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Pattern Formation and Lattice gas Automata
Edited by: Anna T. Lawniczak, University of Guelph, ON, Canada, and Raymond Kapral, University of Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
1996; 346 pp; hardcover
Volume: 6
ISBN-10: 0-8218-0258-5
ISBN-13: 978-0-8218-0258-8
List Price: US$126
Member Price: US$100.80
Order Code: FIC/6
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This book is the Proceedings of The Fields Institute Conference/NATO Advanced Research Workshop held in June 1993. The articles review the diverse recent progress in the theory and development of lattice-gas and lattice Boltzmann methods and their applications to hydrodynamics, multi-phase flows, flows through porous media, reaction-diffusion systems, pattern formation phenomena, and phase separation processes. Discussed here are various aspects of the statistical analysis of these methods, with emphasis on fluctuations and correlations, as well as computational prospects including development of dedicated hardware.


  • up-to-date articles covering theory and applications
  • interdisciplinary approach, which includes mathematics, physics, chemistry, and geophysics
  • abstracts of papers published from 1992 through 1995

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Research mathematicians, physicists, chemists, and engineers in nonequilibrium statistical mechanics, fluid dynamics, pattern formation, stochastic processes, partial differential equations, and numerical methods.

Table of Contents

  • C. Appert, V. Pot, and S. Zaleski -- Liquid-gas models on 2D and 3D lattices
  • B. M. Boghosian and W. Taylor -- Renormalization of lattice gas transport coefficients
  • I. Bonzani, M. A. Cimaschi, and R. Monaco -- The discrete Boltzmann equation for gases with bimolecular or dissociation-recombination reactions
  • E. G. Cohen and F. Wang -- Diffusion and propagation in Lorentz lattice gases
  • S. P. Dawson, B. Hasslacher, and J. E. Pearson -- Lattice gas simulations of replicating domains
  • A. DeMasi -- Spinodal decomposition and interface dynamics for Glauber evolution with Kac potential
  • K. Diemer, A. T. Lawniczak, and R. Kapral -- Fluctuations and chemical waves in a bistable reacting system
  • J. W. Dufty and M. H. Ernst -- Lattice Boltzmann-Langevin equations
  • M. H. Ernst and H. J. Bussemaker -- Instabilities and patterns
  • F. Hayot and L. Wagner -- Vortex street and Lévy walks
  • M. Hénon -- Lattice gases without semi-detailed balance
  • S. Hou, J. D. Sterling, S. Chen, and G. D. Doolen -- A latice Boltzmann subgrid model for high Reynolds number flows
  • N. Margolus -- CAM-8: A computer architecture based on cellular automata
  • E. Presutti -- Critical fluctuations in a spin system
  • Y. H. Qian, S. Succi, F. Massaiol, and S. A. Orszag -- A benchmark for lattice BGK model: Flow over a backward-facing step
  • R. Rechtman and A. Salcido -- Lattice gas self diffusion in random porous media
  • O. Tribel and J. P. Boon -- Lévy laws for lattice gas automata
  • J. R. Weimar and J. P. Boon -- New class of cellular automata for reaction-diffusion systems applied to the CIMA reaction
  • X.-G. Wu and R. Kapral -- Lattice-gas cellular automaton model for one-mode lasers
  • J. Yepez -- A lattice-gas with long-range interactions coupled to a heat bath
  • G. D. Doolen -- Abstracts of Lattice gas/lattice Boltzmann papers, 1992-1995
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