Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model

Details Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model

2004-03-31

arxiv.org/abs/cond-mat/0403769v1

Proceedings of National conference on nonlinear systems and dynamics (NCNSD-2003), page 97 (2003).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

We study the probability distribution of residence time, $T$, of the sand grains in the one dimensional abelian sandpile model on a lattice of $L$ sites, for $T<>L^2$. The distribution function decays as $\exp(-\frac{K_LT}{L^2})$. We numerically calculate the coefficient $K_L$ for the value of $L$ upto 150 . Interestingly the distribution function has a scaling form $\frac{1}{L^a}f(\frac{T}{L^b})$ with $a \neq b$ for large $L$.

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