Dynamics of a the surface of a layer of grains vibrated horizontally
Temporal traces of the mean velocity of grains (red curves) at the surface for a layer of 9 particles diameters depth, oscillated at frequency of 3.5 Hz, in the container frame. The blue dashed lines give the container position proportional to the fictitious force acting on the grains in the accelerated box frame. At an acceleration equal to 0.39 g (a), there is only a small ocillation of the grains around their equilibrium position (see movie) whereas at higher acceleration (curves b, c and d) a clear motion of the grains, relative to the container, can be seen. Notice that on curves (b) and (c), where the acceleration is respectively 0.44 g and 0.46 g, this motion occurs only on a part of the cycle (see movie) whereas on curve (d), where the acceleration is 0.48 g, the motion is fully developed during all the cycle (see movie). More astonishing, plots (b) and (c) the motion starts when the fictitious force acting on the grains is nearly 0 and it stops when this force reaches its extremum !!!