Features of Spatial-Temporal Hierarchical Structures Formation
Keywords:
Dynamic Chaos;, Fractal;, Evolution;, Hausdorf-Bezikovich Dimension;, Topology of Complex Systems.Abstract
The degree of ordering of the structure of technologically important materials formed as a result of the evolution of complex physicochemical systems determines their physical properties, in particular optical. In this regard, the primary task for the theoretical study of methods for obtaining materials with predetermined physical properties is to develop approaches to describe the evolution of fractal (scale-invariant) objects in the formation of self-similar structures in systems exhibiting chaotic behavior. The paper forms an idea of the processes of evolution in materials formed as a result of stochastic processes. It is established that the conduct of ultrametrics in time space allows to characterize the time of the evolutionary process of fractal dimension, which is calculated either theoretically or model. The description of evolutionary processes in a condensed medium, accompanied by topological transformations, is significantly supplemented by the method of describing the stages of evolution of structures, which makes it possible to analyze a wide range of materials and can control their properties, primarily optical. It is shown that the most large-scale invariant structures, due to the investigated properties, can be used as information carriers. It is demonstrated that the presence in physical systems of fractal temporal dimension and generates a self-similar (consisting of parts in a sense similar to the whole object) evolutionary tree, which, in turn, generates spatial objects of non-integer dimension, observed in real situations. On the other hand, temporal fractality provides analysis of systems with dynamic chaos, leading to universal relaxation functions. In particular, in systems with a large-scale invariant distribution of relaxation characteristics, an algebraic law of relaxation is manifested, which leads to rheological models and equations of states, which are characterized by fractional derivatives. It is argued that the fractal dimension of time hierarchies stores information that determines the process of self-organization. Developed in the paper ideas about the processes of building the structure of materials, which lead to the fractal geometry of objects, can be used to predict their properties, in particular, optical.
References
Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. Freeman.
Mandelbrot, B.B. (2004). Fractals and Chaos. Springer. https://doi.org/10.1007/978-1-4757-4017-2
Feder, J. (1988). Fractals. Springer. https://doi.org/10.1007/978-1-4899-2124-6
Manuilenko, O.V., Kudin, D.V., Dulphan, A.Y., & Golota, V.I. (2018). Ozone decay in chemical reactor with the developed inner surface: Air-ethylene mixture. Problems of Atomic Science and Technology, 116(4), 139–143.
Petchenko, O.M., Petchenko, G.O., & Boiko, S.M. (2018). The competition of Mott and Frideel type stoppers as the main blocking mechanisms in mobile dislocations of KBr crystals. Problems of Atomic Science and Technology, 117(5), 24–28.
Petchenko, O.M., Petchenko, G.О., Boiko, S.М., & Bezugly, A.V. (2020). Optical and colorimetrical characteristics of strained LiF crystals under X-ray irradiation. Problems of Atomic Science and Technology, 126(2), 60–63.
Soloviov, S.H. (2019). The fractal nature of strategic communications. Public Administration: Theory and Practice, 1, 33–40. https://doi.org/10.36030/2311-6722-2019-1-33-4 (in Ukrainian)
Pustiulha, S., Samchuk, V., Samostian, V., & Holovachuk, I. (2019). Quantitative analysis of nulldimensional (points) multiplicity by methods of fractal geometry. Applied Geometry and Engineering Graphics, 96, 64–72. https://doi.org/10.32347/0131-579x.2019.96.64-72 (in Ukrainian)
Voss, R.F. (1988). Fractals in nature: from characterization to simulation. In H.O. Peitgen, & D. Saupe (Eds.), The Science of Fractal Images (pp. 21–70). Springer. https://doi.org/10.1007/978-1-4612-3784-6_1
Akhmet, M., Fen, M.O., & Alejaily, E.M. (2020). Dynamics with Chaos and Fractals. Springer. https://doi.org/10.1007/978-3-030-35854-9
Lancia, M.R., & Rozanova-Pierrat, A. (Eds.). (2021). Fractals in Engineering: Theoretical Aspects and Numerical Approximations. SEMA SIMAI Springer Series, vol. 8. Springer. https://doi.org/10.1007/978-3-030-61803-2
Stavrinides S., Ozer M. (Eds.). (2020). Chaos and Complex Systems. SPCOM. Springer. https://doi.org/10.1007/978-3-030-35441-1
Petchenko, G.O., Petchenko, O.M., & Rokhmanov, M.Y. (2017). Nonmonotonical deformation dependance of color center concentration in functional materials. Lighting Engineering & Power Engineering, 49(2), 22–24.
Petchenko, G.O., Petchenko, O.M., Ovchinnikov, S.S., & Rokhmanov, M.Y. (2017). The typical absorption in the irradiated by X-ray and deformed functional materials. Lighting Engineering & Power Engineering, 49(2), 30–33.
Petchenko, G.O., & Petchenko, O.M. (2017). Influence of dislocation structure of LiF crystals on their lighting and colorimetric characteristics. Lighting Engineering & Power Engineering, 50(3), 25–30. (in Ukrainian)
Petchenko, О.М., & Petchenko, G.О. (2019). Analysis of the results obtained by the method of amplitude-independent internal friction on metals and ionic crystals. Lighting Engineering & Power Engineering, 54(1), 30–39. https://doi.org/10.33042/2079-424X-2019-1-54-30-39 (in Ukrainian)
Lobanov, Y.E., Nikitsky, G.I., Petchenko, O.M., & Petchenko, G.O. (2020). The essence and application of the optical absorption method for quantitative and qualitative analysis of radiation defects in optical crystals. Lighting Engineering & Power Engineering, 59(3), 97–100. https://doi.org/10.33042/2079-424X-2020-3-59-97-100
Banerjee, S., Easwaramoorthy, D., & Gowrisankar, A. (2021). Fractal Functions, Dimensions and Signal Analysis. UCS. Springer. https://doi.org/10.1007/978-3-030-62672-3
Skiadas, C.H., & Dimotikalis, Y. (Eds.). (2020). 12th Chaotic Modeling and Simulation International Conference. SPCOM. Springer. https://doi.org/10.1007/978-3-030-39515-5
Nigmatullin, R.R., Lino, P., & Maione, G. (2020). New Digital Signal Processing Methods. Springer. https://doi.org/10.1007/978-3-030-45359-6
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