The purpose of the lattice grain model is to predict the
behavior of large numbers of grains (10,000 to 1,000,000) on
scales much larger than a grain diameter. In this respect, it
goes beyond the particle dynamics calculations of Section 9.2,
which are limited to no more than grains by currently available
computing resources [Cundall:79a], [Haff:87a;87b], [Walton:84a],
[Werner:87a]. The particle dynamics models follow the motion of
each individual grain exactly, and may be formulated in one of
two ways depending upon the model adopted for particle-particle
interactions. In one formulation, the interparticle contact
times are assumed to be of finite duration, and each particle
may be in simultaneous contact with several others
[Cundall:79a], [Haff:87a], [Walton:84a], [Werner:87a]. Each
particle obeys Newton's law, F = ma, and a detailed integration
of the equations of motion of each particle is performed. In
this form, while useful for applications involving a much
smaller number of particles than LGrM allows,