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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2023, Volume 44, Number 3, Pages 86–104
DOI: https://doi.org/10.26117/2079-6641-2023-44-3-86-104
(Mi vkam613)
 

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICAL MODELING

Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport

D. A. Tvyordyjab, E. O. Makarovbc, R. I. Parovikab

a Institute for Cosmophysical Research and Radio Propagation FEB RAS
b Kamchatka State University named after Vitus Bering
c Kamchatka branch Unified Geophysical Service of the RAS
References:
Abstract: Continuous monitoring of variations in the volumetric activity of radon in order to search for its anomalous values preceding seismic events is one of the effective techniques for studying the stress-strain state of the geosphere. We propose a Cauchy problem describing the radon transport taking into account its accumulation in the chamber and the presence of the memory effect of the geo-environment. The model equation is a nonlinear differential equation with non-constant coefficients with a derivative in the sense of Gerasimov-Kaputo of fractional variable order. In the course of mathematical modeling, in MATLAB environment, of radon transport by the ereditary $\alpha$(t)-model a good agreement with experimental data was obtained. This indicates that the ereditary $\alpha$(t)-model of radon transport is more flexible, which allows it to describe various anomalous variations in the values of volumetric activity of radon due to the stress-strain state of the geosphere. It is shown that the order of the fractional derivative can be responsible for the intensity of the radon transfer process associated with the characteristics of the geo-environment. It is shown that due to the order of the fractional derivative, as well as quadratic nonlinearity in the model equation, the results of numerical modeling give a better approximation of the experimental data of radon monitoring than by classical models.
Keywords: mathematical modeling, nonlinear equations, saturation effect, fractional equations, fractional derivatives, hereditarity, memory effects, nonlocality in time, radon volumetric activity, stress-strain state, geo-environment, earthquake precursors.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation МД-758.2022.1.1
The research was carried out within the framework of the grant of the President of the Russian Federation MD-758.2022.1.1 on the topic “Development of mathematical models of fractional dynamics in order to study oscillatory processes and processes with saturation”.
Document Type: Article
UDC: 519.642.2
MSC: Primary 34A08; Secondary 34A34
Language: Russian
Citation: D. A. Tvyordyj, E. O. Makarov, R. I. Parovik, “Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 44:3 (2023), 86–104
Citation in format AMSBIB
\Bibitem{TvyMakPar23}
\by D.~A.~Tvyordyj, E.~O.~Makarov, R.~I.~Parovik
\paper Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 44
\issue 3
\pages 86--104
\mathnet{http://mi.mathnet.ru/vkam613}
\crossref{https://doi.org/10.26117/2079-6641-2023-44-3-86-104}
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  • https://www.mathnet.ru/eng/vkam/v44/i3/p86
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
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