Encoding of Memory in Sheared Amorphous Solids

We show that memory can be encoded in a model amorphous solid subjected to athermal oscillatory shear deformations, and in an analogous spin model with disordered interactions, sharing the feature of a deformable energy landscape. When these systems are subjected to oscillatory shear deformation, they retain memory of the deformation amplitude imposed in the training phase, when the amplitude is below a “localization” threshold. Remarkably, multiple persistent memories can be stored using such an athermal, noise-free, protocol. The possibility of such memory is shown to be linked to the presence of plastic deformations and associated limit cycles traversed by the system, which exhibit avalanche statistics also seen in related contexts.

Figure 1

MSD and distance $d$ (scaled by $N$) between configurations before and after a reading cycle as a function of the amplitude $\gamma$, starting from samples trained by oscillatory deformation at (a) ${\gamma }_1=0.06$ for the BMLJ model and (b) ${\gamma }_1=0.3$ for the NK model. The value at which the training is performed can be easily read, and configurations can be altered by cycles of amplitude $\gamma <{\gamma }_1$, even if obtained after a long series of training oscillations.

Figure 2

(a) Potential energy measured in a reading cycle starting from a BMLJ sample trained at ${\gamma }_1=0.06$ for different oscillation amplitudes $\gamma =0.052$, 0.06, 0.068. The data series almost overlap and are all well fit by the same quadratic profile. In (b)–(d), the quadratic fitting function is subtracted to obtain $\mathrm{\Delta }E$, and the ends of the curves are marked with symbols. The three lines initially follow the same path (for positive strains) and separate as the respective amplitudes are reached. The green line in (c) does join itself at zero strain after a full cycle, but this doesn’t happen for the other oscillation amplitudes (the red and blue lines have loose ends) so that samples leave the stable orbit for $\gamma \ne {\gamma }_1$.

Figure 3

MSD and distance $d$ (scaled by $N$) between configurations before and after a reading cycle as a function of the amplitude $\gamma$, starting from samples trained by oscillatory deformation at (a) ${\gamma }_1=0.06$, ${\gamma }_2=0.04$ (as described in the text) for the BMLJ model and (b) ${\gamma }_1=0.3$, ${\gamma }_2=0.2$ for the NK model. The values at which the training is performed can be easily read even after a large number of oscillations, as samples retain multiple memories of the training phase in a persistent way.

Figure 4

(a) Snapshot of a BMLJ reversible sample trained and read with ${\gamma }_1$ and $\gamma =0.06$. Particles that move more than $0.1{\sigma }_{AA}$ during different transitions occurring in the reading cycle are drawn in different colors at the positions that they occupy at the beginning of the cycle. (b) Plot of the size of clusters of particles that move more than $0.1{\sigma }_{AA}$ (particles belong to the same cluster if their distance is $<1.4{\sigma }_{AA}$) during transitions. Large clusters become increasingly rare as their size grows.