Stochastic generalization for a hyperbolic model of spinodal decomposition

Galenko, Peter; Kharchenko, D. O.; Lysenko, Irina O.

doi:10.1016/j.physa.2010.05.002

Cited by 37 publications

(27 citation statements)

References 23 publications

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“…The noise is affected on the structure with the "shake-up" effect [30,32]. Indeed, locally metastable and structurally mixed states have to be correlated in time and in space, due to the overlapping of the fluctuating atomic configurations [33,34]. In this case, a colored noise should be added to the MPFC equation.…”

Section: Resultsmentioning

confidence: 99%

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Simulation of crystalline pattern formation by the MPFC method

2017

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Abstract.The Phase Field Crystal model in hyperbolic formulation (modified PFC or MPFC), is investigated as one of the most promising techniques for modeling the formation of crystal patterns. MPFC is a convenient and fundamentally based description linking nano-and meso-scale processes in the evolution of crystal structures. The presented model is a powerful tool for mathematical modeling of the various operations in manufacturing. Among them is the definition of process conditions for the production of metal castings with predetermined properties, the prediction of defects in the crystal structure during casting, the evaluation of quality of special coatings, and others. Our paper presents the structure diagram which was calculated for the one-mode MPFC model and compared to the results of numerical simulation for the fast phase transitions. The diagram is verified by the numerical simulation and also strongly correlates to the previously calculated diagrams. The computations have been performed using software based on the effective parallel computational algorithm.

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Section: Resultsmentioning

confidence: 99%

“…In this case, a colored noise should be added to the MPFC equation. Previously, in the analysis of spinodal decomposition, it was notable shown that the consistently introduced colored noise influenced the pattern formation in a great extent [34].…”

Section: Resultsmentioning

confidence: 99%

Simulation of crystalline pattern formation by the MPFC method

2017

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“…Розглянемо клас бінарних систем, що описуються моделем фазово-го розшарування Кана-Хілліярда-Кука з гіперболічним транспор-том (внаслідок ефектів пам'яті) [95,96]. Для широкого кола фізич-них систем, віддалених від рівноваги, таких як неньютонові ріди-ни, швидко охолоджені кристалізовані стопи та системи, матеріяли глибоко заморожені в спинодальній області або загалом системи з пам'яттю, гіпотеза локальної рівноваги не спрацьовує [97,98].…”

Section: статистичне представлення бінарної системи параболічного типunclassified

Modelling of Microstructural Transformations in the Systems Subject to Radiation Influence

2012

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Розвинуто формалізм для послідовного опису мікроструктурних перетво-рень і фазового розшарування у системах, що перебувають у сильно нерів-новажних умовах, викликаних дією опромінення. Аналізу проведено в ра-мках методи фазового поля кристалу, що дає змогу проводити дослідження на просторових масштабах молекулярної динаміки, однак на часових інте-рвалах дифузійної динаміки. Виявлено умови перебігу мікроструктурних перетворень у періодичних однокомпонентних системах кристалічного ти-пу за наявности конкурувальних стохастичних потоків: термічно стиму-льованого та балістичного перемішування атомів. Аналізою поведінки сис-тем на більш високому ієрархічному рівні для бінарних систем еквіатомо-вого складу встановлено реверсивний характер перебігу процесу фазового розшарування. Для систем із несумірними часовими масштабами розпо-всюдження збурень, що характеризуються ефектами пам'яті, виявлено присутність процесів відбору структур за наявности флюктуацій довжин стрибків атомів, вибитих високоенергетичними частинками.Formalism is developed for description of microstructure transformations and phase separation in systems under irradiation. Investigation is made within the scope of the crystal phase-field method. This approach allows one to simulate materials on the molecular-dynamics spatial scales but on the diffusivedynamics temporal scales. Considering a model for a periodic one-component system driven by both competing stochastic fluxes-thermally-stimulated and external ballistic mixing flues of atoms, conditions of microstructuretransformations' appearance are determined. Analysis of the system on a mesoscopic level for a binary equiatomic system is performed. Reentrant character of phase-separation process is revealed. For systems with transient dynamics, for instance, with incommensurable time scales of propagation of disturbances, which are characterized by the memory effects, at presence of fluc- Fiz. Met. 2012, т. 13, сс. 101-187 Оттиски доступны непосредственно от издателя Фотокопирование разрешено только в соответствии с лицензией © 2012 ИМФ (Институт металлофизики им. Г. В. Курдюмова НАН Украины) Напечатано в Украине.

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“…Following the general theory of dynamical stochastic systems the thermally sustained diffusion flux J D can be considered as a dynamical quantity and described by a relaxational MaxwellCattaneo equation [37] with a stochastic contribution ξ, representing flux fluctuations appearing always at a nonzero temperature T . Therefore, the time evolution of the diffusion flux can be described by the Langevin equation of the form [37][38][39] …”

Section: Modelmentioning

confidence: 99%

“…[42], whilst the action of the stochastic multiplicative component of the diffusion flux on the pattern selecting processes in binary systems was considered in Ref. [39].…”

Section: Modelmentioning

confidence: 99%

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

Kharchenko

Lysenko

2011

Open Physics

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Abstract:We apply the phase field crystal method for nonequilibrium patterning to stochastic systems with an external source in which transient dynamics is essential. Considering a prototype model for a one-component periodic system subjected to external influence kind of irradiation we study properties of pattern selection processes and external noise induced pattern-forming transitions. These processes are examined by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed numerically. PACS

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Stochastic generalization for a hyperbolic model of spinodal decomposition

Cited by 37 publications

References 23 publications

Simulation of crystalline pattern formation by the MPFC method

Simulation of crystalline pattern formation by the MPFC method

Modelling of Microstructural Transformations in the Systems Subject to Radiation Influence

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

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