Synthesis of a halo-methylphenylene periphery-functionalized triazine-based dendritic molecule with a 3,3′-dimethyl-biphenyl linker using tris(halo-methylphenylene)triazines as building blocks

A tris(bromo-methylphenylene)triazine and its corresponding phosphine oxide derivative have been synthesized; the latter compound was found to be a potent ligand for the hydroformylation reaction. Suzuki coupling of the mono-pinacolboronate derivative of the former compound with a tris(iodo-methylphenylene)triazine was possible at two of the three iodine atoms, yielding a bromo- and iodo-methylphenylene periphery-functionalized triazine-based dendritic molecule with a 3,3′-dimethyl-biphenyl linker.     

Theoretical and fuzzy modelling of a pharmaceutical batch reactor

This paper deals with the development of a batch-reactor model with a theoretical and a locally affine fuzzy model. The batch reactor is used in the pharmaceutical industry for the production of drugs, where a rapid and precise temperature control is necessary. The model has to be built to include all the main features necessary for the purposes of modelling. The development of the model for the reactor is designed for further control development and simulation purposes, without doing any further experiments on the real process. In our case we use the model for simulating the reactor’s jacket temperature and the reactor’s core temperature. The theoretical model describes all the nonlinearities of the process of heating and cooling the content of the batch reactor. The main contribution of the theoretical model is in the modelling of the heat transfer between the reactor’s jacket and the reactor’s core, mainly caused by the change in the overall heat transfer, which also covers the main nonlinearity. Because of the complexity of the theoretical model a locally affine fuzzy model is also developed.     

Shedding patterns of the near-wake vortices behind a circular cylinder

The unsteady incompressible Navier-Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50–200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi-steady state. A new integral-series method is developed for the far-field streamfunction condition on a finite two-dimensional computational domain. The use of fourth-order Hermitian relations for the convection terms in the conservation-form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex-shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behaviour of the shedding frequency are presented in the main text.     

Second Eigenvalue of Schrödinger Operators¶and Mean Curvature

Let $M$ be a compact immersed submanifold of the Euclidean space, the hyperbolic space or the standard sphere. For any continuous potential q on M, we give a sharp upper bound for the second eigenvalue of the operator −Δ+q in terms of the total mean curvature of M and the mean value of q. Moreover, we analyze the case where this bound is achieved. As a consequence of this result we obtain an alternative proof for the Alikakos–Fusco conjecture concerning the stability of the interface in the Allen–Cahn reaction diffusion model. Received: 18 June 1999 / Accepted: 6 July 1999     

Explosion en temps fini de la solution d'un problème d'évolution de surface de film mince

In this Note, we are interested in the evolution of a surface of a crystal structure, constituted by an elastic substrate and a thin film. If the crystal is constrained, some morphological instabilities may appear. To study these instabilities, we made use of the model developped in Phys. Rev. B 47 (1993) 9760–9777. There, the map f of the free surface of the film satisfies a parabolic partial differential equation, depending on the elastic displacement of the substrate. For simplicity, the substrate is assumed to be linearly elastic and the structure to be infinite in one direction. Then, under some formal asymptotic assumptions, a formal expansion of the displacement can be determined after some appropriate scalings, allowing to derive a simplified parabolic nonlinear equation as in Lods et al. (Asymptotic Anal. 33 (2003) 67–91). We give here some results about the finite-time blow-up and the existence and uniqueness of the solution in an appropriate space. To validate the theoretical results, we also performed some numerical simulations using a pseudo-spectral method and also compute the initial-profile dependent critical value of the parameter θ involved in the nonlinear equation. To cite this article: M. Boutat et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

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.     

再散射输运模型与K+/π+比的系统学

用含再散射效应的简单的强子输运模型,研究了AGS能量(14.6AGeV/c)下p+p、p+Au和Si+Au反应的K⁺/π⁺比值,再现了该比值由P十P到Si十Au不断增长的实验事实.CERN能量(200AGeV/c)和AGS能量下,K⁺/π⁺比值相近的实验事实也得到了解释.     

Application de l'approximation polytropique à la Simulation Numérique Directe de gaz chaudsApplication of the polytropique approximation to Direct Numerical Simulation of heated gases

As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003).