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).     

Viskoelastische Eigenschaften von Polyisobutylenen in verdünnten Lösungen

Zusammenfassung Die Speicher- und VerlustmodulnG undG verdünnter Lösungen (2–4%) dreier Isobutylenpolymerisate mit den Molekulargewichten 0,63, 1,29 und 11×10⁵ wurden in der Apparatur vonBirnboim undFerry über einen Frequenzbereich von 0,4–400 Hz und einen Temperaturbereich von –17,5 bis 25,0° bestimmt. Für die scharf fraktionierten Polymerisate von niederem Molekulargewicht ergab die Frequenzabhängigkeit der Moduln eine ausgezeichnete Übereinstimmung mit der Theorie vonZimm. Die aus den experimentell erhaltenen Kurven ermittelten Molekulargewichte und größten Relaxationszeiten waren von der erwarteten Größenordnung. Für das Polymerisat mit höherem Molekulargewicht entsprach die Frequenzabhängigkeit vonG undG – _s jedoch der Theorie vonRouse. Der Einfluß der hydrodynamischen Wechselwirkung in der Bewegung der Knäuelsegmente, in welchem der Unterschied zwischen den beiden Theorien besteht, erscheint als von der Größe des Molekulargewichts abhängig.

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Summary The storage and loss moduliG andG of dilute (2–4%) solutions of three polyisobutylenes of molecular weight 0.63, 1.29, and 11×10⁵ were determined in the apparatus ofBirnboim andFerry over a frequency range of 0.4 to 400 cps, and a temperature range of –17.0 to 25.0°. The sharply fractionated polymers of low molecular weight showed a frequency dependence in excellent agreement with the theory ofZimm. The experimentally determined molecular weights and terminal relaxation times were of the expected order of magnitude. The frequency dependence of the polymer of highest molecular weight, however, conformed more closely to the theory ofRouse. The influence of the hydrodynamic interaction on the motion of the coil segments, which constitutes the difference in the two theories, appears to depend on the magnitude of the molecular weight.

     

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).