The main areas of research of the laboratory are:
- the creation of new mathematical models about the theory of elasticity, in electrodynamics, acoustics, astrophysics, immunology and pharmacokinetics;
- the study of the properties of these models and of the possibility to identify models (definition and clarification of the basic parameters of the models, of the initial conditions of the studied processes, of the sources and domains).
The main step in the development of research is the mathematical analysis of models (stability, existence and uniqueness of solutions of the corresponding systems of equations of mathematical physics; analysis of the uniqueness and conditional stability of the corresponding inverse problems).
Within the frame of our laboratory:
- We develop numerical algorithms for solving inverse problems in thermoacoustics, immunology, pharmacokinetics and gene networks (paragraphs 4 "Biomedical and veterinary technologies", 5 "Genomic, proteomic and post-genomic technologies" and 22 "technologies to reduce losses from socially important diseases" from the list of critical technologies of the Russian Federation);
- We develop theories of elasticity, electrodynamics and acoustics (paragraphs 19 "Technologies for monitoring and forecasting environmental conditions, preventing and eliminating pollution", 20 "Technologies for search, exploration, and development of fields rich in useful minerals and their production " and 21 "Technologies for preventing and eliminating natural or man-made emergency situations" from the list of critical technologies of the Russian Federation);
- We provided a computational investigation of models on supercomputers using modern parallel computing technologies (paragraph 18 "Technologies and software of distributed and high performance computing systems" from the list of critical technologies of the Russian Federation).
Equations of mathematical physics and methodology of inverse problems integrate a variety of mathematical models (from pharmacokinetics to astronomy.)
Our Laboratory achieved the following results:
- We developed a highly-optimized software package for modeling diffraction of seismic wave fields in three-dimensional layered-block media. This package allows modeling wavefields in complex media in order to find minerals (mostly oil and gas) located in places hard to investigate.
- We studied the problem of the collapse of astrophysical objects. We simulated formation scenarios of new stars within molecular clouds based on their chemical evolution.
- We developed methods and algorithms for solving inverse and ill-posed problems which are useful for medical imaging, ground-penetrating radar and well logging.
- We developed a new algorithm for the numerical calculation of the amplitude of tsunami waves, characterized by its high speed calculation. We created a set of programs based on this algorithm.
- We studied the simplest model of an infectious disease, which is characterized by immunity parameters. It is important to be able to determine these parameters for drawing up individual treatment plan.
- We developed numerical algorithms for determining the parameters of mathematical models of immunology, epidemiology, multicompartment and nonlinear pharmacokinetics for the analysis of blood, urine and statistical data on the basis of iterative methods.
- We conducted analysis of numerical methods.
Expert in this field – Doctor of Physico-Mathematical Sciences,
Sergey Kabanikhin,
ksi52@mail.ru
Section of Function Theory of the Mathematics & Mechanics Department (MMD) NSU
Section of Mathematical methods for Geophysics MMD NSU
Section of Hydrodynamics MMD NSU
Section of computational systems MMD NSU
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences
