Self-organised criticality in dilute lattice

TL;DR

This study investigates how the presence and distribution of holes (dissipative sites) in a lattice affect the criticality in the BTW model, revealing that random distribution causes more dissipation than clustered holes.

Contribution

It introduces an analysis of how different distributions of holes influence the critical exponent in the BTW model, highlighting the impact of spatial arrangement on self-organized criticality.

Findings

Z decreases with more holes in the lattice.

Randomly distributed holes cause more dissipation than clustered holes.

The rate of change of Z varies with hole distribution type.

Abstract

The variation of z in BTW model in presence of holes (dissipative sites) has been studied. The value of z decreases as the fraction of number of holes increases. Interstingly, it is observed that the variation of the rate of change of z with the fraction of number of holes is different for the two different types of distribution of holes over the lattice. When the holes are randomly distributed over the lattice then the dissipation is more compared to that of the case when the holes are present in the form of a single compact cluster with same fraction. The value of z is less in the first case than that observed in the second case.