Journal of Statistical Physics

, Volume 62, Issue 1–2, pp 283–295 | Cite as

Staggered diffusivities in lattice gas cellular automata

  • R. Brito
  • M. H. Ernst
  • T. R. Kirkpatrick
Articles

Abstract

The majority of LGCAs has spurious conservation laws, the so-called staggered invariants, first discovered by Kadanoff, McNamara, and Zanetti. Consequently there are additional hydrodynamic modes of diffusive type, which modify mode coupling theories and the nonlinear fluid dynamic equations. The diffusivities of these staggered modes are evaluated in the mean field approximation for LGCAs on triangular lattices, starting from the Green-Kubo formulas for the staggered diffusivities.

Key words

Staggered invariants lattice gas cellular automata CA-fluids staggered diffusivities Green-Kubo relations 

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References

  1. 1.
    L. P. Kadanoff, G. McNamara, and G. Zanetti,Phys. Rev. A 40:4527 (1989).Google Scholar
  2. 2.
    G. Zanetti,Phys. Rev. A 40:1539 (1989).Google Scholar
  3. 3.
    D. d'Humières, P. Lallemand, and U. Frisch,Europhys. Lett. 2:291 (1986).Google Scholar
  4. 4.
    B. Chopard and M. Droz,Phys. Lett. A 126:476 (1988).Google Scholar
  5. 5.
    S. Chen, M. Lee, K. H. Zhao, and G. D. Doolen,Physica D 37:42 (1989).Google Scholar
  6. 6.
    M. H. Ernst and J. W. Dufty,J. Stat. Phys. 58:57 (1990).Google Scholar
  7. 7.
    M. H. Ernst,Liquids, Freezing and the Glass Transition, D. Levesque, J. P. Hansen, and J. Zinn-Justin, eds. (Elsevier, 1990).Google Scholar
  8. 8.
    P. M. Binder and M. H. Ernst,Physica A 164:91 (1990).Google Scholar
  9. 9.
    H. B. Nielsen and N. Ninomiya,Nucl. Phys. B 185:20 (1981);193:173 (1981).Google Scholar
  10. 10.
    M. H. Ernst,Physica D (1990).Google Scholar
  11. 11.
    T. Naitoh, M. H. Ernst, and J. W. Dufty,Phys. Rev. A 42 (1990).Google Scholar
  12. 12.
    T. R. Kirkpatrick and M. H. Ernst, to be published.Google Scholar
  13. 13.
    J. P. Rivet,Complex Systems 1:839 (1987).Google Scholar
  14. 14.
    M. H. Ernst, inFundamental Problems in Statistical Mechanics, Vol. VII, H. van Beijeren, ed. (North-Holland, Amsterdam, 1990).Google Scholar
  15. 15.
    D. d'Humières and P. Lallemand,Complex Systems 1:599 (1987).Google Scholar
  16. 16.
    U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J. P. Rivet,Complex Systems 1:649 (1987).Google Scholar
  17. 17.
    G. Zanetti, private communication (1990).Google Scholar
  18. 18.
    R. Schmitz and J. W. Dufty,Phys. Rev. A 41:4294 (1990).Google Scholar
  19. 19.
    S. Chapman and T. G. Cowling,The Mathematical Theory of Non-uniform Gases (Cambridge University Press, 1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • R. Brito
    • 1
  • M. H. Ernst
    • 1
  • T. R. Kirkpatrick
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtTA UtrechtThe Netherlands
  2. 2.Institute for Physical Science and Technology and Department of Physics and AstronomyUniversity of MarylandCollege Park

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