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Mathematical Modeling of Layered Nanocomposite of Fractal Structure

Author

Listed:
  • Sergey Korchagin

    (Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia)

  • Ekaterina Romanova

    (Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia)

  • Denis Serdechnyy

    (Department of Innovation Management, State University of Management, Ryazansky Pr., 99, 109542 Moscow, Russia)

  • Petr Nikitin

    (Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia)

  • Vitaliy Dolgov

    (Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia)

  • Vadim Feklin

    (Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia)

Abstract

A model of a layered hierarchically constructed composite is presented, the structure of which demonstrates the properties of similarity at different scales. For the proposed model of the composite, fractal analysis was carried out, including an assessment of the permissible range of scales, calculation of fractal capacity, Hausdorff and Minkovsky dimensions, calculation of the Hurst exponent. The maximum and minimum sizes at which fractal properties are observed are investigated, and a quantitative assessment of the complexity of the proposed model is carried out. A software package is developed that allows calculating the fractal characteristics of hierarchically constructed composite media. A qualitative analysis of the calculated fractal characteristics is carried out.

Suggested Citation

  • Sergey Korchagin & Ekaterina Romanova & Denis Serdechnyy & Petr Nikitin & Vitaliy Dolgov & Vadim Feklin, 2021. "Mathematical Modeling of Layered Nanocomposite of Fractal Structure," Mathematics, MDPI, vol. 9(13), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1541-:d:586618
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    References listed on IDEAS

    as
    1. Matthieu Garcin, 2019. "Hurst Exponents And Delampertized Fractional Brownian Motions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-26, August.
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    Cited by:

    1. Dostonjon Barotov & Aleksey Osipov & Sergey Korchagin & Ekaterina Pleshakova & Dilshod Muzafarov & Ruziboy Barotov & Denis Serdechnyy, 2021. "Transformation Method for Solving System of Boolean Algebraic Equations," Mathematics, MDPI, vol. 9(24), pages 1-12, December.

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