Modeling temporal fluctuations in avalanching system
Abstract
We demonstrate how to model the toppling activity in avalanching systems by stochastic differential
equations (SDEs). The theory is developed as a generalization of the classical mean field
approach to sandpile dynamics by formulating it as a generalization of Itoh’s SDE. This equation
contains a fractional Gaussian noise term representing the branching of an avalanche into small
active clusters, and a drift term reflecting the tendency for small avalanches to grow and large
avalanches to be constricted by the finite system size. If one defines avalanching to take place when
the toppling activity exceeds a certain threshold the stochastic model allows us to compute the
avalanche exponents in the continum limit as functions of the Hurst exponent of the noise. The
results are found to agree well with numerical simulations in the Bak-Tang-Wiesenfeld and Zhang
sandpile models. The stochastic model also provides a method for computing the probability density
functions of the fluctuations in the toppling activity itself. We show that the sandpiles do not belong
to the class of phenomena giving rise to universal non-Gaussian probability density functions for
the global activity. Moreover, we demonstrate essential differences between the fluctuations of total
kinetic energy in a two-dimensional turbulence simulation and the toppling activity in sandpiles
Metadata
Show full item recordThe following license file are associated with this item: