Extreme events-driven glassy behaviour in granular media

Motivated by recent experiment on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator (Nature, 413 (2001) 407), we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: 1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; 2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draw a parallel between macroscopic rearrangements in the system and extreme event whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed a well a the existence of other regimes.