An escapade in the world of sulfenate anions: generation,reactivity and applications in domino processes

An escapade in the world of sulfenate anions is described and shows that these nucleophiles, despite being described as unstable species, are mild and efficient sulfinylating agents, allowing access to a variety of allyl and aryl sulfoxides under smooth and operationally very simple conditions. Their use in asymmetric catalysis is also possible allowing the preparation of enantio-enriched sulfoxides. Moreover, such anions have been involved in the development of two new pseudo–domino processes.     

Theoretical and experimental 1H, 13C and 15N NMR studies of N‐alkylation of substituted tetrazolo[1,5‐a]pyridines

The ¹⁵N as well as ¹H and ¹³C chemical shifts of nine substituted tetrazolopyridines and their corresponding tetrazolopyridinium salts have been determined by using NMR spectroscopy at the natural abundance level of all nuclei in CD₃CN. In this paper, we report, for the first time, the N‐alkylation reaction of electron deficient tetrazolopyridines. The treatment of tetrazolopyridines 5–13 with one equivalent of trialkyloxonium tetrafluoroborate leads to a mixture of two isomers, i.e. N3‐ and N2‐alkyl tetrazolo[1,5‐a]pyridinium salts. It has been observed that the N3‐isomer is always the major isomer, except in the case of the CF₃ substituent, where the two isomers are obtained in the same amount. The quaternary tetrazolopyridinium nitrogen N3 is shielded by around 100 ppm (parts per million) with respect to the parent tetrazolopyridine. Experimental data are interpreted by means of density functional theory (DFT) calculations, including solvent‐induced effects, within the conductor‐like polarizable continuum model (CPCM). Good agreements between theoretical and experimental ¹H, ¹³C and ¹⁵N NMR were found. The combination of multinuclear magnetic resonance spectroscopy with gauge including atomic orbital (GIAO) DFT calculations is a powerful tool in the structural elucidation for both neutral and cationic heterocycles and in the determination of the orientation of N‐alkylation of tetrazolopyridines. Copyright © 2009 John Wiley & Sons, Ltd.     

Étude d'un modèle de fragmentation secondaire pour les brouillards de gouttelettes

In this Note, we first present a model for droplet secondary breakup, in liquid sprays. This model is based on the kinetic theory formalism and uses experimental correlations found in the literature (L.-P. Hsiang, G.M. Faeth, Int. J. Multiphase Flow 19 (5) (1993) 721–735; R. Maxey, J. Riley, Phys. Fluids 26 (4) (1983) 883–889; M. Pilch, C.A. Erdman, Int. J. Multiphase Flow 13 (6) (1987) 741–757) to determine the fragmentation rate and its outcome. We then conduct a mathematical study of the resulting kinetic equation. We prove, under some physically reasonable assumptions, an existence and uniqueness theorem and characterize the long-time behaviour of the solution. To cite this article: G. Dufour et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Computation of high order derivatives in optimal shape design

Summary. In shape optimization problems, each computation of the cost function by the finite element method leads to an expensive analysis. The use of the second order derivative can help to reduce the number of analyses. Fujii ([4], [10]) was the first to study this problem. J. Simon [19] gave the second order derivative for the Navier-Stokes problem, and the authors describe in [8], [11], a method which gives an intrinsic expression of the first and second order derivatives on the boundary of the involved domain. In this paper we study higher order derivatives. But one can ask the following questions: -- are they expensive to calculate? -- are they complicated to use? -- are they imprecise? -- are they useless? \medskip\noindent At first sight, the answer seems to be positive, but classical results of V. Strassen [20] and J. Morgenstern [13] tell us that the higher order derivatives are not expensive to calculate, and can be computed automatically. The purpose of this paper is to give an answer to the third question by proving that the higher order derivatives of a function can be computed with the same precision as the function itself. We prove also that the derivatives so computed are equal to the derivatives of the discrete problem (see Diagram 1). We call the discrete problem the finite dimensional problem processed by the computer. This result allows the use of automatic differentiation ([5], [6]), which works only on discrete problems. Furthermore, the computations of Taylor's expansions which are proposed at the end of this paper, could be a partial answer to the last question. Received January 27, 1993/Revised version received July 20, 1993     

All-fiber add-drop filters based on microfiber knot resonators

We demonstrate an all-fiber add-drop filter composed of a microfiber knot (working as a resonator) and a fiber taper (working as a dropping fiber). The dropping taper can be either parallel or perpendicular to the input port of the filter. A quality factor (Q factor) of 13,000 is obtained from a parallel-coupling 308 microm diameter microknot add-drop filter with a free spectral range (FSR) of 1.8 nm. A Q factor of approximately 3300 is obtained from a cross-coupling 65 microm diameter microknot add-drop filter with a FSR of 8.1 nm. This device is particularly easy to fabricate and to connect to fiber systems.     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

Contrôle par rotation ou par aspiration de l'écoulement autour d'un cylindre calculé par Simulation des Grandes Échelles

Control of the flow around a circular cylinder is studied using Large Eddy Simulation. The influence of control by rotation and suction on the flow characteristics is considered for several Reynolds numbers. Comparisons with experiments were conducted at $\mathit{Re}={10}^5$ for the flow with and without control. A drag reduction up to 30% is obtained for an usual suction intensity. To cite this article: G. Fournier et al., C. R. Mecanique 333 (2005).