  Some general dynamical properties of models for compaction of granular media
based on master equations are analyzed. In particular, a one-dimensional
lattice model with short-ranged dynamical constraints is considered. The
stationary state is consistent with Edward's theory of powders. The system is
submitted to processes in which the tapping strength is monotonically increased
and decreased. In such processes the behavior of the model resembles the
reversible-irreversible branches which have been recently obaserved in
experiments. This behavior is understood in terms of the general dynamical
properties of the model, and related to the hysteresis cycles exhibited by
structural glasses in thermal cycles. The existence of a "normal" solution,
i.e., a solution of the master equation which is monotonically approached by
all the other solutions, plays a fundamental role in the understanding of the
hysteresis effects.
