Dynamics of sandpiles: Physical mechanisms, coupled stochastic equations, and alternative universality classes

We present a set of coupled nonlinear stochastic equations in one space dimension, designed to model the surface of an evolving sandpile. These include nonlinear couplings to represent the constant transfer between relatively immobile clusters and mobile grains, incorporate the presence of tilt, and contain representations of inertia and evolving configurational disorder. The critical behavior of these phenomenological equations is investigated numerically. It is found to be diverse, in the sense that different combinations of noise as well as different symmetries lead to nontrivial exponents. In the cases most directly comparable with previous studies, we find that our equations lead to a surface with a roughness exponent ${\mathrm{\alpha }}^{\mathrm{tilt}}$≊0.40, to be compared with the Edwards-Wilkinson and Kardar-Parisi-Zhang values, namely ${\mathrm{\alpha }}^{\mathrm{EW}}$=1/4 and ${\mathrm{\alpha }}^{\mathrm{KPZ}}$=1/3, respectively. This is, in our view, directly due to the effect of the tilt term. Finally we discuss our results, as well as possible modifications to our equations. © 1996 The American Physical Society.