Spectral distributions for long range perturbations

We study distributions which generalize the concept of spectral shift function, for pseudo-differential operators on . We call such distributions spectral distributions. Relations between relative scattering determinants and spectral distributions are established; they lead to the definition of regularized scattering phase. These relations are analogous to the usual one for the standard spectral shift function. We give several asymptotic properties in the high energy and semiclassical limits where both nontrapping and trapping cases are considered. In particular, we prove Breit-Wigner formulae for the regularized scattering phases, for semiclassical Schrödinger operators with long-range potentials.     

Roughness analysis of the cracked surfaces of a face centered cubic alloy

Intergranular and transgranular fracture surfaces obtained in a face centered cubic alloy are studied using 3D maps reconstructed by scanning electron microscopy stereo imaging. The roughness exponents measured in the intergranular and transgranular surfaces, respectively, zeta = 0.83 +/- 0.05 and zeta = 0.75 +/- 0.05, are in agreement with the universal roughness value of 3D fractures. However, the slightly smaller value related to the transgranular surface could be a consequence of crystallographic transgranular zones disseminated on the surface whose roughness exponent zeta = 0.65 +/- 0.07 is close to the one usually measured on 2D fractures.     

An efficient, stereoselective approach to syn-1,2-diols protected as cyclic carbonates

Enantioenriched 4-hydroxyalk-2-ynyl carbonates (or benzoates) have been prepared by stereoselective zinc-mediated addition of alkyl 2-propynyl carbonates (or their benzoate analogues) to aldehydes. Their partial reduction to Z-olefins followed by cyclization under mild Pd-catalyzed conditions allowed a straightforward access to enantioenriched syn-1,2-diols protected as cyclic carbonates.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

Cover Picture

The cover picture shows how thrombosis occurs in the deep veins of the lower limbs. Stasis, which results from slow and turbulent blood flow, combined with hypercoagulation, caused, for example, by a surgical procedure, may result in thrombus formation. The synthetic sulfated pentasaccharide shown in part is a potent antithrombotic compound that exerts its effect by activation of the plasma protein antithrombin III. Conformationally locked monosaccharides have now been synthesized to demonstrate that L-iduronic acid, one part of the pentasaccharide, must adopt an unusual distorted conformation to activate antithrombin III. Such conformational effects might be relevant in explaining the unique biological properties of glycosaminoglycans that contain L-iduronic acid. In the background of the picture, a flight of vampire bats is attracted by the pentasaccharide. Vampire was the name given to South American blood-sucking bats (Latin name: desmodus rotundus) in 1761 by the French naturalist Georges Louis Leclerc Comte de Buffon (1707-1788). These bats are known to attack cattle and, very rarely, sleeping human beings. Although their saliva has been shown to contain an anticoagulant compound, they would also be happy to benefit from the pentasaccharide mentioned above, to suck the blood out of the vein more easily. More details about this compound which would be helpful to vampire bats are reported by Petitou, Sina? et al. on p. 1670 ff.     

Ouverts d"harmonicité pour les fonctions séparément harmoniques

Let D ^N , G ^M be two open sets, E D and F G two compact sets which satisfy the condition (H) (that is a harmonic condition similar to Leja"s condition). We find an open set ^N+M such that each separately harmonic function f : X : = (D× F) (E × G) (i.e.: for all x in E, f(x,.) is harmonic on G; for all y in F, f(., y) is harmonic on D) extends to a harmonic function on .     

Large intrinsic birefringence in zinc-blende based artificial semiconductors

A new attempt to solve the phase matching problem for semiconductor-based frequency conversion devices, based on the implementation of intrinsic birefringence in artificial materials, is discussed. The first results concerning the growth and characterization of ultrashort period superlattices are presented. To cite this article: J.-M. Jancu et al., C. R. Physique 8 (2007).     

Un modèle hyperbolique diphasique bi-fluide en milieu poreux

We introduce an hyperbolic two-fluid two-pressure model to compute unsteady two-phase flows in porous media. The closure laws comply with the entropy inequality, and a unique set of jump conditions holds within each field. To cite this article: J.-M. Hérard, C. R. Mecanique 336 (2008).