Onsets of avalanches in the BTW model

TL;DR

This paper investigates the initiation times of avalanches in the BTW model through simulations, analyzing their distribution, dependence on system size, and fluctuations near the critical point.

Contribution

It provides new estimates of power-law exponents for avalanche onsets and explores height fluctuations near the SOC transition in the BTW model.

Findings

Power-law dependence of avalanche onsets on system size.

Rapid increase in height fluctuations near the SOC point.

Estimated exponents for onset time distributions.

Abstract

The onsets of toppling and dissipation in the BTW model are studied by computer simulation. The distributions of these two onset times and their dependences on the system size are also studied. Simple power law dependences of these two times on the system size are observed and the exponents are estimated. The fluctuation of the average (spatial) height in the subcritical region is studied and observed to increase very rapidly near the SOC point.