Smoothing of sandpile surfaces after avalanche propagation

We focus on a well-known phenomenon, that of the smoothing of a sandpile surface after the propagation of an avalanche. The intuitive idea behind this phenomenon is very simple: disorder builds up on the surface via small configurational changes until it becomes exceedingly rough. Avalanche propagation on a surface in such a highly metastable state has the effect of removing the disorder by transferring grains from bumps to available voids, and thus leaving behind one which is much smoother. We use the framework of coupled continuum equations and cellular automata to model avalanche propagation in sandpiles, and obtain gratifying agreement with the above intuitive picture. We make specific predictions about the roughening exponents in various experimental situations, in particular to do with those pertaining to intermittent and continuous avalanches.