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Effects of pair correlation on mean-field theory of BTW sand pile model

Author

Listed:
  • Chen, H.-S.
  • Wu, G.Y.

Abstract

We extend the mean-field calculation of BTW sand pile model to one that includes the correlation between pairs of nearest neighbors. Specifically, we derive dynamical equations of both one-site and two-site densities, and solve the equations order by order starting with the mean-field solution. The investigation provides analytical results for both stationary and dynamic states of the sand pile near the critical point, which are valid in the regime where h≪ε2≪1 (h= incoming rate of sand grains, ε=bulk dissipation rate of sand grains). In the stationary case, we evaluate the pair correlation and the correction to the mean-field single-site densities due to the correlation. The correction is found to be of the same order as the mean-field solution. In the dynamic case, the initial state deviates from the stationary state by a small fluctuation, which subsequently decays exponentially, with the time constant being reduced from the corresponding mean-field value. Again, the correction to the time constant in this case is found comparable to the mean-field value itself.

Suggested Citation

  • Chen, H.-S. & Wu, G.Y., 2010. "Effects of pair correlation on mean-field theory of BTW sand pile model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2339-2350.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:12:p:2339-2350
    DOI: 10.1016/j.physa.2010.02.011
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