Sandpile model on Scale Free Networks with preferential sand distribution: a new universality class

Abstract

A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {\em i.e.}: $P_k\sim k^{-α}$. In this model, upon toppling of a critical node sand grains are given one to each of the neighbouring nodes with highest and lowest degrees instead of two randomly selected neighbouring nodes as in a stochastic sandpile model. The critical behaviour of the model is determined by characterizing various avalanche properties at the steady state varying the network structure from scale free to random, tuning $α$ from $2$ to $5$. The model exhibits mean field scaling on the random networks, $α>4$. However, in the scale free regime, $2<α<4$, the scaling behaviour of the model not only deviates from the mean-field scaling but also the exponents describing the scaling behaviour are found to decrease continuously as $α$ decreases. In this regime, the critical exponents of the present model are found to be different from those of the two state stochastic sandpile model on similar networks. The preferential sand distribution thus has non-trivial effects on the sandpile dynamics which leads the model to a new universality class.