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Mathematical Support of Experimental and Theoretical Studies Conducted by JINR

• Application and development of hydro-dynamical models for the analysis of ultra-relativistic nuclear collisions on the accelerator complexes of RHIC, LHC, GSI and JINR. Research on probable stream phenomena on LHC. Modelling of processes of nuclear fragmentation and destruction for the CBM experiment with the help of the FRITIOF model. Mathematical simulation of physical processes in nuclear reactions with heavy nuclei. Theoretical and experimental research of the accelerator-driven transmutation systems. Study of physical aspects of the electro-nuclear way of energy production. Study of secondary space radiation interactions with lead. Modelling of the liquid diffusion processes in porous materials and phosphor-lipid membranes. Research on various methods of determining the centrality of interactions. Modelling of the light nuclei production. Software development and Monte Carlo modelling of COMPASS experiment. Maintenance of computer programs of the primary data processing (SAS, Fitter, Gluplot, etc.) for experiments in FLNP. Development of mathematical methods to solve applied problems arising in ecology and economy.
  
  
• Development of a new finite - element approach with respect to the field vectors for computations of complex magnetic systems of experimental physics. Development of methods of constructing differentiable approximations of a magnetic field based on a multivariate B-spline approximation. Application of the developed methods and algorithms for the differentiable continuation of data of the field from a calculation grid into the working area of the magnets. Computer simulation and optimization of the dipole magnet of the CBM experiment. Development of methods of pulse reconstruction from coordinate measurements of charged particles moving in a heterogeneous magnetic field.
  
  
• Participation in the development and start-up of TDAQ ATLAS on LHC. Creation of a basis for experimental TDAQ testbed in LIT, a prototype of the system to control the experimental data quality with the opportunity of remote access to the TDAQ ATLAS monitoring services, located in Control Room ATLAS at CERN. Development of algorithms for identification of electrons and pions in TRD using neural networks and a nonparametric goodness-of-fit criterion, methods of pulse reconstruction and global tracking for CBM experiment. Development of algorithms and software for track recognition and fitting in STS and TRD detectors for CBM experiment using the Kalman filter, testing of the programs with their inclusion in the software environment of the experiment. Development of algorithms and computer programs for recognition and fitting Cherenkov radiation rings due to the RICH detector data (experiment CBM) with inclusion of the programs in the software environment of the experiment. Development of new algorithms of reconstructing the resonance parameters in the invariant mass spectrum in nucleus - nucleus interactions and hadron jets finding in high-multiplicity events, including the events with polarized protons on the basis of wavelet analysis methods (experiment STAR). Research of the accuracy characteristics of these algorithms. Development of algorithms of vertex finding of events of interacting neutrino with target due to information from the target tracker (experiment OPERA); research on increasing the efficiency of the neural network algorithm at the expense of applying the RBF-network and optimization of training on event types. Development and progress of the methods of applied statistics and modelling with reference to the problems of radiobiology, testing of data acquisition systems (experiment ATLAS) and check-up of hypotheses about the mixes of distributions in the problem of relativistic nuclei fragmentation. Software and methodical support of experiments ATLAS, CMS, CDF, DIRAC, CBM, DUBTO, THERMALIZATION, NUCLEON. Development of the structure of user interfaces integrating interactive tools and telecommunication access to powerful computer resources. Development of effective methods, algorithms and software of the local polynomial approximation and smoothing in an adaptation mode, using the new technology .NET. Research and development of algorithms of reconstruction in the muonic system of the CMS experiment.
  
  
• Modelling of transition processes in various materials (homogeneous, two-layer, anisotropic ones), including phase transitions, change of physico-chemical properties, occurrence of localized structures under action of external energy sources in FLNR installations. Simulation of transition processes in particle physics and nuclear physics: formation of quark - gluon plasma, evolution of dense nuclear matter and inelastic nuclear interaction. Research in spectral properties of scalar mesons in hadron environment with terminal temperature and density in frames of the programme on preparation of experiments on JINR Nuclotron. Study of the processes which can serve as indicators of obtaining a mixed phase of the nuclear matter. Simulation and numerical study of phase transitions in cuprates within the Hubbard two-band model. Mathematical simulation of macroscopic motion and electromagnetic processes of superdense baryon matter of atomic nuclei and neutron stars. Modelling and numerical study of solutions of protein molecules and self-organization in polymers. Numerical modelling of nonadiabatic transitions, Bose condensation and topological effects in nonideal quantum systems. Development of methods and algorithms of solving boundary-value problems for higher-order differential equations with a small parameter at higher derivatives arising at solving relativistic quasipotential equations. Optimization of Lorentz calibration technique for nonperturbative calculations of propagators of gluons and ghosts in the lattice models of gluodynamics. Numerical description of the energy and structure of 0+ states of deformed nuclei. Mathematical modelling of electromagnetic properties of new heterogeneous nanomaterials to estimate a perspective of their application in information and biomedical technologies.
  
  
• Development of algorithms of computer algebra and their software implementation in the GINV system with an open code and in the C language for the purposes of research and solution of the systems of algebraic, differential and difference equations arising in theoretical and mathematical physics. Information support of this work on web-servers   http://invo.jinr.ru   and   http://compalg.jinr.ru 
  
  
• Development of a complex of programs of parallel calculations for mathematical simulation of stochastic processes in advanced turbulence. Research in the processes of formation of singularities in the coupled system of Young-Mills equations with dilaton and in other super-critical systems on the basis of the created programs realizing the developed parallel algorithms. Development of alternative models of quantum computing (with use of Groebner bases, monodrom). Development and software implementation of symbolic numerical algorithms of computing matrix elements for parametric eigen-value problems with orientation to quantum computing. Filling with new programs - generators of the interactive information - analytical system for mathematical simulation of processes of high-energy physics HEPWEB and its integration with the external computing resources (CICC JINR, "Dubna - Grid" metacluster resources, etc.) -   http://HepWeb.jinr.ru   . Development of new approaches to protection of the local area networks, control and modelling of the network traffic. Research of the functionally important genome elements over their electrostatic potentials distributions.
  
  

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