Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Synthesis of polycyclic structures by the Diels-Alder reaction of inner-outer-ring 1,3-bis(trimethylsilyloxy)dienes

A Diels-Alder reaction of novel inner-outer-ring 1,3-silyloxydienes 5-8 with a variety of dienophiles to afford highly functionalized polycyclic structures is reported. The inner-outer-ring 1,3-silyloxydienes 5-8 containing five- to seven-membered carbocyclic and heterocyclic rings were prepared in a single reaction vessel from 2-acetylcyclocarbonyls in quantitative yields. The Diels-Alder reaction with 1,4-benzoquinone (BQ), dimethyl acetylenedicarboxylate (DMAD), and methyl vinyl ketone (MVK) proceeded smoothly at room temperature, affording functionalized polycyclic naphthols, phenols, and enones with high regioselectivity and good yields (39-75%). Moreover, dienes 5-8 also reacted in a hetero-Diels-Alder reaction with benzaldehyde (BA) and N-benzylideneaniline (NBA) in the presence of catalytic amounts of ZnCl2, affording substituted polycyclic pyranones and pyridinones in good yields (40-93%). Overall, our synthetic strategy provides straightforward access to an interesting set of polycyclic structures useful for natural and nonnatural product synthesis.     

A rapid access to chiral alkylidene cyclopentenone prostaglandins involving ring-closing metathesis reaction

A synthesis of the alkylidene cyclopentenone prostaglandin TEI 9826 has been realized. The synthesis involved the preparation of the chiral 1,5-diene 8 using a stereoselective Claisen rearrangement from the allylic alcohol 6 giving the ester 7 after vinylation. Then a key RCM reaction allowed the preparation of the cyclopentenol 9 which, after oxidation, gave the cyclopentenone 10, precursor of the prostaglandin.     

Monte Carlo versus molecular dynamics simulations in heterogeneous systems: an application to the n-pentane liquid-vapor interface

The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.     

Experimental study of the frequency response of electrochemical split probes to transversal velocity fluctuations

An experimental investigation of the frequency response of electrochemical probes to transversal velocity fluctuation is reported. The study has been focused on wall shear stress for a modulated flow due to an oscillating cylinder along its own axes since the wall shear stress has been first numerically determined for this flow. Results indicate that a frequency response correction to probe outputs is required and that this correction depends on the amplitude of fluctuations.List of symbols A total area of the electrode - A _i area of the part i of the electrode - a amplitude of oscillation - C concentration - c fluctuation of concentration - D cylinder diameter - D diffusion coefficient - h dimensionless velocity normal to the wall - H transfer function modulus - K _i transfer coefficient - l electrode length - n frequency - S wall shear - S fluctuation of the wall shear - U mean value of the fluid velocity far from the wall - u streamwise component of the fluid velocity - spanwise component of the fluid velocity (along the cylinder axis) - w component of the fluid velocity perpendicular to the wall - x direction of the mean flow - y direction parallel to the cylinder axis - z direction perpendicular to the wall - v kinematic viscosity - dimensionless distance perpendicular to the wall (z) - dimensionless distance (x) - phase shift - azimuthal angle - modulation frequency     

Thermal decomposition of sodium nitrite and sodium nitrate pre-adsorbed on TiO2 surfaces

The thermal decomposition of sodium nitrite or nitrate pre-adsorbed upon TiO₂ surfaces has been investigated by employing several techniques as infrared spectroscopy (IR) and temperature programmed desorption in conjunction with mass spectrometry analysis (TPD-MS) to study the features observed during these thermal decompositions. Differential thermal analysis (DTA) in combination with X-ray diffraction analysis (XRD) were used to investigate the possibility of a solid state chemical reaction between the solid products originated from the thermal decomposition of the pre-adsorbed species and the TiO₂. On the basis of our results, various characteristic features of these thermal decomposition reactions will be discussed.This work was supported by JUNTA DE ANDALUCIA (financial support for research groups/1990).     

Access to New Endoperoxide Derivatives by Electrochemical Oxidation of Substituted 3‐Azabicyclo[4.1.0]hept‐4‐enes

A series of substituted 3‐azabicyclo[4.1.0]hept‐4‐ene derivatives were prepared and analysed by cyclic voltammetry. Preparative aerobic electrochemical oxidation reactions were then carried out. Three original endoperoxides were isolated, characterised and subjected to antimalarial and cytotoxicity activity assays.