Vol. 11, no.3, 2019
РусскийEnglish
FRACTALS IN PHYSICS
NUMERICAL MODEL OF FRACTALS IN THE PHYSICAL CHEMISTRY OF MATERIALS SCIENCE
Alexander D. Izotov
Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, http://igic.ras.ru/
Moscow 119991, Russian Federation
E-mail: izotov@igic.ras.ru
Feodor I. Mavrikidi
Oil and Gas Research Institute, Russian Academy of Sciences, http://www.ipng.ru/
Moscow 119333, Russian Federation
E-mail: mavrikidi@mail.ru
Received 05.11.2019, peer reviewed 18.11.2019, accepted 25.11.2019
Abstract. The paper substantiates the promise of the model of numerical asymmetry of fractals, which allows, from a single point of view, to cover modern approaches to modeling in chemistry and physics. The basis of the model is the synthesis of two basic number systems of mathematics - real and p-adic numbers. A physical chemistry interpretation of p-adic numbers and their properties is given. The physical chemistry space of the model becomes hyperbolic. The conclusion is made about the need to take into account duality in chemistry. As an illustration serves a model of matter based on Stone duality, which formally represents a pair “substance-properties”. The identity of nonlinear models of the atom and the Universe is shown, which serves as a justification for the periodicity of properties and is consistent with the hyperbolicity of the space of the general theory of relativity. The existence of the “golden section” number as a unit of a new number model is theoretically substantiated. The natural connection between the model and quantum mechanics by means of quantum numbers extracted from the model is shown. This opens up possibilities for the synthesis and interaction of the natural sciences, physics and mathematics, which, in the future, can serve as a model for the co-evolution of nature and technology.
Keywords: material science, fractals, p-adic numbers, number asymmetry, “golden section”, duality of chemistry, Mendeleev’s Periodic Table
PACS: 81.00.00; 05.45.Df; 02.10+p.
RENSIT, 2019, 11(2):279-290 DOI: 10.17725/rensit.2019.11.279
Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/297/11(3)279-290e.pdf