Is there a critical acceleration for the onset of convection?

Abstract

Suppose granular material is shaken vertically with z(t)=A_0 cos(ω_0 t). Can we expect to find convection if A_0ω_0^2 < g? By means of theoretical analysis and computer simulation we find that there is no critical Γ=|A_0|ω_0^2/g for the onset of convection. Instead we propose a modified criterion which coincides with Γ=1 for small frequency ω_0.