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     

Novel 7-substituted quinolone antibacterial agents. Synthesis of 7-alkenyl,cycloalkenyl, and 1,2,3,6-tetrahydro-4-pyridinyl-1,8-naphthyridines

A convergent synthesis of 1,8-naphthyridine antibacterials bearing a carbon-carbon bonded, acyclic or cyclic vinyl substituent at the C-7 position has been achieved. The synthetic methodology is based upon the palladium-catalyzed cross coupling of a 7-chloro-1,8-naphthyridine with an appropriately substituted organotin reagent.     

Ordering of SiO<Subscript>x</Subscript>H<Subscript>y</Subscript>C<Subscript>z</Subscript> islands deposited by atmospheric pressure microwave plasma torch on Si(100) substrates patterned by nanoindentation

SiO _x H _y C _z nanometric layers are deposited from hexamethyldisiloxane by atmospheric pressure microwave plasma torch on Si(100) substrates submitted to temperatures varying on the range [0 °C; 120 °C]. Atomic force microscopy (AFM) characterizations of samples grown at intermediate substrate temperatures (~30 °C) demonstrate a layer-by-layer growth (Frank van der Merwe growth) leading to smooth flat and compact films while films deposited at lower and higher substrates temperatures show an island-like growth (Volmer-Weber growth) generating a high surface roughness. Concomitantly, a detailed infrared spectroscopy analysis of the growing films evidences structural modifications due to changes in the bond types, Si-O-Si conformation and stoichiometry correlated with scanning electron microscopy and AFM characterizations. Then, deposition conditions and specific microstructure are selected with the aim of generating 3-dimensional SiO _x H _y C _z nanostructure arrays on nanoindented Si (100) templates. The first results are discussed.     

Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results.

The propagation of ultrasound through a liquid induces the growth of inceptions and germs into bubbles. In a low frequency reactor, fragmentary transient bubbles emerge due to the acoustic driving. They violently collapse in one cycle and fragment into many smaller bubbles than in turn cavitate. This violent collapse is responsible for the mechanical effects of ultrasounds effects. The latter bubbles gather in a ball-shaped cloud and migrate to pressure antinodes. During their migration, their nonexplosive collapses mainly contribute to activate chemical reactions by producing OH. radicals. Mathematical modelling is performed as a new approach to predict the bubbles field. Through numerical simulation, we determinate emergence sites of mechanically active cavitation bubbles. Calculus are compared with aluminium foil degradation. The modelling of bubble migration allow us to have an insight on the privileged sites of the chemical reactions. Validation of the modelling is made through direct comparison with chemiluminescence photo. All experiments and computations are made in a 28.2 kHz sonoreactor.     

Magnetoresistance measurements of V3Si evidence for precursor effects of the martensitic transformation

We report magnetoresistivity measurements on transforming and non-transforming V₃Si. The martensitic structural transformation (T_m ? 21 K) is induced by annealing. The transforming sample shows large deviations from the Köhler's rule $\text{[Δ?/? = ?(H/?)]}$, at temperatures much higher than T_m. They are attributed to precursor effects of the transition, previously observed by other techniques, and are interpreted in terms of the development of different relaxation times for the scattering of the electrons.     

A quasi-optimal convergence result for fracture mechanics with XFEM

The aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area. The difficulty is caused by the discontinuity of the displacement field across the crack, but we prove that a quasi-optimal convergence rate holds in spite of the presence of elements cut by the crack. The global linear convergence rate is obtained by using an enriched linear finite element method. To cite this article: E. Chahine et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Trennung der organischen S?uren

Ohne Zusammenfassung