On the effect of the drive on self-organized criticality

TL;DR

This paper explores how different state-dependent drives affect the self-organized criticality in the Sandpile model, revealing that favoring certain site heights can preserve or disrupt criticality.

Contribution

It introduces a state-dependent external drive in the Sandpile model and analyzes its impact on criticality and system behavior, extending understanding of self-organized critical systems.

Findings

Favoring sites with height three maintains criticality.

Favoring sites with height two leads to system-wide avalanches.

Stationary states are approached differently depending on the drive.

Abstract

The well known Sandpile model of self-organized criticality generates avalanches of all length and time scales, without tuning any parameters. In the original models the external drive is randomly selected. Here we investigate a drive which depends on the present state of the system, namely the effect of favoring sites with a certain height in the deposition process. If sites with height three are favored, the system stays in a critical state. Our numerical results indicate the same universality class as the original model with random depositition, although the stationary state is approached very differently. In constrast, when favoring sites with height two, only avalanches which cover the entire system occur. Furthermore, we investigate the distributions of sites with a certain height, as well as the transient processes of the different variants of the external drive.