Table of contents

This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass–spring, modal, wave digital, finite difference, digital waveguide and source–filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.

Francium is a candidate for atomic parity non-conservation (PNC) experiments. Its simple atomic structure has been the subject of extensive experimental research facilitated by the ability to trap and cool significant numbers of atoms. The studies include the location of energy levels, their hyperfine splittings and their lifetime. All of these levels are close to the ground state. The results show a remarkable agreement with calculated ab initio properties to a degree that is comparable with other stable alkali atoms. The quantitative understanding of francium has made possible the exploration of avenues for a PNC measurement in the optical and the microwave regimes. These precision experiments have the potential to enhance our understanding of the weak coupling constants between electrons and nucleons, as well as between nucleons.

We review the observations of extrasolar planets, ongoing developments in theories of planet formation, orbital migration and the evolution of multiplanet systems.

The history of electron emission is reviewed from a standpoint of the work function that determines the electron emission capability and of applications in the fields of scientific instruments and displays. For years, in thermionic emission, a great deal of effort has been devoted to the search for low work function materials with high melting temperature, while reduction of the local change in time of the work function rather than the work function itself has been the main issue of field emission investigations. High brightness and long life are the central targets of emission material investigations for scientific instrument applications, while high current density and low power consumption are the guiding principles for display applications.

In most of the present day industries, thermionic emission materials are exclusively used in such fields requiring high current and high reliability as cathode ray tubes, transmission and receiving tubes, x-ray sources and various electron beam machines. Field electron emission sources, however, since applied to high resolution electron microscopes in the 1970s have recently become dominant in research and development in the fields of scientific instruments as well as in the fields of various electron tubes and beam machines.

The main issue in this report is to analyse the work function on the atomic scale and thereby to understand the fundamental physics behind the work function, the change in time of the local work function leading to field emission current fluctuation and the relationship between microscopic (on atomic scale) and macroscopic work functions.

Our attempt is presented here, where the work function on the atomic scale is measured by utilizing a scanning tunnelling microscopy technique, and it is made clear how far the local work function extends its influence over neighbouring sites. As a result, a simple relationship is established between microscopic and macroscopic work functions.

The techniques of neutron diffraction and x-ray diffraction, as applied to structural studies of liquids and glasses, are reviewed. Emphasis is placed on the explanation and discussion of the experimental techniques and data analysis methods, as illustrated by the results of representative experiments. The disordered, isotropic nature of the structure of liquids and glasses leads to special considerations and certain difficulties when neutron and x-ray diffraction techniques are applied, especially when used in combination on the same system. Recent progress in experimental technique, as well as in data analysis and computer simulation, has motivated the writing of this review.