Useful operator in plasma kinetic theory.
Operator used in derivation of plasma kinetic equation, expressing integral of pair correlation function for stable and unstable cases via Fourier transform
PLASMA DYNAMICS↗
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Radar scene generation for tactical decision aids
The Mueller matrix and polarization covariance matrix for polarimetric radar systems was studied. The clutter is modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. A general mixing formula was derived for discrete scatters immersed in a host medium. The results are applicable to general multiphase mixtures. The strong fluctuation theory was used to derive the backscattering cross sections, and was further extended to include higher order co-polarized and cross-polarized moments. A two-layer anisotropic random medium model was developed for the active and passive remote sensing of ice fields. A three-layer random medium model was adopted to study the volume scattering effects for the active and passive microwave remote sensing of snow-covered ice fields. The snow layer was simulated by an isotropic random medium and the ice layer by an anisotropic random medium. The vegetation canopy and snow-covered ice field were studied with a three-layer model, an isotropic random medium layer overlying an anisotropic random medium. The dyadic Green's function of the three-layer medium and the scattered electromagnetic intensities with Born approximation were calculated.
Kong, J. A.↗
Blunt-Body Entry Vehicle Aerothermodynamics: Transition and Turbulence on the CEV and MSL Configurations
Recent, current, and planned NASA missions that employ blunt-body entry vehicles pose aerothermodynamic problems that challenge the state-of-the art of experimental and computational methods. The issues of boundary-layer transition and turbulent heating on the heat shield have become important in the designs of both the Mars Science Laboratory and Crew Exploration Vehicle. While considerable experience in these general areas exists, that experience is mainly derived from simple geometries; e.g. sharp-cones and flat-plates, or from lifting bodies such as the Space Shuttle Orbiter. For blunt-body vehicles, application of existing data, correlations, and comparisons is questionable because an all, or mostly, subsonic flow field is produced behind the bow shock, as compared to the supersonic (or even hypersonic) flow of other configurations. Because of the need for design and validation data for projects such as MSL and CEV, many new experimental studies have been conducted in the last decade to obtain detailed boundary-layer transition and turbulent heating data on this class of vehicle. In this paper, details of several of the test programs are reviewed. The laminar and turbulent data from these various test are shown to correlate in terms of edge-based Stanton and Reynolds number functions. Correlations are developed from the data for transition onset and turbulent heating augmentation as functions of momentum thickness Reynolds number. These correlation can be employed as engineering-level design and analysis tools.
Hollis, Brian R.↗
Monte Carlo simulation of the classical two-dimensional one-component plasma
A Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation are used to study the classical two-dimensional one-component plasma. A fluid phase is found for a specified dimensionless quantity, and a solid phase for higher values of this quantity. It is reported that the solid phase shows directional long range order, noting that in the solid phase positional long range order is lost as the thermodynamic limit is approached. Finally, the results of calculations of the thermodynamic functions and one- and two-particle correlation functions are presented.
Gann, R. C.↗
Remote sensing of Earth Terrain
The Mueller matrix and polarization covariance matrix for polarimetric radar systems were studied. The clutter is modelled by a layer of random permittivity, described by a three dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields. A general mixing formula is derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasistatic analysis, assuming the diameter of the inclusion particles to be much smaller than the wavelength. The results are applicable to general multiphase mixtures.
Kong, J. A.↗
Radar scene generation for tactical decision aids
The Mueller matrix and polarization covariance matrix for polarimetric radar systems was studied. The clutter was modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model was applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. Theoretical predictions are matched with experimental data for vegetation fields. The strong fluctuation theory was used to derive the backscattering cross sections. A two-layer anisotropic random medium model was developed for the active and passive microwave remote sensing of ice fields. A three-layer random medium model was adopted to study the volume scattering effects for the active and passive microwave remote sensing of snow-covered ice fields.
Kong, J. A.↗
Theoretical models for polarimetric radar clutter
The Mueller matrix and polarization covariance matrix are described for polarimetric radar systems. The clutter is modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, corresponding to a covariance matrix with four zero elements. Theoretical predictions are matched with experimental data for vegetation fields.
Borgeaud, M.↗
Short-term time variability of Cygnus X-1
Autocorrelation functions, power-density spectra, and cross-correlation functions were calculated for 71 observations of Cyg X-1 by the Uhuru satellite. The average autocorrelation function and power-density spectrum were found to be independent of energy and consistent with a shot-noise source with a characteristic time constant of 0.45 s. The data in different energy bands were found to be 100 percent correlated.
Weisskopf, M. C.↗
The distribution of galaxies within the 'Great Wall'
The galaxy distribution within the 'Great Wall', the most striking feature in the first three 'slices' of the CfA redshift survey extension is examined. The Great Wall is extracted from the sample and is analyzed by counting galaxies in cells. The 'local' two-point correlation function within the Great Wall is computed and the local correlation length, is estimated 15/h Mpc, about 3 times larger than the correlation length for the entire sample. The redshift distribution of galaxies in the pencil-beam survey by Broadhurst et al. (1990) shows peaks separated about by large 'voids', at least to a redshift of about 0.3. The peaks might represent the intersections of their about 5/h Mpc pencil beams with structures similar to the Great Wall. Under this hypothesis, sampling of the Great Walls shows that l approximately 12/h Mpc is the minimum projected beam size required to detect all the 'walls' at redshifts between the peak of the selection function and the effective depth of the survey.
Ramella, Massimo↗
Ginzburg-Landau theory for the solid-liquid interface of bcc elements. II - Application to the classical one-component plasma, the Wigner crystal, and He-4
The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.
Zeng, X. C.↗
Intensity correlation of ionizing background at high redshifts
Intensity correlation of ionizing background at high redshifts is discussed. The intensity correlation function xi(sub j) and the absorption line equivalent width correlation xi(sub 1/W) are discussed.
Zuo, Lin↗
Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence
Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.
Rubinstein, Robert↗
Structure of correlation tensors in homogeneous anisotropic turbulence
The theory of isotropic tensors, developed by Robertson (1940), Batchelor (1946), and Chandrasekhar (1951), is extended to cover the general case of turbulence with a pseudo-vector-preferred direction, without assuming mirror-reflection invariance. Attention is focused on two-point-correlation functions, and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. The somewhat unexpected result that the vector- and pseudo-vector-preferred-direction cases yield different results is presented: A pseudo-vector-preferred direction allows the correlation matrix one more functional degree of freedom than does the proper vector case. An explicit form of the two-point-correlation tensor in the presence of a uniform mean magnetic field is presented which may be appropriate for use in analysis of magnetic fluctuations in plasma containment devices or the interplanetary medium. A procedure for determining the magnetic helicity from experimental data is presented.
Matthaeus, W. H.↗
Study of random process theory aids digital data processing
Study of techniques for all random process technology, including stationary, nonstationary, and Gaussian bivariate, aids digital data processing. It presents material on digital filtering, correlation function, optimal spectral smoothing, deterministic data processing, and nonstationary spectrum and correlation analyses.
Bordner, G. W.↗
Investigation of surface fluctuating pressures on a 1/4 scale YC-14 upper surface blown flap model
Fluctuating pressures were measured at 30 positions on the surface of a 1/4-scale YC-14 wing and fuselage model during an outdoor static testing program. These data were obtained as part of a NASA program to study the fluctuating loads imposed on STOL aircraft configurations and to further the understanding of the scaling laws of unsteady surface pressure fields. Fluctuating pressure data were recorded at several discrete engine thrust settings for each of 16 configurations of the model. These data were reduced using the technique of random data analysis to obtain auto-and cross-spectral density functions and coherence functions for frequencies from 0 to 10 kHz, and cross-correlation functions for time delays from 0 to 10.24 ms. Results of this program provide the following items of particular interest: (1) Good collapse of normalized PSD functions on the USB flap was found using a technique applied by Lilley and Hodgson to data from a laboratory wall-jet apparatus. (2) Results indicate that the fluctuating pressure loading on surfaces washed by the jet exhaust flow was dominated by hydrodynamic pressure variations, loading on surface well outside the flow region dominated by acoustic pressure variations, and loading near the flow boundaries from a mixture of the two.
Pappa, R. S.↗
The distribution of clusters in the southern ACO catalog
The distribution of rich clusters of galaxies in the new southern catalog of Abell, Corwin, and Olowin (ACO, 1989) is examined. A comparison with the cluster distribution in the northern Abell catalog, published in 1958, is presented. The similarities as well as the differences between the catalogs are highlighted. The angular cluster correlation function of the ACO catalog is consistent with the Abell cluster correlation, showing strong superclustering to about 50/h Mpc. The correlation amplitude scales with depth, as expected for real spatial clustering. Plate-to-plate variation effects are investigated; no significant impact of the latter on the cluster correlation is observed.
Batuski, David J.↗
Random vibrations of laminated plates modeled within the first order shear deformation theory
This paper deals with the dynamic response of anisotropic laminated composite plates to stationary random excitation. The theory of laminated plates used here includes shear deformation and rotary inertia effects in the same manner as Mindlin's theory for isotropic homogeneous plates. Two cases of random pressure fields are considered in this analysis. In the first case, it is modeled as a uniformly distributed load, random in time with an exponential decaying correlation function, while in the second one as a jet noise, fully correlated in one direction and homogeneous in the perpendicular one. The analysis presented herein, as well as the obtained response characteristics, expressed in terms of mean-squares and angle-dependent mean-squares, may be useful in the design of composite plates subjected to random pressure fields and in the evaluation of their reliability.
Cederbaum, G.↗
Theory of the unmagnetized plasma.
The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.
Montgomery, D. C.↗