Self organized criticality in a sandpile model with threshold dissipation

TL;DR

This paper analyzes a one-dimensional nonconservative sandpile model exhibiting critical behavior, providing analytical solutions for correlation functions, and revealing how local height and fluctuation spectra behave.

Contribution

It introduces an analytically solvable one-dimensional sandpile model with threshold dissipation, detailing its critical properties and correlation functions.

Findings

Average local height decreases inversely with distance from boundary

Power spectrum of total mass fluctuations scales as 1/f

Model exhibits nontrivial critical behavior

Abstract

We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set to one, irrespective of the initial value. The model shows nontrivial critical behavior. We solve this model analytically in one dimension for all driving rates. We calculate all the two point correlation functions in this model, and find that the average local height decreases as inverse of the distance from the nearest boundary and the power spectrum of fluctuations of the total mass varies as $1/f$.