In recent years, interest in intermittent dynamics and complex patterns, particularly Self-Organization (SO) [1], has grown, with a focus on more realistic microphysical processes. These systems, where minor disturbances can trigger avalanches across various scales, often exhibit fractal structures and power law dynamics.

Electric discharges are one such system [2], with dissipation occurring in fractal regions and parameters like current and charge following power laws. Unlike the local interactions in the canonical sandpile model [1], electric discharges are governed by non-local effects due to charge dynamics.

In this work, we examine the long-term statistics of simplified electric discharge models, analyzing current, discharged charge, energy dissipation, and event duration. We observe well-defined power laws and global events, highlighting differences in threshold behavior between local and non-local interactions [3].

References

[1] Bak, P. et al., 1987, Phys. Rev. Lett. 59(4), 381.

[2] L. Niemeyer et al., Phys. Rev. Lett., 52(12):1033–1036, 1984.

[3] J. Clark et al, Phys.Rev E, 103(3):032127, 2021.