Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics

Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme.     

Preparation and properties of sol-gel coating films

The present state of our knowledge on sol-gel coating films has been reviewed. A qualitative discussion is made on the limit of the film thickness which can be achieved in the sol-gel method and the factors affecting the film thickness. Considering that properties of the film are intimately related to the microstructure, types of microstructures accomplished by the sol-gel coating are introduced with examples.     

Trends in Preconcentration Procedures for Metal Determination Using Atomic Spectrometry Techniques

 Methods for metal preconcentration are often described in the literature. However, purposes are often different, depending on whether the methods are applied in environmental, clinical or technological fields. The respective method needs to be efficient, give high sensitivity, and ideally also is selective which is useful when used in combination with atomic spectroscopy. This review presents the actual tendencies in metal preconcentration using techniques such as Flame Atomic Absorption Spectrometry (FAAS), Electrothermal Atomic Absorption Spectrometry (ETAAS), Hydride Generation Atomic Absorption Spectrometry (HGAAS), Inductively Coupled Plasma Optical Emission Spectrometry (ICP OES) and Inductively Coupled Plasma Mass Spectrometry (ICP-MS). Procedures based on related to electrochemical, coprecipitation/precipitation, liquid–liquid and solid–liquid extraction and atom trapping mechanisms are presented. Correspondence: Department of Analytical Chemistry, Universidade Estadual de Campinas – UNICAMP, P.O. Box 6154, 13083-970 Campinas, Brazil. e-mail: zezzi@iqm.unicamp.br Received December 20, 2001; accepted October 11, 2002     

Lack of dissipativity is not symplecticness

We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = iy, real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.This research has been supported by project DGICYT PB92-254.     

Hexagonal Ferrites from Melts and Aqueous Solutions,Magnetic Recording Materials

Owing to their particular crystallographic properties, ferrimagnetic hexagonal ferrites exhibit a far greater coercive force than the conventional magnetic pigments. They therefore appear to be suitable for use in magnetic information storage procedures, some of which are novel and are at the development stage. Thus, magnetic tapes of high coercive force containing barium ferrite could be used as master tapes for copying magnetic information or for producing forgery-proof magnetic cards, if magnetic heads having high-order write fields were successfully developed. Moreover, platelet-like ferrite pigments in which the preferred direction of magnetic orientation is perpendicular to the plane of the platelet are of great interest for perpendicular magnetic recording. In this progress report, the crystal structures, magnetic characteristics of hexagonal ferrites, and chemical processes for their production are discussed. In particular, reactions in salt melts or under hydrothermal conditions produce finely divided pigments whose particles have a pronounced hexagonal, plate-like habit, a narrow particle size distribution, and advantageous magnetic properties. The magnetic properties of the pigments crystallized from salt melts may be adjusted by cation exchange.     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.     

Sample preparation for metalloprotein analysis: A case study using horse chestnuts

In the present work, 11 different procedures for protein and metalloprotein extraction from horse chestnuts (Aescullus hippocastanum L.) in natura were tested. After each extraction, total protein was determined and, after protein separation through sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE), those metals belonging to the protein structure were mapped by synchrotron radiation X-ray fluorescence (SRXRF). After mapping the elements (Cr, Fe and Mn) in the protein bands (ca. 33 and 23.7 kDa), their concentrations were determined using atomic absorption spectrometry (ET AAS).

Good results were obtained for protein extraction using a combination of grinding and sonication. However, this strategy was not suitable to preserve metal ions in the protein structure. In fact, there was 42% decrease on Mn concentration using this procedure, compared to that performed with sample agitation in water (taken as reference). On the other hand, when grinding and agitation with an extracting buffer was used, there was a 530% increase of Mn concentration, when compared to the reference procedure.

These results indicate agreement between metal identification and determination in proteins as well as the great influence of the extraction procedure (i.e., the sample preparation step) for preserving metals in the protein structures.     

“Comment” on the Reply to the Paper “On the Elber–Karplus Reaction Path-Following Method and Related Procedures”

The flaws in the Reply [1] to our paper [2] have been pointed out. Elber and Karplus (EK) have not disproved our irrefutable global statement that the energy average cannot be minimized which rebuts the theoretical background of EK-type calculations. Another statement of ours has shown that even a curve for which the average energy is locally minimal for all directional perturbations in the sense of classical variational calculus cannot be identical with the reaction path (RP) defined as a steepest descent path (SDP). EK found an error in the early preprint of our theoretical paper [3] and because of this error they qualified our correct variational statement as false for all the SDPs consisting of a straight line each. Mixing global and variational arguments, EK refuted our criticism in a logically incorrect manner. In this Comment we prove that both of our earlier statements invariably remain in force and the criticism included in those has been as well-established and solid as was before.     

Evaluation of the Coulomb energy in relativistic self-consistent-field theory

 Computational schemes are presented with which to evaluate the electrostatic Coulomb energy in relativistic molecular electronic structure calculations using a basis of four-component Dirac spinor amplitudes. We demonstrate that algorithms may be constructed and implemented which differ only in minor details from those in common use in nonrelativistic quantum chemistry, and that the four-component formalism is neither as complicated nor as expensive as has been suggested recently in the literature. Spherically symmetrical atomic basis sets are presented which indicate that accurate representations of the Coulomb energy may be obtained using modest expansions of the electronic density in a scalar auxiliary basis set of spherical harmonic Gaussian-type functions. Received: 15 April 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Study of cryostructurization of polymer systems

Summary A possibility of obtaining insoluble gels with the help of freezing-thawing procedures was demonstrated on an example of aqueous solutions of a thiol-containing poly(acryl amide) derivative. The gel formation was proved to occur as a result of oxidation of free SH groups of polymer chains by water-dissolved air oxygen.