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 577 records · Page 32

Predicting the Galactic population of free-floating planets from realistic initial conditions

ABSTRACT We present the first prediction for the mass distribution function of Galactic free-floating planets (FFPs) that aims to accurately include the relative contributions of multiple formation pathways and stellar populations. We derive our predicted distribution from dedicated simulations of planet birth, growth, migration, and ejection around circumbinary systems and extend these results to also include the contributions from single and wide binary systems. Our resulting FFP mass distribution shows several distinct features, including a strong peak at ${\sim} 8\, {\rm M}_{\oplus }$ arising from the transition between pebble and gas accretion regimes and a trough at ${\sim} 1\, {\rm M}_{\oplus }$ due to the shift in the dominant ejection process from planet–planet scattering to ejection through interactions with stars in circumbinary systems. We find that interactions with the central binary in close circumbinary systems are likely the dominant progenitor for FFPs more massive than Earth, leading to a steep power-law dependence in mass that agrees well with existing observations. In contrast, we find planet–planet scattering events in single and wide binary systems likely produce the majority of planets at Mars mass and below, resulting in a shallower power-law dependence. Our results suggest that existing extrapolations into the sub-terrestrial mass range may significantly overestimate the true FFP abundance. The features we predict in the mass distribution of FFPs will be detectable by upcoming space-based microlensing surveys and, if observed, will provide key insight into the origins of FFPs and the environments in which they form.

Coleman, Gavin A. L. (ORCID:0000000151118963)↗

An intense soft high-latitude X-ray source H2156-304 - A new BL Lacertae object

The discovery of an intense high-latitude soft X-ray source (designated H2156-304) detected with the low-energy detectors of the HEAO A-2 experiment is reported. The error box of the source includes a 14th mag starlike object that may be coincident with the radio source PKS 2155-304 and has been suggested as a BL Lac candidate. Intensity variations of H2156-304 on time scales of about 1 sec to 1 day are discussed, along with a probable flare from the source. The derived energy spectrum of the source is shown to be well fitted by either a two-temperature thermal model with temperatures of 16 million and 1.6 million K or a single power-law model with a spectral index of 2.4 + or - 0.3. Hydrogen column densities of approximately 2.5 x 10 to the 20th and 2.0 x 10 to the 20th H atoms/sq cm are obtained for the two-temperature and power-law models, respectively. The emission mechanism of H2156-304 is considered, and the characteristics of this source are compared with those of three known soft X-ray-emitting BL Lac objects.

Agrawal, P. C.↗

The spectra and light curves of two gamma-ray bursts

Observations made by the Hard X-ray and Low Energy Gamma-Ray Experiment on board HEAO-1 of the spectra and light curves of two gamma-ray bursts for which localized arrival directions will become available are presented. The burst of October 20, 1977 is found to exhibit a fluence of 0.000031 + or - 0.000005 erg/sq cm over the energy range 0.135-2.05 MeV and a duration of 38.7 sec, while that of November 10, 1977 is found to have a fluence of 0.000021 + or - 0.000008 erg/sq cm between 0.125 and 3 MeV over 2.8 sec. The light curves of both bursts exhibit time fluctuations down to the limiting time resolution of the detectors. The spectrum of the October burst can be fit by a power law of index -1.93 + or -0.16, which is harder than any other gamma-burst spectrum yet reported. The spectrum of the second burst is softer (index -2.4 + or - 0.7), and is consistent with the upper index in the double power law fit to the burst of April 27, 1972.

Knight, F. K.↗

Faraday rotation fluctutation spectra observed during solar occultation of the Helios spacecraft

Faraday rotation (FR) measurements using linearly polarized radio signals from the two Helios spacecraft were carried out during the period from 1975 to 1984. This paper presents the results of a spectral analysis of the Helios S-band FR fluctuations observed at heliocentric distances from 2.6 to 15 solar radii during the superior conjunctions 1975-1983. The mean intensity of the FR fluctuations does not exceed the noise level for solar offsets greater than ca. 15 solar radii. The rms FR fluctuation amplitude increases rapidly as the radio ray path approaches the Sun, varying according to a power law (exponent: 2.85 +/- 0.15) at solar distances 4-12 solar radii. At distances inside 4 solar radii the increase is even steeper (exponent: 5.6 +/- 0.2). The equivalent two-dimensional FR fluctuation spectrum is well modeled by a single power-law over the frequency range from 5 to 50 mHz. For heliocentric distances larger than 4 solar radii the spectral index varies between 1.1 and 1.6 with a mean value of 1.4 +/- 0.2, corresponding to a 3-D spectral index p = 2.4. FR fluctuations thus display a somwhat lower spectral index compared with phase and amplitude fluctuations. Surprisingly high values of the spectral index were found for measurements inside 4 solar radii (p = 2.9 +/- 0.2). This may arise from the increasingly dominant effect of the magnetic field on radio wave propagation at small solar offsets. Finally, a quasiperiodic component, believed to be associated with Alfven waves, was discovered in some (but not all!) fluctuation spectra observed simultaneously at two ground stations. Characteristic periods and bulk velocities of this component were 240 +/- 30 sec and 300 +/- 60 km/s, respectively.

Andreev, V.↗

Spectral development of a solar X-ray burst observed on OSO-7.

The UCSD solar X-ray instrument on the OSO-7 satellite observes X-ray bursts in the 2- to 300-keV range with 10.24-sec time resolution. Spectra obtained from the proportional counter and scintillation counter are analyzed for the event of Nov. 16, 1971, at 0519 UT in terms of thermal (exponential spectrum) and nonthermal (power law) components. The energy content of the approximately 20,000,000 K thermal plasma increased with the 60-sec duration hard X-ray burst, which entirely preceded the 5-keV soft X-ray maximum. If the hard X-rays arise by thick target bremsstrahlung, the nonthermal electrons above 10 keV have sufficient energy to heat the thermally emitting plasma. In the thin target case the collisional energy transfer from nonthermal electrons suffices if the power law electron spectrum is extrapolated below 10 keV, or if the ambient plasma density exceeds 4 x 10 to the 10th power per cu cm.

Mckenzie, D. L.↗

The 3000 A bump in quasars

New observations of the 3000 A bump in quasars are presented and some simple considerations regarding its physical origin are addressed. Absolute spectrophotometry of 30 quasars with redshifts between 0.53 and 0.70 was obtained with the multichannel spectrometer on the 5 m Hale telescope with a rest wavelength coverage of 2000-5000 A. The continuum observations are well represented by a single power law plus a smooth, broad bump and superposed Fe II multiplets. The strength of the bump correlates fairly well with that of H-beta but poorly with those of the Mg II and Fe II lines. Models consisting of a power law and optically thick hydrogen continua with temperatures of about 12,000 K, and Balmer-edge optical depths equal to three fit the observed energy distributions well. The physical conditions and continuum emission of a dense slab of hydrogen heated by gamma rays are analyzed.

Oke, J. B.↗

Approximate supernova remnant dynamics with cosmic ray production

Supernova explosions are the most violent and energetic events in the galaxy and have long been considered probably sources of Cosmic Rays. Recent shock acceleration models treating the Cosmic Rays (CR's) as test particles nb a prescribed Supernova Remnant (SNR) evolution, indeed indicate an approximate power law momentum distribution f sub source (p) approximation p(-a) for the particles ultimately injected into the Interstellar Medium (ISM). This spectrum extends almost to the momentum p = 1 million GeV/c, where the break in the observed spectrum occurs. The calculated power law index approximately less than 4.2 agrees with that inferred for the galactic CR sources. The absolute CR intensity can however not be well determined in such a test particle approximation.

Voelk, H. J.↗

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

Statistical study of precipitating electrons

Energy spectra of precipitating electrons are fitted to the sum of three distributions: a power law, a Maxwellian and a Gaussian. This fitting procedure determines seven parameters which characterize the essential features of each spectrum. These characteristic parameters are used to carry out various studies involving precipitating electrons. It is shown that the absence of the power-law population from a particular spectrum is related to the softness of the precipitating primary flux, that the Maxwellian temperature and the Gaussian peak energy have a positive correlation the strength of which varies with local time, that the upward moving Gaussian population has a loss cone distribution, and that the one dimensional velocity distribution parallel to the magnetic field occasionally displays a plateau or a hump on the tail.

Fontheim, E. G.↗

Is walking a random walk? Evidence for long-range correlations in stride interval of human gait

Complex fluctuation of unknown origin appear in the normal gait pattern. These fluctuations might be described as being (1) uncorrelated white noise, (2) short-range correlations, or (3) long-range correlations with power-law scaling. To test these possibilities, the stride interval of 10 healthy young men was measured as they walked for 9 min at their usual rate. From these time series we calculated scaling indexes by using a modified random walk analysis and power spectral analysis. Both indexes indicated the presence of long-range self-similar correlations extending over hundreds of steps; the stride interval at any time depended on the stride interval at remote previous times, and this dependence decayed in a scale-free (fractallike) power-law fashion. These scaling indexes were significantly different from those obtained after random shuffling of the original time series, indicating the importance of the sequential ordering of the stride interval. We demonstrate that conventional models of gait generation fail to reproduce the observed scaling behavior and introduce a new type of central pattern generator model that sucessfully accounts for the experimentally observed long-range correlations.

Hausdorff, Jeffrey M.↗

Properties of the Chandra Sources in M81

The Chandra X-Ray Observatory obtained a 50 ks observation of the central region of M81 using the ACIS-S in imaging mode. The global properties of the 97 X-ray sources detected in the inner 8.3' x 8.3' field of M81 are examined. Roughly half the sources are concentrated within the central bulge. The remainder are distributed throughout the disk, with the brightest disk sources lying preferentially along spiral arms. The average hardness ratios of both bulge and disk sources are consistent with power-law spectra of index Gamma equals approximately 1.6, indicative of a population of X-ray binaries. A group of much softer sources is also present. The background-source-subtracted log N-log S distribution of the disk follows a power law of index approximately -0.5 with no change in slope over three decades in flux. The log N-log S distribution of the bulge follows a similar shape but with a steeper slope above approximately 4 x 10(exp 37) ergs/s. There is unresolved X-ray flux from the bulge with a radial profile similar to that of the bulge sources. This unresolved flux is softer than the average of the bulge sources, and extrapolating the bulge log N-log S distribution toward weaker sources can account for only 20% of the unresolved flux. No strong time variability was observed for any source with the exception of one bright, soft source.

Tennant, Allyn F.↗

PSR J0007+7303 in the CTA1 SNR: New Gamma-ray Results from Two Years of Fermi-LAT Observations

One of the main results of the Fermi Gamma-Ray Space Telescope is the discovery of gamma-ray selected pulsars. The high magnetic field pulsar, PSR J0007+7303 in CTA1, was the first ever to be discovered through its gamma-ray pulsations. Based on analysis of 2 years of LAT survey data, we report on the discovery of I-ray emission in the off-pulse phase interval at the approx. 6sigma level. The flux from this emission in the energy range E > or =::: 100 MeV is F(sub 100) = (1.73+/-0.40) x 10(exp -8) photons/sq cm/s and is best fitted by a power law with a photon index of Gamma = 2.54+/-0.14. The pulsed gamma-ray flux in the same energy range is F(sub 100) = (3.95+/-0.07) x 10(exp -7) photons/sq cm/s and is best fitted by an exponentially-cutoff power-law spectrum with a photon index of Gamma = 1.41+/-0.23 and a cutoff energy E(sub c) = 4.04+/-0.20 GeV. We find no flux variability neither at the 2009 May glitch nor in the long term behavior. We model the gamma-ray light curve with two high-altitude emission models, the outer gap and slot gap, and find that the model that best fits the data depends strongly on the assumed origin of the off-pulse emission. Both models favor a large angle between the magnetic axis and observer line of sight, consistent with the nondetection of radio emission being a geometrical effect. Finally we discuss how the LAT results bear on the understanding of the cooling of this neutron star.

Abdo, A. A.↗

XMM-Newton and Chandra Observations of the Candidate Fermi-LAT Pulsar 4FGL J1015.5-6030

4FGL J1015.5-6030 is an unidentified Fermi-LAT source hosting a bright, extended X-ray source whose X-ray spectrum is consistent with that of a young pulsar, yet no pulsations have been found. Here we report on XMM-Newton timing and Chandra imaging observations of the X-ray counterpart of 4FGL J1015.5-6030. We find no significant periodicity from the source and place a 3σ upper limit on its pulsed fraction of 34%. The Chandra observations resolve the point source from the extended emission. We find that the point source's spectrum is well fit by a blackbody model, with temperature kT = 0.205 ± 0.009 keV, plus a weak power-law component, which is consistent with a thermally emitting neutron star with a magnetospheric component. The extended emission spans angular scales of a few arcseconds up to about 30'' from the point source and its spectrum is well fit by a power-law model with a photon index Γ = 1.70 ± 0.05. The extended emission's spectrum and 0.5–10 keV luminosity of 4 × 10 32 erg s −1 (at a plausible distance of 2 kpc) are consistent with that of a pulsar wind nebula. Based on a comparison to other GeV and X-ray pulsars, we find that this putative pulsar is likely a middle-aged (i.e., τ ∼ 0.1–1 Myr) radio-quiet pulsar with Ė~10 34 -10 35 erg s −1 .

Pulsars↗

Superclustering in the explosion scenario

A simple toy model is used to study the spatial distribution of rich clusters in a generic type of explosion scenario. The model, parameterized by the distribution of shell radii and the filling factor, places spherical shells at random and identifies each 'knot' as a cluster. The resulting cluster correlation function is close to a power law extending to the diameter of the largest spheres. Richer clusters form at the intersections of bigger shells and so have stronger correlations. Typical shell radii and filling factors are required to produce the observed number density of clusters. Models with a power-law radius distribution also reproduce the richness distribution of clusters in the Abell catalog. Supercluster multiplicity functions, void probabilities, number counts, topology statistics, and velocity correlations confirm the presence of strong superclustering and quantify the non-Gaussian nature of the model.

Weinberg, David H.↗

Satellite observation of atmospheric nuclear gamma radiation

Satellite observations of the spectrum of gamma radiation from the earth's atmosphere in the energy interval from 300 keV to 8.5 MeV were obtained with a gamma-ray spectrometer during 1980-1983. A total of 20 atmospheric line features are superimposed on a continuum background which is modeled using a power law with an index of -1.16. The line energies and intensities are consistent with production by secondary neutrons interacting with atmospheric N-14 and O-16. The intensity and spectrum of photons at energies below the 511-keV line, in excess of a power law continuum, are explained by Compton scattering of the annihilation line photons in traversing an average of 21 g/sq cm of atmosphere.

Letaw, John R.↗

Discovery of an Extreme MeV Blazar with the Swift Burst Alert Telescope

The Burst Alert Telescope (BAT) onboard Swift detected bright emission from 15-195 keV from the source SWIFT J0746.3+2548 (J0746 in the following), identified with the optically-faint (R approx. 19), z=2.979 quasar SDSS J074625.87+244901.2. Here we present Swift and multiwavelength observations of this source. The X-ray emission from J0746 is variable on timescales of hours to weeks in 0.5-8 keV and of a few months in 15-195 keV, but there is no accompanying spectral variability in the 0.5-8 keV band. There is a suggestion that the BAT spectrum, initially very hard (photon index Gamma approx. 0.7), steepened to Gamma approx. 1.3 in a few months, together with a decrease of the 15-195 keV flux by a factor approx. 2. The 0.5-8 keV continuum is well described by a power law with Gamma approx. 1.3, and spectral flattening below 1 keV. The latter can be described with a column density in excess of the Galactic value with intrinsic column density Nz(sub H) approx. 10(exp 22)/sq cm , or with a flatter power law, implying a sharp (Delta(Gamma) less than or approx. 1) break across 16 keV in the quasar's rest-frame. The Spectral Energy Distribution of J0746 is double-humped, with the first component peaking at IR wavelengths and the second component at MeV energies. These properties suggest that J0746 is a a blazar with high gamma-ray luminosity and low peak energy (MeV) stretching the blazar sequence to an extreme.

Sambruna, R. M.↗

van der Waals corrected density functionals for cylindrical surfaces: Ammonia and nitrogen dioxide adsorbed on a single-walled carbon nanotube

In this work, we extend the damped Zaremba-Kohn model (dZK) for long-range dispersion interaction between a molecule and a planar surface to molecules adsorbed on a curved cylindrical surface, and employ this extended model as an additive correction to the semilocal density functionals PBE (Perdew-Burke-Ernzerhof) and SCAN (strongly constrained and appropriately normed). The resulting PBE+vdW (van der Waals)-dZK and SCAN+vdW-dZK are applied to two systems, NH3 and NO2 molecules adsorbed on a single-wall carbon nanotube (CNT), for calculations of binding energies and equilibrium distances. For comparison, the results from vdW nonlocal functionals, such as SCAN+rVV10 and PBE+rVV10, are also presented. The binding energies from PBE+rVV10 (Vydrov and Van Voorhis), SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK are about 70–115 meV for the system of CNT + NH 3 and 300–500 meV for the system of CNT + NO 2 . The results from PBE+vdW-dZK and SCAN+vdW-dZK are closer to each other than those from PBE+rVV10 and SCAN+rVV10 are. The relatively closer results from PBE+vdW-dZK and SCAN+vdW-dZK indicate the consistency of our developed vdW–dZK model for cylindrical surfaces. All methods, including PBE, SCAN, PBE+rVV10, SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK, give approximately the same binding energy differences between two adsorption configurations (types I and II) for the two systems. This implies that the two adsorption sites have approximately the same adsorption stability. The exponent of the vdW interaction power law from our vdW-dZK model for the two systems is about 0 at short distance, largely due to the damping factor, and tends slowly to –4 to –4.5 at distances D about 20–50 Å. At even larger distances, the vdW power-law exponent approaches –5. This feature is very similar to the one calculated with random-phase approximation and renormalization group approaches, supporting the applicability of our methods. Our developed vdW-dZK method provides a highly efficient and reliable method for large systems with cylindrical surfaces, such as vdW interactions with nanotubes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Searching for fat tails in CRISPR-Cas systems: Data analysis and mathematical modeling

Understanding CRISPR-Cas systems—the adaptive defence mechanism that about half of bacterial species and most of archaea use to neutralise viral attacks—is important for explaining the biodiversity observed in the microbial world as well as for editing animal and plant genomes effectively. The CRISPR-Cas system learns from previous viral infections and integrates small pieces from phage genomes called spacers into the microbial genome. The resulting library of spacers collected in CRISPR arrays is then compared with the DNA of potential invaders. One of the most intriguing and least well understood questions about CRISPR-Cas systems is the distribution of spacers across the microbial population. Here, using empirical data, we show that the global distribution of spacer numbers in CRISPR arrays across multiple biomes worldwide typically exhibits scale-invariant power law behaviour, and the standard deviation is greater than the sample mean. We develop a mathematical model of spacer loss and acquisition dynamics which fits observed data from almost four thousand metagenomes well. In analogy to the classical ‘rich-get-richer’ mechanism of power law emergence, the rate of spacer acquisition is proportional to the CRISPR array size, which allows a small proportion of CRISPRs within the population to possess a significant number of spacers. Our study provides an alternative explanation for the rarity of all-resistant super microbes in nature and why proliferation of phages can be highly successful despite the effectiveness of CRISPR-Cas systems.

59 BASIC BIOLOGICAL SCIENCES↗