Stochastic analysis of two-dimensional grain growth

Consideration of the physics and topology of the two-dimensional grain grow th suggests that a stochastic expression is required for individual grain g rowth rates. Two sources for the stochastic behaviour are topological switc hing events and the average linear correlation between grain size and topol ogical class. A size-based continuum stochastic formulation is presented on the basis of topological correlation. This analysis leads to a Fokker-Plan ck equation for the size distribution, which yields a unique self similar a symptotic state that is reached from arbitrary initial states. Grain size d istributions obtained from these considerations are in good agreement with experimental observations.