Mixed formulations for a class of variational inequalitiesFormulations mixtes pour une classe d'inéquations variationnelles

This Note is an attempt to extend the mixed finite element method to a class of variational inequalities including the problems of Signorini and of unilateral contact in elasticity with or without friction. Existence and uniqueness for the continuous and the discrete problems as well as error estimates are established in a general abstract framework. As a result, the mixed approximation of the Signorini problem is proved to converge with an error bound in h^3/4. To cite this article: L. Slimane et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 87–92     

Three-stage sequential extraction procedure for metal partitioning in polluted soils and sediments

The sequential extraction procedure proposed by the Standard, Measurements and Testing program "SM&T" of the European Union has been applied to evaluate the amounts of Cr, Cu, Mn, Ni, Pb and Zn, extracted at each stage and indirectly their mobility and bioavailability in soil and sediment samples from a polluted area. Analysis of the extracts was carried out by flame atomic absorption spectrometry (FAAS). No significant matrix interferences were found except for Cr in the acetic acid and hydroxylammonium chloride extracts, which required determination by the standard additions method. Both of soils and sediments studied show similar partitioning of Mn, Ni, Cu and Cr. Mn and Ni can be considered to have significant component bound to the acido-soluble fraction, whereas, Cr and Cu occur largely in the organic and residual phases. The partitioning of Pb and Zn was different between soil and sediment. In terms of mobility and bioavailability, in soils, Ni and Mn can be regarded as moderately available followed by a lower availability of Pb while Cu, Zn and Cr have a very limited availability. In sediments, a higher availability (short-medium term) of Mn and Zn was presumed followed by a lower availability of Ni and Pb, whereas, Cu and Cr, occurring largely in the organic and residual phases, were of very limited availability.     

Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation

Journal of Thermal Analysis and Calorimetry - The effect on the entropy production and MHD convection of the hybrid nanofluid Al2O3–Cu/water (water with Cu and Al2O3 nanoparticles) in a...     

Direct Evidence for Intermolecular Oxidative Addition of σ(SiSi) Bonds to Gold

Oxidative addition plays a major role in transition‐metal catalysis, but this elementary step remains very elusive in gold chemistry. It is now revealed that in the presence of GaCl₃, phosphine gold chlorides promote the oxidative addition of disilanes at low temperature. The ensuing bis(silyl) gold(III) complexes were characterized by quantitative ³¹P and ²⁹Si NMR spectroscopy. Their structures (distorted Y shape) and the reaction profile of σ(Si? Si) bond activation were analyzed by DFT calculations. These results provide evidence for the intermolecular oxidative addition of σ(Si? Si) bonds to gold and open promising perspectives for the development of new gold‐catalyzed redox transformations.     

Enhanced π‐Backdonation from Gold(I): Isolation of Original Carbonyl and Carbene Complexes

The specific electronic properties of bent o‐carborane diphosphine gold(I) fragments were exploited to obtain the first classical carbonyl complex of gold [(DPCb)AuCO]⁺ (ν(CO)=2143 cm^?1) and the diphenylcarbene complex [(DPCb)Au(CPh₂)]⁺, which is stabilized by the gold fragment rather than the carbene substituents. These two complexes were characterized by spectroscopic and crystallographic means. The [(DPCb)Au]⁺ fragment plays a major role in their stability, as substantiated by DFT calculations. The bending induced by the diphosphine ligand substantially enhances π‐backdonation and thereby allows the isolation of carbonyl and carbene complexes featuring significant π‐bond character.     

An SFG/DFG investigation of CN− adsorption at an Au electrode in 1-butyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl) amide ionic liquid

In this paper we report an SFG/DFG investigation of the adsorption of CN^? – used as a probe molecule to study the electrochemical double-layer structure – at a polycrystalline Au electrode in 1-butyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl) amide ([BMP][TFSA]) room-temperature ionic liquid (RTIL). The adsorption of CN^? yielded single SFG and DFG bands in the range from ca. 2125 to 2135 cm^?1, exhibiting a Stark tuning of ca. 3 cm^?1 V^?1. Vibrational resonances – corresponding to modes of the RTIL coadsorbed with CN^?, were found in the range from ca. 1200 to 1500 cm^?1. The study of the double-layer structure was complemented by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) measurements, from which the differential double-layer capacity (C_DL) was estimated.