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Mathematical Support of Experimental and Theoretical Studies Conducted by JINR

• Development and application of Monte Carlo models for the analysis of ultra-relativistic nuclear collisions on the accelerators RHIC, LHC, JINR, GSI. Ultra-relativistic Quantum Molecular Dynamics model simulation of processes of nucleus fragmentation and destruction in nuclear interactions in experiments CBM, PANDA. Modeling the multiple emission of intermediate mass fragments for experiment FASA. Calculations of cross-sections in experiment NIS. Software development and Monte Carlo modeling in experiment COMPASS. Numerical study of processes inside electronuclear systems at Nuclotron beams. Development of software for on- and off-line data processing for experiments in FLNP (SAS, Fitter, etc.). Development and implementation of algorithms for track recognition, mathematical data processing, statistical analysis of physical information for experiment TESLA. Development of efficient methods, algorithms, and codes (using the new .NET technique) of local adaptive polynomial smoothing with the aim of improving the speed, precision and stability of data processing. Modelling moisture diffusion in porous materials measured in neutron scattering experiments. Preparation of the program of measurements for the VHM-problem investigation and development of a neural networks approach for the top-quark mass determination in the CDF experiment.
  
  
• Development of optimization methods based on functional minimization with applications to complex magnetic systems. Development of computer simulation of the superconducting dipole magnet for experiment CBM. Simulation and computation of the magnetic system of the GSI accelerating installation.
  
  
• Development of new data handling algorithms for RICH detectors (experiment CBM). Neural network based algorithms for the target tracker (experiment OPERA). Research and development of pattern recognition algorithms of the hard muon reconstruction in the CMS Endcap Muon system. Increasing the efficiency of algorithms of reconstruction of charged particles trajectories in experiment H1. Development of new algorithms for global event reconstruction in experiment CBM. Development and maintenance of specialized program complexes for simulation of experimental setups and data analysis at the RHIC, LHC, GSI, and JINR. Development of the computation and communication module prototype intended for the real-time data treatment and analysis in the ATLAS TDAQ system.
  
  
• Development of algorithms for the reconstruction of the microscopic nucleus-nucleus potential at intermediate energies. Numerical studies of light nuclei with neutron halo within microscopic and semi-microscopic models. Development of improved quasiparticle-phonon nuclear models and software. Elaboration of a discrete symmetry model of nuclear structure taking into account quark and nucleon correlations. Study of the behaviour of few particle systems in external fields. Definition of resolvent intervals in Bayesian automatic adaptive quadrature. Modeling structure and properties of organic materials within the small-angle neutron experiments in FLNP. Numerical investigations of nonlinear non-homogeneous processes induced in materials by charged particle beams (in FLNR experiments). Calculations of spin effects in deep inelastic lepton-nucleon scattering processes. Study of the meson and quark-gluon properties within quark models with separable interaction. Qualitative analysis of singularity formation in Yang-Mills dilaton bound states. Development of algorithms and codes for computing cavities in macromolecules. Creating a software complex for mathematical simulation of interacting protein macromolecules with the solvent. Development of methods and algorithms for solving boundary value problems for relativistic quasi-potential equations. Theoretical and numerical investigations of quantum systems within model interacting potentials. Development of methods and algorithms for solving quantum mechanical systems in non-homogeneous fields. Study of particle-like excitations in dissipative systems within models of astrophysics, condensed matter physics and nonlinear optics. Modeling gravitating super-dense rotational configurations in astrophysical problems. Further research in quantum statistical properties of polymers.
  
  
• Further optimization and extension of the built-in algorithms for the C/C++ based open source software GINV oriented to computing involutive and/or Groebner bases for systems of multivariate polynomial equations. In particular, implementation in GINV of algorithms for computing the greatest common divisor of multivariate polynomials. An implementation in Maple of involutive algorithms for linear differential and difference systems, in order to generate difference schemes for linear PDEs and to reduce loop Feynman integrals. Design and implementation in C of algorithms for analysis and simplification of discrete relation systems for their application to simulation of quantum circuits. Information support of research at JINR based on the use of computer algebra systems and software packages.
  
  
• Development of parallel algorithms for solving strongly anisotropic widespread turbulence phenomena. Parallel algorithms and programs for modeling the decay of self-similar solutions of interacting Yang-Mills fields with the dilaton. Development of the C# package QuPol created for interactive graphical assembling a circuit representing quantum computation and generating the polynomial system associated with the circuit and such that its solution space completely characterizes the quantum circuit. Algorithmic study of converting an arbitrary quantum circuit into an equivalent one constructed from the Hadamard and Toffoli gates only. Symbolic-numeric investigation of evolution for finite-dimensional quantum systems in view of their application to quantum computing and quantum informatics. Installation of interactive informational-analytical system for mathematical simulation of high energy physics processes. Numerical and analytical investigation of two-mode systems allowing for quantum information processing: topological coherent modes of trapped atoms and nonlinear spin assemblies. Creation of an interactive information analytical system for mathematical simulation of HEP processes. Creation of a monitoring system for the JINR LAN information traffic; research of the JINR network traffic. Studying the role of the electrostatic potential in the problem of molecular recognition.
  

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