Fluctuations in Processes of Phase-Separations and Intermittent Droplet Growth

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Abstract
A simple cascade model for the fluctuation is renormalized. This procedure gives a nonconventional kinetic exponent. Fluctuations in the process of the phase-separation are discussed on the basis of the cascade model. The log-normality of the probability distribution of increments of droplet (or domain) sizes is found. Then we show that the geometric mean is a suitable method of taking the ensemble average of local kinetic equations. This leads to the conclusion that more than two growth mechanisms with different kinetic exponents can coexist with invariant ratios, drastically modifying the average kinetic exponent. Two nonconventional kinetic exponents are then derived. These are, however, previously predicted.

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