2D pair-correlation function, g(x,y), in simulations of non-Brownian sheared viscous suspensions.
Left: Final state after cyclic shear of strain amplitude 3. The dark outline around the white central region signifies that many particle pairs will collide for a strain larger than 3. Thus, the system "remembers" this amplitude.
Right: Transient state after cyclic shear of two amplitudes in the pattern 3,2,2,2,2,2, repeat.... There are sharp boundaries identifying both memories. In the final steady state, the system will clear out the entire central region (as in the left picture) thus forgetting the amplitude 2.
Some non-equilibrium systems can store information of their external driving in an unexpected manner. They “learn” multiple driving amplitudes that can subsequently be read out. Notably, only one memory is retained after many driving cycles, even if all of the amplitudes are continually fed in. If noise is added, the system can store all memories indefinitely. While exceedingly counterintuitive, these properties can be understood from simple considerations, in the case of a simple model of sheared viscous suspensions (originally developed by Corte et al. to model the reversibility-irreversibility transition in these systems---see L. Corte et al., Nature Phys. 4, 420, 2008). Furthermore, the memory phenomenon is expected to be generic—the same effect is seen in simulations and experiments on traveling charge-density waves. We are exploring a variety of systems with both simulation and experiment, to understand the sufficient conditions for these memories to exist.
“Multiple transient memories in experiments on sheared non-Brownian suspensions.”, J. D. Paulsen, N. C. Keim, and S. R. Nagel, Phys. Rev. Lett. 113, 068301 (2014)
“Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticity,” N. C. Keim, J. D. Paulsen, and S. R. Nagel, Phys. Rev. E, 88, 032306 (2013).
“Generic transient memory formation in disordered systems with noise”, N.C. Keim and S.R. Nagel, Phys. Rev. Lett. 107, 010603 (2011).
“Noise Stabilization of Self-Organized Memories,” M. L. Povinelli, S. N. Coppersmith, L. P. Kadanoff, S. R. Nagel, S. C. Venkataramani, Phys. Rev. E 59, 4970-4982 (1999).
“Self-Organized Short-Term Memories,” S. N. Coppersmith, T. C. Jones, L. P. Kadanoff, A. Levine, J. P. McCarten, S. R. Nagel, S.C. Venkataramani, and X. Wu, Phys. Rev. Lett. 78, 3983-3986 (1997).