In the kinetic theory of dislocations, the evolution of the dislocation density was governed by a hierarchy of kinetic equations in which a number of source terms associated with cross-slip and short-range (junction and annihilation) reactions were included. In the present study, these sources were modelled by considering cross-slip and short-range reactions to be stochastic processes in time. The concepts of marked point process and time series were used to analyze the statistical properties of these processes in both time and frequency domains. The statistical data required to perform this analysis was obtained for copper crystals using the method of dislocation dynamics simulation. The temporal correlations and correlation times of cross-slip and short-range reactions were computed. It was found that the correlation time for cross-slip was the largest of all correlation times and, as such, it was considered here to be the coarse graining time-scale in continuum dislocation dynamics. Using this mesoscopic time-scale, the continuous source terms in the kinetic equations of dislocations were modelled and their rate parameters were determined.

Temporal Statistics and Coarse Graining of Dislocation Ensembles. J.Deng, A.El-Azab: Philosophical Magazine, 2010, 90[27-28], 3651-78