Climbing of dislocations in nonequilibrium patterns

Abstract

The steady-state climbing motion of isolated dislocations is studied both analytically and numerically in several two-dimensional model systems. Numerical measurements of the wave vector at which the defect is stationary are generally found to be in agreement with predicted values. Measurements of the climbing velocity as a function of wave vector reveal a basic difference between relaxational and nonrelaxational models, and this is understood in terms of a formalism which does not depend on a perturbation expansion near onset. Finally, the effects of coupling to a drift velocity generated by vertical vorticity are explicitly studied. The behavior in this case is of the same characteristic form as general nonrelaxational models without vorticity.