Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 50. no. 1. P. 134 – 148. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2025-50-1-134-148
Research Article
Full text in Russian
MSC 86-10

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Mathematical Modeling of Radon Transport in the Aerated Zone of Porositic Geomedium under Conditions of its Stress-Strain State

G. A. Skovpen¹, R. I. Parovik²^{\ast}

¹Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Petropavlovsk-Kamchatsky, Pogranichnaya str., 4, Russia
²Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, 684034, Paratunka, Pogranichnaya str., 4, Mirnaya, 7, Russia

Abstract. The article uses a mathematical model to study anomalous changes in radon volume activity at a certain point in a porous geoenvironment under its stress-strain state. The stress state of the geoenvironment is described using a stress or activation function, which is included in the model equation as a source of radon inflow along with the intensity of its emanation. The model equation is a linear ordinary differential equation of the first order, which is solved using the integral Laplace transform, taking into account the initial condition. In the resulting analytical solution, the activation function is selected in the form of two exponentials. The first exponent describes the growth of stress in the geoenvironment, and the second its unloading. As a result of computer modeling in the Maple2021 environment, calculated curves of radon volume activity were obtained, which describe bay-shaped anomalies similar to those obtained during radon monitoring at the Petropavlovsk-Kamchatsky geodynamic test site.

Key words: mathematical model, radon transfer, activation function, Maple2021, anomalies.

Received: 17.03.2025; Revised: 02.04.2025; Accepted: 03.04.2025; First online: 18.04.2025

For citation. Skovpen G. A., Parovik R. I. Mathematical modeling of radon transport in the aerated zone of porositic geomedium under conditions of its stress-strain state. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 50: 1, 134-148. EDN: TCDSUJ. https://doi.org/10.26117/2079-6641-2025-50-1-134-148.

Funding. The work was carried out within the framework of the state assignment of IKIR FEB RAS No. 124012300245-2.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: parovik@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Skovpen G. A., Parovik R. I., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Information about the authors

Skovpen Glafira Andreevna – postgraduate student of the Department of Computer Science and Mathematics, Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, Russia ORCID 0000-0002-9781-7249.

Parovik Roman Ivanovich – Doctor of Physico-Mathematical Sciences, Professor, Leading Researcher at the Laboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, S. Paratunka, Russia, ORCID 0000-0002-1576-1860.

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