Wavelength Selection of Patterns in a Vibrated Granular Layer

We present a numerical study on the pattern formation in a two-dimensional vibrated granular layer by a molecular dynamics algorithm. Through analysing the granular density distribution, we can explore the inner movement process of particles. It is confirmed that there are a dispersive regime and a saturation regime for frequency dependence, between which a critical frequency exists. It is found that there is another saturation regime for thickness dependence. The wavelength increases with increasing layer thickness, but there is a critical thickness after which the wavelength is unchanged.