Scientific Seminar «Mathematical modeling of radon volumetric activity variations taking into account hereditarity» (based on Dr. Sci. Dissertation) has taken place

The presentation was made by the Researcher of the Laboratory of Electromagnetic Radiation of IKIR FEB RAS, Cand. Sci. (Phys.-Math.) Tverdiy Dmitriy Alexandrovich.

Academic Advisor is the Chief Researcher of the Laboratory of Physical Process Modeling of IKIR FEB RAS, Dr. Sci. (Phys.-Math.), Senior Lecturer, Professor of FEB RAS Parovik Roman Ivanovich.

In the course of the presentation Dmitriy presented the results of his dissertation investigation (the subject is registered in Uzbekistan State Commission for Academic Degrees and Titles (VAK) No. В2025.4.DSc/Т1002) on the possibility to generalize the existing mathematical models for radon volumetric activity (RVA) dynamics in an accumulation chamber by the fractional derivative method to specify the process modeling by means of taking into account the time non-locality of radon transfer process.

New theoretical and practice results in the field of fractional calculus were presented. New mathematical hereditary models for RVA were suggested. They are based on Riccati equation with non-constant coefficients and fractional Gerasimov-Caputo variable-order derivative. The models make it possible to model the RVA dynamics more accurately. Effective parallel hybrid algorithms, realizing numerical methods to solve direct problems for RVA hereditary models, were developed. This allowed the researchers to reduce the time for solving direct and coefficient inverse problems.

The efficiency and complexity of the algorithms were assessed. New numerical algorithm was developed on the basis of iteration Levenberg-Marquardt method for solving coefficient inverse problems on the identification of RVA hereditary model parameters for known experimental data. A number of practical problems of mathematical modeling was solved on the basis of RVA experimental data in terms of RVA accumulation, decay, anomalous values and in the vicinity of the strong earthquake, which occurred in Kamchatka on August 17, 2024.

A software complex was developed in the form of an application with graphic user interface for GNU/Linux operation systems making it possible to solve the problems of mathematical modeling of RVA variations, processing and visualization of data and results.

The presentation aroused keen interest, questions and discussion of the investigation results.

The dissertation investigation on the subject «Mathematical modeling of radon volumetric activity variations taking into account hereditarity» by Tverdiy D.A. was recommended for presentation for the Doctor of Science degree (Dr. Sci.) of Uzbekistan Republic in the field of study «05.01.07 – Mathematical modeling. Numerical methods and program complexes» (technical sciences).