How many memories can be stored in a disordered material?

Jammed packings have long been used to model return point memory. In this process, a cyclic shear is applied for several training cycles at a given amplitude to establish a memory. The system will retain this memory if smaller amplitude oscillations are applied, however, as soon as a perturbation is applied with an amplitude larger than that of the training amplitude, the system forgets the original memory. While theoretically and experimentally useful, this setup can only hold one memory at a given time. Several recent studies have sought to extend this model by applying perpendicular oscillations, but these efforts are met with limited success and a fundamental upper limit of 2 stored memories in a 3D system. Here we describe a localized perturbative scheme which allows several spatially independent memories to be stored, thus vastly expanding the utility of mechanical memory storage in disordered systems.