If the motion of granular material occurs slowly, particles will stay in contact and interact frictionally with their neighbors over long periods of time. This is the ``quasi-static'' regime of granular flow and has been classically studied using modified plasticity models [21,20,34] based on a Coulomb friction criterion [68,69].
At the other extreme is the rapid-flow regime which corresponds to high-speed flows [193,52]. Instead of moving in many-particle blocks, each particle moves freely and ``independently''. In the rapid-flow regime, the velocity of each particle may be decomposed into a sum of the mean velocity of the bulk material and an apparently random component to describe the motion of the particle relative to the mean. The analogy between the random motion of the granular particles and the thermal motion of molecules in the kinetic-theory picture of gases is so strong that the mean-square value of the random velocities is commonly referred to as the ``granular temperature'' - a term first used by Ogawa [171]. As pointed out in the introduction, however, granular temperature has nothing to do with environmental thermal temperature, which usually plays no role in the dynamics of granular flows. Nevertheless, using this kinetic analogy, granular temperature generates pressure and governs the internal transport rates of mass, momentum and energy. Thus, while the term temperature sometimes leads to some semantical confusion for the uninitiated, the physical analogy between the two temperatures is so apt that its use has become standard throughout the field.