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.     

Stabilisation d'ondes électromagnétiques dans un domaine extérieur 2D

We consider the stabilization of Maxwell equations in two dimensional on the exterior of an arbitrary bounded obstacle. Using some results concerning of wave equations with Neumann boundary condition in the exterior domain. We deduce under the ‘exterior geometric control condition’ the behavior of the solution for large time. To cite this article: A. Moulahi, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Spiro compounds with fragments of 4-azafluorene-[indeno)2,3-e)-1,2-dihydropyridine] and pyrazoline

9-Phenacylidene-4-azaf luorene and 9-bromo-9-(-bromophenacyl)-4-azafluorene have been used in the synthesis of spiro compounds with fragments of substituted pyrazolines. 1-Methyl-2-oxo-5 phenacylidene-indeno[2, 3-e]-1,2-dihydropyridine and hydrazine gave 1-methyl-2-oxo-3 phenylspiro[indeno(2, 3-e)-1,2-dihydropyridine-5,5-pyrazoline-2].     

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.     

Synthesis of Inorganic Compounds (Metal, Oxide and Hydroxide) in Polyol Medium: A Versatile Route Related to the Sol-Gel Process

A new route for the preparation of powdery metal, oxide and hydroxide materials is presented as a chimie douce alternative to the sol-gel method. It consists in the reduction or the hydrolysis of a metal salt dissolved and heated in a polyol medium. It appears through zinc and cobalt examples that the use of acetate precursors contrarily to chloride or sulfate ones leads to the precipitation of a solid (metal, oxide, hydroxide) whose nature depends on two main factors: the hydrolysis ratio, defined by the water to metal molar ratio, and the reaction temperature. As in the sol-gel method, acetate leads to the formation of intermediate alkoxyacetate complex. The absence of water favors metal formation while its presence favors oxide or hydroxyacetate formation.     

Thermodynamic studies on the ferroelectric phase transition in neutron irradiated (LixK1−x)2SO4 crystals at high temperature

Thermodynamic studies of (Li_xK_1?x)₂SO₄, LKS, mixed crystals have been made in the concentration range (x=0.1, 0.2, ...,x=0.5). The thermal behaviour has been investigated by differential thermal analysis, DTA, and differential scanning calorimeter, DSC, in the vicinity of high temperature phases. Also, the effect of the thermal neutron irradiations on the thermal properties of mixed crystals was studied. The results showed a change in the transition temperatureT _c, as well as the value of specific heatC _p at transition temperature, due to the change of stoichiometric ratio and radiation doses. The change of enthalpy and entropy of mixed crystals have been estimated numerically.