Physical Sandbox System

Consider a cubic box filled with sand. One of the retaining wall of the box can be lowered in arbitrary slow rate so to unload the sand from the box. As the lowering wall moves slow enough, we can expect the sand tumble out sporadically forming distinct avalanche events instead of a continuous out flow. This gives us a very simple avalanche system.

We can characterize each avalanche of the system by its sizes in the three directions, the horizontal direction parallel to the lowering wall, the direction perpendicular to the wall and the vertical height direction, as well as the total amount of sand got displaced.

A very interesting observation is that when we plot the frequency of the avalanches for a given size versus the size on a double log scale, we find the resulting curve is a straight line. This means the distribution follows power-law decay and we can't define a typical size for the avalanches.