3 - Systems Exhibiting SOC

Summary

Introduction

In this chapter we examine the extent to which self-organized criticality is of relevance to real physical systems. A large number of experiments have purported to reveal generic SOC behavior. We do not pretend to know the final and definite answer. Some systems are more accessible to experimentation than others. It is easier to settle the question concerning the distribution of avalanche sizes in a pile of a certain granular material than to determine the properties of biological evolution. Self-organized criticality might, in the end, not be the most useful way to describe some of the dynamical systems we discuss in this book. However, I consider it an undeniable achievement the degree to which SOC developments have revived interest in the dynamics of (say) sandpiles. In this chapter we discuss the phenomenological implications of a set of experimental observations.

According to the seminal 1987 paper by Bak, Tang, and Wiesenfeld (BTW), the hallmark of SOC is its lack of any scale, in time as well as in space. As a consequence, we observe spatial fractals and temporal 1/f fluctuations. Thus the strategy for our experimental search for SOC is clear. Measure some of the time-dependent quantities of the system. Construct the power spectrum of the signal. If the spectrum behaves like l/f^β with β ≃ 1, must we then be dealing with SOC? No, not necessarily so (O'Brien and Weissman 1992, 1994). In fact, most power spectra found in connection with the search for SOC extend only over a narrow frequency interval.