Abstract
A class of simple two-dimensional cellular automata with particle conservation is proposed for easy simulations of interacting particle systems. The automata are defined by the exchange of states of neighboring cells, depending on the configurations around the cells. By attributing an energy to a configuration of cells, we can select significant rules from the huge number of possible rules and classify them into several groups, based on the analogy with a binary alloy. By numerical calculations, cluster growth is found in two kinds of phases which reveal gas-solid coexistence and liquid droplets. Normalized scaling functions are obtained, and dynamical scaling is examined.
Similar content being viewed by others
References
S. Wolfram,Rev. Mod. Phys. 55:601 (1983).
G. Y. Vichniac,Physica 10D:96 (1984); T. Toffoli,Physica 10D:117 (1984); T. Toffoli and N. Margolus,Cellular Automata Machines (MIT Press, Cambridge, Massachusetts, 1987).
U. Frish, B. Hasslache, and Y. Pomeau,Phys. Rev. Lett. 56:1505 (1986); J. B. Salem and S. Wolfram, inTheory and Application of Cellular Automata, S. Wolfram, ed. (World Scientific, Singapore, 1986), p. 362.
Y. Pomeau,J. Phys. A: Math. Gen. 18:L415 (1984); M. Cruetz,Ann. Phys. 167:62 (1986).
Y. Pomeau and G. Y. Vichniac,J. Phys. A: Math. Gen. 21:3297 (1988).
S. Takesue,Phys. Rev. Lett. 59:2499 (1987).
T. Kohyama,Prog. Theor. Phys. 81:47 (1989).
A. Rucklidge and S. Zaleski,J. Stat. Phys. 51:299 (1988).
K. Kawasaki, inPhase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, London, 1972), p. 443.
J. Hardy, Y. Pomeau, and O. de Pazzis,J. Math. Phys. 14:1746 (1973); J. Hardy, O. de Pazzis, and Y. Pomeau,Phys. Rev. A 13:1949 (1976).
J. D. Gunton, M. San Miguel, and P. S. Saint, inPhase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1983); J. L. Lebowitz, J. Marro, and M. H. Kalos,Acta Met. 30:297 (1982); Y. Oono and S. Puri,Phys. Rev. Lett. 58:836 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kohyama, T. Cluster growth in particle-conserving cellular automata. J Stat Phys 63, 637–651 (1991). https://doi.org/10.1007/BF01029203
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01029203