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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ftmdpi:oai:mdpi.com:/2227-7390/11/4/850/ 2023-08-20T04:07:40+02:00 Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber Dmitrii Tverdyi Evgeny Makarov Roman Parovik 2023-02-07 application/pdf https://doi.org/10.3390/math11040850 EN eng Multidisciplinary Digital Publishing Institute Engineering Mathematics https://dx.doi.org/10.3390/math11040850 https://creativecommons.org/licenses/by/4.0/ Mathematics; Volume 11; Issue 4; Pages: 850 mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect fractional Riccati equation Gerasimov–Caputo type derivative Text 2023 ftmdpi https://doi.org/10.3390/math11040850 2023-08-01T08:41:30Z 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. Text Kamchatka MDPI Open Access Publishing Mathematics 11 4 850 |
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mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect fractional Riccati equation Gerasimov–Caputo type derivative |
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mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect fractional Riccati equation Gerasimov–Caputo type derivative Dmitrii Tverdyi Evgeny Makarov Roman Parovik Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber |
topic_facet |
mathematical modeling radon volumetric activity earthquake precursors saturation effect heredity memory effect fractional Riccati equation Gerasimov–Caputo type derivative |
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. |
format |
Text |
author |
Dmitrii Tverdyi Evgeny Makarov Roman Parovik |
author_facet |
Dmitrii Tverdyi Evgeny Makarov Roman Parovik |
author_sort |
Dmitrii Tverdyi |
title |
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_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_sort |
hereditary mathematical model of the dynamics of radon accumulation in the accumulation chamber |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2023 |
url |
https://doi.org/10.3390/math11040850 |
genre |
Kamchatka |
genre_facet |
Kamchatka |
op_source |
Mathematics; Volume 11; Issue 4; Pages: 850 |
op_relation |
Engineering Mathematics https://dx.doi.org/10.3390/math11040850 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/math11040850 |
container_title |
Mathematics |
container_volume |
11 |
container_issue |
4 |
container_start_page |
850 |
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1774719483519172608 |