Issue 3/2009

UDK 539.1.01
ON PHYSICAL MEANING OF THE WEYL VECTOR / M. V. Gorbatenko // P. 3

The paper describes a unique phenomenon – the possibility of establishing, in certain space regions, the one-to-one correspondence between equations related to absolutely different physical phenomena: (1) phenomena associated with the Weyl degrees of freedom in plane space; (2) phenomena, which can be described in terms of half-integer spin particles and observed quantities corresponding to a full set of bispinors.
The phenomenon established opens wide prospects for resolving in future the «old» disputable issue concerning the physical meaning of the Weyl vector. The paper discusses, in particular, the possibility of identifying the Weyl vector with the current density vector of bispinors constituting a bispinor matrix included in the Dirac equation. Some other issues are also discussed.

UDK 539.17
APPROXIMATE ANALYTIC SOLUTION OF EIGENVALUE PROBLEM FOR ONE-VELOCITY KINETIC NEUTRON TRANSPORT EQUATION IN CASE OF A HOMOGENEOUS SPHERE OF AN ARBITRARY MATERIAL WITH ANY OPTIC DEPTH / N. B. Babichev, P. V. Zabusov, I. V. Lutikov, V. P. Neznamov // P. 14

A homogeneous sphere, in which neutron transport distribution function variation with time obeys the exponential law e^λt, where λ is kinetic equation main eigenvalue, has been considered. Formula for λ has been obtained, which is characterized by high accuracy for any values of an arbitrary material sphere optic depth.

UDK 539.18
CALCULATION OF MATRIX ELEMENTS IN THE FOLDY-WOUTHUYSEN REPRESENTATION / V. P. Neznamov, A. A. Sadovoy, A. S. Ul’yanov // P. 18

The paper compares the methods used to calculate matrix elements of the operator of radail electron coordinates in an arbitrary order in the Foldy-Wouthuysen representation and with the use of the Dirac equation for ls-states of the hydrogen-like and helium-like ions of transuranic elements. The obtained analytical and numerical results for ls-states of the hydrogen-like and helium-like ions proves that the wave function reduction requirement is met with transformation to the Foldy-Wouthuysen representation and confirms that matrix elements can be calculated using only one component (either upper, or lower) of the Dirac bispinor wave function.

UDK 532.5.013.4
OPTIMIZATION OF COMPRESSION OF GAS IN INERTIAL CONFINEMENT FUSION TARGETS ON THE BASIS OF EXACT SOLUTION OF THE PROBLEM OF SELF-SIMILAR COMPRESSION WAVE / L. V. Ktitorov // P. 25

The problem of the centered wave isentropic compression of the ideal gas is considered. Initially the gas is supposed to be uniform and motionless. Lagrange variables are used; the problem is transformed to the form that allows us to get the self-similar solution of the problem in the unified manner both for the cases of cylindrical and spherical geometry. So we unify the previously got results. The characteristics of the gas motion are calculated including the velocity and acceleration of the outside surface of the gas.
The aim of this paper is to derive an optimal function of time and coordinates for the energy input and apply it to numerical modeling of compression of heavy-ion fusion targets. The function should provide compressing the gas up to densities ~100 g/cm³ with minimal energy consumption. This function was derived on the basis of the obtained solution of the self-similar problem.
A set of 1D numerical calculations was performed using the numerical code H3T. The process of compression of typical HIF target was calculated using the optimal function for the energy input. Real dimensions and common equations of state were used. It was proved that the necessary super high values of gas density could be reached with the total energy consumption only 500 KJ for each centimeter of the target length. So it was proved that the used method produced benefit of 5 – 10 times of value of total consumed energy as compared with the other methods of energy input.

UDK 532.5.013.4
EVOLUTION OF DISTURBANCES OF ADIABATIC COMPRESSION OF IDEAL GAS BY THIN SHELL / L. V. Ktitorov // P. 35

The system of equations describing evolution of small perturbations of the thin shell without inner structure is derived in the case when acceleration of the shell depends on time. Cases of plane, cylindrical, and spherical shell are considered.
These equations are solved and the increments of perturbation growth are calculated in case of the shell provides isentropic compression of the ideal gas.
It was proved that growth of amplitude of perturbation of the shell given in the form of plane waves is confined both in plane and cylindrical geometry. We calculated the limit of such perturbations growth. It was also proved that there was no limit for the growth of angular harmonic – type perturbations, both in cylindrical and spherical geometry. Increment of growth of perturbation amplitude was calculated in all cases.
A set of 2D numerical calculations was performed using the numerical code H3T. The process of adiabatic compression of typical heavy-ion fusion target was studied using computer modeling. The evolution of disturbances of the shell was studied as well. Real dimensions and common equations of state were used. It was proved that the growth of perturbation amplitude in numerical calculations were in reasonable agreement with the theoretical results.  

UDK 532.517.4+519.63
LASER INVESTIGATION OF TURBULENT MIXING IN THREE-LAYER GASEOUS SYSTEMS / N. V. Nevmerzhitsky, A. N. Razin, E. D. Senkovsky, V. I. Dudin, E. A. Sotskov, A. A. Nikulin, L. V. Tochilina, O. L. Krivonos // P. 44

Results are presented on turbulent mixing development at the interfaces in three-layer gaseous systems after passage of a steady shock with a Mach number M~1,3. Three series of experiments have been conducted. In the first series, the second interface was oriented at a 60°( angle with respect to the shock propagation direction, and the first interface was transverse to the shock tube. In the second series, the first interface had two bends (tilting step), and the second interface was oriented transversely to the shock tube. In the third series, the first interface was oriented at a 60( angle with respect to the shock propagation direction, and the second interface was oriented transversely to the shock tube. Various combinations of gases were used: air, SF₆, He.
The flow structure was recorded by a schlieren camera with laser backlighting. New experimental data have been obtained on turbulent mixing development in essentially two-dimensional flows. These data are very useful for understanding of the physics of this phenomenon, and for the verification of physical models and numerical techniques to model turbulent mixing.

UDK 519.6
ABOUT SCHEME VISCOSITY EFFECT IN LES SIMULATIONS OF TURBULENT FLOW IN PLANE CHANNEL / M. S. Popov, V. P. Statsenko // P. 55

Analysis is presented of scheme viscosity effect which arises in LES simulations of turbulent flow in plane channel. Calculations were carried out with STAR-CD code. The setup of calculations is analogous to that in known DNS simulations of such flow.

UDK 539.17
EIGENVALUES OF ONE-VELOCITY NEUTRON TRANSPORT EQUATION IN HOMOGENEOUS SYSTEMS / N. B. Babichev, B. V. Bezhentsev, P. S. Bondarev, P. V. Zabusov // P. 68

Exact formulae describing general eigenvalues dependence on physical values have been obtained. These formulae are correct in homogeneous simply connected systems bounded by non-concave surfaces with any isotope configuration.

UDK 539.17
THE DIRAC EQUATION IN THE GENERALIZED STANDARD MODEL WITH A FINITE MASS PARAMETER, M / V. P. Neznamov // P. 71

The papers [2] - [9] develop the M.A.Markov’s idea of a finite mass (M) of elementary particles and describe the construction of the relevant apparatus of local quantum theory with introduction of de Sitter’s five-dimensional space.  
The given paper considers, within this model, the Dirac equation properties for a fermion of mass m on the mass surface .
The paper shows that free Hamiltonian and Hamiltonian with interaction are pseudo-Hermitian.
If we accept the appropriate rules of manipulating pseudo-Hermitian Hamiltonians (see [15], [16], [17]), it is possible to construct the consistent quantum theory, which final results are coincident (at least, within perturbation theory) with the results obtained using the ordinary Dirac equation.