Test runs: left panel: azimutally averaged radial profile of the normalized surface density for a fiducial case with no companion. The expected theoretical asymptotic behaviour in r^-1.5 is plotted as a reference. The initial extension of the parent body ring is set to r = 1. Right panel: azimutally averaged radial profile of the normalized surface density for a companion of eccentricity e_b = 0.5 as compared to the results of Thébault et al. (2010) with a different code. For this with-companion run, distances have been normalized to the theoretical limit for orbital stability r_crit (see Sect. 3.1).