9 - Mechanisms

Summary

How does SOC work? What are the necessary and sufficient conditions for the occurrence of SOC? Can the mechanism underlying SOC be put towork in traditional critical phenomena? These questions are at the heart of the study of SOC phenomena. The hope is that an SOC mechanism would not only give insight into the nature of the critical state in SOC and its long-range, long-time correlations, but also provide a procedure to prompt this state in other systems. In the following, SOC is first placed in the context of ordinary critical phenomena, focusing on the question to what extent SOC has been preceded by phenomena with very similar features. The theories of these phenomena can give further insight into the nature of SOC. In the remainder, the two most successful mechanisms are presented, the second of which, the Absorbing State Mechanism (AS mechanism), is the most recent, most promising development. A few other mechanisms are discussed briefly in the last section.

SOC mechanisms generally fall in one of three categories. Firstly, there are those that show that SOC is an instance of generic scale invariance, by showing that SOC models cannot avoid being scale invariant, because of their characteristics, such as bulk conservation and particle transport. The mechanism developed by Hwa and Kardar (1989a), Sec. 9.2, is the most prominent example of this type of explanation. This approach focuses solely on criticality and dismisses any self-organisation.