Temporal statistics and coarse graining of dislocation ensembles

In the kinetic theory of dislocations, the evolution of the dislocation density is 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 are included. In the present study, these sources are modeled by considering cross-slip and short-range reactions to be stochastic processes in time. The concepts of marked point process and time series are used to analyze the statistical properties of these processes in both time and frequency domains. The statistical data required to perform this analysis has been obtained for copper crystals using the method of dislocation dynamics simulation. The temporal correlations and correlation times of cross-slip and short-range reactions have been computed. It is found that the correlation time for cross-slip is the largest of all correlation times and, as such, it is 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 have been modeled and their rate parameters are determined.