Résolution des équations de dispersion–diffusion en présence de forts gradientsResolution of advection–diffusion equation in presence of sharp gradient

In order to resolve the convection terms in the simulation of coastal flows, we propose a numerical method based on the Total Variation Diminishing scheme completed with the Artificial Compression Method to reduce the artificial diffusion and to sharpen the tracer profile in strong gradient regions. This method was applied successfully at discontinuous regions, but out of these regions a limitation of its application is necessary. An application is made to estimate the width of the fresh water band in the Eastern English Channel. To cite this article: C. Sart et al., C. R. Mecanique 330 (2002) 159–165.     

More results on the Ashkin-Teller model

We analyze the low-temperature phase diagram of the Ashkin-Teller model for real values of the quadratic and quartic coupling constants.     

Effets des forces de Coriolis sur le seuil convectif stationnaire d'une couche liquide confinée en cellule de Hele–Shaw annulaire en rotationEffects of the Coriolis forces on the stationary convectif threshold of a liquid layer confined in an annular Hele–Shaw Cell in rotation

The convective instability of a horizontal liquid layer confined in an annular Hele–Shaw cell subject to a constant rotation and submitted to a centrifugal gradient of temperature is investigated. Using a linear stability analysis, we study the effects of both Coriolis forces and curvature aspect on the stationary convective threshold when the Prandtl number is of the order of unity or larger than unity. We show that the Coriolis forces have a stabilizing effect, and the wave number is independent of these forces. However, a multicellular regime in the radial direction is observed for small Ekman numbers. The results related to the influence of the curvature are also shown. To cite this article: S. Ramezani et al., C. R. Mecanique 330 (2002) 633–640.     

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

Synthesis,characterization and applications of polysiloxane networks with immobilized pyrogallol ligands

A porous, solid insoluble polysiloxane‐immobilized ligand system bearing pyrogallol active sites of the general formula P? (CH₂)₃? NH(CH₂)₃OC₆H₃(OH)₂ (where P represents [Si? O]_n siloxane network) has been prepared by the reaction of 3‐aminopropylpolysiloxane with 1,3‐dibromopropane followed by the reaction with pyrogallol. ¹³C CP‐MAS NMR and X‐ray photoelectron spectroscopy confirmed that the pyrogallol is chemically bonded to the siloxane backbone. Thermal analysis showed that the ligand system is stable under nitrogen at relatively high temperature. The polysiloxane–pyrogallol ligand system exhibits high potential for the uptake of the metal ions (Fe³⁺, Co²⁺, Ni²⁺ and Cu²⁺). Complexation of the pyrogallol ligand system for the metal ions at the optimum conditions was found to be in the order Fe³⁺ > Cu²⁺ > Ni²⁺ > Co²⁺. Copyright © 2005 John Wiley & Sons, Ltd.     

Triple collisions in the isosceles three body problem with small mass ratio

We use a slightly modified version of McGehee's transformation to study the triple collisions of the isosceles three body problem in a way that allows us to let the mass ratio go to zero. We study the limiting case and show that the collision manifold changes topologically, which affects the behaviour of near collision orbits. We also obtain new information about the flow on the collision manifold when the mass ratio is small.     

Solubility of polycyclic aromatics in binary solvent mixtures using activity coefficient models

Polycyclic aromatic hydrocarbons (PAHs) precipitation is one of the major problems in the hydrocracking units. In this investigation, pyrene and phenanthrene were selected because they were found to be in higher concentrations in the feed to hydrocracking units. Their solubilities were investigated in toluene solvent mixture of iso-octane and heptane over a temperature range from 293 to 323 K. The experimental solubility data were used to predict the interaction parameters for seven different solid–liquid equilibrium models. The following activity coefficient models were used; Wilson, NIBS/Redlich–Kister, UNIQUAC, modified UNIFAC, modified UNIFAC (Dortmund), Flory–Huggins and Sheng. The interaction parameters were expressed as a second-order polynomial function in temperature. In order to test the models, the average absolute deviation percentage (AADP) was used. The overall AADP was found to range from approximately 7 to 14%. The models can be arranged according to their accuracy in a descending order based on AADP as follows: NIBS/Redlich–Kister, Wilson, UNIQUAC, Sheng, Flory–Huggins, modified UNIFAC (Dortmund) and finally modified UNIFAC. All models used in this work gave reasonable results; however, the group contribution models can also be used as a predictive tool for the solubility measurement of pyrene and phenanthrene in other solvents containing the same groups of the solvents used in this study.     

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.     

Exploiting the 1,2,3‐Triazole Moiety to Generate Carbazole Molecular Architectures through Click Approach

Reaction of 3,6‐dichlorocarbazole with propargyl bromide in the presence of a basic medium gave an N‐propargylated carbazole. The latter compound was converted into molecular architectures containing 1,2,3‐triazole moiety through Cu(I)‐catalyzed 1,3‐cycloaddition reaction with different azides. Similarly, 2‐azidomethyl benzothiazole was cliched with N‐Boc‐protected N´‐propargyl glutamate to give the biomolecule 2‐triazolylmethyl product.