Dissipative sandpile on growing random graph

Abstract

In this paper, a BTW type dissipative sandpile model is developed and studied on growing random graphs(GRG). The GRG are generated over a two dimensional square lattice throwing bonds of arbitrary length. A GRG is identified by the number of external bonds added per lattice site (b) to the system. For each graph, the dissipation rate 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. For each graph, the model evolves to a steady state at which the critical behavior is studied as a function of b.