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On Various Questions in Nonequilibrium Statistical Mechanics Relating to Swarms and Fluid Flow

Russell Kim Standish

Chapters 1 and 5 review the field to set the context of the work. Except where stated, all other chapters report my own original work. Russell Standish


I wish to thank Denis Evans for the supervision of the work in this thesis, Brian Robson for his continuing support, Robert Robson for his encouragement and advice, Leo Brewin for his comprehensive knowledge of the MSP operating system, and Bill Alford for his advice on TeX related matters, without which this thesis would have been much more difficult to write. I would also like to thank all the staff and students of the Department of Theoretical Physics, who have over the years provided much stimulating conversation and ideas. Last, but not least, I would like to thank my dearest friend Kim Crichton for her unwavering support throughout this thesis.

Much of the computation described here was performed on the Fujitsu VP100 of the Australian National University Supercomputer Facility.

I gratefully acknowledge the financial assistance of a Commonwealth Postgraduate Research Award.

This thesis has been typeset by the author using LaTeX, a macro package written by Leslie Lamport for Donald Knuth's TeX typesetting system. The source was typed on a MacIntosh, using a macro package written by the author for Matthias Aebi's MEdit text editor. Andrew Trevorrow's OzTeX, a public domain MacIntosh version of LaTeX, was used to preview the document whereas the final version was produced using a Vax. The figures were produced using a picture macro package written by Brendan McKay, the Vax installation of which was done by Bill Alford. Figures gif to gif were produced by Arnstein Pritz's FPLoT program, and the plates produced using Uniras.


This thesis is based in part on the following publications:

Standish RK (1987),
``Nonhydrodynamic Contributions to End Effects in Time of Flight Swarm experiments'', Aust J Phys, 40,519-525

Standish RK and Kumar K (1987),
``End Effects in Time of Flight Experiments'', proc. 5th Intl Swarm Seminar, Birmingham, p104-107

Evans D and Standish RK (1990),
"Non-equilibrium Statistical Mechanics and Molecular Dynamics Calculations" in Computer Modelling of Fluids, Polymers and Solids CRA Catlow et al.(eds.) p125-154

Standish RK (1989)
``Motion of Charged Particles in a Homogeneous Reacting Medium with a One-dimensional Geometry'', Aust J Phys, 42, 223-232

Standish RK and Evans DJ (1990),
``On the Nonlinear Burnett Coefficients'', to be published in Phys. Rev. A.


The cutting edge of nonequilibrium statistical mechanics has for some time now been concerned with the question of relaxing the approximations used to generate the hydrodynamic equations. In particular, we are interested in form and effects of the Burnett, or higher order transport coefficients, and also in short timescale effects. The motivation for studying these phenomena in swarms comes from the desire for accurate transport data, which is approaching the level of accuracy where these effects are significant. The motivation for studying these effects in high density fluids comes from understanding the behaviour of non-Newtonian fluids.

In this thesis, the theory of nonhydrodynamic phenomena is developed within the framework of the linear Boltzmann equation, and applied to several experimental configurations used in swarm physics. The latter part of the thesis develops fluctuation expressions for the nonlinear Burnett coefficients similar to the Green-Kubo expressions used for linear transport coefficients. A numerical simulation of a simple fluid is used to test these expressions.

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