Effects of pair correlation on mean-field theory of BTW sand pile model |
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Authors: | H-S Chen |
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Institution: | Department of Electrical Engineering, National Tsing-Hua University, Hsin-Chu, 300, Taiwan |
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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. |
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Keywords: | Sand pile Self-organized criticality Mean-field theory |
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