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Conclusion

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.



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Russell Standish
Thu May 18 11:43:52 EST 1995