Pradhan, Punyabrata ; Dhar, Deepak (2006) Probability distribution of residence times of grains in models of rice piles Physical Review E, 73 (2). 021303_1-021303_12. ISSN 1063-651X
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Official URL: http://pre.aps.org/abstract/PRE/v73/i2/e021303
Related URL: http://dx.doi.org/10.1103/PhysRevE.73.021303
Abstract
We study the probability distribution of residence time of a grain at a site, and its total residence time inside a pile, in different rice pile models. The tails of these distributions are dominated by the grains that get deeply buried in the pile. We show that, for a pile of size L, the probabilities that the residence time at a site or the total residence time is greater than t, both decay as 1/t(ln t)x for Lω«t«exp(Lϒ) where ϒ is an exponent ≥1, and values of x and ϒ in the two cases are different. In the Oslo rice pile model we find that the probability of the residence time Ti at a site i being greater than or equal to t is a nonmonotonic function of L for a fixed t and does not obey simple scaling. For model in d dimensions, we show that the probability of minimum slope configuration in the steady state, for large L, varies as exp(-kLd+2) where k is a constant, and hence ϒ=d+2.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |
ID Code: | 9300 |
Deposited On: | 02 Nov 2010 12:32 |
Last Modified: | 16 May 2016 19:07 |
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