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Nonlinear Problems of Computational and Mathematical Physics: Algorithms, Software, and Investigations

Scientific Programme:

• Development of statistical methods for the mathematical modeling of interactions of particles with nuclei and substance. Creation of a modern version of the program DUBNA-CASCADE for Monte-Carlo simulation of transport and interaction of particles with nuclei.
• Development of methods for modeling and processing experimental data, including the development and introduction of new methods for data filtering and data compression as well as pattern recognition. Introduction of the results in the software for experimental investigation.
• Creation of methods and numerical algorithms for magnetic fields calculation and particle beams transport. Introduction and maintenance of modern computer programs for magnetic fields calculations.
• Creation of numerical methods and software for mathematical simulation of complex physics systems. Development of a program library for calculation of stationary and dynamic models of quantum mechanics and field theory oriented to the vector-parallel computing systems.
• Development of methods, algorithms and software of computer algebra. Introduction and maintenance of modern systems of analytical calculations.
• Development of numerical and analytical methods for a research in nonlinear models of theoretical physics.
• Creation of systems for experimental data processing in particle physics, including the development of algorithms, software and architecture of computing clusters. Application of the developed systems for mathematical processing of experimental data.
• Information support of the research on the basis of the Web-technologies.

• Creation of a standard program package for mathematical experiments with fissionable sub-critical systems with updated constant support, including more perfect models of decay of excited nuclei and optimized algorithms for calculations of the particle trajectories in multicomponent heterogeneous media. Matching with the experiment of the cascade calculus of nucleus-nucleus interactions in the field of the energies exceeding several tens of GeV.
  Modeling of the experiments carried out in cooperation with MRTI on the creation of the gas-discharge generator of thermonuclear neutrons and possibility of its use as a neutron source in electronuclear installations.
• a) Development of program packages for simulation, processing and visualization of data with the use of systems ROOT, GEANT, LAHET, FRITIOF for experiments STAR, COMPASS, HEND, SPHERE, FAZA. Research in the spacial-temporal characteristics of the nuclear substance in the course of nuclear collisions, simulation of spin effects in the experiments with polarized beams for the installation STAR.
  Development of a method and algorithms for calculations of the sections of diffraction processes in p, pp, pA, and A collisions.
  Creation of a mathematical model to achieve a high efficiency of the pattern recognition when restoring events at the installation COMPASS. Development of algorithms for particle identification on the data from the RICH-detectors of experiment COMPASS. Creation of a mathematical model of the neutron and gamma irradiation of the Mars surface on the basis of the measurements of fast neutrons with the detector HEND which is part of the scientific equipment placed onboard the American orbital ship.
  Simulation of the processes of the neutron fields generation at the installation SPHERE; development and maintenance of program-event generators for modeling the processes of nuclei fragmentation, processes of complete destruction of nuclei and dynamics of nuclear interactions on the basis of measurements at the installations FAZA and SPHERE. Construction of a model of fission of superheavy nuclei fission in cooperation with FLNR. Increasing the efficiency of the track reconstruction program for external HERA-B track detector.
  b) Creation of a mathematical model of the DUBTO installation, participation in the development of the program of data monitoring for experiment DUBTO. Development of the program for a real-time analysis and visualization of data for experiments DEMON and CORSET.
  Development of the tracking program; development of the programs of modeling for experiment DIRAC. Optimization of the installations geometry, liquidation of the background sources, valuation of its resolution, development of the neural network trigger.
  Analysis of the experimental data obtained from the installations DIRAC, DUBTO, CORSET, DEMON. Development of algorithms of filtering 2-dimensional images on the basis of wavelet-transformations. Creation of the program library of a fast analysis of signals on the basis of the wavelets of the second generation.
  Research on the fractal properties of thin films by methods of neutron reflectometry and development of methods for analysis of physical processes in a pre-surface layer of fractal objects.
• Development of methods and algorithms for simulation of three-dimensional electromagnetic fields. Numerical simulation of the spacial distribution of ponderomotive forces. Development of numerical methods and algorithms for construction of three-dimensional differentiable approximations of electrical and magnetic fields. Computations for the installation ALICE. Calculation of the elements of the magnetic system of transportation of the low-charge beams for the project DRIBs (FLNR) for optimization of its elements.
  Development of a mathematical model of a sound formation and a heat release in the vicinity of the accelerated ions trajectories taking into account the correct setting of the process dynamics. Selection of a mathematical model for the description of the nuclei diffusion processes through the powdery targets of heavy elements and realization of preliminary calculations. Creation of algorithms and computer program for simulation of thermal relaxation of the energy released taking into account the processes of the electron-phonon interaction.
  Creation of an algorithm and a program for a numerical solving of an initial problem for the system ODE with parametric integrals in coefficients.
• Numerical methods for research on the properties of two-photon states of deformed nuclei.
  Development and application of the numerical methods to calculations of characteristics of generating doubled nuclear systems and fusion of nuclei in the reactions with heavy ions.
  Calculations of the vibration states constructed on manyquiasiparticle isomers in deformed nuclei. Development of a model for calculation of the optical potentials of nucleon-nucleus and nucleus-nucleus scattering of exotic systems. Creation of Newtonian schemes for computing the quantum mechanics systems dynamics taking into account stochastic interactions. Simulation by the methods of molecular dynamics of thermoelastic processes arising in metals exposed to high-energy ions.
  
• First version of packages written in Reduce, Mathematica and C/C++ for completion to an involution of the linear systems of partial differential equations. Design and partial implementation of a recursive algorithm for reduction of a certain class of Feynman diagrams to the basic integrals. A C program for computing cohomologies of infinite-dimensional graded Lie algebras and superalgebras and a Reduce program for calculation of the Stark and Zeeman effects.
• Elaboration of an appropriate perturbation theory for the sigma models and the string theory within the functional integral method. Derivation of new results for observable (the average energy, the pion norm, the fermion propagators) within the theory with dynamical fermions. Derivation of exact resonance solutions in the modified models with the quantum potential determined by the nonlinear Schrodinger type equation.
• Development of a computing cluster RISK for processing simulated information and experimental data.
  Development of integrated and distributed soft- and hardware platform on the basis of the local linux-cluster and facilities of the JINR computer centre (robot mass storage etc).
  Elaboration of a system PAS - the intellectual tools of autosupport of distributed data processing with the use of the shell-languages for realization of scenarios.
  Development of methods for absolute calibration and accounting of the time variations of the function of the magnetic field on the basis of the definition of the parameters of model of the trajectories of the particles (solving a system of the differential equations) registered in the bench-mark's processes.
  Development of the program complex BISON for mathematical processing of simulated information and experimental data in research of charm particles and searching for multiquark states.
  Creation and preparation for physics analysis of the data banks (DST and others) as results of for mathematical data processing.
• Development of the WWW-server on computer physics using the experience of the leading world servers in this direction.

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