Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber
Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its val...
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/850 |
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| author | Dmitrii Tverdyi Evgeny Makarov Roman Parovik |
| author_facet | Dmitrii Tverdyi Evgeny Makarov Roman Parovik |
| author_sort | Dmitrii Tverdyi |
| collection | DOAJ |
| description | Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying the stress–strain state of the geo-environment with the possibility of building strong earthquake forecasts. The model equation of radon transfer, taking into account its accumulation in the chamber and the presence of the hereditary effect (heredity or memory), is a nonlinear differential Riccati equation with non-constant coefficients with a fractional derivative in the sense of Gerasimov–Caputo, for which local initial conditions are set (Cauchy problem). The proposed hereditary model of radon accumulation in the chamber is a generalization of the previously known model with an integer derivative (classical model). This fact indicates the preservation of the properties of the previously obtained solution according to the classical model, as well as the presence of new properties that are applied to the study of radon volumetric activity at observation points. The paper shows that due to the order of the fractional derivative, as well as the quadratic nonlinearity in the model equation, the results of numerical simulation give a better approximation of the experimental data of radon monitoring than by classical models. This indicates that the hereditary model of radon transport is more flexible, which allows using it to describe various anomalous effects in the values of radon volume activity. |
| first_indexed | 2024-03-11T08:28:12Z |
| format | Article |
| id | doaj.art-446b19ba83b84b81947e3a259255d57b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:12Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-446b19ba83b84b81947e3a259255d57b2023-11-16T21:54:56ZengMDPI AGMathematics2227-73902023-02-0111485010.3390/math11040850Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation ChamberDmitrii Tverdyi0Evgeny Makarov1Roman Parovik2Laboratory of Electromagnetic Radiation, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Mirnaya St., 7, 684034 Paratunka, Kamchatskiy Kray, RussiaLaboratory of Acoustic and Radon Monitoring, Kamchatka Branch of the Federal State Budgetary Institution of Science Federal Research Center “Unified Geophysical Service of the Russian Academy of Sciences”, Piip Boulevard, 9, 683023 Kamchatskiy Kray, Petropavlovsk-Kamchatsky, RussiaLaboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Mirnaya St., 7, 684034 Paratunka, Kamchatskiy Kray, RussiaMathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying the stress–strain state of the geo-environment with the possibility of building strong earthquake forecasts. The model equation of radon transfer, taking into account its accumulation in the chamber and the presence of the hereditary effect (heredity or memory), is a nonlinear differential Riccati equation with non-constant coefficients with a fractional derivative in the sense of Gerasimov–Caputo, for which local initial conditions are set (Cauchy problem). The proposed hereditary model of radon accumulation in the chamber is a generalization of the previously known model with an integer derivative (classical model). This fact indicates the preservation of the properties of the previously obtained solution according to the classical model, as well as the presence of new properties that are applied to the study of radon volumetric activity at observation points. The paper shows that due to the order of the fractional derivative, as well as the quadratic nonlinearity in the model equation, the results of numerical simulation give a better approximation of the experimental data of radon monitoring than by classical models. This indicates that the hereditary model of radon transport is more flexible, which allows using it to describe various anomalous effects in the values of radon volume activity.https://www.mdpi.com/2227-7390/11/4/850mathematical modelingradon volumetric activityearthquake precursorssaturation effecthereditymemory effect |
| spellingShingle | Dmitrii Tverdyi Evgeny Makarov Roman Parovik Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber Mathematics mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect |
| title | Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
| title_full | Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
| title_fullStr | Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
| title_full_unstemmed | Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
| title_short | Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
| title_sort | hereditary mathematical model of the dynamics of radon accumulation in the accumulation chamber |
| topic | mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect |
| url | https://www.mdpi.com/2227-7390/11/4/850 |
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