Interaction of inner and outer layers in plane and radial wall jets

Large eddy simulations of turbulent radial and plane wall jets were performed at different Reynolds numbers using the Lagrangian dynamic eddy viscosity subgrid-scale model. The results were validated with experimental data available in the literature. Compared to the plane ones, the radial wall jets have an extra direction for expansion, which causes faster decay rates. Thus, the resulting pressure gradient distributions are different. However, the comparison of the results with the turbulent boundary layers under adverse and favourable pressure gradients reveals that these pressure gradients are not strong enough to cause any fundamental physical difference between plane and radial wall jets. In both cases, the local Reynolds number is an important determining factor in characterisation of the flow. The joint probability density function analysis shows that the local Reynolds number determines the level of intrusion of the outer layer into the inner layer: the lower the local Reynolds number, the stronger is the interaction of the inner and outer layers. These results can be used to clarify the scatter of the reported log-law constants in the literature.     

Dynamics of supersonic plane plasma jets

Using a fast photorecorder (FPR), the process of flight and reflection from a wall of a plane pulsed plasma jet in a closed gas-filled cylindrical volume is investigated. It is shown that, in an electrical-discharge source, a plane jet is formed from a set of individual flames. The gasdynamic structure of an individual flame is investigated. From the change in jet velocity at the pressure discontinuity, the plasma temperature in the discharge channel and in the jet is estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 44–47, May, 1982.It remains to thank V. V. Pozdeev for providing the FPR, S. S. Smolyakov for useful discussions, and N. V. Nosov for participation in individual experiments.     

Identification of dynamic patterns and their velocities in thermal plasma jets

The paper presents a new method for identification of dynamic structures in a plasma jet using CCD camera records of its radiation and shows also possible application of the method for evaluations of plasma velocity. The evaluation of CCD images is based on the subtraction and correlation analysis of succeeding pictures in the recorded sequence. The results show that plasma jets include various types of structures moving downstream. The quantity, evolution and velocity of the detected patterns depend on the input gas flow rate. The measurements included also parallel records of local plasma jet radiation detected by photodiode arrays. The evaluation of the photodiode records in the form of long time series was founded upon the fast Fourier transform, especially on the analysis of phase angle shifts between signals coming from photodiode pairs situated along the plasma flow. These phase shifts yielded plasma flow velocity that was compared with the velocities of structures identified by the analysis of CCD camera images.     

Interaction of two spin subsystems with different wavevectors

The possibility of the transition of a spin system from an incommensurable to a commensurable phase via a phase with different wavevectors of individual subsystems is shown in the mean-field approximation.     

Interaction of plane electromagnetic-gravitational waves

The solution in the general theory of relativity of the problem of the interaction of plane electromagnetic-gravitational waves is derived in this paper by means of an electromagnetic generalization of the problem of the collision of plane gravitational pulses. It is shown that the interaction of waves leads to a physical singularity on a spacelike hypersurface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 65–70, October, 1978.In conclusion, the author thanks Professor D. D. Ivanenko for his comments.     

Round and plane jets in a transverse acoustic field

Results of experimental studies on round and plane, macro- and microjets subjected to transverse acoustic field at low Reynolds numbers are presented. A new phenomenon associated with transformation of the round microjet to the plane one under acoustic forcing is revealed. Also, bifurcation of the round microjet is observed. It is shown that both plane macro- and microjets are prone to a sinusoidal instability. As is found, the plane microjet becomes twisted at its periphery in the direction of the oscillatory flow velocity induced by acoustic waves. Acoustic influence both upon the pseudo-plane and the planemicrojets results in their sinusoidal oscillations and bifurcation. New phenomena observed in the present experiments on the round and plane microjets are caused by a proportionality of the acoustic energy with that of the microjets.     

Turbulent plane wall jets over smooth and rough surfaces

Large-eddy simulations were carried out to study the effects of surface roughness on a plane wall-jet using the Lagrangian dynamic eddy-viscosity subgrid-scale model, at Re = 7500 (based on the jet bulk velocity and height). Results over both smooth and rough surfaces were validated by experimental data at the same Reynolds number. As the jet is injected into the still environment, large-scale rollers are generated in the shear layer between the high-momentum fluid of the jet and the surrounding and are convected downstream with the flow. To understand the extent to which the outer-layer structures modify the flow in the inner layer and the extent to which the effect of roughness spreads away from the wall, both instantaneous and mean flow fields were investigated. The results revealed that, for the Reynolds number and roughness height considered in this study, the effect of roughness is mostly confined to the near-wall region of the wall jet. There is no structural difference between the outer layer of the wall jet over the smooth and rough surfaces. Roughness does not affect the size of the outer-layer structures or the scaling of the profiles of Reynolds stresses in the outer layer. However, in the inner layer, roughness redistributes stresses from streamwise to wall-normal and spanwise directions toward isotropy. Contours of joint probability-density function of the streamwise and wall-normal velocity fluctuations at the bottom of the logarithmic region match those of the turbulent boundary layer at the same height; while the traces of the outer-layer structure were detected at the top of the logarithmic region, indicating that they do not affect the flow very close to the wall, but still modify a major portion of the inner layer. This modification must be taken into consideration when the inner layer of a wall jet is compared with the conventional turbulent boundary layer.     

Interaction of two light beams with different polarizations in TGS

By ellipsometric measurements we have observed the polarization variations of the primary light beam, with wavelength λ₁=5145 ?, interacting with the secondary light beam of controlled variable polarization, transmitted through a TGS crystal layer. We present a theoretical explanation based on the second-order optical nonlinearity of TGS. Received: 4 December 2001 / Revised version: 28 May 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +48-22/660-5447, E-mail: petyk@if.pw.edu.pl     

Some novel plane trajectories for carbon atoms and fullerenes captured by two fixed parallel carbon nanotubes

The movement of atoms and molecules at the nanoscale constitutes a fundamental problem in physics, especially following the motion of atoms in many-body systems condensing together to form molecular structures. A number of simplified nanoscale dynamical problems have been analyzed and here we investigate the classical orbiting problem around two centers of attraction at the nanoscale. An example of such a system would be a carbon atom or a fullerene orbiting in a plane which is perpendicular to two fixed parallel carbon nanotubes. We model the van der Waals forces between the molecules by the Lennard-Jones potential. In particular, the total pairwise potential energies between carbon atoms on the fullerene and the carbon nanotubes are approximated by the continuous approach, so that the total molecular energy can be determined analytically. Since we assume that such interactions occur at a sufficiently large distance, the classical two center problem analysis is legitimate to determine various novel trajectories of the atom and fullerene numerically. It is clear that the oscillatory period of the atom for some bounded trajectories reaches terahertz frequencies. We comment that the continuous approach adopted here has the merit of a very fast computational time and can be extended to more complicated structures, in contrast to quantum mechanical calculations and molecular dynamics simulations.     

Reflection,transmission and mode conversion of plane sound waves at a plane interface between two different anisotropic solids

The boundary problem for an incident plane sound wave at a plane interface of two anisotropic solids is treated and presented in a form suitable for numerical calculations.     

Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency

A theory is developed for the diffraction of light by two spatially separated parallel ultrasonic progressive waves of different frequency. The preliminary theories ofRaman andNath [C. V.Raman and N. S.Nath, Proc. Indian Acad. Sci. A2, 406–412; 413–420 (1935)] for normal and oblique incidence are taken to be valid. The resulting equations are extensions of earlier results of R.Mertens, Z. Physik160, 291–296 (1960). The predicted periodicity of the diffraction spectrum with increasing sound beam separation agrees with the well known periodicity of the light intensity distributions in the Fresnel zone of the phase grating formed by the first ultrasonic wave. Results of numerical calculations are presented to illustrate features of the theoretical results, as reflected in the first order of diffraction for 3.0 and 6.0 Mc ultrasonic waves in water.     

Interaction of superdislocations with a plane interface

Using the linear isotropic elasticity-theory approximation, an analysis is made of the splitting of linear superdislocations with an arbitrary Burgers vector near plane interfaces of different types as defined by Head [4].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 9, pp. 11–15, September, 1971.     

Comparison of different joint configurations between two parallel SS-laminated BSCCO/Ag tapes

Stainless steel laminated BSCCO/Ag tapes are commercially available for HTS pancake magnet development. The joint between pancakes could be achieved in several configurations like straight lap joint, cross-bridge joint and combination of both. Each type of joint shows different characteristic. We have experimentally studied the characteristic of three types of joint configuration between two pancakes made of SS-laminated BSCCO/Ag tape at 77 K. We have developed two types of cross-bridge joint and one with combination of both straight lap joint and cross-bridge joint. The joint resistance for all three configurations has been compared. The rise in temperature at each joint has been estimated. The joint configuration with the combination of both straight lap joint and cross-bridge joint has given lowest joint resistance which is 0.25 μΩ at 77 K but this configuration has more locally heated zones.     

Improved matrix inversion in image plane parallel MRI

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.     

Minimum perimeter partitions of the plane into equal numbers of regions of two different areas

We identify the minimum-perimeter periodic tilings of the plane by equal numbers of regions (cells) of areas 1 and λ (minimal tilings), with at most two cells of each area per period and for which all cells of the same area are topologically equivalent. For λ close to 1 the minimal tiling is hexagonal. For smaller values of λ the minimal tilings contain pairs of 5/7, 4/8 and 3/9 cells, the cells with fewer sides having smaller area. The correlation between area fraction and number of sides in the minimal tilings is approximately linear and consistent with Lewis' law. Received 27 June 2001 and Received in final form 29 August 2001     

Interaction of plane gravitational waves with variable polarization

A solution is obtained in the paper, in the general theory of relativity, for the interaction of plane gravitational waves with variable polarization, by the application of Geroch's method to Szekeres' problem of the interaction of plane linearly polarized gravitational waves. An analysis is carried out of the solution obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 79–84, September, 1979.The author thanks Yu. G. Sbytov and Professor D. D. Ivanenko for attention to the work.     

An electron in the field of two classical plane waves propagating in slightly different directions

Solutions of the Dirac and Klein-Gordon equations have been obtained for an electron moving in the field of two plane waves propagating in slightly different directions. The solutions were obtained as an expansion in terms of the small angle between the two waves. Terms linear in this angle were considered.     

Normal transmission and reflection of monoclinic absorbing plane parallel plate

The formulae for reflectivity and transmissivity of monoclinic absorbing plane parallel crystal plate (of a specially chosen orientation) for normally incident light are derived. These are compared with usually used relations, which are exactly valid for higher symmetries.