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NASA NTRS1981

Alternative methods to smooth the Earth's gravity field

Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.

Jekeli, C.↗

NASA NTRS1984

An efficient approximate factorization implicit scheme for the equations of gasdynamics

An efficient implicit finite-difference algorithm for the gas dynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved while maintaining the same favorable stability characteristics and generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows about a NACA 0012 airfoil. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations. It is shown that the method offers advantages over the conventional Beam and Warming scheme and can retrofit existing Beam and Warming codes with minimal effort.

Barth, T. J.↗

NASA NTRS1985

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Barth, T. J.↗

NASA NTRS1985

Effects of upstream-biased third-order space correction terms on multidimensional Crowley advection schemes

The impact of upstream-biased corrections for third-order spatial truncation error on the stability and phase error of the two-dimensional Crowley combined advective scheme with the cross-space term included is analyzed, putting primary emphasis on phase error reduction. The various versions of the Crowley scheme are formally defined, and their stability and phase error characteristics are intercompared using a linear Fourier component analysis patterned after Fromm (1968, 1969). The performances of the schemes under prototype simulation conditions are tested using time-dependent numerical experiments which advect an initially cone-shaped passive scalar distribution in each of three steady nondivergent flows. One such flow is solid rotation, while the other two are diagonal uniform flow and a strongly deformational vortex.

Schlesinger, R. E.↗

NASA NTRS1987

Structural characterization and gas reactions of small metal particles by high resolution in-situ TEM (Transmission Electron Microscopy) and TED (Transmission Electron Diffraction)

The detection and size analysis of small metal particles supported on amorphous substrates becomes increasingly difficult when the particle size approaches that of the phase contrast background structures of the support. An approach of digital image analysis, involving Fourier transformation of the original image, filtering, and image reconstruction was studied with respect to the likelihood of unambiguously detecting particles of less than 1 nm diameter on amorphous substrates from a single electron micrograph.

Heinemann, K.↗

NASA NTRS1988

Temperature Fluctuations During Crystal Growth

Technique developed to deconvolve period and relative amplitude of fluctuations of heat flow inBridgman crystal growth. Temperature-measuring device with enough sensitivity and frequency response to make desired measurements inserted close as possible to substance monitored. Time-dependent temperature response recorded, and time domain response converted to frequency domain for further analysis. Fast fourier transform (FFT) of data on temperature oscillations shows particular behavior at some specific frequencies corresponding with striations, or defects observed on crystal. Useful procedure to help determine sources of some growth-induced crystalline defects. Other processes sensitive to small temperature fluctuations, such as diffusion, precipitation, and corrsion, benefit from technique.

Fripp, Archibald L., Jr.↗

NASA NTRS1987

Planetary studies; Proceedings of the Topical Meeting C3, Workshop III, and Symposium 8 of the Twenty-sixth COSPAR Plenary Meeting, Toulouse, France, June 30-July 11, 1986

Topics discussed in this issue include the atmospheres and ionospheres of planets and comets, future planetary missions, and latest results on Venus and Uranus missions. Papers are presented on the structure of the atmospheres of Mars and Venus below 100 kilometers, the structure of the atmospheres of Mars and Venus from the analysis of Fourier spectrometer measurements aboard Venera 15, physical parameters for the Saturn atmosphere computed by using Voyager data, hot hydrogen and deuterium in the exosphere of Venus, the theory and observations of cometary ionospheres, and the scientific goals of the Phobos mission. Additional papers are on the geological interpretation of a segment of Venus from radar images of the USSR spacecrafts Venera-15 and -16, the low-energy plasma in the Uranian magnetosphere, the initial estimates of Venus winds from ground-based radio tracking of the Vega balloons, the results of the Vega 1 balloon nephelometer experiment, and meteorological variations in the middle clouds of Venus from Vega balloon in situ measurements.

Keating, G. M.↗

NASA NTRS1989

Assessment of numerical techniques for unsteady flow calculations

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Hsieh, Kwang-Chung↗

NASA NTRS1989

A computer control system for the alternating gradient magnetometer

An alternating gradient magnetometer was interfaced to a computer for the automation of data taking. Using a fast Fourier transform analysis system data can be acquired and processed in real time. Data are stored on disk and can be recalled for plotting and further analysis. With the addition of a simple liquid nitrogen cryostat, magnetization measurements can be performed in the range from 300 to 77 K. Results are reported on three different types of piezoelectric transducers.

Garland, Michael M.↗

NASA NTRS1993

On waveform multigrid method

Waveform multigrid method is an efficient method for solving certain classes of time dependent PDEs. This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace analysis, practical convergence rate estimates of the waveform multigrid iterations are obtained. Experimental results show that the analysis yields accurate performance prediction.

Taasan, Shlomo↗

NASA NTRS1992

Fourier Transform Fabry-Perot Interferometer

We are developing a compact, rugged, high-resolution remote sensing instrument with wide spectral scanning capabilities. This relatively new type of instrument, which we have chosen to call the Fourier-Transform Fabry-Perot Interferometer (FT-FPI), is accomplished by mechanically scanning the etalon plates of a Fabry-Perot interferometer (FPI) through a large optical distance while examining the concomitant signal with a Fourier-transform analysis technique similar to that employed by the Michelson interferometer. The FT-FPI will be used initially as a ground-based instrument to study near-infrared atmospheric absorption lines of trace gases using the techniques of solar absorption spectroscopy. Future plans include modifications to allow for measurements of trace gases in the stratosphere using spectral lines at terahertz frequencies.

Snell, Hilary E.↗

NASA NTRS1993

Time-accurate Navier-Stokes calculations with multigrid acceleration

An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.

Melson, N. D.↗

NASA NTRS1993

Unsteady aerodynamic models for maneuvering aircraft

Forced oscillation tests over a large angle-of-attack range for an F-18 model are conducted in the NASA Langley 12-foot low-speed tunnel. The resulting dynamic longitudinal data are analyzed with an unsteady aerodynamic modeling method based on Fourier functional analysis and the indicial formulation. The method is extensively examined and improved to automate the calculation of model coefficients, and to evaluate more accurately the indicial integral. The results indicate that the general model equation obtained from harmonic test data in a range of reduced frequency is capable of accurately modeling the nonlinear responses with large hysteresis effect, except in the region where a delayed flow reattachment occurs at low angles of attack in down strokes. The indicial formulation is used to calculate the response to harmonic motion, harmonic ramp motion, constant-rate pitching motion and smaller-amplitude harmonic motion. The results show that more accurate results can be obtained when the motion starts from a low angle of attack where hysteresis effect is not important.

Hu, Chien-Chung↗

NASA NTRS1993

The source of 5 minute period photospheric umbral oscillations

We observed the oscillations in the umbrae of two sunspots, using the MCCD imaging spectrograph at the Mees Solar Observatory on Haleakala, Maui. We perform four spatial analyses of the umbral velocity and find that (1) there is more power traveling toward the center of the umbrae than leaving the center of the umbrae (this provides a direct measure of the absorption of p-modes by the sunspot umbrae); (2) the umbral oscillations display power in the same spatial and temporal frequency band as the quiet-sun oscillations; (3) Fourier-Bessel analysis of one umbra shows no obvious resonant frequencies which might represent natural oscillation modes; and (4) the centers of the umbrae have less rms velocity at high spatial wavenumber than the edges of the umbrae. We conclude: (1) the photospheric umbral oscillations are driven by a source external to the sunspot, the global p-mode oscillations; (2) there are no resonant frequencies in the oscillations; and (3) the absorption of acoustic waves occurs inside the umbrae.

Penn, M. J.↗

NASA NTRS1994

Apparatus and method for determining the mass density of a filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament, inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data, processing the data using a fast-fourier transform analysis, and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

NASA NTRS1997

Apparatus and Method for Determining the Mass Density of a Filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament. inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data. processing the data using a fast-fourier transform analysis. and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Diskin, Boris↗

NASA NTRS1997

Non-Invasive Measurement of Pulsatile Intracranial Pressures Using Ultrasound

Early detection of elevated intracranial pressure (ICP) will aid clinical decision-making for head trauma, brain tumor and other cerebrovascular diseases. Conventional methods, however, require surgical procedures which take time and are accompanied by increased risk of infection. Accordingly we have developed and refined a new ultrasound device to measure skull movements which are known to occur in conjunction with altered ICP. The principle of this device is based upon pulse phase locked loop (PPLL), which enables us to detect changes in distance on the order of microns between an ultrasound transducer on one side of the skull and the opposite inner surface of the cranium. The present study was designed to verify this measurement technique in cadavera. Transcranial distance was increased in steps of 10 mmHg from zero to 50 mmHg by saline infusion into the lateral ventricle of two cadavera. In separate experiments, pulsations of ICP with the amplitudes of zero to 2 mmHg were generated by rhythmic injections of saline using a syringe. When the ICP was stepwise increased from zero to 50 mmHg, transcranial distance increased in proportion with the ICP increase (y=12 x - 76, r=0.938), where y is changes in transcranial distance in microns and x is ICP in mmHg. In the data recorded while ICP pulsations were generated, fast Fourier transform analysis demonstrated that cranial pulsations were clearly associated with ICP pulsations. The results indicate that changes in transcranial distance is linearly correlated with those in ICP, and also that the PPLL device has sufficient sensitivity to detect transcranial pulsations which occur in association with the cardiac cycle. By analyzing the magnitude of cranial pulsations, we may be able to estimate the pressure-volume index in the cranium. As a result, estimates of intracranial compliance may be possible by using the PPLL device. Further studies are necessary in normal subjects and patients.

Ueno, Toshiaki↗