Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamiqueOn some limits in charged particle physics towards (magneto)hydrodynamic equations

We discuss the connection between different scalings limits of the quantum-relativistic Dirac–Maxwell system. In particular we give rigorous results for the quasi-neutral/non-relativistic limit of the Vlasov–Maxwell system: we obtain a magneto-hydro-dynamic system when we consider the magnetic field as a non-relativistic effect and we obtain the Euler equation when we see it as a relativistic effect. A mathematical key is the modulated energy method. To cite this article: Y. Brenier et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 239–244.     

Polar factorization and monotone rearrangement of vector-valued functions

Given a probability space (X, μ) and a bounded domain Ω in ?^d equipped with the Lebesgue measure |·| (normalized so that |Ω| = 1), it is shown (under additional technical assumptions on X and Ω) that for every vector-valued function u ∈ L^p (X, μ; ?^d) there is a unique “polar factorization” u = ?Ψs, where Ψ is a convex function defined on Ω and s is a measure-preserving mapping from (X, μ) into (Ω, |·|), provided that u is nondegenerate, in the sense that μ(u^?1(E)) = 0 for each Lebesgue negligible subset E of ?^d. Through this result, the concepts of polar factorization of real matrices, Helmholtz decomposition of vector fields, and nondecreasing rearrangements of real-valued functions are unified. The Monge-Ampère equation is involved in the polar factorization and the proof relies on the study of an appropriate “Monge-Kantorovich” problem.     

Synthesis and physico-chemical characteristics of nanosized particles produced by laser ablation of a nickel target in water

Ablation of Ni targets in water by laser impact (532 nm, 40 mJ/pulse, 10 Hz and 8 ns duration) focused on massive samples (2 mm diameter) generates colloids with fine nanoparticles. The amount of metal released in the solution (measured by mass loss of the target or ICP) was found to increase first linearly with time, but slower after 8 min of impact. The size distribution of the nanoparticles thus produced was measured (by TEM) to be in the range 3–5.3 nm in diameter, with a tendency for the size to be smaller for larger number of laser shots. Actually, nickel oxide nanoparticles were produced, rather than nickel nanoparticles as it was shown by HRTEM. XPS photoemission measurements evidenced the presence of nickel oxide species on the crater of the nickel sample surface after laser ablation.     

Localized virtual and occupied molecular orbitals

This report describes the generation of localized from canonical molecular orbitals such that the method (1) be consistently applicable to occupied bond, lone pair and unoccupied orbitals and (2) permit symmetry related orbitals in molecules of two-fold or higher symmetry. Minimization of populations completely external to each local pair region effectively meets these criteria. Finally, conventional strategy for finding the global extremization point is costly in time and memory to implement; a much more efficient numerical search procedure for the global extremum is described. Results for ethylene, butadiene and benzene are presented to clarify the difficulties and their resolution.     

$L^p$ Approximation of maps by diffeomorphisms

It is shown that if then every map of class can be approximated in the -norm by a sequence of orientation-preserving diffeomorphims These conclusions hold provided that is open, bounded, and that In addition, is contained in the -neighborhood of the convex hull of All these conclusions fail for The main ingredients of the proof are the polar factorization of maps [4] and an approximation result for measure-preserving maps on the unit cube for which we provide a proof based on the concept of doubly stochastic measures (Corollary 1.1). Received: 25 My 2001 / Accepted: 25 October 2001 / Published online: 29 April 2002 RID="*" ID="*" en détachement de l'Université Paris 6, France The second author gratefully acknowledges the support of National Science Foundation grants DMS-99-70520, and DMS-00-74037     

Growth and spectroscopic properties of Yb-doped Li6Y(BO3)3 single crystal

The spectroscopic properties of high-quality Czochralski grown 20% Yb³⁺-doped Li₆Y(BO₃)₃ single crystal as new promising laser material are presented. The crystal was seeded-grown in the 〈0 1 0〉 direction and its crystallinity was measured using X-ray rocking curve analysis. Low temperature transmission spectrum exhibits broad bands in a short range of wavelengths and two sharp lines at 972.5 and 978 nm, interpreted as two zero-lines of two nonequivalent Yb³⁺ centers inside the lattice. The fluorescence lifetimes associated to these two intense lines are different: 0.867 and 1.33 ms. An attempt of determination of the Stark sublevels energies of the ⁴F_5/2 and ⁴F_7/2 manifolds of the two Yb³⁺ nonequivalent ions is given. The polarized absorption and emission spectra were also recorded at room temperature and we conclude that the most favorable emission line for laser application could be around 1042 nm in n_g polarization.     

GdAl3(BO3)4和Nd离子掺杂的倍频与自变频激光晶体研究

采用熔盐顶部籽晶法从K2Mo3O10-B2O3助熔剂中生长出尺寸为20 mm的优质GdAl3(BO3)4(简称GAB)和Nd3+激活的自变频激光晶体.确定了GAB晶体的透光波长范围、折射率和倍频系数随波长的变化,结果表明其在整个透光范围内均可实现相位匹配.测定了Nd3+∶GAB晶体在室温下的偏振吸收、荧光光谱和荧光寿命,进行了光谱计算,测试了晶体的自变频激光性能,实现了紫外-可见光-红外-中红外多波段激光输出.