A COARSE-GRAINED MODEL FOR GRANULAR COMPACTION AND RELAXATION

We introduce a theoretical model for the compaction of granular materi als by discrete vibrations which is expected to hold when the intensit y of vibration is low. The dynamical unit is taken to be clusters of g ranules that belong to the same collective structure. We rigourously c onstruct the model from first principles and show that numerical solut ions compare favourably with a range of experimental results. This inc ludes the logarithmic relaxation towards a statistical steady state, t he effect of varying the intensity of vibration resulting in a so-call ed 'annealing' curve, and the power spectrum of density fluctuations i n the steady state itself. A mean-field version of the model is introd uced which shares many features with the exact model and is open to qu antitative analysis.