Cellular Automata and Modeling of Complex Physical Systems

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.

Autorentext
Dr. Nino Boccara is Professor Emeritus of Physics at the University of Illinois at Chicago, Professor Emeritus of Mathematics at the Ecole Supérieure de Physique et Chimie de la Ville de Paris, and Former Director of Research in Theoretical Physics at the CNRS.

Inhalt
I Information Theory and Statistical Physics.- Cellular Automata, Dynamics and Complexity.- Scaling Properties of a Family of Transformations Defined on Cellular Automaton Rules.- Entropy and Correlations in Dynamical Lattice Systems.- Cellular Automata Probability Measures.- Complex Computing with Cellular Automata.- Phase Transitions of Two-State Probabilistic Cellular Automata with One Absorbing Phase.- Simulating the Ising Model on a Cellular Automaton.- Domain Growth Kinetics: Microscopic Derivation of the t1/2 Law.- Critical Behavior in Cellular Automata Models of Growth.- II Lattice Gas Theory and Direct Applications.- Deterministic Cellular Automata with Diffusive Behavior.- Cellular Automata Approach to Diffusion Problems.- Long-Time Decay of Velocity Autocorrelation Function of Two- Dimensional Lattice Gas Cellular Automata.- Evidence for Lagrangian Tails in a Lattice Gas.- The Construction of Efficient Collision Tables for Fluid Flow Computations with Cellular Automata.- Lattice Boltzmann Computing on the IBM 3090 Vector Multiprocessor.- Bibliography on Lattice Gases and Related Topics.- III Modeling of Microscopic Physical Processes.- Multi-species Lattice-Gas Automata for Realistic Fluid Dynamics.- Immiscible Lattice Gases: New Results, New Models.- Lattice Gas Simulation of 2-D Viscous Fingering.- Dynamics of Colloidal Dispersions via Lattice-Gas Models of an Incompressible Fluid.- Strings: A Cellular Automata Model of Moving Objects.- Cellular Automata Approach to Reaction-Diffusion Systems.- Simulation of Surface Reactions in Heterogeneous Catalysis: Sequential and Parallel Aspects.- IV Complex Macroscopic Behavior, Turbulence.- Periodic Orbits in a Coupled Map Lattice Model.- Phase Transitions in Convection Experiments.- Using Coupled Map Lattices to Unveil Structures in the Space of Cellular Automata.- V Design of Special-Purpose Computers.- A Cellular Automata Machine.- Index of Contributors.