SCALING PROPERTIES OF SELF-ORGANIZED CRITICALITY

The scaling properties of a sandpile-type system which displays self-organized criticality are investigated analytically and numerically in two and three dimensions. An earlier clump-based analytical model is modified and extended to account for the scalings and probability distributions of avalanche size, radius, duration, and maximum power in this system, and the scalings of the avalanche sizes with parameters of the driving and system size are also investigated in detail. Comparison with numerical results shows that this model can account for the probability distributions and scaling exponents of both scalar and vector fields in two and three dimensions, once one basic exponent has been determined numerically or by other means.