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 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗
NASA NTRS2022

Enhancement of a global lake and reservoir database to aid climate studies and resource monitoring utilizing satellite radar altimetry

Here, we describe the expansion and enhancement of a large (surface area ≥100 sq. km) lake and reservoir database (1.GREALD). These efforts have also resulted in the spin-off of two additional databases, one containing lakes and reservoirs (2.GREALD, area 10–99 sq. km), and the other containing ephemeral lakes (3.GELD, area ≥100 sq. km). These databases are unique sources for projects that utilize satellite radar altimeter data to monitor surface water levels. While 1.GREALD aims to be a complete catalog, 2.GREALD focuses on reservoirs in response to applied sciences programs that monitor water and energy resources. The creation of 3.GELD has climate change objectives as well as water resources and ecosystem conservation applications. The recording of information pertaining to the potential overpasses (waterbody crossings) of the current and archive satellite altimeters is a primary objective as is the need to highlight any form of controlled water level variation. The permanent water databases now contain 6282 entries, half experience some form of anthropogenic influence and ∼430 have been identified as potential climatically sensitive terminal lakes. The revised integral surface area distribution is a power law with exponent −1.016. Statistics reveal that with altimetric repeat visit times of 10-day to monthly, at least 80% of the permanent water bodies (≥10 sq. km) have been overflown at some period since the 1990s. Current information on water use and reservoir formation date show that the primary use of the reservoir class is hydroelectric power, and that China, Brazil, India, Turkey, and Vietnam dominate the dam building in recent decades.

Charon M. Birkett↗
NASA NTRS1980

Long-time creep behavior of the niobium alloy C-103

The creep behavior of C-103 was studied as a function of stress, temperature, and grain size for test times to 19000 hr. Over the temperature range 827 to 1204 C and the stress range 6.89 to 138 MPa, only tertiary (accelerating) creep was observed. The creep strain epsilon can be related to time t by an exponential relation epsilon = epsilon(0) + K e raised to power (st) - 1), where epsilon (0) is initial creep strain, K is the tertiary creep strain parameter, and s is the tertiary creep rate parameter. The observed stress exponent 2.87 is similar to the three power law generally observed for secondary (linear) creep of Class I solid solutions. The apparent activation energy 374 kj/g mol is close to that observed for self diffusion of pure niobium. The initial tertiary creep rate was slightly faster for fine grained than for coarse-grained material. The strain parameter K can be expressed as a combination of power functions of stress and grain size and an exponential function of temperature. Strain time curves generated by using calculated values for K and s showed reasonable agreement with observed curves to strains of at least 4 percent. The time to 1 percent strain was related to stress, temperature, and grain size in a similar manner as the initial tertiary creep rate.

Titran, R. H.↗
NASA NTRS1992

The void spectrum in two-dimensional numerical simulations of gravitational clustering

An algorithm for deriving a spectrum of void sizes from two-dimensional high-resolution numerical simulations of gravitational clustering is tested, and it is verified that it produces the correct results where those results can be anticipated. The method is used to study the growth of voids as clustering proceeds. It is found that the most stable indicator of the characteristic void 'size' in the simulations is the mean fractional area covered by voids of diameter d, in a density field smoothed at its correlation length. Very accurate scaling behavior is found in power-law numerical models as they evolve. Eventually, this scaling breaks down as the nonlinearity reaches larger scales. It is shown that this breakdown is a manifestation of the undesirable effect of boundary conditions on simulations, even with the very large dynamic range possible here. A simple criterion is suggested for deciding when simulations with modest large-scale power may systematically underestimate the frequency of larger voids.

Kauffmann, Guinevere↗
NASA NTRS1979

Scaling laws and edge effects for polymer surface discharges

Specimens of Mylar sheet were exposed to a 20 kV electron beam. The resulting surface discharge arcs were photographed and the discharge current into a metal backing plate measured as a function of time. The area of the Mylar sheet was defined by a round aperture in a close-fitting metal mask, and the current pulse characteristics were plotted against area on log-log paper. The plots appear as straight lines (due to power-law behavior) with slopes of 0.50 for the peak current, 1.00 for the charge released, 1.49 for the energy and 0.55 for the pulse duration. Evidence is presented for the occurrence of banded charge distributions near grounded edges, on both Teflon and Mylar.

Balmain, K. G.↗
NASA NTRS1995

Spectroscopy of luminous infrared galaxies at 2 microns: 1. The ultraluminous galaxies (L(sub IR) approximately greater than 10 (exp 12) solar luminosity)

We present high-quality spectra covering the K window at a resolving power of 340 for a sample of 13 ultraluminous (L(sub IR) approximately greater than 10(exp 12) solar luminosity) infrared-selected galaxies, and line fluxes for a comparison sample of 24 lower luminosity galaxies. The 2 micrometers spectra of 10 of the ultraluminous galaxies are characterized by emission and absorption features commonly associated with stars and star formation; two others have the red power-law spectra and Br gamma line widths of Seyfert 1 galaxies; the final galaxy has strong emission from hot dust. We have found no broad-line active nuclei not already known from optical observations, despite the fact that the extinction at 2 micrometers is 1/10 that at optical wavelengths; any putative Seyfert 1 nuclei must be deeply buried. Powerful continua and emission lines from H2 and Br gamma are detected in all the ultraluminous galaxies. Comparing the H2 1-0 S(1), Br gamma, and 2 micrometers and far-infrared luminosities to those of the lower luminosity galaxies yields several major results. First, the dereddened Br gamma emission, relative to the far-infrared luminosity is significantly depressed in the ultraluminous sample, when compared to the lower luminosity galaxies. Five of the ultraluminous galaxies have L(sub Br gamma)L(sub IR) ratios lower than for any of the comparison objects. Second, the H2 1-0 S(1) luminosity is also responsible, directly or indirectly, for producing the excited H2, and that the H2 apparently comes from optically thin regions in both classes of objects. Third, eight of the 13 ultraluminous systems have lower 2 micrometers/far-infrared luminosity ratios than any of the lower luminosity galaxies, and five of these are the galaxies also deficient in Br gamma. These three findings may be understood if the the H2, Br gamma, and 2 mircometers continua in the ultraluminous galaxies arise from spatially distinct regions, with the continuum and Br gamma largely coming from volumes optically thick even at 2 micrometers, and obscured in such a fashion that the extinctions measured using optical spectroscopy do not properly measure the true optical depths. If this is the case, then even near-infrared spectroscopy may be unable to exclude the presence of undetected powerful active galactive nuclei in the ultraluminous galaxies.

Goldader, Jeffrey D.↗
NASA NTRS1993

A Simple Theory of Capillary-Gravity Wave Turbulence

Employing a recently proposed 'multi-wave interaction' theory [JFM, 243, 623-625], spectra of capillary-gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The resultant absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear Rossby waves) intractable by small-perturbation techniques, even in the weak turbulence limit. The analytical solution obtained in the present work is shown to be in good agreement with experimental data. Its low- and high-frequency limits yield power-laws characterizing spectra of purely gravity and capillary waves, respectively. In the limits of weak and strong linearity, these reduce of the Zakharov-Filonenko and Phillips spectra, respectively.

Glazman, Roman E.↗
NASA NTRS1972

The large Reynolds number - Asymptotic theory of turbulent boundary layers.

A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.

Mellor, G. L.↗
NASA NTRS1981

The structure of giant elliptical galaxies in poor clusters of galaxies

Detailed photographic surface photometry is presented of the nine first brightest galaxies in poor clusters suspected of being cD galaxies. The surface photometry is put on an absolute scale, using multiaperture photoelectric photometry. Oemler (1976) and de Vaucouleurs (1948) laws are fitted to the profiles to derive structural parameters, and the structural properties of the galaxies are compared with those of the cD galaxies in rich clusters studied by Oemler (1976) and those of normal ellipticals studied by Kormendy (1977). It is found that (1) the profiles of first brightest galaxies are well fitted by an r to the 1/4 power law over a range of more than nine magnitudes and down to the faintest light levels observed and (2) structural parameters characterizing only the central part of first brightest galaxies in poor and rich clusters, and excluding the envelope component in the case of rich clusters, smoothly extend properties exhibited by normal ellipticals. These observations are consistent with the idea that the central part of first brightest galaxies in both poor and rich clusters is made up by the mergers of smaller galaxies.

Thuan, T. X.↗
NASA NTRS1994

Characteristics of the persistent emission of SGR 1806-20

Earlier, using the X-ray satellite ASCA, we had identified the soft gamma-ray burst repeater (SGR) 1806-20 with a persistent X-ray source, AX 1805.7-2025 which is located close to the center of the radio supernova remnant G10.0-0.3. A burst seen by Burst and Transient Source Experiment (BATSE) was shown to be centered on G10.0-0.3. Here we report detailed temporal and spectral analysis of the persistent source. We find that AX 1805.7-2025 is a very compact source, size less than 30 sec in diameter, with a power-law spectrum. The count rate from AX 1805.7-2025 is steady on timescales of minutes, days, and 1 week. Most supernova remnants have extended X-ray emission ascribed to shocked gas. We set an upper limit to an extended X-ray emission both in continuum and line emission. We conclude that an isolated neutron star, most likely a pulsar, powers the radio remnant G10.0-0.3. Finally, we note that the persistent spectrum appears to be less absorbed than the burst spectrum.

Sonobe, T.↗
DOE OSTI2022

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

Here, using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

36 MATERIALS SCIENCE↗
NASA NTRS1982

Creep crack-growth: A new path-independent integral (T sub c), and computational studies

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Stonesifer, R. B.↗
DOE OSTI2020

Multiwavelength Observations of 2HWC J1928+177: Dark Accelerator or New TeV Gamma-Ray Binary?

2HWC J1928+177 is a Galactic TeV gamma-ray source detected by the High Altitude Water Cherenkov (HAWC) Observatory up to ~56 TeV. The HAWC source, later confirmed by the High Energy Stereoscopic System, still remains unidentified as a dark accelerator since there is no apparent supernova remnant or pulsar wind nebula detected in the lower-energy bands. The radio pulsar PSR J1928+1746, coinciding with the HAWC source position, has no X-ray counterpart. In this work, our SED modeling shows that inverse Compton scattering in the putative pulsar wind nebula can account for the TeV emission only if the unseen nebula is extended beyond $r\sim 4^{\prime} $. Alternatively, TeV gamma-rays may be produced by hadronic interactions between relativistic protons from an undetected supernova remnant associated with the radio pulsar and a nearby molecular cloud G52.9+0.1. NuSTAR and Chandra observations detected a variable X-ray point source within the HAWC error circle, potentially associated with a bright infrared (IR) source. The X-ray spectra can be fitted with an absorbed power-law model with N H = (9 ± 3) × 10 22 cm –2 and Γ X = 1.6 ± 0.3 and exhibit long-term X-ray flux variability over the last decade. If the X-ray source, possibly associated with the IR source (likely an O star), is the counterpart of the HAWC source, it may be a new TeV gamma-ray binary powered by collisions between the pulsar wind and stellar wind. Follow-up X-ray observations are warranted to search for diffuse X-ray emission and determine the nature of the HAWC source.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

Correlation techniques and measurements of wave-height statistics

Statistical measurements of wave height fluctuations have been made in a wind wave tank. The power spectral density function of temporal wave height fluctuations evidenced second-harmonic components and an f to the minus 5th power law decay beyond the second harmonic. The observations of second harmonic effects agreed very well with a theoretical prediction. From the wave statistics, surface drift currents were inferred and compared to experimental measurements with satisfactory agreement. Measurements were made of the two dimensional correlation coefficient at 15 deg increments in angle with respect to the wind vector. An estimate of the two-dimensional spatial power spectral density function was also made.

Guthart, H.↗
NASA NTRS1988

Polarization asymmetry in two-electron photodetachment - A cogent test of the ionization threshold law

A very sensitive test of the electron-atom ionization threshold law is suggested: for spin-aligned heavy negative ions it consists of measuring the polarization asymmetry A(PA) coming from double detachment by left- versus right-circularly polarized light. The respective yields are worked out for the Te(-) (5p)5 2P(3/2) ion. The Coulomb-dipole theory predicts A(PA) to be the ratio of two oscillating functions in sharp contrast to any power law (specifically that of Wannier, 1953) for which the ratio is expected to be a smooth function of energy.

Temkin, A.↗
NASA NTRS1988

Crater size estimates for large-body terrestrial impact

Calculating the effects of impacts leading to global catastrophes requires knowledge of the impact process at very large size scales. This information cannot be obtained directly but must be inferred from subscale physical simulations, numerical simulations, and scaling laws. Schmidt and Holsapple presented scaling laws based upon laboratory-scale impact experiments performed on a centrifuge (Schmidt, 1980 and Schmidt and Holsapple, 1980). These experiments were used to develop scaling laws which were among the first to include gravity dependence associated with increasing event size. At that time using the results of experiments in dry sand and in water to provide bounds on crater size, they recognized that more precise bounds on large-body impact crater formation could be obtained with additional centrifuge experiments conducted in other geological media. In that previous work, simple power-law formulae were developed to relate final crater diameter to impactor size and velocity. In addition, Schmidt (1980) and Holsapple and Schmidt (1982) recognized that the energy scaling exponent is not a universal constant but depends upon the target media. Recently, Holsapple and Schmidt (1987) includes results for non-porous materials and provides a basis for estimating crater formation kinematics and final crater size. A revised set of scaling relationships for all crater parameters of interest are presented. These include results for various target media and include the kinematics of formation. Particular attention is given to possible limits brought about by very large impactors.

Schmidt, Robert M.↗
NASA NTRS1973

Results on the energy dependence of cosmic ray charge composition

Measurements using a balloon-borne ionization spectrometer on the differential energy spectra of the heavy nuclei of the galactic cosmic radiation are reported. The spectra of individual elements up to oxygen and groups of nuclei up through iron were measured up to almost 100 GeV/nucleon. The energy spectrum of the secondary nuclei, B+N, is steeper than that of the primary nuclei, C+O, by gamma = 0.21 + or - .09 in agreement with other authors. The spectral shapes found are reasonably well represented by single power laws between 2 and 60 GeV/nucleon. Data are consistent with the decrease in the secondary to primary ratio found by others above 20 GeV/nucleon, but it shows no evidence for any sudden change in this ratio within counting statistics. The most dramatic finding is that the spectrum of the iron nuclei is flatter than that of the carbon and oxygen nuclei by 0.57 + or - 0.14 of a power. The experimental techniques for charge and energy determination are presented and corrections due to nuclear disintegration and losses of energy out the bottom of the spectrometer are discussed.

Balasubrahmanyan, V. K.↗
DOE OSTI2023

Single‐Step Deformation Processing of Ultrathin Lithium Foil and Strip

Abstract Next‐generation, high‐efficiency energy storage and conversion systems require development of lithium metal batteries. But the high cost of production and constraints on thickness of lithium (anode) foils continue to limit adoption for integration into battery cell architectures. Here, a novel lithium anode manufacturing solution is demonstrated – single‐step production of ultrathin gauge foil formats directly from solid ingot. Hybrid cutting‐based deformation processes, involving large plastic strains and strain rates, produce foil to sub‐10 µm thickness, with surface quality even superior to present Li anode processing routes. Energy analysis shows the single‐stage processing is ≈50% more efficient than conventional processing by extrusion‐rolling. Through in situ force measurements and high‐speed imaging of the cutting it also characterize – for the first time – the flow stress of Li to strain rates of 800 sec −1 , revealing a power‐law relationship. The results present a paradigm shift in manufacturing and integration of solid lithium anodes for energy applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗