Lattice Gas Hydrodynamics

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Cambridge University Press, Sep 15, 2005 - Mathematics - 312 pages
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Lattice gas hydrodynamics describes the approach to fluid dynamics using a micro-world constructed as an automaton universe, where the microscopic dynamics is based not on a description of interacting particles, but on the laws of symmetry and invariance of macroscopic physics. We imagine point-like particles residing on a regular lattice, where they move from node to node and undergo collisions when their trajectories meet. If the collisions occur according to some simple logical rules, and if the lattice has the proper symmetry, then the automaton shows global behavior very similar to that of real fluids. This book carries two important messages. First, it shows how an automaton universe with simple microscopic dynamics--the lattice gas--can exhibit macroscopic behavior in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations that capture the essentials of actual fluctuations in real fluids.
 

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Contents

general formalism
10
various examples
34
Chapter 4 Equilibrium statistical mechanics
68
ChapmanEnskog method
109
Chapter 6 Linearized hydrodynamics
137
Chapter 7 Hydrodynamic fluctuations
153
projectors approach
183
Chapter 9 Hydrodynamic regimes
199
Chapter 10 Lattice gas simulations
207
Chapter 11 Guide for further reading
233
Appendix Mathematical details
250
References
275
Author index
281
Subject index
285
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About the author (2005)

Jean Pierre Boon has made important contributions to many areas of nonlinear dynamics and statistical mechanics. These cover at least three areas of research: time-correlation-function descriptions of liquid-state dynamics and transport, light-scattering studies, and cellular automaton theory and simulations. These subjects have been described in both Lattice Gas Hydrodynamics and Molecular Hydrodynamics (with Sidney Yip), both of which are definitive contributions to their respective fields. With his far-sighted appreciation of the complex nature of the physics of fluids and the theoretical and experimental techniques for their study, Jean Pierre Boon anticipated many years ago the approach now widely known as multiscale modelling, which aims to bridge the length- and time-scale gaps between the microscopic and the macroscopic domains.

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