Dhar, Deepak ; Pradhan, Punyabrata (2004) Probability distribution of residence times of grains in sandpile models Journal of Statistical Mechanics: Theory and Experiment, 2004 (5). 05002_105002_11. ISSN 17425468

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Official URL: http://iopscience.iop.org/17425468/2004/05/P05002
Related URL: http://dx.doi.org/10.1088/17425468/2004/05/P05002
Abstract
We show that the probability distribution of the residence times of sand grains in sandpile models, in the scaling limit, can be expressed in terms of the probability of survival of a single diffusing particle in a medium with absorbing boundaries and spacedependent jump rates. The scaling function for the probability distribution of residence times is nonuniversal, and depends on the probability distribution according to which grains are added at different sites. We determine this function exactly for the onedimensional sandpile when grains are added randomly only at the ends. For sandpiles with grains added everywhere with equal probability, in any dimension, and of arbitrary shape, we prove that, in the scaling limit, the probability that the residence time is greater than t is exp (t/M bar) , where M bar is the average mass of the pile in the steady state. We also study finite size corrections to this function.
Item Type:  Article 

Source:  Copyright of this article belongs to Institute of Physics Publishing. 
Keywords:  Granular Matter; Exact Results; Selforganized Criticality (theory); Driven Diffusive Systems (theory) 
ID Code:  9384 
Deposited On:  02 Nov 2010 12:19 
Last Modified:  16 May 2016 19:12 
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