Influence of the Electromagnetic Forces on Momentum and Heat Transfer in a 3-Phase ac Plasma Reactor

A new 3-phase ac plasma reactor has been developed within the framework of research on hydrocarbon cracking for the production of carbon black and hydrogen. ^(1,2) One of the main characteristics of the system is related to the 3-phase, 50 Hz ac current plasma generator which induces a very particular arc motion affecting the heat and mass transfer inside the reactor. In a first step, the general flow inside the reactor in the absence of hydrocarbon injection has been studied. A simplified approach to characterize the heat and mass transfer inside the reactor is presented in this paper. The arc zone analysis is carried out simultaneously by a theoretical analysis of the electromagnetic forces and by an ultrahigh-speed cine-camera analysis. The flow in the reactor is modeled with a CFD commercial code. Results are compared with experimental temperature measurements.     

Vanishing Cycles of Irregular D-Modules

Considering a holonomic -module and a hypersurface, we define a finite family of -modules on the hypersurface which we call modules of vanishing cycles. The first one had been previously defined and corresponds to formal solutions. The last one corresponds, via Riemann-Hilbert, to the geometric vanishing cycles of Grothendieck-Deligne. For regular holonomic -modules there is only one sheaf and for non regular modules the sheaves of vanishing cycles control the growth and the index of solutions. Our results extend to non holonomic modules under some hypothesis.     

Curvelets and Fourier Integral Operators

A recent body of work introduced new tight-frames of curvelets E. Candès, D. Donoho, in: (i) Curvelets – a suprisingly effective nonadaptive representation for objects with edges (A. Cohen, C. Rabut, L. Schumaker (Eds.)), Vanderbilt University Press, Nashville, 2000, pp. 105–120; (ii) http://www.acm.caltech.edu/~emmanuel/publications.html, 2002 to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimally sparse representations of Fourier Integral Operators. To cite this article: E. Candès, L. Demanet, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Image inverse d'un D-module and Newton Polygon)

We show that, under conditions about the microcharacteristic variety of a coherent -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.     

Salem Numbers and Growth Series of Some Hyperbolic Graphs

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the -regular graphs associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m 2 mod 4; and when = 3 and m 4 mod 12, for instance, they have a factor of X ² – X + 1). We then derive some regularity properties for the coefficients f _n of the growth series: they satisfy K ⁿ – R < f _n < K ⁿ + R for some constants K, R < 0, < 1.     

Identification of distinct Brønsted acidic sites in zeolite mordenite by proton localization and [27Al]-1H REAPDOR NMR

[27Al]-1H REAPDOR (Rotational Echo Adiabatic Passage DOuble Resonance) NMR experiments distinguish structurally dissimilar Br?nsted acid sites located in main 8 and 12 membered-ring channels of the zeolite mordenite.