Cellular Automata and Modeling of Complex Physical Systems: Proceedings of the Winter School, Les Houches, France, February 21–28, 1989 PDF
Preview Cellular Automata and Modeling of Complex Physical Systems: Proceedings of the Winter School, Les Houches, France, February 21–28, 1989
Springer Proceedings in Physics 46 Springer Proceedings in Physics Managing Editor: H. K. V. Lotsch Volume 30 Short-Wavelength Lasers and Their Applications Editor: C. Yamanaka Volume 31 Quantum String Theory Editors: N. Kawamoto and T. Kugo Volume 32 Universalities in Condensed Matter Editors: RJullien, L. Peliti, R Rammal, and N. Boccara Volume 33 Computer Simulation Studies in Condensed Matter Physics: Recent Developments Editors: D. P. Landau, K. K. Mon, and H.-B. Schuttler Volume 34 Amorphous and Crystalline Silicon Carbide and Related Materials Editors: G. L. Harris and C. Y.-W. Yang Volume 35 Polycrystalline Semiconductors: Grain Boundaries and Interfaces Editors: H. J. MOiler, H. P. Strunk, and J. H. Werner Volume 36 Nonlinear Optics of Organics and Semiconductors Editor: T. Kobayashi Volume 37 Dynamics of Disordered Materials Editors: D. Richter, A. J. Dianoux, W. Petry, and J. Teixeira Volume 38 Electroluminescence Editors: S. Shionoya and H. Kobayashi Volume 39 Disorder and Nonlinearity Editors: A. R Bishop, D. K. Campbell, and S. Pnevmatikos Volume 40 Static and Dynamic Properties of Liquids Editors: M. Davidovic and A. K. Soper Volume 41 Quantum Optics V Editors: J. D. Harvey and D. F. Walls Volume 42 Molecular Basis of Polymer Networks Editors: A. Baumgartner and C. E. Picot Volume 43 Amorphous and Crystalline Silicon Carbide II: Recent Developments Editors: M. M. Rahman, C. Y.-W. Yang, and G. L. Harris Volume 44 Optical Fiber Sensors Editors: H. J. Arditty, J. P. Dakin, and R. Th. Kersten Volume 45 Computer Simulation Studies in Condensed Matter Physics II: New Directions Editors: D. P. Landau, K. K. Mon, and H.-B. Schuttler Volume 46 Cellular Automata and Modeling of Complex Physical Systems Editors: P. Manneville, N. Boccara, G. Y. Vichniac, and R Bidaux Volumes 1 - 29 are listed on the back inside cover Cellular Automata and Modeling of Complex Physical Systems Proceedings of the Winter School, Les Houches, France, February 21 - 28, 1989 Editors: P. Manneville, N. Boccara, G. Y. Vichniac, and R. Bidaux With 125 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Dr. Paul Manneville Institut de Recherche Fondamentale, Service de Physique du Solide et de Resonance Magnetique, Centre d'Etudes Nucleaires de Sac lay, F-91191 Gif-sur-Yvette Cedex, France Professor Nino Boccara Centre de Physique, Universite Scientifique et Medicale, F-74310 Les Houches, France Dr. Gerard Y. Vichniac Plasma Fusion Center, Massachusetts Institute ofTechnology, Cambridge, MA 02139, USA Dr. Roger Bidaux Institut de Recherche Fondamentale, Service de Physique du Solide et de Resonance Magnetique, Centre d'Etudes Nucleaires de Saclay, F-91191 Gif-sur-Yvette Cedex, France ISBN-13: 978-3-642-75261-2 e-ISBN-13: 978-3-642-75259-9 001: 10.1007/978-3-642-75259-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions ofthe German Copyright Law of September 9,1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1989 Softcover reprint of the hardcover 1s t edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and there fore free for general use. Printing: Weihert-Druck GmbH, 0-6100 Darmstadt Binding: J. ScMffer & Co. KG., 0-6718 GrOnstadt 2154/3150-543210 - Printed on acid-free paper Preface Les Houches This volume contains the proceedings of an International Winter Workshop on Cellular Automata and the Modeling of Complex Physical Systems held at the "Centre de Physique des Houches", February 21-28, 1989. The topics treated included general aspects of the theory of cellular automata and its relation with statistical physics, lattice gas theory and applications; the modeling of microscopic physical processes and complex macroscopic behavior; and the design of special-purpose computers. Critical reviews of earlier work and recent achievements in these fields were presented by about 30 participants coming from different disciplines: mathematics, physics, information theory, computer science, etc. They should be thanked for having maintained a particularly stimulating atmosphere both during and between the sessions. The workshop was supported by: - the Centre de Physique des Houches and the Universite Scientifique et Medicale de Grenoble, - the Centre National de la Recherche Scientifique (PICS program), a - the Institut de Recherche F ondamentale of the Commissariat l' Energie Atom- ique, - the Direction des Recherches et Etudes Techniques of the Ministere de la Defense, - the Ministere de la Recherche et de la Technologie. Saclay, France P. Manneville September 1989 N. Boccara G.Y. Vichniac R. Bidaux v Contents Introduction By P. Manneville Part I Information Theory and Statistical Physics Cellular Automata, Dynamics and Complexity By E. Goles (With 10 Figures) ............................. 10 Scaling Properties of a Family of Transformations Defined on Cellular Automaton Rules By N. Boccara (With 4 Figures) ............................ 21 Entropy and Correlations in Dynamical Lattice Systems By K. Lindgren (With 8 Figures) ........................... 27 Cellular Automata Probability Measures By M.G. Nordahl (With 10 Figures) ......................... 41 Complex Computing with Cellular Automata By J. Signorini (With 3 Figures) ............................ 57 Phase Transitions of Two-State Probabilistic Cellular Automata with One Absorbing Phase By R. Bidaux, N. Boccara, and H. Chate (With 3 Figures) .......... 73 Simulating the Ising Model on a Cellular Automaton By O. Parodi and H. Ottavi (With 3 Figures) ................... 82 Domain Growth Kinetics: Microscopic Derivation of the tl/2 Law By E. Domany and D. Kandel (With 8 Figures) ................. 98 Critical Behavior in Cellular Automata Models of Growth By J. Myczkowski and G. Vichniac (With 3 Figures) .............. 112 Part II Lattice Gas Theory and Direct Applications Deterministic Cellular Automata with Diffusive Behavior By C.D. Levermore and B.M. Boghosian .... . . . . . . . . . . . . . . . . .. 118 Cellular Automata Approach to Diffusion Problems By B. Chopard and M. Droz (With 6 Figures) .................. 130 VII Long-Time Decay of Velocity Autocorrelation Function of Two Dimensional Lattice Gas Cellular Automata By D. Frenkel (With 5 Figures) ............................ 144 Evidence for Lagrangian Tails in a Lattice Gas By P.-M. Binder (With 1 Figure) ........................... 155 The Construction of Efficient Collision Tables for Fluid Flow Computations with Cellular Automata By J.A. Somers and P.e. Rem (With 6 Figures) ................. 161 Lattice Boltzmann Computing on the mM 3090 Vector Multiprocessor By S. Succi, R. Benzi, E. Foti, F. Higuera, and F. Szelenyi (With 3 Figures) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178 Bibliography on Lattice Gases and Related Topics By D. d'Humieres ..................................... 186 Part ill Modeling of Microscopic Physical Processes Multi-species Lattice-Gas Automata for Realistic Fluid Dynamics By K. Molvig, P. Donis, R. Miller, J. Myczkowski, and G. Vichniac (With 8 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 206 Immiscible Lattice Gases: New Results, New Models By D.H. Rothman (With 4 Figures) .. . . . . . . . . . . . . . . . . . . . . . . .. 232 Lattice Gas Simulation of 2-D Viscous Fingering By M. Bonetti, A. Noullez, and J.-P. Boon (With 1 Figure) 239 Dynamics of Colloidal Dispersions via Lattice-Gas Models of an Incompressible Fluid By A.J.C. Ladd and D. Frenkel ............................ 242 Strings: A Cellular Automata Model of Moving Objects By B. Chopard (With 7 Figures) ............................ 246 Cellular Automata Approach to Reaction-Diffusion Systems By D. Dab and J.-P. Boon (With 8 Figures) .................... 257 Simulation of Surface Reactions in Heterogeneous Catalysis: Sequential and Parallel Aspects By B. Sente, M. Dumont, and P. Dufour ...................... 274 Part IV Complex Macroscopic Behavior, Turbulence Periodic Orbits in a Coupled Map Lattice Model By F. Bagnoli, S. Isola, R. Livi, G. Martlnez-Mekler, and S. Ruffo (With 4 Figures) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 282 Phase Transitions in Convection Experiments By F. Bagnoli, S. Ciliberto, R. Livi, and S. Ruffo (With 3 Figures) 291 VIII Using Coupled Map Lattices to Unveil Structures in the Space of Cellular Automata By H. Chate and P. Manneville (With 6 Figures) ................ 298 Part V Design of Special-Purpose Computers A Cellular Automata Machine By F. Bagnoli and A. Francescato (With 11 Figures) 312 Index of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 319 IX Introduction P. Manneville Institut de Recherche Fondamentale, DPh-G/PSRM, CEN Saclay, F-91191 Gif-sur-Yvette Cedex, France Invented in 1948 by von Neumann and Ulam, cellular automata (CA) are fully discrete dynamical systems with their dynamical variables defined at the nodes of a lattice and taking their values in a finite set. The dynamics results from the synchronous application of a local transition rule at each lattice site, the new value of a cell variable being a function of current values of the variables in cells belonging to a small neighborhood around the site. From the point of view of physics, it is straightforward to interpret the lattice as a discretized version of the physical space, the variables as occupation numbers of particles with a discrete repartition of internal states, and the evolution rules as propagation and collision rules for these particles. Lattice gases defined in this way evolve according to some fully discrete dynamics which may seem more accessible to analysis than the realistic fully continuous molecular dynamics. These systems therefore present themselves as ideal testing grounds for the explicit derivation of macroscopic equations describing continuous media but also, at a more practical level, as promising alternative tools for simulating fluid flows in nearly realistic conditions. This seemingly reductive approach of continuous physics has in fact far reaching applications since other elementary processes more complicated than plain collisions although still simple, discrete, and defined on a lattice, can serve to model complex microscopic natural phenomena such as diffusion reaction or catalysis. Furthermore, one can imagine getting valuable information on nonlinear evolution problems at a macroscopic level by means of an adequate decomposition of the processes into discrete local steps amenable to the CA framework, with obvious implications for all kinds of pattern forming systems. The Workshop held at the Centre de Physique, Les Houches, from 21 to 28 February 1989 was devoted to a presentation of recent achievements in the fields evoked above, including some aspects of CA theory in relation to general problems of information theory and statistical physics (Part I) lattice gases theory and direct applications (Part II), problems arising in the modeling of microscopic physical processes (Part III),some aspects of complex macroscopic behavior mostly in connection with turbulence (Part IV), and also the design of special purpose computers (Part V). Springer Proceedings in Physics, Yol. 46 Cellular Automata and Modeling or Complex Physical Systems EdilOrs: P. Manneville· N. Boccara· G. Y. Yichniac· R. Bida"x © Springer·Yerlag Berlin, Heidelberg 1990 1. General Aspects and Applications to Problems of Fundamental Physics In spite of their simple definition, CA can display complex behavior. Prelim inary, though fundamental, questions are therefore those of the nature of the evolution in the long term and how it can be classified. These problems were approached along two different lines by E. Goles (Santiago) and N. Boccara (Saclay). Goles [1] concentrated his attention on the asymptotic dynamical be havior of Potts and bounded threshold CA, showing in particular that the Potts automata, driven to a fixed point by a Hamiltonian sequential dynamics can dis play simple or complex dynamics when driven by a synchronous application of the same rule. Boccara [2] gave numerical evidence that Wolfram's classification of one-dimensional two-state CA is preserved under transformations involving blocks of cells with block variables defined by a majority rule, and that statistical quantities for class-3 CA fulfill simple scaling properties. In recent years, a lot of work has been done to characterize chaos in systems with a continuous phase space and the ergodic theory of strange at tractors makes an ample use of information theoretical concepts for describing correlations and randomness. K. Lindgren (Goteborg) developed the applica tion of these concepts to automata in one or more dimensions, and further to lattice gases [3]. In the same vein, M. Nordahl (Copenhagen) discussed invariant probability measures on deterministic CA and various related concepts used to quantify complexity as opposed to randomness [4]. From a more historical point of view, J. Signorini (Paris) reviewed the computational capabilities of cellular automata inherent in their complex behavior [5]. Skipping the discussion of ergodic properties of deterministic CA, one can make a direct connection with statistical mechanics by considering CA ruled by probabilistic evolution laws. In this context, R. Bidaux (Saclay) presented joint work with H. Chate and N. Boccara [6] aiming at a description of probabilistic CA in the spirit of mean-field theory. Local rules were constructed to yield first order phase transitions at the mean-field level and comparisons with simulation results were carried out showing qualitative to semi-quantitative agreement upon increasing the space dimension, except in one dimension where the transition was shown to remain continuous though with critical exponents different from those of directed percolation. Still in the field of statistical mechanics, there were three other contribu tions. The first one, presented by O. Parodi (Marseilles)' was concerned with testing CA models which simulate the behavior of the 2-D Ising model [7] at equilibrium. Several new approaches to the problem of the energy transfer at low temperature were developed, which lead to a better account of the vicinity of the critical temperature Te. The second, by E. Domany (Weizmann Inst.), was devoted to a two-dimensional kinetic problem, that of the shrinking of an ordered domain of a spin system quenched into the coexistence region below 2
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