The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Synthesis of tridimensional polymers by the copolymerization of phenylglycidylether with aromatic diglycidylethers

Copolymers from phenylglycidylether and several aromatic diglycidylethers are prepared using different ratios of difunctional comonomers and the AIP/ZnCl₂ initiator system. It is found that the percentage of incorporated comonomer depends on the nature of the aromatic moiety introduced. The copolymers are characterized by ¹³C-NMR spectroscopy and turn out to be completely regular and with a high degree of isotacticity (about 80%) that confirms the high degree of regio- and stereoselectivity of the initiator system used. The thermal characteristics of copolymer networks are investigated using differential scanning calorimetry and thermogravimetry. Two fusion endotherms are observed which vary with the degree of crosslinking. By thermogravimetric analyses the thermal stability is found to increase when the crosslinking degree does. © 1994 John Wiley & Sons, Inc.     

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.     

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.     

Electronic Structure of Rh(2)(&mgr;-CO)(CO)(2)(H(2)PCH(2)PH(2))(2). An Example of a Non-A-Frame Structure

Calculations based on density functional theory (DFT) and Hartree-Fock configuration interaction (HF-CI) methodology have been carried out to investigate the rhodium-rhodium coupling in Rh(2)(CO)(2)(dppm)(2), 1 (dppm = Ph(2)PCH(2)PPh(2)) and in Rh(2)(&mgr;-CO)(CO)(2)(dppm)(2), 2. DFT geometries, obtained with the Dgauss program, are in good agreement with those determined from X-ray, but HF geometries, calculated using the same basis sets, yield bond distances systematically too long. Calculations indicate that the rhodium atoms in 1 are linked by a single bond. The insertion of a semibridging carbonyl between the two metal atoms leads to a shortening of the rhodium-rhodium distance and also to a noticeable weakening of the metal-metal interaction. Both effects, and also the stabilization of the HOMO of 2, are related to an observed change from square planar to tetrahedral of the ligand environment of the Rh atom proximal to the inserted CO. Both MO analysis and bond characterization from the topology of the charge density confirm the existence of a bonding interaction between the semibridging carbonyl and the distal rhodium atom. The electronic structures of the dicationic complex [Rh(2)(CO)(3)(dppm)(2)](2+) and of the A-frame-like, isoelectronic system Rh(2)Br(2)(&mgr;-CO) (dppm)(2) are also discussed. The electron deformation density is derived from 2 by means of several methodological approaches, namely, HF, HF-CI, DFT, and DFT + gradient corrections. The HF deformation density obtained in the plane containing the metals and the three CO ligands is discussed, as well as the "correlation density" obtained from the difference maps DFT - HF and CI - HF.     

Exploring the self-assembly of dumbbell-shaped polyoxometalate hybrids,from molecular building units to nanostructured soft materials

The formation of hierarchical nanostructures using preformed dumbbell-like species made of covalent organic–inorganic polyoxometalate (POM)-based hybrids is herein described. In this system, the presence of charged subunits (POM, metal linkers, and counter ions) in the complex molecular architecture can drive their aggregation, which results from a competition between the solvation energy of the discrete species and intermolecular electrostatic interactions. We show that the nature of the POM and the charge of the metal linker are key parameters for the hierarchical nanoorganization. The experimental findings were corroborated with a computational investigation combining DFT and molecular dynamics simulation methods, which outlines the importance of solvation of the counter ion and POM/counter ion association in the aggregation process. The dumbbell-like species can also form gels, in the presence of a poorer solvent, displaying similar nanoorganization of the aggregates. We show that starting from the designed molecular building units whose internal charges can be controlled by redox trigger we can achieve their implementation into soft nanostructured materials through the control of their supramolecular organization.

The formation of hierarchical nanostructures using supramolecular dumbbell-like species made of organic–inorganic polyoxometalate-based hybrids is investigated by combination of SAXS and computational methods.     

Energy decomposition in molecular complexes: implications for the treatment of polarization in molecular simulations

This study examines the contribution of electrostatic and polarization to the interaction energy in a variety of molecular complexes. The results obtained from the Kitaura-Morokuma (KM) energy decomposition analysis at the HF/6-31G(d) level indicate that, for intermolecular distances around the equilibrium geometries, the polarization energy can be determined as the addition of the polarization energies of interacting blocks, as the mixed polarization term is typically negligible. Comparison of KM and QM/MM results shows that the electrostatic energy determined in the KM method is underestimated (in absolute value) by QM/MM methods. The reason of such underestimation can be attributed to the simplified representation of treating the interaction between overlapping charge distribution by the interaction of a QM molecule with a set of point charges. Nevertheless, the polarization energies calculated by KM and QM/MM methods are in close agreement. Finally, a consistent, automated strategy to derive charge distributions that include implicitly polarization effects in pairwise, additive force fields is presented. The strategy relies in the simultaneous fitting of electrostatic and polarization energies computed by placing a suitable perturbing particle at selected points around the molecule. The suitability of these charges to describe molecular interactions is discussed.