Avalanching Systems with Longer Range Connectivity: Occurrence of a Crossover Phenomenon and Multifractal Finite Size Scaling

Abstract

Many out-of-equilibrium systems respond to external driving with nonlinear and self-similar dynamics. This near scale-invariant behavior of relaxation events has been modeled through sand pile cellular automata. However, a common feature of these models is the assumption of a local connectivity, while in many real systems, we have evidence for longer range connectivity and a complex topology of the interacting structures. Here, we investigate the role that longer range connectivity might play in near scale-invariant systems, by analyzing the results of a sand pile cellular automaton model on a Newman-Watts network. The analysis clearly indicates the occurrence of a crossover phenomenon in the statistics of the relaxation events as a function of the percentage of longer range links and the breaking of the simple Finite Size Scaling (FSS). The more complex nature of the dynamics in the presence of long-range connectivity is investigated in terms of multi-scaling features and analyzed by the Rank-Ordered Multifractal Analysis (ROMA).

Stochastic sandpile model on small-world networks: Scaling and crossover

“…A similar observation is also reported by Benella et.al. [42] in a recent study of avalanching systems with long range connectivity. Since FSS fails in the SWN regime, the φ dependent coexistence scaling could be useful to verify the scaling form of the probability distribution functions.…”