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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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Issue N^{o} 2, 2011  APPLICATION OF THE VARIATIONAL PRINCIPLES OF MECHANICS TO CONSTRUCT TIMEDISCRETE DIFFERENCE GASDYNAMIC MODELS.8. IMPLICIT FINITEDIFFERENCE SCHEMES WITH PHASE VOLUME AND CANONICITY PRESERVED
Yu. A. Bondarenko VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
It has been proved for the finitedifference schemes of Lagrangian gas dynamics built with the variational method using the time and spacediscrete definition of the principle of least action (HamiltonOstrogradskii principle) that they preserve phase volume and canonicity (Hamiltonicity). The paper also proves that implicit finitedifference schemes with constant weight = 1/2 (in equations for coordinates and velocity) do not preserve phase volume and, far less, canonicity for an arbitrary, variable time step with any way of choosing the hidden generalized coordinates and hidden generalized momentum (such difference schemes could not be built with the stepwise variational method). Key words: Lagrangian gas dynamics, principle of least action, variational difference schemes, schemes with weights, variable time step, phase volume, canonicity, hidden variables.
 DIFFERENCE SCHEMES FOR MOLECULAR DYNAMICS. 1. COMPARATIVE ANALYSIS OF STABILITY, ACCURACY, AND EFFICIENCY V. N. Sofronov, K. S. Mokina, V. E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
Investigations of accuracy have been performed for the most extensively used difference schemes for MD simulations. The paper concludes that difference schemes with canonicity of phase flow demonstrate the best ratio between the accuracy and efficiency. The paper offers the RKN4 scheme, which is a threestage difference scheme of the fourth order of approximation. It allows reduction (by 3 to 4 orders) in the amplitude error and total energy disbalance in comparison with the Verlet scheme very often used for the molecular dynamics problems. Thus, it becomes possible to reduce the problem runtime while preserving the given computation accuracy. Key words: molecular dynamics, Hamiltonian systems, phase error, splitting method, preservation of the phase flow canonicity, MD difference schemes.
 QUASIDIFFUSION METHOD APPLICATION TO SOLVE 2D AXIALLYSYMMETRIC PROBLEMS OF RADIATION TRANSPORT IN SPECTRALKINETIC SCENARIO USING A SQUARE GRID N. G. Karlykhanov, A. V. Urakova, S. A. Shnitko VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The paper considers an implicit scheme used to solve the radiation transport equation in quasidiffusion approximation along with the energy equation in a 2D case using a square grid. For the transport equation we use a conservative monotone difference scheme of the first accuracy order. Since it is a wellknown fact that there are no linear, monotone, difference schemes of the second accuracy order for hyperbolic equation systems, we propose a hybrid difference scheme to solve the quasidiffusion type equations. It is a combination of schemes of the first and second orders of accuracy and provides the monotone behavior of solution. The method of singling out a diagonal element is used to solve quasidiffusion equations along with the energy equation. Key words: radiation transport equation, quasidiffusion equations, equation of energy.
 DS_{n}SCHEME FOR THE 2D KINETIC EQUATION OF RADIATION TRANSPORT IN SPHERICAL COORDINATES A. I. Bochkov, V. V. Suchkova, A. P. Trubitsyn VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The paper describes the numerical method used to solve the 2D timedependent kinetic equation of radiation transport in spherical coordinates. The finitedifference approximation to the equation has been built on nonorthogonal quadrangular spatial grids using a scheme with additional relations and is the conservative one. An algorithm has been developed on the base of the sweep scheme to solve the resultant system of grid equations. The scheme testing results are given for a 1D problem with a source. Key words: axial symmetry, 2D radiation transport equation, spherical coordinate system, solution scheme.
 ABOUT DIFFUSION PROPERTIES OF THE ROMB SCHEME FOR P_{1}EQUATIONS A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The paper analyzes the diffusion properties of the ROMB scheme for transport equations in P_{1}approximation. One of the requirements to a fine difference scheme for the transport equation in P_{1}approximation is to realize asymptotic diffusion limit. The standard Riemann scheme has no such asymptotic diffusion limit in problems of the diffusion nature, i. e. in problems accounting transport equations within asymptotic small absorption and small sources. It is shown that the ROMB scheme do have such asymptotic diffusion limit. Key words: ROMB scheme, asymptotic diffusion limit.
 MATHEMATICAL MODELING OF THE BIOCRYSTAL GROWING PROCESS USING THE FREE DIFFUSION METHOD V. P. Ginkin, O. M. Ginkina, S. M. Ganina VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The mathematical model of the biocrystal growing process using the free diffusion method is described. The model computation results are presented. They allow understanding the main mechanisms in nucleation and growth of biocrystals and outline the ways to improve the quality and size of crystals growing under the governing effect of temperature field. Key words: protein crystallization, precipitator, temperature, oversaturation, heatandmass transport, nucleation of crystals, growth of crystals, mathematical model, free diffusion method.
 THE PROCEDURE OF GLOBALLY RECONSTRUCTING A SPACE GRID AND REGRIDDING BY THE EXAMPLE OF 2D COMPUTATIONS WITH KORONA CODE V. I. Tarasov, A. G. Kozub, I. V. Syrova, N. V. Chukhmanov, A. K. Menshikova, E. A. Frolova, A. M. Ovchinnikov, A. Yu. Ovsyannikov VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The paper presents a general scheme for the global reconstruction of a space grid and regridding within a single procedure. The procedure stages are described and for each stage a userfriendly interface is demonstrated. The procedure applicability, its manifold possibilities of changing the topology of computational grids, and a sufficiently high quality of the regridding process have been demonstrated by the example of reconstructing a grid for multipledomain 2D computations using KORONA code. Key words: a single procedure, space grid, global reconstruction, InterVal2D code for regridding, KORONA code, multipledomain 2D computations.
 VIRTUALIZATION AS A PROCEDURE USED TO IMPROVE THE PERFORMANCE OF TECHNICAL MEANS OF ITINFRASTRUCTURE M. Yu. Osipov, I. L. Bondar', R. A. Semenov, T. Yu. Serova VANT. Ser.: Mat. Mod. Fiz. Proc. 2011. No 2. P. 317.
The server virtualization procedure used to deploy network services in local area networks is considered and the ideas of building a virtual ITinfrastructure are described. The paper formulates the advantages of the given approach to technical means of ITinfrastructure and presents the functional diagram of the ITinfrastructure on the base of the virtualization procedure developed and used at RFNCVNIIEF. Key words: virtualization, ITinfrastructure, server, local area network, network services, virtual computer, system resources, VMware.
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