prediction for an elastic line, Eq. (\[eq:fpin\]), we need to specify a line energy: We identify the wave vector corresponding to the pinning length as $q_{\rm p} = 2 \pi/L_{\rm p}$ and obtain the corresponding line energy from Figure \[fig:eqdis\], thus assuming that pinning is controlled by an effective value of the line energy on the scale of the pinning length. This allows us to calculate a pinning force from Eq. (\[eq:fpin\]), from which the predicted crss derives by simply setting $f_{\rm c} = \tau_{\rm c}b$. Predicted crss values are compared to values deduced from the simulations in Figure \[fig:crss\], top. It can be seen that in the regime of weak pinning, here up to a force amplitude of about $\hat{f}=$0.02 N/m, corresponding to a pinning length of about 100$b$, the simulated crss data (black squares in Figure \[fig:crss\], top) follow to a good approximation the prediction for an elastic line (red circles in Figure \[fig:crss\], top). Deviations occur in the regime of strong pinning, corresponding to the regime where the pinning length deviates from the weak pinning result and tends towards a saturation: In this regime, we see a cross-over from an exponent $p=4/3$ in the $\tau_{\rm c} \propto 