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Memory on multiple time-scales in an Abelian sandpile

Author

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  • Sokolov, Andrey
  • Melatos, Andrew
  • Kieu, Tien
  • Webster, Rachel

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.

Suggested Citation

  • Sokolov, Andrey & Melatos, Andrew & Kieu, Tien & Webster, Rachel, 2015. "Memory on multiple time-scales in an Abelian sandpile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 295-301.
    • Handle: RePEc:eee:phsmap:v:428:y:2015:i:c:p:295-301
    DOI: 10.1016/j.physa.2015.02.001
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    References listed on IDEAS

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    1. Ivashkevich, E.V. & Ktitarev, D.V. & Priezzhev, V.B., 1994. "Waves of topplings in an Abelian sandpile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(3), pages 347-360.
    2. Amir Abdolvand & Afshin Montakhab, 2010. "Scaling and complex avalanche dynamics in the Abelian sandpile model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(1), pages 21-30, July.
    3. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
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    Keywords

    Abelian sandpile; Hidden Markov model;

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