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NASA NTRS1970

Spatial cyclotron damping

To examine spatial electron cyclotron damping in a uniform Vlasov plasma, it is noted that the plasma response to a steady-state transverse excitation consists of several terms (dielectric-pole, free-streaming, and branch-cut), but that the cyclotron-damped pole term is the dominant term for z l = c/w sub ce provided (w sub pe/w sub ce) squared (c/a) is much greater than 1. If the latter inequality does not hold, then the free-streaming and branch-cut terms persist well past z = c/w sub ce as w sub 1 approaches w sub ce, making experimental measurement of cyclotron damping essentially impossible. Considering only (w sub pe/w sub ce) squared (c/a) is much greater than 1, it is shown how collisional effects should be estimated and how a finite-width excitation usually has little effect on the cyclotron-damped part of the response. Criteria is established concerning collisional damping, measurable damping length sizes, and allowed uncertainty in the magnetic field Beta. Results of numerical calculations, showing the regions in the appropriate parameter spaces that meet these criteria, are presented. From these results, one can determine the feasibility of, or propose parameter values for, an experiment designed to measure spatial cyclotron damping. It is concluded that the electron temperature T sub e should be at least 1 ev., and preferably 10 ev. or higher, for a successful experiment.

Olson, C. L.↗

NASA NTRS1995

A high spectral resolution VLA search for H I absorption towards A496, A1795, and A2584

In this paper, we present the results of a Very Large Array (VLA) search for H I absorption with high spectral resolution (1.6 km/s) towards A496, A1795, A2584, and A2597. These observations are well matched to the properties of cold, optically thick H I clouds, where the line width is given by the width of an individual cloud rather than the dispersion in an ensemble of clouds. We do not detect any H I absorption with narrow linewidths in these clusters. Our limits mainly apply to clouds which are larger than a few tenths parsec-i.e., if the clouds are much smaller than the background radio source and have a low covering factor in velocity space, they could still escape detection. The estimated limits on column density (for clouds in this regime of parameter space) are 2-3 orders of magnitude less than the 10(exp 21)/sq cm required to explain the x-ray absorption seen in some cooling flow clusters. The combination of our high spectral resolution H I absorption searches with the existing lower spectral resolution H I absorption searches and the searches for H I emission makes it unlikely that atomic hydrogen is the dominant component of the cold x-ray absorbing gas in the inter-cloud medium (ICM).

O'Dea, Christopher P.↗

NASA NTRS2007

Sensitivity Testing of the NSTAR Ion Thruster

During the Extended Life Test of the DS1 flight spare ion thruster, the engine was subjected to sensitvity testing in order to characterize the macroscopic dependence of discharge chamber sensitivity to a +\-3% vatiation in main flow, cathode flow and beam current, and to +\5% variation in beam and accelerator voltage, was determined for the minimum- (THO), half- (TH8) and full power (TH15) throttle levels. For each power level investigared, 16 high/low operating conditions were chosen to vary the flows, beam current, and grid voltages in in a matrix that mapped out the entire parameter space. The matrix of data generated was used to determine the partial derivative or senitivity of the dependent parameters--discharge voltage, discharge current, discharge loss, double-to-single-ion current ratio, and neutralizer-keeper voltage--to the variation in the independent parameters--main flow, cathode flow, beam current, and beam voltage. The sensititivities of each dependent parameter with respect to each independent parameter were determined using a least-square fit routine. Variation in these sensitivities with thruster runtime was recorded over the duration of the ELT, to detemine if discharge performance changed with thruster wear. Several key findings have been ascertained from the sensitivity testing. Discharge operation is most sensitve to changes in cathode flow and to a lesser degree main flow. The data also confirms that for the NSTAR configuration plasma production is limited by primary electron input due to the fixed neutral population. Key sensitivities along with their change with thruster wear (operating time) will be presented. In addition double ion content measurements with an ExB probe will also be presented to illustrate beam ion production and content sensitivity to the discharge chamber operating parameteres.

electric propulsion↗

NASA NTRS1982

The dependence of the shape and stability of captive rotating drops on multiple parameters

Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Ungar, L. H.↗

NASA NTRS2004

Switching LPV Control for High Performance Tactical Aircraft

This paper examines a switching Linear Parameter-Varying (LPV) control approach to determine if it is practical to use for flight control designs within a wide angle of attack region. The approach is based on multiple parameter-dependent Lyapunov functions. The full parameter space is partitioned into overlapping subspaces and a family of LPV controllers are designed, each suitable for a specific parameter subspace. The hysteresis switching logic is used to accomplish the transition among different parameter subspaces. The proposed switching LPV control scheme is applied to an F-16 aircraft model with different actuator dynamics in low and high angle of attack regions. The nonlinear simulation results show that the aircraft performs well when switching among different angle of attack regions.

Lu, Bei↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle/Multi-Pixel Polarimetric Measurements

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth's atmosphere.

linearization↗

NASA NTRS2014

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

adjoint methods↗

NASA NTRS1999

CONSTELL: NASA's Satellite Constellation Model

The CONSTELL program represents an initial effort by the orbital debris modeling group at NASA/JSC to address the particular issues and problems raised by the presence of LEO satellite constellations. It was designed to help NASA better understand the potential orbital debris consequences of having satellite constellations operating in the future in LEO. However, it could also be used by constellation planners to evaluate architecture or design alternatives that might lessen debris consequences for their constellation or lessen the debris effects on other users of space. CONSTELL is designed to perform debris environment projections rapidly so it can support parametric assessments involving either the constellations themselves or the background environment which represents non-constellation users of the space. The projections need to be calculated quickly because a number of projections are often required to adequately span the parameter space of interest. To this end CONSTELL uses the outputs of other NASA debris environment models as inputs, thus doing away with the need for time consuming upfront calculations. Specifically, CONSTELL uses EVOLVE or ORDEM96 debris spatial density results as its background environment, debris cloud snapshot templates to simulate debris cloud propagation, and time dependent orbit profiles of the intact non- functional constellation spacecraft and upper stages. In this paper the environmental consequences of the deployment of particular LEO satellite constellations using the CONSTELL model will be evaluated. Constellations that will undergo a parametric assessment will reflect realistic parameter values. Among other results the increase in loss rate of non-constellation spacecraft, the number of collisions involving constellation elements, and the replacement rate of constellation satellites as a result of debris impact will be presented.

Theall, Jeffrey R.↗

NASA NTRS2004

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Astronomical objects known as planetary nebulae (PNe) consist of a shell of gas expelled by an aging medium-sized star as it makes its transition from a red giant to a white dwarf. In many cases this gas shell can be approximately described as a prolate ellipsoid. Knowledge of the physics of ionization processes in this gaseous shell enables us to construct a model in three dimensions (3D) called the Ionization-Bounded Prolate Ellipsoidal Shell model (IBPES model). Using this model we can generate synthetic nebular images, which can be used in conjunction with Hubble Space Telescope (HST) images of actual PNe to perform Bayesian model estimation. Since the IBPES model is characterized by thirteen parameters, model estimation requires the search of a 13-dimensional parameter space. The 'curse of dimensionality,' compounded by a computationally intense forward problem, makes forward searches extremely time-consuming and frequently causes them to become trapped in local solutions. We find that both the speed and of the search can be improved by judiciously reducing the dimensionality of the search space. Our basic approach employs a hierarchy of models of increasing complexity that converges to the IBPES model. Earlier studies establish that a hierarchical sequence converges more quickly, and to a better solution, than a search relying only on the most complex model. Here we report results for a hierarchy of five models. The first three models treat the nebula as a 2D image, while the last two models explore its characteristics as a 3D object and enable us to characterize the physics of the nebula. This five-model hierarchy is applied to HST images of ellipsoidal PNe to estimate their geometric properties and gas density profiles.

Huyser, Karen A.↗

NASA NTRS2012

Astrophysical Model Selection in Gravitational Wave Astronomy

Theoretical studies in gravitational wave astronomy have mostly focused on the information that can be extracted from individual detections, such as the mass of a binary system and its location in space. Here we consider how the information from multiple detections can be used to constrain astrophysical population models. This seemingly simple problem is made challenging by the high dimensionality and high degree of correlation in the parameter spaces that describe the signals, and by the complexity of the astrophysical models, which can also depend on a large number of parameters, some of which might not be directly constrained by the observations. We present a method for constraining population models using a hierarchical Bayesian modeling approach which simultaneously infers the source parameters and population model and provides the joint probability distributions for both. We illustrate this approach by considering the constraints that can be placed on population models for galactic white dwarf binaries using a future space-based gravitational wave detector. We find that a mission that is able to resolve approximately 5000 of the shortest period binaries will be able to constrain the population model parameters, including the chirp mass distribution and a characteristic galaxy disk radius to within a few percent. This compares favorably to existing bounds, where electromagnetic observations of stars in the galaxy constrain disk radii to within 20%.

hierarchical↗

NASA NTRS1983

Computational methods for estimation of parameters in hyperbolic systems

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

Banks, H. T.↗

NASA NTRS1992

Aircraft ride quality controller design using new robust root clustering theory for linear uncertain systems

The aspect of controller design for improving the ride quality of aircraft in terms of damping ratio and natural frequency specifications on the short period dynamics is addressed. The controller is designed to be robust with respect to uncertainties in the real parameters of the control design model such as uncertainties in the dimensional stability derivatives, imperfections in actuator/sensor locations and possibly variations in flight conditions, etc. The design is based on a new robust root clustering theory developed by the author by extending the nominal root clustering theory of Gutman and Jury to perturbed matrices. The proposed methodology allows to get an explicit relationship between the parameters of the root clustering region and the uncertainty radius of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The bounds derived on the parameter perturbation for robust root clustering are then used in selecting the robust controller.

Yedavalli, R. K.↗

NASA NTRS2011

Gravitational-Wave Data Analysis with Spinning Merger-Ringdown Waveforms

The recent availability of high-quality, gravitational merger-ringdown waveforms from spinning black-hole systems has made possible the development of multi-mode GW templates for use in data-analysis studies of current and proposed interferometric GW detectors. We report on recent work at NASA Goddard, analyzing the most significant modes from aligned-spin black-hole-binary mergers. From these, we have developed time-domain merger-ringdown GW templates covering the aligned-spin portion of parameter space. We also discuss how using the full information content of aligned-spin mergers can significantly reduce uncertainties in some parameters, emphasizing the significant gains possible in the last stages of merger, inaccessible to inspiral-only post-Newtonian templates.

Kelly Bernard J.↗

NASA NTRS2024

Development of a Data Fusion Methodology for Lineload Aerodynamic Databases for a Launch Vehicle during Liftoff and Transition

The need for databases for the distributed loading on launch vehicles during the early portion of flight necessitates the use of expensive computational flows in regimes where wake effects dominate. While also being expensive, this is a regime that computational tools tend to historically have problems simulating accurately. To help tackle this problem, a method of data fusion to combine computational results to wind tunnel derived force and moment data is developed. Using this method, significant reduction in computational costs and increases in confidence of the final product is possible and has been used to generate several databases for the Space Launch System (SLS) at NASA. While the full details of database generation are not part of this work, the crucial method at its core is developed here. Two SLS geometries are used throughout the work to demonstrate the techniques. These are two of the larger geometries and represent both planned crewed missions to the Moon as well as potential cargo missions to deep space. The method uses principal component analysis (PCA) to generate a reduced ordered model (ROM) to help fill in the full parameter space. Other similar techniques are explored, but were not found to have a significant result on the predictions of the ROM. Because the full number of components are kept to generate the model, this lack of difference is expected. This method is then extended to ensure that predicted surfaces match trusted force and moment data derived from wind tunnel testing. This extension is done by setting up a constrained optimization problem in order to minimize the deviation from the surface resolved computational data while still integrating to the desired values. When generating the constrained optimization problem, a weighting factor to balance these competing needs is introduced. The work compares previously introduced weighting terms from similar work to the proposed terms and shows that the previously used terms do not have as desirable behavior in this flow regime. This method is then expanded by developing a technique to incorporate uncertainty quantification into the developed data fusion methodology. This expansion takes a two pronged approach. One examines transferring the uncertainties in the force and moment database and characterizes how those adjustments change the predicted lineloads. The second looks at model form error and looks how rebuilding the model using slightly different data changes the predictions. These two terms are then combined in order to create an uncertainty model that takes both effects into account. The limitations of the proposed methods is then discussed as well as possible techniques to address these shortcomings.

Launch Vehicles↗

NASA NTRS1994

Viscosity estimates for the crust and upper mantle from patterns of lacustrine shoreline deformation in the Eastern Great Basin

The deformed shorelines of Lake Bonneville constitute a classic source of information on lithospheric elastic thickness and upper mantle viscosity. We describe and apply a new model to a recently augmented data set. New data better constrain both the complex spatio-temporal pattern of the lake load and the crustal deformation response to that load. The history of lake level fluctuations has been significantly refined and somewhat modified. This is due to both more radiocarbon dates from within the Bonneville basin and to an improved calibration of the radiocarbon timescale itself. The data which constrain the crustal deformation pattern consist of ages and shoreline elevations from several hundred points which sample three major levels of Lake Bonneville and corresponding elevations from the high stands of three smaller lakes situated to the west of Lake Bonneville. The geometry of the Earth model incorporates an arbitrary number of layers overlying a half-space, and the rheology of each level can accommodate an arbitrary number of Maxwell viscoelastic elements in parallel. The inverse modeling comprises three complementary approaches: for the simplest configurations, we performed a direct search of the parameter space and delineated the irregular boundary of the subspace of acceptable models. For more complex configurations, we constrained the elastic parameters to their seismically determined values and then solved for viscosity versus depth profiles by either expressing the log(viscosity) versus log(depth) profile as a series of specially constructed orhtogonal polynomials, or by allowing each of 8-10 layers (plus the half-space) to have an independently determined viscosity. We found that the data do not strongly support (nor can they conclusively exclude) a more complex rheology than simple Maxwell viscoelasticity. The orthogonal polynomial solution exhibits an essentially monotonic decrease in viscosity with depth.

Bills, Bruce G.↗

NASA NTRS1980

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

Geisler, J. E.↗

NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

Fluid reduced-order models (ROMs) which capture the flow physics within the problem's physical domain are usually constrained in accuracy to only the parameter points, e.g. Reynolds and Mach numbers, at which reference data was provided. Interpolation-focused quantity-of-interest ROMs are often structured differently and fail to provide flow volume data with the same quality - if at all. In this paper, techniques which reside at the intersection of these two ROM schools - flow physics ROMs which can be interpolated within a parameter space of interest - are explored. Using a combination of existing and novel techniques, emergent physics are identified using a fluid ROM at parameter points which are not provided in the ROM's training data.

uncertainty quantification↗

NASA NTRSDate not supplied

Quantifying Emergent Fluid Dynamics Using Reynolds-Interpolated Fluid Reduced-order Models

uncertainty quantification↗