Bak--Tang--Wiesenfeld model for various topologies and ranges of interaction

TL;DR

This study uses computer simulations to analyze the Bak--Tang--Wiesenfeld model across different topologies and interaction ranges, confirming a universal avalanche size distribution exponent.

Contribution

It demonstrates that the avalanche size distribution exponent remains consistent across various substrate topologies and neighborhoods, regardless of interaction range.

Findings

The avalanche size distribution follows a power law with an exponent around 1.208.

The exponent is invariant across different topologies and interaction ranges.

Properly chosen grain deposition is crucial for observing the power law behavior.

Abstract

In this paper, the Bak--Tang--Wiesenfeld model for various substrate topologies and a variety of neighborhoods is reconsidered. With computer simulation, we study the distribution of avalanche sizes. Using the Z-score we confirm that independently of the substrate topology and the range of neighborhood, the exponent that governs the power law of the probability distribution of the size of avalanches is the same and approximately equal 1.208(39). However, this requires a smartly chosen number of deposited grains in relation to the linear size of the system.