A review of continuous modeling of periodic pattern formation with modified phase-field crystal models

Starodumov, Ilya; Ankudinov, Vladimir; Nizovtseva, Irina

doi:10.1140/epjs/s11734-022-00518-5

Cited by 11 publications

(8 citation statements)

References 123 publications

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“…Further investigations of active PFC models can be found in references [27][28][29][91][92][93][94]. A review of PFC models is given by references [95,96], the derivation of PFC models from DDFT is discussed in references [51,97]. Reference [90] discusses the occurrence of localized states (LSs) in a number of passive and active PFC models.…”

Section: Introductionmentioning

confidence: 99%

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Vrugt

Holl

Aron

et al. 2022

Modelling Simul. Mater. Sci. Eng.

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We discuss an active phase field crystal (PFC) model that describes a mixture of active and passive particles. First, a microscopic derivation from dynamical density functional theory (DDFT) is presented that includes a systematic treatment of the relevant orientational degrees of freedom. Of particular interest is the construction of the nonlinear and coupling terms. This allows for interesting insights into the microscopic justification of phenomenological constructions used in PFC models for active particles and mixtures, the approximations required for obtaining them, and possible generalizations. Second, the derived model is investigated using linear stability analysis and nonlinear methods. It is found that the model allows for a rich nonlinear behavior with states ranging from steady periodic and localized states to various time-periodic states. The latter include standing, traveling, and modulated waves corresponding to spatially periodic and localized traveling, wiggling, and alternating peak patterns and their combinations.

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Section: Introductionmentioning

confidence: 99%

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Vrugt

Holl

Aron

et al. 2022

Modelling Simul. Mater. Sci. Eng.

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“…Finally, further overview articles covering (also) DDFT have been published; in particular an extensive review of PFT by Schmidt [20], a tutorial on active DDFT by Löwen [255], and several reviews on biology and medicine [256][257][258][259][260][261], coarse-graining [35,262], electrochemistry [263][264][265][266][267][268][269][270][271], multiscale modeling [272], PFC models [273], and polymers [274][275][276][277][278][279] in which DDFT is mentioned. In our view, this large number of overview articles published in two years further highlights how timely the topic is.…”

Section: Overview Articlesmentioning

confidence: 99%

Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

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“…При этом, несомненным преимуществом континуального метода КФП является скорость вычислений и возможность естественного учета дислокаций и поверхностной энергии межфазного фронта [20,21]. Развитие двухмодовой модели КФП [22,23] позволит описывать кристаллизацию и упорядочение в высоконеравновесных условиях [24], моделировать кристаллизацию сложных решеток, таких как ГЦК и ГПУ [25]. Перспективным и многообещающим является возможность учета решеток различных сингоний в единой модели с изотропным оператором, отвечающим за межчастичное взаимодействие [26].…”

Section: Introductionunclassified

Formation and Stability of the Crystalline Structures in the Two-mode Phase-field Crystal Model

Ankudinov¹

2022

HFIM

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Аннотация. Двухмодовая модель кристаллического фазового поля представляет собой расширенную классическую модель, позволяющую учитывать гексагональные и другие сложные решетки с помощью параметра порядка, периодического в кристаллической и имеющего постоянное значение в разупорядоченной фазе. С помощью двухмодовой модели кристаллического фазового поля исследованы режимы кристаллизации двумерных структур. Была обнаружена квазикристаллическая анизотропная полосчатая фаза, качественно соответствующая фазам, полученным в коллоидных растворах. Исследована стабильность структур при переходах между кристаллами с симметрией различного порядка, построена фазовая диаграмма существования структур, найдена кривая плавления. В качестве промежуточной фазы при последовательных переходах обнаружены признаки существования кристалла с симметрией 5-го порядка.

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A review of continuous modeling of periodic pattern formation with modified phase-field crystal models

Cited by 11 publications

References 123 publications

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Derivation and analysis of a phase field crystal model for a mixture of active and passive particles

Perspective: New directions in dynamical density functional theory

Formation and Stability of the Crystalline Structures in the Two-mode Phase-field Crystal Model

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