On the Rayleigh–Bénard instability as the nonequilibrium phase transition

Lukashev, E. A.; Radkevich, E. V.; Yakovlev, N. N.; Vasilâ2teva, O. A.

doi:10.1063/1.5013954

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…В численном эксперименте (случай одной пространственной переменной) на интервале x ∈ (0,1) для  e = 0 005 , мы рассмотрим возмущение однородного потока управлением краевым условием, порождающим самовозбуждение турбулизации. Приведём численный эксперимент смешанной задачи для одномерной системы (11)…”

Section: Introductionunclassified

Hydrodynamic instabilities and nonequilibrium phase transitions

Radkevich

Lukashev

Васильева

2019

Доклады Академии наук

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For laminar-turbulent transition model is built reconstruction of the initial stage of instability as a nonequilibrium phase transition, the mechanism of which is diffusion stratification. It is shown that the Gibbs free energy deviations from the homogeneous state (relative to the instability under consideration) is an analogue Ginzburg-Landau potentials. Numerical experiments were performed. Self-excitation of a homogeneous state by edge control condition of increasing speed. Under external influence (increase in speed at the input), there is a transition to chaos through bifurcations of period doubling, when the internal control parameter (analogue of the Reynolds number) changes, like the Feigenbaum period doubling cascade.

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Section: Introductionunclassified

Hydrodynamic instabilities and nonequilibrium phase transitions

Radkevich

Lukashev

Васильева

2019

Доклады Академии наук

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“…В цикле работ [1,2,4,5,7,8,10,11,17,18,21,23,24,26,31] исследуется класс критических процессов, объединенных общей гипотезой, что они есть неравновесные фазовые переходы (ламинарно-турбулентный переход, неустойчивость Рэлея Бенара, кристаллизация бинарных сплавов, разрушение конструкционных материалов, неустойчивость Марангони).…”

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К 75-Летию Профессора Евгения Владимировича Радкевича

Андреев¹,

Радченко²,

Козлова³

et al. 2018

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

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26 января 2018 г. исполнилось 75 лет доктору физико-математических наук, профессору Евгению Владимировичу Радкевичу. В настоящей заметке приводятся сведения из научной биографии этого крупного ученого, который хорошо известен в России и за рубежом. Обсуждаются его работы, которые внесли существенный вклад во многие области науки и техники.

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The heating rate influence on the dynamics of sample destruction

Vasil'eva,

Hohonov

2024

E3S Web Conf.

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We consider a mathematical model of the dynamics of the initial stage of destruction of a homogeneous sample under the influence of heating. For the mathematical description of the process we apply recently proposed mathematical model of a non-equilibrium phase transitions formulated in terms of the Cahn-Hillard theory of spinodal decomposition. The mathematical model is one-dimensional in spatial variables. The mathematical model is an initial boundary value problem for a system of four nonlinear partial differential equations of the fourth order. The mathematical model is formulated for the given variables. Using the specified mathematical model, the influence of the heating rate of the left end of the sample on the dynamics of the initial stage of sample destruction was studied. A modified finite difference method of the second order of accuracy is used as one of the numerical methods. The description and analysis of examples of the obtained numerical results are carried out. The obtained results of numerical studied of the mathematical model demonstrate a nonlocal character of the process. The directions of further investigations of the initial stage of homogeneous samples and structures destruction are discussed.

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On the Rayleigh–Bénard instability as the nonequilibrium phase transition

Cited by 4 publications

References 24 publications

Hydrodynamic instabilities and nonequilibrium phase transitions

Hydrodynamic instabilities and nonequilibrium phase transitions

К 75-Летию Профессора Евгения Владимировича Радкевича

The heating rate influence on the dynamics of sample destruction

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