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

Entropy

Simone Benella¹  Giuseppe Consolini²  Fabio Giannattasio³  Tom T.S. Chang⁴  Marius Echim⁵ 

[1] Dipartimento di Scienze Pure ed Applicate, Università degli Studi di Urbino Carlo Bo, 61029 Urbino, Italy;INAF-Istituto di Astrofisica e Planetologia Spaziali, 00133 Roma, Italy;Istituto Nazionale di Geofisica e Vulcanologia, 00143 Roma, Italy;Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA;Royal Belgian Institute for Space Aeronomy, B-1180 Brussels, Belgium;

关键词: avalanche dynamics;    network;    near-criticality behavior;    finite size scaling;    multifractal analysis;   

DOI  :  10.3390/e19080383

来源: DOAJ

【 摘 要 】

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).

【 授权许可】

Unknown