Geodesic
Hybrid stochastic fractal-based approach to modelling ferroelectrics switching kinetics in injection mode
Matematičeskoe modelirovanie, Tome 31 (2019) no. 9, pp. 131-144.

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The paper is devoted to development and implementation of hybrid stochastic fractalbased approach to mathematical modeling electron-induced kinetics of ferroelectrics polarization switching as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes an initial value problem for the fractional order differential equation. Computational schemes for solving fractional differential problem were constructed using Adams–Bashforth–Moulton type predictor-corrector methods. The stochastic algorithm based on Monte-Carlo method was proposed to simulate the domain nucleation process during restructuring domain structure in ferroelectrics. The ferroelectrics polarization switching current in electron injection mode was evaluated to demonstrate computational experiment results with comparison of experimental data.
Keywords: fractal model, ferroelectric switching, Monte-Carlo method, fractional-order differential equation, “predictor-corrector” method. 
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L. I. Moroz; A. G. Maslovskaya. Hybrid stochastic fractal-based approach to modelling ferroelectrics switching kinetics in injection mode. Matematičeskoe modelirovanie, Tome 31 (2019) no. 9, pp. 131-144. http://geodesic.mathdoc.fr/item/MM_2019_31_9_a6/

[1] S. V. Bozhokin, D. A. Parshin, Fraktaly i multifraktaly, NITs «Reguliarnaia i khaoticheskaia dinamika», Izhevsk, 2001, 128 pp.

[2] J. W. Kantelhard, Fractal and multifractal time series, Institute of Physics, Martin-Luther-University (Germany), Halle-Wittenberg, 2010, 42 pp.

[3] A. Arneodo, N. Decoster, 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 (2000), 567–600 | DOI

[4] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives. Theory and Application, Gordon and Breach Science Publishers, Switzerland, Philadelphia, Pa, USA, 1993, 976 pp. | MR

[5] I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Mathematics in science and engineering, 198, Acad. Press Inc., San Diego, CA, USA, 1999, 340 pp. | MR | Zbl

[6] I. Petras, Fractional-order nonlinear systems. Modeling, analysis and simulation, Springer-Verlag, Berlin–Heidelberg, 2011, 218 pp. | Zbl

[7] A. N. Bogolyubov, A. A. Koblikov, D. D. Smirnova, N. E. Shapkina, “Matematicheskoe modelirovanie sred s vremennoj dispersiej pri pomoshchi drobnogo differentsirovaniya”, Matematicheskoe modelirovanie, 25:12 (2013), 50–64 | MR | Zbl

[8] K. Diethelm, N. J. Ford, A. D. Freed, Yu. Luchko, “Algorithms for the fractional calculus: a selection of numerical method”, Comput. Methods Appl. Mech. Engrg., 194 (2005), 743–773 | DOI | MR | Zbl

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

[10] W. Deng, “Short memory principle and a predictor-corrector approach for fractional differentional equations”, J. of Computational and Applied Math., 206 (2007), 174–188 | DOI | MR | Zbl

[11] S. Bhalekar, V. D. Gejji, “A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order”, Journal of Fractional Calculus and Applications, 1:5 (2011), 1–9 | MR

[12] R. Scherera, S. L. Kallab, Y. Tangc, J. Huang, “The Grunwald-Letnikov method for fractional differential equations”, Comp. Math. with Applications, 62 (2011), 902–917 | DOI | MR

[13] T. Ozaki, “Ferroelectric domain structure characterized by prefractals of the pentad cantor sets in KH$_2$PO$_4$”, Ferroelectrics, 172 (1995), 65–77 | DOI

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

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

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

[17] J. F. Scott, Fractal dimensions in switching kinetics of ferroelectrics, University of Cambridge Press, Cambridge, 1998, 9 pp.

[18] R. P. Meilanov, S. A. Sadykov, “Fractal model for polarization switching kinetics in ferroelectric crystals”, Technical Physics, 44 (1999), 595–596 | DOI

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

[20] A. G. Maslovskaya, I. B. Kopylova, “Analysis of polarization switching in ferroelectric crystals in the injection mode”, Journal of Experimental and Theoretical Physics, 109:1 (2009), 90–94 | DOI

[21] M. Omura, Y. Ishibashi, “Simulations of polarization reversals by a two-dimensional lattice model”, Japanese Journal of Applied Physics, 31 (1992), 3238–3240 | DOI