Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2

Research Article

Frequency Distributions of Sand Pile Models

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  • @INPROCEEDINGS{10.1007/978-3-642-02469-6_51,
        author={Ruey-Tarng Liu},
        title={Frequency Distributions of Sand Pile Models},
        proceedings={Complex Sciences. First International Conference, Complex 2009, Shanghai, China, February 23-25, 2009, Revised Papers, Part 2},
        proceedings_a={COMPLEX PART 2},
        year={2012},
        month={5},
        keywords={power law frequency distribution sand pile},
        doi={10.1007/978-3-642-02469-6_51}
    }
    
  • Ruey-Tarng Liu
    Year: 2012
    Frequency Distributions of Sand Pile Models
    COMPLEX PART 2
    Springer
    DOI: 10.1007/978-3-642-02469-6_51
Ruey-Tarng Liu1,*
  • 1: National Chung-Hsing University
*Contact email: rtliu@phys.nchu.edu.tw

Abstract

We calculated the frequency distributions of cluster sizes in the sand pile models. Two cellular automata models differing in the rules of adding sand particles are used. For the model with local perturbation only, the distribution shows a power law behavior regardless of the spatial dimension that the sand pile is situated at. For the other model where the perturbation generated by the addition of a sand particle is not confined to one site only, the distribution is generally a power law plus an exponential cutoff. These results are consistent with what was found previously for another complex system using a model of constrained minority game. The frequency distributions in higher dimensions than two are also calculated and discussed.