  The theory of the depinning transition of elastic manifolds in random media
provides a framework for the statistical dynamics of dislocation systems at
yield. We consider the case of a single flexible dislocation gliding through a
random stress field generated by a distribution of immobile dislocations
threading through its glide plane. The immobile dislocations are arranged in a
"restrictedly random" manner and provide an effective stress field whose
statistical properties can be calculated explicitly. We write an equation of
motion for the dislocation and compute the associated depinning force, which
may be identified with the yield stress. Numerical simulations of a discretized
version of the equation confirm these results and allow us to investigate the
critical dynamics of the pinning-depinning transition.
