Next theme	Prev. theme
to field of reseach	to contents

Mathematical Support of Experimental and Theoretical Studies Conducted by JINR

• Research into quark models of interacting hot and dense nuclear matter (the quarkonic phase) for the description of expected processes in the NICA experiment. Development of mathematical tools and of numerical calculation methods. Upgrade of the computational programs used to simulate nuclear processes. Investigation of angular and energy characteristics of nucleon and meson fields in nucleus - nucleus interactions in the energy range of about 10 GeV. Analysis and interpretation of experimental data received in the currently running experiments. Study of the dilepton pair emission in heavy ion collisions characterized by ion energies in the center of mass system of 4 - 11 GeV/nucleon. Microscopic analysis of the mechanisms of the kaon scattering on nuclei of carbon and calcium in terms of the models describing the structure of these nuclei. Numerical analysis of the mechanisms of ⁶Íå + ¹²Ñ scattering within microscopic models of the nucleus - nucleus potentials under use of various models for the ⁶Íå nucleus density. Comparison with the available experimental data. Investigation of the unitary corrections to the Moliere theory of multiple scattering of interest to the DIRAC experiment. Study of the effects of the Coulomb interaction between pions in K_e4-decays for experiment NA-48/2. Assessment of the importance of the confinement effects on the quark and gluon propagation through nuclear matter (experiment ATLAS). Generalization of the nonlinear thermal spike model, development of numerical methods, algorithms and computer programs with the aim of modeling the thermo-elastic waves and power loss of the heavy ions inside the electronic and ionic sublattices by including the ion motion inside the material. Study of the mutual influence of the moisture and heat transfer processes in porous materials by taking into consideration the presence of the air in the material's pores within a model described by three nonlinear equations, which include all the thermophysical parameters of the porous material, water, dry air, and vapor. Numerical simulation of the nanostructure and properties of the multi-component poly-disperse phosphor-lipid vesicular systems in terms of the temperature and of their chemical compositions.
  
  
• Computer simulation of the magnetic systems for the accelerators SIS100 and SIS300 designed within the FAIR project. Optimization of the magnetic system parameters of the CBM experiment. Development of numerical methods for modelling and optimization of the magnetic systems for physical experiments conducted by JINR. Development of methods for modelling the steady operating modes of the multi-purpose isochronous cyclotrons. Development of finite-element numerical methods with high-order harmonic basis functions under use of adaptive meshes for solving elliptic boundary-value problems and their application to magnetostatics.
  
  
• Mathematical simulation of hadronic phase transitions of colliding nuclei in small spatial regions within the nonlinear sigma-model. Application of these developments to the description of the cumulative effect as well as of new experiments planned at VBLHEP JINR. Research and construction of a realistic model of the electron energy losses in the transition radiation detector TRD of the CBM experiment. Research on the distribution of time-of-flight of the charged particles registered in RPC detector of the CBM experiment; development of the time-of-flight algorithms of particle identification. Development and application of the wavelet analysis methods for searching resonant peaks in invariant mass spectra. Development and debugging of the remote monitoring system of data quality and of the states of the subsystems of the ATLAS detector, pilot data processing of the calibration measurements of the ATLAS installation. Development of neural network algorithms and software and their adaptation to the conditions of experimental data analysis at ATLAS. Processing of CMS cosmic muon data and of experimental data expected from the LHC collider. Improvement of the hard muon event reconstruction code for the CMS experiment. Measurement of diffraction vector meson cross-sections and calculation of diffraction structure functions on the experimental data obtained in the Forward Proton Spectrometer (FPS) of the H1 detector at the HERA collider. Simulation of the propagation of the electromagnetic pulse distributions generated in the two-component scintillating environment for the BOREXINO experiment. Development and maintenance of a tracking program for microdrift chambers (MDC) of the DIRAC installation.
  
  
• Development of effective methods and algorithms of data processing based on a coordinate-parametric polynomial model and 4-point transforms. Modeling, in the mean field approximation, of the high critical temperature superconducting phase transition in cuprates within the two-zone Hubbard model under boundary conditions following from the -T phase diagrams. Development of a model and a program for computing track formation in the high-temperature superconductors YBa₂CU₃O₇ and Bi₂Sr₂CaCu₂O_x, carrying out calculations. Mathematical simulation of the electromagnetic properties of the various metallic nanostructures entering as basic working elements in receivers and radiation sources of electromagnetic waves. Construction of models describing the electromagnetic radiation of complex structures containing nanoparticles (bound system nanoparticle - quantum point and micro-strip elements containing nanostructures). Mathematical simulation of the propagation of electromagnetic impulses in nano-containing composite media (such as a layer of nanoparticles - dielectric - semiconductor). Development and application of new and existing methods for analytical solution of evolution models of the mathematical physics to problems related to the burial of radioactive waste and the study of radiation transformations in geological materials. Development of mathematical simulation methods for the evolution of localized nanostructures in nonlinear media. Numerical study in the mechanisms of formation and evolution of the localized excitations described by dynamic nonlinear equations (dynamic polaron model, Josephson junction models, nonlinear optics models); identification of critical modes following from the physical characteristics of the environment. Numerical and analytical study of bifurcation points in models of fast rotating gravitating systems. Modeling and calculation of the parameters of self-oscillating reaction intermediates; carrying out numerical studies; comparison with experimental data. Modeling optical fibers for the transmission of signals with predetermined spectral characteristics, using the generalized Schroedinger equation. Determination of the dipole momenta of delta-resonances in radiative pion-nucleon scattering reactions within a field-theoretic approach with meson-nucleon and quark-gluon degrees of freedom. Carrying out calculations of the cross-sections of CO₂ ionization by electronic impact at high-energy collisions. Development of variation-iteration schemes for numerical solution of photo-absorption models. Mathematical simulation of energy-dependent potential quantum holes in nanoelectronics. Development of methods and algorithms for solving boundary-value problems associated to high order differential equations with Coulomb potential and their application to the scattering problem for a differential equation of the fourth order with a small parameter at the highest derivative. Development of mathematical methods for analyzing and modeling the evolution of the Universe in presence of different sources described by a nonlinear spinor field. Numerical study of complex dynamical systems describing non-equilibrium processes in nanomaterials. Development of algorithms and creation of software packages for solving renormgroup nonlinear systems of equations for the analysis of abnormal scaling of a passive scalar or with vector impurity turbulent medium. Development and implementation of an adaptive algorithm with local mesh densification of the time and spatial coordinates for the definition of threshold configurations of supercritical systems of nonlinear evolution equations.
  
  
• Modelling the dynamics of carbon and hydrocarbon nanostructures by means of discrete systems on symmetric lattices. Study of the gauge invariance in such systems and of its connection with the quantization. Investigation of quantum models on regular graphs, in particular, on lattices of (hydro)carbon nanostructures by methods of computer algebra and computational group theory. Development of numerical and analytical algorithms for the study of the dynamics of quantum models of semiconducting nanostructures with oscillator and Coulomb potentials in external fields. The C++ implementation of involutive algorithms for constructing Boolean Groebner bases with the aim of solving problems of Boolean satisfiability and quantum computing. Use of the OpenCL and CUDA technologies to speed-up parallel computations of algebraic Groebner and involutive bases by means of graphic processors. Implementation in the Aldor/Axiom frame of symbolic algorithms for Clifford algebras which are generalizations of the Dirac algebra of gamma-matrices. Study of the dynamics of entangled states of qubits and qutrits in a strong laser field. Creation of computer programs in the Maple language for computing two-loop propagator Feynman diagrams with arbitrary particle masses and for numerical - analytical computation of one-loop scalar integrals with 2, 3, 4 and 5-dots on the internal line for massless particles.
  
  
• Development of a program for modelling quantum computations in the language Mathematica by embedding quantum algorithms into it and inclusion of this program in the international database containing the quantum computing simulators. Development of algorithmic methods for the quantitative analysis of the entanglement of mixed two-qubit states, as a basic resource in the quantum computing. Conducting research for the derivation of results on the proved candidates for quantum qubits and development of alternative models of the quantum computing. Development of methods for the genetic classification of the protein structures. Computing within a distributed computer system of the maps of DNA and protein molecular surfaces; development of corresponding software. Numerical simulation of the nonlinear evolution of biophysical systems and study of their equilibrium states.
  
  

Next theme	Prev. theme
to field of reseach	to contents