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NASA NTRS1986

Effects of the oceans on polar motion: Extended investigations

A method was found for expressing the tide current velocities in terms of the tide height (with all variables expanded in spherical harmonics). All time equations were then combined into a single, nondifferential matrix equation involving only the unknown tide height. The pole tide was constrained so that no tidewater flows across continental boundaries. The constraint was derived for the case of turbulent oceans; with the tide velocities expressed in terms of the tide height. The two matrix equations were combined. Simple matrix inversion then yielded the constrained solution. Programs to construct and invert the matrix equations were written. Preliminary results were obtained and are discussed.

Dickman, Steven R.↗

NASA NTRS1985

On the emission region of gamma ray bursts

Within the last few years the rapid accumulation of gamma ray burst spectral data, especially those of KONUS and solar maximum mission, has made the confrontation between theories of the gamma ray emission mechanisms and observations much more urgent and challenging. At present the most viable mode seems to be some combination of inverse Comptonization and synchrotron emission. Here, an attempt is made to limit the acceptable parameter space of the emission region by taking into account the maximum set of observational constraints. These are then applied to two specific scenarios: surface emission versus magnetospheric emission. Some observable predictions based on these scenarios are considered.

Liang, E. P.↗

NASA NTRS1997

An Adaptive Flow Solver for Air-Borne Vehicles Undergoing Time-Dependent Motions/Deformations

This report describes a concurrent Euler flow solver for flows around complex 3-D bodies. The solver is based on a cell-centered finite volume methodology on 3-D unstructured tetrahedral grids. In this algorithm, spatial discretization for the inviscid convective term is accomplished using an upwind scheme. A localized reconstruction is done for flow variables which is second order accurate. Evolution in time is accomplished using an explicit three-stage Runge-Kutta method which has second order temporal accuracy. This is adapted for concurrent execution using another proven methodology based on concurrent graph abstraction. This solver operates on heterogeneous network architectures. These architectures may include a broad variety of UNIX workstations and PCs running Windows NT, symmetric multiprocessors and distributed-memory multi-computers. The unstructured grid is generated using commercial grid generation tools. The grid is automatically partitioned using a concurrent algorithm based on heat diffusion. This results in memory requirements that are inversely proportional to the number of processors. The solver uses automatic granularity control and resource management techniques both to balance load and communication requirements, and deal with differing memory constraints. These ideas are again based on heat diffusion. Results are subsequently combined for visualization and analysis using commercial CFD tools. Flow simulation results are demonstrated for a constant section wing at subsonic, transonic, and a supersonic case. These results are compared with experimental data and numerical results of other researchers. Performance results are under way for a variety of network topologies.

Singh, Jatinder↗

NASA NTRS2002

Analysis of the Magneto-Hydrodynamic (MHD) Energy Bypass Engine for High-Speed Air-Breathing Propulsion

The performance of the MHD energy bypass air-breathing engine for high-speed propulsion is analyzed in this investigation. This engine is a specific type of the general class of inverse cycle engines. In this paper, the general relationship between engine performance (specific impulse and specific thrust) and the overall total pressure ratio through an engine (from inlet plane to exit plane) is first developed and illustrated. Engines with large total pressure decreases, regardless of cause or source, are seen to have exponentially decreasing performance. The ideal inverse cycle engine (of which the MHD engine is a sub-set) is then demonstrated to have a significant total pressure decrease across the engine; this total pressure decrease is cycle-driven, degrades rapidly with energy bypass ratio, and is independent of any irreversibility. The ideal MHD engine (inverse cycle engine with no irreversibility other than that inherent in the MHD work interaction processes) is next examined and is seen to have an additional large total pressure decrease due to MHD-generated irreversibility in the decelerator and the accelerator. This irreversibility mainly occurs in the deceleration process. Both inherent total pressure losses (inverse cycle and MHD irreversibility) result in a significant narrowing of the performance capability of the MHD bypass engine. The fundamental characteristics of MHD flow acceleration and flow deceleration from the standpoint of irreversibility and second-law constraints are next examined in order to clarify issues regarding flow losses and parameter selection in the MM modules. Severe constraints are seen to exist in the decelerator in terms of allowable deceleration Mach numbers and volumetric (length) required for meaningful energy bypass (work interaction). Considerable difficulties are also encountered and discussed due to thermal/work choking phenomena associated with the deceleration process. Lastly, full engine simulations utilizing inlet shock systems, finite-rate chemistry, wall cooling with thermally balanced engine (fuel heat sink), fuel injection and mixing, friction, etc. are shown and discussed for both the MHD engine and the conventional scramjet. The MHD bypass engine has significantly lower performance in all categories across the Mach number range (8 to 12.2). The lower performance is attributed to the combined effects of 1) additional irreversibility and cooling requirements associated with the MHD components and 2) the total pressure decrease associated with the inverse cycle itself.

Riggins, David W.↗

NASA NTRS1987

Three dimensional numerical scattering from ocean-like surfaces

A new method of calculating the electric field scattered from two-dimensional conducting rough surfaces is presented. This method uses the operator conjugate gradients technique and the extended boundary condition equation. This avoids the build-up of round-off errors encountered in the inversion of large matrices. It also avoids the singularities of the integral kernels usually encountered in the method of moments. Techniques for improving the rate of convergence by applying physical constraints are discussed. This method is presently being used to calculate the polarization signatures from simulated ocean-like surfaces.

Rodriguez, Ernesto↗

NASA NTRS1989

An entropy method for induced drag minimization

A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained for several wing configurations including a comparison of wing extension, winglets, and in-plane wing sweep, with and without a constraint on wing-root bending moment. Like the classical lifting-line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportioinal to the wing aspect ratio. Unlike the classical theory, it predicts that induced drag is Reynolds number dependent and that the optimum spanwise circulation distribution is non-elliptic.

Greene, George C.↗

NASA NTRS2000

The Spectral Evolution of Solar Flare Hard X-Ray Emission Observed with BATSE

We present a more detailed characterization of spectral evolution in solar flare hard X-ray emission than has been previously described. Our characterization is consistent with some earlier results but utilizes higher time resolution data and reveals nuances in spectral evolution that have never been reported. We employ an underutilized data set, the Burst and Transient Source Experiment (BATSE) solar flare catalog, for our investigation and different methodology than previous studies. Our findings support the conclusion that properties of the particle Abstract: acceleration mechanism in flares, such as the acceleration rate or efficiency, are indeed important to understanding spectral evolution. On the other hand, time-of-flight models, which assume accelerator properties to be negligible, cannot explain the observed detailed spectral evolution, and correlations that we would expect to exist between spectral evolution patterns and parameters derived from time-of-flight model inversions are not supported by the data. In this fashion, we establish an observational context in which to interpret future High Energy Solar Spectroscopic Imager (HESSI) observations and delineate some constraints for theoretical models of particle acceleration.

Newton, Elizabeth K.↗

NASA NTRS2020

H- and Dissociation in Ultra-hot Jupiters: A Retrieval Case Study of WASP-18b

Atmospheres of a number of ultra-hot Jupiters (UHJs) with temperatures gsim2000 K have been observed recently. Many of these planets show largely featureless thermal spectra in the near-infrared observed with the HST WFC3 spectrograph (1.1–1.7 μm) even though this spectral range contains strong H2O opacity. Recent works have proposed the possibility of H- opacity masking the H2O feature and/or thermal dissociation of H2O causing its apparent depletion at the high temperatures of UHJs. In this work, we test these hypotheses using observations of the exoplanet WASP-18b as a case study. We report detailed atmospheric retrievals of the planet using the HyDRA retrieval code, extended to include the effects of H- opacity and thermal dissociation. We report constraints on the H2O, CO, and H- abundances as well as the pressure–temperature profile of the dayside atmosphere for retrievals with and without H-/dissociation for each data set. We find that the H2O and H- abundances are relatively unconstrained given the featureless WFC3 spectra. We do not conclusively detect H- in the planet, contrary to previous studies that used equilibrium models to infer its presence. The constraint on the CO abundance depends on the combination of WFC3 and Spitzer data, ranging from solar to super-solar CO values. We additionally see signs of a thermal inversion from two of the data sets. Our study demonstrates the potential of atmospheric retrievals of UHJs, including the effects of H- and thermal dissociation of molecules.

Siddharth Gandhi↗

NASA NTRS1981

Grid-generated isotropic homogeneous turbulence at high Reynolds numbers

Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.

Rosen, G.↗

NASA NTRS1982

Emission mechanisms of the March 5th 1979 gamma ray transient

This paper reviews the spectral and temporal constraints on the emission mechanisms of the initial burst and subsequent pulses of the March 5, 1979 gamma-transient. Interpretation of the hard tail above 300 keV as due to inverse comptonization, when combined with the synchrotron-pair annihilation model of Ramaty et al. (1981), makes it possible to derive from first principles the intrinsic luminosity of the source. This is in general agreement with that expected from N49 in LMC. The pulsed emissions have characteristics difficult to explain in terms of conventional models.

Liang, E. P. T.↗

NASA NTRS1986

An inverse method for subcritical flows

An exact method is presented for two-dimensional subsonic flow within the limitations of the tangent gas approximation. While Woods (1961) studied these equations and proposed iterative methods for the solution of both the iterative and inverse problems, the inverse method here presented is noniterative and exact. It is shown that the direct Euler solution over the designed airfoil is very close to the input speed distribution, and that the constraints necessitated by upstream condition and closure requirements are easily incorporated.

Daripa, P. K.↗

NASA NTRS2004

Crustal structure of Mars from gravity and topography

Mars Orbiter Laser Altimeter (MOLA) topography and gravity models from 5 years of Mars Global Surveyor (MGS) spacecraft tracking provide a window into the structure of the Martian crust and upper mantle. We apply a finite-amplitude terrain correction assuming uniform crustal density and additional corrections for the anomalous densities of the polar caps, the major volcanos, and the hydrostatic flattening of the core. A nonlinear inversion for Moho relief yields a crustal thickness model that obeys a plausible power law and resolves features as small as 300 km wavelength. On the basis of petrological and geophysical constraints, we invoke a mantle density contrast of 600 kg m-3; with this assumption, the Isidis and Hellas gravity anomalies constrain the global mean crustal thickness to be >45 km. The crust is characterized by a degree 1 structure that is several times larger than any higher degree harmonic component, representing the geophysical manifestation of the planet's hemispheric dichotomy. It corresponds to a distinction between modal crustal thicknesses of 32 km and 58 km in the northern and southern hemispheres, respectively. The Tharsis rise and Hellas annulus represent the strongest components in the degree 2 crustal thickness structure. A uniform highland crustal thickness suggests a single mechanism for its formation, with subsequent modification by the Hellas impact, erosion, and the volcanic construction of Tharsis. The largest surviving lowland impact, Utopia, post-dated formation of the crustal dichotomy. Its crustal structure is preserved, making it unlikely that the northern crust was subsequently thinned by internal processes.

Neumann, G. A.↗

NASA NTRS2009

Predictions of Gamma-ray Emission from Globular Cluster Millisecond Pulsars Above 100 MeV

The recent Fermi detection of the globular cluster (GC) 47 Tucanae highlighted the importance of modeling collective gamma-ray emission of millisecond pulsars (MSPs) in GCs. Steady flux from such populations is also expected in the very high energy (VHE) domain covered by ground-based Cherenkov telescopes. We present pulsed curvature radiation (CR) as well as unpulsed inverse Compton (IC) calculations for an ensemble of MSPs in the GCs 47 Tucanae and Terzan 5. We demonstrate that the CR from these GCs should be easily detectable for Fermi, while constraints on the total number of MSps and the nebular B-field may be derived using the IC flux components.

Venter, C.↗

NASA NTRS1986

Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics

The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.

Rodriguez, G.↗

NASA NTRS1981

A study of high density bit transition requirements versus the effects on BCH error correcting coding

Several methods for increasing bit transition densities in a data stream are summarized, discussed in detail, and compared against constraints imposed by the 2 MHz data link of the space shuttle high rate multiplexer unit. These methods include use of alternate pulse code modulation waveforms, data stream modification by insertion, alternate bit inversion, differential encoding, error encoding, and use of bit scramblers. The psuedo-random cover sequence generator was chosen for application to the 2 MHz data link of the space shuttle high rate multiplexer unit. This method is fully analyzed and a design implementation proposed.

Ingels, F.↗

NASA NTRS1986

Short-lived solar burst spectral component at f approximately 100 GHz

A new kind of burst emission component was discovered, exhibiting fast and distinct pulses (approx. 60 ms durations), with spectral peak emission at f approx. 100 GHz, and onset time coincident to hard X-rays to within approx. 128 ms. These features pose serious constraints for the interpretation using current models. One suggestion assumes the f approx. 100 GHz pulses emission by synchrotron mechanism of electrons accelerated to ultrarelativistic energies. The hard X-rays originate from inverse Compton scattering of the electrons on the synchrotron photons. Several crucial observational tests are needed for the understanding of the phenomenon, requiring high sensitivity and high time resolution (approx. 1 ms) simultaneous to high spatial resolution (0.1 arcsec) at f approx. 110 GHz and hard X-rays.

Kaufmann, P.↗

NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison w/ LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

Koshak, William↗

NASA NTRS1988

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Banks, H. T.↗