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Self-similar grain size distribution in three dimensions: A stochastic treatment



Geoffrey B. McFadden, C.S. Pande


In this paper, a stochastic formulation of three dimensional grain growth is presented. It employs the recent extension of von Neumann law to three dimensions As expected our analysis leads to a Fokker-Planck equation for the size distribution, which should yield a unique self-similar asymptotic state that could be reached from any arbitrary initial state. The approximate solution of the Fokker-Planck equation presented here is based on the assumption of quasi-stationary distributions reached in the long time limit. The resulting grain size distributions, obtained both numerically and analytically, are shown to be in good agreement with each other and also with those obtained from computer simulations, indicating the validity of the stochastic approach.
ACTA Materialia


grain growth, stochastic Fokker-Planck equation, von Neumann law, self-similar asymptotic state, grain size distribution


McFadden, G. and Pande, C. (2010), Self-similar grain size distribution in three dimensions: A stochastic treatment, ACTA Materialia, [online], (Accessed June 23, 2024)


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Created February 1, 2010, Updated June 2, 2021