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Mathematical Support of Experimental and Theoretical Studies Conducted by JINR

• Modeling electronuclear installations controlled by electron beams. Modeling photonuclear reactions of 30 MeV - 1 GeV electron beams with various targets. Mathematical simulation of nuclear physical processes accompanying interactions of relativistic nucleons and nuclei with matter. Simulation of neutron generation inside large targets under irradiation with highly energetic particles and nuclei. Study of the proton fraction of the secondary particle flux in electronuclear targets and blankets. Analysis of the possibility of using easy material thin targets in an accumulating ring for ~ 100 MeV protons or deuterons. Simulation of polarization processes in the experiment STAR at RHIC. Nuclear structure modeling and visualization within discrete symmetry models. Numerical investigation of the scattering mechanism in the reaction ⁸He+p and of the structure of the exotic nucleus ⁸He and generalization of the microscopic model to the case of kaon-nuclear scattering. Generalization of the methods and software devoted to small-angle neutron scattering experimental data processing to encompass nanostructures and synchrotron scattering data on multi-component phosphor-lipid membranes. Generalization of the nonlinear thermal spike model to the description of thermo-elastic waves and power losses of the heavy ions inside the electronic and ionic subsystems. Study of the mutual influence of the moisture and heat transfer processes in porous materials within a comprehensive nonlinear model. Calculation of nuclear reaction cross-sections in the area of ultralow energies under consideration of electronic device screening. Mathematical simulation of hadron phase transitions achievable at the JINR accelerating installations. Computation of radiative corrections to the K_e4-decay probability rate (for the NA48/2 experiment). Calculation of total inelastic cross-sections of the interaction of K-atoms with atoms of the target (for experiment DIRAC). Computation of quarkonia pair (J/ and ) cross-section definition in proton - proton and nucleus - nucleus collisions (for experiments ATLAS and ALICE). Modeling and calculation of nuclear effects in the creation of large transverse pulse hadrons in nucleon-nucleon, nucleon-nucleus and nucleus-nucleus collisions at RHIC and LHC energies.
  
  
• Computer simulation and optimization of superconducting magnets for the accelerator SIS100 designed within the FAIR project. Use of existing and newly developed software for modeling magnetic systems for experiments conducted by JINR. Computer simulation of the dipole magnet and the absorber for the CBM experiment. Development of methods for modeling the operating modes of the multi-purpose isochronous cyclotron. Development of finite element numerical methods with high order harmonic basis functions for solving elliptic boundary-value problems and their application to magnetostatics.
  
  
• Futher development of the TDAQ WEB Monitoring Interface for remote access to the Control Room ATLAS at CERN and implementation in LIT the remote monitoring of data received during sessions of ATLAS experiment. Development of neural network algorithms and software and their tuning to the conditions of data analysis at ATLAS. Development of methods and algorithms for event reconstruction in the CBM experiment: particle identification by RICH, TRD, MUCH, RPC detectors; track recognition in STS, TRD, MUCH, and global tracking for the complete system of detectors, including RICH. Investigations in the design optimization of various CBM components (RICH, TRD, MUCH, etc.). Development of a software complex for event visualization in CBM, participation in the activities on the development of the CBM framework software complex. Participation in the development and implementation of mathematical support of the projects NICA-MPD and CBM on search and study of mixed phase in high energy heavy ion collisions. Development of new wavelet algorithms for resonance parameter reconstruction in the invariant mass spectrum of nucleus-nucleus interactions and the search for hadron jets in high multiplicity events, including events with polarized protons (experiment STAR). Development of algorithms of search for neutrino-target vertex using information from the target tracker (experiment OPERA). Improvement of the hard muon event reconstruction code for the CMS experiment: search for new di-muon resonances and test of Standard Model predictions on the Drell-Yan processes in the TeV mass region. Analysis of diffractive photo-production of vector mesons and calculation of structure functions from data obtained in the Forward Proton Spectrometer of the H1 detector at the HERA collider.
  
  
• Numerical analysis of the evolution of time-periodic particle-like excitations in a model describing the signal transmission inside optical fibers by a nonlinear parametrically driven Schroedinger equation with dissipation. Study of the conditioning classes in the Bayesian adaptive quadrature. Development of effective methods, algorithms and codes using adaptive local polynomial approximation and smoothing. Further work on effective methods and algorithms of data processing based on coordinate-parametrical polynomial model and 4-point transforms. Study of the two-photon decays of the scalar mesons in a linear sigma-model at finite temperature. Numerical and analytical investigation of the bifurcation points in models of fast-rotating gravitating systems. 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. Dynamics derivation based on characteristic polynomials of n-th degree and applications. Development of variation-iterative schemes for the numerical solution of atom and molecule ionization models, and of ion channeling in crystals. Quantum-mechanical modeling of the propagation of the electromagnetic impulses in multi-component media; development of "reaction-drift-diffusion" type models for multi-component media. Study of the evolution of the fundamental and the excited states of the polaron, within the selflocalizing model of electrons in ionic crystals, in terms of the characteristics of the medium. Modeling the critical modes in double-layer heterogeneous Josephson junctions. Numerical study of the dynamics of the complex systems of nonlinear equations describing the ultra-cold atom behaviour in lattices generated from the double-well potentials. Development of a model and a code for computing track formation in the high-temperature superconductor Bi₂Sr₂CaCu₂O_x . Mathematical modeling of electromagnetic properties of metallic nanostructures entering as basic working elements in receivers and emitters of electromagnetic waves in SHF and UHF ranges; derivation of models describing the electromagnetic radiation of complex structures containing nanoparticles, such as coupled systems of nanoparticles and quantum dots, or microstrips containing discontinuous film; mathematical modeling of the propagation of the electromagnetic impulses in composite environments with nanoparticles (such as a layer nanoparticles-dielectric-semiconductor). Research of string Bianchi I and VI cosmological models in the presence of a magnetic fluid. Development of analytical and numerical methods of computing probabilities of pair creation of charged particles at predefined parameters of the external field. Development of analytical and numerical methods for the reconstruction of the potential in models of nano-dimensional quantum structures and waveguides under the consideration of the charge carrier effective mass dependence on the space variable.
  
  
• Development of algorithms for completion to involution of algebraic and polynomial-nonlinear differential systems with their implementation in Maple and C++. Parallelization of involutive algorithms for constructing polynomial Groebner bases for the purposes of their implementation on the multiprocessor complex available in LIT. Adaptation of the Common Lisp version of the computer algebra system Reduce to GNU Common Lisp for purposes of speed-up of computation with the system. Implementation of the kernel of system Axiom in CMUCL. Improvement of the algorithm for computing two-loop Feynman diagrams of propagator type with arbitrary masses and its implementation in Maple. Design implementation in Maple and Mathematica of algorithms for normalizing Hamiltonians of oscillator type and for constructing integrals of motion for dynamical systems. Simulation with a C ++ program of dynamics of carbonic and hydrocarbonic nanostructures on lattices with nontrivial symmetries. Development of methods and algorithms for solving boundary-value problems for high-order differential equations with a small parameter at higher derivatives by using symbolic computations in MAPLE.
  
  
• Implementation in the Mathematica program designed for simulation of quantum computation some special algorithms for computing unitary matrix determined by the input quantum circuit. Computation of restrictions on the group invariants for two-qubit mixed quantum systems (entanglement) that follow from the physical properties of the density matrix. Studies on physically well-founded candidates for quantum qubits and on the development of alternative models of quantum computing. Development of algorithms and software for quantum information transfer models. Development of analytical and numerical methods, of adaptive and parallel algorithms for solving nonlinear equations and systems of nonlinear evolution equations arising in the study of overcritical systems, of three-dimensional macromolecular structures, and in the computation of the interaction of protein molecules with liquids. Study of the functionally important genome elements from the distributions of their electrostatic potentials. Molecular cartography of DNA, RNA and proteins using a distributed computing environment. Numerical modeling of the nonlinear evolution of the biophysical systems. Development of new approaches to local network protection, control and modeling of the network traffic. Stable separation of various components of the time series of interest. New formulations and solutions of computing process optimization problems in Grid-systems under highly intensive user service requirements and various distribution time laws of application receipt.
  
  

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