Abstract
Shortly after the seminal paper "Self-Organized Criticality: An
explanation of 1/f noise" by Bak et al. (1987), the idea has been
applied to solar physics, in "Avalanches and the Distribution of Solar
Flares" by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics
took place, where the SOC concept was initially applied to solar flares,
stellar flares, and magnetospheric substorms, and later extended to the
radiation belt, the heliosphere, lunar craters, the asteroid belt, the
Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole
objects, cosmic rays, and boson clouds. The application of SOC concepts
has been performed by numerical cellular automaton simulations, by
analytical calculations of statistical (powerlaw-like) distributions
based on physical scaling laws, and by observational tests of
theoretically predicted size distributions and waiting time
distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated
also vigorous debates about the discrimination between SOC models,
SOC-like, and non-SOC processes, such as phase transitions, turbulence,
random-walk diffusion, percolation, branching processes, network theory,
chaos theory, fractality, multi-scale, and other complexity phenomena.
We review SOC studies from the last 25 years and highlight new trends,
open questions, and future challenges, as discussed during two recent
ISSI workshops on this theme.
