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NASA NTRS1993

Excitation of positive ions by low-energy electrons - Relevance to the Io Torus

The importance of measuring electron-ion excitation cross sections in singly and multiply charged positive ions is outlined, and recent results for Mg II and O II ions are given using the JPL's electron energy-loss merged-beams apparatus. Theoretical comparisons are given with two five-state close-coupling calculations. The energy variation of the collision strength is fitted with a semiempirical analytic function which includes approximations to polarization, resonance, and exchange contributions. In O II, first spectra anywhere of electron excitation of the optically allowed transitions are presented. In addition, excitations of two low lying, optically forbidden transitions are detected for the first time.

Smith, Steven J.↗

NASA NTRS1993

The quantum dynamics of electronically nonadiabatic chemical reactions

Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms.

Truhlar, Donald G.↗

NASA NTRS1994

Q-derivatives, coherent states and squeezing

We show that the q-deformation of the Weyl-Heisenberg (q-WH) algebra naturally arises in discretized systems, coherent states, squeezed states and systems with periodic potential on the lattice. We incorporate the q-WH algebra into the theory of (entire) analytical functions, with applications to theta and Bloch functions.

Celeghini, E.↗

NASA NTRS1994

Noise Radiation by Instability Waves in Coaxial Jets

In this paper predictions are made for the noise radiation from supersonic coaxial jets. The noise in the downstream arc of a supersonic jet is dominated by highly directional radiation from the supersonically convecting large scale structures in the jet mixing layer. Since the mean flow is not described easily in terms of simple analytic functions, a numerical prediction is made for its development. The compressible Reynolds-averaged boundary layer equations in cylindrical polar coordinates are solved. A mixing length turbulence model is used. Empirical correlations are developed the effects of velocity and temperature ratio and Mach number. Both normal and inverted velocity profiles are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The large scale structures are modeled as instability waves. The noise radiation generated by the instability waves is determined by a matching between the inner instability wave solution and the outer acoustic solution. Predictions are made for the differences between the noise radiated by coaxial jets with different operating conditions and a single equivalent jet with the same exit area, thrust, and mass-flow.

Dahl, Milo D.↗

NASA NTRS1994

The Aeroacoustics of Supersonic Coaxial Jets

Instability waves have been established as the dominant source of mixing noise radiating into the downstream arc of a supersonic jet when the waves have phase velocities that are supersonic relative to ambient conditions. Recent theories for supersonic jet noise have used the concepts of growing and decaying linear instability waves for predicting radiated noise. This analysis is extended to the prediction of noise radiation from supersonic coaxial jets. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytic functions, a numerical prediction is made for its development. The Reynolds averaged, compressible, boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed for the effects of velocity and temperature ratios and Mach number. Both normal and inverted velocity profile coaxial jets are considered. Comparisons with measurements for both single and coaxial jets show good agreement. The results from mean flow and stability calculations are used to predict the noise radiation from coaxial jets with different operating conditions. Comparisons are made between different coaxial jets and a single equivalent jet with the same total thrust, mass flow, and exit area. Results indicate that normal velocity profile jets can have noise reductions compared to the single equivalent jet. No noise reductions are found for inverted velocity profile jets operated at the minimum noise condition compared to the single equivalent jet. However, it is inferred that changes in area ratio may provide noise reduction benefits for inverted velocity profile jets.

Dahl, Milo D.↗

NASA NTRS1995

Supersonic coaxial jet noise predictions

Predictions are made for the noise radiation from supersonic, coaxial jets. These predictions are based on the assumption that the noise radiation in the downstream direction of supersonic jets is dominated by sound generated by instability waves with supersonic phase velocities relative to ambient. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytical functions, a numerical prediction is made for its development. The compressible, Reynolds averaged, boundary layer equations are solved with a modified mixing length turbulence model. The model has been calibrated to account for compressibility and temperature effects on the rate of mixing. Both normal and inverted velocity profile jets are considered. Predictions are made for the differences between the noise radiated by coaxial jets with difference operating conditions and a single reference jet with the same thrust, mass flow, and exit area. The effects of area ratio changes and simulated enhanced mixing on noise radiation are also considered.

Dahl, Milo D.↗

NASA NTRS1995

Bounce-averaged Hamiltonian for charged particles in an axisymmetric but nondipolar model magnetosphere

Schulz, Michael↗

NASA NTRS1995

Modeling of collision-induced infrared absorption spectra of H2 pairs in the first overtone band at temperatures from 20 to 500 K

A simple formalism is presented that permits quick computations of the low-resolution, rotovibrational collision-induced absorption (RV CIA) spectra of H2 pairs in the first overtone band of hydrogen, at temperatures from 20 to 500 K. These spectra account for the free-free transitions. The sharp dimer features, originating from the bound-free, free-bound, and bound-bound transitions are ignored, though their integrated intensities are properly accounted for. The method employs spectral model line- shapes with parameters computed from the three lowest spectral moments. The moments are obtained from first principles expressed as analytical functions of temperature. Except for the sharp dimer features, which are absent in this model, the computed spectra reproduce closely the results of exact quantum mechanical lineshape computations. Comparisons of the computed spectra with existing experimental data also show good agreement. The work interest for the modeling of the atmospheres of the outer planets in the near-infrared region of the spectrum. The user-friendly Fortran program developed here is available on request from the authors.

Zheng, Chunguang↗

NASA NTRS1995

Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations

Near-infrared images of the Galactic bulge at 1.25, 2.2, 3.5, and 4.9 microns obtained by the Diffuse Infrared Background Experiment (DIRBE) onboard the Cosmic Background Explorer (COBE) satellite are used to characterize its morphology and to determine its infrared luminosity and mass. Earlier analysis of the DIRBE observations (Weiland et al. 1994) provided supporting evidence for the claim made by Blitz & Spergel (1991) that the bulge is bar-shaped with its near end in the first Galactic quadrant. Adopting various triaxial analytical functions to represent the volume emissivity of the source, we confirm the barlike nature of the bulge and show that triaxial Gaussian-type functions provide a better fit to the data than other classes of functions, including an axisymmetric spheroid. The introduction of a `boxy' geometry, such as the one used by Kent, Dame, & Fazio (1991) improves the fit to the data. Our results show that the bar is rotated in the plane with its near side in the first Galactic quadrant creating an angle of 20 deg +/- 10 deg between its major axis and the line of sight to the Galactic center. Typical axis ratios of the bar are (1:0.33 +/- 0.11:0.23 +/- 0.08), resembling the geometry of prolate spheroids. There is no statistically significant evidence for an out-of-plane tilt of the bar at 2.2 microns, and marginal evidence for a tilt of approximately equal 2 deg at 4.9 microns. The introduction of a roll around the intrinsic major axis of the bulge improves the `boxy' appearance of some functions. A simple integration of the observed projected intensity of the bulge gives a bulge luminosity of 1.2 x 10(exp 9), 4.1 x 10(exp 8), 2.3 x 10(exp 8), and 4.3 x 10(exp 7) solar luminosity, respectively, at 1.25, 2.2, 3.5, and 4.9 microns wavelength for a Galactocentric distance of 8.5 kpc. The 2.2 microns luminosity function of the bulge population in the direction of Baade's window yields a bolometric luminosity of L(sub bol) = 5.3 x 10(exp 9) solar luminosity. Stellar evolutionary models relate this luminosity to the number of main-sequence progenitor stars that currently populate the red giant branch. Combined with the recent determination of the main-sequence turnoff mass for the bulge by the Hubble Space Telescope (Holtzman et al. 1993) we derive a photometrically determined bulge mass of approximately equal to 1.3 x 10(exp 10) solar mass for a Salpeter initial mass function extended down to 0.1 solar mass.

Dwek, E.↗

NASA NTRS1994

Advanced Video Analysis Needs for Human Performance Evaluation

Evaluators of human task performance in space missions make use of video as a primary source of data. Extraction of relevant human performance information from video is often a labor-intensive process requiring a large amount of time on the part of the evaluator. Based on the experiences of several human performance evaluators, needs were defined for advanced tools which could aid in the analysis of video data from space missions. Such tools should increase the efficiency with which useful information is retrieved from large quantities of raw video. They should also provide the evaluator with new analytical functions which are not present in currently used methods. Video analysis tools based on the needs defined by this study would also have uses in U.S. industry and education. Evaluation of human performance from video data can be a valuable technique in many industrial and institutional settings where humans are involved in operational systems and processes.

Campbell, Paul D.↗

NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗

NASA NTRS1994

Rigorous Justification of the Localized Approximation to the Beam-Shape Coefficients in Generalized Lorenz-Mie Theory: On-Axis Beams - Part 1

Generalized Lorenz-Mie theory describes electromagnetic scattering of an arbitrary light beam by a spherical particle. The computationally most expensive feature of the theory is the evaluation of the beam-shape coefficients, which give the decomposition of the incident light beam into partial waves. The so-called localized approximation to these coefficients for a focused Gaussian beam is an analytical function whose use greatly simplifies Gaussian-beam scattering calculations. A mathematical justification and physical interpretation of the localized approximation is presented for on-axis beams.

Lock, James A.↗

NASA NTRS1999

Ocean Turbulence: Two-Point Closure Model Momentum, Heat and Salt Vertical Diffusivities in the Presence of Shear - Paper 3

In papers 1 and 2 we have presented the results of the most updated 1-point closure model for the turbulent vertical diffusivities of momentum, heat and salt, K(sub m,h,s). In this paper, we derive the analytic expressions for K(sub m,h,s) using a new 2-point closure model that has recently been developed and successfully tested against some approx. 80 turbulence statistics for different flows. The new model has no free parameters. The expressions for K(sub m, h. s) are analytical functions of two stability parameters: the Turner number R(sub rho) (salinity gradient/temperature gradient) and the Richardson number R(sub i) (temperature gradient/shear). The turbulent kinetic energy K and its rate of dissipation may be taken local or non-local (K-epsilon model). Contrary to all previous models that to describe turbulent mixing below the mixed layer (ML) have adopted three adjustable "background diffusivities" for momentum. heat and salt, we propose a model that avoids such adjustable diffusivities. We assume that below the ML, K(sub m,h,s) have the same functional dependence on R(sub i) and R(sub rho) derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking measured by Gargett et al. (1981). The procedure frees the model from adjustable background diffusivities and indeed we use the same model throughout the entire vertical extent of the ocean. Using the new K(sub m,h, s), we run an O-GCM and present a variety of results that we compare with Levitus and the KPP model. Since the traditional 1-point (used in papers 1 and 2) and the new 2-point closure models used here represent different modeling philosophies and procedures, testing them in an O-GCM is indispensable. The basic motivation is to show that the new 2-point closure model gives results that are overall superior to the 1-point closure in spite of the fact that the latter rely on several adjustable parameters while the new 2-point closure has none. After the extensive comparisons presented in papers 1 and 2, we conclude that the new model presented here is overall superior for it not only is parameter free but also 2 because is part of a more general turbulence model that has been previously successfully tested on a wide variety of other types of turbulent flows.

Canuto, V. M.↗

NASA NTRS1994

Goal Directed Model Inversion: A Study of Dynamic Behavior

Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome 0 "would have been right if the outcome had been the desired one." The algorithm then proceeds as follows: (1) store the action that produced the wrong outcome as a "target" (2) redefine the wrong outcome as a desired goal (3) submit the new desired goal to the system (4) compare the new action with the target action and modify the system by using a suitable algorithm for credit assignment (Back propagation in our example) (5) resubmit the original goal. Prior publications by our group in this area focused on demonstrating empirical results based on the inverse kinematic problem for a simulated robotic arm. In this paper we apply the inversion process to much simpler analytic functions in order to elucidate the dynamic behavior of the system and to determine the sensitivity of the learning process to various parameters. This understanding will be necessary for the acceptance of GDMI as a practical tool.

Colombano, Silvano P.↗

NASA NTRS2001

An Evaluation of Fractal Surface Measurement Methods for Characterizing Landscape Complexity from Remote-Sensing Imagery

The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.

Lam, Nina Siu-Ngan↗

NASA NTRS2002

Application of Modern Design of Experiments to CARS Thermometry in a Model Scramjet Engine

We have applied formal experiment design and analysis to optimize the measurement of temperature in a supersonic combustor at NASA Langley Research Center. We used the coherent anti-Stokes Raman spectroscopy (CARS) technique to map the temperature distribution in the flowfield downstream of an 1160 K, Mach 2 freestream into which supersonic hydrogen fuel is injected at an angle of 30 degrees. CARS thermometry is inherently a single-point measurement technique; it was used to map thc flow by translating the measurement volume through the flowfield. The method known as "Modern Design of Experiments" (MDOE) was used to estimate the data volume required, design the test matrix, perform the experiment and analyze the resulting data. MDOE allowed us to match the volume of data acquired to the precision requirements of the customer. Furthermore, one aspect of MDOE, known as response surface methodology, allowed us to develop precise maps of the flowfield temperature, allowing interpolation between measurement points. An analytic function in two spatial variables was fit to the data from a single measurement plane. Fitting with a Cosine Series Bivariate Function allowed the mean temperature to be mapped with 95% confidence interval half-widths of +/- 30 Kelvin, comfortably meeting the confidence of +/- 50 Kelvin specified prior to performing the experiments. We estimate that applying MDOE to the present experiment saved a factor of 5 in data volume acquired, compared to experiments executed in the traditional manner. Furthermore, the precision requirements could have been met with less than half the data acquired.

Danehy, P. M.↗

NASA NTRS1999

Cone-Probe Rake Design and Calibration for Supersonic Wind Tunnel Models

A series of experimental investigations were conducted at the NASA Langley Unitary Plan Wind Tunnel (UPWT) to calibrate cone-probe rakes designed to measure the flow field on 1-2% scale, high-speed wind tunnel models from Mach 2.15 to 2.4. The rakes were developed from a previous design that exhibited unfavorable measurement characteristics caused by a high probe spatial density and flow blockage from the rake body. Calibration parameters included Mach number, total pressure recovery, and flow angularity. Reference conditions were determined from a localized UPWT test section flow survey using a 10deg supersonic wedge probe. Test section Mach number and total pressure were determined using a novel iterative technique that accounted for boundary layer effects on the wedge surface. Cone-probe measurements were correlated to the surveyed flow conditions using analytical functions and recursive algorithms that resolved Mach number, pressure recovery, and flow angle to within +/-0.01, +/-1% and +/-0.1deg , respectively, for angles of attack and sideslip between +/-8deg. Uncertainty estimates indicated the overall cone-probe calibration accuracy was strongly influenced by the propagation of measurement error into the calculated results.

Won, Mark J.↗

NASA NTRS2008

Development of Solar Wind Model Driven by Empirical Heat Flux and Pressure Terms

We are developing a time stationary self-consistent 2D MHD model of the solar corona and solar wind as suggested by Sittler et al. (2003). Sittler & Guhathakurta (1999) developed a semiempirical steady state model (SG model) of the solar wind in a multipole 3-streamer structure, with the model constrained by Skylab observations. Guhathakurta et al. (2006) presented a more recent version of their initial work. Sittler et al. (2003) modified the SG model by investigating time dependent MHD, ad hoc heating term with heat conduction and empirical heating solutions. Next step of development of 2D MHD models was performed by Sittler & Ofman (2006). They derived effective temperature and effective heat flux from the data-driven SG model and fit smooth analytical functions to be used in MHD calculations. Improvements of the Sittler & Ofman (2006) results now show a convergence of the 3-streamer topology into a single equatorial streamer at altitudes > 2 R(sub S). This is a new result and shows we are now able to reproduce observations of an equatorially confined streamer belt. In order to allow our solutions to be applied to more general applications, we extend that model by using magnetogram data and PFSS model as a boundary condition. Initial results were presented by Selwa et al. (2008). We choose solar minimum magnetogram data since during solar maximum the boundary conditions are more complex and the coronal magnetic field may not be described correctly by PFSS model. As the first step we studied the simplest 2D MHD case with variable heat conduction, and with empirical heat input combined with empirical momentum addition for the fast solar wind. We use realistic magnetic field data based on NSO/GONG data, and plan to extend the study to 3D. This study represents the first attempt of fully self-consistent realistic model based on real data and including semi-empirical heat flux and semi-empirical effective pressure terms.

Sittler, Edward C., Jr.↗