Translational and Rotational Dynamical Heterogeneities in Granular Systems

We use x-ray tomography to investigate the translational and rotational dynamical heterogeneities of a three dimensional hard ellipsoid granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated or anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly, these clusters are formed already at time scales that are much shorter than the $\alpha$-relaxation time, in stark contrast to the behavior found in glass-forming systems.

Figure 1

Snapshots showing the fast translating (FT, blue) and fast rotating (FR, yellow) particles [$\gamma =0.10(\mathrm{L})$, $t=1000$]. Also shown are the particles that are FT as well as FR (FB, green). Note that both types of particles form clusters and that these clusters overlap significantly. Panels (a) and (b) are for the filter time $t_f=50$ and $t_f=200$, respectively.

Figure 2

Cluster size distribution $P(s)$ for FT, FR, ST, and SR. (The first three sets have been shifted vertically.) The solid black lines are the distributions obtained by randomly picking particles in the system. The dashed red lines are fits to the data with a power law with exponents stated next to these lines. (a) Different strain amplitude $\gamma$. (b) Different filter times $t_f$.

Figure 3

Radius of gyration of the FT clusters vs $s$ for different values of $\gamma$. Black dots are the average at fixed $s$. The solid lines are a guide to the eye with slope 0.5. For the sake of clarity the data for $\gamma <0.2$ have been shifted to the right by 10, $10^2$, and $10^3$.

Figure 4

Probability that a particle that was fast or slow at $t=0$ is still fast or slow at time $t$. Black solid lines are exponential fits to the data at short times. Panels (a) and (b) are for the TDOF and RDOF, respectively. The data for SR are fitted with a power law (black dashed line). The FR and FR data have been shifted vertically.

Figure 5

Probability that a particle is undergoing a FT as well as FR (ST and FR) as a function of the filter time $t_f$. The different symbols correspond to different strain amplitudes. The dashed line shows the probability at long times.