Possible Zero-Flux Transport induced by Density Waves in a Tube filled   with Solid Helium
  Macroscopic derivation of the entrainment in a supersolid cylinder induced by a surface elastic wave (of small amplitude) propagating along the flexible interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. We obtain the critical bounds for zero-volume-flow-rate states corresponding to specific rarefaction measure and wave number which is relevant to the rather small critical velocity or disappearance of supersolid flows reported by Rittner and Reppy. 
Kwang-Hua W. Chu