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.     

Domain decomposition for an asymptotic geological fault modeling

We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

Supercritical fluid extraction for liquid chromatographic determination of carotenoids in Spirulina Pacifica algae: a chemometric approach

An experimental design procedure was used to investigate the effects of some operating parameters on the supercritical fluid extraction of carotenoids beta-carotene, beta-cryptoxanthin and zeaxanthin from Spirulina Pacifica algae, a carotenoid-rich dietary product. Variables tested were temperature and pressure of the supercritical fluid, dynamic extraction time and percentage of ethanol added as the modifier. Each variable was tested at three levels; 31 experiments were performed in random order. Analyses of the extracts were performed by high-performance liquid chromatography with UV-Vis photodiode array detection. Analytical responses (chromatographic peak areas) were processed by using a stepwise multiple regression analysis, in order to find polynomial functions describing the relationships between variables and responses. For all the analytes the experimental conditions providing the highest extraction yield inside the experimental domain considered were found. Supercritical fluid extraction results obtained in these conditions were compared with those obtained by performing solvent extraction in order to evaluate the effectiveness of the supercritical fluid extraction procedure.     

Complexation of Al(III) by 8-Hydroxyquinoline and Drastic Fluorescence Enhancement in Reverse Micelles

Complexation of Al^IIIby 8-hydroxyquinoline and fluorescence behavior of the quinolinate(s) were studied in reverse micellar systems at low water content, and compared to aqueous media. Two surfactants were used: one was cationic (CTAC: cetyltrimethylammonium chloride) and the other was anionic (AOT: sodium bis(2-ethylhexyl)sulfosuccinate). The results obtained in the CTAC/dichloromethane system (W= [H₂O]/[surfactant] = 0.9) showed that complexation occurred very likely in the oil phase and no micellar effect was observed. On the contrary, in the presence of AOT, specific micellar effects were observed due to the presence of the anionic polar heads: stabilization of the positively charged 1:1 and 1:2 chelates, at the expense of the neutral water-insoluble 1:3 chelate which is formed in aqueous solutions under similar conditions;drastic fluorescence enhancement factorsof 120 and 100 in AOT/heptane (W= 1.5) and AOT/dichloromethane (W= 1.6), respectively. Such factors have never been reported so far in either hydroorganic or direct micellar systems. In return, the length of time for the production of the complex(es) is increased because of the microheterogeneity of the medium and the small sizes of the water pools.     

Glycoconjugate libraries accessed by multicomponent reactions

Glycobiology opens a wide field for new therapeutic approaches. However, the complexity and unavailability of various carbohydrate test compounds has excluded this class of natural products from modern screening systems. Alternatively, glycomimetics are considered to be more drug-like candidates for development. By means of multicomponent condensations (MCCs) utilizing suitable carbohydrate synthons, rapid and effective access to glycoconjugate libraries can be obtained. The flexibility of MCCs allows the assembly of diverse carbohydrate containing libraries. It may be assumed that MCCs containing carbohydrate moieties will play an important role in glycomimetic chemistry and biology.     

Synthesis and properties of water-soluble gold colloids covalently derivatized with neutral polymer monolayers

Citrate-capped gold nanoparticles as well as planar gold surfaces can be efficiently grafted with a covalently attached polymer monolayer a few nanometers thick, by simple contact of the metal surface with dilute aqueous solutions of hydrophilic polymers that are end-capped with disulfide moieties, as shown by UV/vis absorption, dynamic light scattering, and surface plasmon resonance studies. The hydrophilic polymer-coated gold colloids can be freeze-dried and stored as powders that can be subsequently dissolved to yield stable aqueous dispersions, even at very large concentrations. They allow for applying filtrations, gel permeation chromatography, or centrifugation. They do not suffer from undesirable nonspecific adsorption of proteins while allowing the diffusion of small species within the hydrogel surface coating. In addition, specific properties of the original hydrophilic polymers are retained such as a lower critical solution temperature. The latter feature could be useful to enhance optical responses of functionalized gold surfaces toward interaction with various substrates.     

Stereoselective Syntheses of Tetrahydroesterastin-β -Lactam Analogues

A total synthesis of the optically active tetrahydroesterastin β -lactam analogue 2 using Miller's hydroxamate approach is described (Scheme 2). Significant modification of published procedures has resulted in a short and facile stereospecific preparation of the N-[(benzyloxycarbonyl)methyl]-β -lactam 17 starting from the readily available D -serine. This material served as intermediate for the preparation of a variety of N-[(benzyloxycarbonyl)methyl]tetrahydroesterastin β-lactam analogues (Scheme 5).     

Design and synthesis of push-pull chromophores for second-order nonlinear optics derived from rigidified thiophene-based pi-conjugating spacers.

Two series of push-pull chromophores built around thiophene-based pi-conjugating spacers rigidified either by covalent bonds or by noncovalent intramolecular interactions have been synthesized and characterized by UV-vis spectroscopy, electric field induced second harmonic generation (EFISH) and differential scanning calorimetry. Comparison of the linear and second-order nonlinear optical properties of chromophores based on a covalently bridged dithienylethylene (DTE) spacer with those of their analogues based on open chain DTE shows that the rigidification of the spacer produces a considerable bathochromic shift of the absorption maximum together with a dramatic enhancement of the molecular quadratic hyperpolarizability (mu beta) which reaches values among the highest reported so far. A second series of NLO-phores has been derived from a 2,2'-bi(3,4-ethylenedioxythiophene) (BEDOT) pi-conjugating spacer. As indicated by X-ray and UV-vis data, rigidification of the spacer originates in that case, from noncovalent intramolecular interactions between sulfur and oxygen atoms. Again, comparison with the parent compounds based on an unsubstituted bithiophene spacer reveals a marked red shift of the absorption maximum and a large enhancement of mu beta. In an attempt to distinguish the contribution of the electronic and geometrical effects of the ethylenedioxy group, a third series of NLO-phores based on 3,4-ethylenedioxythiophene (EDOT) and 3,4-dihexyloxythiophene spacers has been synthesized. Comparison with compounds based on unsubstituted thiophene shows that, despite a red shift of lambda(max), introduction of alkoxy groups leads to a decrease of mu beta. Theoretical calculations indicate that this effect results from a decrease of the dipole moment (mu) caused by the auxiliary electron-donor alkoxy groups on the thiophene ring. In contrast, replacement of BT by BEDOT produces an increase of mu, which associated with the noncovalent rigidification of the BT system accounts for the observed enhancement of mu beta.