L'approche variationnelle de la fatigue : des premiers résultats

By using a principle of least energy and a Dugdale surface energy with an irreversibility condition, we build a debonding model of thin films valid both for monotone and cyclic loading. We show that, if the internal length introduced in Dugdale model is small in comparison to the film length, then the growth of the debonding follows Griffith's law under monotone loading and a Paris-type law under cycling loading. To cite this article: A. Jaubert, J.-J. Marigo, C. R. Mecanique 333 (2005).     

A collision strategy for particles in particulate flow simulationsSur le traitement des collisions lors de la simulation numérique des écoulements particulaires

A novel collision strategy has been implemented for simulation of particulate flows using a Lagrange multiplier/fictitious domain method. In this Note, we present this new collision strategy that is based on Newton's principle of transfer of momentum. With this method, we have simulated motion of two discs under the influence of gravity in a viscous fluid, and the motion of 1008 discs under the effect of gravity. To cite this article: P. Parthasarathy, C. R. Mecanique 330 (2002) 77–81.     

Caractéristique directionnelle calculée et mesurée d'une sonde électrochimiqueCalculated and measured directional characteristic of an electrochemical probe

The present paper demonstrates how the directional characteristics of an actual three-segment electrodiffusional sensor can be calculated from the probe image. It was shown that utilization of ‘ideal’ directional characteristics lead to an important (up to 15^°) error in flow angle determination. The directional characteristics calculated from the probe image improve significantly (up to 50%) the accuracy of the flow angle measurements. To cite this article: F. Barbeu et al., C. R. Mecanique 330 (2002) 433–436.     

Preliminary selection of clay minerals for the removal of pharmaceuticals,bisphenol A and triclosan in acidic and neutral aqueous solutions

Pharmaceuticals, personal care products and endocrine disruptors demonstrate huge potential to cause adverse ecological health effects at very low concentration in aquatic environment. There is a need to improve current purification technologies used in sewage and drinking-water treatment plants. This article aims at providing new insights into the recent development of natural and modified clay-based sorbents for the removal of aqueous contaminants such as pharmaceuticals and personal care products. The removal of six widely used pharmaceuticals: ibuprofen, diclofenac, ketoprofen, carbamazepine, as well as endocrine disrupting chemicals – bisphenol A and a bactericidal agent, triclosan – was examined by sorption onto eight adsorbents. Sorption was performed using natural and modified clay minerals – montmorillonite (Mt), vermiculite (VER), bentonite (B), kaolinite (K), commercial acid activated montmorillonites K10 and K30, and two carbonaceous-mineral nanocomposites, MtG5%T, BAlG3%C. This study showed that among the tested natural clays, vermiculite is the most promising sorbent for the removal of pharmaceuticals in purification processes. Among the modified clay minerals, the best results were achieved for carbonaceous bentonite and two acid activated montmorillonites K10 and K30. However, the removal of acidic pharmaceuticals on montomorillonite K10 and carbonaceous bentonite was strongly dependent on the pH value. In the case of vermiculite and acid-modified montmorillonite K30, the sorption of the selected compounds was not significantly affected by pH, which is crucial in wastewater treatment. The sorption constant divided by the specific surface area (K_d/A) is proposed to assess whether the surface area or chemical properties of the materials control the sorption process. K_d/A values were relatively high in the case of vermiculite, so it should be noticed that individual and specific surface properties of vermiculite were of crucial importance for sorption.     

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

Parametric excitation of waves on a free boundary of a horizontal fluid layer

We consider the dynamical stability of horizontal fluid layer, performing harmonic oscillations in vertical direction. The continued fractions approach allowed us to avoid the conventional restriction to the case of small viscosity and almost-resonant frequencies. Our numerical results cover a wide range of the parameters (viscosity, amplitude and frequency of the oscillation, and depth of the layer). To cite this article: V.I. Yudovich et al., C. R. Mecanique 332 (2004).     

Application de l'approximation polytropique à la turbulence statistique en moyenne de FavreApplication of the polytropic approximation to turbulence statistics using Favre averaging

The application of the polytropic approximation connecting the quantities of corresponding state, to experimental analysis, is clarified. A method of polytropic determination of the exponent χ (variable but non-fluctuating) in each point of the flow is given. This approximation makes it possible the generation of representative signals of fluctuating quantities, like pressure or density. For heated gases, the problem of measurement of the equations terms written with Favre averaging is thus almost solved. Then, measurement of χ allows the determination by the experiment of crucial terms like turbulent fluxes of mass and momentum, and presso correlation. To cite this article: C. Rey, S. Benjeddou, C. R. Mecanique 332 (2004).     

Eléments finis stochastiques en élasticité linéaireA stochastic finite element method in linear mechanics

The stochastic finite element method presented in this Note consists in representing in a probabilistic form the response of a linear mechanical system whose material properties and loading are random. Each input random variable is expanded into a Hermite polynomial series in standard normal random variables. The response (e.g., the nodal displacement vector) is expanded onto the so-called polynomial chaos. The coefficients of the expansion are obtained by a Galerkin-type method in the space of probability. To cite this article: B. Sudret et al., C. R. Mecanique 332 (2004).