In this thesis, I have established that if the linear Boltzmann operator
has a discrete spectrum, then a hydrodynamic regime occurs
after a characteristic time 
in which the spatial moments of the
density have constant time derivatives. However, in time-of-flight
experiments, non-hydrodynamic and higher-order (non-Fickian) diffusion
effects are significant at times much greater that 
, unless
explicitly recognised and accounted for. In parallel plane steady state
Townsend experiments, there appears to be no such effects in the drift
region away from the electrodes. It would be desirable to establish a
non-hydrodynamic theory of the Townsend-Huxley experiment. The obvious way
to do this is to generalize the parallel plane theory to two dimensions.
The generalization of the saddle point method to higher dimensions goes
through in a fairly straight-forward manner [Malgrange
[1974], Hamm
[1977]]
, however the
asymptotic arguments at large z and 
are not easy to
generalize.
A complete theory of end-effects is not possible until boundary effects
have been analysed. This is a difficult problem that people have been
tackling for nearly 50 years with marginal success. Another problem this
thesis sheds a little light on is the form of the spectrum of the linear
Boltzmann operator. Since it is known that a discrete spectrum gives rise
to a hydrodynamic regime, runaway must occur only when the spectrum is
continuous. However, it is known that runaway occurs when 
converges [Cavalleri and Paveri-Fontana
[1972]]
, so there is a clear link
between 
and the spectrum.
The final portion of the thesis deals with the non-linear Burnett coefficients. General fluctuation expressions have been developed for these coefficients, and have been applied to some simple computational models of dense fluids. However, it is still too early to tell whether the non-linear Burnett coefficients actually exist in the thermodynamic limit.