Fractional non-Brownian motion and trapping-time distributions of grains in rice piles.

Abstract

Non-Gaussian height fluctuations occurring on the fueling time scale of a slowly driven rice pile match those observed in some turbulent/critical phenomena, 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 increments. 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 quantitatively determines the trapping-time distribution of grains in rice piles upon incorporating a continuous representation of the additional height fluctuations that occur on the time scale between fueling events.