Characterization of structural reorganization in rice piles - art. no. 016116

Diagnostics applied to a rice-pile cellular automaton reveal different mech anisms producing power-law behaviors of statistical attributes of grains wh ich are germane to self organised critical phenomena. The probability distr ibutions for these quantities can be derived from two distinct random walk models that account for correlated clustered behavior through incorporating fluctuations in the number of steps in the walk. The first model describes the distribution for a spatial quantity, the resultant flight length of gr ains. This has a power-law tail caused by grains moving through a discrete, power-law distributed number of random steps of finite length. Developing this model into a random walk obtains distributions for the resultant fligh t length with characteristics similar to Levy distributions. The second ran dom walk model is devised to explain a temporal quantity, the distribution of ''trapping'' or ''residence'' times of grains at single locations in the pile. Diagnostics reveal that the trapping time can be constructed as a su m of "subtrapping times," which are described by a Levy distribution where the number of terms in the sum is a discrete random variable accurately des cribed by a negative binomial distribution. The infinitely divisible, two-p arameter, limit distribution for the resultant of such a random walk is dis cussed, and describes a dual-scale power-law behavior if the number fluctua tions are strongly clustered. The form for the distribution of transit time s of rains results as a corollary.