\hat{f}^p$ relationship to an exponent of 1. The transition occurs at a pinning length of $L_{\rm p} \approx 5 \xi$, for larger pinning lengths the weak pinning relations are well fulfilled.

We next turn to the possibility of predicting the crss on the basis of the pinning length alone using Eq. (\[eq:fpin\]). As can be seen in Figure \[fig:crss\], bottom, this equation produces excellent results in the weak pinning regime $L_{\rm p} > 100 b = 5 \xi$.

![Top: critical resolved shear stress as function of amplitude $\hat{f}$ of the random force field, full squares: crss values determined from our simulations, open circles: prediction from Eq. (\[eq:fpin\]); bottom: critical resolved shear stress as function of pinning length (pinning length as in Figure \[fig:pinlength\]), full squares: crss values determined from our simulations, open circles: prediction from Eq. (\[eq:fpinL\]). \[fig:crss\]](CRSS.pdf){width="3.3in"}

This finding is important because it suggests that, in the weak pinning regime, estimates of the zero-temperature critical resolved shear stress can be obtained by studying the static properties of a dislocation at zero stress on scales of the pinning length only - scales that are accessible to molecular or even ab-initio simulation methods. Depinning, on the other hand, involves complex spatio-temporal 