Fig. 1: Cluster formation of C-particles under vibration.
a 4000 steel C-particles entangle in a conical container under vibration. The C-particle geometry is shown in the callout. C-particles with θ = 25° form a long cluster at t = 8.0 s (b) and a compact, rigid cluster at t = 120 s that retains its in-container shape (c). More results are shown in Supplementary Movie 2. d DEM simulation of sequentially lifted C-particles (θ = 20°, N = 4000) after t = 53 s of vibration under gravity. In this trial, the number of particles in the 442 clusters are s1 = 3097, s2 = 167, s3 = 54, …, s442 = 1. Relative size of the largest lifted cluster S1 increases with vibration time t in experiments (e) and simulations (f, g). Raw data are in Supplementary Fig. 1b–e. Susceptibility χ(t) in experiments (h) and simulations (i). In e–i, markers indicate ensemble averages, and shaded areas indicate standard error bands. j Heat map of ensemble-averaged S1 for lifted clusters at various t and θ. The blue region at small θ indicates that particles are not yet entangled; the blue region at large θ indicates that the clusters are easily broken when lifted.
