Simulation Study of Internal and Surface waves of Vertically Vibrated   Granular Materials
  Molecular dynamical (MD) simulations are performed to simulate two dimensional vibrofluidized granular materials in this work. Statistics on simulation results indicate that there exist shocks propagating upward in each vibrating cycle. Under certain driving parameters surface waves similar to Faraday instability in normal fluid coexist with internal waves. Relationship between the two kinds of waves is explored. Moreover simulation results indicate that periodically structured bottom can change the dispersion relationship and amplitude of surface waves. 
Kai Huang, Guoqing Miao, Peng Zhang, Yifei Zhu and Rongjue Wei