Topological characterization of memories formed under oscillatory shear

Disordered systems of particles undergoing oscillatory shear below yield have the remarkable
tendency to fall into trajectories that revisit a configuration encountered by a previous cycle.
This is not only surprising in that a disordered system can happen to do this at all, but instead
in the incredible ease at which these systems reach these states and the rapid and directed
evolution in stroboscopic dynamics. Unfortunately, we currently lack a clear structural
measure that can be associated with this change in dynamical behavior. Here we consider 2D
simulations of jammed Hertzian bidisperse particles and subject the samples to athermal
quasistatic shear. We analyze the structural changes in stoboscopic frames using persistent
homology techniques and find that microscopic topological features develop in these systems
that encode memory of the training amplitude. We apply similar methodology to an experimental system, a cyclic-sheared 2D jammed colloidal suspension, to understand structural signals associated with yielding and memory.