce bond alternation in aromatic rings. Crystal studies do not allow one to operate with liquids that are more common in organic chemistry. This paper presents the first possible evidence of spectroscopic manifestations of the AGIBA effect. Raman spectra of the liquid toluene are analyzed. It is found that instead of being single, the line corresponding to the ring breathing vibrations is clearly split by 1.0–1.4 cm^?1, thus indicating the presence of two (cis‐ and trans‐) AGIBA isomers. The energy difference between these isomers estimated in temperature dependent Raman studies is found equal to 6.68 kJ mol^?1. The low‐wavenumber line therefore corresponds to the cis‐AGIBA isomer and the high‐wavenumber line to the trans‐AGIBA isomer stabilized by the AGIBA effect. Copyright © 2007 John Wiley & Sons, Ltd.     

Mixing properties of mim diodes in the infrared

Point contact MIM diodes of different materials have been tested as harmonic mixers at 29 THz and 88 THz. From the analysis of the I-V static characteristic quantitative informations have been obtained about the effectiveness of the diodes as high order mixers.     

Light reflection from finite conductors with a Gaussian random roughness using Kirchhoff and geometric optics approximations

A comparison between exact solutions and two approximate models, Kirchhoff approximation (KA) and geometric optics approximation (GOA), for reflection from random Gaussian rough conductive metallic surfaces for three regimes of correlation length in both cases of polarization TM and TE has been reported. The phenomenon of excitation of surface plasmons (SPs) has been shown only at TM polarization for KA. The domains of validity of both approximate models have been quantified. It is shown that accuracy and efficiency of any approximate method depended of various parameters: surface roughness, polarization, SPs effects, wavelength, and surface materials. KA is efficient for weakly rough surfaces with correlation length greater than wavelength, but when rms height increases GOA is more suitable than KA. Excitation of SPs is observed only at TM-polarized light, only for weakly rough surfaces with correlation length less than wavelength using KA and not GOA.     

Estimation du nombre des μ-valeurs propres

La notion de -valeur propre de –+V sera définie pour un ouvert borné de R ^d ; étant une mesure dans la classe de Kato généralisée. On établira une estimation du nombre des -valeurs propres inférieures à un réel positif E.The notion of -eigenvalue of –+V will be defined for a bounded open subset of R ^d ; is in the generalized Kato class. An estimate for the number of -eigenvalues which are smaller then a positive real E is given.     

A hierarchy of coupled maps

A large number of logistic maps are coupled together as a mathematical metaphor for complex natural systems with hierarchical organization. The elementary maps are first collected into globally coupled lattices. These lattices are then coupled together in a hierarchical way to form a system with many degrees of freedom. We summarize the behavior of the individual blocks, and then explore the dynamics of the hierarchy. We offer some ideas that guide our understanding of this type of system. (c) 2002 American Institute of Physics.     

Hydrophobic hydration of tert-butyl alcohol studied by Brillouin light and inelastic ultraviolet scattering

The longitudinal viscosity of diluted water-tert-butyl alcohol solutions in the 10 GHz frequency region has been measured by means of Brillouin light scattering and inelastic ultraviolet scattering. The main advantage of our hypersonic investigation compared to more traditional ultrasonic measurements is that in the gigahertz frequency range slow relaxation processes involving the alcohol dynamics are completely unrelaxed, so that the measured viscosity mainly originates from the hydrogen bond restructuring of water. In contrast with previous determinations, we estimate an activation energy which is independent from the alcohol mole fraction up to X = 0.1, and comparable to that of bulk water. A simple two-component model is used to describe the steep increase of viscosity with increasing alcohol mole fraction, and a retardation factor 1.7 ± 0.2 is found between the relaxation times of hydration and bulk water. These findings endorse a dynamic scenario where the slowing down of hydration water is mainly due to a reduction of configurational entropy and does not involve an arrested, icelike, dynamics.     

Molecular dynamics of liquid acetone determined by depolarized Rayleigh and low-frequency Raman scattering spectroscopy

Slow to ultrafast dynamics of liquid acetone at variable temperature was investigated by depolarized Rayleigh and low-frequency Raman scattering spectroscopy, in the region 0-200 cm(-1). A detailed analysis was performed on the spectra and corresponding time responses, and a consistent view of the molecular dynamics of this dipolar solvent was obtained. The effects of temperature on the spectra were interpreted, and distinct dynamical processes identified. At very low frequencies, or long time scales, acetone dynamics is characterized by a slow diffusive reorientation obeying the Stokes-Einstein-Debye hydrodynamic theory only in the limit of subslip boundary conditions. An alternative model based on the microviscosity concept proved to be able to reproduce this correlation time and its temperature dependence. A comparative analysis of collective and single-molecule reorientational times, these latter estimated from intramolecular Raman spectra, led to an orientational correlation parameter g(2) of unity, which denotes a statistical disorder of molecular polarizability tensors. A fast local restructuring process is putatively responsible for an additional contribution at subpicosecond time scales often referred to as intermediate response in other molecular liquids. The high frequency portion of the dynamical susceptibility showed the signature of librational intermolecular motions, giving rise to an ultrafast decay of the time correlation function of polarizability anisotropy. The overall approach, which provided valuable information on dynamics, structure and molecular interactions of neat acetone, will be applied to acetone electrolytic solutions.