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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2012  A POLINOMIAL APPROXIMATION METHOD FOR THE STEP OPERATOR OF THE HEAT CONDUCTIVITY EQUATION
O. M. Kozyrev, V. P. Litvinov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 312.
Given here is for solving the boundaryvalue problems of the heat conductivity equation. The method is based on constructing a difference step operator in the form of an operator polynomial. The operator polynomial is constructed in the space of Fourier images using Chebyshev and Lanczos polynomials. The solution algorithm represents explicit stepwise calculations and is implemented in the form of {it predictorcorrector} scheme. The method is easy to implement and can be efficiently parallelized. The method is described by the example of Cauchy problem for the linear heat conductivity equation. Results of numerical solutions for some wellknown test problems are presented. Key words: heat conductivity equation, Fourier image, Chebyshev and Lanczos polynomial.
 A PENOMENOLOGICAL MODEL OF THE DAMAGE EVOLUTION KINETICS IN SOLIDS UNDER PULSE IMPACTS S. S. Sokolov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 1326.
A phenomenological model of kinetics describing the origination and evolution of damages in solid materials under the effect of pulse loadings and compaction of fractured materials under the effect of compression forces is presented. A continualkinetic approach was used to construct the model, in which fracturing is simulated as the process of accumulating damages under the effect of tensile stresses and shear strains. Results of the numerical simulation of fracture in wedgelike uranium samples and a flat aluminum sample are given along with comparison between the calculated results and experimental data. Key words: phenomenological model, origination and evolution of damages, fracture due to shear strains and tensile stresses, compacting, validation simulations.
 NUMERICAL STUDY OF ENERGETIC PARAMETERS OF A SUPERSONIC CHEMICAL OXYGENIODINE LASER WITH FLOW MIXING VARIATIONS Yu. N. Deryugin, B. A. Vyskubenko, D. K. Zelenskiy, S. P. Il`in, Yu. V. Kolobyanin, E. A. Kudryashov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 2738.
The paper presents a mathematical model and a 3D computational technique for studying the structure of nonequilibrium flows and determining the energy characteristics of a chemical oxygeniodine laser. The mathematical model includes the main kinetic processes in an active medium of the laser and the processes of generating laser radiation both in stable and unstable resonators. A 3D computational technique is based on solving both complete and parabolic NavierStokes equations and allows describing nonequilibrium fluxes of subsonic and supersonic flows (including those in the resonator area), and supersonic flow mixing, as well as determining the energy parameters of the laser. The energy parameters of a supersonic oxygeniodine laser with mixing devices of various types have been studied numerically. For each type of mixing device, there have been identified optimum conditions with respect to geometry and composition of the injected gas under which maximum values of the laser energy parameters can be implemented. It is demonstrated that all the studied configurations of mixing devices are acceptable and allow achieving high enough energy parameters of the laser. Maximum values of parameters  radiation power ≈ 99 kW, specific energy rejection 300 J/g, chemical efficiency 35%  have been achieved for a nozzle unit with a threerow tube injector and this result is in a good agreement with the achieved results of experiments. Key words: chemical oxygeniodine laser, mathematical model, computational technique, radiation generation parameters, chemical efficiency.
 ESTIMATION OF THE EFFICIENCY OF CODES FOR STIFF DIFFERENTIAL EQUATION SYSTEMS IN PROBLEMS OF COMBUSTION PHYSICS V. K. Ryabinin VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 3947.
The efficiency of three codes, which are the integrators of ordinary differential equation systems of a high degree of mathematical stiffness, has been studied. Such equations occur during the description of kinetics of branched chain reactions typical for the combustion processes and explosive transformations. The integrators have been tested by the example of three model problems, which are specific to the gaseous combustion physics. Key words: mathematical simulation, combustion, chemical kinetics, stiff differential equations, software testing.
 SYSTEMS FOR COMPUTER SIMULATION OF HIGHENERGY NUCLEAR REACTIONS AND PREPARATION OF ACTIVATION NUCLEAR DATA A. A. Andrianov, Yu. A. Korovin, I. S. Kuptsov, A. A. Natalenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 4859.
The paper describes integrated software systems IViS SMPI and InIS HAND developed by the authors to improve the effectiveness of fundamental and application studies in the field of constant supply for the simulation of advanced nuclear power reactors. The algorithm of acquiring nucleophysical data using the developed software, which is based on the advanced methods of the multiplecriteria decisionmaking theory, is described. Key words: models of highenergy nuclear reactions, software systems, interactive media, methods of multiplecriteria decisionmaking theory, factorial analysis, estimated nucleophysical data.
 NUMERICAL SIMULATION OF UNSTEADYSTATE HEATANDMASS TRANSPORT PROCESSES IN A GASWATEROIL MIXTURE MOOVING THROUGH THE CENTRIFUGAL ELECTRICAL PUMP PASSAGE V. M. Konyukhov, I. V. Konyukhov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 6069.
A mathematical model of transient thermohydrodynamic processes taking place in a multiplestage immersion centrifugal electrical pump during the replacement of water by a threephase mixture in the stage of putting a production oil well into operation has been constructed. A numerical model and a corresponding software complex have been developed. The specific features of water replacement by a wateroilgas mixture in the pump passages and variations in the performance characteristics of the pump stages have been studied on the base of computational experiments. Key words: mathematical support, software complex, numerical simulation, multiphase fluxes, oil stratum, producing well, centrifugal electrical pump, data bank.
 THE EFFECT OF MICROVOLUME PARAMETERS OF VLSI CIRCUIT COMPONENTS ON THE ENERGY OUTPUT DUE TO THE IMPACT OF PROTONS A. V. Afonin, L. A. Grishantseva, V. A. Polunin, A. I. Chumakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2012. No 4. P. 7073.
Reduction of active dimensions of components in integrated circuits leads to a higher sensitivity to local radiation effects caused by nuclear particles. The paper describes efforts on the numerical simulation by GEANT4 code of the energy output processes under the effect of 15 ÷ 1 000 MeV protons in VLSI circuit components with a variety of their shapes and scales in the standard environment. The results obtained for sensitive areas of micron scales demonstrate that the energy output maximum in a microvolume weakly depends on the charge accumulation conditions; account for particles generated outside the sensitive volume provides an almost 3 times increase of the probability of energy output; a maximum value of energy output actually remains unchanged with proton energies above 50 MeV. Key words: proton radiation, integrated circuit, energy output, charge collection effect, GEANT4 numerical code.
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