Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo

Andriy Gusak, Tetiana Zaporozhets

Bohdan Khmelnytsky National University of Cherkasy, 81 Shevchenko Blvd., 18031 Cherkasy, Ukraine

Received: 17.06.2018. Download: PDF

Development of the non-linear kinetic mean-field model suggested by George Martin in 1990 is discussed. Its steady-state limit is shown to coincide with Khachaturyan’s model. It is proved rigorously that Martin’s model and its 3$D$ version always provide decrease of free energy and are unable to model any overcoming of free-energy barrier, including nucleation. To enable nucleation processes within the mean-field models, the introduction of noise is necessary. Contrary to common way of noise introduction (noise of concentration), we introduce the noise of jump frequencies as a basic reason of fluctuations. The new method is called as Stochastic Kinetic Mean Field (SKMF). In this paper, we investigate and compare the dispersion and spatial correlations of concentration fluctuations by three methods—direct Monte Carlo simulation, numeric simulation by SKMF method, and analytic approximation within the scope of SKMF. Comparison confirms the correspondence of frequency noise to the averaging over finite number of Monte Carlo runs (over finite number of copies of the canonical ensemble).

Key words: kinetics, mean-field approximation, diffusion, noise, fluctuation, correlation, probability.



PACS: 05.40.Ca, 61.72.Bb, 64.60.Cn, 64.60.De, 66.30.Ny, 66.30.Pa, 81.30.Hd

Citation: Andriy Gusak and Tetiana Zaporozhets, Martin’s Kinetic Mean-Field Model Revisited—Frequency Noise Approach versus Monte Carlo, Metallofiz. Noveishie Tekhnol., 40, No. 11: 1415—1435 (2018)

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