Abstract
We use molecular-dynamics simulations to study the formation of surface waves in vertically vibrated granular material. We find that the horizontal movements of particles, which are essential for the formation of the waves, consist of two distinct processes. First, the movements sharply increase while the particles are colliding with a bottom plate, where the duration of the collisions is very short compared to the period of the vibration. Next, the movements gradually decrease between the collisions, during which the particles move through the material. We also find that the horizontal velocity field after the collisions is strongly correlated to the surface profile before the collisions.