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.     

Mechanical and physico-chemical characterization of cyclodextrin finished polyamide fibers

We present the study of the cyclodextrin (CDs) finishing of polyamide fibers (PA) by means of citric acid (CTR) as crosslinking agent. We observed that the mode of grafting happened by the formation of a crosslinked polymer formed between CTR and CDs. This polymer physically adhered to the fibers network and was resistant to hot water washings. Modified fibers were characterized by evaluating the contact angle with a polar liquid and by studying the hysteresis of damping of PA fibers (Cahn balance) with various grafting rates and by studying the absorptivity of grafted fabrics via the technique of the posed drop (Digidrop^® instrument). Then a mechanical characterization of the PA fabrics grafted with various proportions of CDs was accomplished, by traction and tear tests by using a tensile-test bench Lohmergy. Finally a topographic study of PA grafted surfaces was approached by atomic force microscopy (AFM and LFM; contact and non-contact mode) which permitted to evaluate the roughness and the chemical heterogeneity of the grafted surfaces.     

Gas diffusion-flow injection determination of total inorganic carbon in water using tungsten oxide electrode

A novel gas diffusion-flow injection method has been developed for the rapid and sensitive determination of total inorganic carbon (TIC) in water. The method is based on the diffusion of CO₂ across gas permeable membrane from a donor stream containing 0.1 M HCl to an acceptor stream of sodium acetate (10⁻⁵ mol l⁻¹ and pH 10). The CO₂ trapped in the acceptor stream passes through an electrochemical flow cell contains a tungsten oxide wire and a silver/silver chloride electrode, where it was sensitively detected. The parameters affecting the sensitivity of the electrode such as buffer concentration, pH, flow rate and injected volume were studied in detail. The electrode response was linear in the concentration range from 5 to 100 μg ml⁻¹ CO₃²⁻ with a correlation coefficient (R²) of 0.998. Precision (R.S.D.) was 1.42% for 20 μg ml⁻¹ standard solution of CO₃²⁻ (n=10). The detection limit was 0.20 μg ml⁻¹ CO₃²⁻. The method was evaluated by the injection of real natural water samples and an average recovery of 100.1% was obtained. The sampling rate was 30 samples h⁻¹. The method is simple, feasible with satisfactory accuracy and precision and thus could be used for monitoring TIC in water.     

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.     

On the Topology of Fibrations with Section and Free Loop Spaces

We relate the brace products of a fibration with section tothe differentials in its Serre spectral sequence. In the particularcase of free loop fibrations, we establish a link between thesedifferentials and Browder operations in the fiber. Applicationsand several calculations (for the particular cases of spheresand wedges of spheres) are given. 2000 Mathematical SubjectClassification: 55P35, 55Q15, 55R05, 55R20.