Critical States in a Dissipative Sandpile Model

TL;DR

This paper investigates a two-dimensional directed dissipative sandpile model, revealing that its steady states are critical and exhibit mean-field behavior, influenced by infinite avalanches in open systems.

Contribution

It introduces a detailed analysis of critical states in a dissipative sandpile model, emphasizing the role of infinite avalanches in open systems.

Findings

Steady states are critical when grains are dropped at the top or everywhere.

Critical behavior is mean-field like.

Infinite avalanches influence the criticality in open systems.

Abstract

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.