Sandpiles on Watts-Strogatz type small-worlds

Jani Lahtinen*, János Kertész, Kimmo Kaski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

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.

Original languageEnglish
Pages (from-to)535-547
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume349
Issue number3-4
DOIs
StatePublished - 15 Apr 2005
Externally publishedYes

Keywords

  • Scaling laws
  • Self-organized criticality
  • Small-world networks

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