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 in order to treat the yield strength anomaly in L12 intermetallic compounds. In addition to numerical solutions, the latter work had also furnished deterministic mean-field equations for the dynamics. Fixed-point stability analysis was used here in order to solve the mean-field equations analytically. The analytical solutions were compared with the previously obtained numerical solutions. As in the case of numerical exact solutions, the mean-field solutions exhibited a pinning/de-pinning 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