SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Perturbation expansions for ground state function of helium atom, using Hartree or Hartree-Fock model Hamiltonian, based on Weiss-Martin variation-perturbation calculation
Matched asymptotic expansion method applied to ordinary and optimal trajectory problems in hypervelocity flight dynamics
Displacement correlations and frequency spectra for mass disordered lattices, deriving cluster expansion for phonon Green function
Differential approximation for radiant energy loss in nonequilibrium plasma generated from truncated Taylor series expansion of radiation source function
Lattice parameter and thermal expansion of AlAs as function of temperature, indicating lattice match at 900 C with GaAs
The upper atmosphere model draws heavily on the behavior of the earth's upper atmosphere which exhibits cyclic as well as irregular variations in density profile, temperature, pressure, and composition in unison with solar activities as deduced from the more recent land-based and satellite observations. The lift and drag model is designed specifically for inertially stabilized vehicles of the Mariner class, with possible extension to gravity gradient stabilized vehicles of the GEOS class. The model considers operation in the free molecular flow regimes with large Knudsen numbers. The vehicle is considered a composite structure with basic components having well-defined shapes, each with its own surface characteristics in terms of temperature, reflectivity, and accommodation of free stream molecules. The model takes into account both the calculation of precise aerodynamic force coefficients in terms of expansion of modified Bessel functions in speed ratios and angle of attack, and approximate force coefficients when the speed ratios approach infinity. Other considerations include specular and diffused reflectivity, shielding, and shadow effects.
The transmission parameters for the dynamic characteristics of a feedline were approximated using both power and product series expansions. The feedline transfer functions of a shuttle orbiter feedline configuration were obtained using power and product series approximations of 60th, 120th, 180th, and 240th, order. Bode plots using the above polynomial approximations were obtained and the results compared with the exact solution. The exact solution to the feedline transfer function was obtained by using the transcendental terms appearing in the transmission parameters. The results show that the shuttle orbiter feedline may be modeled adequately by using polynomial approximations for the transcendental functions appearing in the transmission parameters. The power series approach was shown to be preferable to the product series method.
The design principles, description, functional operation, and recommended expansion and enhancements are presented for the Space Ultrareliable Modular Computer interpretive simulator. Included as appendices are the user's manual, program module descriptions, target instruction descriptions, simulator source program listing, and a sample program printout. In discussing the design and operation of the simulator, the key problems involving host computer independence and target computer architectural scope are brought into focus.
The economic aspects of Federal regulation of airlines are discussed. The problems involved in obtaining capital resources for airline operations and expansion are analyzed. The functions of various agencies and their impact on the economic status of the airlines are explained.
The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order l equal to or greater than 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic scattering.
A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.
The design of a linear projector for use with the normal modes of a model of atmospheric circulation is discussed. A central element in any normal mode initialization scheme is the process by which a set of data fields - winds, temperatures or geopotentials, and surface pressures - are expressed ("projected') in terms of the coefficients of a model's normal modes. This process is completely analogous to the Fourier decomposition of a single field (indeed a FFT applied in the zonal direction is a part of the process). Complete separability in all three spatial dimensions is assumed. The basis functions for the modal expansion are given. An important feature of the normal modes is their coupling of the structures of different fields, thus a coefficient in a normal mode expansion would contain both mass and momentum information.
The computer-assisted C-matrix, Loewdin-alpha-function, single-center expansion method in spherical harmonics has been applied to the three-center nuclear-attraction integral (potential due to the product of separated Slater-type orbitals). Exact formulas are produced for 13 terms of an infinite series that permits evaluation to ten decimal digits of an example using 1s orbitals.
A procedure utilizing an expansion of proper orthogonal functions (or modes) to predict a fully developed flow in channel is derived. To examine numerical and conceptual difficulties, preliminary computations are performed with assigned mean velocity, and turbulence is expressed with only the first mode. The nonlinear interactions of the components of the first mode are treated specifically, with the influence of higher modes neglected; this treatment required adjustment of the skewness and effective Reynolds number to assure energy equilibrium of the first mode. Computational results show that the first mode possesses the structural character similar to that of the entire flow.
Two pressure chambers, for compression experiments with liquids from zero to 2.2 GPa pressure, are described. The experimentally measured compressions are then compared to theoretical values given by an isothermal model of equation of state recently introduced for solids. The model describes the pressure and bulk modulus as a function of compression for different types of lubricants with a very high accuracy up to the pressure limit of the high pressure chamber used (2.2 GPa). In addition the influence of temperature on static solidification pressure was found to be a simple function of the thermal expansion of the fluid.
The successful parametric modeling of the aerodynamics for an airplane operating at high angles of attack or sideslip is performed in two phases. First the aerodynamic model structure must be determined and second the associated aerodynamic parameters (stability and control derivatives) must be estimated for that model. The purpose of this paper is to document two versions of a stepwise regression computer program which were developed for the determination of airplane aerodynamic model structure and to provide two examples of their use on computer generated data. References are provided for the application of the programs to real flight data. The two computer programs that are the subject of this report, STEP and STEPSPL, are written in FORTRAN IV (ANSI l966) compatible with a CDC FTN4 compiler. Both programs are adaptations of a standard forward stepwise regression algorithm. The purpose of the adaptation is to facilitate the selection of a adequate mathematical model of the aerodynamic force and moment coefficients of an airplane from flight test data. The major difference between STEP and STEPSPL is in the basis for the model. The basis for the model in STEP is the standard polynomial Taylor's series expansion of the aerodynamic function about some steady-state trim condition. Program STEPSPL utilizes a set of spline basis functions.
A procedure utilizing an expansion of proper orthogonal functions (or modes) to predict a fully developed flow in channel is derived. To examine numerical and conceptual difficulties, preliminary computations are performed with assigned mean velocity, and turbulence is expressed with only the first mode. The nonlinear interactions of the components of the first mode are treated specifically, with the influence of higher modes neglected; this treatment required adjustment of the skewness and effective Reynolds number to assure energy equilibrium of the first mode. Computational results show that the first mode possesses the structural character similar to that of the entire flow.
An extensive set of X-band microwave backscatter measurements has been analyzed to determine its dependence on winds near the surface, atmospheric stability, and long-wave slopes. These radar measurements, made from a tower in the Gulf of Mexico, were performed in conjunction with an extensive set of simultaneous environmental measurements. The CW microwave system operated at an incidence angle of 45 deg, with antennas directed into winds and waves. Model functions for the radar cross section (RCS) and the modulation transfer function (MTF) are developed that depend on the geophysical variables, including wind stress. Statistical analysis shows that these models functions yield a significant smaller error when fit to the RCS data than a simple wind-speed function displays. A Taylor-series expansion of the returned power from a small area provides a unified function that demonstrates the complementary roles of wave slope and atmospheric fluctuations on both the RCS, the MTF, and the coherence. The issue of linearity of the MTF is addressed with this data set, yielding evidence that this is a valid assumption. These results have direct application to the remote sensing of the mean and fluctuating winds, and the wave spectrum with coherent and incoherent active radars.