Explicit limits for nonperiodic homogenization and reduction of dimensionLimites explicites pour l'homogénéisation non-périodique et la réduction de dimension

The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982.     

Unsteady axisymmetric stagnation flow on a circular cylinder

Unsteady, axisymmetric stagnation flow about a circular cylinderis examined when the far-field flow is a periodic function oftime with a fixed time average and an oscillatory part of prescribedamplitude and frequency. Solutions are computed for arbitraryvalues of the Reynolds number, quantifying the effects of surfacecurvature, and a frequency parameter based on the period ofthe far-field flow. It is found that solutions remain regularand periodic provided that the far-field amplitude lies belowa critical value. Above this value, solutions terminate in afinite-time singularity. The blow-up time is delayed by increasingthe curvature of the surface. These results are corroboratedby asymptotic predictions valid in the limits of small and largeamplitude and frequency. For large Reynolds number, the problemreduces to the two-dimensional stagnation-point flow againsta plane wall studied by previous authors.     

Corrigendum to “EuBaFe2O5+w: Valence mixing and charge ordering are two separate cooperative phenomena” [J. Solid State Chem. 180 (2007) 148-157]

An error in the expression for the Fe²⁺, Fe³⁺ valence-mixing probability in RBaFe₂O_5+w is acknowledged and correct formula is derived. The new formula slightly improves the least-squares fit to the experimental concentrations of the Mössbauer component Fe^2.5+ as a function of the oxygen-nonstoichiometry parameter w for R=Eu.     

Pure-silica optical waveguides, fiber couplers, and high-aspect ratio submicrometer channels for electrokinetic separation devices

A new fabrication procedure for integration of ultraviolet transparent pure-silica planar waveguides, fiber couplers and high-aspect ratio submicrometer channels is presented. Only a single photolithographic mask step is required. The channels are 80-90 microm deep and the width can be reduced to about 0.5 microm, corresponding to a height-to-width ratio of more than 150. The core of the waveguides consists of pure silicon dioxide, which is favorable over doped silica, due to the absence of absorption centers associated with the dopants. This furthermore improves the long-term stability of the waveguides, because of an increased radiation resistance of the glass. The propagation loss decreases from 1.0 dB/cm at 200 nm to 0.2 dB/cm at 800 nm, which, to our knowledge, is the lowest propagation loss reported for integrated planar waveguides in the ultraviolet wavelength region to date. The effective optical path length is 1.2 mm for an absorbance cell with a nominal length of 1.0 mm, indicating effective suppression of stray light. The limit of detection for paracetamol when present in the entire channel network was determined to 3 microg/mL. Finally, the applicability of the fabricated devices for capillary electrophoresis was evaluated by separation of caffein, paracetamol and ketoprofone using absorbance detection at 254 nm.     

Independent component analysis yields chemically interpretable latent variables in multivariate regression

This work shows that independent component analysis (ICA) can be used to obtain statistically independent and, therefore, chemically interpretable latent variables (LVs) in multivariate regression. Two novel algorithms based on ICA are introduced and compared with two classical methods on simulated data: principal component regression and partial least-squares regression. All methods compared yield accurate predictions, but only those based on ICA yield LVs that are chemically interpretable. Practical limitations of ICA-based regression with respect to the underlying assumptions, sample size, and measurement noise are discussed and illustrated by means of simulations.     

Two-proton correlations in the target fragmentation region of nuclear collisions at 200A GeV

Correlations between protons are studied in the target fragmentation region of reactions of protons and¹⁶O with C, Cu, Ag, Au and of³²S with Al and Au at 200A GeV. The emitted protons were measured with the Plastic Ball detector in the WA80 experiment at the CERN SPS. The comparison of the correlation function with calculations, assuming a spherical, gaussian shaped source with a lifetime τ=0 fm/c, allows the extraction of radius parameters. The values are very close to those expected from the geometry of the target nuclei and increase with the target mass as αA _Target ^1/3 . Even in proton induced reactions the whole target nucleus is involved. The dependence of the radii on centrality, polar angleθ _lab, and energy, and their relation to measured proton yields are presented.     

A fluorinated selenide linker for solid-phase synthesis of n-pentenyl glycosides

[reaction: see text] A fluorine-labeled selenide linker for installing terminal isolated olefins has been synthesized in high overall yield. The resin-bound linker could be glycosylated both with glycosyl trichloroacetimidates and glycosyl fluorides. The linker did not decompose after oxidation with tBuOOH but underwent beta-elimination when it was subjected to heat. This allowed the released n-pentenyl glycoside 15 to be isolated in excellent yield and purity after filtration.     

Interferences in the determination of total nitrogen in natural waters by photo-oxidation to nitrate-nitrite mixture

The method proposed by Armstrong, Williams and Strickland for the photo-oxidation of total nitrogen in sea-water to nitrate and nitrite has been studied in some detail, to extend its use to fresh and brackish waters, applying a more accurate method for the determination of the reaction products. Variables influencing the yield of nitrate and nitrite are irradiation time, pH and type of buffer, kind of nitrogen compound and its concentration, and the concentrations of oxygen, carbon dioxide, organic matter and salts, especially bromides, even at the low concentrations found in brackish waters. All these variables interact in a rather complicated way. Interferences from halides, organic matter and carbon dioxide are considerably reduced by ensuring that the pH is kept at 8.5-9 during the irradiation. Because pure solutions of many substances give quantitative yields (> or = 98%) in the pH-range 7-9 usually recommended, whereas others require lower pH for maximal oxidation, a method has been developed involving photo-oxidation first at pH 2.1 and then at pH 8.5-9. In the absence of interfering concentrations of halides the relative increase in yield by an initial irradiation at low pH is especially large (10-36%) for proteins, organic nitrogen in fresh waters, uric acid and urea. A comparison is made between determination of total nitrogen in some natural waters by using photo-oxidation and by a Kjeldahl method modified to give total nitrogen. By making use of the optimal conditions presented in this paper, a negative error of less than 8% is expected in the determination of total nitrogen in fresh waters. For saline waters the error will probably be larger, at least at a high ratio of organic to inorganic nitrogen.     

Consolidation behavior in sedimentation of TiO(2) suspensions in the presence of electrolytes

The consolidation of TiO(2) suspensions (anatase and rutile) due to gravity sedimentation in the presence of electrolytes has been investigated as a function of pH. Sodium and barium nitrate were used as flocculating electrolytes. The particle interaction was related to the zeta potential and the thickness of the electrical double layer, kappa(-1), by utilizing the repulsive barrier in the classical DLVO theory. The stability of the suspensions was represented as the average final solids content of the sediment cake, phi(fin). The batch sedimentation process was followed by scanning the sample cell with X-rays, from which the solids content and the particle size were calculated. Generally, dense sediments, with phi(fin) up to volume fractions of 0.5, were found for stable suspensions. Flocculated suspensions produced sediments with low phi(fin). The phi(fin) was observed to increase linearly with increasing repulsive barrier. However, at pH values only slightly higher than the isoelectric point (pH(iep)) the phi(fin) remained low until it returned to linearity at a pH much higher than pH(iep). This was attributed to the stronger affinity of sodium than of nitrate for the particle surface, which may be explained by the higher negative hydration energy of sodium. The stronger affinity of sodium was also shown as unsymmetrical distribution of phi(fin) around pH(iep), with stronger flocculation at pH>pH(iep). The interpretation of phi(fin) as a function of the repulsive barrier (or kappa(-1)) also made it possible to distinguish between the adsorption mechanisms of ions from solution. Addition of electrolyte at a fixed low and high pH (surface positively and negatively charged, respectively) clearly showed the specificity in adsorption and consequent flocculation of the barium ion from the indifferent nitrate. Sodium was, however, again observed to flocculate the TiO(2) suspensions slightly more strongly than nitrate.     

Upper limit for thermal direct photon production in heavy-ion collisions at 60 and 200A·GeV

The production of direct photons has been investigated in reactions ofp and¹⁶O projectiles at 60 and 200A·GeV with C and Au nuclei. Photon and ⁰ spectra have been measured in the pseudorapidity range 1.52.1 for the transverse momentum region 0.4 GeV/cp _T 2.8 GeV/c employing the lead-glass spectrometer SAPHIR. An upper limit of 15% at the 90% confidence level for the direct photon signal relative to the neutral pion production is obtained from the comparison of measured photon spectra with Monte Carlo simulations of the hadronic background based on the reconstructed yield of ⁰ and mesons. Consequences for a possible phase transition to a quark-gluon plasma are discussed.