Chaos, Solitons and Fractals 130 (2020) 109519 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Comparing spatio-temporal networks of intermittent avalanche events: Experiment, model, and empirical data Dionessa C. Biton a , Anjali B. Tarun b , Rene C. Batac a,∗ a Physics Department, College of Science, De La Salle University, 2401 Taft Avenue, Manila, Philippines b Medical Image Processing Lab (MIP:Lab), Institute of Bioengineering, School of Engineering, École polytechnique fédérale de Lausanne, Geneva, Switzerland a r t i c l e i n f o Article history: Received 24 July 2019 Revised 11 October 2019 Accepted 11 November 2019 Keywords: Granular materials Sandpile model Earthquakes Scaling phenomena in complex systems Avalanches Self-organization of complex systems a b s t r a c t Relaxational processes in many complex systems often occur in the form of avalanches resulting from internal cascades from across the system scale. Here, we probe the space, time, and magnitude signa- tures of avalanching behavior using a network of temporally-directed links subject to a spatial distance criterion between events in the entire catalog. We apply this method onto three systems with avalanche- like characteristics: (i) highly controllable scaled experiments, particularly that of a slowly-driven pile of granular material in a quasi-two-dimensional setup with open edges; (ii) the sandpile, a numerical model of nearest-neighbor interactions in a grid; and (iii) substantially complete empirical data on earthquakes from southern California. Apart from the recovery of the fat-tailed statistics of event sizes, we recover similar power-laws in the spatial and temporal aspects of the networks of these representative systems, hinting at possible common underlying generative mechanisms governing them. By consolidating the re- sults from experiments, numerical models, and empirical data, we can gain a better understanding of these highly nonlinear processes in nature. © 2019 Published by Elsevier Ltd. 1. Introduction Many complex, nonlinear dynamical systems in living sys- tems [1–3], in nature [4–6], in the laboratory [7–9], and in hu- man interactions [10–12] result in bursty signatures in space, time, and magnitude domains. These systems may be understood from a general framework of avalanches, here loosely used to describe pro- cesses in which the slow and continuous process of energy accu- mulation is interrupted by intermittent episodes of sudden relax- ations that cascade within the system. Empirical studies on these intermittent cascading behaviors, especially of large-scale natural phenomena, reveal the long-tailed statistics of the resulting re- laxations [13–15], oftentimes attributed to self-organized criticality (SOC) [16,17]. Due to the wide classes of systems exhibiting bursti- ness [18], “crackling” [19], or avalanche-like characteristics [20], much can still be learned about the commonalities in the gener- ative mechanisms underlying their occurrences. To this end, one can use a multitude of complementary approaches, such as empir- ical data analyses, theoretical and numerical modeling and simula- tions, and scaled experimentation. ∗ Corresponding author. E-mail address: rene.batac@dlsu.edu.ph (R.C. Batac). Long-period records of empirical data can be accessed through various catalogs. In some cases, however, especially for the large- scale systems in nature, the long observation times required to generate a single event or a sequence of correlated events pro- hibits a detailed observation of the internal cascade mechanisms at work. To this end, one can complement the analysis using highly controllable scaled systems in the laboratory, or through numer- ical simulations in a computer. For example, granular piles pro- vide for a controllable setup that can be simultaneously tracked in space, time, and avalanche magnitude domains. Previous works have shown that actual sand mounds [21] and other variations of such granular avalanche experiments [22] indeed follow the power-law statistics of avalanche sizes as predicted by the SOC theory. Moreover, some authors have identified regimes of insta- bility within a granular pile in the form of inter-grain shape fac- tors, allowing for a spatio-temporal window of prediction of the avalanche occurrence [23]. This, in turn, may prove to be useful for intervention and suppression of the avalanches [24]. Interestingly, the SOC theory that is deemed to be under- lying these cascaded avalanching systems is introduced through the sandpile [25], a discrete mathematical model inspired by the assumed dynamical behavior of a slowly-driven pile [16]. Here, avalanches are generated from a continuous addition of an exter- nal trigger energy or stress into random location in a grid of cells that may contain energy states only up to a threshold value. Upon https://doi.org/10.1016/j.chaos.2019.109519 0960-0779/© 2019 Published by Elsevier Ltd.