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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Can we identify lensed gamma-ray bursts?

A gravitationally lensed gamma-ray burst (GRB) would appear as multiple bursts with identical light curves, separated in time and differing only by the scaling of their amplitudes. In reality, the detected bursts will be noisy, and therefore they may be difficult to identify as lensed images. Furthermore, faint, intrinsically similar, yet distinct light curves may be falsely identified as lensing events. In this paper we develop two statistical tests to distinguish noisy burst light curves. We use Fourier analysis techniques to analyze the signals for both intrinsic variability and variability due to noise. We are able to determine the noise level, and we compare the bursts only at frequency channels that are signal dominated. Utilizing these methods, we are able to make quantitative statements about whether two bursts are distinct. We apply these statistics to scaled versions of two subbursts of GRB 910503 -- subbursts previously investigated by Wambsganss using a different statistical test. We find that our methods are able to distinguish these bursts at slightly smaller amplitudes than those at which Wambsganss's method succeeds. We then apply our techniques to 'candidate' lensing events taken from the Burst and Transient Source Experiment (BATSE) catalog, and we find that nearly all of them, except for the very shortest ones (durations approx. less than 3 sec), are distinguishable. We therefore expect that a majority of bursts will be distinguishable from one another.

Nowak, Michael A.↗
NASA NTRS1995

Lightning-channel morphology by return-stroke radiation field waveforms

Simultaneous video and wideband electric field recordings of 32 cloud-to-ground lightning flashes in Florida were analyzed to show the formation of new channels to ground can be detected by examination of the return-stroke radiation fields alone. The return-stroke E and dE/dt waveforms were subjectively classified according to their fine structure. Then the video images were examined field by field to identify each waveform with a visible channel to ground. Fifty-five correlated waveforms and channel images were obtained. Of these, all 34 first-stroke waveforms (multiple jagged E peaks, noisy dE/dt), 8 of which were not radiated by the chronologically first stroke in the flash, came from new channels to ground (not previously seen on video). All 18 subsequent-stroke waveforms (smoothly rounded E and quiet dE/dt after initial peak) were radiated by old channels (illuminated by a previous stroke). Two double-ground waveforms (two distinct first-return-stroke pulses separated by tens of microseconds or less) coincided with video fields showing two new channels. One `anomalous-stroke' waveform (beginning like a first stroke and ending like a subsequent) was produced by a new channel segment to ground branching off an old channel. This waveform classification depends on the presence or absence of high-frequency fine structure. Fourier analysis shows that first-stroke waveforms contain about 18 dB more spectral power in the frequency interval from 500 kHz to at least 7 MHz than subsequent-stroke waveforms for at least 13 microseconds after the main peak.

Willett, J. C.↗
NASA NTRS1995

Two-dimensional structure of slow shocks

The two-dimensional (2-D) structure of switch-off slow magnetosonic shocks is investigated using an electromagnetic hybrid (fluid electrons, kinetic ions) code. It is shown that the basic physical processes occurring at 1-D slow shocks are also operative in 2-D. Specifically, the interaction between the upstream ions and those streaming away from the shock results in the excitation of Alfven/ions-cyclotron (AIC) waves. Depending on the plasma parameters, these waves may either stay in the upstream or convect back into the shock resulting in a non-steady shock behavior which prevents the formation of a trailing wave train. Despite this similarity, some slow shocks which are steady in 1-D are found to be non-steady in 2-D. Fourier analysis of the waves downstream of non-steady shocks identifies them as AIC, demonstrating that the waves remain on the same branch as they convect from upstream into the downstream region.

Omidi, N.↗
NASA NTRS1994

Direct calculations of waves in fluid flows using high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expression for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations. The numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the Courant-Friedrichs-Lewy (CFL) limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about six - eight grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 - 300 time steps. Three numerical examples of waves in compressible flow are included: (1) sound propagation in a duct with linear shear, (2) linear wave growth in a compressible free shear layer, and (3) vortex pairing in a compressible free shear layer perturbed at two frequencies.

Yu, Sheng-Tao↗
NASA NTRS1998

Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.

Rubinstein, Robert↗
NASA NTRS1999

HRDI Observations of Inertia-Gravity Waves in the Mesosphere and Lower Thermosphere

Vertical profiles of High-resolution Doppler imager (HRDI) mesospheric winds have small-scale structure (vertical wavelengths between 10 and 20 km) that is virtually always present. Fourier analysis of HRDI zonal and meridional wind profiles have been carried out, and the spectral characteristics are sorted by latitude, month and local time. Power spectral density (PSD) exhibits a universal exp(-km) structure in the 10-20km wavelength regime, with K lying between 2 and 3. The observed PSD for wavelengths between 10 and 20 km is a factor of 3 higher than a null spectrum constructed from HRDI reported error bars multiplied by randomly varying numbers between -1 and +1. Stokes parameters were consolidated by month into Northern and Southern hemisphere middle and high latitudes belts (40-72 degrees), tidal belts (32-16 degrees) and a tropical belt (8S-8N). Vertical waves between 10 and 15 km in wavelength are about 10-15% polarized everywhere. The inferred propagation direction in the middle and high latitude Southern hemisphere is predominantly meridional during solstice, and significantly more zonal during equinoxes. In the tropical belt, the wave orientations are nearly North-South during solstices, with a slightly higher east-west component during equinox. In the tidal belts where the background wind includes a strong meridional tidal wind, the preferred wave orientation has a significant zonal component during equinox. These findings are consistent with the interpretation of wave filtering by the background wind.

Lieberman, Ruth S.↗
NASA NTRS2001

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗
NASA NTRS2002

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Beggs, John H.↗
NASA NTRS2001

An Implicit LU/AF FDTD Method

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗
NASA NTRS1993

Effect of upright tilt on ventricular/vascular coupling in chronically instrumented primates

Studies of the hydraulic loading conditions on the heart in humans, especially pulsatile load, have primarily been limited to the supine state. Therefore, we have chosen a nonhuman primate model, the baboon, to assess left ventricular/vascular coupling in both supine and upright positions. Primate subjects were studied by catheterization under sedation and then after surgical implantation of transducers. This allowed the evaluation of postural stress in the chronically instrumented conscious baboon and then after light dissociative doses of ketamine. Basic hemodynamic variables were evaluated for baboons in supine and upright positions. Fourier analysis was applied to aortic pressure and flow to obtain input and characteristic impedance and the ratio of pulsatile (Wp) to total (Wt) left ventricular power (Wp/Wt). The aortic reflected, or backward, pressure was also calculated. Peripheral resistance increased (P = 0.01) and reflected pressure decreased (17.74 +/- 1.50 vs. 15.21 +/- 2 mmHg; P < 0.01) in upright subjects. Characteristic impedance and Wp/Wt were unchanged. Postoperatively, peripheral resistance increased (2,651 +/- 311 vs. 3,667 +/- 276; P < 0.05) and mean power and Wt decreased (P < 0.01) without changes in reflected pressure. All variables were unchanged after light dissociative doses of ketamine. Thus there is no significant change in efficiency of left ventricular/vascular coupling formulated in terms of Wp/Wt or input impedance with postural stress.

NASA Program Space Physiology and Countermeasures↗
NASA NTRS1943

Periodic Heat Transfer at Small Pressure Fluctuations

The effect of cyclic gas pressure variations on the periodic heat transfer at a flat wall is theoretically analyzed and the differential equation describing the process and its solution for relatively. Small pressure fluctuations developed, thus explaining the periodic heat cycle between gas and wall surface. The processes for pure harmonic pressure and temperature oscillations, respectively, in the gas space are described by means of a constant heat transfer coefficient and the equally constant phase angle between the appearance of the maximum values of the pressure and heat flow most conveniently expressed mathematically in the form of a complex heat transfer coefficient. Any cyclic pressure oscillations, can be reduced by Fourier analysis to harmonic oscillations, which result in specific, mutual relationships of heat-transfer coefficients and phase angles for the different harmonics.

Pfriem, H.↗
NASA NTRS1997

Wavelet Methods Developed to Detect and Control Compressor Stall

A "wavelet" is, by definition, an amplitude-varying, short waveform with a finite bandwidth (e.g., that shown in the first two graphs). Naturally, wavelets are more effective than the sinusoids of Fourier analysis for matching and reconstructing signal features. In wavelet transformation and inversion, all transient or periodic data features (as in compressor-inlet pressures) can be detected and reconstructed by stretching or contracting a single wavelet to generate the matching building blocks. Consequently, wavelet analysis provides many flexible and effective ways to reduce noise and extract signals which surpass classical techniques - making it very attractive for data analysis, modeling, and active control of stall and surge in high-speed turbojet compressors. Therefore, fast and practical wavelet methods are being developed in-house at the NASA Lewis Research Center to assist in these tasks. This includes establishing user-friendly links between some fundamental wavelet analysis ideas and the classical theories (or practices) of system identification, data analysis, and processing.

Le, Dzu K.↗
NASA NTRS2007

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

Swanson, Roy C., Jr.↗
NASA NTRS1997

Ellipsometer

In an ellipsometer, a phase-modulated, polarized light beam is applied to a sample, electrical signals are obtained representing the orthogonal planes of polarization of the light after it has interacted with the sample and the constants of the sample are calculated from the two resulting electrical signals. The phase modulation is sufficiently small so that the calibration errors are negligible. For this purpose, the phase modulator, phase modulates the light within a range of no more than ten degrees peak to peak. The two electrical signals are expanded by Fourier analysis and the coefficients thereof utilized to calculate psi and delta.

Ducharme, Stephen Paul↗
NASA NTRS1995

Small modulation ellipsometry

In an ellipsometer, a phase-modulated, polarized light beam is applied to a sample, electrical signals are obtained representing the orthogonal planes of polarization of the light after it has interacted with the sample and the constants of the sample are calculated from the two resulting electrical signals. The phase modulation is sufficiently small so that the calibration errors are negligible. For this purpose, the phase modulator phase modulates the light within a range of no more than ten degrees modulations peak to peak. The two electrical signals are expanded by Fourier analysis and the coefficients thereof utilized to calculate psi and delta.

Ducharme, Stephen P.↗
NASA NTRS2006

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Helenbrook, B. T.↗
NASA NTRS2006

SABER (TIMED) and MLS (UARS) Temperature Observations of Mesospheric and Stratospheric QBO and Related Tidal Variations

More than three years of temperature observations from the SABER (TIMED) and MLS WARS) instruments are analyzed to study the annual and inter-annual variations extending from the stratosphere into the upper mesosphere. The SABER measurements provide data from a wide altitude range (15 to 95 km) for the years 2002 to 2004, while the MLS data were taken in the 16 to 55 km altitude range a decade earlier. Because of the sampling properties of SABER and MLS, the variations with local solar time must be accounted for when estimating the zonal mean variations. An algorithm is thus applied that delineates with Fourier analysis the year-long variations of the migrating tides and zonal mean component. The amplitude of the diurnal tide near the equator shows a strong semiannual periodicity with maxima near equinox, which vary from year to year to indicate the influence from the Quasi-biennial Oscillation (QBO) in the zonal circulation. The zonal mean QBO temperature variations are analyzed over a range of latitudes and altitudes, and the results are presented for latitudes from 48"s to 48"N. New results are obtained for the QBO, especially in the upper stratosphere and mesosphere, and at mid-latitudes. At Equatorial latitudes, the QBO amplitudes show local peaks, albeit small, that occur at different altitudes. From about 20 to 40 km, and within about 15" of the Equator, the amplitudes can approach 3S K for the stratospheric QBO or SQBO. For the mesospheric QBO or MQBO, we find peaks near 70 km, with temperature amplitudes reaching 3.5"K, and near 85 km, the amplitudes approach 2.5OK. Morphologically, the amplitude and phase variations derived from the SABER and MLS measurements are in qualitative agreement. The QBO amplitudes tend to peak at the Equator but then increase again pole-ward of about 15" to 20'. The phase progression with altitude varies more gradually at the Equator than at mid-latitudes. A comparison of the observations with results from the Numerical Spectral Model (NSM) reveals that there is qualitative agreement. The NSM generates the QBO extending from the stratosphere into the upper mesosphere, with temperature variations extending to mid latitudes, but the predicted amplitudes are smaller than those observed.

Huang, Frank T.↗
NASA NTRS2006

Discerning Trends in Performance Across Multiple Events

Mass Data is a computer program that enables rapid, easy discernment of trends in performance data across multiple flights and ground tests. The program can perform Fourier analysis and other functions for the purposes of frequency analysis and trending of all variables. These functions facilitate identification of past use of diagnosed systems and of anomalies in such systems, and enable rapid assessment of related current problems. Many variables, for computation of which it is usually necessary to perform extensive manual manipulation of raw downlist data, are automatically computed and made available to all users, regularly eliminating the need for what would otherwise be an extensive amount of engineering analysis. Data from flight, ground test, and simulation are preprocessed and stored in one central location for instantaneous access and comparison for diagnostic and trending purposes. Rules are created so that an event log is created for every flight, making it easy to locate information on similar maneuvers across many flights. The same rules can be created for test sets and simulations, and are searchable, so that information on like events is easily accessible.

Slater, Simon↗