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At least 703 records · Page 39
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NASA NTRS1993

Applications of computer algebra to distributed parameter systems

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Storch, Joel A.↗
NASA NTRS1989

Numerical study of a delta planform with multiple jets in ground effect

The flow past a 60-deg delta wing equipped with two thrust-reverser jets near the inboard trailing edge has been analyzed by numerical solution of the 3D thin-layer Navier-Stokes equations. An implicit, partially flux-split, approximately-factored Navier-Stokes solver coupled with a multiple grid embedding scheme has been adapted to this problem. Studies of the impact of numerical parameters (e.g., grid refinement and dissipation levels), and flow-field parameters such as the height of the delta wing above the ground plane and the jet size on the solution, were performed. Results of these numerical studies indicate some challenges in the accurate resolution of complex 3D free shear layers and jets. Nevertheless, flow features such as jet deformation and ground vortex formation observed in experimental flow visualizations are captured. Further, comparisons with experimental data confirm the ability to simulate the loss of wing-borne lift, commonly referred to 'suckdown, as the delta planform flies at slow speeds in close proximity to the ground. Detailed analysis of the numerical results has also given additional insight into the structure of the ground vortex and the mechanisms of lift loss.

Chawla, K.↗
NASA NTRS2017

Quantitative EPMA Compositional Mapping of NWA 2995: Characterization, and Petrologic Interpretation of Mafic Clasts

We present the first fully quantitative compositional maps of lunar meteorite NWA 2995 using electron microprobe stage mapping, and compare selected clast mineralogy and chemistry. NWA 2995 is a feldspathic fragmental breccia containing numerous highland fine grained lithologies, including anorthosite, norite, olivine basalt, subophitic basalt, gabbro, KREEP-like basalt, granulitic and glassy impact melts, coarse-grained mineral fragments, Fe-Ni metal, and glassy matrix [1]. Chips of NWA 2995, representing these diverse materials, were analyzed by INAA and fused-bead electron-probe microanalysis (EPMA); comparison of analytical data suggests grouping of lunar meteorites NWA 2995, 2996, 3190, 4503, 5151, and 5152. The mean composition of NWA 2995 corresponds to a 2:1 mixture of feldspathic and mare material, with approximately 5% KREEP component [2]. Clast mineral chemistry and petrologic interpretation of paired stone NWA 2996 has been reported by Mercer et al. [3], and Gross et al. [4]. This study combines advances in quantitative EPMA compositional mapping and data analysis, as applied to selected mafic clasts in a polished section of NWA 2995, to investigate the origin of mafic lithic components and to demonstrate a procedural framework for petrologic analysis.

Carpenter, P. K.↗
NASA NTRS1981

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Noor, A. K.↗
NASA NTRS1981

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigenmode of the panel. In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths. The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.

Noor, A. K.↗
NASA NTRS2016

Elevated Aerosol Layers and Their Radiative Impact over Kanpur During Monsoon Onset Period

Accurate information about aerosol vertical distribution is needed to reduce uncertainties in aerosol radiative forcing and its effect on atmospheric dynamics. The present study deals with synergistic analyses of aerosol vertical distribution and aerosol optical depth (AOD) with meteorological variables using multisatellite and ground-based remote sensors over Kanpur in central Indo-Gangetic Plain (IGP). Micro-Pulse Lidar Network-derived aerosol vertical extinction (sigma) profiles are analyzed to quantify the interannual and daytime variations during monsoon onset period (May-June) for 2009-2011. The mean aerosol profile is broadly categorized into two layers viz., a surface layer (SL) extending up to 1.5 km (where sigma decreased exponentially with height) and an elevated aerosol layer (EAL) extending between 1.5 and 5.5 km. The increase in total columnar aerosol loading is associated with relatively higher increase in contribution from EAL loading than that from SL. The mean contributions of EALs are about 60%, 51%, and 50% to total columnar AOD during 2009, 2010, and 2011, respectively. We observe distinct parabolic EALs during early morning and late evening but uniformly mixed EALs during midday. The interannual and daytime variations of EALs are mainly influenced by long-range transport and convective capacity of the local emissions, respectively. Radiative flux analysis shows that clear-sky incoming solar radiation at surface is reduced with increase in AOD, which indicates significant cooling at surface. Collocated analysis of atmospheric temperature and aerosol loading reveals that increase in AOD not only resulted in surface dimming but also reduced the temperature (approximately 2-3 C) of lower troposphere (below 3 km altitude). Radiative transfer simulations indicate that the reduction of incoming solar radiation at surface is mainly due to increased absorption by EALs (with increase in total AOD). The observed cooling in lower troposphere in high aerosol loading scenario could be understood as a dynamical feedback of EAL-induced stratification of lower troposphere. Further, the observed radiative effect of EALs increases the stability of the lower troposphere, which could modulate the large-scale atmospheric dynamics during monsoon onset period. These findings encourage follow-up studies on the implication of EALs to the Indian summer monsoon dynamics using numerical models.

aerosol vertical distribution↗
NASA NTRS1999

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Keppenne, Christian L.↗
NASA NTRS2017

Precision Projector Laboratory: Detector Characterization with an Astronomical Emulation Testbed

As astronomical observations benefit from improved sensitivity, the effectiveness of scientific programs is becoming limited by systematics that often originate in poorly understood image sensor behavior. Traditional, bottom-up detector characterization methods provide one way to model underlying detector physics, and generate ever more faithful numerical simulations, but this approach is vulnerable to preconceptions and over-simplification. The alternative top-down approach is laboratory emulation, which enables observation, calibration, and analysis scenarios to be tested without relying on a complete understanding of the underlying physics. This complements detector characterization and simulation efforts by testing their validity. We describe a laboratory facility and experimental testbed that supports the emulation of a wide range of mission concepts such as gravitational weak lensing measurements by WFIRST and high precision spectrophotometry of transiting exoplanets by JWST. An Offner relay projects readily customizable "scenes" (e.g. stars, galaxies, spectra) with very low optical aberration over the full area of a typical optical or near infrared image sensor. f/8 and slower focal ratios may be selected, spanning those of most proposed space missions and approximating the point spread function (PSF) size of seeing limited ground based surveys. Diffraction limited PSFs are projected over a wide field of view and wavelength range to deliver highly predictable image patterns down to sub-pixel scales with stable intensity and fine motion control. The testbed enables realistic validation of detector performance on science-like images, which aids mission design and survey strategy, as well as targeted investigations of various detector effects.

Seshadri, Suresh↗
NASA NTRS1986

A refined shear deformation theory for the analysis of laminated plates

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Reddy, J. N.↗
NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗
NASA NTRS1997

NGC 5291: Implications for the Formation of Dwarf Galaxies

The possible formation and evolution of dwarf irregular galaxies from material derived from perturbed evolved galaxies is addressed via an H I study of a likely example, the peculiar system NGC 5291. This system, located in the western outskirts of the cluster Abell 3574, contains the lenticular galaxy NGC 5291 which is in close proximity to a disturbed companion and is flanked by an extensive complex of numerous knots extending roughly 4 min north and 4 min south of the galaxy. In an initial optical and radio study, Longmore et al. (1979, MNRAS, 188, 285) showed that these knots have the spectra of vigorous star-forming regions, and suggested that some may in fact be young dwarf irregular galaxies. High resolution 21-cm line observations taken with the VLA are presented here and reveal that the H I distribution associated with this system encompasses not only the entire N-S complex of optical knots, but also forms an incomplete ring or tail that extends approximately 3 min to the west. The H I associated with NGC 5291 itself shows a high velocity range; the Seashell is not detected. The formation mechanism for this unusual system is unclear and two models - a large, low-luminosity ram-swept disk, and a ram-swept interaction-are discussed. The H I in the system contains numerous concentrations, mostly along the N-S arc of the star-forming complexes, which generally coincide with one or more optical knots; the larger H I features contain several x 10(exp 9) solar mass of gas. Each of the knots is compared to a set of criteria designed to determine if these objects are bound against their own internal kinetic energy and are tidally stable relative to the host galaxy. An analysis of the properties of the H I concentrations surrounding the optical star-forming complexes indicates that at least the largest of these is a bound system; it also possesses a stellar component. It is suggested that this object is a genuinely young dwarf irregular galaxy that has evolved from the material associated with the system and that this entire complex contains several proto- or young dwarf irregular galaxies in various stages of development. We are therefore witnessing the early evolution of a number of genuinely young galaxies. Given the evident importance of the NGC 5291 system as a 'nursery' for young galaxies, careful modeling is required if we are to understand this remarkable galaxy.

Malphrus, Benjamin K.↗
NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
NASA NTRS1998

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗
NASA NTRS1984

Numerical simulation of the transonic flowfield for wing/nacelle configurations

An efficient grid-interfacing zonal algorithm has been developed for computing the three-dimensional transonic flow field about wing/nacelle multicomponent configurations. The algorithm uses the full-potential formulation and the AF2 fully-implicit approximate factorization scheme. The flow field position is computed using a component-adaptive grid approach in which separate grids are employed for the individual components in the multicomponent configuration, where each component grid is optimized for a particular geometry such as the wing or nacelle. The wing and nacelle component grids are allowed to overlap, and flow field information is transmitted from one grid to another through the overlap region using trivariate interpolation. This paper presents a discussion of the computational methods used to generate both the wing and nacelle component grids, the technique used to interface the component grids, and the method used to obtain the inviscid multicomponent flow field solution. Computed results and correlations with experiment are presented to illustrate application of the analysis.

Atta, E. H.↗
NASA NTRS1989

Application of Landsat Thematic Mapper data for coastal thermal plume analysis at Diablo Canyon

The possibility of using Landsat Thematic Mapper (TM) thermal data to derive absolute temperature distributions in coastal waters that receive cooling effluent from a power plant is demonstrated. Landsat TM band 6 (thermal) data acquired on June 18, 1986, for the Diablo Canyon power plant in California were compared to ground truth temperatures measured at the same time. Higher-resolution band 5 (reflectance) data were used to locate power plant discharge and intake positions and identify locations of thermal pixels containing only water, no land. Local radiosonde measurements, used in LOWTRAN 6 adjustments for atmospheric effects, produced corrected ocean surface radiances that, when converted to temperatures, gave values within approximately 0.6 C of ground truth. A contour plot was produced that compared power plant plume temperatures with those of the ocean and coastal environment. It is concluded that Landsat can provide good estimates of absolute temperatures of the coastal power plant thermal plume. Moreover, quantitative information on ambient ocean surface temperature conditions (e.g., upwelling) may enhance interpretation of numerical model prediction.

Gibbons, D. E.↗
NASA NTRS1974

Comparison of interference-free numerical results with sample experimental data for the AEDC wall-interference model at transonic and subsonic flow conditions

Numerical results obtained from two computer programs recently developed with NASA support and now available for use by others are compared with some sample experimental data taken on a rectangular-wing configuration in the AEDC 16-Foot Transonic Tunnel at transonic and subsonic flow conditions. This data was used in an AEDC investigation as reference data to deduce the tunnel-wall interference effects for corresponding data taken in a smaller tunnel. The comparisons were originally intended to see how well a current state-of-the-art transonic flow calculation for a simple 3-D wing agreed with data which was felt by experimentalists to be relatively interference-free. As a result of the discrepancies between the experimental data and computational results at the quoted angle of attack, it was then deduced from an approximate stress analysis that the sting had deflected appreciably. Thus, the comparisons themselves are not so meaningful, since the calculations must be repeated at the proper angle of attack. Of more importance, however, is a demonstration of the utility of currently available computational tools in the analysis and correlation of transonic experimental data.

Newman, P. A.↗
NASA NTRS1993

Three-dimensional analysis of anisotropic spatially reinforced structures

The material-adaptive three-dimensional analysis of inhomogeneous structures based on the meso-volume concept and application of deficient spline functions for displacement approximations is proposed. The general methodology is demonstrated on the example of a brick-type mosaic parallelepiped arbitrarily composed of anisotropic meso-volumes. A partition of each meso-volume into sub-elements, application of deficient spline functions for a local approximation of displacements and, finally, the use of the variational principle allows one to obtain displacements, strains, and stresses at anypoint within the structural part. All of the necessary external and internal boundary conditions (including the conditions of continuity of transverse stresses at interfaces between adjacent meso-volumes) can be satisfied with requisite accuracy by increasing the density of the sub-element mesh. The application of the methodology to textile composite materials is described. Several numerical examples for woven and braided rectangular composite plates and stiffened panels under transverse bending are considered. Some typical effects of stress concentrations due to the material inhomogeneities are demonstrated.

Bogdanovich, Alexander E.↗
NASA NTRS2022

Vicarious Calibration of the Long Near Infrared Band: Cross-Sensor Differences in Sensitivity

Numerous assumptions and approximations are employed when translating satellite-derived radiance to surface remote sensing reflectance (RRS) for ocean color applications. Among these is the vicarious calibration coefficient (g) of the “long” near infrared band (NIRL) used for atmospheric correction. For this band, the prelaunch calibration has always been deemed sufficient [thus g(NIRL) = 1.00] as long as other bands are vicariously calibrated. Recent research, however, suggests that Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua RRS time series is quite sensitive to g(NIRL) (and associated vicarious gains in other bands). In this work, we assessed the sensitivity of Visible Infrared Imaging Radiometer Suite onboard the Suomi National Polar-orbiting Partnership satellite (VIIRS/SNPP) RRS to NIRL calibration and compared our results to previous MODIS/Aqua and Sea-viewing Wide Field-of-View Sensor onboard OrbView2 (SeaWiFS)/OrbView2 analysis. In doing so, we note that g(NIRL) sensitivities of mission-averaged RRS time series are lower for VIIRS and Sea-WiFS, relative to MODIS. At the scale of monthly climatologies (MCs), however, all sensors show prominent g(NIRL) sensitivity with that of SeaWiFS being the most substantial. These findings informed simulation analyses, whereby we identified signal-tonoise ratio (SNR) and radiant path geometry, as well as their interaction, as having notable impacts on g(NIRL) sensitivity. As such, g(NIRL) sensitivity is a necessary consideration for reflectance uncertainty budgets, especially for sensors with higher NIR SNR or particular prevailing radiant path geometries. Given the geometry components embedded within g(NIRL) sensitivity, such studies should be coupled with cross-sensor intercalibrations [e.g., using simultaneous same view (SSV) measurements] toward minimizing NIRL errors between satellite instruments, but such efforts will not completely remediate remaining cross-sensor biases in RRS. Index Terms—Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua, ocean color, ocean gyres, Sea-viewing Wide Field-of-View Sensor onboard OrbView2 (SeaWiFS), system vicarious calibration (SVC), Visible Infrared Imaging Radiometer Suite onboard the Suomi National Polar-orbiting Partnership satellite (VIIRS/SNPP).

MODIS↗