$30^\circ$ sliding path at zero load. Two periods of the quasi static model are shown. The solid (cyan) line and the dashed (magenta) line give the unrelaxed and relaxed energy curves for the quasi-static model, as seen also in figure \[fig:2\]. The black circles are fully relaxed data points of the shearing calculation which shows periodic behavior after the first slip with a considerably shorter period than the quasi-static calculation.[]{data-label="fig:shear_30"}](shear_30.pdf){width="0.9\linewidth"}

This good agreement of our quasi-static results with the shearing calculations adds a convincing argument in favor of our model and justifies the seemingly *ad-hoc* application of unrelaxed energy surfaces. As the periodic paths that were tested in this way turn out to bound the friction force from below and above (see section \[sec:Res\]), it is reasonable to assume that the method will also yield plausible results for aperiodic paths for which the shearing calculations become extremely time consuming. The shearing was carried out at constant distance and not constant load, which would allow to adjust the distance between the slabs. This would decrease the pinning and lower the energy barrier, bringing $E_{\mathrm{shear}}$ even closer to the values obtained with our quasi-static model. We want to mention that our energies 