The physics of swarms and some basic questions of kinetic theory

This report provides an introduction to the physics of swarms to those interested in kinetic theory. After a brief historical sketch the principles of experiments and their phenomenological analysis are discussed. The relation of this analysis to kinetic theory and the potential of the experiments for studying the nature of hydrodynamic regime and the nonhydrodynamic effects is pointed out. Recent advances in the kinetic theory of swarms in free space are surveyed. They include results such as the generalised Einstein relations and others from the momentum transfer theory, which point to some interesting properties of the many averages that occur in kinetic theory and their relation to thermodynamics, as well as the more technical advances in analysing the structure of the collision operator and solutions of kinetic equations which have lead to very precise calculations of the transport coefficients. The use of theory and experiment in precise determination of cross-sections, potentials and reaction rates is illustrated. Observations showing the effects of finite enclosures are summarised and a theory of swarms in a finite enclosure is outlined. The implications of the subject for kinetic theory are discussed.