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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2010  ACCOUNTING FOR TRANSPORT EFFECTS IN RADIATION TRANSPORT SIMULATIONS IN THE DIFFUSION APPROXIMATION
N. G. Karlykhanov, M. Yu. Kozmanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 39.
Two approaches for including transport effects in radiation transport simulations in the spectral diffusion approximation are considered. The range of applicability of the proposed approaches is studied. It is shown that the simulation results obtained using the proposed approaches  provided that some conditions are satisfied  are close to the simulation results obtained in the transport statement. Key words: radiation transport, spectral quasidiffusion, spectral diffusion, accounting for transport effects.
 MATHEMATICAL MODELING OF SHOCKWAVE VISCOUS HEATCONDUCTING GAS FLOWS BASED ON THE ASYMPTOTIC MODEL A. L. Adrianov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 1026.
We model the interaction of a pressure discontinuity with a shear layer in viscous and nonviscous problem statements. The pressure discontinuity is represented schematically by a curvilinear surface of a strong gas dynamic discontinuity, which satisfies generalized zero and firstorder asymptotic relations accounting for viscosity and heat conduction. A timeindependent analytical solution to the problem is obtained. One of particular solutions is compared with the corresponding numerical solution of complete NavierStokes equations. It is shown that explicit neglecting of this viscosityheat conduction factor in the differential model in perturbed flow simulations may lead to a wrong result. The influence of the boundary effect on the viscosityheat conduction factor is analyzed. Key words: curvilinear pressure discontinuity, viscous heatconducting perfect gas, shear layer, schematic representation of pressure discontinuity as a surface of strong gas dynamic discontinuity, generalized differential conditions (relationships) on curvilinear pressure discontinuity, NavierStokes equations, Reynolds number, asymptotic approach, boundary effect, additional differential constraint, vortexlb model, nonviscous solution, analytical solution.
 ON TEMPERATURE DEPENDENCE OF INTERATOMIC POTENTIAL FOR MOLECULAR DYNAMICS SIMULATION OF URANIUM DIOXIDE PROPERTIES Yu. S. Nagornov, R. Yu. MakhmudAkhunov, B. М. Kostishko, V. N. Golovanov, V. V. Svetukhin, А. V. Kats VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 2734.
The new approach to choose the interatomic interaction potential for simulation of thermal properties change of stoichiometric uranium dioxide using molecular dynamics method has been applied. According to Ehrenfest theorem and time averaged interaction potential, the potential parameters have been chosen as slowly varying temperature dependencies. The calculated values of constant grid, enthalpy and heat capacities for constant volume and pressure agree with test data within small limits for a wide range of temperatures from 250 tolb 3,150 K, which is confirmed by perspectiveness of the given approach. Key words: molecular dynamics, uranium dioxide, simulation, potential.
 AN INTEGRATED SIMULATION SUPPORT SYSTEM FOR THE LEGAK3D CODE P. A. Avdeev, M. V. Artamonov, S. M. Bakhrakh, S. V. Velichko, V. F. Spiridonov, M. M. Pristash VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 3543.
We discuss a service part of the LEGAK3D code, which serves for preprocessing, simulation support and postprocessing of simulation results. In addition to different kinds of visualization and editing of all problem components, the system enables highlevel operations with these components (design), such as transfer of components from one section to another with addition of new or replacement of existing components. Analysis of simulation results is provided both by means of context menu during data display, and by individual tools (including external applications). Key words: LEGAK3D code, simulation support, postprocessing, problem section.
 INTEGRAL PERFORMANCE INDICES FOR MULTIPROCESSORS Yu. G. Bartenev, G. G. Bliznyuk, Yu. V. Logvin, Yu. V. Shatokhina VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 4451.
Described here is the calculation technique of the main integral performance indices for multiprocessors in terms of hardware operation (operability, loss due to fault/fail, maintenance and downtime of equipment), as well as in terms of hardware efficiency (parallel problems load, mean size of counting problems, CPU downtime). Evaluation technique has been developed for CPU downtime due to fault/fail of different components of computation system and reliability figure analysis characterizing performance reliability of robust component subset of computational system. The common form for integral performance indices of computation systems has been suggested for the enterprises using different multiprocessor systems, which gives the possibility to compare the operation efficiency. Given here is the integral performance indices calculation for real computation systems using the described technique. Key words: multiprocessor performance, multiprocessor efficiency, multiprocessor computation indices.
 SOME DATA FORMATS FOR REPRESENTATION OF ARBITRARYTYPE 2D UNSTRUCTURED GRIDS A. A. Voropinov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 5263.
A number of data formats are considered for the representation of arbitrarytype 2D (surface) unstructured grids (composed of arbitrary polygons, with an arbitrary number of edges in nodes). The proposed data formats use the principle of distinguishing the grid's key element. We provide measured memory consumption and estimated speed of processing for the proposed data formats. The overhead for executing the algorithms to collect grid element neighborhood data was measured for the case of gas dynamics simulations using the TIM2D code. Key words: arbitrarytype unstructured grid, data format.
 A NEUTRON SOURCE FOR A HYBRID (FUSION + FISSION) SYSTEM E. A. Zabrodina, D. G. Koshkarev, M. D. Churazov VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 6470.
Steadystate burning of a deuterium streem in the Zpinch configuration is considered in the hydrodynamic approximation. Assessment of the possible use of produced neutrons in a hybrid (Fusion + Fission) energy system is provided. Key words: hybrid energy system, Zpinch, deuterium plasma streem, uranium blanket.
 ON REGULAR RECOVERY ALGORITHM FOR NONSMOOTH SOLUTIONS OF FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND Т. I. Serezhnikova VANT. Ser.: Mat. Mod. Fiz. Proc. 2010. No 4. P. 7178.
Analyzed here is the technique and numerical experiments for (onedimensional) Fredholm integral equations of the first kind at geophysical field extension and antenna synthesis. The regular algorithm is based on Tykhonov regularity using Lipschitz space norm function as a stabilizer, additional use of proxtechnique and subgradient processes for nonsmooth minimization problems. The short description of the used convergence theorems (with references) and subgradients applicability is given. Simulation results are described; estimated accuracy is given as well as recommendations for practical parameterization of computations and accuracy control. Numerical experiments confirm that the suggested technique can be used in mathematical simulation of various applied problems to reestablish Fredholm integral equation of the first kind. The given technique can be used to reestablish smooth (continuous) solutions, as well as kinked, discontinuous, maximumclose solutions. Key words: Fredholm integral equation, nonsmooth solution, Tykhonov regularity, proximal method, subgradient process.
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