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).     

Purification of transferrin by magnetic immunoaffinity beads

Immunoaffinity adsorbent for transferrin (Tf) purification was prepared by immobilizing anti‐transferrin (Anti‐Tf) antibody on magnetic monosizepoly(glycidyl methacrylate) beads, which were synthesized by dispersion polymerization technique in the presence of Fe₃O₄nanopowder and obtained with an average size of 2.0 μm. The magnetic poly(glycidyl methacrylate) (mPGMA) beads were characterized by Fourier transform infrared spectroscopy, swelling tests, scanning electron microscopy, electron spin resonance spectroscopy, thermogravimetric analysis and zeta sizing analysis. The density and swelling ratio of the beads were 1.08 g/cm³ and 52%, respectively. Anti‐Tf molecules were covalently coupled through epoxy groups of mPGMA. Optimum binding of anti‐Tf was 2.0 mg/g. Optimum Tf binding from aqueous Tf solutions was determined as 1.65 mg/g at pH 6.0 and initial Tf concentration of 1.0 mg/mL. There was no remarkable loss in the Tf adsorption capacity of immunoaffinity beads after five adsorption–desorption cycles. Tf adsorption from artificial plasma was also investigated and the purity of the Tf molecules was shown with gel electrophoresis studies.     

Syntheses,characterization of and studies on the electrochemical behaviour of ferrocenyl dithiophosphonates and 4-methoxyphenyl dithiophosphonates

Some 1,3-dithiadiphosphetane 2,4-disulfides (X₂P₂S₄, X: Fc, FcLR; X: CH₃O?C₆H₄?, LR) were allowed to react with alcohols to obtain dithiophosphonic acids (X(OR)PS₂H). These were converted to the corresponding ammonium salts. The salts were of the structures [Fc(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for I; 1-phenyl-1-propyl- for II; 3-pentyl- for III; 3-phenyl-1-propyl- for IV and [CH₃O?C₆H₄(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for V and 1-phenyl-1-propyl- for VI. To the best of our knowledge, all the compounds except V were prepared for the first time.

The compounds synthesized were characterized by elemental analysis, NMR (¹H, ¹³C, ³¹P), MS, FTIR, and Raman spectroscopies. Electrochemical behaviors of I–VI at disposable pencil graphite electrode (PGE) were investigated by using cyclic voltammetry (CV) and square-wave voltammetry (SWV). Adsorption and diffusion patterns of all the compounds on the PGE were also studied.

Two electroactive groups were identified in the compounds I–IV and only one in V and VI. The ferrocenyl groups of I-IV were oxidized at around 0.4 V. The same compounds display a second, more intense CV band at 0.8 V. The corresponding band for the compounds V–VI appears at around 0.6 V with a much weaker intensity. It is suggested that the ferrocenyl group introduced into the structures stabilizes the radical species formed as the product of the oxidation of the dithiophosphonato group.     

A general variable neighborhood search variants for the travelling salesman problem with draft limits

In this paper, we present two general variable neighborhood search (GVNS) based variants for solving the traveling salesman problem with draft limits (TSPDL), a recent extension of the traveling salesman problem. TSPDL arises in the context of maritime transportation. It consists of finding optimal Hamiltonian tour for a given ship which has to visit and deliver products to a set of ports while respecting the draft limit constraints. The proposed methods combine ideas in sequential variable neighborhood descent within GVNS. They are tested on a set of benchmarks from the literature as well as on a new one generated by us. Computational experiments show remarkable efficiency and effectiveness of our new approach. Moreover, new set of benchmarks instances is generated.     

The intermediate disorder regime for a directed polymer model on a hierarchical lattice

We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\le s$ it is known that the model exhibits strong disorder for all positive values of the inverse temperature $\beta$, and thus weak disorder reigns only for $\beta =0$ (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature $\beta \equiv {\beta }_n$ vanishes at an appropriate rate as the size $n$ of the system grows. Our analysis requires separate treatment for the cases $b<s$ and $b=s$. In the case $b<s$ we prove that when the inverse temperature is taken to be of the form ${\beta }_n=\stackrel{?}{\beta }{(b/s)}^{n/2}$ for $\stackrel{?}{\beta }>0$, the normalized partition function of the system converges weakly as $n\to \infty$ to a distribution $L\left(\stackrel{?}{\beta }\right)$ and does so universally with respect to the initial weight distribution. We prove the convergence using renormalization group type ideas rather than the standard Wiener chaos analysis. In the case $b=s$ we find a critical point in the behavior of the model when the inverse temperature is scaled as ${\beta }_n=\stackrel{?}{\beta }/n$; for an explicitly computable critical value ${\kappa }_b>0$ the variance of the normalized partition function converges to zero with large $n$ when $\stackrel{?}{\beta }\le {\kappa }_b$ and grows without bound when $\stackrel{?}{\beta }>{\kappa }_b$. Finally, we prove a central limit theorem for the normalized partition function when $\stackrel{?}{\beta }\le {\kappa }_b$.     

Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

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).