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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1989

Fractal applications to complex crustal problems

Complex scale-invariant problems obey fractal statistics. The basic definition of a fractal distribution is that the number of objects with a characteristic linear dimension greater than r satisfies the relation N = about r exp -D where D is the fractal dimension. Fragmentation often satisfies this relation. The distribution of earthquakes satisfies this relation. The classic relationship between the length of a rocky coast line and the step length can be derived from this relation. Power law relations for spectra can also be related to fractal dimensions. Topography and gravity are examples. Spectral techniques can be used to obtain maps of fractal dimension and roughness amplitude. These provide a quantitative measure of texture analysis. It is argued that the distribution of stress and strength in a complex crustal region, such as the Alps, is fractal. Based on this assumption, the observed frequency-magnitude relation for the seismicity in the region can be derived.

Turcotte, Donald L.↗
NASA NTRS1991

Slope variations on the surface of Phobos

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and microstructures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from about 12 deg on a 61 m scale to about 7 deg on a 216 - 272 m scale. On the same scales, a value of the order of 2 percent has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.

Muinonen, Karri↗
NASA NTRS1991

Cosmic rays from primordial black holes

The quark and gluon emission from primordial black holes (PBHs) which may have formed from initial density perturbations or phase transitions in the early universe are investigated. If the PBHs formed from scale-invariant initial density perturbations in the radiation dominated era, it is found that the emission can explain or contribute significantly to the extragalactic photon and interstellar cosmic-ray electron, positron, and antiproton spectra around 0.1-1 GeV. In particular, the PBH emission strongly resembles the cosmic-ray gamma-ray spectrum between 50 and 170 MeV. The upper limits on the PBH density today from the gamma-ray, e(+), e(-), and antiproton data are comparable, provided that the PBHs cluster to the same degree as the other matter in the Galactic halo.

Macgibbon, Jane H.↗
NASA NTRS1992

Recognizing Patterns In Log-Polar Coordinates

Log-Hough transform is basis of improved method for recognition of patterns - particularly, straight lines - in noisy images. Takes advantage of rotational and scale invariance of mapping from Cartesian to log-polar coordinates, and offers economy of representation and computation. Unification of iconic and Hough domains simplifies computations in recognition and eliminates erroneous quantization of slopes attributable to finite spacing of Cartesian coordinate grid of classical Hough transform. Equally efficient recognizing curves. Log-Hough transform more amenable to massively parallel computing architectures than traditional Cartesian Hough transform. "In-place" nature makes it possible to apply local pixel-neighborhood processing.

Weiman, Carl F. R.↗
NASA NTRS1992

Edge detection algorithm for SST images

An algorithm to detect fronts in satellite-derived sea surface temperature fields is presented. Although edge detection is the main focus, the problem of cloud detection is also addressed since unidentified clouds can lead to erroneous edge detection. The algorithm relies on a combination of methods and it operates at the picture, the window, and the local level. The resulting edge detection is not based on the absolute strength of the front, but on the relative strength depending on the context, thus, making the edge detection temperature-scale invariant. The performance of this algorithm is shown to be superior to that of simpler algorithms commonly used to locate edges in satellite-derived SST images. This evaluation was performed through a careful comparison between the location of the fronts obtained by applying the various methods to the SST images and the in situ measures of the Gulf Stream position.

Cayula, Jean-Francois↗
NASA NTRS1992

Lava flows are fractals

Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.

Bruno, B. C.↗
NASA NTRS1992

Limits of Gaussian fluctuations in the cosmic microwave background at 19.2 GHz

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power-law spectra for n values between -2 and 1. An upper bound is placed on the quadrupole anisotropy of Delta T/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of the modeling of the Galaxy could yield a significant reduction of these upper bounds.

Boughn, S. P.↗
NASA NTRS1992

Structure in the COBE differential microwave radiometer first-year maps

Results of the first year of data from the differential microwave radiometers on the Cosmic Background Explorer are presented. Statistically significant structure that is well described as scale-invariant fluctuations with a Gaussian distribution is shown. The rms sky variation, smoothed to a total 10-deg FWHM Gaussian, is 30 +/-5 micro-K for Galactic latitude greater than 20-deg data with the dipole anisotropy removed. The rms cosmic quadrupole amplitude is 13 +/-4 micro-K. The angular autocorrelation of the signal in each radiometer channel and cross-correlation between channels are consistent and give a primordial fluctuation power-law spectrum with index of 1.1 +/-0.5, and an rms-quadrupole-normalized amplitude of 16 +/-4 micro-K. These features are in accord with the Harrison-Zel'dovich spectrum predicted by models of inflationary cosmology.

Smoot, G. F.↗
NASA NTRS1992

Minimum entropy deconvolution and blind equalisation

Relationships between minimum entropy deconvolution, developed primarily for geophysics applications, and blind equalization are pointed out. It is seen that a large class of existing blind equalization algorithms are directly related to the scale-invariant cost functions used in minimum entropy deconvolution. Thus the extensive analyses of these cost functions can be directly applied to blind equalization, including the important asymptotic results of Donoho.

Satorius, E. H.↗
NASA NTRS1992

The x ray variability of AGN and the anomalous behavior of NGC6814

The power spectra of the X-ray variable AGN are typically scale invariant with no characteristic timescale. The one strong exception to this is NGC6814, where the EXOSAT data showed evidence for a periodic component at 12200 plus or minus 100 seconds. The power spectra of a GINGA lightcurve from this source, found using simulation techniques to account for the uneven sampling, also cannot be well fit by a single power law. A folded light curve analysis of the GINGA data shows a strong peak in the variance, indicative of a periodic component, at 12130.9 plus or minus 0.6 seconds. A second GINGA observation of this source taken one year later is consistent with the periodicity maintaining phase coherence for 7 periods in the range of 12110-12145 seconds. Including the limits from the folding selects a period of 12130.39 plus or minus 0.05 seconds. Phase coherence is not maintained between this and the EXOSAT observations, as the structure of the folded light curves is very different. Thus the periodicity is long lived and stable, but phase coherence is only maintained on timescales of approximately 1 year.

Done, C.↗
NASA NTRS1992

Dark matter, long-range forces, and large-scale structure

If the dark matter in galaxies and clusters is nonbaryonic, it can interact with additional long-range fields that are invisible to experimental tests of the equivalence principle. We discuss the astrophysical and cosmological implications of a long-range force coupled only to the dark matter and find rather tight constraints on its strength. If the force is repulsive (attractive), the masses of galaxy groups and clusters (and the mean density of the universe inferred from them) have been systematically underestimated (overestimated). We explore the consequent effects on the two-point correlation function, large-scale velocity flows, and microwave background anisotropies, for models with initial scale-invariant adiabatic perturbations and cold dark matter.

Gradwohl, Ben-Ami↗
NASA NTRS1991

Limits on Gaussian fluctuations in the cosmic microwave background at 19.2 GHz

The Northern Hemisphere data from the 19.2 GHz full sky survey are analyzed to place limits on the magnitude of Gaussian fluctuations in the cosmic microwave background implied by a variety of correlation functions. Included among the models tested are the monochromatic and Gaussian-shaped families, and those with power law spectra for n from -2 to 1. We place an upper bound on the quadrupole anisotropy of DeltaT/T less than 3.2 x 10 exp -5 rms, and an upper bound on scale-invariant (n = 1) fluctuations of a2 less than 4.5 x 10 exp -5 (95 percent confidence level). There is significant contamination of these data from Galactic emission, and improvement of our modeling of the Galaxy could yield a significant reduction of these upper bounds.

Boughn, S. P.↗
NASA NTRS1991

Dark matter or new physics?

Several proposals for a new physics to explain the deviation of galactic rotation curves from their expected Keplerian falloff with distance are discussed. Emphasis is given to a locally scale-invariant theory of gravity posed by the authors. The observational consequences of this theory are pointed out.

Kazanas, Demosthenes↗
NASA NTRS1993

The soft X-ray background and galaxy clusters

We show that the background flux observed in X-rays around 1 keV sets a tight upper limit to the evolution of X-ray-emitting clusters of galaxies, once the contribution of the sources now resolved is subtracted. Specifically, if the clustering proceeds up a scale-invariant hierarchy in a critical universe, the intracluster gas content must increase faster than the dynamical mass. We model such evolution in terms of infall of the intergalactic medium into the hierarchically growing potential wells, limited by the intergalactic temperature. Thus the soft X-ray background provides constraints to the dynamical clustering and to the history of the intergalactic medium, which extend those being provided by the z-resolved luminosity functions in X-rays and complement those expected from measuring the Comptonization parameter in the microwave and far-IR bands.

Burg, R.↗
NASA NTRS1992

The X-ray variability of AGN and the anomalous behavior of NGC 6814

The power spectra of the X-ray variable AGN are typically scale invariant with no characteristic timescale. The one strong exception to this is NGC 6814, where the EXOSAT data showed evidence for a periodic component at 12200 +/- 100 seconds. The power spectra of a GINGA lightcurve from this source, found using simulation techniques to account for the uneven sampling, also cannot be well fit by a single power law. A folded light curve analysis of GINGA data shows strong evidence for this periodic component. A second GINGA observation of this source taken one year later is consistent with the phenomena being completely periodic and phase coherent for 7 periods in the range of 12,110-12,145 seconds. Including the (optimistic) limits from the folding selects a period of 12130.39 +/- 0.05 seconds. Phase coherence is not maintained between this and the EXOSAT observations, as the structure of the folded light curves is very different. Thus the periodicity is long lived and stable, but phase coherence is only maintained on timescales of about 1 year.

Done, C.↗
NASA NTRS1991

Analysis of regional deformation and strain accumulation data adjacent to the San Andreas fault

A new approach to the understanding of crustal deformation was developed under this grant. This approach combined aspects of fractals, chaos, and self-organized criticality to provide a comprehensive theory for deformation on distributed faults. It is hypothesized that crustal deformation is an example of comminution: Deformation takes place on a fractal distribution of faults resulting in a fractal distribution of seismicity. Our primary effort under this grant was devoted to developing an understanding of distributed deformation in the continental crust. An initial effort was carried out on the fractal clustering of earthquakes in time. It was shown that earthquakes do not obey random Poisson statistics, but can be approximated in many cases by coupled, scale-invariant fractal statistics. We applied our approach to the statistics of earthquakes in the New Hebrides region of the southwest Pacific because of the very high level of seismicity there. This work was written up and published in the Bulletin of the Seismological Society of America. This approach was also applied to the statistics of the seismicity on the San Andreas fault system.

Turcotte, Donald L.↗
NASA NTRS1994

Second-order reconstruction of the inflationary potential

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Liddle, Andrew R.↗
NASA NTRS1994

On the rms anisotropy at 7 deg and 10 deg observed in the COBE-DMR two year sky maps

The frequency-independent rms temperature fluctuations determined from the Cosmic Background Explorer-Differential Microwave Radiometer (COBE-DMR) two-year sky maps are used to infer the parameter Q(sub rms-PS), which characterizes the normalization of power-law models of primordial cosmological temperature anisotropy, for a forced fit to a scale-invariant Harrison-Zel'dovich (n = 1) spectral model. Using a joint analysis of the 7 deg and 10 deg 'cross'-rms derived from both the 53 and 90 GHz sky maps, we find Q(sub rms-PS) = 17.0(sub -2.1 sup +2.5) micro Kelvin when the low quadrupole is included, and Q(sub rms-PS) = 19.4(sub -2.1 sup +2.3) micro Kelvin excluding the quadrupole. These results are consistent with the n = 1 fits from more sensitive methods. The effect of the low quadrupole derived from the COBE-DMR data on the inferred Q(sub rms-PS) normalization is investigated. A bias to lower Q(sub rms-PS) is found when the quadrupole is included. The higher normalization for a forced n = 1 fit is then favored by the cross-rms technique.

Banday, A. J.↗