  Nonlinear relaxation dynamics of a vertically-vibrated granular pile is
experimentally studied. In the experiment, the flux and slope on the relaxing
pile are measured by using a high-speed laser profiler. The relation of these
quantities can be modeled by the nonlinear transport law assuming the uniform
vibro-fluidization of an entire pile. The fitting parameter in this model is
only the relaxation efficiency, which characterizes the energy conversion rate
from vertical vibration into horizontal transport. We demonstrate that this
value is a constant independent of experimental conditions. The actual
relaxation is successfully reproduced by the continuity equation with the
proposed model. Finally its specific applicability toward an astrophysical
phenomenon is shown.
