Part II - Models and numerics

Summary

Many different models have been developed in order to study particular features of SOC, such as 1/f noise, non-conservation and anisotropy. In Part II, some of the more important models are introduced and their general properties discussed. At the beginning of each section, the definition and characteristics of each model are catalogued in a box and the exponents listed in a table. Each section is essentially independent, discussing a model in its own right for its particular qualities. Nevertheless, relations to other models are emphasised and a minimal set of common observables (see Sec. 1.3), in particular exponents (Ch. 2), is discussed for each of them.

The attempt to tabulate exhaustively all numerical estimates for exponents of the various models is futile; it is practically impossible to find all published exponents for a model. It is similarly fruitless to draw a clear line between genuine estimates and exponents derived from others using (assumed) scaling relations. Wherever possible, exponents are only listed if the sole underlying assumption is simple scaling as stated in the caption. The tables of exponents therefore serve only to illustrate the variety and sometimes the disparity of results. The exponents are listed in historical order, which often means that the data towards the bottom of the tables are based on more extensive numerics and are thus more reliable. The tables should enable the reader to judge whether a given model displays systematic, robust scaling behaviour or not.