Optimum parameters for the generalized ADI method

Summary. In the context of the generalized ADI method, we are concerned with the problem of finding in the set of rational functions r with numerator degree m and denominator degree n an element that minimizes where E,F are disjoint real intervals. By extending a recent analysis by Levin and Saff, we present an explicit formula for choosing the pair (m,n) for given m +n. Furthermore, we provide a characterization of and a Remes type algorithm for its determination. Extensive numerical computations furnish some comparison of with asymptotically optimal solutions based on Fejér-Walsh and Leja-Bagby points. Received September 6, 1996 / revised version received June 30, 1997     

Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Ionic relaxation in nematic liquid crystal cells

We investigate the dependence of the relaxation time of the current flowing in a nematic cell submitted to an external dc voltage on the physical properties of the substrate. We show that previously presented analyses of the same problem are not very useful for practical applications. We compare our theoretical predictions with experimental data, and show that the agreement is rather good. The influence of the adsorption-desorption phenomenon on the relaxation time is also discussed.     

Du discret au continu pour des modèles de réseaux aléatoires d'atomes

We study in this Note the continuum (macroscopic) limit for some atomistic models for crystals. The purpose is to derive densities of mechanical energies from microscopic models. In contrast to the setting of a previous study, where the microscopic structure was assumed to be periodic, it is modelled here by a stochastic lattice, which enjoys some stationarity and ergodicity properties, following notions previously introduced elsewhere. To cite this article: X. Blanc et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

绝缘层上半导体多晶膜激光再结晶临界条件

从理论的角度分析了绝缘衬底对其上面半导体多晶膜激光熔化再结晶过程的影响, 发现低导热的绝缘层使产生固一液相变的临界激光功率有明显的降低.用喇曼光谱测量了激光再结晶SOI层中的应力. 应力的出现是多晶膜内曾经发生过固一液相的佐证.从这一思想出发, 对LPCVD方法制备的大量SOI 样品进行激光再结晶临界条件的研究, 证明了忽略绝缘层低热导影响的模型不能解释实验结果, 而经过修正的公式则可以较好地拟合实验结果, 关键词：     

Spectroscopic and Structural Study of the 1：2 Aluminium（Ⅲ） Complex of Quercetin

Complex formation between aluminium and quercetin（Q） in methanol was investigated by means of 27^Al solid-state, 13^C and 1^H NMR and MS（ESI）, UV and IR spectra. Formation of the 1：2 complex was favored in methanol relative to all other solvent and the predominant species observed of Al（Ⅲ） has a 1：2 stoichiometry. The fine structure of 1：2 aluminum complex of quercetin was that the aluminum central atom chelated with two quereetin molecules and two methoxyl groups between two five membered rings, its coordination is six, the chelated site was 3-hydroxy-4-carbonyl.     

Tight-binding method modelling of photonic crystal waveguides

We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics, the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority of this method over plane wave based techniques.     

A high-pressure Raman and X-ray diffraction study of the perovskite SrCeO3

A high-pressure structural study of SrCeO₃ has been performed at room temperature by Raman spectroscopy and X-ray diffraction up to 32 and 45 GPa, respectively. A first-order reversible phase transition is observed at about 12 GPa in both techniques. A second weak structural change, taking place between 18 and 25 GPa, can be suspected from Raman data. The increase in the number of Raman bands and diffraction lines is an indication that the symmetry is lowered and the compound does not evolve towards the ideal cubic perovskite structure. A Rietveld analysis of X-ray data was performed for the low-pressure phase and the atomic positions and the cell lattice parameters variations are reported in this paper. The volume compressibility derived from Raman modes (5.6×10⁻¹² Pa⁻¹), involving mainly bond-stretching for each type of polyhedron, is found to be close to the one obtained from volume cell variations measured by X-ray diffraction (7.9×10⁻¹² Pa⁻¹).