Synchronization mechanism of sharp edges in rings of Saturn
  We propose a new mechanism which explains the existence of enormously sharp edges in the rings of Saturn. This mechanism is based on the synchronization phenomenon due to which the epicycle rotational phases of particles in the ring, under certain conditions, become synchronized with the phase of external satellite, e.g. with the phase of Mimas in the case of the outer B ring edge. This synchronization eliminates collisions between particles and suppress the diffusion induced by collisions by orders of magnitude. The minimum of the diffusion is reached at the center of the synchronization regime corresponding to the ratio 2:1 between the orbital frequency at the edge of B ring and the orbital frequency of Mimas. The synchronization theory gives the sharpness of the edge in few tens of meters that is in agreement with available observations. 
D. L. Shepelyansky, A. S. Pikovsky, J. Schmidt and F. Spahn