Vol. 17/2012

SECTION 1

Solution of the Problem of Uniqueness and Hermiticit of Hamiltonians for Dirac Particles in Gravitational Fields

M. V. Gorbatenko, V. P. Neznamov

The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians.

The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin 1/2 particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are non-unique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian.

The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors.

For description of the dynamics of spin 1/2 particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians, but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.

The Vortex Model of the Effect, the Dynamic Shift Imposes on Inert and Power Materials

V. G. Morozov, I. I. Karpenko, S. A. Saveliev, V. B. Titova

The integrated approach used to simulate elastoplastic flows of inert materials and explosion of solid HE under shear dynamic loads was identified. The model is a focal one, based on the leading role of vortex flow. Melting and ignition occurred near the hot spot area, where the shear velocity jumps up. The mechanism of jump formation based on the direct interaction of vortices with the wall, with no thermodynamic equilibrium established (which means melting without thermal conductivity and burning contrary to Arrhenius mode). Energy transfer inside the focus was according to the vortex mechanism. Macroscopic kinetic equations of transfer into plasticity and HE burning were derived.

SECTION 2

Automated Software System to Control Multi-Cluster Computational Complex

A. B. Kiselev, Yu. G. Bartenev, A. M. Vargin, S. N. Kiselev, S. I. Kolpakov, V. K. Fyodorov

The software system, designed to control batched tasks processing at multi-cluster computational complex is presented. The architecture and designation of the system are disclosed and the associated sub-systems and components are reported.

USE OF GRAPHICAL ARITHMETIC ACCELERATORS as Applied to Solution of TRANSPORT EQUATION AND MOLECULAR DYNAMICS PROBLEMS

B. L. Voronin, A. M. Erofeev, A. N. Zalyalov, S. A. Grushin, A.K. Zhitnik, 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

Feasibility of computational systems with hybrid architecture, containing arithmetic accelerators based on graphical processors, used to solve transport equations by Monte-Carlo method and molecular dynamics problems is studied. 

Analysis of the initial algorithms is presented and aspects of implementation of codes for hybrid systems are described. Test results are discussed.

A NUMERICAL MODEL, Describing Fragmentation  OF THIN METAL SHELLs

V. Yu. Meltsas, G. F. Portnyagina

The paper presents the model, describing fracture of thin metal spherical shells subject to intensive loading, resulting in formation of two fractions of fragments, for which mass-spectrum calculation had been done. Further motion of fragments follows the model of heterogeneous medium, consisting of gas and solid particles. Examples of calculations simulating spatial separation of fragments, depending on their size, are presented.

SNDMA TECHNIQUE FOR FLOWS OF EMITTING NONEQUILIBRIUM MOLECULAR PLASMA

V. D. Atamanenko, G. V. Dolgoleva, V. A. Zhmailo, I. V. Popov

The paper describes SNDMA technique for the calculation of flows of emitting nonequilibrium molecular plasma along with the calculation of kinetics of chemical, photochemical, plasmochemical, photo- and radiation-plasmochemical reactions in air plasma.

The description of a physical model and a numerical technique are given, the numerical simulation results are compared with the analytical solutions to test problems.

SOLVING THE HEAT TRANSFER EQUATION ON UNSTRUCTURED DIRICHLET GRIDS USING THE COST-EFFECTIVE SCHEME

I. D. Sofronov, A. I. Panov, A. V. Samodolov

The paper describes a cost-effective difference scheme used to solve the multidimensional heat transfer equation on unstructured Dirichlet grids. The scheme was proposed and substantiated by I. D. Sofronov. A distinctive feature of the scheme is that it is applicable on strongly non-uniform grids of cells with a variable number of nodes. The scheme can be used for numerically solving both the linear and quasi-linear heat conductivity problems

in 2D and 3D cases.

ARTIFICIAL VISCOSITY MATRIX FOR 2-D LAGRANGIAN GAS-DYNAMICS, Enabling THE Reduced “ENTROPY TRACE" in Numerical Computations

A. M. Stenin, E. A. Solovieva

The artificial diffusion of mass, pulse and total energy are introduced in a conservative manner into the system of equations of gas dynamics, describing 2-D flows in Eulerian coordinates. The formulations, stating the velocity of artificial diffusion of mass in equation of continuity and the formulations for artificial viscosities in equations of motion and energy were derived after changing the current coordinates for the Lagrangian ones. Artificial viscosity in equations of motion is represented by a tensor, proportional to strain rate tensor deviator. The results of test calculations demonstrate high effectiveness of the new system of viscosities, which is proved by the reduced «entropy trace» in numerical solution of the equations within Lagrangian gas dynamics.

PREPARATION OF INITIAL DATA FOR 2D PROBLEMS USING SolidEditor and 2D-RND CODES

P. V. Cherenkov, O. N. Borisenko, M. V. Cherenkova, V. I. Tarasov, K. K. Olesnitskaya, T. Yu. Bakanova, M. G. Kuznetsov, D. A. Shutov, A. S. Sergeeva

The paper describes the initial data preparation procedure in SolidEditor and 2D-RND codes developed at RFNC-VNIIEF for 2D computational physics problems. This is a unified procedure, to a maximum possible extent, for all codes used at the RFNC-VNIIEFs Department of Mathematics and it allows arranging effective data exchange between program codes. SolidEditor provides well-developed capabilities of setting, analyzing and editing the physical and mathematical problem statements. These capabilities significantly facilitate the initial data preparation process for the problems to be solved in series. 2D-RND code is used to calculate the required initial data (grid and grid value distribution calculations).

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