Closed model for granular compaction under weak tapping.

A one-dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated with the creation and destruction of empty sites. The model is shown to be consistent with Edwards' thermodynamics theory of powders. The relationship with lattice models in which the number of particles is not conserved is discussed.