Generalized quasilinearization method for a second order ordinary differential equation with Dirichlet boundary conditions

We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.

     

A flux‐splitting solver for shallow water equations with source terms

This paper introduces a stable flux‐splitting solver for one‐dimensional (1D) shallow water equations. This solver is specifically designed to satisfy a strengthened consistency condition for stationary solutions that ensures the stability and accuracy of the scheme. It applies to channels with variable depth and width, including terms modelling friction at bottom and vertical walls. Some numerical tests by comparison to both analytical solutions and experimental measurements show the good performances of the scheme. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact and approximate forms of the kinetic energy functional<Emphasis Type="Italic"> T</Emphasis><Subscript>s</Subscript>[ρ] for molecules obtained via local-scaling transformations

By means of a constructive procedure based on local-scaling transformations, we have obtained the following exact form for the noninteractive kinetic energy functional of general molecular systems: where (r) is the local-scaling transformation function, T _W[] is the von Weiszäcker term and ^l _N (r _l ) and ^l _N (r _l ) are the radial and angular enhancement factors, respectively, within an atomic domain _I. The terms ^C _N (r _l ) and ^C _N (r _l ) (where C stands for complement of I) contain all contributions to the radial and angular enhancement factors within _I coming from the tails of functions centered on nuclei outside _I. Also, in the context of an atoms-in-a-molecule approach, we discuss the construction of approximations to the kinetic energy enhancement factors appearing in the previous expression for T _s[]. Acknowledgement.The authors gratefully acknowledge support of this work by FONACIT of Venezuela through Group Project No. G-97000741.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002)     

A classical dynamics method for H2 diffraction from metal surfaces

We present a discretization method that allows one to interpret measurements on diffraction of diatomic molecules from solid surfaces using six-dimensional (6D) classical trajectory calculations. It has been applied to the D2NiAl(110) and H2Pd(111) systems (which are models for activated and nonactivated dissociative chemisorption, respectively) using realistic potential energy surfaces obtained from first principles. Comparisons with experimental results and 6D quantum dynamical calculations show that, in general, the method is able to predict the relative intensity of the most important diffraction peaks. We therefore conclude that classical mechanics can be an efficient guide for experimentalists in the search for the most significant diffraction channels.     

A theoretical NMR study of polymorphism in crystal structures of azoles and benzazoles

The NMR chemical shifts of two azoles and one benzazole whose crystal structures present polymorphism have been computed using the GIPAW approach. ¹⁵N and ¹³C nuclei have been studied. Statistical analysis of the computed ¹³C and ¹⁵N chemical shifts indicates that the GIPAW chemical shifts reproduce with a high degree of accuracy those experimentally reported. This methodology can be used to identify other polymorphic crystal structures.     

Anti-periodic solutions for evolution equations associated with maximal monotone mappings

In this work, we study the anti-periodic problem for a nonlinear evolution inclusion where the nonlinear part is an odd maximal monotone mapping and the forcing term is an anti-periodic mapping. Several existence results are obtained under suitable conditions. An example is presented to illustrate the results.