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NASA NTRS1982

Theoretical studies of photoexcitation and ionization in H2O

Theoretical studies using Franck-Condon and static-exchange approximations are reported for the complete dipole excitation and ionization spectrum in H2O, where (1) large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground state equilibrium geometry, and (2) previously devised moment-theory techniques are employed in constructing the continuum oscillator-strength densities from the calculated spectra. Comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact-excitation cross sections, and dipole and synchrotron-radiation studies of partial-channel photoionization cross sections. The calculated partial-channel cross sections are found to be atomic-like, and dominated by 2p-kd components. It is suggested that the latter transition couples with the underlying 1b(1)-kb(1) channel, accounting for a prominent feature in recent synchrotron-radiation measurements.

Diercksen, G. H. F.↗

NASA NTRS1990

Two-dimensional radiation and scattering at short wave length

In the present investigation of radiation and scattering by objects when the wavelengths are much smaller than the characteristic dimensions of the radiator or scatterer, the boundary-element method is used to obtain computational accuracy and efficiency. The approach employed for wavelengths less than 5 percent of object characteristic dimensions involves cubic elements, approximate polynomial and asymptotic evaluations of the fundamental solution, and a tailoring of the order of the Gaussian quadrature according to the local demands dictated by the distance between sending and receiving points. The method addresses the propagation of low-frequency sound over large terrain features.

Yoon, W. S.↗

NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗

NASA NTRS1994

Optimizing the Zeldovich approximation

We have recently learned that the Zeldovich approximation can be successfully used for a far wider range of gravitational instability scenarios than formerly proposed; we study here how to extend this range. In previous work (Coles, Melott and Shandarin 1993, hereafter CMS) we studied the accuracy of several analytic approximations to gravitational clustering in the mildly nonlinear regime. We found that what we called the 'truncated Zeldovich approximation' (TZA) was better than any other (except in one case the ordinary Zeldovich approximation) over a wide range from linear to mildly nonlinear (sigma approximately 3) regimes. TZA was specified by setting Fourier amplitudes equal to zero for all wavenumbers greater than k(sub nl), where k(sub nl) marks the transition to the nonlinear regime. Here, we study the cross correlation of generalized TZA with a group of n-body simulations for three shapes of window function: sharp k-truncation (as in CMS), a tophat in coordinate space, or a Gaussian. We also study the variation in the crosscorrelation as a function of initial truncation scale within each type. We find that k-truncation, which was so much better than other things tried in CMS, is the worst of these three window shapes. We find that a Gaussian window e(exp(-k(exp 2)/2k(exp 2, sub G))) applied to the initial Fourier amplitudes is the best choice. It produces a greatly improved crosscorrelation in those cases which most needed improvement, e.g. those with more small-scale power in the initial conditions. The optimum choice of kG for the Gaussian window is (a somewhat spectrum-dependent) 1 to 1.5 times k(sub nl). Although all three windows produce similar power spectra and density distribution functions after application of the Zeldovich approximation, the agreement of the phases of the Fourier components with the n-body simulation is better for the Gaussian window. We therefore ascribe the success of the best-choice Gaussian window to its superior treatment of phases in the nonlinear regime. We also report on the accuracy of particle positions and velocities produced by TZA.

Melott, Adrian L.↗

NASA NTRS1972

Optimum frame synchronization.

This paper considers the optimum method for locating a sync word periodically imbedded in binary data and received over the additive white Gaussian noise channel. It is shown that the optimum rule is to select the location that maximizes the sum of the correlation and a correction term. Simulations are reported that show approximately a 3-dB improvement at interesting signal-to-noise ratios compared to a pure correlation rule. Extensions are given to the phase-shift keyed sync case where the detector output has a binary ambiguity and to the case of Gaussian data.

Massey, J. L.↗

NASA NTRS1992

Progress in integrated-circuit horn antennas for receiver applications. Part 1: Antenna design

The purpose of this work is to present a systematic method for the design of multimode quasi-integrated horn antennas. The design methodology is based on the Gaussian beam approach and the structures are optimized for achieving maximum fundamental Gaussian coupling efficiency. For this purpose, a hybrid technique is employed in which the integrated part of the antennas is treated using full-wave analysis, whereas the machined part is treated using an approximate method. This results in a simple and efficient design process. The developed design procedure has been applied for the design of a 20, a 23, and a 25 dB quasi-integrated horn antennas, all with a Gaussian coupling efficiency exceeding 97 percent. The designed antennas have been tested and characterized using both full-wave analysis and 90 GHz/370 GHz measurements.

Eleftheriades, George V.↗

NASA NTRS2013

Spectral State Evolution of 4U 1820-30: the Stability of the Spectral Index of Comptonization Tail

We analyze the X-ray spectra and their timing properties of the compact Xray binary 4U 1820-30. We establish spectral transitions in this source seen with BeppoSAX and the Rossi X-ray Timing Explorer (RXTE). During the RXTE observations (1996 - 2009), the source were approximately approximately 75% of its time in the soft state making the lower banana and upper banana transitions combined with long-term low-high state transitions. We reveal that all of the X-ray spectra of 4U 1820-30 are fit by a composition of a thermal (blackbody) component, a Comptonization component (COMPTB) and a Gaussian-line component. Thus using this spectral analysis we find that the photon power-law index Gamma of the Comptonization component is almost unchangeable (Gamma approximately 2) while the electron temperature kTe changes from 2.9 to 21 keV during these spectral events. We also establish that for these spectral events the normalization of COMPTB component (which is proportional to mass accretion rate ˙M) increases by factor 8 when kTe decreases from 21 keV to 2.9 keV. Before this index stability effect was also found analyzing X-ray data for Z-source GX 340+0 and for atolls, 4U 1728-34, GX 3+1. Thus, we can suggest that this spectral stability property is a spectral signature of an accreting neutron star source. On the other hand in a black hole binary Γ monotonically increases with ˙Mand ultimately its value saturates at large ˙M.

evolution↗

NASA NTRS1974

Star adaptation for two-algorithms used on serial computers

Two representative algorithms used on a serial computer and presently executed on the Control Data Corporation 6000 computer were adapted to execute efficiently on the Control Data STAR-100 computer. Gaussian elimination for the solution of simultaneous linear equations and the Gauss-Legendre quadrature formula for the approximation of an integral are the two algorithms discussed. A description is given of how the programs were adapted for STAR and why these adaptations were necessary to obtain an efficient STAR program. Some points to consider when adapting an algorithm for STAR are discussed. Program listings of the 6000 version coded in 6000 FORTRAN, the adapted STAR version coded in 6000 FORTRAN, and the STAR version coded in STAR FORTRAN are presented in the appendices.

Howser, L. M.↗

NASA NTRS1975

A mathematical examination of the press model for atmospheric turbulence

The random process used to model atmospheric turbulence in aircraft response problems is examined. The first, second, and higher order probability density and characteristic functions were developed. The concepts of the Press model lead to an approximate procedure for the analysis of the response of linear dynamic systems to a class of non-Gaussian random processes. The Press model accounts for both the Gaussian and non-Gaussian forms of measured turbulence data. The nonstationary aspects of measured data are explicitly described by the transition properties of the random process. The effects of the distribution of the intensity process upon calculated exceedances are examined. It is concluded that the press model with a Gaussian intensity distribution gives a conservative prediction of limit load values.

Sidwell, K.↗

NASA NTRS1982

On conforming mixed finite element methods for incompressible viscous flow problems

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Gunzburger, M. D↗

NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1987

Detection of signals by weighted integrate-and-dump filter

A Weighted Integrate and Dump Filter (WIDF) is presented that results in reducing those losses in telemetry symbol signal to noise ratio (SNR) which occur in digital Integrate and Dump Filters (IDFs) when the samples are not phase locked to the input data symbol clock. The Minimum Mean Square Error (MMSE) criterion is used to derive a set of weights for approximating the analog integrate and dump filter, which is the matched filter for detection of signals in additive white Gaussian noise. This new digital matched filter results in considerable performance improvement compared to unweighted digital matched filters. An example is presented for a sampling rate of four times the symbol rate. As the sampling offset (or phase) varies with respect to the data symbol boundaries, the output SNR varies 1 dB for an unweighted IDF, but only 0.3 dB for the optimum WIDF, averaged over random data patterns. This improvement in performance relative to unweighted IDF means that significantly lower sampling and processing rates can be used for given telemetry symbol rates, resulting in reduced system cost.

Sadr, R.↗

NASA NTRS1989

Superbubble blowout dynamics

Multiple supernovae and stellar winds from OB associations carve large holes filled with hot gas in the galactic disk. These superbubbles sweep up H I into cold, thin, dense shells and eventually grow large enough to blow completely out of the galactic H I disk. When superbubbles blow out of the disk, they vent hot gas and supernova energy into the galactic corona. In this paper ZEUS, a two-dimensional hydrodynamics code, is used to model the blowout of a superbubble from exponential and Gaussian models for the vertical density stratification. The results are compared to those from the Kompaneets (thin-shell) approximation. It is found that this approximation works very well, and that most of the mass of the shell remains in the plane, with 5 percent of it accelerating upward. The venting of the hot gas and the stability of the shell depends strongly on the model of the density distribution. It is suggested that the low galactic halo actually consists of a froth of merged superbubbles.

Mac Low, Mordecai-Mark↗

NASA NTRS1975

Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation

A simplified technique is proposed for calculating multidimensional Hermite-Gaussian quadratures that involves taking the square root of a matrix by the Cholesky algorithm rather than computation of the eigenvectors of the matrix. Ways of reducing the dimension, number, and order of the quadratures are set forth. If the function f(x) under the integral sign is not well approximated by a low-order algebraic expression, the order of the quadrature may be reduced by factoring f(x) into an expression that is nearly algebraic and one that is Gaussian.

Mcreynolds, S. R.↗

NASA NTRS1973

First-excursion probability in non-stationary random vibration.

The first-excursion probability of a non-stationary Gaussian process with zero mean has been studied. Within the framework of the point process approach, a variety of analytical approximations applicable to stationary random processes is extended herein to non-stationary random processes. The extension is possible owing to a recent definition of non-stationary envelope processes proposed by the author. With the aid of numerical examples, merits of each approximation are examined by comparing with the results of simulation. It is found that under non-stationary excitations with short duration, the Markov approximation is the best among all the approximations discussed in this paper.

Yang, J.-N.↗

NASA NTRS1987

Accurate ab initio calculations which demonstrate a 3Pi(u) ground state for Al2

The computational requirements for accurately describing the spectroscopic constants for all three candidates for the ground state of Al2 are determined. Full CI(FCI) calculations are used to calibrate approximate methods of including the electron correlation. CASSCF/MRCI calculations which accurately reproduce the FCI results in the valence DZ + 2d Gaussian basis are carried to chemical accuracy by using extensive one-particle basis sets. The effect of 2s and 2p correlation and relativistic effects are considered as well as the valence 3s and 3p correlation. Several excited states are also considered. It is shown that the computed vibrational frequency of the (2) 3Pi(g) state and the Franck-Condon factors for the (1) 3Pi(u) - (2) 3Pi(g) transition are consistent with the spectrum obtained by Douglas et al. (1983) and Abe and Kolb (1983). It is therefore concluded that the ground state is 3Pi(u).

Bauschlicher, Charles W., Jr.↗

NASA NTRS1994

The phenomenological status of late time phase transition models after cosmic background radiation anisotropy measurements

Some relatively model-independent results for structure formation via late time phase transitions (LTPT) are discussed. In particular, generic LTPT power spectra are presented. The implication of the recent Cosmic Background Explorer (COBE) detection of the cosmic background radiation (CBR) anisotropy at large angular scales (greater than or approximately equal to 7 deg) and the tight upper limits from small angular scales (approximately 1 deg) to LTPT models are discussed. Special attention is focused on the observational constraints and possible non-Gaussian signatures of CBR temperature anisotropies from LTPT and other non-Gaussian models. It is shown that while LTPT have been seriously constrained by the recent data, viable models do remain which provide more power on the 100-200 Mpc scales than do more traditional primordial Gaussian density fluctuation models. Tests for such models are presented, including possible anisotropies on angular scales less than 8 min.

Luo, Xiaochun↗