Search NASA⌕ Search

SEARCH · Search NASA

Results for “Scale Invariance”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1991

The cosmic microwave background

Recent limits on spectral distortions and angular anisotropies in the cosmic microwave background are reviewed. The various backgrounds are described, and the theoretical implications are assessed. Constraints on inflationary cosmology dominated by cold dark matter (CDM) and on open cosmological models dominated by baryonic dark matter (BDM), with, respectively, primordial random phase scale-invariant curvature fluctuations or non-gaussian isocurvature fluctuations are described. More exotic theories are addressed, and I conclude with the 'bottom line': what theorists expect experimentalists to be measuring within the next two to three years without having to abandon their most cherished theories.

Silk, Joseph↗
NASA NTRS1993

Scientific results from COBE

NASA's Cosmic Background Explorer (COBE) carries three scientific instruments to make precise measurements of the spectrum and anisotropy of the cosmic microwave background (CMB) radiation on angular scales greater than 7 deg and to conduct a search for a diffuse cosmic infrared background (CIB) radiation with 0.7 deg angular resolution. Data from the Far-Infrared Absolute Spectrophotometer (FIRAS) show that the spectrum of the CMB is that of a blackbody of temperature T = 2.73 +/- 0.06 K, with no deviation from a blackbody spectrum greater than 0.25% of the peak brightness. The first year of data from the Differential Microwave Radiometers (DMR) show statistically significant CMB anisotropy. The anisotropy is consistent with a scale invariant primordial density fluctuation spectrum. Infrared sky brightness measurements from the Diffuse Infrared Background Experiment (DIRBE) provide new conservative upper limits to the CIB. Extensive modeling of solar system and galactic infrared foregrounds is required for further improvement in the CIB limits.

Bennett, C. L.↗
NASA NTRS1995

Spatial and Spatial Frequency Spreads of Masking: Measurements and A Contrast-Gain-Control Model

Masked pattern detection is affected by the mask's proximity to the target in both the spatial and the spatial frequency domains. We measured contrast thresholds for detection of a Gabor patch centered in a sample of static band-pass noise with a central noise-free aperture. To examine spatial spread, target and mask frequency were identical, at either 2, 4, or 8 cycles/degree (cpd), and the radius of the aperture was 0, 1/2 or 1 cycle of the noise band's center frequency. The results suggest that the spatial spread of masking is scale invariant, with the largest radius producing little masking. To examine spatial frequency spread, a radius of 0 (no aperture) was used with all pairings of 2, 4, and 8 cpd for target and mask. The results suggest that masking is asymmetrical over log frequency: 8 z 0 cpd noise masks a 2 cpd target, but 2 cpd noise does not mask an 8 cpd target. We have used these results to calibrate a model of contrast-gain-control.

Solomon, Joshua A.↗
NASA NTRS1995

Spatial and Spatial Frequency Spreads Of Masking: Measurements and a Contrast-Gain-Control Model

Masked pattern detection is affected by the mask's proximity to the target in both the spatial and the spatial frequency domains. We measured contrast thresholds for detection of a Gabor patch centered in a sample of static band-pass noise with a central noise-free aperture. To examine spatial spread, target and mask frequency were identical, at either 2, 4, or 8 cycles/degree (cpd), and the radius of the aperture was 0, 1/2 or 1 cycle of the noise band's center frequency. The results suggest that the spatial spread of masking is scale invariant, with the largest radius producing little masking. To examine spatial frequency spread, a radius of 0 (no aperture) was used with all pairings of 2,4, and 8 cpd for target and mask. The results suggest that masking is asymmetrical over log frequency: 8 cpd noise masks a 2 cpd target, but 2 cpd noise does not mask an 8 cpd target. We have used these results to calibrate a model of contrast-gain-control.

Solomon, J. A.↗
NASA NTRS2004

Magnectic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth s core and uncertainty. If this agrees with the seismologic value, then the hypotheses pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth s core, this yields a JGR-PI, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change.In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length- scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto- geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core- source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte↗
NASA NTRS1994

Statistical mechanics in biology: how ubiquitous are long-range correlations?

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.

Non-NASA Center↗
NASA NTRS2004

Magnetic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothesis passes the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale range. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length-scale 1/k, if one presumes kinetic energy is converted in either eddy-overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small-scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magnetogeostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as a barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte V.↗
NASA NTRS1992

Fractal landscape analysis of DNA walks

By mapping nucleotide sequences onto a "DNA walk", we uncovered remarkably long-range power law correlations [Nature 356 (1992) 168] that imply a new scale invariant property of DNA. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences, but not in cDNA sequences or intron-less genes. In this paper, we present more explicit evidences to support our findings.

NASA Program Space Physiology and Countermeasures↗
NASA NTRS2004

Magnetic Probing of Core Geodynamics

To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynmcal hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothes pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at lentgh-scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto-geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core- mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order l20 years is pseudo-scale-invarient. Magnetic spectra of other planets may differ; however, if a transition to non-conductmg fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.

Voorhies, Coerte V.↗
NASA NTRS1992

Long-range correlations in nucleotide sequences

DNA sequences have been analysed using models, such as an n-step Markov chain, that incorporate the possibility of short-range nucleotide correlations. We propose here a method for studying the stochastic properties of nucleotide sequences by constructing a 1:1 map of the nucleotide sequence onto a walk, which we term a 'DNA walk'. We then use the mapping to provide a quantitative measure of the correlation between nucleotides over long distances along the DNA chain. Thus we uncover in the nucleotide sequence a remarkably long-range power law correlation that implies a new scale-invariant property of DNA. We find such long-range correlations in intron-containing genes and in nontranscribed regulatory DNA sequences, but not in complementary DNA sequences or intron-less genes.

NASA Discipline Cardiopulmonary↗