Connections between response modes in a horizontally driven granular material.

The behavior of a horizontally vibrated quasi-two-dimensional granular system is observed over a wide range of time scales by mapping the velocity fields at the boundary by using high-speed video and decomposing the behavior of the system into the harmonic, subharmonic, and convective responses. The observed relationships between these responses, as well as the fast shearing and the gap that opens between the material and the sidewalls, lead to a refinement of the current convection model, and also reveal that shearing is completely accounted for by the harmonic response. We find that internal degrees of freedom are always significant under horizontal vibration, as the specific boundary conditions (open surface and horizontal driving) give rise to a surface layer whose motion is decoupled by a narrow shear band from that of the bulk. All observed responses are related to this shear band. For example, the specific shape of the shear band gives rise to the surprising presence of period doubling and period quadrupling. As compared to the case of vertical excitation, all the observed responses now arise through new mechanisms.