Avalanching Systems with Longer Range Connectivity: Occurrence of a Crossover Phenomenon and Multifractal Finite Size Scaling
by
Simone Benella 1, Giuseppe Consolini 2,*
, Fabio Giannattasio 3, Tom T.S. Chang 4 and Marius Echim 5,6
Simone Benella 1, Giuseppe Consolini 2,*, Fabio Giannattasio 3, Tom T.S. Chang 4 and Marius Echim 5,6
1
Dipartimento di Scienze Pure ed Applicate, Università degli Studi di Urbino Carlo Bo, 61029 Urbino, Italy
2
INAF-Istituto di Astrofisica e Planetologia Spaziali, 00133 Roma, Italy
3
Istituto Nazionale di Geofisica e Vulcanologia, 00143 Roma, Italy
4
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
5
Royal Belgian Institute for Space Aeronomy, B-1180 Brussels, Belgium
6
Institute of Space Science, 077125 Magurele, Romania
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(8), 383; https://doi.org/10.3390/e19080383
Received: 4 April 2017 / Revised: 11 July 2017 / Accepted: 13 July 2017 / Published: 26 July 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
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).
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Keywords:
avalanche dynamics; network; near-criticality behavior; finite size scaling; multifractal analysis
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MDPI and ACS Style
Benella, S.; Consolini, G.; Giannattasio, F.; Chang, T.T.; Echim, M. Avalanching Systems with Longer Range Connectivity: Occurrence of a Crossover Phenomenon and Multifractal Finite Size Scaling. Entropy 2017, 19, 383.
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