Mathematical Modeling of Layered Nanocomposite of Fractal Structure
Sergey Korchagin,
Ekaterina Romanova,
Denis Serdechnyy,
Petr Nikitin,
Vitaliy Dolgov,
Vadim Feklin
Affiliations
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
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.
