Local smoothing in sandpiles: Spanning avalanches, bifurcation, and temporal oscillations.

Abstract

The manipulation of the self-organized critical systems by repeatedly deliberate local relaxations (local smoothing) is considered. During a local smoothing, the grains diffuse to the neighboring regions, causing a smoothening of the height filed over the system. The local smoothings are controlled by a parameter ζ which is related to the number of local smoothening events in an avalanche. The system shows some new (mass and time) scales, leading to some oscillatory behaviors. A bifurcation occurs at some ζ value, above which some oscillations are observed for the mean number of grains, and also in the autocorrelation functions. These oscillations are associated with spanning avalanches which are due to the accumulation of grains in the smoothed system. The analysis of the rare event waiting time confirms also the appearance of a new time scale.