Recent precise measurements of cosmic ray (CR) spectra reveal features that challenge the hypothesis of CR origin. The results of hybrid simulations focused on the injection phase of the diffusive shock acceleration (DSA) and analytic modeling provide an explanation for an "anomaly" in the measured CR rigidity spectra. Moreover, the simulations have captured a new phenomenon in the DSA: the spectrum steepening associated with the variation of shock obliquity along its face. Both results make a step forward to reconcile the DSA with high-precision observations.<eng>
