On the formation and stability of dislocation patterns. II. Two- dimensional considerations (Q1071593)

We consider the motion and interaction of dislocation species on the slip plane via two-dimensional partial differential equations of the reaction- diffusion type. We distinguish between slow moving dislocations with mobilities along both the slip direction and the direction perpendicular to it (random motion), and fast moving dislocations with mobility along the slip direction only (stress-driven motion). The competition between gradients and nonlinearities leads to stable periodic dislocation structures with wavevector parallel to the slip direction, and an intrinsic wavenumber given by the same formula as in the one dimensional analysis of part I [see the summary above (Zbl 0586.73184)]. In addition to the one-dimensional results, however, we find here that splitting of the periodic structures and development of superdefects is possible, according to experimental observations.