This is a thesis in two parts, both of which fit firmly in the
framework of non-equilibrium statistical mechanics. When
referring to atoms or molecules at sufficiently low density that
collisions in the system are dominated by few body interactions, so that the
mesoscopic picture applies (see page 
) this is
sometimes
called kinetic theory.
The first part of the thesis relates to the kinetic theory of
swarms. A swarm is a collection of charged particles
moving
through a neutral background gas. Typically, these may be
electrons inside a discharge tube, or within a gaseous state
laser. The prime application of the work here are swarm
experiments, whereby atomic collision cross sections
are obtained
by using kinetic theory to calculate various macroscopic
properties from a ``trial'' cross-section, which can in turn be
compared with experimental measurement. This is clearly an
ambiguous process, but experiments can be done with sufficient precision
to extract reasonable cross-sections. The main advantage
of this method over its main competitor, namely beam
experiments
, is that the low
energy regime can be studied, where beams are difficult to focus.
Recent developments in the beam technique have blurred the
distinction between these two methods, particularly in electrons,
however, swarm methods still have a rôle to play with
measurements involving more complex ions and molecules.
The second part of this thesis relates to fluid flow. Here the
interest is in understanding how fluids respond to a stress which
caused the fluid to depart from equilibrium. For instance, we may
wish to understand the behaviour of oil in a bearing, where oil
is constantly shearing due to the influence of two surfaces
moving past each other. Here, the idea would be to take data on
the way that the molecules interact,
and predict how the fluid would behave under these situations.
Both the theories of swarms and of fluid flow have a common origin within the atomic theory of matter. However, at an early stage, the theories diverge. Swarms are generally so dilute that the interactions between the charged particles are negligible in comparison with interactions between charged and neutral particles. The resulting theory is therefore linear in regard to the density of the charged particles. By contrast, in fluid flow the interactions involve many particles, and consequently the theory is highly non-linear in the density.