Mathematical Modeling of Layered Nanocomposite of Fractal Structure

Mathematics

Vitaliy Dolgov¹  Vadim Feklin¹  Sergey Korchagin¹  Ekaterina Romanova¹  Petr Nikitin¹  Denis Serdechnyy² 

[1] Department of Data Analysis and Machine Learning, Financial University under the Government of Russian Federation, Shcherbakovskaya Str., 38, 105187 Moscow, Russia;Department of Innovation Management, State University of Management, Ryazansky Pr., 99, 109542 Moscow, Russia;

关键词: composite materials;    fractional model;    mathematical modeling;    fractals;    nonlinear dynamics;   

DOI  :  10.3390/math9131541

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown