Fillips in Sandpiles; Spanning Avalanches, Bifurcation and Temporal oscillations

TL;DR

This paper investigates how deliberate local relaxations called fillips influence sandpile dynamics, leading to new oscillatory behaviors, bifurcations, and spanning avalanches, with a mean field analysis supporting these findings.

Contribution

It introduces the concept of fillips in sandpile models, revealing their impact on avalanche dynamics, oscillations, and bifurcations, supported by a mean field theoretical approach.

Findings

Oscillatory behaviors emerge at certain fillip parameters.

Bifurcation occurs, leading to oscillations in energy and autocorrelation.

Spanning avalanches are linked to energy accumulation and oscillations.

Abstract

The manipulation of the self-organized critical systems by repeatedly deliberate local relaxations (fillips) affect considerably the dynamics of avalanches and change their evolution. During a fillip, the energy diffuses to the neighboring regions, causing a smoothening of the height filed over the system. The fillips are controlled by a parameter $\zeta$ which is related to the number of local smoothening events in an avalanche. The system shows a new (mass and time) scales, leading to some oscillatory behaviors. A bifurcation occurs at some $\zeta$ value, above which some oscillations occur in the mean energy, and also in the autocorrelation functions. These oscillations are associated with \textit{spanning avalanches} which are due to the accumulation of energy in the smoothed system. The analysis of the rare event waiting time (REWT) confirms also the appearance of this new time scale. A mean field analysis is presented to explain some results.