Comparing spatio-temporal networks of intermittent avalanche events: Experiment, model, and empirical data

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 signatures 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 results from experiments, numerical models, and empirical data, we can gain a better understanding of these highly nonlinear processes in nature.