Hybrid Stochastic Fractal-Based Approach to Modeling the Switching Kinetics of Ferroelectrics in the Injection Mode

Moroz, L. I.; Maslovskaya, A. G.

doi:10.1134/s207004822003014x

Cited by 13 publications

(13 citation statements)

References 12 publications

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“…At the same time, the main advantage of this paper is the obtained formula for the solution of the evolution equation with the relatively wide conditions imposed upon the right-hand side, where the derivative at the left-hand side is supposed to be of the fractional order. This problem appeals to many ones that lie in the framework of the theory of differential equations, for instance in the paper [34] the solution of the evolution equation can be obtained in the analytical way if we impose the conditions upon the right-hand side. We can also produce a number of papers dealing with differential equations which can be studied by this paper abstract methods [30], [32], [31], [38], [43].…”

Section: Introductionmentioning

confidence: 99%

Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Kukushkin

2022

Mathematics

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Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of the convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms of the norm, we construct a sequence of contours of the power type that contrasts the results by Lidskii, where a sequence of contours of the exponential type was used.

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Section: Introductionmentioning

confidence: 99%

Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Kukushkin

2022

Mathematics

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“…We consider the evolution equations with the right-hand side -an operator function of the polynomial type. This problem appeals to many ones that lie in the framework of the theory of differential equations for instance in the paper [32] the solution of the evolution equation modeling the switching kinetics of ferroelectrics in the injection mode can be obtained in the analytical way if we impose the conditions upon the right-hand side. Thus, we can claim that the offered approach is undoubtedly novel and relevant.…”

Section: Introductionmentioning

confidence: 99%

Evolution Equations in Hilbert Spaces via the Lacunae Method

Kukushkin¹

2022

Preprint

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In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and uniqueness theorem and find a solution in the form of a series on the root vectors of the right-hand side. As an application we consider fractional differential equations of various kinds. Such operators as the Riemann-Liouville fractional differential operator, the Riesz potential, the difference operator have been involved.

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“…The fractional order derivatives have been introduced to describe the non-linear mechanical and electric behavior of ferroelectric polymer composites in [25]. Moreover, a numerical solution of an fractional ordinary differential equation underlies the model of polarization switching current induced in ferroelectrics by electron beam irradiation [26,27].…”

Section: Introductionmentioning

confidence: 99%

Time-fractional Landau–Khalatnikov model applied to numerical simulation of polarization switching in ferroelectrics

Maslovskaya

Moroz

2022

Nonlinear Dyn

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Ferroelectrics are complex structured media that exhibit fractal properties and memory effects in terms of a number of dynamic characteristics. The most relevant applications of ferroelectrics in science and technology are associated with the primary mechanisms of polarization switching and domain structure dynamics induced by external exposure. In this study, we propose a time-fractional modification of the Landau -Ginzburg -Devonshire -Khalatnikov model to describe the dynamics of ferroelectric polarization switching. To solve the time-fractional cubic-quintic partial differential equation numerically, a computational scheme is derived. The technique combines an iterative procedure and an implicit finite-difference scheme based on an approximation of Caputo derivative. A series of computational experiments are presented to visualize polarization switching characteristics on the example of thin films of barium titanate. A variation of the order of fractional derivative as a numerical characteristic of the memory effect allows one to "adjust" suitable regimes of simulated dynamical system. The obtained findings indicate that the generalized time-fractional model can provide better reproduction of experimental data in comparison with the classical analogue. KeywordsLandau-Khalatnikov model • Ferro electrics switching • Timefractional partial differential equation • Caputo derivative • Iterative finite difference scheme This work was supported by the Russian Foundation for Basic Research (project no. 20-31-90075).

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Hybrid Stochastic Fractal-Based Approach to Modeling the Switching Kinetics of Ferroelectrics in the Injection Mode

Cited by 13 publications

References 12 publications

Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent

Evolution Equations in Hilbert Spaces via the Lacunae Method

Time-fractional Landau–Khalatnikov model applied to numerical simulation of polarization switching in ferroelectrics

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