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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

SAGE 2-Umkehr case study of ozone differences and aerosol effects from October 1984 to April 1989

A comparison of 1262 cases of coincident ozone profiles derived from 666 Umkehrs at 17 different stations and 901 SAGE 2 profiles within 1000 km and 12 hours between October 1984 and April 1989 indicates the following layer percentage differences with 2-sigma error bars: layer three 14.6 plus/minus 3.3 percent, layer four 17.6 plus/minus 1.1 percent, layer five -1.3 plus/minus 0.5 percent, layer six -5.7 plus/minus 0.7 percent, layer seven -1.0 plus/minus 0.7 percent, layer eight 4.2 plus/minus 0.7 percent, and layer nine 6.8 plus/minus 1.2 percent. Comparing SAGE 2-Umkehr differences to SAGE 1 version 5.5-Umkehr differences shows SAGE 2 higher than or equal to SAGE 1 relative to Umkehr in all layers except layer three. Adjustment for this bias would produce trends derived from SAGE 2-SAGE 1 differences and Umkehr observations in the 1980s more nearly equal to each other in layers six, seven, and eight. A possible explanation of these differences is a systematic shift in the reference altitude between SAGE 1 and SAGE 2, but there is no independent evidence of this. While the shape of the vertical profile of differences at 17 individual Umkehr stations (mostly in mid-latitudes) is generally consistent at all stations except at Poker Flat, Seoul, and Lauder, significant variation does exists among the stations. The profile of mean difference is similar to previously observed differences between Umkehr and both SAGE 2 and SBUV and also to an eigenvector analysis, but with site-dependent amplitude discrepancies. Because of the close correspondence of stratospheric aerosol optical depth at the SAGE 2-measured 0.525 micron wavelength and the extrapolated 0.32 Umkehr wavelength determined in this study, we use the 0.525 micron data to determine the aerosol effect of Umkehr profiles. The aerosol errors to the Umkehr ozone amounts in percent ozone amount per 0.01 stratospheric aerosol optical depth range from plus 2 percent in layer six to minus 3 percent in layer nine. These results agree with previous theoretical and empirical studies within their respective error bounds in layers nine, eight, and five. The result in layer six differs significantly from previous works. In view of the fact that SAGE 2 and Umkehr produce different ozone retrievals in layers eight and nine and because the intra-layer correlation of SAGE 2 ozone and aerosol in layers eight and nine in non-zero, one must exercise some caution in attributing the entire SAGE 2-Umkehr differences in the upper layers to an aerosol effect.

Newchurch, M. J.↗
NASA NTRS1994

An analysis of spectral envelope-reduction via quadratic assignment problems

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

George, Alan↗
NASA NTRS1994

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Costiner, Sorin↗
NASA NTRS1995

An algorithm for the basis of the finite Fourier transform

The Finite Fourier Transformation matrix (F.F.T.) plays a central role in the formulation of quantum mechanics in a finite dimensional space studied by the author over the past couple of decades. An outstanding problem which still remains open is to find a complete basis for F.F.T. In this paper we suggest a simple algorithm to find the eigenvectors of F.T.T.

Santhanam, Thalanayar S.↗
NASA NTRS1994

Benchmark problems in computational aeroacoustics

A recent directive at NASA Langley is aimed at numerically predicting principal noise sources. During my summer stay, I worked with high-order ENO code, developed by Dr. Harold Atkins, for solving the unsteady compressible Navier-Stokes equations, as it applies to computational aeroacoustics (CAA). A CAA workshop, composed of six categories of benchmark problems, has been organized to test various numerical properties of code. My task was to determine the robustness of Atkins' code for these test problems. In one category, we tested the nonlinear wave propagation of the code for the one-dimensional Euler equations, with initial pressure, density, and velocity conditions. Using freestream boundary conditions, our results were plausible. In another category, we solved the linearized two-dimensional Euler equations to test the effectiveness of radiation boundary conditions. Here we utilized MAPLE to compute eigenvalues and eigenvectors of the Jacobian given variable and flux vectors. We experienced a minor problem with inflow and outflow boundary conditions. Next, we solved the quasi one dimensional unsteady flow equations with an incoming acoustic wave of amplitude 10(exp -6). The small amplitude sound wave was incident on a convergent-divergent nozzle. After finding a steady-state solution and then marching forward, our solution indicated that after 30 periods the acoustic wave had dissipated (a period is time required for sound wave to traverse one end of nozzle to other end).

Porter-Locklear, Freda↗
NASA NTRS1993

A tool for manual endmember selection and spectral unmixing

Sampling a continuous radiance spectrum in many narrow contiguous spectral bands results in a high covariance between the bands. Hence, the true dimensionality of imaging spectrometer data is not determined by the number of spectral bands, but by the number of spectrally unique signatures whose mixtures reproduce the spectral variance observed in an image. Methods to unmix high dimensional multispectral data use principal components analysis to reduce the dimensionality. The variance of the spectral data is modeled as a linear combination of a finite set of endmembers in the space of the eigen-vectors that account for most of the variance. The number and characteristics of these endmembers are determined not only by the number and characteristics of the spectrally unique materials on the surface but also by processes (e.g., illumination, atmospheric scattering and absorption) affecting the signal received by the sensor. Selection of endmember spectra has typically been from a library. However, since most libraries are incomplete and do not account for the processes mentioned above, we have devised a computer display that allows researchers to explore interactively the eigenvector space of a representative and mean-corrected subset of the image data in search of extreme spectra to designate as endmembers. This display, which is based on parallel coordinates, is unique in the area of multidimensional visualization in that it includes not only a passive view of higher dimensional data but also the capability to interact and move geometrical objects in higher dimensional spaces.

Bateson, C. Ann↗
NASA NTRS1995

Separation analysis, a tool for analyzing multigrid algorithms

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

Costiner, Sorin↗
NASA NTRS1994

Principal modes of atmospheric circulation anomalies associated with global angular momentum fluctuations

This paper provides a description of the variability of global atmospheric angular momentum (GAM) and its relationship with principal modes of three-dimensional atmospheric circulation anomalies. The data used are 5-day mean global wind fields from the European Centre for Medium-Range Weather Forecasts initialized dataset for 1980-1989. Significant seasonal variation of GAM is observed with maxima in April and November and a minimum during late July. The amplitude of the annual cycle is largest in the upper troposphere and decreases toward the surface. Although the lower tropospheric contribution to the total angular momentum is relatively small, its annual cycle is out of phase with those of the upper atmosphere and GAM. Also identified is a distinct semiannual component, with double peaks appearing in April and November. This signal is most noticeable in the upper troposphere above the 300-mb level. The principal modes of zonal-mean angular momentum and meridional circulation anomalies and their coupled modes are obtained by using empirical orthogonal function analysis and singular value decomposition. It is shown that the leading modes of the angular momentum and meridional circulation are coupled with each other and are responsible for much of the variability in GAM. The coupled modes represent fluctuations of upper-level subtropical zonal flow, which are linked to the modulation of Hadley circulation intensity in both hemispheres. It is found that GAM is highly correlated with the first eigenvector of upper-level streamfunction anomalies, which consists of a superrotational flow in the tropics and subtropics, except over the central Pacific where a 'blocked' flow with two subtropical anticyclonic circulation cells straddling the equator is found. Much of the blocked flow is due to the establishment of dipole anomalies in the velocity potential with centers over the central Pacific and the Maritime Continent on the interannual time scale. On the intraseasonal time scale, GAM fluctuation is dominated by superrotational flow in the tropics, with the blocked flow present to a much lesser extent. The associated velocity potential anomaly has a weak dipole structure with centers over the Indian Ocean and the eastern Pacific. The implications of the above results on the total angular momentum balance of the earth-atmosphere system are also discussed.

Kang, In-Sik↗
NASA NTRS1994

Passive microwave observations of the Wedell Sea during austral winter and early spring

The results of multispectral passive microwave observations (6.7 to 90-GHz) are presented from the cruises of the FS Polarstern in the Weddell Sea from July to December 1986. This paper includes primarily the analysis of radiometric observations taken at ice station sites. Averaged emissivity spectra for first-year (FY) ice were relatively constant throughout the experiment and were not statistically different from FY ice signatures in the Arctic. Detailed ice characterization was carried out at each site to compare the microwave signatures of the ice with the physical properties. Absorption optical depths of FY ice were found to be sufficiently high that only the structure in the upper portions of the ice contributed significantly to interstation emissivity variations. The emissivities at 90-GHz, e(90), had the greatest variance. Both e(90) at vertical polarization and GR(sub e)(90, 18.7)(defined as (e(sub V)(90)-e(sub V)(18.7))/e(sub V)(90 + e(sub V)(18.7)) depended on the scattering optical depth which is a function of the snow grain diameter and layer thickness. The variance showed a latitude dependence and is probably due to an increase in the strength of snow metamorphism nearer the northern edge of the ice pack. The contribution of variations of near-surface brine volume to the emissivity was not significant over the range of values encountered at the station sites. Emissivity spectra are presented for a range of thin ice types. Unsupervised principal component analysis produced three significant eigenvectors and showed a separation among four different surface types: open water, thin ice, FY ice, and FY ice with a thick snow cover. A comparison with SMMR satellite data showed that average ice concentrations derived from the ship's ice watch log were consistent with the satellite concentrations. The surface based emissivities for FY ice were also compared with emissivities calculated from scanning multichannel microwave radiometer (SMMR) satellite radiances. Best agreement was found at 6.7 and 10-GHz, while at 18 and 37-GHz, SMMR emissivities were slightly lower than surface based results. For the three lower frequencies agreement was found within a confidence limit of 95% and for 37-GHz within about 90%.

Grenfell, T. C.↗
NASA NTRS1994

Lifetimes and eigenstates in atmospheric chemistry

The time scales and mode of the atmosphere's response to chemical perturbations are defined by the eigenvalues and eigenvectors of the system. The eigenstates of a simplified one-box CH4-CO-OH system are analyzed. The longest time constant (smallest eigenvalue) always exceeds the lifetime defined by the steady-state loss frequency for CH4, the longest lived gas. Thus, the extent of a CH4 perturbation -- the methane response time -- is always longer than predicted by the steady-state lifetime and is independent of size of the perturbation in the linear limit. This lengthening of the atmospheric recovery time can be diagnosed by how close we are to a chemically unstable troposphere, i.e., how much OH production exceeds that minimum needed to oxidize just the global emissions of CH4, CO, and other hydrocarbons and species.

Prather, Michael J.↗
NASA NTRS1993

Linear static structural and vibration analysis on high-performance computers

Parallel computers offer the oppurtunity to significantly reduce the computation time necessary to analyze large-scale aerospace structures. This paper presents algorithms developed for and implemented on massively-parallel computers hereafter referred to as Scalable High-Performance Computers (SHPC), for the most computationally intensive tasks involved in structural analysis, namely, generation and assembly of system matrices, solution of systems of equations and calculation of the eigenvalues and eigenvectors. Results on SHPC are presented for large-scale structural problems (i.e. models for High-Speed Civil Transport). The goal of this research is to develop a new, efficient technique which extends structural analysis to SHPC and makes large-scale structural analyses tractable.

Baddourah, M. A.↗
NASA NTRS1995

Spectral ordering techniques for incomplete LU preconditoners for CG methods

The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

Clift, Simon S.↗
NASA NTRS1995

Minimization of the Vibration Energy of Thin-Plate Structures and the Application to the Reduction of Gearbox Vibration

While the vibration analysis of gear systems has been developed, a systematic approach to the reduction of gearbox vibration has been lacking. The technique of reducing vibration by shifting natural frequencies is proposed here for gearboxes and other thin-plate structures using the theories of finite elements, modal analysis, and optimization. A triangular shell element with 18 degrees of freedom is developed for structural and dynamic analysis. To optimize, the overall vibration energy is adopted as the objective function to be minimized at the excitation frequency by varying the design variable (element thickness) under the constraint of overall constant weight. Modal analysis is used to determine the sensitivity of the vibration energy as a function of the eigenvalues and eigenvectors. The optimum design is found by the gradient projection method and a unidimensional search procedure. By applying the computer code to design problems for beams and plates, it was verified that the proposed method is effective in reducing vibration energy. The computer code is also applied to redesign the NASA Lewis gear noise rig test gearbox housing. As one example, only the shape of the top plate is varied, and the vibration energy levels of all the surfaces are reduced, yielding an overall reduction of 1/5 compared to the initial design. As a second example, the shapes of the top and two side plates are varied to yield an overall reduction in vibration energy of 1/30.

Inoue, Katsumi↗
NASA NTRS1994

Structural Health Monitoring of Large Structures

This paper describes a damage detection and health monitoring method that was developed for large space structures using on-orbit modal identification. After evaluating several existing model refinement and model reduction/expansion techniques, a new approach was developed to identify the location and extent of structural damage with a limited number of measurements. A general area of structural damage is first identified and, subsequently, a specific damaged structural component is located. This approach takes advantage of two different model refinement methods (optimal-update and design sensitivity) and two different model size matching methods (model reduction and eigenvector expansion). Performance of the proposed damage detection approach was demonstrated with test data from two different laboratory truss structures. This space technology can also be applied to structural inspection of aircraft, offshore platforms, oil tankers, ridges, and buildings. In addition, its applications to model refinement will improve the design of structural systems such as automobiles and electronic packaging.

Kim, Hyoung M.↗
NASA NTRS1996

Coherent States on Riemann Surfaces as m-Photon States

Coherent states on the m-sheeted sphere (for the SU(2) group) are used to define analytic representations. The corresponding generators create and annihilate clusters of m-photons. Non-linear Hamiltonians that contain these generators are considered and their eigenvectors and eigenvalues are explicitly calculated. The Holstein-Primakoff and Schwinger formalisms in this context are also discussed.

Vourdas, A.↗
NASA NTRS1996

Predictions of Control Inputs, Periodic Responses and Damping Levels of an Isolated Experimental Rotor in Trimmed Flight

Since the early 1990s the Aeroflightdynamics Directorate at the Ames Research Center has been conducting tests on isolated hingeless rotors in hover and forward flight. The primary objective is to generate a database on aeroelastic stability in trimmed flight for torsionally soft rotors at realistic tip speeds. The rotor test model has four soft inplane blades of NACA 0012 airfoil section with low torsional stiffness. The collective pitch and shaft tilt are set prior to each test run, and then the rotor is trimmed in the following sense: the longitudinal and lateral cyclic pitch controls are adjusted through a swashplate to minimize the 1/rev flapping moment at the 12 percent radial station. In hover, the database comprises lag regressive-mode damping with pitch variations. In forward flight the database comprises cyclic pitch controls, root flap moment and lag regressive-mode damping with advance ratio, shaft angle and pitch variations. This report presents the predictions and their correlation with the database. A modal analysis is used, in which nonrotating modes in flap bending, lag bending and torsion are computed from the measured blade mass and stiffness distributions. The airfoil aerodynamics is represented by the ONERA dynamic stall models of lift, drag and pitching moment, and the wake dynamics is represented by a state-space wake model. The trim analysis of finding, the cyclic controls and the corresponding, periodic responses is based on periodic shooting with damped Newton iteration; the Floquet transition matrix (FTM) comes out as a byproduct. The stabillty analysis of finding the frequencies and damping levels is based on the eigenvalue-eigenvector analysis of the FTM. All the structural and aerodynamic states are included from modeling to trim analysis. A major finding is that dynamic wake dramatically improves the correlation for the lateral cyclic pitch control. Overall, the correlation is fairly good.

Gaonkar, G. H.↗
NASA NTRS1990

A Shifted Block Lanczos Algorithm 1: The Block Recurrence

In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

Grimes, Roger G.↗
NASA NTRS1997

HARP: A Dynamic Inertial Spectral Partitioner

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effecfive in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their wide-spread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigerivectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel WI version of HARP has also been implemented on IBM SP2 and Cray T3E. Parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications.

Simon, Horst D.↗