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.     

Transport-diffusion et viscosité évanescente

In this paper, we study a convection-diffusion model with respect to a vector field having log-Lipschitz regularity. More precisely, we are interested in the viscous repartition of the mass for the solutions of the corresponding equation. We prove that mass is essentially concentrated around the image, through the flow, of the initial support. This allows us, for non-regular bidimensional vortex patches, to prove the global L^p convergence of the Navier–Stokes vorticity ω_ν to the Eulerian vorticity ω, with p>1. To cite this article: T. Hmidi, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Behaviour of Pluronic P84 block copolymer micelles above the gelification temperature as probed by positron annihilation lifetime spectroscopy

The new method based on positron annihilation lifetime spectroscopy (PALS) to determine both the mean core radius, R(core), and aggregation number, N(ag), of micelles is applied to the study of aqueous solutions of the triblock Pluronic P84 copolymer as a function of temperature (T), beyond the gelification point (334 K). Two long-lived components appear in the PALS spectra, ascribed to triplet positronium in the water bulk (o-Ps(aq)) and in the organic core of the micelles (o-Ps(org)). Of the various fitting parameters, only the lifetime of the latter species, tau4, and the micellar parameters, R(core) and N(ag), disclose the occurrence of gelification by first increasing up to 334 K, then decreasing. By contrast to what is known in case of phase transition, none of the parameters shows any abrupt change at 334 K, whereas the macroscopic viscosity of the solutions suffers a drastic increase. This is attributed to the fact that positronium is sensitive to the microviscosity of the solutions. At the transition point, the properties of the polyoxipropylene aggregates forming the organic core of the P84 micelles are not greatly affected. Furthermore, the fact that the experimental N(ag) values coincide with those calculated for spheres, from the R(core) values, indicates that the shape of the P84 cores does not change significantly after gelification. The onset of gelification results from a decrease in the hydrogen bonding interactions in the solution with an ensuing relative increase in the interactions between the polyoxipropylene (PPO) groups, initially forming the corona of the P84 micelles, in an intermicellar mode. This increased solicitation of the PPO groups outside their initial location would result in depletion in the number of surfactant molecules forming the micelles, viz. a decrease in both R(core) and N(ag) above 334 K. From the data, additional information can be gained regarding the local viscosity and surface tension in the micellar cores.     

Boundary Regularity of Rotating Vortex Patches

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is C ^∞, provided the patch is close to the bifurcation circle in the Lipschitz norm. The rotating patch is also convex if it is close to the bifurcation circle in the C ² norm. Our proof is based on Burbea’s approach to V-states.     

Mechanism and Linear Free Energy Relationships in Michael‐Type Addition of 4‐Substituted Anilines to Activated Olefin in Acetonitrile

Kinetic studies for the Michael‐type reactions of ethyl‐3‐(4′‐N,N‐dimethylaminophenyl)‐2‐(nonafluorobutane)sulfonylpro‐penoate 1 with 4‐X‐substituted anilines 2a–e (X = OCH₃, CH₃, H, F, and Cl) have been investigated in acetonitrile at 20°C. A quadratic dependence of the pseudo–first‐order rate constants (k_obsd) versus [ 2a–e ] has been observed and has been interpreted in terms of a dimer nucleophile mechanism. The finding of a relatively large negative ρ value (?3.09) for the Hammett plot suggests that the intermediate ( I^± ) is highly zwitterionic in nature. A linear correlation (r² = 0.9989) between the Hammett's substituent constants σ and nucleophilicity parameters N of 4‐X‐substituted anilines in acetonitrile has been observed. The electrophilicity parameters E of the olefin 1 is evaluated, using the correlations σ versus N and log k versus σ and compared with the electrophilicities of analogously Michael acceptors.     

Short Synthesis of Functionalized Cyclic Homoallylsilanes

The synthesis of functionalized cyclic homoallylsilanes 5 and 6 was described starting from functional cycloalkenols 1 and 2, in which the addition of silylcuprate to the functional acetates 3 and 4 were used as the key reaction step.     

Existence globale pour le système d'Euler incompressible 2-D dans B∞,11

We prove a global well-posedness result for the two-dimensional Euler system in the critical Besov space $B_{\infty ,1}^1$. We also establish a uniform estimate on the viscosity for the incompressible Navier–Stokes system in that space. An inviscid limit result is also given. To cite this article: T. Hmidi, S. Keraani, C. R. Acad. Sci. Paris, Ser. I 341 (2005).