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Cellular Automaton Fluids: Basic Theory (1986)


References

[1] S. Wolfram ed., Theory and Applications of Cellular Automata (World Scientific, 1986).

[2] S. Wolfram, Cellular automata as models of complexity, Nature 311:419 (1984).

[3] N. Packard and S. Wolfram, Two-dimensional cellular automata, J. Stat. Phys. 38:901 (1985).

[4] D. J. Tritton, Physical Fluid Dynamics (Van Nostrand, 1977).

[5] W. W. Wood, Computer studies on fluid systems of hard-core particles, in Fundamental Problems in Statistical Mechanics 3, E. D. G. Cohen, ed. (North-Holland, 1975).

[6] J. Hardy, Y. Pomeau, and O. de Pazzis, Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions, J. Math. Phys. 14:1746 (1973); J. Hardy, O. de Pazzis, and Y. Pomeau, Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions, Phys. Rev. A 13:1949 (1976).

[7] U. Frisch, B. Hasslacher, and Y. Pomeau, Lattice gas automata for the Navier--Stokes equation, Phys. Rev. Lett. 56:1505 (1986).

[8] J. Salem and S. Wolfram, Thermodynamics and hydrodynamics with cellular automata, Theory and Applications of Cellular Automata, S. Wolfram, ed. (World Scientific, 1986).

[9] D. d'Humieres, P. Lallemand, and T. Shimomura, An experimental study of lattice gas hydrodynamics, Los Alamos preprint LA-UR-85-4051; D. d'Humieres, Y. Pomeau, and P. Lallemand, Simulation d'allees de Von Karman bidimensionnelles a l'aide d'un gaz sur reseau, C. R. Acad. Sci. Paris II 301:1391 (1985).

[10] J. Broadwell, Shock structure in a simple discrete velocity gas, Phys. Fluids 7:1243 (1964).

[11] H. Cabannes, The discrete Boltzmann equation, Lecture Notes, Berkeley (1980).

[12] R. Gatignol, Theorie cinetique des gaz a repartition discrete de vitesse (Springer, 1975).

[13] J. Hardy and Y. Pomeau, Thermodynamics and hydrodynamics for a modeled fluid, J. Math. Phys. 13:1042 (1972).

[14] S. Harris, The Boltzmann Equation (Holt, Rinehart and Winston, 1971).

[15] R. Caflisch and G. Papanicolaou, The fluid-dynamical limit of a nonlinear model Boltzmann equation, Commun. Pure Appl. Math. 32:589 (1979).

[16] B. Nemnich and S. Wolfram, Cellular automaton fluids 2: Basic phenomenology, in preparation.

[17] S. Wolfram, SMP Reference Manual (Inference Corporation, Los Angeles, 1983); S. Wolfram, Symbolic mathematical computation, Commun. ACM 28:390 (1985).

[18] A. Sommerfeld, Thermodynamics and Statistical Mechanics (Academic Press, 1955).

[19] S. Wolfram, Origins of randomness in physical systems, Phys. Rev. Lett. 55:449 (1985).

[20] S. Wolfram, Random sequence generation by cellular automata, Adv. Appl. Math. 7:123 (1986).

[21] J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, 1980).

[22] E. M. Lifshitz and L. P. Pitaevskii, Statistical Mechanics, Part 2 (Pergamon, 1980), Chapter 9.

[23] R. Liboff, The Theory of Kinetic Equations (Wiley, 1969).

[24] D. Levermore, Discretization effects in the macroscopic properties of cellular automaton fluids, in preparation.

[25] E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon, 1981).

[26] P. Resibois and M. De Leener, Classical Kinetic Theory of Fluids (Wiley, 1977).

[27] L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, 1959).

[28] M. H. Ernst, B. Cichocki, J. R. Dorfman, J. Sharma, and H. van Beijeren, Kinetic theory of nonlinear viscous flow in two and three dimensions, J. Stat. Phys. 18:237 (1978).

[29] J. R. Dorfman, Kinetic and hydrodynamic theory of time correlation functions, in Fundamental Problems in Statistical Mechanics 3, E. D. G. Cohen, ed. (North-Holland, 1975).

[30] R. Courant and K. O. Friedrichs, Supersonic Flows and Shock Waves (Interscience, 1948).

[31] D. Levermore, private communication.

[32] J. Milnor, private communication.

[33] V. Yakhot, B. Bayley, and S. Orszag, Analogy between hyperscale transport and cellular automaton fluid dynamics, Princeton University preprint (February 1986).

[34] H. S. M. Coxeter, Regular Polytopes (Macmillan, 1963).

[35] M. Hammermesh, Group Theory (Addison-Wesley, 1962), Chapter 9.

[36] L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, 1977), Chapter 12.

[37] H. Boerner, Representations of Groups (North-Holland, 1970), Chapter 7.

[38] L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, 1975), Section 10.

[39] D. Levine et al., Elasticity and dislocations in pentagonal and icosahedral quasicrystals, Phys. Rev. Lett. 14:1520 (1985).

[40] L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, 1978), Chapter 13.

[41] B. K. Vainshtein, Modern Crystallography, (Springer, 1981), Chapter 2.

[42] J. H. Conway and N. J. A. Sloane, to be published.

[43] R. L. E. Schwarzenberger, N-Dimensional Crystallography (Pitman, 1980).

[44] J. Milnor, Hilbert's problem 18: On crystallographic groups, fundamental domains, and on sphere packing, Proc. Symp. Pure Math. 28:491 (1976).

[45] B. G. Wybourne, Classical Groups for Physicists (Wiley, 1974), p. 78; R. Slansky, Group theory for unified model building, Phys. Rep. 79:1 (1981).

[46] B. Grunbaum and G. C. Shephard, Tilings and Patterns (Freeman, in press); D. Levine and P. Steinhardt, Quasicrystals I: Definition and structure, Univ. of Pennsylvania preprint.

[47] N. G. de Bruijn, Algebraic theory of Penrose's non-periodic tilings of the plane, Nedl. Akad. Wetensch. Indag. Math. 43:39 (1981); J. Socolar, P. Steinhardt, and D. Levine, Quasicrystals with arbitrary orientational symmetry, Phys. Rev. B 32:5547 (1985).

[48] R. Penrose, Pentaplexity: A class of nonperiodic tilings of the plane, Math. Intelligencer 2:32 (1979).

[49] J. P. Rivet and U. Frisch, Automates sur gaz de reseau dans l'approximation de Boltzmann, C. R. Acad. Sci. Paris II 302:267 (1986).

[50] P. J. Davis, Circulant Matrices (Wiley, 1979).

[51] L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, 1978), Chapter 5.

[52] E. Kolb and S. Wolfram, Baryon number generation in the early universe, Nucl. Phys. B 172:224 (1980), Appendix A.

[53] I. S. Gradestyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1965).

[54] U. Frisch, private communication.

[55] P. Roache, Computational Fluid Mechanics (Hermosa, Albuquerque, 1976).

[56] S. Omohundro and S. Wolfram, unpublished (July 1985).

[57] D. d'Humieres, private communication.

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