Comparison of dephasing times for vibrational and rotational coherent anti-Stokes Raman scattering: implications for velocimetry

Time-domain coherent anti-Stokes Raman scattering experiments have been carried out by probing vibrational and pure rotational lines of nitrogen in the Doppler broadened regime. The theoretical analysis of the transient responses outlines the role of the geometrical effects. For pure rotational CARS, it is shown that the main contribution to the dephasing of the Raman coherence results from the change in direction between the pump and anti-Stokes wave vectors whereas the difference between the modulus of these two wave vectors accounts for dephasing in vibrational CARS. Furthermore, we demonstrate that the range of operation of time-domain CARS velocimetry is extended by probing pure rotational lines. The predictions are validated by experiments which are performed both in a static gas cell and in a Mach 10 supersonic flow. Received: 30 March 2000 / Revised version: 9 June 2000 / Published online: 13 September 2000     

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).     

Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the functional renormalization group flow. Breaking is shown to occur below a critical dimension d(DR) ? 5.1 and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.     

A neutron powder diffraction study of the helimagnetic structure of TlCo2Se2−xSx

The magnetic layer structure of TlCo₂Se_2−xS_x has been thoroughly re-investigated with neutron powder diffraction. The cobalt magnetic moments are ferromagnetically arranged within the layers, but the interlayer coupling differs profoundly with varying composition (x): the spins in TlCo₂Se₂ form a helix along the c-axis with a turning-angle of ∼119° at 1.4 K. This kind of helical structure prevails for 0≤x≤1.5 with a gradual decrease of the angle with increasing sulphur content, down to 34°, showing an almost linear relationship with the interlayer distance of Co-Co. For x≥1.75 the interlayer coupling changes to ferromagnetic. Unexpectedly, two helices were found to coexist at x=0.5 and x=1.0. The interaction between adjacent cobalt layers is there characterized by an incommensurate angle (106°, resp., 73°) together with a commensurate angle of 90°. The magnetic structures have been refined as two magnetic phases, each having a characteristic wave vector. A tentative model where the symmetry of the structure and the interlayer distance compete is considered for explaining the simultaneous occurrence of the two kinds of diffraction profile satellites.     

Etude comparative des proprietes magnetiques des oxydes lamellaires ACrO2 (A = Li,Na, K)—I: Etude par effet Mössbauer de LiCrO2 dope par le fer

A Mössbauer study of the dimensionality of magnetic interactions in the layer oxide LiCr_0.99Fe_0.01O₂ shows a 2-D behaviour.     

Erratum: Symmetric iterative interpolation processes

Communicated by Charles A. Micchelli.     

Sur les valeurs propres d'un oscillateur harmonique perturbé

Sans résumé Dedicated to Professor Shmuel Agmon     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Existence and convergence for quasi‐static evolution in brittle fracture

This paper investigates the mathematical well‐posedness of the variational model of quasi‐static growth for a brittle crack proposed by Francfort and Marigo in [15]. The starting point is a time discretized version of that evolution which results in a sequence of minimization problems of Mumford and Shah type functionals. The natural weak setting is that of special functions of bounded variation, and the main difficulty in showing existence of the time‐continuous quasi‐static growth is to pass to the limit as the time‐discretization step tends to 0. This is performed with the help of a jump transfer theorem which permits, under weak convergence assumptions for a sequence {u_n} of SBV‐functions to its BV‐limit u, to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence {u_n}. In particular, it is shown that the notion of minimizer of a Mumford and Shah type functional for its own jump set is stable under weak convergence assumptions. Furthermore, our analysis justifies numerical methods used for computing the time‐continuous quasi‐static evolution. © 2003 Wiley Periodicals, Inc.     

Graphes et ordonnés démontables, propriété de la clique fixe

This work extends to dismantable graphs many properties of dismantable posets dealing with products, exponentiation, existence of paths in a graph of all homomorphisms, fixed clique property, etc. We show that a poset is dismantlable in the sense of Rival if and only if its comparability graph is dismantlable, thus proving that, for posets, dismantlability is a comparability invariant. We establish the analogues for graphs of results of Duffus, Poguntke and Rival about fixed point sets and cores in posets.