Figure 1

Cage jump spatiotemporal organization. Top left: Comparison between the relative averaged relaxation $Q_t(a^{*},{\tau }^{*})/⟨Q_t{⟩}_t$ [gray (cyan)] and the relative percentage $P_t({\tau }^{*})/⟨P_t{⟩}_t$ of particles that have not jumped between $t_0$ and $t_0+{\tau }^{*}$ (black). Inset: Trajectory of a single particle over $14{\tau }_{\alpha }$. Color changes when the particle jumps. Top right: (inner top) Map of $Q_{t_0}({\tau }^{*})$; (inner bottom) particles having jumped during the same lag ${\tau }^{*}$; jumping time is color-coded. Bottom left: Cumulative probability distribution function of the lag between adjacent clusters ${\tau }_1$ (thick green curve), compared to the corresponding curve for a random distribution of clusters (black). Inset: PDF of ${\tau }_1$ (circles). The exponential distribution with same mean is shown for comparison (solid line), as well as exponentials of typical time scale ${\tau }_S$ and ${\tau }_L$ (dotted lines). Bottom right: Spatiotemporal view of the cage jumps in a specific region of space, projected on the $x$ axis. The cluster size is color-coded. Note the aggregation of clusters in avalanches. The typical time scales of the dynamics are shown.Reuse & Permissions

Figure 2

Top: Cage jumps occurring between $t$ and $t+{\tau }_S$ for two different isoconfigurational trajectories, on top of a DW factor map computed at time $t$. Bottom left: Cage jumps occurring in 6 isoconfigurational trajectories between $t$ and $t+{\tau }_S$ tile the high DW regions. Color bar indicates the DW values in levels of gray. Bottom right: Average $⟨(\mathrm{DW}{)}^J⟩$ over the particles having jumped between $t$ and $t+\tau$, divided by the average $⟨\mathrm{DW}⟩$ over all particles, as a function of the lag time $\tau$. Inset: PDF of $(\mathrm{DW}{)}^J$ for the particles jumping in $[t;t+\tau ]$ for several values of $\tau$. The black curve is the PDF for all particles.Reuse & Permissions

Figure 3

Left: Cage jumps occurring in $\tau =17$ on top of a map of the relative difference $(\mathrm{DW}(t+\tau )-\mathrm{DW}(t))/⟨\mathrm{DW}⟩$. Right: Normalized ${\Delta }^J(r)=⟨|\delta (\mathrm{DW}{)}_i|{⟩}_r^J-⟨|\delta (\mathrm{DW}{)}_i|{⟩}_{\infty }^J$ (blue circles) where $⟨|\delta (\mathrm{DW}{)}_i|{⟩}_r^J$ is the absolute difference of DW over $\tau =17$ averaged over the particles in the disk of radius $r$ around a given cage jump. The analogous quantity for the density of jumps ${\rho }^J(r)=⟨{\delta }_i{⟩}_r^J-⟨{\delta }_i{⟩}_{\infty }^J$ (red squares) where ${\delta }_i$ is 1 if particle $i$ jumps between $t$ and $t+\tau$ and 0 otherwise. Error bars: standard deviation.Reuse & Permissions