Symmetry and Memory in Driven Disordered Systems

Abstract

Steadily shearing a non-Brownian suspension forms a memory of direction in its structure, while periodically shearing it forms a memory of amplitude. Our experiments show that these memories coexist and compete within a limited memory capacity. A specific oscillatory amplitude, previously associated with a critical transition, suppresses the directional (fore-aft) asymmetry. A similar picture is known in amorphous solids. We propose that these competing kinds of memory are a motif for non-equilibrium systems coupled to a scalar drive and are a basic example of interplay between memories.

Figures (6)

• Figure 1: Writing and reading memories in non-Brownian suspensions. (a) Experimental setup. Circular arrows are shear directions. (b) Memory of direction. Inset: Protocol. Initial steady shear (black) in CCW direction precedes readout (red or blue). Main panel: Normalized viscosity (see text) during readouts. Resuming same direction (red) yields same viscosity; reversing (blue) causes a drop. (c) Memory of amplitude. Inset: Oscillatory protocol with amplitude $\gamma_T = 0.6$ and readout (red). Main panel: Viscosity during readout (black). Derivative (red curve) peaks at $\gamma_T$.
• Figure 2: Memories of direction and amplitude can coexist. (a) Schematic of protocols that combine memories. Readout (red) matches direction of preparation. Oscillatory portion shows amplitudes $\gamma_T=0.6$ (solid) and $\gamma_T=1.4$ (dashed). Only five cycles are shown for clarity (see text). (b) Protocol with readout (blue) in opposite direction. To avoid introducing a reversal at $\gamma = 0$ we add a half-cycle. (c) Normalized viscosity during readouts. Red and blue curves are from protocols (a) and (b) respectively; solid and dashed lines represent the two $\gamma_T$. Insets: Derivative of viscosity shows peaks at $\gamma_T$.
• Figure 3: Effect of oscillatory shear on memory of direction. Magenta circles: Asymmetry $\delta$ corresponds to area between blue and red curves in Fig. \ref{['fig:modap_vis_dvis']}c (protocols reproduced in lower-left insets). With sufficiently large amplitude $\gamma_T$, $\delta = 0$ and there is no trace of the direction of initial shear. Blue diamonds: Results when oscillatory shear always ends in the same direction as preparation (protocols in upper-right insets). Amplitude $\gamma_T \approx 1.6$ erases memory of direction; $\gamma_T > 1.6$ forms a new one.
• Figure 4: Memory peaks for training amplitudes from 0.2 to 2. Beyond 1.6, the amplitude memory is not discernible from the background even after 40 cycles of training. Black curve with $\gamma_T = 0.0$ (no training) is equivalent to resumption of steady shear in Fig. \ref{['fig:full']}(b). Insets: Viscosity curves and abbreviated protocol.
• Figure 5: Turning points are remembered separately. Plot shows first derivative of viscosity during readout. The red curve’s peak corresponds to the memory of $\gamma_{+}$, while the blue curve’s peak represents the memory of $\gamma_{-}$. The dashed red and blue peaks show $\gamma_{+}$ and $\gamma_{-}$ when the direction of the initial steady shear is reversed relative to their respective readout directions, which attenuates the memory of amplitude.