Acousto-optic mode coupling of partially coherent light in two-mode optical fibers

An acoustic pulse propagating on a two-mode fiber can act as a beam splitter in a scanning interferometer. When this device is employed in white-light interferometry, the effects of distributed coupling and dispersive interferometer arms need to be considered. A theory suitable for treating acousto-optic interaction of partially coherent light in a moving interaction region was developed. It was found that differential optical dispersion should be negligible and the acoustic pulse length short. Also the coherence time should be short but long compared to the intermodal group delay difference over a pulse length. Experiments with long acoustic pulses were performed, and fairly good agreement with theory was obtained.     

Specific high performance liquid chromatographic determination of the molecular weight and concentration of hyaluronic acid in complex mixtures by labelled hyaluronate binding proteins.

A simple High performance liquid chromatographic (HPLC) method for the specific determination of the molecular weight and concentration of hyaluronic acid (HA) in complex mixtures has been developed. Hyaluronate-binding proteins isolated from bovine cartilage labelled by 125I or fluoresceinisothiocyanate were used as specific markers. The specific binding affinities of the markers were compared and were found to have association constants of 1.6 x 10(7) M-1 and 1.2 x 10(7) M-1 respectively. The HA levels and molecular weight distributions can be easily determined in the range 10-500 ng/mL in complex mixtures by the use of markers, molecular sieving HPLC columns and appropriate detectors. It has been demonstrated clearly that the method is useful for the highly specific determination of the parameters in complex biological samples such as serum and synovial fluids and is recommended for clinical applications.     

The critical probability for random Voronoi percolation in the plane is 1/2

We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ², and form the Voronoi tessellation of ℝ² with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These results are analogous to Kesten's results for bond percolation in ℤ². The result corresponding to Harris' Theorem for bond percolation in ℤ² is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting. For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof of Kesten's Theorem for ℤ²; we hope they will be applicable in other contexts as well. Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900 Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland     

Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces

We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field problem. The tools include coupling arguments, as well as regularity and moment estimates for solutions of certain diffusive partial differential equations.     

Phase diagram of a two-frequency chiral nematic mixture in an electric field

The behaviour of a chiral nematic mixture with low frequency dielectric relaxtion was studied between two electrodes, with homeotropic anchoring, in the presence of an AC electric field E. The phase diagram in the parameter plane (d/p, E) was determined for this mixture which could be dielectrically negative or positive in different frequency ranges. The determination was carried out by changing the sample thickness d and both the amplitude and frequency of the electric field at a constant cholesteric pitch p.     

Pourquoi, pour qui enseigner les mathématiques? Une mise en perspective historique de l’évolution des programmes de mathématiques dans la société française au XXe siècle

Evolutions of mathematical curricula in French society have been marked by the successive answers intitutions have given to the following question since one century: Why and whom teaching mathematics? Here I present two of these, one given in 1908 and one in 1967. Each symbolises a breaking period of reforms in secondary mathematics teaching in France. We will see in the two first part of this paper that they belong to two different worlds, with social, institutional, ideological and mathematical specific features. In the third part, I’ll focus on geometry, showing the effects of the different answers concerning the public and the aims of mathematical teaching.     

LIDAR mapping of ozone-episode dynamics in Paris and intercomparison with spot analyzers Supplementary material available at http://link.springer.de/journals/apb

Continuous mapping of an ozone episode in Paris in June 1999 has been performed using a differential absorption lidar system. The 2D ozone concentration vertical maps recorded over 33 h at the Champ de Mars are compiled in a video clip that gives access to local photochemical dynamics with unprecedented precision. The lidar data are compared over the whole period with point monitors located at 0-, 50-, and 300-m altitudes on the Eiffel Tower. Very good agreement is found when spatial resolution, acquisition time, and required concentration accuracy are optimized. Sensitivity to these parameters for successful intercomparison in urban areas is discussed. Received: 11 February 2002 / Published online: 14 March 2002     

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.     

Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutionsVibration d'une coque élastique mince pré-contrainte I

We study the vibration of an elastic thin shell which is pre-constrained by a large displacement with a small deformation. In this first Note we prove the solutions exist and we investigate both the interior regularity and the boundary regularity which is known to be important in the shape differentiation of hyperbolic equations. To cite this article: J. Cagnol, J.-P. Zolésio, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 161–166