Cellular Automata and Modeling of Complex Physical Systems

1. Front Matter

   Pages I-IX

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2. Introduction

   1. Introduction

      • P. Manneville

      Pages 1-7

3. Information Theory and Statistical Physics

   1. Front Matter

      Pages 9-9

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   2. Cellular Automata, Dynamics and Complexity

      • E. Goles

      Pages 10-20

   3. Scaling Properties of a Family of Transformations Defined on Cellular Automaton Rules

      • N. Boccara

      Pages 21-26

   4. Entropy and Correlations in Dynamical Lattice Systems

      • K. Lindgren

      Pages 27-40

   5. Cellular Automata Probability Measures

      • M. G. Nordahl

      Pages 41-56

   6. Complex Computing with Cellular Automata

      • J. Signorini

      Pages 57-72

   7. Phase Transitions of Two-State Probabilistic Cellular Automata with One Absorbing Phase

      • R. Bidaux, N. Boccara, H. Chaté

      Pages 73-81

   8. Simulating the Ising Model on a Cellular Automaton

      • O. Parodi, H. Ottavi

      Pages 82-97

   9. Domain Growth Kinetics: Microscopic Derivation of the t½ Law

      • E. Domany, D. Kandel

      Pages 98-111

   10. Critical Behavior in Cellular Automata Models of Growth

       • J. Myczkowski, G. Vichniac

       Pages 112-115

4. Lattice Gas Theory and Direct Applications

   1. Front Matter

      Pages 117-117

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   2. Deterministic Cellular Automata with Diffusive Behavior

      • C. D. Levermore, B. M. Boghosian

      Pages 118-129

   3. Cellular Automata Approach to Diffusion Problems

      • B. Chopard, M. Droz

      Pages 130-143

   4. Long-Time Decay of Velocity Autocorrelation Function of Two-Dimensional Lattice Gas Cellular Automata

      • D. Frenkel

      Pages 144-154

   5. Evidence for Lagrangian Tails in a Lattice Gas

      • P.-M. Binder

      Pages 155-160

   6. The Construction of Efficient Collision Tables for Fluid Flow Computations with Cellular Automata

      • J. A. Somers, P. C. Rem

      Pages 161-177

   7. Lattice Boltzmann Computing on the IBM 3090 Vector Multiprocessor

      • S. Succi, R. Benzi, E. Foti, F. Higuera, F. Szelényi

      Pages 178-185

   8. Bibliography on Lattice Gases and Related Topics

      • D. d’Humières

      Pages 186-204

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

• Computer Science
• Diffusion
• catalysis
• colloid
• convection
• dynamical systems
• entropy
• fluid dynamics
• kinetics
• statistical physics
• structure
• turbulence
• fluid- and aerodynamics

• Service de Physique du Solide et de Résonance Magnétique, Centre d’Etudes Nucléaires de Saclay, Institut de Recherche Fondamentale, Gif-sur-Yvette Cedex, France

  Paul Manneville, Roger Bidaux

• Centre de Physique, Université Scientifique et Médicale, Les Houches, France

  Nino Boccara

• Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, USA

  Gérard Y. Vichniac

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