A minimal model for slow dynamics: Compaction of granular media under   vibration or shear
  Based on experiments of the compaction of granular materials under periodic shear of a packing of glass beads, a minimal model for the dynamics of the packing density as a function of time is proposed. First, a random ``energy landscape'' is created by a random walk (RW) in energy. Second, an ensemble of RWs is performed for various temperatures in different temperature-time sequences. We identify the minimum (mean) of the energy landscape with the maximum (random) density. The temperature scaled by the step-size of the energy landscape determines the dynamics of the system and can be regarded as the agitation or shear amplitude. The model reproduces qualitatively both tapping and shear experiments.   {\bf Key-words}: Compaction, crystallization, Sinai-diffusion, random walks, quenched disorder 
Stefan Luding (1), Maxime Nicolas (2) and Olivier Pouliquen (2) ((1)   ICA1, Stuttgart, Germany (2) IUSTI, Marseille, France)