  We propose a theory of shear flow in dense granular materials. A key
ingredient of the theory is an effective temperature that determines how the
material responds to external driving forces such as shear stresses and
vibrations. We show that, within our model, friction between grains produces
stick-slip behavior at intermediate shear rates, even if the material is
rate-strengthening at larger rates. In addition, externally generated acoustic
vibrations alter the stick-slip amplitude, or suppress stick-slip altogether,
depending on the pressure and shear rate. We construct a phase diagram that
indicates the parameter regimes for which stick-slip occurs in the presence and
absence of acoustic vibrations of a fixed amplitude and frequency. These
results connect the microscopic physics to macroscopic dynamics, and thus
produce useful information about a variety of granular phenomena including
rupture and slip along earthquake faults, the remote triggering of
instabilities, and the control of friction in material processing.
