Asymmetric Response of a Jammed Plastic Bead Raft

The successful development of an effective temperature would be an important step in the application of statistical mechanics principles to systems driven far from equilibrium. One direction that has shown promise is the use of fluctuation-dissipation relations. However, driven systems break time-reversal symmetry, and understanding the implications of this for fluctuation-dissipation relations is a critical step in developing effective temperatures. Here we study the response function in a driven system of plastic beads as a function of the density in order to elucidate the generality of the use of fluctuation-dissipation relations. We find that even when a linear response is observed, the time scale of the response is dependent on the direction of the applied stress.

Figure 1

(a) Averaged angular response (solid black line) to an applied square-wave voltage pulse corresponding to an applied torque (dashed red line). The angle and applied torque have been scaled to appear on the same plot. (b) Time series of angular response (solid black line) given an applied square-wave voltage pulse that corresponds to an applied torque (dashed red line). The angle and applied torque have been scaled to appear on the same plot.

Figure 2

The symbols are the final averaged angular displacement of the inner cylinder as a function of the applied voltage pulse given an external rotation rate of $0.01\mathrm{rad}/\mathrm{s}$ and a packing fraction of 0.75. The applied torque is linear in the applied voltage.

Figure 3

Plot of the response times as a function of rotation rate for three different packing fractions (0.72 □, 0.745 ○, 0.77 ▵). Solid symbols correspond to applying a torque in the direction of flow, and open symbols correspond to a torque opposite the flow. The inset is a plot of the correlation times as a function of rotation rate for the same three packing fractions.

Figure 4

(a) Parametric plots of the angular response function versus the angular correlation function. The solid lines are for the response when the applied torque is in the direction of flow. The dashed lines are for the response when the applied torque is in the opposite direction of the flow. In order of decreasing amplitude for the response, the curves are for packing fractions of 0.72, 0.74, and 0.78. (b) A close-up of the two curves for packing fraction 0.78. The dashed and solid lines are the same curves as in (a). Inset in (b) is the correlation function for a packing fraction of 0.78 as a function of time.