Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-10-08
Phys. Rev. E 69, 026107 (2004)
Physics
Condensed Matter
Statistical Mechanics
many pages but not so many text, 5 figures
Scientific paper
10.1103/PhysRevE.69.026107
The Oslo sandpile model, or if one wants to be precise, ricepile model, is a cellular automaton designed to model experiments on granular piles displaying self-organized criticality. We present an analytic treatment that allows the calculation of the transition probabilities between the different configurations of the system; from here, using the theory of Markov chains, we can obtain the stationary occupation distribution, which tell us that the phase space is occupied with probabilities that vary in many orders of magnitude from one state to another. Our results show how the complexity of this simple model is built as the number of elements increases, and allows, for a given system size, the exact calculation of the avalanche size distribution and other properties related to the profile of the pile.
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