  We investigate experimentally the behavior of the rate of growth of a column
of grains, in a partially filled vertically shaken U-tube. For the set of
frequencies used we identify three qualitatively different behaviors for the
growth rate $\gamma$ as a function of the dimensionless acceleration $\Gamma$:
1) an interval of zero growth for low $\Gamma$ with a smooth change to nonzero
growth, analogous to a continuous phase transition; 2) a sigmoidal region for
$\gamma$ at intermediate values of the dimensionless acceleration $\Gamma$; and
3) an abrupt change from high values of $\gamma$ to zero growth at high values
of $\Gamma$, similar to a first order phase transition. We obtain that our data
is well described by a simple differential equation for the change of the
growth rate with the dimensionless acceleration of the vertical vibrations.
