Transition from noncollisional to collisional rings. This is explored by simulations with various initial optical depths τ₀ from 0.00025 to 0.06, all using a mass anomaly µ = 0.1. Snapshots of the particle distributions in polar coordinates are shown at various times, using the radial range 1.88–2.28 centered around the resonant semimajor axis a_1/3 ≈ 2.08. The label T_c in the second column indicates the average time interval between impacts, in units of the particle orbital periods. The rightmost column shows the time evolution of the vertical angular momentum L_z distribution with time up to 30 000 central body revolutions. The lowermost simulation (τ₀ = 0.06) is the same as the one shown in the last row of Fig. 5, where it is displayed up to T = 5000.