Ki. Hopcraft et al., Fractional non-Brownian motion and trapping-time distributions of grains in rice piles - art. no. 026121, PHYS REV E, 6402(2), 2001, pp. 6121
Non-Gaussian height fluctuations occurring on the fueling time scale of a s
lowly driven rice pile match those observed in some turbulent/critical phen
omena, forming an anticorrelated random fractal process with Hurst exponent
H = 0.2. Inspired by this observation, the concept of fractional Brownian
motion (FBM) is extended to treat stochastic processes with skewed incremen
ts. Simulations of this process for antipersistent motion have first return
time distribution deviating from the t(-2+H) law for FBM. The first return
time distribution of this fractional non-Brownian motion describes and qua
ntitatively determines the trapping-time distribution of grains in rice pil
es upon incorporating a continuous representation of the additional height
fluctuations that occur on the time scale between fueling events.