Issue 1-2/2010

ABSTRACTS:

UDK 530.145
FOLDY-WOUTHUYSEN TRANSFORMATION WITH DIRAC MATRICES IN CHIRAL REPRESENTATION / V. P. Neznamov // Р. 3

The paper offers an expression of the general Foldy-Wouthuysen transformation in the chiral representation of Dirac matrices and in the presence of boson fields В^µ(х, t) interacting with fermion field ψ(х, t)

UDK 539.17
TYPICAL MAIN EIGENVALUES OF NEUTRON KINETIC EQUATION DEPENDENCES ON OPTIC DEPTH OF AN ARBITRARY HOMOGENEOUS SYSTEM / N. B. Babichev, P. V. Zabusov, I. V. Lutikov, V. P. Neznamov // P. 6

A set of homogeneous objects with an arbitrary configuration has been considered, in which neutron distribution function time evolution obeys exponential law e^λt, where λ is the main eigenvalue of particle transport equation. Dependence of λ on system optic depth р, which represents quantity of total neutron paths within an object’s typical size R has been investigated. In particular, it is shown, that in case of inert and active media, function λ(р) is characterized by single minimum point. In case of weak neutron absorbent, function λ(р) has two extreme points (minimum and maximum). And if the media is a good absorbent, given function is decreasing within the whole system optic depth variation range 0 < р < ∞.

UDK 539.1.01
THE EXPANSIONS OF THE KERR SOLUTION IN CARTESIAN HARMONIC COORDINATES / M. V. Gorbatenko, T. M. Gorbatenko // P. 12

The work presents the procedure of the finding of expansions (were representing in our article in 2004) for the metric components of outer part of the Kerr solution in Cartesian harmonic coordinates. The procedure involves two coordinate’s conversions (from Boyer-Lindquist coordinates to primary and secondary Kerr coordinates), the finding of harmonic coordinates by means of de Donder conditions solution and the transition from Kerr solution in secondary coordinates to Kerr solution in harmonic coordinates. Then the tedious calculations, concerned with two parameter expansions of the metric components, are performing. The expansions may be used in the tasks using the method Einstein-Infeld-Hoffman, in the tasks of the dynamics of the motion of the particle with half-integer spin in gravitational field etc.

UDK 530.145
ELECTRON SELF-ENERGY IN PSEUDO-HERMITIAN QUANTUM ELECTRODYNAMICS WITH A MAXIMAL MASS М / V. P. Neznamov // Р. 25

The electron self-energy (self-mass) is calculated on the basis of the model of quantum field theory with maximal mass М, developed by V.G.Kadyshevsky et al. within the pseudo-Hermitian quantum electrodynamics in the second order of the perturbation theory. In theory, there is the natural cut – off of large transmitted momentum in intermediate states because of presence of the universal mass M. As a result, the electron self–mass is finite and depends on the transmitted maximum momentum k_max=AMf(p), (M/m>>1, A<<M/m, f(p)<<M/m) Two interpretations of the obtained results are possible at defined М and A. The first interpretation allows confirming quantitatively the old concept of elementary particle mass sources defined by interaction of particles with self–gauge fields. The second interpretation results in the possibility not to renormalize the mass (at least in the second order of perturbation theory) owing to the zero mass operator Σ(p).

UDK 530.145; 514.764.2; 530.145.7
ON THE PROBLEM OF UNIQUENESS AND HERMITIAN PROPERTY OF HAMILTONIANS USED FOR THE DESCRIPTION OF SPIN 1/2 PARTICLE DYNAMICS IN GRAVITY FIELDS / M. V. Gorbatenko, V. P. Neznamov // P. 33

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 field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. 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.
The paper also shows that the dynamics of spin 1/2 particles in stationary gravitational fields can be described not only within the formalism of pseudo-Hermitian Hamiltonians, but also using an alternative approach, which uses the Parker scalar product.

UDK 519.6?533.9
TURBULENT FLOW THROUGH 5X5 ROD BUNDLE: COMPARISON OF RANS NUMERICAL PREDICTIONS WITH LDA EXPERIMENTAL DATA / Yu. B. Bazarov, Yu. D. Bogunenko, G. A. Bondarenko, E. D. Vishnevetsky, A. V. Kunin, A. I. Logvinov, E. E. Meshkov, M. S. Popov, I. N. Nikitin,  A. A. Ryabov,  Yu. K. Semenov,  V. A. Starodubtsev,  V. P. Statsenko, C. P. Tzanos,  M. B. Dzodzo // P. 48

Turbulent water flow in 5x5 square-pitch rod bundle was investigated by means of RANS simulations using k-ε turbulence models. The simulations were performed for full rod bundle model as well as for two subchannels in the central part of rod bundle. This paper presents an analysis of obtained numerical results. Moreover, these numerical results are compared with results of LDA measurements performed for the same 5x5 square-pitch rod bundle on Sarov hydraulic facility.

UDK 519.6, 531.51
NUMERICAL SIMULATION OF THE TURBULENT MIXING PROBLEM AT UNIFORM COMPRESSION / A. R. Guzhova, O. G. Sin’kova, V. P. Statsenko,  Yu. V. Yanilkin // Р. 60

Direct numerical simulation by 3D TREK code is used to investigate the development of turbulent mixing at uniform compression of gas volume. Computation results are compared to the corresponding solutions of this problem on the strength of k-ε model, which are obtained both analytically and numerically by 2D EGAK code. The analytical solutions are obtained for spherical, cylindrical and plane geometries.