Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Electron spin resonance of diluted solid solutions of MnO2 in Y2O3

Electron spin resonance spectra of Mn²⁺ in diluted solid solutions of MnO₂ in Y₂O₃ have been studied at room temperature for Mn concentrations between 0.20 and 2.00 mol%. Isolated Mn²⁺ ions in sites with two different symmetries were observed, as well as Mn²⁺ ions coupled by the exchange interaction. The relative concentration of isolated to coupled Mn²⁺ ions decreases with increasing manganese concentration. The results are consistent with the assumption that the manganese ions occupy preferentially the C₂ symmetry sites. A theoretical calculation based on this model yields an effective range of the exchange interaction between Mn²⁺ ions of 0.53 nm, of the same order as that of Mn²⁺ ions in CaO.     

Portable and Automatic Mössbauer Analysis

A portable Mössbauer spectrometer, developed for extraterrestrial applications, opens up new industrial applications of MBS. But for industrial applications, an available tool for fast data analysis is also required, and it should be easy to handle. The analysis of Mössbauer spectra and their parameters is a barrier for the popularity of this wide-applicable spectroscopic technique in industry. Based on experience, the analysis of a Mössbauer spectrum is time-consuming and requires the dedication of a specialist. However, the analysis of Mössbauer spectra, from the fitting to the identification of the sample phases, can be faster using by genetic algorithms, fuzzy logic and artificial neural networks. Industrial applications are very specific ones and the data analysis can be performed using these algorithms. In combination with an automatic analysis, the Mössbauer spectrometer can be used as a probe instrument which covers the main industrial needs for an on-line monitoring of its products, processes and case studies. Some of these real industrial applications will be discussed.     

An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Monte Carlo study of interfacial silicon suboxide layers and oxidation kinetics

A simple simulation scheme that simultaneously describes the growth kinetics of SiO₂ films at the nanometer scale and the SiO_x/Si interface dynamics (its extent, and spatial/temporal evolution) is presented. The simulation successfully applies to experimental data in the region above and below 10 nm, reproduces the Deal and Grove linear-parabolic law and the oxide growth rate enhancement in the very thin film regime (the so-called anomalous region). According to the simulation, the oxidation is governed mainly by two processes: (a) the formation of a transition suboxide layer and (b) its subsequent drift towards the silicon bulk. We found that it is the superposition of these two processes that produces the crossover from the anomalous oxidation region behavior to the linear-parabolic law.