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Sandpiles on Watts–Strogatz type small-worlds

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  • Lahtinen, Jani
  • Kertész, János
  • Kaski, Kimmo

Abstract

We study a one-dimensional sandpile model in small-world networks with long-range links either by introducing them randomly to fixed connection topology (quenched randomness) or to temporary connection topology (annealed randomness) between cells to allow a grain to topple from a cell to a neighbouring or distant cell. These models are investigated both analytically and by computer simulations, and they show self-organized criticality unlike the original one-dimensional sandpile model. The simulations also show that the distribution of avalanche size undergoes a transition from a non-critical to a critical regime. In addition we have found that for annealed and quenched randomness there is a scaling for the size-distribution of avalanches with a single power-law exponent, which is the same as that found for the standard sandpile model in higher dimensions. We also show that the average number of grains in the system follows power-law behaviour as a function of the probability of long-range links with different exponents for the annealed and quenched systems.

Suggested Citation

  • Lahtinen, Jani & Kertész, János & Kaski, Kimmo, 2005. "Sandpiles on Watts–Strogatz type small-worlds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 535-547.
    • Handle: RePEc:eee:phsmap:v:349:y:2005:i:3:p:535-547
    DOI: 10.1016/j.physa.2004.10.024
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. de Arcangelis, L & Herrmann, H.J, 2002. "Self-organized criticality on small world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 545-549.
    3. Lee, D.-S. & Goh, K.-I. & Kahng, B. & Kim, D., 2004. "Sandpile avalanche dynamics on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 84-91.
    4. Lahtinen, Jani & Kertész, János & Kaski, Kimmo, 2002. "Random spreading phenomena in annealed small world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 571-580.
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    Cited by:

    1. Lee, Ya-Ting & Chen, Chien-chih & Chang, Young-Fo & Chiao, Ling-Yun, 2008. "Precursory phenomena associated with large avalanches in the long-range connective sandpile (LRCS) model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5263-5270.
    2. Wu, Tingwei & Xia, Yongxiang & Liang, Yuanyuan, 2024. "Load cascades in spatial networks: A sandpile model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 644(C).

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