Table of contents

This review is concerned with modern theoretical approaches to turbulence, in which the problem can be seen as a branch of statistical field theory, and where the treatment has been strongly influenced by analogies with the quantum many-body problem. The dominant themes treated are the development (since the 1950s) of renormalized perturbation theories (RPT) and, more recently, of renormalization group (RG) methods. As fluid dynamics is rarely part of the physics curriculum, in section 1 we introduce some background concepts in fluid dynamics, followed by a skeleton treatment of the phenomenology of turbulence in section 2, taking flow through a straight pipe or a plane channel as a representative example. In section 3, the general statistical formulation of the problem is given, leading to a moment closure problem, which is analogous to the well known BBGKY hierarchy, and to the Kolmogorov -5/3 power law, which is a consequence of dimensional analysis. In section 4, we show how RPT have been used to tackle the moment closure problem, distinguishing between those which are compatible with the Kolmogorov spectrum and those which are not. In section 5, we discuss the use of RG to reduce the number of degrees of freedom in the numerical simulation of the turbulent equations of motion, while giving a clear statement of the technical problems which lie in the way of doing this. Lastly, the theories are discussed in section 6, in terms of their ability to meet the stated goals, as assessed by numerical computation and comparison with experiment.

Even if neutrino masses are unknown, we know neutrinos are much lighter than the other known fermions, and we do not have a good explanation for it. The explanation given in the Standard Model of elementary particles is that neutrinos are exactly massless. However, this is a rather ad hoc proposition, since the masslessness of the neutrinos is not ensured by any basic principle. Non-zero neutrino masses arise in many extensions of the Standard Model. Massive neutrinos and their associated properties, such as the Dirac or Majorana character of neutrinos, their mixings, lifetimes and magnetic or electric moments, may have very important consequences in astrophysics, cosmology and particle physics. Here we explore these consequences and the constraints they already impose on neutrino properties, as well as the large body of experimental and observational efforts currently devoted to elucidate the mystery of neutrino masses. Several hints for non-zero masses in solar and atmospheric neutrinos, which will be confirmed or rejected in the near future, make this field of research particularly exciting at present.

Advances in ion-source, accelerator and beam-cooling technology have made it possible to produce high-quality beams of atomic ions in arbitrary charged states as well as molecular and cluster ions that are internally cold. Ion beams of low emittance and narrow momentum spread are obtained in a new generation of ion storage-cooler rings dedicated to atomic and molecular physics. The long storage times ( approximately 5<or approximately= tau <or approximately=days) allow the study of very slow processes occurring in charged (positive and negative) atoms, molecules and clusters. Interactions of ions with electrons and/or photons can be studied by merging the stored ion beam with electron and laser beams. The physics of storage rings spans particles having a charge-to-mass ratio ranging from <0.002(C₆₀⁺ and C₇₀⁺) to 0.4-1.0 (H⁺, D⁺, He²⁺, ..., U⁹²⁺) and collision processes ranging from <1 MeV to approximately 70 GeV. It incorporates, in addition to atomic and molecular physics, tests of fundamental physics theories and atomic physics bordering on nuclear and chemical physics. This exciting development concerning ion storage rings has taken place within the last five to six years.

An overview is given of the possibilities and limitations of secondary ion mass spectrometry as an analytical tool in the investigation of near-perfect, i.e. almost atomically sharp, dopant and impurity distributions. The operating principles of the technique and the various quantification schemes are briefly presented. The most elaborate discussion pertains to the factors that determine the attainable depth resolution and what can be done to improve things, both from an experimental and from a theoretical point of view. Emphasis is placed on semiconductors and other brittle target materials, but the implications for metals are indicated.