Hysteresis in vibrated granular media

Some general dynamical properties of models for compaction of granular medi a based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The st ationary state is consistent with Edward's theory of powders. The system is submitted to processes in which the tapping strength is monotonically incr eased and decreased. In such processes the behavior of the model resembles the reversible irreversible branches which have been recently observed in e xperiments. This behavior is understood in terms of the general dynamical p roperties of the model, and related to the hysteresis cycles exhibited by s tructural glasses in thermal cycles. The existence of a "normal" solution, i,e., a special solution of the master equation which is monotonically appr oached by all the other solutions, plays a fundamental role in the understa nding of the hysteresis effects. (C) 2000 Elsevier Science B.V. All rights reserved.