Multiple transient memories, originally discovered in charge-density-wave
conductors, are a remarkable and initially counterintuitive example of how a
system can store information about its driving. In this class of memories, a
system can learn multiple driving inputs, nearly all of which are eventually
forgotten despite their continual input. If sufficient noise is present, the
system regains plasticity so that it can continue to learn new memories
indefinitely. Recently, Keim & Nagel showed how multiple transient memories
could be generalized to a generic driven disordered system with noise, giving
as an example simulations of a simple model of a sheared non-Brownian
suspension. Here, we further explore simulation models of suspensions under
cyclic shear, focussing on three main themes: robustness, structure, and
overdriving. We show that multiple transient memories are a robust feature
independent of many details of the model. The steady-state spatial distribution
of the particles is sensitive to the driving algorithm; nonetheless, the memory
formation is independent of such a change in particle correlations. Finally, we
demonstrate that overdriving provides another means for controlling memory
formation and retention