Multi-dimensional memory in low-friction granular materials

To explore what features of multi-dimensional training can be remembered in granular materials, the response of a small, two-dimensional packing of hydrogel spheres to two independent types of shear is measured. Packings are trained <i>via</i> the application of several identical shear cycles, either of a single shear type or combinations of the two types. The memory is then read out using a standard protocol capable of revealing memories as a cusp at the point where readout reaches the training strain. The ability to read out a memory is sensitive not only to the type of deformation applied but also to the order in which different types of training are performed, underscoring the importance of thinking of memories not as single remembered amplitude but as a learned path through phase space. Moreover, while memory capacity (one or multiple) and type of memory (direction, amplitude, duration) have become standard ways of classifying memories, the non-abelian nature of the readout process suggests an additional axis to consider.