Evolution over time (in units of the orbital period T _pl at a = a(0) = 1) of the orbital elements for a planet subject to disk-driven migration and e- and i-damping. The planet and disk parameters are reported above each panel. In all panels, we plot the outcome of a hydrosimulation (labeled “fargOCA”) and of two N-body integrations (one with the classical Cresswell & Nelson 2008 damping prescription, labeled “CN2008, orig.,” and one with our modified prescription for τ _e and τ _i , labeled “CN2008, mod.”), as shown in the legend at the bottom. Each column represents a different initial condition for the eccentricity and inclination of the planet, where either e, or i, or both, are initialized at h. We plot on the top row the evolution of the semimajor axis (notice that the curves for the two N-body integrations largely overlap) and on the bottom rows that of the eccentricity and/or inclination. Notice the log scale on the vertical axis, which we use in order to observe the slope of the curves, which is a measure of τ _e and τ _i ; the small oscillations in orbital elements (noticeable especially in the eccentricity evolution) have a frequency equal to the orbital frequency and have a relatively constant amplitude.