Annual Report 2002
In 2002, computer simulation methods and software for data processing were developed on the basis of new methods of information filtering, compression and visualization, and image recognition .
An effective algorithm for selection of useful events based on a multilayer feed-forward neural network was proposed and applied to simulated and real data analysis for the DUBTO experiment .
Algorithms and software have been developed for the analysis of angular distributions of secondary particles with the help of wavelet transformations (WASP), for data filtering with the use of a lifting scheme (WALF), for experimental data fitting (FITTER) .
One of the results obtained in 2002 is related to creation of a distributed CHARM system for data processing and data storage in the field of particle physics. The hard- and software complex, based on the local Linux-cluster RISK-2002, the LPP computer farm, and the robotized central mass memory, is used for proccessing of simulated information and experimental data obtained from the EXCHARM set-up .
A mathematical procedure was developed to calculate the probability of generating a compound nucleus at nuclei interaction in reactions with heavy ions within the model of the double nuclear system, created at FLNR and developed at BLTP .
Analytical and numerical methods have been developed to model the electromagnetic activity of a paramagnetic neutron star. The periods of nonradial torsional pulsations have been studied analytically and numerically . The model is currently used in interpreting observational data on pulsars and magnetars.
In the framework of the development and application of algorithms and software for numerical research in the heavy ion relativistic collisions, a combination of the quantum molecular dynamics model and the evaporation model of de-exciting nuclei describes well the spectra of secondary protons and neutrons up to the energies of striking particles ~ 300 MeV . Investigation on colour transparency, exotic nuclei properties, fragmentation and multifragmentation processes in hadron and nucleus-nucleus collisions was performed .
A high-accuracy approximation method for linear evolutionary operators in Hilbert space has been created and theoretically proved. The method is based on discretization of the time variable of the original equation with the help of Magnus expansion for evolution operator and subsequent approximation of this expansion by rational functions of stability .
New variation-iteration algorithms were constructed and implemented in the FORTRAN language for solving with a predetermined accuracy the bound state problems and three quantum particle scattering problems with point or Coulomb pair interactions in the adiabatic representation. A numerical analysis and testing of the designed algorithms on the models of three quantum particles with point interactions and for the study of the transfer ionization reactions at supersmall scattering angles have been performed .
An analysis of relativistic field-theoretical equations was presented for photon-proton scattering reactions . The numerical solutions of these equations were compared to new experimental data for reactions with final states. A generalization for the inverse scattering problem is considered.
The interlacing operator technique is applied to discrete equations. It allows one to generate new families of precisely solved Jacobi matrices. It shows that the obtained thus Jacobi matrices lead to new precisely solved nonlocal potentials of the Schrodinger equation . Discrete algebraic Darboux transformations and a factorization procedure have been obtained for a system of coupled Schrodinger equations, permitting generation of series of potential matrices with predetermined spectral characteristics for which the system of discrete Schrodinger equations has precise solutions .
A program  has been worked out for a numerical solution of the system of partial differential equations, describing the energy relaxation in the vicinity of an ion trajectory moving in a substance and in the field of a pulsed energy release stipulated by slowing down the ion beams in the substance. A mathematical model of radiation damages appearing in a number of radiation-stable insulators has been constructed.
A new method  for computing the coil potential in modelling the 3D nonlinear magnetic fields, which does not result in accumulation of the errors, was suggested. The method has been developed on the basis of field measurements of data for the EXCHARM experiment.
Some topics on applicability of the involutive bases technique to optimization problems of integer programming were considered. Restrictions have been revealed with the help of computer experiments, and some ways of modifying the involutive approach directed at overcoming these restrictions have been planned .
The designed original algorithms and software were applied to investigate the mechanical model for SU(2) gauge theory. It was found out that, in contrast to the instant form of this mechanical model, its light-cone version possesses not only the first-class constraints but also the second-class ones .
A new much more effective algorithm of calculating cohomologies has been proposed which is based on splitting large cochain complexes into minimally possible subcomplexes .
Some procedures of semiclassical quantization of normal forms based on the algebraic perturbation theory implemented in Reduce and included in the QUANTGIT computer program. This program is a core of the software complex oriented to simulation of dynamic and atomic systems in external fields .
The electronuclear systems consisting of two "cascade" subcritical assemblies, a liquid metal reactor on fast neutrons used as a booster, and a thermal reactor, where main heat production takes place, were simulated by the Monte-Carlo method. Reactors of VVER-1000, MSBR-1000, and CANDU-6 types are considered. The research results show that the two-reactor systems with an enriched uranium booster and a liquid cadmium valve are the most effective ones from the viewpoint of high output characteristics and safe functioning .
An urgent problem of nuclear waste transmutation and discussion of various approaches and methods of transmutation of the isotopes, which, in view of their high radioactivity and migrations in the biosphere, require obligatory transmutation, were considered in review .
The modern state of research in the area of computer simulation of physical and biological systems by molecular dynamics methods (MD) is given in review . Special features of computer simulation of molecular and atomic systems based on parallel and vector calculations were analyzed. On the basis of application of methods of the MD simulation, calculations have been done allowing a dynamics analysis of condensed systems (clusters, liquids, etc.) and nuclei phenomena at a molecular level.
© Laboratory of Information Technologies, JINR, Dubna, 2003