Mathematical Modeling of Layered Nanocomposite of Fractal Structure
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, calcula...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/13/1541 |
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| author | Sergey Korchagin Ekaterina Romanova Denis Serdechnyy Petr Nikitin Vitaliy Dolgov Vadim Feklin |
| author_facet | Sergey Korchagin Ekaterina Romanova Denis Serdechnyy Petr Nikitin Vitaliy Dolgov Vadim Feklin |
| author_sort | Sergey Korchagin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T09:51:10Z |
| format | Article |
| id | doaj.art-c6cbd04cf2a2409d83e1a29b3bf4827b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:51:10Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c6cbd04cf2a2409d83e1a29b3bf4827b2023-11-22T02:45:49ZengMDPI AGMathematics2227-73902021-07-01913154110.3390/math9131541Mathematical Modeling of Layered Nanocomposite of Fractal StructureSergey Korchagin0Ekaterina Romanova1Denis Serdechnyy2Petr Nikitin3Vitaliy Dolgov4Vadim Feklin5Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, RussiaDepartment of Innovation Management, State University of Management, Ryazansky Pr., 99, 109542 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, RussiaDepartment of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, RussiaA 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.https://www.mdpi.com/2227-7390/9/13/1541composite materialsfractional modelmathematical modelingfractalsnonlinear dynamics |
| spellingShingle | Sergey Korchagin Ekaterina Romanova Denis Serdechnyy Petr Nikitin Vitaliy Dolgov Vadim Feklin Mathematical Modeling of Layered Nanocomposite of Fractal Structure Mathematics composite materials fractional model mathematical modeling fractals nonlinear dynamics |
| title | Mathematical Modeling of Layered Nanocomposite of Fractal Structure |
| title_full | Mathematical Modeling of Layered Nanocomposite of Fractal Structure |
| title_fullStr | Mathematical Modeling of Layered Nanocomposite of Fractal Structure |
| title_full_unstemmed | Mathematical Modeling of Layered Nanocomposite of Fractal Structure |
| title_short | Mathematical Modeling of Layered Nanocomposite of Fractal Structure |
| title_sort | mathematical modeling of layered nanocomposite of fractal structure |
| topic | composite materials fractional model mathematical modeling fractals nonlinear dynamics |
| url | https://www.mdpi.com/2227-7390/9/13/1541 |
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