Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model

Abstract

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.

many pages but not so many text, 5 figures

References in corpus (3)

• Local Distributions and Rate Fluctuations in a Unified Scaling Law for Earthquakes
• The Oslo rice pile model is a quenched Edwards-Wilkinson equation
• Anomalous Transport in Conical Granular Piles

Cited by in corpus (3)

• The three faces of entropy for complex systems -- information, thermodynamics and the maxent principle
• Correlations and hyperuniformity in the avalanche size of the Oslo Model
• Sampling rare fluctuations of height in the Oslo ricepile model