Harmonic Framework Research Articles

Quantum corrected cell model for an anharmonic generalized Lennard-Jones solid

A simple method is proposed to dispose the quantum effect and anharmonic effect at the same time. Considering the quantum effect is remarkable only at low temperature, and tends to zero at high temperature, the potential energy of an atom is expanded harmonically to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends to zero at low temperature, it was disposed by using a classical approximation. The universal formalism is applied to the generalized Lennard-Jones solid. The comparison shows that the results with and without anharmonic effect are in agreement with each other at some low temperature, to which the Einstein model is applicable. The results without anharmonic effect become divergent at slightly higher temperatures; however, the results including anharmonic effect are in good agreement with the experimental data of solid xenon. The method proposed in this paper can be extended to other potentials to develop practical molecular thermodynamic equations of state for solids.

The European Board of Surgery Qualification.

THE STATUTORY purpose of the European Union of Medical Specialists is the harmonization and improvement of the quality of medical specialist practice in the European Union (EU). Education is a key element in this field, and the European Union of Medical Specialists has been pursuing the formulation of a common policy in the field of training for many years. In 1993 the Charter on Training of Medical Specialists in the European Community was adopted by the Management Council of the European Union of Medical Specialists. The council consists of the delegates of the national specialist organizations in the EU. The charter forms a framework for harmonization of postgraduate specialist training in the EU in each specialty. It is in this context that the section of surgery of the European Union of Medical Specialists founded the European Board of Surgery (EBS) in 1994. The EBS, composed of representatives of the national

Fiscal federalism as a catalyst for policy development? In search of a framework for European direct tax harmonization

Abstract This article combines the literature on federalism and fiscal federalism with a policy perspective on the European direct tax policy process. The different ‘frames’ articulated by two distinct advocacy coalitions, an ‘intergovernmental’ coalition, centred around member states (politicians and public administrations), and a ‘supranational’ coalition, composed of the Commission, experts with policy‐relevant knowledge and corporate actors, are investigated. The author considers the extent to which adoption of federal strategies is a precondition for policy development in European Union corporate direct tax policy. The conclusion is that the prospects for corporate direct tax harmonization remain extremely constrained, but strategies based upon and sensitive to federal principles may reveal crucial resources for the supranational coalition.

Spherical harmonic representation of the gravitational potential of discrete spherical mass elements

SUMMARY We present expressions in a spherical harmonic framework for the gravitational potential of discrete point, surface, and volume mass elements located at any depth within a sphere. Through analysis of the spherical harmonic spectrum, insight is gained into the properties of the potentials arising from a variety of mass distributions. A point mass at the surface of a sphere displays the richest harmonic spectrum in all degrees; spectra become increasingly reddened as the source mass is distributed through larger elements of area or volume, or is located at greater depths below the surface of the reference sphere. The spectra of dipolar distributions, useful in representing compensated masses, are depressed, especially in the low harmonic degrees, relative to the spectra of monopole elements.

Closed-shell three-connected clusters: topological and group-theoretical aspects

Group-theoretical and topological arguments are presented within the tensor surface harmonic framework in order to predict polyhedral geometries for three-connected pseudo-spherical clusters, such as the C2n fullerenes. Topological and symmetry relationships between polyhedra, their duals, edge-figures and truncated derivatives are outlined. A general way of generating closed-shell three-connected cluster geometries, by polyhedral truncation, is presented. Finally, group-theoretical and topological aspects of alternancy in three-dimensional clusters are discussed.

Spherical harmonic representation of the gravitational potential of a point mass, a spherical cap, and a spherical rectangle

The gravitational potentials of a point mass, a spherical cap, and a spherical rectangle are presented in a spherical harmonic framework. The point mass displays the richest harmonic spectrum at all degrees. Equal mass distributed as a spherical cap or rectangle shows loss of representation at high degrees; the spectral weakening moves to progressively lower degrees as the mass is distributed more widely. The spectrum of a cap is less smooth than that of a similar rectangle with the same area. The characteristics of these three mass configurations are compared with those of other mass distributions and modeling techniques.

Crystal Dynamics of Rubidium. I. Measurements and Harmonic Analysis

Dispersion curves for lattice vibrations propagating along the five major symmetry directions in a single crystal of rubidium have been measured using inelastic neutron scattering. Care has been taken to identify spurious peaks in the neutron groups and to correct for effects of instrumental resolution. The results, at 12, 85, 120, and 205 °K, have been analyzed within the harmonic framework to yield atomic force constants, which were used to compute the phonon frequency distribution and frequency contours in the (100) and [Formula: see text] planes. A reciprocal space analysis has also been performed. The results are compared with previous measurements on the lighter alkali metals, and with the calculations of Toya and of Price, Singwi, and Tosi.

The music of a Lunda Kalendi

In the last issue of the Journal I gave some details of an eight-keyed Lunda Kalendi with the tuning and the harmonic framework of the music. Since then I have been able to write down the variations. I am greatly indebted to Mr. Noah Kambidima, the owner of this kalendi who has not only spent a great deal of time helping me to write down his music but also lent me his instrument to practise upon so that I could learn to play the music myself.