Dissipative sandpile models with universal exponents

Abstract

We consider a dissipative variant of the stochastic-Abelian sandpile model on a two-dimensional lattice. The boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability epsilon. It is shown that the scaling properties of this model are in the universality class of the stochastic-Abelian models with conservative dynamics and open boundaries. In particular, the dissipation rate epsilon can be adjusted according to a suitable function epsilon = f(L), such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size L.

Critical properties of a dissipative sandpile model on small-world networks

“…Therefore a crossover from diffusive to super diffusive sand transport occurs as RL is evolved to RN. It can be seen that not only the scaling of n φ and s φ are same but also the magnitude of n φ is just twice of s φ for both φ = 0 and φ = 1 on a given L. On RL it was already known that n φ = 2 s φ [35,40]. Such a relationship is then also valid on RN.…”

Dissipative sandpile on growing random graph

“…Dissipation factor ε G on a graph G b is defined as ε G =1/<n G >, where <n G > is the average number steps for a random walker to reach the boundary of the lattice starting from a randomly chosen node of the graph G b [3] and it is calculated as:…”

“…al, is the prototypical model to study SOC [1]. The universality class of BTW type dissipative sandpile model (DSM) is found to be different on regular lattice and on random network [2,3]. It is intriguing to study how this model behaves on a graph which evolves from a regular lattice to a random network.…”

Effects of pair correlation on mean-field theory of BTW sand pile model

“…Effect of bulk dissipation has been studied in the continuous version of BTW model in connection with 1/f noise [23], and other models as well [26,27]. Moreover, for comparison, the contrasting systems of sand piles with fixed energy have been studied and their universality classes have been derived [12].…”