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The self-contained electromagnetic-reaction-type force-actuator system developed by NASA/UVA for the verification of spacecraft-structure vibration-control laws is characterized and demonstrated. The device is controlled by a dedicated microprocessor and has dynamic characteristics determined by Fourier analysis. Test data on a cantilevered beam are shown.
The statistical techniques most often used in space physics include Fourier analysis, linear correlation, auto- and cross-correlation, power spectral density, and superposed epoch analysis. Tests are presented which can evaluate the significance of the results obtained through each of these. Data presented without some form of error analysis are frequently useless, since they offer no way of assessing whether a bump on a spectrum or on a superposed epoch analysis is real or merely a statistical fluctuation. Among many of the published linear correlations, for instance, the uncertainty in the intercept and slope is not given, so that the significance of the fitted parameters cannot be assessed.
A theoretical model for mid- and high-latitude electric fields and currents is constructed using Fourier analysis methods. A two-dimensional planar ionosphere with an enhanced conductivity auroral belt and field-aligned currents at the edges is employed. The postulate that the electric field and currents adjust self-consistently to minimize the global Joule dissipation rate defines a theoretical relation between the primary and secondary field-aligned currents. This so-called minimal dissipation configuration is examined using several input field-aligned current models, and graphical solutions for the electric field and ionospheric current are shown. A detailed discussion and interpretation of the solutions with relation to diverse observations and high-latitude phenomenology are included.
A rocket radio propagation experiment is described in which the electron density profile of the nighttime E region is obtained with an accuracy of 100 per cu cm. The factors limiting the accuracy of the experiment are found to be related to atmospheric and receiver noise and to the use of a magnetometer to determine the spin rate of the rocket. The Fourier analysis used for the frequency measurement may also contribute error under conditions of steep electron density gradients. The accuracy being achieved appears to be adequate for present applications of the experiment.
The stress wave factor (SWF) signal is utilized for the nondestructive evaluation of plates containing perpendicular edge cracks. The effects of the existence lateral location and depth of the crack on the magnitude spectra of individual reflections in the SWF signal are studied. If the reflections in the SWF signal are not overlapped the short time Fourier analysis is applied. If the reflections are overlapped the short time homomorphic analysis (cepstrum analysis) is applied. Several reflections which have average resonant frequencies approximately at 0.9, 1.3, and 1.7 MHz are analyzed. It is observed that the magnitude ratios evaluated at average resonant frequencies decrease more with increasing d/h if the crack is located between the transducers, where h is plate thickness and d is crack depth. Moreover, for the plates, crack geometries, reflections, and frequencies considered, the average decibel drop depends mainly on the dimensionless parameter d/h and it is approximately -1 dB per 0.07 d/h. Changes in the average resonant frequencies of the magnitude spectra are also observed due to changes in the location of the crack.
The rediscovery that the Sun and the solar wind can undergo important changes on historical time scales has brought into question the stability of the cyclic behavior of past time series of solar and solar-terrestrial origin. It was found by Vector Fourier analysis that the solar 11 year cycle is present in the series of 10Be, delta 180, in ice cores and of thermoluminescence (TL) in sea sediments during the last Millennia with a frequency modulation, related to the Sun behavior, as tested by comparison with the Sunspot number R sub z series. It was shown that the cyclogram of the series of yearly Aurorae from 1721 to 1979 linear-regression-corrected-for-R sub z is straight for the periodicity zeta=11,1y, which indicates that such periodicity is constant in time corresponding to the only line present in the 11y band. The maxima of this component appear at the same time together with the high speed solar wind streams taking place in coronal holes situated in high heliolatitudes. It is evidenced that the 11 year cycle has undergone frequency oscillations on a time scale of two centuries, although it is very difficult to determine the periodicities with high accuracy.
Photoelectric observations of short term light variations (shadow bands) at the 16 Feb. 1980 total solar eclipse have been made using a set of spatially separated PIN diodes. Light variations in a bandpass of 1-500 Hz were detected during the half-minutes preceding and following the total phase. Fourier analysis of the noise spectrum of the variations reveals a sharp drop-off for frequencies above 50 Hz and an overall spectrum quite similar to previously reported power spectra of stellar scintillation. This is consistent with an atmospheric origin for the shadow bands. Cross-correlations between the detector outputs are low, suggesting a short persistence time for the turbulent elements causing the patterns.
New JHKLM photometry of SS 433 showing short time scale variabilities is reported for the period of 1983 July 16-22 UT. The entire body of infrared data included in this paper, Giles et al. (1980), and Catchpole et al. (1981), is examined with reference to periods of 164 days and 13.08 days. Comparison of the infrared light curves with the optical light curves of Leibowitz et al. (1984) makes it possible to conclude, within the context of an accretion disk model, that the majority of the infrared flux in the SS 433 system comes from the disk, and that the hot spot responsible for the 'hump' in the visual and infrared light curves has a color similar to the average of the disk. A two-dimensional Fourier analysis of the infrared data suggests that the brightness maximum occurs when, seen from the compact star, the noncompact companion passes through a fixed elongation relative to the disk line of nodes with the orbital plane, if the precession is prograde.
The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.
Morrison's iterative noise removal method is studied by characterizing its effect upon systems of differing noise level and response function. The nature of data acquired from a linear shift invariant instrument is discussed so as to define the relationship between the input signal, the instrument response function, and the output signal. Fourier analysis is introduced, along with several pertinent theorems, as a tool to more thorough understanding of the nature of and difficulties with deconvolution. In relation to such difficulties the necessity of a noise removal process is discussed. Morrison's iterative noise removal method and the restrictions upon its application are developed. The nature of permissible response functions is discussed, as is the choice of the response functions used.
The mean temperature field at various pressure levels for January and July for both hemispheres are given. In summer (July in the Northern Hemisphere, January in the Southern Hemisphere) the fields are nearly zonally symmetric, but in winter large longitudinal variations are evident. These are mainly of low wave number, i.e., they may be represented by Fourier analysis around the globe using just a few (one or two) waves. This is the basis for representing the climatology of longitudinal variation in terms of wave components, since the fields may be defined with fewer values than by using a grid in longitude that has a sufficiently small interval to adequately represent the smooth variations. The amplitude and phase of temperature and geopotential height for wave numbers one and two, with In(pressure) as the vertical coordinate are given. The fields were calculated and plotted at pressure intervals of 0.2 in In(pressure) and at latitude intervals of 4 deg, but were interpolated to intervals of 0.5 in In(pressure) (approximately 3.5 km) and 10 deg latitude for tabulation. Tables and figures give wave coefficients for the monthly mean temperature fields. Thus they represent the quasi-statinary planetary waves.
Bedrest deconditioning is suspected to reduce cardiac function. However, quantitation of subtle decreases in cardiac reserve may be difficult. Normal subjects show considerable variability in heart rate response, reflected by a relatively broadband interbeat interval power spectrum. We hypothesized that the deconditioning effects of bedrest would induce narrowing of this spectrum, reflecting a reduction in the autonomically-modulated variability in heart rate. Ten aerobically conditioned men (average 35-50 years) underwent orthostatic tolerance testing with lower body negative pressure pre-bedrest and after 10 days of bedrest, while on placebo and after intravenous atropine. Spectra were derived by Fourier analysis of 128 interbeat interval data sets from subjects with sufficient numbers of beats during matched periods of the protocol. Data suggest that atropine unmasks the deconditioning effect of bedrest in athletic men, evidenced by a reduction in interbeat interval spectral power compared with placebo. Spectral analysis offers a new means of quantitating the effects of bedrest deconditioning and autonomic perturbations on cardiac dynamics.
The full approximation scheme multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computations required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. Results comparing pressure distributions with experimental data using both splitting types are shown. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined. Using the multigrid method on both subsonic and transonic wing calculations, the final lift coefficient is obtained to within 0.1 percent of its final value in a few as 15 cycles for a mesh with over 210,000 points. A spectral radius of 0.89 is achieved for both subsonic and transonic flow over the ONERA M6 wing while a spectral radius of 0.83 is obtained for supersonic flow over an analytically defined forebody. Results compared with experiment for all cases show good agreement.
The stress wave factor (SWF) signal is utilized for the nondestructive evaluation of plates containing perpendicular edge cracks. The effects of the existence lateral location and depth of the crack on the magnitude spectra of individual reflections in the SWF signal are studied. If the reflections in the SWF signal are not overlapped the short time Fourier analysis is applied. If the reflections are overlapped the short time homomorphic analysis (cepstrum analysis) is applied. Several reflections which have average resonant frequencies approximately at 0.9, 1.3, and 1.7 MHz are analyzed. It is observed that the magnitude ratios evaluated at average resonant frequencies decrease more with increasing d/h if the crack is located between the transducers, where h is plate thickness and d is crack depth. Moreover, for the plates, crack geometries, reflections, and frequencies considered, the average decibel drop depends mainly on the dimensionless parameter d/h and it is approximately -1 dB per 0.07 d/h. Changes in the average resonant frequencies of the magnitude spectra are also observed due to changes in the location of the crack.
The X-ray flux from Sco X-1 can vary quasi-periodically. Fourier analysis of 5-20 keV X-ray data taken while the source was quiescent shows a power density peak at 6 Hz, with a 2 Hz FWHM, and which corresponds to 5 percent of the flux (rms amplitude). No 6 Hz peak was observed when the source was more active, but rather a broad distribution of excess power up to 25 Hz was seen. The mode of variability switched from one to the other within 500 s, settling into the 6 Hz mode about 1 hr into quiescence. A different mode of quasi-periodic oscillation with power in a broad band between 14 and 24 Hz, corresponding to a 6 percent rms amplitude, occurred for short periods during the active phase whenever the flux reached the quiescent level.
Ozone observations made by Stratospheric Aerosol and Gas Experiment (SAGE) and meteorological temperature data are used to study the coupling of radiation and dynamics in the stratosphere. Both radiative heating and cooling rates are calculated using the observations as a function of altitude, longitude, latitude, and season. Fourier analysis of heating/cooling rates is performed to gain an understanding of the radiation-planetary wave interactions. High correlation is seen to exist between solar heating and the temperature distribution of the upper stratosphere. Radiative damping coefficients are derived and it is found that the coupling between ozone and temperature can produce significant variations in the damping rate which, in turn, critically depends on the vertical structure of the planetary waves.
A preliminary search has begun for evidence of tides in the 1-hr average line-of-sight mesospheric velocity data from the Urbana radar in the period 1978 to 1982, inclusive. Observations are restricted to the southeasterly component of those velocities. Since observations are only available for a fraction of a day due to the absence of night-time ionization in the Urbana mesosphere, it was decided to adopt an unusual procedure in the search; namely, to perform a Fourier analysis in the vertical direction and look for rotation in phase of vectors representing spatial frequency components. Propagating tidal modes would then show as vectors with a net rotation corresponding to their downward phase velocity. Five year monthly averages of hourly mean horizontal velocities inferred from the Urbana data are given. Consistent diurnal variation is seen for a number of months. These data were analyzed for vertical spatial periods of 3, 4.5, 6, 9, 12, and 24 km. When plotted as a function of time of day, many of the phasors tended to show a net rotation. The sense of rotation of a spinning vector in the complex plane can be determined objectively by computing the signed area swept out by the vector in saving from point to point. This calculation, indicated downward motion in 8 out of 12 months for the 9-km component and in 11 out of 12 months for the 24-km component. A comparison of the magnitudes of the 6 modes showed that the primary component was the 24-km component, a result confirmed by the tidal models of Forbes.
A search for fast variations in the Fe XXI emission was made for ten flares using the Fourier analysis. Three examples were described. The main results are summarized.