Mathematical Modeling of Layered Nanocomposite of Fractal Structure

Sergey Korchagin, Ekaterina Romanova, Denis Serdechnyy, Petr Nikitin, Vitaliy Dolgov and Vadim Feklin
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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

Mathematics, 2021, vol. 9, issue 13, 1-10

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.

Keywords: composite materials; fractional model; mathematical modeling; fractals; nonlinear dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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