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Mathematical Support of Experimental and Theoretical Studies Conducted by JINR

• Modeling neutron spectra, energy transfer and isotope formation under the interaction of 100 MeV electrons with uranium and wolfram targets. Modeling of the polarization processes (STAR experiment at RHIC accelerator). Modeling and visualization of nuclear structure based on the occurrence of internal discrete symmetries. Participation in mathematical support of the simulation and implementation of the NICA-MPD project devoted to the search of the existence of and investigation of the properties of the mixed phase in relativistic high energy heavy ion collisions. Development of methods and program complexes for modeling elastic and inelastic collisions of the hadrons and the nuclei with nuclei at intermediate energies, taking into account their microscopic structure. Application of the developed methods and programs to the processing of experimental data on the interaction of exotic nuclei with stable ones, collected in FLNR-JINR. Investigation of the structure and properties of one- and many-component phosphor-lipid membranes within unilamellar vesicles versus temperature and phase state of the membrane, on data collected in FLNP small angle scattering experiments. Numerical modeling of the humidity transport in porous materials, taking into account the interaction between the humidity and heat transport processes. Further development of the interactive information - analytical system HEPWEB for mathematical simulation of processes in HEP: filling with new generator programs (PITHIA, AMPT, HSD) and consecutive integration with external computing complexes.
  
  
• Development of computer modeling and parameter optimization of the dipole magnets in the CBM experiment. Computation of the field map within the working area of the magnets and derivation of differential approximations based on three-dimensional spline approximants. Development of algorithms and calculation procedures, based on finite element as well as finite difference methods, of integral boundary equations in problems arising in the design of complex installations of experimental physics. Development of methods of modeling the operating modes of the multi-purpose isochronous cyclotron.
  
  
• Completion of the elaboration and development of the TDAQ WEB Monitoring Interface for remote access to the Control Room ATLAS at CERN and implementation in LIT of a pilot mode of the remote monitoring of data received during sessions of the ATLAS experiment. Debugging of the DQM Framework system for the ATLAS experiment data quality estimation control. Application of artificial neural network approach to solving the hadron calorimetry problems in ATLAS experiment. Development of methods and algorithms for event reconstruction in CBM experiment: electron identification and pion suppression in TRD with the help of statistical criteria and neural networks, track reconstruction in STS and TRD, particle identification with the help of RICH, global tracking – the connection of the trajectories restored in various CBM detectors. Research on optimization of the construction of different CBM elements (RICH, TRD, MUCH, etc.). Development of a software complex for event visualization in CBM, participation in work on the development of the CBM Framework software complex. Development of new algorithms of reconstructing the resonance parameters in the invariant mass spectrum in nucleus-nucleus interactions and hadron jets recognition in high-multiplicity events, including the events with polarized protons on the basis of wavelet analysis methods (experiment STAR). Development of search algorithms of the event vertex describing neutrino interaction with the target, from data accumulated by target tracker (experiment OPERA). Development of methods and algorithms of polynomial spline–approximation with automatic knot detection and their software realization. Development of the hard muon event reconstruction program in the CMS experiment. Search for new di-muon resonances and testing the Standard Model predictions on the Drell-Yan processes in the TeV mass region. Analysis of diffractive photo-production of vector mesons using experimental data obtained in the Forward Proton Spectrometer of the H1 detector at the HERA collider. Participation in the processing and analysis of data collected on the neutron and neutrino beams of the U-70 accelerator. Development of methods of computing transition formfactors from arbitrary bound states of hydrogen-like atoms to pi-states of the continuous spectrum. Application of the developed algorithms to the interpretation of DIRAC experiment data. Investigation of the intensification at the phase transition point and of the possibility of resonant intensifications of the two-photon spectra at finite densities. Evaluation of the probability of formation of the quark-gluon plasma in central nucleus-nucleus collisions and comparison of the computed output with the experimental data. Neural network support of R&D at the stages of creation of installation NUCLEON and experimental data analysis.
  
  
• Theoretical and numerical analysis of models described by non-linear Schredinger equations. Development of analytical algorithmic methods of exact integration of differential equations in partial derivatives and application of these methods to various models of mathematical physics. Modeling of critical parameters in non-homogeneous Jophenson junctions. Modeling and numerical investigation of the symmetry induced features within the two-band Hubbard model of high critical temperature superconductivity. Study of phase transitions in one-layer and two-layer materials under consideration of the non-linearity of the thermal parameters. Development of a new theoretical approach to the nuclear electrical PIGMI resonance. Numerical investigation of particle-like excitations within the dynamic polaron model. Development of an exact self-consistent theory of the Bose condensed systems. Computation of the basic thermodynamic and dynamic characteristics in systems with broken gauge symmetry. Development of the method of self-similar factor-approximants. Use of the factor-approximants for the computation of critical indices of critical phenomena and for solving differential equations. Research in the soliton-like solutions in supercritical systems of coupled systems of nonlinear wave equations. Numerical investigation of the evolution of economical and biological systems which show complex behaviour exhibiting dynamic phase transitions and strong non-linear effects. Development of an elasto-dynamic model for the study of the optical response of dielectric nano-particles, computation of the oscillation energy spectrum of a spherical nano-particle in the long-wave approximation. Development of mathematical methods of reconstruction of the potential of quantum wells under use of the Darboux transformation for modeling one-dimensional nano-objects.
  
  
• Development of the first version of an involutive algorithm for solving systems of non-linear partial differential equations by a divide-and-conquer approach consisting in their splitting in algebraic simple subsystems followed by the reduction of each of the subsystems to involution. Partial realization of the involution algorithm in Maple language. Realization of computer algebra system Reduce on Common Lisp in order to remove the memory restriction in 128 Mb imposed by the available implementation for 32-bit computers. Creation of a C program for study of the symmetry properties of discrete dynamic systems.
  
  
• Creation of a program in Mathematica language for graphic implementation of quantum schemes and computation of its corresponding unitary matrix defininig the quantum computation. Implementation in C++ language of the algorithm of reduction to involution of the polynomial systems, over a finite field, which characterize the quantum computations. Identification of functionally important elements of the genome from the distributions of their electrostatic potentials. Molecular cartography of DNA, RNA, and proteins in a distributed computing environment. Development of new approaches to LAN protection, control and simulation of the network traffic. Stable separation of the various components of time series (trend determining components, chaotic components of various origins, anomalous components). Investigation of new formulations and solutions of the problem of optimizing computational processes in Grid-systems for the calculation of intricate complex problems and problems associating huge input task requests, characterized by different temporal distribution laws of the requests. Development of a theory for the entanglement regularization in systems of cold atoms in traps with coherent topologic modes. Study of the possibility of use of the directional entanglement for information processing and in quantum computations. Modeling quantum computers and quantum systems both by using exactly solved stationary and non-stationary problems in reduced dimensionality spaces and by using numerical or numerical-analitic methods.
  
  

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