Narrow ring perturbed by an outer planet. a) Normalized surface density profile viewed head-on, for the nominal case with μ = 0.002, a_p = 75  AU and τ_O = 2 × 10^-3 (run C). The planet’s location is marked by the ⊕ symbol; b) azimuthally averaged radial distribution of the geometrical cross-section as a function of particle sizes (as parameterized by their β ratio) for run C; c) same as b), but for a denser and more collisionally active disc with τ = 2 × 10^-2 (run E); d) same as b), but for a more tenuous disc with τ = 5 × 10^-5 (run D).