Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

A Bayesian record linkage model incorporating relational data

In this article, we introduce a novel Bayesian approach for linking multiple social networks in order to discover the same real world person having different accounts across networks. In particular, we develop a latent model that allows us to jointly characterize the network and linkage structures relying on both relational and profile data. In contrast to other existing approaches in the machine learning literature, our Bayesian implementation naturally provides uncertainty quantification via posterior probabilities for the linkage structure itself or any function of it. Our findings clearly suggest that our methodology can produce accurate point estimates of the linkage structure even in the absence of profile information, and also, in an identity resolution setting, our results confirm that including relational data into the matching process improves the linkage accuracy. We illustrate our methodology using real data from popular social networks such as Twitter , Facebook , and YouTube .     

Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

Variational Evaluation of the HSSH FIR Transitions: The Anomalous K-Doubling

The roto-torsional energy levels of HSSH and DSSD up to J = 20 are evaluated variationally with a Hamiltonian expressed in terms of internal coordinates. The kinetic and potential parameters are derived from ab initio calculations with full optimization of the geometry. The calculated levels are employed for the determination of the centrifugal distortion constants. HSSH is a near-prolate symmetric rotor. The most stable C(2) conformer, calculated with MP4(SDQ)/cc-pVQZ, exhibits a 90.55 degrees dihedral angle. For J = 0, the lowest energies of HSSH and DSSD are 413.4876 cm(-1) (n = 1), 798.0304 cm(-1) (n = 2) and 1151.5773 cm(-1) (n = 3), and 304.3185 cm(-1) (n = 1), 594.2919 cm(-1) (n = 2), and 869.3508 cm(-1) (n = 3), respectively. For J = 60, the ab initio calculations allow the reproduction of the anomalous type-K doubling predicted with perturbation theory. Copyright 2000 Academic Press.     

On the efficiency of small-angle Čerenkov second harmonic generation in optical waveguides

It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P ₂ L ²), and linearly (P ₂ L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P ₂ L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L ^3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too.     

Graphic tool to produce tailored symmetrical phase-shifting algorithms

We employ the Fourier-transform graphic representation of a set of antisymmetrical and symmetrical sampling reference harmonics to obtain new symmetrical phase-shifting algorithms tailored to specific characteristics. As an example, a new detuning-insensitive seven-point algorithm, with a third signal harmonic insensitivity and which is detuning insensitive at this frequency, is derived.     

Partie 1: La nouvelle enceinte destinée à Ia production de I'or colloidal radioactif 198 Au

Une nouvelle enceinte destinée à la production de l,or colloïdal radioactif¹⁹⁸Au à usage thérapeutique et diagnostique est construite dans le Laboratoire de Chimie de Haute Activité à l'Institut des Sciences Nucléaires ?Boris Kidri?”. L'enceinte comporte deux appareils pour la préparation des colloïdes de l'or radioactif, permettant une production permanente méme au cas où l'un des appareils est accidenté. C'est grâce à une conception originale de la protection en plomb que l'accès aus appareils et aux stocks des effluents est rendu facile et ainsi que les systèmes de commande des processus des processus chimiques et la manipulation dans l,enceinte sont bien simplifiés     

Formation and Evolution of Carbonate Species in Na-Doped Al2O3 and V2O5-Al2O3

A study is carried out by FT-IR spectroscopy of the carbonate species formed upon interaction of CO₂ with alumina and vanadia-alumina catalysts doped with sodium. It is found that the presence of sodium enhances the ability of the catalyst surface to adsorb CO₂, yielding to carbonate formation. The species formed changes in the presence of vanadium, shifting the ν_COO stretching bands towards higher wavenumbers than those recorded in Na-Al₂O₃ systems.     

Synthesis and physical properties of Ca- and Ta-modified (K,Na)NbO3 lead-free piezoelectric ceramics

Polycrystalline samples of lead-free Ca and Ta co-substituted potassium sodium niobate (K_0.5Na_0.5NbO_3, KNN) ceramics have been prepared by solid state reaction technique. X-ray diffraction showed formation of a single-phase perovskite structure with orthorhombic symmetry. Substitution inhibits the grain growth, improves densification and decreases the ferro-paraelectric phase transition temperature. Temperature dependent dielectric permittivity studies demonstrate significant decrease in peak-permittivity values in the substituted samples. Bulk longitudinal piezoelectric coefficient is significantly enhanced, up to ～155 pC/N for (K_0.48Na_0.48Ca_0.02)(Nb_0.85Ta_0.15O₃) as compared to 95 pC/N for pristine KNN ceramic. Local piezoelectric properties have been observed by piezoresponse force microscopy (PFM) technique. Distinct piezocontrast was studied in both vertical and in-plane modes of PFM for all samples. The samples exhibit self-polarization effect in the unpoled state and effective local vertical piezoelectric coefficient was the largest in Ca and Ta co-substituted sample whereas the in-plane piezoelectric coefficient was maximum for Ca-substituted KNN sample. These studies are important for using substituted lead free KNN materials in various piezoelectric applications.