Lattice Gas Hydrodynamics

Description

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 which capture the essentials of actual fluctuations in real fluids.

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.

'It is a pleasure to read the book. Equations, of which there are many, are carefully composed and easily deciphered. The text is well written and comprehensible, covering an immense amount of material. Advanced students of physics, mathematics and, probably, engineering, will find this book useful.' Henrik Jeldtoft Jensen, Times Higher Education Supplement 'This excellent book systematically develops lattice gas theory, starting from the microscopic evolution equations and properties of the underlying lattice ... For graduate students entering into the subject area of lattice gases or related methods this book would be an excellent starting point. But also for experts in related fields of fluid dynamics and statistical physics will this book serve as a very good introduction.' Eirik G. Flekkoy, European Journal of Mechanical B-Fluids '... this book is certainly an excellent introduction to the physics of lattice gas automata and to the hydrodynamic flows that take place in them.' Journal of Statistical Physics '... it may serve as a useful review of the attempts in the last fifteen years, 1986 to present, to apply cellular automata to simulate fluid dynamics.' Zentralblatt MATH