Top

Mathematical Models and Computer Simulations

Published in:

01-05-2020

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

Authors: L. I. Moroz, A. G. Maslovskaya

Published in: Mathematical Models and Computer Simulations | Issue 3/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving fractional differential problem are constructed using the Adams–Bashforth–Moulton type predictor-corrector methods. The stochastic algorithm based on the Monte Carlo method is proposed to simulate the domain nucleation process during restructuring the domain structure in ferroelectrics. The polarization switching current of ferroelectrics in the electron injection mode is evaluated to demonstrate the computational experiment results with a comparison of the experimental data.

previous article Nonstationary Contrast Structures of Reaction-Diffusion Problems with Roots of Noninteger Multiplicities in Inhomogeneous Media

next article Comparison of Gradient Approximation Methods in Schemes Designed for Scale-Resolving Simulations

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

S. V. Bozhokin and D. A. Parshin, Fractals and Multifractals (RKhD, Izhevsk, 2001) [in Russian].

J. W. Kantelhard, Fractal and Multifractal Time Series (Inst. Phys., Martin-Luther-Univ., Halle-Wittenberg, 2010).

A. Arneodo, N. Decoster, and S. G. Roux, “A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces,” Eur. Phys. J. B 15, 567–600 (2000).CrossRef

S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Application (Gordon and Breach Science, Switzerland, Philadelphia, PA, 1993).MATH

I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Vol. 198 of Fractional Differential Equations (Academic, San Diego, CA, 1999), p. 340.

I. Petras, Fractional-Order Nonlinear Systems. Modeling, Analysis and Simulation (Springer, Berlin, Heidelberg, 2011).CrossRef

A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova, and N. E. Shapkina, “Mathematical modelling of media with time dispersion using fractional derivatives,” Mat. Model. 25 (12), 50–64 (2013).MathSciNetMATH

K. Diethelm, N. J. Ford, A. D. Freed, and Yu. Luchko, “Algorithms for the fractional calculus: a selection of numerical method,” Comput. Methods Appl. Mech. Eng. 194, 743–773 (2005).MathSciNetCrossRef

R. Garrapa, “Numerical solution of fractional differential equations: a survey and software tutorial,” Mathematics 6 (16), 1–23 (2018).

10.

W. Deng, “Short memory principle and a predictor-corrector approach for fractional differentional equations,” J. Comput. Appl. Math. 206, 174–188 (2007).MathSciNetCrossRef

11.

S. Bhalekar and V. D. Gejji, “A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order,” J. Fract. Calculus Appl. 1 (5), 1–9 (2011).

12.

R. Scherera, S. L. Kallab, Y. Tangc, and J. Huang, “The Grünwald-Letnikov method for fractional differential equations,” Comput. Math. Appl. 62, 902–917 (2011).MathSciNetCrossRef

13.

T. Ozaki, “Ferroelectric domain structure characterized by prefractals of the pentad cantor sets in KH₂PO₄,” Ferroelectrics 172, 65–77 (1995).CrossRef

14.

N. M. Galiyarova, A. B. Bey, E. A. Kuznetzov, and Y. I. Korchmariyuk, “Fractal dimensionalities and microstructural parameters of piezoceramics PZTNB-1,” Ferroelectrics 307, 205–211 (2004).CrossRef

15.

B. Tadic, “Switching current noise and relaxation of ferroelectric domains,” Eur. Phys. J. B 28, 81–89 (2002).CrossRef

16.

M. K. Roy, J. Paul, and S. Dattagupta, “Domain dynamics and fractal growth analysis in thin ferroelectric films,” IEEE Xplore 109, 014108–014108 (2010).

17.

J. F. Scott, Fractal Dimensions in Switching Kinetics of Ferroelectrics (Cambridge Univ. Press, Cambridge, 1998).

18.

R. P. Meilanov and S. A. Sadykov, “Fractal model for polarization switching kinetics in ferroelectric crystals,” Tech. Phys. 44, 595–596 (1999).CrossRef

19.

A. G. Maslovskaya and T. K. Barabash, “Dynamic simulation of polarization reversal processes in ferroelectric crystals under electron beam irradiation,” Ferroelectrics 442, 18–26 (2013).CrossRef

20.

A. G. Maslovskaya and I. B. Kopylova, “Analysis of polarization switching in ferroelectric crystals in the injection mode,” J. Exp. Theor. Phys. 109, 90–94 (2009).CrossRef

21.

M. Omura and Y. Ishibashi, “Simulations of polarization reversals by a two-dimensional lattice model,” Jpn. J. Appl. Phys. 31, 3238–3240 (1992).CrossRef

Title: Hybrid Stochastic Fractal-Based Approach to Modeling the Switching Kinetics of Ferroelectrics in the Injection Mode
Authors: L. I. Moroz
A. G. Maslovskaya
Publication date: 01-05-2020
Publisher: Pleiades Publishing
Published in: Mathematical Models and Computer Simulations / Issue 3/2020
Print ISSN: 2070-0482
Electronic ISSN: 2070-0490
DOI: https://doi.org/10.1134/S207004822003014X

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2020

Basic Aspects of Actively Shielding against External Noise

Numerical Simulation of the Recirculation Flow during the Supersonic Separation of Moving Bodies

Analysis of the Effect Made by the Variable Heat Capacity on the Characteristics of Pressure Pulsations in a High-Speed Air Intake Using the RANS/ILES Method

Modeling Unsteady Phenomena in an Axial Compressor

Study of the Influence of the Temperature Field’s Nonuniformity on the Pressure Pulsations in the Inlet Duct Using the RANS/ILES Method

Comparison of Gradient Approximation Methods in Schemes Designed for Scale-Resolving Simulations

Premium Partner