Mathematical representation of current density profiles from ion thrusters
Ion thrustor ion beam current density profiles mathematical representation by two parameter equation
Reynolds, T. W.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The summation-dial, a vectorial representation of time series data
Summation dial vectorial representation of stationary and nonstationary time series data, relating rhythms in bed rest study
Hetherington, N. W.↗
A surface-layer representation of the lunar gravitational field
Dynamic derivation of surface layer representation of lunar gravitational field from Doppler observations on polar and equatorial lunar orbiters
Buechler, G.↗
A characteristic surface representation of the effects of off-optimum propulsion parameters on low-thrust performance
Solar electric multimission spacecraft design, discussing off-optimum propulsion parameters effects on low thrust performance by characteristic surface representation
Atkins, K. L.↗
Jones's matrix representation of optical instruments. I - Beam splitters
Jones reflection and transmission matrices representation for beam splitters, investigating reversibility and action on incident light amplitude and/or phase
Fymat, A. L.↗
Generalized representation of electric fields in interaction gaps of klystrons and traveling wave tubes with axial symmetry
Analytic expressions for axial and radial electric fields in axisymmetric interaction gaps of klystrons and coupled cavity traveling wave tubes are derived. Introduction of the field shape parameter m results in both limiting cases of the field at the tunnel tips, that is, E equal to a constant and E approaching infinity as well as a continuous transition between these two limits. The transition represents actual, practical fields. This representation may be used to replace the somewhat arbitrary expressions being applied by various researchers to describe the fields.
Kosmahl, H. G.↗
An explicit form of the Mie phase matrix for multiple scattering calculations in the I, Q, U, and V representation
An explicit expression is obtained for the phase matrix in the I, Q, U, and V Stokes vector representation for a system containing a polydispersion of spherical particles. All of the symmetry relations derived by Hovenier using general arguments are established explicitly. Convenient algorithms are given for the computation of the phase matrix for a spherical polydispersion. Since this theory is so vitally important in radiative transfer, many researchers will need to compute these functions for realistic aerosols distributions. Therefore, results are presented for a haze L distribution so that other researchers will have a way of checking their programs which compute these quantities.
Kattawar, G. W.↗
Rational function representation of flap noise spectra including correction for reflection effects
A rational function is presented for the acoustic spectra generated by deflection of engine exhaust jets for under-the-wing and over-the-wing versions of externally blown flaps. The functional representation is intended to provide a means for compact storage of data and for data analysis. The expressions are based on Fourier transform functions for the Strouhal normalized pressure spectral density, and on a correction for reflection effects based on the N-independent-source model of P. Thomas extended by use of a reflected ray transfer function. Curve fit comparisons are presented for blown flap data taken from turbofan engine tests and from large scale cold-flow model tests. Application of the rational function to scrubbing noise theory is also indicated.
Miles, J. H.↗
Electromagnetic field representation in inhomogeneous anisotropic media
Some of the basic developments in the theory of electromagnetic field representation in terms of Hertz vectors are reviewed. A solution for the field in an inhomogeneous anisotropic medium is given in terms of the two Hertz vectors. Conditions for presentation of the field in terms of uncoupled transverse electric and transverse magnetic modes, in a general orthogonal coordinate system, are derived when the permeability and permittivity tensors have only diagonal components. These conditions are compared with some known special cases.
Mohsen, A.↗
Rational functional representation of flap noise spectra including correction for reflection effects
A rational function is presented for the acoustic spectra generated by deflection of engine exhaust jets for under-the-wing and over-the-wing versions of externally blown flaps. The functional representation is intended to provide a means for compact storage of data and for data analysis. The expressions are based on Fourier transform functions for the Strouhal normalized pressure spectral density, and on a correction for reflection effects based on Thomas' (1969) N-independent-source model extended by use of a reflected ray transfer function. Curve fit comparisons are presented for blown-flap data taken from turbofan engine tests and from large-scale cold-flow model tests. Application of the rational function to scrubbing noise theory is also indicated.
Miles, J. H.↗
Representation of magnetic fields in space
Several methods by which a magnetic field in space can be represented are reviewed with particular attention to problems of the observed geomagnetic field. Time dependence is assumed to be negligible, and five main classes of representation are described by vector potential, scalar potential, orthogonal vectors, Euler potentials, and expanded magnetic field.
Stern, D. P.↗
Spline function approximation techniques for image geometric distortion representation
Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.
Anuta, P. E.↗
A combined representation method for use in band structure calculations. 1: Method
A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence.
Friedli, C.↗
Report on the status of a slotted wind tunnel wall representation using the vortex-lattice technique
A combined analytical/experimental program for development of an improved slotted wind-tunnel wall representation is described. The effort is scheduled for completion in 1977. The vortex-lattice technique which is being used as the primary analytical tool for representing both the wind-tunnel and the lifting model is discussed. Comparisons of results obtained to date with available data are presented.
Heltsley, F. L.↗
The relationship between mean anomaly block sizes and spherical harmonic representations
The frequently used rule specifying the relationship between a mean gravity anomaly in a block whose side length is theta degrees and a spherical harmonic representation of these data to degree l-bar is examined in light of the smoothing parameter used by Pellinen (1966). It is found that if the smoothing parameter is not considered, mean anomalies computed from potential coefficients can be in error by about 30% of the rms anomaly value. It is suggested that the above mentioned rule should be considered only a crude approximation.
Rapp, R. H.↗
On the representation matrices of the spin permutation group
A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.
Wilson, S.↗
A new concept in laser-assisted chemistry - The electronic-field representation
Electronic-field representation is proposed as a technique for laser-assisted chemistry. Specifically, it is shown that several field-assisted chemical processes can be described in terms of mixed matter-field quantum states and their associated energies. The technique may be used to analyze the effects exerted by an intense laser on both bound and unbound molecular systems, and to investigate other field-induced effects including multiphoton processes, emission, and photodissociation.
George, T. F.↗
An elliptic representation of coupled boundary layers and inviscid core for computation of separated internal flows
This report presents a viscous-inviscid calculation method for the prediction of turbulent incompressible flows in diffusers with small regions of stall. Integral turbulent boundary layer equations (BLE) are used to provide boundary conditions for a finite difference representation of the inviscid core. The BLE are applied at the floating displacement-thickness line, resulting in a simulataneous set of nonlinear block tridiagonal equations which are solved iteratively using a sucessive line-relaxation technique. Results of the method have been applied to calculate the performance of a variety of asymmetric stalled diffusers.
Ghose, S.↗