Issue 3/2008

UDK 539.1.01; 514.83
DIRAC PARTICLE IN A GRAVITATIONAL FIELD / M. V. Gorbatenko, T. M. Gorbatenko // P. 3

It is considered a motion of Dirac particle in a gravitational field described by Kerr solution. It is proved that an evolution of the particle wave function is determined by the Hermitian Hamiltonian if an accompanied frame is used.

UDK 533.9 … 16
CALCULATION OF PLASMA TRANSPORT COEFFICIENTS USING SELF CONSISTENT HARTREE-FOCK-CLATER POTENTIALS / M. Vronsky, E. Karpovtsev, E. Popov // P. 11

Given here are the formulas for heat and electric conductivity coefficient calculation using Chapman-Enskog method for nonideal plasma with self-consistent Hartree-Fock-Slater potential calculated with THERMOS code. The approximate Boltzmann equation solution is defined for the density of plasma electronic component in which transport cross-section defined by self-consistent Hartree-Fock-Slater potential is taken for the second part corresponding to the electron collision. Given here are the results of coefficient calculations and their comparison with calculation results derived by other methods

UDK 532.517.4
TURBULENT SUBGRID MODEL FOR TURBULENT MIXING COMPUTATIONS / V. G. Morozov, B. M. Zhogov, S. A. Saveliev, V. B. Titova // P. 21

Mixing of heavy jets penetrating a light medium is considered. Primary jets are computed by direct numerical simulations. 2D jet mixing equations are derived on the assumption that the mixing is produced due to lateral vortices. Its approximate solution gives the eddy drift velocity. Assuming that matter is dragged by eddies we obtain the following expression for the concentration transport velocity. Using this expression, we set up equations for the mass flux, mixing, energy flux and the momentum flux tensor produced by turbulence. These quantities are substituted into the gas dynamics equation for numerical computations. At that, mixing of two substances in one cell is computed in a simplified manner accounting for the exchange with neighbor cells. The model is implemented in the Meduza-P 2D gas dynamics code. Test computations of a flow around a "heavy" corner have shown quite a good agreement with experimental data.

UDK 519.642.2:532.529:541.182.213
MODELING PARTICLE FORMATION KINETICS IN FOR TWO-PHASE DISPERSE SYSTEMS. COMPUTATION OF THE PRECIPITATION FORMATION PROCESSES IN THE CONDITIONS OF THE MONTANA EXPERIMENT / A. M. Petrov // P. 27

Theoretical and computational models for droplet and ice particle formation kinetics in mixed clouds were developed earlier in [1–3]. Alongside kinetic equations, these models involve equations of mass and thermal balance, accounts for the difference in rates of vapor condensation above water and ice, uses actual condensation and coagulation growth rates, describes the phase transition dynamics.
The developed numerical model is used here for computation of the precipitation formation processes in the conditions of the Montana experiment of 07/19/1981 [4–5].

UDK 539.17
NON-STATIONARY MILNE’S PROBLEM WITH A CONSTANT VOLUMETRIC SOURCE OF NEUTRONS IN A SEMI-INFINITE INERT MEDIUM / N. B. Babichev, I. V. Lutikov,
A. A. Sevastyanov // P. 35

A version of the Milne’s Problem has been solved that had not been considered before, i.e. the formulation with equilibrium neutron density linearly growing with time.

UDK 539.17
AN APPROXIMATE METHOD TO DETERMINE NEITRON SPECTRUM AND OTHER CHARACTERISTICS IN OPTICALLY THICK HYDROGEN-CONTAINING SYSTEMS /
N. B. Babichev, V. G. Morozov,A. A. Sevastyanov // P. 39

Approximate solutions of the kinetic equation are found for homogeneous optically thick hydrogen-containing systems with admixtures of fissile materials and neutron absorbers. The theoretical results are in satisfactory agreement with experiments and can be useful for validation of mathematical techniques for solving neutron transport spectral equation in systems where thermal motion of hydrogen nuclei must be considered.

UDK 539.17
NEW ANALYTICAL FORMULAE FOR CALCULATING NEUTRON DIFFUSION CONSTANT / N. B. Babichev, B. V. Bezhencev, P. S. Bondarev // P. 44

Approximate analytical solutions have been found for transcendental equations that are solved within the asymptotic diffusion theory jointly with the neutron diffusion equation. These analytical solutions are very accurate, so solving the transcendent equations numerically is not required. As a result, neutron diffusion constant has been explicitly correlated as a function of various parameters through analytical formulae that need no further refinement within the asymptotic theory.

UDK 539.171
THE BACKWARD COMPTON SCATTERED X-RAY RADIATION IN THE LAYERED MEDIUMS / A. Yu. Stavtsev, Y. V. Shtotsky // P. 49

There were explored the contributions in the field of the transmitted and mirrored gamma-quantum with the energy of 100–400 keV, endured single and multiple scatter. The simulations were held by Monte-Carlo method, using the Knuth’s random-number generator. There were examined cases of square unlimited (x, y) and limited (30x30 mm) uminum patterns of the thickness t. The dependences of the reflectance, reflected energy flux and typical active spot size were obtained for semi-infinite medium of aluminum, iron, tin and lead. There were also researched the influence of the heterogeneous composition structure on the reflected energy flux and the active spot size.