Sandpiles on Watts-Strogatz type small-worlds

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.