Effective Dimension Transition of the Dynamics of Granular Materials in   the Pipe
  Phase transition of strongly excited granular materials in 2D pipe is investigated numerically. By changing the ratio between width of the pipe and the height of the granular bed, we observe the transition between the 1 dimensional like state and the actual 2 dimensional state. Moreover, it is found that the character of the transition changes when the magnitude of dissipation passes through a critical value. 
Akinori Awazu