DYNAMICS OF SANDPILES - PHYSICAL-MECHANISMS, COUPLED STOCHASTIC-EQUATIONS, AND ALTERNATIVE UNIVERSALITY CLASSES

We present a set of coupled nonlinear stochastic equations in one spac e dimension, designed to model the surface of an evolving sandpile. Th ese include nonlinear couplings to represent the constant transfer bet ween relatively immobile clusters and mobile grains, incorporate the p resence of tilt, and contain representations of inertia and evolving c onfigurational disorder. The critical behavior of these phenomenologic al equations is investigated numerically. It is found to be diverse, i n the sense that different combinations of noise as well as different symmetries lead to nontrivial exponents. In the cases most directly co mparable with previous studies, we find that our equations lead to a s urface with a roughness exponent alpha(tilt)approximate to 0.40, to be compared with the Edwards-Wilkinson and Kardar-Parisi-Zhang values, n amely alpha(EW) = 1/4 and alpha(KPZ) = 1/3, respectively. This is, in our view, directly due to the effect of the tilt term. Finally we disc uss our results, as well as possible modifications to our equations.