The monograph «Mathematical modeling of radon volumetric activity variations taking into account the heredity: model, solution methods, program» has been published

Author: researcher of the Laboratory of Electromagnetic Radiation IKIR FEB RAS, Cand. Sci. (Phys.-Math.) Tverdiy Dmitriy Alexandrovich.

The monograph is devoted to some issues of mathematical modeling of radon volumetric activity as a precursor of strong earthquakes in Kamchatka.

Radon is a radioactive inert gas, continuously recorded by gas-discharge counters installed in special accumulation chambers. Within the theory of emanation method, monitoring of radon gas concentration change in the underground, atmospheric air and in water is one of the methods for investigating the processes in the Earth crust during earthquake source preparation.

The investigation tool within the theory of the emanation method is mathematical modeling. However, there are often cases when radon has high migratory aptitude. It is impossible to explain this only by diffusion mechanism and, thus, to describe it by process classical models.

Thus, the main attention in the research is given to the issues of application of fractional derivative methods for description of the process within the framework of anomalous diffusion to take into account the non-locality of radon mass-transfer process and, as a sequence, to generalize the radon volumetric activity model on the basis of an ordinary time derivative. It is assumed that the fractional derivative order is associated with geological medium permeability.

The investigation is represented in the form of a triad: mathematical model — solution method — software. The book describes the required methodology, new hereditary models of radon volumetric activity are proposed taking into the account the heredity effect, methods of model equation solution are described and parallel realization of numerical solution algorithm for a PC is presented.

When solving the geophysical problems, there are often cases, when model parameters are determined inaccurately as long as it is impossible to make direct measurements deep under the ground or it is just impossible to measure mathematical model parameters but only to estimate them on the basis of experimental data. Thus, to determine the optimal values for the parameters of the hereditary model of radon volumetric activity, an inverse problem was formulated, a method for its solution was described and software realization of the algorithm was suggested.

One of the main research tasks is the development of a software complex combining all the required tools for solving the problems associated with mathematical modeling of radon volumetric activity in the theory of fractional derivative method, solution of direct and inverse problems, processing of experimental and model data and result visualization. As a consequence, FEVO software complex was developed for GNU/Linux operation system family.

The FEVO software complex was written in C language using the API GTK of version 4.0, API OpenMP of version 5.2, API CUDA of version 12.0, Gnuplot of version 6.0.

The book can be useful for the lecturers, senior students, postgraduates studying «Applied Mathematics and Informatics» and related specialties as well as for the researchers working in these fields of science.

The monograph was supported by the Russian Scientific Foundation Grant No. 23-71-01050 on the subject «Development of a software complex for modeling and analysis of radon volumetric activity as a precursor of strong earthquakes in Kamchatka».

Full text of the monograph is available here.