  We use numerical simulations to study the behavior of 2D frictionless disk
systems under cyclic shear as a function of reversal amplitude \gamma_r. Our
studies focus on mean bulk and disk dynamics. These measurements suggest a
crossover from a subdiffusive, \gamma_r dependent regime to a regime where the
grain motions are diffusive, with properties dependent only on total shear
strain. We discuss model stochastic processes that are consistent with these
observations. Finally, we introduce a modified Mean-Squared Displacement (mMSD)
which takes into account the motion of the neighborhood of nearby grains and
yields new insights into local displacement fluctuations. We find that scaling
properties of the displacement distributions are consistent with well studied
stochastic models of anomalous diffusion and suggest scale-invariant cage
dynamics.
