Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Ab-initio molecular dynamics based on non-local density functional procedure with Gaussian basis; study of structural and temperature behaviour of metallic clusters

An ab-initio molecular dynamics procedure without precalculation of the Born-Oppenheimer energy surface based on an iterative non-local density functional method employing Gaussian atomic basis has been developed. Analytical gradients are calculated and used for the propagation of nuclei. Sufficiently long trajectories can be calculated at an acceptable computational cost, allowing for analysis of dynamical behaviour of small metallic clusters. This is illustrated on an example of the Li₈ cluster. Temperature behaviour of different type of isomers has been investigated. Calculated power spectra allow to identify the presence of more than one isomeric forms along the given trajectories.     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.     

Observation of B-->eta'K* and evidence for B+-->eta'rho+

We present an observation of B-->eta'K*. The data sample corresponds to 232x10(6) BB[over ] pairs collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the Stanford Linear Accelerator Center. We measure the branching fractions (in units of 10(-6)) B(B(0)-->eta'K*0)=3.8+/-1.1+/-0.5 and B(B+-->eta'K*+)=4.9(1.7)(+1.9)+/-0.8, where the first error is statistical and the second systematic. A simultaneous fit results in the observation of B-->eta'K* with B(B-->eta'K*)=4.1(-0.9)(+1.0)+/-0.5. We also search for B-->eta'rho and eta'f(0)(980)(f(0)-->pi+pi-) with results and 90% confidence level upper limits B(B+-->eta'rho+)=8.7(-2.8-1.3)(+3.1+2.3) (<14), B(B(0)-->eta'rho0)<3.7, and B(B(0)-->eta'f(0)(980)(f(0)-->pi+pi-))<1.5. Charge asymmetries in the channels with significant yields are consistent with zero.     

The Origin of the Selectivity and Activity of Ruthenium‐Cluster Catalysts for Fuel‐Cell Feed‐Gas Purification: A Gas‐Phase Approach

Gas‐phase ruthenium clusters Ru_n⁺ (n=2–6) are employed as model systems to discover the origin of the outstanding performance of supported sub‐nanometer ruthenium particles in the catalytic CO methanation reaction with relevance to the hydrogen feed‐gas purification for advanced fuel‐cell applications. Using ion‐trap mass spectrometry in conjunction with first‐principles density functional theory calculations three fundamental properties of these clusters are identified which determine the selectivity and catalytic activity: high reactivity toward CO in contrast to inertness in the reaction with CO₂; promotion of cooperatively enhanced H₂ coadsorption and dissociation on pre‐formed ruthenium carbonyl clusters, that is, no CO poisoning occurs; and the presence of Ru‐atom sites with a low number of metal–metal bonds, which are particularly active for H₂ coadsorption and activation. Furthermore, comprehensive theoretical investigations provide mechanistic insight into the CO methanation reaction and discover a reaction route involving the formation of a formyl‐type intermediate.     

Coal analysis by diffuse reflectance near-infrared spectroscopy: Hierarchical cluster and linear discriminant analysis

An extensive study was carried out in coal samples coming from several origins trying to establish a relationship between nine coal properties (moisture (%), ash (%), volatile matter (%), fixed carbon (%), heating value (kcal/kg), carbon (%), hydrogen (%), nitrogen (%) and sulphur (%)) and the corresponding near-infrared spectral data. This research was developed by applying both quantitative (partial least squares regression, PLS) and qualitative multivariate analysis techniques (hierarchical cluster analysis, HCA; linear discriminant analysis, LDA), to determine a methodology able to estimate property values for a new coal sample. For that, it was necessary to define homogeneous clusters, whose calibration equations could be obtained with accuracy and precision levels comparable to those provided by commercial online analysers and, study the discrimination level between these groups of samples attending only to the instrumental variables. These two steps were performed in three different situations depending on the variables used for the pattern recognition: property values, spectral data (principal component analysis, PCA) or a combination of both. The results indicated that it was the last situation what offered the best results in both two steps previously described, with the added benefit of outlier detection and removal.     

A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane

The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies, consideration has been given principally to pure initial-value problems where the wave profile is imagined to be determined everywhere at a given instant of time and the corresponding solution models the further wave motion. The practical, quantitative use of the Korteweg-de Vries equation and its relatives does not always involve the pure initial-value problem. Instead, initial-boundary-value problems often come to the fore. A natural example arises when modeling the effect in a channel of a wave maker mounted at one end, or in modeling near-shore zone motions generated by waves propagating from deep water. Indeed, the initial-boundary-value problem

studied here arises naturally as a model whenever waves determined at an entry point propagate into a patch of a medium for which disturbances are governed approximately by the Korteweg-de Vries equation. The present essay improves upon earlier work on (0.1) by making use of modern methods for the study of nonlinear dispersive wave equations. Speaking technically, local well-posedness is obtained for initial data in the class for \frac34$"> and boundary data in , whereas global well-posedness is shown to hold for when , and for when . In addition, it is shown that the correspondence that associates to initial data and boundary data the unique solution of (0.1) is analytic. This implies, for example, that solutions may be approximated arbitrarily well by solving a finite number of linear problems.