- Symbolic-numerical solution of problems in quantum physics and wave optics, automation of the processing of experimental data obtained using accelerators, numerical computation of stochastic dynamics problems.
- Enhancement of functional models for optical and quantum-physical devices based on wave optical and quantum-mechanical effects; Modification of continuous numerical computation for solving direct problems of simulation of waveguide propagation of electromagnetic radiation in integrated optical waveguides, diffraction of polarized monochromatic electromagnetic radiation on subwave optical grating and evolution of small-size quantum mechanical systems.
- Computer implementation of symbolic numerical algorithms for solving initial boundary problems for corresponding systems of partial differential equations and studying their stability-like and symmetry properties.
- Development of research techniques for Markov and single-step processes; enhancement of research techniques for stochastic and statistic processes.
- Computer implementation of analytical and numerical algorithms for solving initial boundary value problems for the corresponding systems of partial differential equations, stochastic differential equations, integro-partial differential equations.
Study of Hamilton action construction for various types of motion equations of infinite-dimensional systems and representability of equations in the form of Euler-Lagrange equations with nonpotential force densities, Hamilton equations and Hamilton admissible equations.
Creation of information technology in the form of complex methods for managing radio resources in heterogeneous 5G wireless networks that support Internet of Things technologies.
The main goal of the Project is to create a practical center at the international level to improve computational methods for applied problems in mathematical physics. Currently, the Center's employees are focused on the implementation of symbolic-numerical algorithms for solving problems in quantum physics and wave optics as well as automated processing of experimental data obtained from accelerators.
The Center develops, approbates, and enhances computer data processing methods together with colleagues from the Laboratory of Information Technologies at the Joint Institute for Nuclear Research (JINR). The development, approbation, and improvement of symbolic-numerical algorithms for solving quantum physics problems are conducted together with colleagues from the Laboratory of Theoretical Physics at JINR. The work on the study of numerical computations of stochastic dynamics problems is carried out together with employees from the International Scientific Center at JINR, Jozef Šafárik Slovak University, the Federal Research Center “Informatics and Management”, and the M.V. Keldysh Institute of Applied Mathematics.
The research results can be used by education institutions to train highly qualified staff in Russia and abroad.
Research results will be applied in the following areas:
- software development to support the Internet of Things technology with radio resource management of heterogeneous 5G wireless networks. For example, design of automated systems for nursing.
- statistical analysis of customer movements in wireless networks in order to identify the spatial and probabilistic characteristics of traffic as well as reliability of network connections. For example, design of autopilot systems for automobiles and railway vehicles.
- design devices for nuclear electronics to record elementary particles and photon radiation. For example, design of devices for counting pulse from integrating detectors as well as the classification of types of elementary particles and studies of their energy spectrum when it is required to analyze the pulse shape of particles, determine its amplitude and relative time delay between pulses; for analysis of elementary particles’ directional distribution.
- design devices for working with small-size quantum systems, i.e. systems containing structural elements about 1-100 nm in size that determine their basic properties and characteristics. For example, design of nanodevices (nanopumps, nanomotors, nanorobots, nanomannipulators, etc.) and creation of nanomaterials with specified properties (super strength, superhardness, complete absorption or reflection of electromagnetic radiation, etc.).
- analysis of stochastic dynamics of physical, technical, and economic systems that are random in nature. For example, design of aircrafts: planes, unmanned aerial vehicles, missiles; development of monitoring systems of high-rise buildings and structure stability (stability during earthquakes), development of monitoring systems for macroeconomic dynamics, etc.
- design of nanoscale integrated optical systems and devices for optical interconnection and information processing. For example, design of data-transmission systems via fiber-optic communication channels.