Table of contents

Considerable publicity has accompanied Song and Richards' recent measurement of the rotation of the Earth's inner core and the observation of a reversal of the magnetic field in Glatzmaier and Roberts' computer model of the geodynamo. Additionally, the Galileo spacecraft has returned data suggesting the existence of magnetic fields in Io, Ganymede and perhaps Europa. These have given further impetus to the growing interest and activity in the problem of planetary magnetic-field generation and the core flows responsible for it. Here, the current understanding of this problem is reviewed in the light of many recent developments from theory, experiment and observation. The essential aspects of geodynamo theory are included, with further details being available in many recent reviews. The fundamental results of hydromagnetic flow in rapidly rotating systems are followed by a discussion of the latest thinking on the power source for the geodynamo. This replenishes the energy of some basic state but it may be instabilities of this basic state that result in the complex motions responsible for field generation. We discuss instabilities deriving their energy from buoyancy, the magnetic field and shear in the core flow. Our computational models can usually be run using an arbitrary choice of parameters. From this we learn of potential pitfalls when planetary values are used. In particular, the problems associated with the low values of the Ekman number E and Roberts number q are highlighted. Approaches to overcoming these are discussed and the resulting progress in producing full numerical dynamo models is reviewed. Finally, we discuss how the ideas and models developed primarily with the Earth in mind can be adapted and applied to the other planets and satellites known to have magnetic fields.

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.