Non-explosion en temps grand et stabilité de solutions globales des équations de Navier–StokesNon-blowup at large times and stability for global solutions to the Navier–Stokes equations

Suppose there exists a global solution u to the incompressible Navier–Stokes equations, such that $\text{u∈}\text{C}{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{1/2}}\text{)}$. We prove that its $\text{H}\text{?}{}^{\mathrm{1/2}}$ norm goes to 0 at infinity. We next use this fact to control the $\text{L}{}^2{}_{\mathrm{t}}\text{(}\text{H}\text{?}{}^{\mathrm{3/2}}\text{)}$ norm of u, and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289–292.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

Overloaded elution band profiles of ionizable compounds in reversed‐phase liquid chromatography: Influence of the competition between the neutral and the ionic species

The parameters that affect the shape of the band profiles of acido‐basic compounds under moderately overloaded conditions (sample size less than 500 nmol for a conventional column) in RPLC are discussed. Only analytes that have a single pK_a are considered. In the buffer mobile phase used for their elution, their dissociation may, under certain conditions, cause a significant pH perturbation during the passage of the band. Two consecutive injections (3.3 and 10 μL) of each one of three sample solutions (0.5, 5, and 50 mM) of ten compounds were injected on five C₁₈‐bonded packing materials, including the 5 μm Xterra‐C₁₈ (121 Å), 5 μm Gemini‐C₁₈ (110 Å), 5 μm Luna‐C₁₈(2) (93 Å), 3.5 μm Extend‐C₁₈ (80 Å), and 2.7 μm Halo‐C₁₈ (90 Å). The mobile phase was an aqueous solution of methanol buffered at a constant _W^WpH of 6, with a phosphate buffer. The total concentration of the phosphate groups was constant at 50 mM. The methanol concentration was adjusted to keep all the retention factors between 1 and 10. The compounds injected were phenol, caffeine, 3‐phenyl 1‐propanol, 2‐phenyl butyric acid, amphetamine, aniline, benzylamine, p‐toluidine, procainamidium chloride, and propranololium chloride. Depending on the relative values of the analyte pK_a and the buffer solution pH, these analytes elute as the neutral, the cationic, or the anionic species. The influence of structural parameters such as the charge, the size, and the hydrophobicity of the analytes on the shape of its overloaded band profile is discussed. Simple but general rules predict these shapes. An original adsorption model is proposed that accounts for the unusual peak shapes observed when the analyte is partially dissociated in the buffer solution during its elution.     

Separation mechanism of nortriptyline and amytriptyline in RPLC

The single and the competitive equilibrium isotherms of nortriptyline and amytriptyline were acquired by frontal analysis (FA) on the C18- bonded discovery column, using a 28/72 (v/v) mixture of acetonitrile and water buffered with phosphate (20 mM, pH 2.70). The adsorption energy distributions (AED) of each compound were calculated from the raw adsorption data. Both the fitting of the adsorption data using multi-linear regression analysis and the AEDs are consistent with a trimodal isotherm model. The single-component isotherm data fit well to the tri-Langmuir isotherm model. The extension to a competitive two-component tri-Langmuir isotherm model based on the best parameters of the single-component isotherms does not account well for the breakthrough curves nor for the overloaded band profiles measured for mixtures of nortriptyline and amytriptyline. However, it was possible to derive adjusted parameters of a competitive tri-Langmuir model based on the fitting of the adsorption data obtained for these mixtures. A very good agreement was then found between the calculated and the experimental overloaded band profiles of all the mixtures injected.     

Diasteroselective synthesis of new spiropiperidine scaffolds from the CN(R,S) building block

A methodology allowing the construction of spiropiperidine scaffolds similar to those found in naturally occurring alkaloids has been developed. This approach begins with the well-established CN(R,S) strategy, the spiro-center being built by way of an intramolecular attack of a nitrile function by an organolithium species obtained by a halogen/lithium exchange reaction mediated by either t-BuLi or lithium naphthalenide.     

Early reactions of light-induced protochlorophyllide and chlorophyllide transformations analyzed in vivo at room temperature with a diode array spectrofluorometer

The steps of protochlorophyllide (Pchlide) photoreduction and subsequent chlorophyllide (Chlide) transformations which occur in the seconds to minutes time-scale were studied using a diode array spectrofluorometer in dark-grown barley leaves. The intensity of the excitation light was varied between 3 and 2,500 micromol m(-2) s(-1) and a series of fluorescence spectra were recorded at room temperature in the seconds and minutes time scales. In certain experiments, 77-K emission spectra were measured with the same equipment. The high quality of the spectra allowed us to run spectral resolution studies which proved the occurrence, at room temperature, of multiple Pchlide and Chlide forms found previously in 77-K spectra. The comparison of the 77-K and room-temperature spectra showed that the fluorescence yields of the nonphotoactive 633-nm Pchlide form and of the Chlide product emitting at 678 nm were temperature independent. The fluorescence intensity of aggregated NADPH-pigment-POR complexes (photoactive 656-nm Pchlide and 693-nm Chlide forms) were strongly increased at 77 K, while that of the NADP(+)-Chlide-POR (684-686-nm Chlide form) was much less affected by temperature. Information was obtained also about the dynamics of the transformation of pigment forms in the light at different photon densities. At low light intensities, the phototransformation of the 642-644-nm Pchlide form was faster than that of the 654-656-nm form. The relative amplitudes of Gaussian components related to different Chlide forms found after exposure to a constant amount of photons strongly depended on the light intensity used. Strong quenching of all Chlide components occurred upon prolonged exposure to high intensity light. These effects are discussed by considering the interconversion processes between different forms of the pigment-protein complexes, their relative fluorescence yields and energy migration processes.     

Cyclic organohydroborate complexes of metallocenes: VIII. Triphenylsiloxy derivatives of Group IV organometallic systems, Cp2M(OSiPh3)X (M=Ti, Zr, Hf; X=Cl, {(μ-H)2BC8H14})

Group IV metallocene triphenylsiloxy chlorides, Cp₂MCl(OSiPh₃) (1, M=Ti; 2, M=Zr; 3, M=Hf), and cyclic organohydroborates, Cp₂M(OSiPh₃){(μ-H)₂BC₈H₁₄} (4, M=Zr; 5, M=Hf), were synthesized and characterized. The new hafnocene chloride derivative 3 was obtained by treating Cp₂HfCl₂ with triphenylsilanol and piperidine. The 18-electron cyclic organohydroborates 4 and 5 were afforded by reacting 2 and 3 with K[H₂BC₈H₁₄], the potassium salt of the 9-BBN dimer. Reaction of 1 with K[H₂BC₈H₁₄] causes reduction of the Ti(IV) center and produces the well-known Ti(III), 17-electron, paramagnetic dimer [Cp₂Ti(μ-Cl)₂TiCp₂] (6). Single-crystal X-ray diffraction structures of 3, 4, 5, and 6 were determined.     

Noncovalent functionalization of multi-walled carbon nanotubes by pyrene containing polymers

Multi-walled carbon nanotubes (MWNTs) have been solubilized in water and in various organic solvents by noncovalent side-wall functionalization by pyrene containing polymers.     

Synthesis of new crosslinkable co-polymers containing a push-pull zinc porphyrin for non-linear optical applications

In this paper, the synthesis of a crosslinkable co-polymer containing new push-pull arylethynyl zinc porphyrins is described. The synthesis of porphyrin chromophores, analogous to Therien's porphyrin (J. Am. Chem. Soc.1996, 118, 1497-1503) functionalized with a methacrylic polymerizable group and a carboxylic acid crosslinking group was achieved with a new synthetic procedure leading to a higher overall yield compared to what was previously reported in the literature for similar and simpler structures. Radical copolymerization of the porphyrin chromophore with glycidyl methacrylate has then been carried out with success. This work opens a perspective on the possibility to integrate porphyrinic chromophore with high first-order molecular quadratic hyperpolarizability coefficient in opto-electronic devices.