Fig. 5: Jamming at infinite τp and force chains.
a Kinetic-energy time series as f is lowered, shows complete jamming at f ≈ 1.6. b The variation of the mean kinetic energy with f, shows a continuous transition at f = f *(∞) ≈ 1.6, that goes as 〈E〉 ~ ∣f − f *(∞)∣3/2, shown with dashed line. Error bars denote a standard deviation over 32 independent initial conditions. c The probability distribution of the x component of the total force acting on a particle (passive LJ + active forces), P(Fx) at different values of f, is broad with exponential tails, with a width that decreases continuously with f (inset). From each particle, we have subtracted the centre-of- mass force. At the jamming transition, f = fc, the distribution becomes a delta function at Fx = 0, the force-balanced state. d At the jamming critical point, the forces on the particles are distributed along force chains, as highlighted in the colour map of thresholded forces. The forces are evaluated using a local coarse graining of inter-particle forces acting along each bond between local neighbours, time averaged over δt = 5. The colour represents the strength or magnitude of the forces (shown in the colour bar). Away from the jamming critical point, either by increasing f keeping τp fixed, or decreasing τp keeping f fixed, the force chains dynamically remodel whilst still being embedded in a static contact network. This is seen as a blurring of the colour map of thresholded forces (at f = 3.0 and 2.3) away from the sharp force chains at f = 1.6. e The dynamics of the force chains show a distribution of lifetimes in the force-balanced configuration. The mean lifetime of the force-balanced configurations, computed for f = 1.6 at varying τp, diverges as one moves towards the jamming critical point as a power law, \({\tau }_{F} \sim {\tau }_{p}^{z}\), with z = 0.71 (shown with dashed line).
