Onset of fluidization in vertically shaken granular material

When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation, and other effects. There is a controversial discussion in the literature as to whether there exists a threshold for the Froude number Gamma=A(0)omega(2)(0)/g, below which these effects cannot be observed anymore. By means of theoretical analysis and computer simulation we find that there is no such single threshold. Instead, we propose a modified criterion that coincides with the critical Froude number Gamma(c)=1 for small driving frequency omega(0).