Advertisement

Monte Carlo Simulation of Large Eden Clusters on a Cray-2

  • D. Stauffer
  • John G. Zabolitzky

Abstract

One of the simplest mathematical models of growth is the Eden model1. Consider an Infinite square lattice in two dimensions with all lattice sites empty, except one single occupied site initially. The growth process then may be completely defined by the single sentence, to be applied recursively: Occupy at random one of the empty sites neighbouring an occupied site. In spite of this remarkably simple definition the objects generated by this procedure exhibit astonishingly complex properties.

Keywords

Line Length Eden Simulation Simple Mathematical Model Occupied Site Asymptotic Regime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Eden, in “Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability”, F. Neyman, ed., University of California, Berkeley, 1961Google Scholar
  2. 2a.
    F. Leyvraz, J. Phys. A18, L941 (1985)CrossRefGoogle Scholar
  3. 2b.
    D. Stauffer, Phys. Rev. Lett. 41, 1333 (1978)CrossRefGoogle Scholar
  4. 2c.
    H. P. Peters, D. Stauffer, H. P. Holters, K. Loewenich, Z. jPhys. B34, 399 (1979)CrossRefGoogle Scholar
  5. 2d.
    ML. Plischke, Z. Racz, Phys. Rev. Lett. 53, 415 (1984)CrossRefGoogle Scholar
  6. 2e.
    ML. Plischke, Z. Racz, Phys. Rev. Lett. 54, 2056 (1985)CrossRefGoogle Scholar
  7. 2f.
    Z. Racz, M. Plischke, Phys. Rev. A31, 985 (1985)CrossRefGoogle Scholar
  8. 2g.
    R. Jullien, R. Botet, Phys. Rev. Lett. 54, 2055 (1985)CrossRefGoogle Scholar
  9. 2h.
    R. Jullien, R. Botet, J. Phys. A18, 2279 (1985)CrossRefGoogle Scholar
  10. 3a.
    P. Freche, D. Stauffer, H. E. Stanley, J.Phys. A18, L1163 (1985)CrossRefGoogle Scholar
  11. 3b.
    R. Hirsch, D. E. Wolf, J. Phys. A19, L251 (1986); D. E. Wolf, unpublished; P. Meakin, R. Botet, R. Jullien, Europhys. Lett., in printCrossRefGoogle Scholar
  12. 4.
    J. G. Zabolitzky, D. Stauffer, Phys. Rev. A34, 1523 (1986); D. Stauffer, J. G. Zabolitzky, Phys. Rev. Lett., in printCrossRefGoogle Scholar
  13. 5a.
    F. Family, T. Vicsek, J. Phys. A18, L75 (1985)CrossRefGoogle Scholar
  14. 5b.
    M. Kardar, G. Parisi, Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986)CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • D. Stauffer
    • 1
  • John G. Zabolitzky
    • 1
  1. 1.Supercomputer Institute and School of Physics and AstronomyUniversity of MinnesotaMinneapolisUSA

Personalised recommendations