Effect of vertical vibrations on avalanches in granular systems

We discuss the effect of vertical vibration on the dynamics of avalanches on the surface of quasi-two-dimensional granular systems using a minimal ``mesoscopic'' model in a regime where no bulk convection of the grains is present. We give a simple picture of why large vibration strengths or high vibration frequencies can drastically reduce the static limit of the dynamic friction coefficient entering the minimal model. We derive an exact relation for the minimal angle of repose and perform an asymptotic analysis to obtain the time evolution of the angle of the free surface, which compares well with a recent experiment.