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Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber

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  • Dmitrii Tverdyi

    (Laboratory of Electromagnetic Radiation, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Mirnaya St., 7, 684034 Paratunka, Kamchatskiy Kray, Russia
    These authors contributed equally to this work.)

  • Evgeny Makarov

    (Laboratory 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, Russia
    These authors contributed equally to this work.)

  • Roman Parovik

    (Laboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Mirnaya St., 7, 684034 Paratunka, Kamchatskiy Kray, Russia
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Dmitrii Tverdyi & Evgeny Makarov & Roman Parovik, 2023. "Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:850-:d:1060884
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    References listed on IDEAS

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    1. F R Johnston & J E Boyland & M Meadows & E Shale, 1999. "Some properties of a simple moving average when applied to forecasting a time series," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1267-1271, December.
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    Cited by:

    1. Dmitrii Tverdyi & Roman Parovik, 2023. "Hybrid GPU–CPU Efficient Implementation of a Parallel Numerical Algorithm for Solving the Cauchy Problem for a Nonlinear Differential Riccati Equation of Fractional Variable Order," Mathematics, MDPI, vol. 11(15), pages 1-21, July.

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