Fig. 2: Dynamics of cyclic shear demonstrates the absence of caging but pronounced memory effect.
From: From creep to flow: Granular materials under cyclic shear
a, b Mean squared displacement in horizontal directions vs. shear cycle number Δn for the ABS and BUMP systems, respectively. Errors are smaller than the size of the symbols. A universal crossover from sub-diffusion (dashed lines) to normal diffusion is observed and occurs at the Γ-dependent yielding strain Δγc. Panel b also includes two trajectories, Γ = 0.05 and 0.1, using a higher sampling rate (factor of 5 and 10/3 respectively), to validate our measurements with a lower sampling rate. c Γ-dependent diffusion coefficient D for the two systems. A crossover at Γ ≈ 0.1 is found for the ABS system, but not for the BUMP system. d and e Memory effect (M is defined in Eq. (1)) as a function of Δγ for both systems from which we define the strain ΔγM (triangles) corresponding to the vanishing of M. Color codes are the same as in panels a and b and errors are estimated to be 0.02. In certain cases, ΔγM is estimated from a linear extrapolation of M(Δγ). f For both systems Δγc(Γ) tracks ΔγM(Γ) and one observes for the ABS system again a crossover at Γ ≈ 0.1. The data of Γ = 0.03 for the BUMP systems are not shown due to the poor statistics. Error bars represent the standard deviations from different realizations for ABS and fitting uncertainty for BUMP.
