Multiple Transient Memories in Experiments on Sheared Non-Brownian Suspensions

Abstract

A system with multiple transient memories can remember a set of inputs but subsequently forgets almost all of them, even as they are continually applied. If noise is added, the system can store all memories indefinitely. The phenomenon has recently been predicted for cyclically sheared nonBrownian suspensions. Here we present experiments on such suspensions, finding behavior consistent with multiple transient memories and showing how memories can be stabilized by noise.PACS numbers: 05.65.+b, 82.70.Kj A physical system has memory if it is endowed with the basic operations of imprinting, retrieval, and erasure. Common examples are mechanical marking or the flipping of magnetic domains. More exotic examples include return-point memory [1,2] and aging and rejuvenation in glasses [3,4]. These systems all support the intuition that (i) the more times an input is presented the stronger the memory becomes, and (ii) random noise is detrimental to memory retention. However, both attributes are violated by multiple transient memories, which have been seen in traveling charge-density waves [5,6] and predicted for sheared non-Brownian suspensions [7,8]. The experiments reported here on sheared suspensions demonstrate that noise can stabilize this form of memory retention.Keim and Nagel [7] described how multiple transient memories could occur in a simplified model of a suspension under cyclic shear: When sheared repeatedly between strain amplitudes γ = 0 and γ = γ 1 , a suspension can organize into a reversible steady state, thereby encoding a memory of γ 1 . The memory appears as a sudden drop in reversibility as the strain amplitude is swept past γ 1 . Multiple memories can be formed if several amplitudes, γ 1 < γ 2 < ... < γ n , are repeatedly applied. However, once the suspension relaxes to a state that is completely reversible up to amplitude γ n , it is also reversible for all γ < γ n ; thus the memories of all the smaller training amplitudes are effectively erased. The presence of noise was predicted to prevent the system from reaching a fully reversible state so that other memories could be retained.For multiple transient memories in charge-density waves, the role of noise was only demonstrated in a simulation [6]; in experiments [5] the ambient noise could not be varied and was assumed to be strong enough so that the system could remember all inputs. In the present paper, we cyclically shear neutrally buoyant, non-Brownian suspensions at low Reynolds number. By varying the noise, we demonstrate explicitly that noise is required to retain a memory of all input strain amplitudes at long times. This provides a concrete example of the emergence of plasticity in memory.Experiment.-In the experiment, a viscous suspension is cyclically sheared in a 6.3 mm gap between two cylinders in a circular Couette geometry (with an inner cylinder radius of 36.6 mm). The suspension is composed of PMMA spheres (Cospheric, LLC) in a mixture of Triton X-100, water, and zinc chloride (dynamic viscosity µ = 4,300 mPa s) that is index a...

Memory formation and evolution of the vortex configuration associated with random organization

“…Note again that this experiment is always conducted for the input vortex configuration corresponding to the irreversible state near RIT (d d c inp  ). In the colloidal system, by contrast, the input configuration corresponding to the reversible state (d d c inp < ) was used [25,26]. Accordingly, when the readout experiment was carried out using d smaller than d inp , one would never observe collisions between the particles, and transient phenomena never appear.…”

“…It has been shown numerically and experimentally in the colloidal system that the information of the training (input) shear amplitude d inp ( d c < ) is stored in the configuration of the particles, and this memory is readable not only from the configuration in the reversible state but also from that in the transient state before the system reaches the final reversible state [25,26]. Using the vortex system, we also examine the memory effect of the training amplitude d inp , which may be stored in the input configuration of the transient state as well as the steady state.…”

“…In particular, it is of great interest how random organization evolves with the increase in the cycle number n of the ac shear. Related to this problem, theoretical [25] and experimental [26] studies on the colloidal system have found that the information of the input shear amplitude is memorized in the configuration of the particle distributions, and it is readable by a subsequent readout experiment with various shear amplitudes.…”

“…Then, we explore whether we can experimentally obtain the information as to how the random organization evolves with an increase in the cycle numbers n of ac shear. For this purpose, we have conducted two-step measurements [25,26] for a stripshaped a-Mo x Ge 1−x film [5,23] where the reordering of the vortex distributions is exclusively determined by the local shear due to the random pinning potential and ac drive. In the first input (or training) experiment, we initially prepared the most disordered vortex distribution [27], which was subsequently subjected to an ac drive with a moderately small displacement amplitude d inp slightly larger than d c .…”

Period proliferation in periodic states in cyclically sheared jammed solids

“…Once it returns to that configuration, the dynamics repeats itself indefinitely. At low densities in the absorbing state, the particles follow the flow without ever making contact with one another so that the system moves back and forth along a flat direction in the energy landscape [2][3][4], and particles return to their original positions after a single shear cycle: T = 1. As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations.…”