Stochastic kinetic mean field model

Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, V. M.; Tomán, János J.; Gajdics, Bence; Гусак, А. М.

doi:10.1016/j.cpc.2016.03.003

Cited by 29 publications

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“…Because of the discontinuous character of the phenomenon, its modelling required application of the stochastic versions of KMF [9,10] since this version was specially designed to describe the ability of systems to overcome energetic barriers.…”

Section: Kmf-simulation Results For the Binary System With L1 0 -Typementioning

confidence: 99%

“…The method called 'kinetic mean field' was originally proposed by George Martin in 1990 [4] as a pseudo-1D-algorithm. The technique was then applied to nanofilms with diffusion asymmetry in the series of papers by Z. Erdelyi, D. Beke et al [5][6][7][8], extended to 3D [9], and recently generalized to first-order transformations by introducing dynamic noise of jump frequencies in the kinetic master equations ('stochastic KMF' (SKMF) [10].) The Martin's version of KMF approach is not the only one [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…(We will not discuss here the special precautions made in SKMF to avoid the going of the probabilities beyond the interval [0, 1]; see Ref. [10] in detail. )…”

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confidence: 99%

“…[10], the next logical step was introduced. Dynamic noise of frequencies (instead of or additionally to initial noise of concentrations) was introduced providing the possibility for the overcoming the nucleation barriers.…”

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confidence: 99%

“…[10], changing the noise amplitude, one may tune the kinetic Monte Carlo with various numbers of runs. (We will not discuss here the special precautions made in SKMF to avoid the going of the probabilities beyond the interval [0, 1]; see Ref.…”

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confidence: 99%

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Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

2017

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Tracer diffusion and 'chemical' (atomic) ordering processes in two facecentred cubic (f.c.c.) binary systems mimicking Ni 3 Al and FePt were simulated by means of the kinetic mean-field (KMF) method originally proposed by G. Martin in 1990. The systems simulated within the present work were modelled with fixed pair-interaction parameters and saddlepoint energies adopted earlier via the comparison of Monte Carlo method modelling and experimental data. In a simulation of tracer migration as well as ordering, the focus was attracted to comparison of activation energies rather than pre-exponential factors of kinetic coefficients. Generally, the mean-field models cannot properly take into account correlation effect that could be important for the tracer diffusion especially for the B2 structures. However, at least for the f.c.c. structures, application of KMF to diffusion and ordering seems demonstrating very reasonable results qualitatively similar to those obtained in kinetic Monte Carlo (KMC) method and realistic experiments. Modelling of Ni-and Al-tracer diffusion in Ni 3 Al system shows higher diffusivity of Ni atoms as compared with Al ones that is attributed to easier intrasublattice diffusion channel for the Ni atoms in the L1 2 -Ni 3 Al superstructure. Also, the obtained activation energy for the tracer Al atoms is higher, and its value is closer to activation energy of ordering kinetics. Computer experiments for the ordering kinetics showed that, in contrast to exchange mechanism, L1 2 -type ordering kinetics is described via two relaxation times in case of the vacancy diffusion mechanism. Modelling of the discontinuous process of the surface-induced re-orientation of the monatomic Fe and Pt planes in thin FePt film was, in turn, a good test for the stochastic variant of the KMF (SKMF) method. The fact that implementation of the stochastic noise was Fiz. Met. 2017, т. 3, сс. 205- В работе рассматривается диффузия меченых атомов и процесс «хими-ческого» (атомного) упорядочения в двух бинарных системах с гране-центрированной кубической (ГЦК) структурой Ni 3 Al и FePt с использо-ванием среднеполевого кинетического метода (KMF), предложенного Ж. Мартаном в 1990 г. Для указанных систем использовались фикси-рованные значения парных энергий взаимодействия и энергий седловой точки, подобранные ранее путём сравнения моделирования методом Монте-Карло и экспериментальных данных. В моделировании диффу-зии меченых атомов, а также упорядочения их основной акцент на-правлен на сравнение энергий активации, а не предэкспонентных мно-жителей кинетических коэффициентов. В общем случае модели средне-го поля не могут правильно учитывать корреляционный эффект, кото-рый может быть существенным для диффузии меченых атомов, особен-но для структур типа В2. Однако, по крайней мере, для ГЦК-структур, применение KMF к диффузии и упорядочению демонстрирует доста-точно реалистичные результаты, качественно схожие с теми, которые Keywords: kinetic mean-field method, tracer diffusion, ordering kinetics, atomistic simulation, intermetallics....

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Section: Kmf-simulation Results For the Binary System With L1 0 -Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…(We will not discuss here the special precautions made in SKMF to avoid the going of the probabilities beyond the interval [0, 1]; see Ref. [10] in detail. )…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

2017

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“Predator and Prey” Model Revisited – Influence of External Fluxes and Noise

Huriev

Гусак

2020

J Math Sci

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Well-known predator-prey model is modified in two ways. First, regular adding or regular deleting of preys or/and predators is considered. Steady-state and stability diagram is found. Second, random fluctuations of the birthrate and other kinetic coefficients are studied -parabolic law of random walk in (X,Y)-space is found and proved for small deviations from steady-state.MSC 2010. 34A34, 34F05, 34D08

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Diffusion-Controlled Phase Transformations in Open Systems

Гусак

Storozhuk

2017

Handbook of Solid State Diffusion, Volume 2

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Stochastic kinetic mean field model

Cited by 29 publications

References 10 publications

Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

Simulation of the Tracer Diffusion, Bulk Ordering, and Surface Reordering in F.C.C. Structures by Kinetic Mean-Field Method

“Predator and Prey” Model Revisited – Influence of External Fluxes and Noise

Diffusion-Controlled Phase Transformations in Open Systems

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