The ME [18] is a continuity equation (with the source term) for the SDF of defect clusters in a discreet space of their size. This equation provides the most accurate description of cluster evolution in the framework ofthe mean-field approach describ­ing all possible stages, that is, nucleation, growth, and coarsening of the clusters due to reactions with mobile defects (or solutes) and thermal emission of these same species. The ME is a set of coupled differential equations describing evolution of the clusters ofeach particular size. It can be used in several ways. For short times, that is, a small number of cluster sizes, the set of equations can be solved numerically.74 For longer times the relevant physical processes require accounting for clusters containing a very large number of PDs or atoms (^106 in the case of one-component clusters like voids or dislocation loops and ^1012 in the case of two-component particles like gas bubbles). Numerical integration of such a system is feasible on modern computers, but such calculations are overly time consuming. Two types of procedures have been developed to deal with this situation: grouping techniques (see, e. g., Feder et a/.,69

Wagner and Kampmann,70 and Kiritani75) and differ­ential equation approximations in continuous space of sizes (see, e. g., Goodrich67,68, Bondarenko and Konobeev,76 Ghoniem and Sharafat,77 Stoller and Odette,78 Hardouin Duparc eta/.,79 Wehner and Wolfer,80 Ghoniem,81 and Surh eta/.82). The correspon­dence between discrete microscopic equations and their continuous limits has been the subject of an enormous amount of theoretical work. The equations of thermodynamics, hydrodynamics, and transport equations, such as the diffusion equation, are all exam­ples of statistically averaged or continuous limits of discrete equations for a large number of particles. The extent to which the two descriptions give equiva­lent mathematical and physical results has been con­sidered by Clement and Wood.83 In the following two sections, we briefly discuss these methods.