A fixed-point analysis was presented for the equations which described the motion of a dislocation in the presence of thermally activated cross-slip pinning events. A stochastic finite-difference model had previously been proposed with regard to the yield strength anomaly which was observed in L12 intermetallic compounds (where the strength increased with increasing temperature). In addition to numerical solutions, deterministic mean-field equations had also been derived in order to describe the dynamics. A fixed-point stability analysis was used here to solve these mean-field equations analytically. The analytical solutions were compared with previously obtained numerical solutions. As in the case of the exact (numerical) solutions, the mean-field solutions exhibited a pinning/depinning transition.

Dislocation Pinning/Depinning Transition: Fixed-Point Analysis. D.G.Tekleab, J.W.Lawson, M.S.Daw: Physical Review B, 2000, 62[2], 839-43