Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting

The interaction of three-dimensional isotropic turbulence with a plane shock at Mach numbers of $M=2.0$ and $M=3.0$ is investigated via direct numerical simulation. The numerical scheme is based on a characteristic-type formulation of the Navier–Stokes equations and uses fifth-order upwind schemes in space, a fourth order Runge Kutta scheme in time and a shock-fitting as inlet condition. The isotropic turbulence was generated in a separate computation based on a prescribed energy spectrum. This turbulent flow is considered as frozen, and is convected through the shock with a prescribed average shock speed. An FFT interpolation is used to obtain the upstream values at the instantaneous shock location. Turbulence enhancement is observed, and the evolution of velocity fluctuations as well as turbulence microscales are in good agreement with the behaviour observed using shock-capturing. To cite this article: J. Sesterhenn et al., C. R. Mecanique 333 (2005).     

Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

<Emphasis Type="Italic">p</Emphasis>-Laplace Operator and Diameter of Manifolds

Let be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian and we prove that the limit of when is 2/d(M), where d(M) is the diameter of M. Moreover, if is an oriented compact hypersurface of the Euclidean space or , we prove an upper bound of in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of then: . Mathematics Subject Classifications (2000): 53A07, 53C21.     

Norme composée et norme associée généralisée d'une matrice

Sans résumé     

Polymer-nanoparticle complexes: from dilute solution to solid state

We report on the formation and the structural properties of "supermicellar" aggregates made from mineral nanoparticles and polyelectrolyte-neutral block copolymers in aqueous solutions. The mineral particles put under scrutiny are ultrafine and positively charged yttrium hydroxyacetate nanoparticles. Combining light, neutron, and X-ray scattering experiments, we have characterized the sizes and the aggregation numbers of the organic-inorganic complexes. We have found that the hybrid aggregates have typical sizes in the range of 100 nm and exhibit a remarkable colloidal stability with respect to ionic strength and concentration variations. Solid films with thicknesses up to several hundreds of micrometers were cast from solutions, resulting in a bulk polymer matrix in which nanoparticle clusters are dispersed and immobilized. It was found in addition that the structure of the complexes remains practically unchanged during film casting.     

Polystyrene-graft-polyglycerol resins: a new type of high-loading hybrid support for organic synthesis

The preparation of a dendritic graft polymer by a very efficient synthesis of polyglycerol directly on a polystyrene resin is presented. This one-step process can be performed on a multigram scale to provide a chemically stable polymeric support. The resulting hybrid polymers were fully characterized by diverse analytical methods (NMR, IR, ESEM, UV detection of cleaved protecting groups, and mass-spectrometric methods). They combine a high loading capacity (up to 4.3 mmol g(-1)) with good swelling properties in a wide range of solvents (including water), which is the major drawback for many existing solid phase supports. In comparison to the widely employed PEGylated resins, these hybrid materials offer a 10-fold higher loading capacity. Their suitability as supports for organic synthesis and for the immobilization of reagents has been demonstrated. These materials also swell in water, and consequently, it should be possible to use these new hybrid materials for synthesis in protic solvents.