Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Power Law”

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 199 records · Page 11

Characterization of Mode I and Mode II delamination growth and thresholds in AS4/PEEK composites

Composite materials often fail by delamination. The onset and growth of delamination in AS4/PEEK, a tough thermoplastic matrix composite, was characterized for mode 1 and mode 2 loadings, using the Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) test specimens. Delamination growth per fatigue cycle, da/dN, was related to strain energy release rate, G, by means of a power law. However, the exponents of these power laws were too large for them to be adequately used as a life prediction tool. A small error in the estimated applied loads could lead to large errors in the delamination growth rates. Hence strain energy release rate thresholds, G sub th, below which no delamination would occur were also measured. Mode 1 and 2 threshold G values for no delamination growth were found by monitoring the number of cycles to delamination onset in the DCB and ENF specimens. The maximum applied G for which no delamination growth had occurred until at least 1,000,000 cycles was considered the threshold strain energy release rate. Comments are given on how testing effects, facial interference or delamination front damage, may invalidate the experimental determination of the constants in the expression.

Martin, Roderick H.↗

Gamma-ray emission and electron acceleration in solar flares

Recent observations have extended the spectra of the impulsive phase of flares to the GeV range. Such high-energy photons can be produced either by electron bremsstrahlung or by decay of pions produced by accelerated protons. In this paper we investigate the effects of processes which become important at high energies. We examine the effects of synchrotron losses during the transport of electrons as they travel from the acceleration region in the corona to the gamma-ray emission sites deep in the chromosphere and photosphere, and the effects of scattering and absorption of gamma rays on their way from the photosphere to space instruments. These results are compared with the spectra from so-called electron-dominated flares, observed by GRS on the Solar Maximum Mission, which show negligible or no detectable contribution from accelerated protons. The spectra of these flares show a distinct steepening at energies below 100 keV and a rapid falloff at energies above 50 MeV. Following our earlier results based on lower energy gamma-ray flare emission we have modeled these spectra. We show that neither the radiative transfer effects, which are expected to become important at higher energies, nor the transport effects (Coulomb collisions, synchrotron losses, or magnetic field convergence) can explain such sharp spectral deviations from a simple power law. These spectral deviations from a power law are therefore attributed to the acceleration process. In a stochastic acceleration model the low-energy steepening can be attributed to Coulomb collision and the rapid high-energy steepening can result from synchrotron losses during the acceleration process.

Petrosian, Vahe↗

Dip Spectroscopy of the Low Mass X-Ray Binary XB 1254-690

We observed the low mass X-ray binary XB 1254-690 with the Rossi X-ray Timing Explorer in 2001 May and December. During the first observation strong dipping on the 3.9-hr orbital period and a high degree of variability were observed, along with "shoulders" approx. 15% deep during extended intervals on each side of the main dips. The first observation also included pronounced flaring activity. The non-dip spectrum obtained using the PCA instrument was well-described by a two-component model consisting of a blackbody with kT = 1.30 +/- 0.10 keV plus a cut-off power law representation of Comptonized emission with power law photon index 1.10 +/- 0.46 and a cut-off energy of 5.9(sup +3.0, sub -1.4) keV. The intensity decrease in the shoulders of dipping is energy-independent, consistent with electron scattering in the outer ionized regions of the absorber. In deep dipping the depth of dipping reached 100%, in the energy band below 5 keV, indicating that all emitting regions were covered by absorber. Intensity-selected dip spectra were well-fit by a model in which the point-like blackbody is rapidly covered, while the extended Comptonized emission is progressively overlapped by the absorber, with the, covering fraction rising to 95% in the deepest portion of the dip. The intensity of this component in the dip spectra could be modeled by a combination of electron scattering and photoelectric absorption. Dipping did not occur during the 2001 December observation, but remarkably, both bursting and flaring were observed contemporaneously.

Smale, Alan P.↗

The RHESSI Microflare Height Distribution

We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6-10 keV count-rate when RHESSI's full sensitivity was available in order to find the smallest events (Christe et al., 2008). Between March 2002 and March 2007, a total of 25,006 events were found. Source locations were determined in the 4-10 keV, 10-15 keV, and 15-30 keV energy ranges for each event. In order to extract the height distribution from the observed projected source positions, a forward-fit model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best flare height distribution is given by g (h) oc exp(-h/lambda) where lambda = 6.1 plus or minus 0.3 Mm is the scale height. A power law height distribution with a negative power law index, gamma = 3.1 plus or minus 0.3 is also consistent with the data. Interpreted as thermal loop top sources, these heights are compared to loops generated by a potential field model (PFSS). The measured flare heights distribution are found to be much steeper than the potential field loop height distribution which may be a signature of the flare energization process.

Christe, P.↗

Indentation law for composite laminates

Static indentation tests are described for glass/epoxy and graphite/epoxy composite laminates with steel balls as the indentor. Beam specimens clamped at various spans were used for the tests. Loading, unloading, and reloading data were obtained and fitted into power laws. Results show that: (1) contact behavior is not appreciably affected by the span; (2) loading and reloading curves seem to follow the 1.5 power law; and (3) unloading curves are described quite well by a 2.5 power law. In addition, values were determined for the critical indentation, alpha sub cr which can be used to predict permanent indentations in unloading. Since alpha sub cr only depends on composite material properties, only the loading and an unloading curve are needed to establish the complete loading-unloading-reloading behavior.

Yang, S. H.↗

Indentation law for composite laminates

Static indentation tests are described for glass/epoxy and graphite/epoxy composite laminates with steel balls as the indentor. Beam specimens clamped at various spans were used for the tests. Loading, unloading, and reloading data were obtained and fitted into power laws. Results show that: (1) contact behavior is not appreciably affected by the span; (2) loading and reloading curves seem to follow the 1.5 power law; and (3) unloading curves are described quite well by a 2.5 power law. In addition, values were determined for the critical indentation, alpha sub cr which can be used to predict permanent indentations in unloading. Since alpha sub cr only depends on composite material properties, only the loading and an unloading curve are needed to establish the complete loading-unloading-reloading behavior. Previously announced in STAR as N82-15123

Yang, S. H.↗

The X-ray spectra of blazars: Analysis of the complete EXOSAT archive

We analyzed the 0.1-10 keV spectra of 26 blazars (21 BL Lac objects and 5 highly polarized quasars), on the basis of 93 exposures taken from the EXOSAT archives. Fits were performed first with a single power-law model. Indications are found that better fits can be obtained with models where the slope steepens at higher energies. We therefore considered a broken power law and found that in a large fraction of the spectra the fit is significantly improved. Fits with a power law + oxygen edge at 0.6 keV are also explored.

Sambruna, Rita M.↗

XMM-Newton Archival Study of the ULX Population in Nearby Galaxies

We have conducted an archival XMM-Newton study of the bright X-ray point sources in 32 nearby galaxies. From our list of approximately 100 point sources, we attempt to determine if there is a low-state counterpart to the Ultraluminous X-ray (ULX) population. Indeed, 16 sources in our sample match the criteria we set for a low-state ULX, namely, L(sub X) greater than 10(exp 38 ergs per second) and a spectrum best fit with an absorbed power law. Further, we find evidence for 26 high-state ULXs which are best fit by a combined blackbody and a power law. As in Galactic black hole systems, the spectral indices, GAMMA, of the low-state objects, as well a s the luminosities, tend to be lower than those of the high-state objects. The observed range of blackbody temperatures is 0.1-1 keV with the most luminous systems tending toward the lowest temperatures. We also find a class of object whose properties (luminosity, blackbody temperature, and power law slopes) are very similar to those of galactic stellar mass black holes. In addition, we find a subset of these objects that can be best fit by a Comptonized spectrum similar to that used for Galactic black holes in the very high state, when they are radiating near the Eddington limit.

Winter, Lisa M.↗

Luminosity enhancement in relativistic jets and altered luminosity functions for beamed objects

Due to relativistic effects, the observed emission from relativistic jets is quite different from the rest frame emission. Systematic differences between the observed and intrinsic intensities of sources in which jet phenomena are occurring are discussed. Assuming that jets have a power law luminosity function of a slope B, the observed luminosity distribution as a function of the velocity of the jet, the spectral index of the rest frame emission, and the range of angles of the jets relative to our line of sight are calculated. The results is well-approximated by two power laws, the higher luminosity end having the original power law index X and the lower luminosity end having a flattened exponent independent of B and only slightly greater than 1. A model consisting of beamed emission from a jet and unbeamed emission from a stationary central component is investigated. The luminosity functions for these two-component sources are calculated for two ranges of angles. For sources in which beaming is important, the luminosity function is much flatter. Because of this, the relative numbers of ""beamed'' and ""unbeamed'' sources detected on the sky depend strongly on the luminosity at which the comparison is made.

Urry, C. M.↗

Luminosity enhancement in relativistic jets and altered luminosity functions for beamed objects

Due to relativistic effects, the observed emission from relativistic jets is quite different from the rest frame emission. Systematic differences between the observed and intrinsic intensities of sources in which jet phenomena are occurring are discussed. Assuming that jets have a power law luminosity function of a slope B, the observed luminosity distribution as a function of the velocity of the jet, the spectral index of the rest frame emission, and the range of angles of the jets relative to our line of sight are calculated. The results is well-approximated by two power laws, the higher luminosity end having the original power law index X and the lower luminosity end having a flattened exponent independent of B and only slightly greater than 1. A model consisting of beamed emission from a jet and unbeamed emission from a stationary central component is investigated. The luminosity functions for these two-component sources are calculated for two ranges of angles. For sources in which beaming is important, the luminosity function is much flatter. Because of this, the relative numbers of 'beamed' and 'unbeamed' sources detected on the sky depend strongly on the luminosity at which the comparison is made. Previously announced in STAR as N84-12889

Urry, C. M.↗

Swift Observations Of High-z Radio-loud Quasars Detected With Bat

We present follow-up Swift observations of 4 high-z radio-loud quasars detected with the BAT during the 15-month survey in 15-150 keV. The 0.5-8-keV spectra are best fitted either with a power law with no excess absorption over the Galactic value (0212+735, 0836+710, 2149--307 in higher state) or by a downward-curved broken power law model (0537--286, 2149--307 in lower state). The BAT spectra integrated over the whole 15 months of the survey are fitted with a single power law, with a range of spectral slopes, Gamma=l.3-2.3. Comparison with previous SAX observations shows that there is a trend for the 15-150-keV continuum to soften with fading intensity; on the contrary, little or no spectral variations are observed at medium-hard X-rays. This may suggest either/both dramatic variability above 10-keV, or/and two separate spectral components.

Sambruna, Rita M.↗

Stochastic Growth Theory of Spatially-Averaged Distributions of Langmuir Fields in Earth's Foreshock

Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution is power-law P(bar)(log E) in the wave field E with the bar denoting this averaging over position, In this paper it is shown that stochastic growth theory (SGT) can explain a power-law spatially-averaged distributions P(bar)(log E), when the observed power-law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.

Boshuizen, Christopher R.↗

The discovery and properties of the ultra-soft X-ray transient EXO 1846-031

We report the discovery of a previously uncataloged ultra-soft X-ray transient EXO 1846-031 which was in outburst during 1985 April to September. The X-ray spectrum consists of an ultra-soft component and a high-energy power-law tail that extends to at least 25 keV. The ultra-soft component may be modeled by either a cutoff power-law or a multicolor blackbody disk model. The latter model allows the evolution in spectrum and intensity observed during the outburst to be accounted for by the change in a single parameter - the temperature at the innermost disk radius. We demonstrate that at least one other accretion disk model is able to account for these changes by the variation of a single parameter. During one of the three EXOSAT observations, EXO 1846-031 exhibited significant intensity variability which probably originates from the power-law component. We derive a position for this unidentified source and present the results of a search for the optical counterpart.

Parmar, A. N.↗

The Far Ultraviolet M-dwarf Evolution Survey. I. The Rotational Evolution of High-energy Emissions

M-dwarf stars are prime targets for exoplanet searches because of their close proximity and favorable properties for both planet detection and characterization. However, the potential habitability and atmospheric characterization of these exoplanetary systems depends critically on the history of high-energy stellar radiation from X-rays to NUV, which drive atmospheric mass loss and photochemistry in the planetary atmospheres. With the Far Ultraviolet M-dwarf Evolution Survey, we have assessed the evolution of the FUV radiation, specifically eight prominent emission lines, including Lyα, of M-dwarf stars with stellar rotation period and age. We demonstrate tight power-law correlations between the spectroscopic FUV features, and measure the intrinsic scatter of the quiescent FUV emissions. The luminosity evolution with rotation of these spectroscopic features is well-described by a broken power law, saturated for fast rotators, and decays with increasing Rossby number, with a typical power-law slope of −2, although likely shallower for Lyα. Our regression fits enable FUV emission-line luminosity estimates relative to bolometric from known rotation periods to within ∼0.3 dex, across eight distinct UV emission lines, with possible trends in the fit parameters as a function of source layer in the stellar atmosphere. Our detailed analysis of the UV luminosity evolution with age further shows that habitable-zone planets orbiting lower-mass stars experience much greater high-energy radiative exposure relative the same planets orbiting more massive hosts. Around early- to mid-M dwarfs, these exoplanets, at field ages, accumulate up to 10–20× more EUV energy, relative to modern Earth. Moreover, the bulk of this UV exposure likely takes place within the first Gyr of the stellar lifetime.

J Sebastian Pineda↗

Solar Flare X-Ray Source Motion as a Response to Electron Spectral Hardening

Context. Solar flare hard X-rays (HXRs) are thought to be produced by nonthermal coronal electrons stopping in the chromosphere, or remaining trapped in the corona. The collisional thick target model (CTTM) predicts that more energetic electrons penetrate to greater column depths along the flare loop. This requires that sources produced by harder power-law injection spectra should appear further down the legs or footpoints of a flareloop. Therefore, the frequently observed hardening of the injected power-law electron spectrum during flare onset should be concurrent with a descending hard X-ray source. Aims. To test this implication of the CTTM by comparing its predicted HXR source locations with those derived from observations of a solar flare which exhibits a nonthermally-dominated spectrum before the peak in HXRs, known as an early impulsive event. Methods. HXR images and spectra of an early impulsive C-class flare were obtained using the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI). Images were reconstructed to produce HXR source height evolutions for three energy bands. Spatially-integrated spectral analysis was performed to isolate nonthermal emission, and to determine the power-law index of the electron injection spectrum. The observed height-time evolutions were then fit with CTTM-based simulated heights for each energy, using the electron spectral indices derived from the RHESSI spectra. Results. The flare emission was found to be dominantly nonthermal above approx. 7 keV, with emission of thermal and nonthermal X-rays likely to be simultaneously observable below that energy. The density structure required for a good match between model and observed source heights agreed with previous studies of flare loop densities. Conclusions. The CTTM has been used to produce a descent of model HXR source heights that compares well with observations of this event. Based on this interpretation, downward motion of nonthermal sources should indeed occur in any flare where there is spectral hardening in the electron distribution during a flare. However, this would often be masked by thermal emission associated with flare plasma pre-heating. As yet, flare models that predict transfer of energy from the corona to the chromosphere by means other than a flux of nonthermal electrons do not predict this observed source descent. Therefore, flares such as this will be key in explaining this elusive energy transfer process.

X-rays↗

OSSE observations of 3C 273

We report results of multiple observations of the quasar 3C 273 with the Oriented Scintillation Spectrometer Experiment (OSSE) instrument on the Compton Gamma Ray Observatory. These observations span the period from 1991 June through 1993 January and represent the most sensitive observations to date in low-energy gamma rays. The source was detected at historically weak 100 keV fluxes compared with previous measurements. Variability by factors of approximately 3 on timescales of approximately equal 2 months was observed in the energy band 50-150 keV. The data are well described by a single power law with a proton number index Gamma = 1.7 +/- 0.1. No significant change of Gamma was observed during changes in intensity. Thermal models do not provide acceptable fits to the data. When the OSSE data are combined with contemporaneous measurements by COMPTEL and EGRET, the spectrum is seen to break at an energy of 1.0(+0.9, -0.4) MeV to a softer power law with Delta Gamma = 0.7(+0.06, -0.11), forming a power law with Gamma = 2.4 between approximately 1 MeV and several GeV.

Johnson, W. N.↗

Measurement of cosmic-ray proton and helium spectra during the 1987 solar minimum

The differential cosmic-ray proton and helium spectra have been measured during the 1987 solar minimum using a balloon-borne superconducting magnetic spectrometer launched from Prince Albert, Canada. The changing geomagnetic cutoff along the balloon trajectory was observed in the low-energy proton data to be about 25 percent below the nominal calculated values. The absolute particle fluxes were approximately equal to the highest fluxes observed at the previous solar minimum in 1977. Above 10 GV the observed spectra are represented by a power law in rigidity with spectral indices of 2.74 + or - 0.02 for protons and 2.68 + or - 0.03 for helium. The measurements above 200 MeV per nucleon are consistent with rigidity power-law interstellar spectra modulated with the solar modulation parameter phi = 500 MV. The energy dependence of the proton-to-helium ratio is consistent with rigidity power-law injection spectra and rigidity-dependent propagation without reacceleration.

Seo, E. S.↗

Ionospheric scintillation by a random phase screen Spectral approach

The theory developed by Briggs and Parkin, given in terms of an anisotropic gaussian correlation function, is extended to a spectral description specified as a continuous function of spatial wavenumber with an intrinsic outer scale as would be expected from a turbulent medium. Two spectral forms were selected for comparison: (1) a power-law variation in wavenumber with a constant three-dimensional index equal to 4, and (2) Gaussian spectral variation. The results are applied to the F-region ionosphere with an outer-scale wavenumber of 2 per km (approximately equal to the Fresnel wavenumber) for the power-law variation, and 0.2 per km for the Gaussian spectral variation. The power-law form with a small outer-scale wavenumber is consistent with recent F-region in-situ measurements, whereas the gaussian form is mathematically convenient and, hence, mostly used in the previous developments before the recent in-situ measurements. Some comparison with microwave scintillation in equatorial areas is made.

Rufenach, C. L.↗