Figure 2.

(a) The global first Lyapunov vector δU versus time. The blue curve is measured with respect to the ideal trajectory of the unjamming transition, whereas the black curve is with respect to the ideal trajectory of the jamming transition. In the blue curve, the solid line is in the unjamming regime and the dashed line extends the curve in the jamming regime. In the black curve, the solid line is in the jamming regime and the dashed line extends the curve in the unjamming regime. (b) The global velocity V versus time. The inset shows the number of avalanche particles N versus time. (c) η versus V inside (solid squares) and outside (open squares) the unjamming regime, where η is computed from the blue lines in panel (a) as plotted in the inset. (d) δU (the blue lines in (a)) versus V inside (main panel) and outside (inset) the unjamming regime. (e) η versus V inside (solid squares) and outside (open squares) the jamming regime, where η is computed from the black lines in panel (a) as plotted in the inset. (f) δU (the black lines in (a)) versus V inside (main panel) and outside (inset) the jamming regime. Here in the units of δU, η, and V, D represents the average diameter of the disk.