The question of whether dislocations could travel faster than shear or longitudinal waves was addressed. The Peierls model, as modified so as to account for drag and gradient effects, yielded a kinetic relationship between the applied shear stress and the speed of a uniformly moving dislocation. This relationship predicted intersonic and supersonic speeds at sufficiently high stresses. However, it also predicted the existence of regimes of unstable motion; in agreement with atomistic simulations.

Supersonic Dislocation Kinetics from an Augmented Peierls Model. P.Rosakis: Physical Review Letters, 2001, 86[1], 95-8