9. Physical Soc Models

In physics, you don't have to go around making trouble for yourself, – nature does it for you. All science is either physics or stamp collecting. Why is the concept of self-organized criticality (SOC), such an interdisciplinary subject, being applied in geophysics, astrophysics, or financial physics with equal fervor? On the most general level, the common denominator of all SOC processes in different science disciplines is the statistics of nonlinear processes, which exhibit omnipresent powerlaw distributions. Nonlinear processes are characterized by a nonlinear growth phase, during which coherent growth is enabled, which has multiplicative characteristics, in contrast to linear processes with incoherent and additive characteristics. Thus, incoherent random processes exhibit binomial, Gaussian, Poissonian, or exponential distribution functions, while coherent processes exhibit powerlaw-like distributions. This is the fundamental trait that earthquakes, solar flares, or stock market crashes have in common, although the underlying physics could not be more different. Therefore, it is important to understand that the powerlaw feature does not require any particular physical model: it can all be explained by mathematical theory in terms of statistical probabilities, as we discussed in Chapters 3 and 4. SOC behavior can thus also be simulated by mathematical rules, as we illustrated in terms of cellular automaton models in Chapter 2. Consequently, our treatment of SOC systems has been entirely physics-free so far, not requiring any particular physical model to understand the observed statistical distributions and correlations. However, there are some free parameters we used in our analytical SOC models (Chapter 3) that can only be explained in terms of a physical model for a particular phenomenon, such as the value α i of the powerlaw slope for each parameter distribution i, or the powerlaw indices β i j between various correlated parameters i and j. At this point, SOC models become specific because the physics of solar flares is different from the physics of tectonic plates. In the following we will focus on specific physical models of astrophysical SOC processes.