Memory on multiple time-scales in an Abelian sandpile

Andrey Sokolov, Andrew Melatos, Tien Kieu and Rachel Webster

Physica A: Statistical Mechanics and its Applications, 2015, vol. 428, issue C, 295-301

Abstract: We report results of a numerical analysis of the memory effects in two-dimensional Abelian sandpiles. It is found that a sandpile forgets its instantaneous configuration in two distinct stages: a fast stage and a slow stage, whose durations roughly scale as N and N2 respectively, where N is the linear size of the sandpile. We confirm the presence of the longer time-scale by an independent diagnostic based on analysing emission probabilities of a hidden Markov model applied to a time-averaged sequence of avalanche sizes. The application of hidden Markov modelling to the output of sandpiles is novel. It discriminates effectively between a sandpile time series and a shuffled control time series with the same time-averaged event statistics and hence deserves further development as a pattern-recognition tool for Abelian sandpiles.

Keywords: Abelian sandpile; Hidden Markov model (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:428:y:2015:i:c:p:295-301

DOI: 10.1016/j.physa.2015.02.001

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