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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 4, 2011  ANALYSIS OF SOME SCHEMES FOR SOLVING RADIATION TRANSPORT EQUATIONS USING THE QUASIDIFFUSION METHOD
S. A. Grabovenskaya, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 315.
Four schemes for solving heat radiation transport problems using the quaildiffusion method are considered: the ROMB scheme  linear and homogeneous; the TVD scheme  nonlinear, as well as two new schemes  linear and nonhomogeneous. The conditions of stability, positivity and monotony are considered for these schemes. It is shown that in contrast to the earlier used RIMB and TVD schemes, new schemes are positive in the parabolic quasidiffusion approximation. Key words: heat radiation transport, quasidiffusion approximation.
 EFFICIENT BOUNDARY CONDITIONS ON THE SURFACES OF THIN CYLINDRICAL BODIES AND ON THE BOUNDARIES OF HOLLOW CYLINDRICAL CHANNELS V. A. Starkov, I. F. Polivanov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 1628.
Efficient boundary conditions for the surface of thin (d << h) cylindrical rod placed into a decelerating environment are formulated. The neutron beam flow rate in the decelerator is described by the transport equation in the P_{1}approximation; at that it is supposed that the azimuth dependence of the neutron flow rate located on the rod surface is present. Similar problem is solved for a cylindrical channel with account for the neutron flow rate dependence on the channel height and perimeter. Analytical expressions and tabular function values included into the boundary conditions are given in the paper. Key words: research reactors, transport equation P_{1}approximation, interactions matrix, Bessel function, neutron flow density, albedo.
 TESTS FOR THE PROGRAMS USING A HYBRID MODEL FOR PLASMA DYNAMICS NUMERICAL SIMULATION A. I. Golubev, N. P. Pyatakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 2938.
The analytical solutions for two model problems were found: the Cauchy problem for the Vlasov kinetic equation with special initial ion distribution at their motion in predetermined homogeneous magnetic field, and the problem for the system of equations of electron gas dynamics and Maxwell equations for the case of perfectly conducting plasma. The solution of the second problem is obtained using the method of trial functions. These solutions can be used for testing the application programs which realize the hybrid plasma model. Key words: Vlasov kinetic equation, Cauchy problem, method of characteristics, electron hydrodynamics equations, Maxwell equations, trial functions method.
 MOLECULAR DYNAMICS DIFFERENCE SCHEMES. 3. TEST SIMULATION RESULTS V. N. Sofronov, K. S. Mokina, V. E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 3949.
The simulation results for the test problem built on exact solutions for Newton, Morse and LennardJones potentials are discussed in this paper. The problem parameters were used for checking the stability, accuracy and conservatism of the Verlet difference scheme  the most widespread scheme in the molecular dynamics simulations, and of the RKN4 threephase scheme belonging to the class of schemes preserving the canonical character of the phase flow, chosen as an alternative of the former. The behaviors of the difference schemes and the numerical solutions were studied for the case of breach of the conditions of analytical solution stability. The RKN4 scheme has demonstrated high conservatism on asymptotically big times, and significant gain in the accuracy/efficiency ratio in comparison with Verlet. Key words: molecular dynamics, Newton potential, classical and modified Morse potential, LennardJones potential, molecular dynamics difference schemes.
 PROGRAM COMPLEX "MOLOKH" FOR MOLECULARDYNAMIC SIMULATION OF PROCESSES IN CONDENSED MATERIALS F. A. Sapozhnikov, G. V. Ionov, V. V. Dryomov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 5057.
During the previous decade RFNCVNIIEF has been developing the program "Molokh" for parallel calculations on supercomputers using the method of classical molecular dynamics with high parallelization coefficient. A set of test has been developed for the analysis of the efficiency of the developed algorithms. It can be used for the comparison of two different moleculardynamic complexes. Key words: molecular dynamics, list of neighbors, crystalline structure, parallelization efficiency.
 NONEQUILIBRIUM MODEL FOR THE CALCULATION OF THE TWOCOMPONENT LIQUID CRYSTALLIZATION V. P. Ginkin, S. M. Ganina, K. G. Chernov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 5865.
A nonequilibrium model of the twocomponent liquid crystallization is proposed; here the Stefan problem with two boundaries is solved: solid phase  a twophase transition zone and twophase zone  liquid phase. The twophase zone is represented by a porous environment with varying porosity. Additional force of resistance to the liquid flow in porous environment is taken into account similarly to the Darsy law. The solutions with linear and quadratic dependences of the inclusion volume fraction on temperature are compared with each other. The calculation results are presented for the crystallization experiment with Sn with 20% of Pb using the method of oriented vertical crystallization, performed from top to bottom towards the gravitation vector. Key words: twocomponent liquids, crystallization, mathematical model, flow in porous environments, Stefan problem, numerical calculation method, experiment calculation.
 SOFTWAREHARDWARE COMPLEXES BASED ON THE COMPUTER SYSTEMS WITH ARITHMETIC ACCELERATORS FOR SIMULATIONS USING THE MONTECARLO CODE AND MOLECULAR DYNAMICS METHOD. B. L. Voronin, S. A. Grushin, A. K. Zhitnik, A. N. Zalyalov, S. V. Kopkin, I. A. Kryuchkov, A. G. Mal'kin, S. P. Ognev, V. I. Roslov, A. S. Rybkin, S. A. Stepanenko, R. M. Shagaliev, V. V. Yuzhakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 6671.
The study results of the possibility of the creation of softwarehardware complexes based on the computer systems which integrate the processors with the architecture x86 and arithmetic accelerators intended for simulation using the MonteCarlo code and the molecular dynamics method when solving special problems for the purposes of atomic power engineering are presented. Key words: hybrid computer systems, arithmetic accelerators, MonteCarlo code, molecular dynamics method.
 AN STK SOFTWARE FOR THE STUDY OF THE EXECUTION EFFICIENCY FOR PARALLEL APPLICATIONS D. A. Novaev, Yu. G. Bartenev, D. I. Lipov, S. I. Kolpakov, A. B. Kiselev, T. N. Serova, L. V. Hudyakova VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 7281.
The description of the composition and the ability of the software intended for the acquisition and representation of data on the efficiency of multiprocessor computer resources employment by tasks performed in the parallelization mode is presented in the paper. Key words: multiprocessor computer, execution efficiency for parallel tasks, interprocessor exchange interface (MPI), inputoutput, tools for parallel application profiling.
 MATHEMATICAL CLASSIFICATION MODELS FOR MULTICHANNEL SIGNALS OF THE ELECTRIC FIELD OF A HEART I. P. Polyakova, T. B. Feofanova, N. V. Luk'yanova VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 4. P. 8288.
Neuronet models for decreasing the size of the data array obtained at multichannel registration of electrocardiogram are discussed. The model based on the selforganization algorithm is used for the detection of meaningful features in the input data array. The proposed models were tested on the determination of the anomalous impulse paths in patients' hearts suffering of the preexcitation syndrome. Key words: neuronets, generalized Hebb algorithm, selforganization maps, multichannel electrocardiogram signals.
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