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.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

Colorimetric determination of macrolide antibiotics using ferric ion

Macrolide antibiotics such as erythromycin, oleandomycin, spiromycin, and tylosin are found to react with Fe(3+) in the presence of an acetic acid-sulfuric acid mixture to form a colored product having a useful absorption band at 592 nm. Troleandomycin forms only a weakly colored product upon reaction. The molar absorptivity is about 2900 1 mol(-1) cm(-1) for erythromycin and the detection limit is 5 mug ml(-1). This colorimetric method permits the analysis of fermentation broths containing either erythromycin or tylosin without a separation step.     

Photoelectrochemistry on Ru(II)-2,2'-bipyridine-phosphonate-derivatized TiO2 with the I3-/I- and quinone/hydroquinone relays. Design of photoelectrochemical synthesis cells

Photocurrent measurements have been made on nanocrystalline TiO2 surfaces derivatized by adsorption of a catalyst precursor, [Ru(tpy)(bpy(PO3H2)2)(OH2)]2+, or chromophore, [Ru(bpy)2 (bpy(PO3H2)2)]2+ (tpy is 2,2':6',2' '-terpyridine, bpy is 2,2'-bipyridine, and bpy(PO3H2)2 is 2,2'-bipyridyl-4,4'-diphosphonic acid), and on surfaces containing both complexes. This is an extension of earlier work on an adsorbed assembly containing both catalyst and chromophore. The experiments were carried out with the I3-/I- or quinone/hydroquinone (Q/H2Q) relays in propylene carbonate, propylene carbonate-water mixtures, and acetonitrile-water mixtures. Electrochemical measurements show that oxidation of surface-bound Ru(III)-OH2(3+) to Ru(IV)=O(2+) is catalyzed by the bpy complex. Addition of aqueous 0.1 M HClO4 greatly decreases photocurrent efficiencies for adsorbed [Ru(tpy)(bpy(PO3H2)2)(OH2)]2+ with the I3-/I- relay, but efficiencies are enhanced for the Q/H2Q relay in both propylene carbonate-HClO4 and acetonitrile-HClO4 mixtures. The dependence of the incident photon-to-current efficiency (IPCE) on added H2Q in 95% propylene carbonate and 5% 0.1 M HClO4 is complex and can be interpreted as changing from rate-limiting diffusion to the film at low H2Q to rate-limiting diffusion within the film at high H2Q. There is no evidence for photoelectrochemical cooperativity on mixed surfaces containing both complexes with the IPCE response reflecting the relative surface compositions of the two complexes. These results provide insight into the possible design of photoelectrochemical synthesis cells for the oxidation of organic substrates.     

Some applications of thermomagnetometry to the study of chromindur alloys

Thermomagnetic experiments are shown to be a useful and rapid technique for studying phase changes involving magnetic materials. Particular examples are chosen from Chromindur II (Fe28Cr10.5Co) alloys having different thermal histories. The Curie temperature of the single phase alloy is found to be ～650°C and the metastable spinodal decomposition boundary is at essentially the same temperature. The Cr-rich near equilibrium decomposition product is less magnetic and has a lower T_c, while the Cr-deficient product is more magnetic, with a T_c ? 720°C.Comparisons are made at different heating and cooling rates between temperatures measured using magnetic standards and those measured by a thermocouple in close proximity to the sample.     

The mechanisms of decomposition of the 1- and 2-phenyltetralin radical cations

Mechanisms for decomposition of 1- and 2-phenyltetralins were investigated using low resolution mass spectrometry and metastable ion techniques. Four primary decompositions were observed for 1-phenyltetralin radical cations: (1) the loss of C₆H₆ via a 1,4-elimination; (2) the elimination of ethene via competing losses from carbons 3 + 4 and carbons 2 + 3; (3) the loss of C₈H₈, probably through a stepwise Diels-Alder cycloreversion to expel styrene; and (4) the loss of methyl radical involving carbon 2 and possibly carbon 4. Three major decompositions were observed for 2-phenyltetralin radical cations: (1) the loss of C₈H₈, possibly through a Diels-Alder cycloreversion to expel styrene; (2) the loss of C₆H₆ via a 1,3 elimination; and (3) the loss of methyl radical from carbon 1. Various exchange reactions occur prior to these losses, but they proved to be incomplete even for metastable ions.