Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXPONENTIAL FUNCTION”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

The radial variation of H i velocity dispersions in dwarfs and spirals

Gas velocity dispersions provide important diagnostics of the forces counteracting gravity to prevent collapse of the gas. We use the 21 cm line of neutral atomic hydrogen (H i) to study H i velocity dispersion (σ{sub H I}) and H i phases as a function of galaxy morphology in 22 galaxies from The H i Nearby Galaxy Survey. We stack individual H i velocity profiles and decompose them into broad and narrow Gaussian components. We study the H i velocity dispersion and the H i surface density, Σ{sub H I}, as a function of radius. For spirals, the velocity dispersions of the narrow and broad components decline with radius and their radial profiles are well described by an exponential function. For dwarfs, however, the profiles are much flatter. The single Gaussian dispersion profiles are, in general, flatter than those of the narrow and broad components. In most cases, the dispersion profiles in the outer disks do not drop as fast as the star formation profiles derived in the literature. This indicates the importance of other energy sources in driving σ{sub H I} in the outer disks. The radial surface density profiles of spirals and dwarfs are similar. The surface density profiles of the narrow component decline more steeply than those of the broad component, but not as steep as what was found previously for the molecular component. As a consequence, the surface density ratio between the narrow and broad components, an estimate of the mass ratio between cold H i and warm H i, tends to decrease with radius. On average, this ratio is lower in dwarfs than in spirals. This lack of a narrow, cold H i component in dwarfs may explain their low star formation activity.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

The BMW analytic aerodynamic drag method for the Vinti satellite theory

In order to retain separability in the Vinti theory of earth satellite motion when a non conservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which reproduces tabular values of static model atmospheric densities at all altitudes to within ninety-eight percent and simultaneously reduces the variational equations to indefinite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program. Results of the BMW (Bonavito, Mistretta, Watson) theory for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by the BMW theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time.

Watson, J. S.↗
DOE OSTI2013

Hadron transverse momentum distributions in muon deep inelastic scattering at 160 GeV/c

Multiplicities of charged hadrons produced in deep inelastic muon scattering off a 6 LiD target have been measured as a function of the DIS variables x Bj , Q 2 , W 2 and the final state hadron variables p T and z . The p$2\atop{T}$ distributions are fitted with a single exponential function at low values of p$2\atop{T}$ to determine the dependence of ⟨p$2\atop{T}$⟩ on x Bj , Q 2 , W 2 and z . The z -dependence of ⟨p$2\atop{T}$⟩ is shown to be a potential tool to extract the average intrinsic transverse momentum squared of partons, ⟨ k $2\atop{⊥}$⟩, as a function of x Bj and Q 2 in a leading order QCD parton model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocks

The spatial heterogeneity of land surfaces affects energy, moisture, and greenhouse gas exchanges with the atmosphere. However, representing the heterogeneity of terrestrial hydrological and biogeochemical processes in Earth system models (ESMs) remains a critical scientific challenge. We report the impact of spatial scaling on environmental controls, spatial structure, and statistical properties of soil organic carbon (SOC) stocks across the US state of Alaska. We used soil profile observations and environmental factors such as topography, climate, land cover types, and surficial geology to predict the SOC stocks at a 50 m spatial scale. These spatially heterogeneous estimates provide a data set with reasonable fidelity to the observations at a sufficiently high resolution to examine the environmental controls on the spatial structure of SOC stocks. We upscaled both the predicted SOC stocks and environmental variables from finer to coarser spatial scales ( s = 100, 200, and 500 m and 1, 2, 5, and 10 km) and generated various statistical properties of SOC stock estimates. We found different environmental factors to be statistically significant predictors at different spatial scales. Only elevation, temperature, potential evapotranspiration, and scrub land cover types were significant predictors at all scales. The strengths of control (the median value of geographically weighted regression coefficients) of these four environmental variables on SOC stocks decreased with increasing scale and were accurately represented using mathematical functions ( R 2 = 0.83–0.97). The spatial structure of SOC stocks across Alaska changed with spatial scale. Although the variance (sill) and unstructured variability (nugget) of the calculated variograms of SOC stocks decreased exponentially with scale, the correlation length (range) remained relatively constant across scale. The variance of predicted SOC stocks decreased with spatial scale over the range of 50 m to ~ 500 m, and remained constant beyond this scale. The fitted exponential function accounted for 98 % of variability in the variance of SOC stocks. We found moderately accurate linear relationships between mean and higher-order moments of predicted SOC stocks ( R 2 ∼ 0.55–0.63). Current ESMs operate at coarse spatial scales (50–100 km), and are therefore unable to represent environmental controllers and spatial heterogeneity of high-latitude SOC stocks consistent with observations. We conclude that improved understanding of the scaling behavior of environmental controls and statistical properties of SOC stocks could improve ESM land model benchmarking and perhaps allow representation of spatial heterogeneity of biogeochemistry at scales finer than those currently resolved by ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocks

The spatial heterogeneity of land surfaces affects energy, moisture, and greenhouse gas exchanges with the atmosphere. However, representing heterogeneity of terrestrial hydrological and biogeochemical processes in earth system models (ESMs) remains a critical scientific challenge. We report the impact of spatial scaling on environmental controls, spatial structure, and statistical properties of soil organic carbon (SOC) stocks across the US state of Alaska. We used soil profile observations and environmental factors such as topography, climate, land cover types, and surficial geology to predict the SOC stocks at a 50 m spatial scale. These spatially heterogeneous estimates provide a dataset with reasonable fidelity to the observations at a sufficiently high resolution to examine the environmental controls on the spatial structure of SOC stocks. We upscaled both the predicted SOC stocks and environmental variables from finer to coarser spatial scales ( s = 100, 200, 500 m, 1, 2, 5, 10 km) and generated various statistical properties of SOC stock estimates. We found different environmental factors to be statistically significant predictors at different spatial scales. Only elevation, temperature, potential evapotranspiration, and scrub land cover types were significant predictors at all scales. The strengths of control (the median value of geographically weighted regression coefficients) of these four environmental variables on SOC stocks decreased with increasing scale and were accurately represented using mathematical functions ( R 2 = 0.83–0.97). The spatial structure of SOC stocks across Alaska changed with spatial scale. Although the variance (sill) and unstructured variability (nugget) of the calculated variograms of SOC stocks decreased exponentially with scale, the correlation length (range) remained relatively constant across scale. The variance of predicted SOC stocks decreased with spatial scale over the range of 50 to ~ 500 m, and remained constant beyond this scale. The fitted exponential function accounted for 98% of variability in the variance of SOC stocks. We found moderately-accurate linear relationships between mean and higher-order moments of predicted SOC stocks ( R 2 ~ 0.55–0.63). Current ESMs operate at coarse spatial scales (50–100 km), and are therefore unable to represent environmental controllers and spatial heterogeneity of high-latitude SOC stocks consistent with observations. We conclude that improved understanding of the scaling behavior of environmental controls and statistical properties of SOC stocks can improve ESM land model benchmarking and perhaps allow representation of spatial heterogeneity of biogeochemistry at scales finer than those currently resolved by ESMs.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Ultraviolet radiation effects on the infrared damage rate of a thermal control coating

The effects of ultraviolet radiation on the infrared reflectance of ZnO silicone white thermal coatings were investigated. Narrow band ultraviolet radiation for wavelengths in the 2200A to 3500A range by a monochromator and a high pressure, 150-W Eimac xenon lamp. The sample was irradiated while in a vacuum of at least 0.000001 torr, and infrared reflectance was measured in situ with a spectroreflectometer at 19,500A. Reflectance degradation was studied as a function of wavelength, time, intensity, and dose. Damage was wavelength dependent at constant exposure, but no maximum was evident above the shortest wavelength investigated here. The degradation rate at constant intensity was an exponential function of time and varies with intensity.

Bass, J. A.↗
NASA NTRS1979

Development of a winter wheat adjustable crop calendar model

The author has identified the following significant results. Least squares techniques were applied for parameter estimation of functions to predict winter wheat phenological stage with daily maximum temperature, minimum temperature, daylength, and precipitation as independent variables. After parameter estimation, tests were conducted using independent data. It may generally be concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson triquadratic form, in general use for spring wheat, yielded good results, but special techniques and care are required. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with averaged daily environmental values as independent variables.

Baker, J. R.↗
DOE OSTI2021

Interface pinning causes the hysteresis of the hydride transformation in binary metal hydrides

Hydriding and dehydriding transitions in bulk and nanocrystalline binary metal hydrides were studied using the Pd-H model system by measuring pressure-composition isotherms with in situ x-ray diffractometry. Nanocrystalline Pd showed a smaller pressure hysteresis, solvus hysteresis, and hysteresis in lattice parameter, compared to bulk Pd. The time-dependence of pressure equilibration was measured after dosing with aliquots of hydrogen, giving equilibration times that were much faster in the single-phase regions than in the two-phase plateaus. In the broad two-phase plateaus, the pressure relaxations were exponential functions of time. An explanation of hysteresis is developed that is based on a dissipative potential barrier that impedes the motion of the interface due to interactions between lattice defects and the two-phase interface. The exponential pressure relaxations and hysteresis are consistent for this mechanism. For a simple model of the pinning potential, the potential barrier maximum is an order of magnitude less than typical grain boundary energies. These pinning effects are substantially different in the nanocrystalline Pd, suggesting differences in the hydriding mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Manifestation of dynamic chaos in spin-spin relaxation processes in a solid

The results of several experiments on the dynamics of paramagnetic spin systems are analyzed on the basis of the theory developed here. It is shown that the asymptotic expressions for time correlation functions of various (high) orders are mutually similar and have a characteristic form [18], which probably indicates the 'forgetting' of the initial conditions due to the development of Lyapunov instability in the dynamic system. The existence of exponential functions with close exponents, which describe the damping of correlations in the experimental observation of signals from free NMR precession and their buildup in experiments on multiquantum NMR, are manifestations of this instability because the Lyapunov exponents exist in pairs. The results suggest the development of 'deterministic chaos' in the systems under investigation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

A COMPARATIVE STUDY OF OPTICAL/ULTRAVIOLET VARIABILITY OF NARROW-LINE SEYFERT 1 AND BROAD-LINE SEYFERT 1 ACTIVE GALACTIC NUCLEI

The ensemble optical/ultraviolet (UV) variability of narrow-line Seyfert 1 (NLS1)-type active galactic nuclei (AGNs) is investigated, based on a sample selected from the Sloan Digital Sky Survey (SDSS) Stripe 82 region with multi-epoch photometric scanning data. As a comparison, a control sample of broad-line Seyfert 1 (BLS1)-type AGNs is also incorporated. To quantify properly the intrinsic variation amplitudes and their uncertainties, a novel method of parametric maximum likelihood is introduced that has, as we argued, certain virtues over previously used methods. The majority of NLS1-type AGNs exhibit significant variability on timescales from about 10 days to a few years with, however, smaller amplitudes on average compared to BLS1-type AGNs. About 20 NLS1-type AGNs that show relatively large variations are presented and may deserve future monitoring observations, for instance, reverberation mapping. The averaged structure functions of variability, constructed using the same maximum likelihood method, show remarkable similarity in shape for the two types of AGNs on timescales longer than about 10 days, which can be approximated by a power law or an exponential function. This, along with other similar properties, such as the wavelength-dependent variability, is indicative of a common dominant mechanism responsible for the long-term optical/UV variability of both NLS1- and BLS1-type AGNs. Toward the short timescales, however, there is tentative evidence that the structure function of NLS1-type AGNs continues to decline, whereas that of BLS1-type AGNs flattens with some residual variability on timescales of days. If this can be confirmed, it may suggest that an alternative mechanism, such as X-ray reprocessing, starts to dominate in BLS1-type AGNs, but not in NLS1-type AGNs, on such timescales.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1947

The Oscillating Circular Airfoil on the Basis of Potential Theory

Proceeding from the thesis by W. Kinner the present report treats the problem of the circular airfoil in uniform airflow executing small oscillations, the amplitudes of which correspond to whole functions of the second degree in x and y. The pressure distribution is secured by means of Prandtl's acceleration potential. It results in a system of linear equations the coefficients of which can be calculated exactly with the aid of exponential functions and Hankel's functions. The equations necessary are derived in part I; the numerical calculation follows in part II.

Schade, T.↗
NASA NTRS2008

Multispectral Emission of the Sun during the First Whole Sun Month: Magnetohydrodynamic Simulations

We demonstrate that a three-dimensional magnetohydrodynamic (MHD) simulation of the corona can model its global plasma density and temperature structure with sufficient accuracy to reproduce many of the multispectral properties of the corona observed in extreme ultraviolet (EW) and X-ray emission. The key ingredient to this new type of global MHD model is the inclusion of energy transport processes (coronal heating, anisotropic thermal conduction, and radiative losses) in the energy equation. The calculation of these processes has previously been confined to one-dimensional loop models, idealized two-dimensional computations, and three-dimensional active region models. We refer to this as the thermodynamic MHD model, and we apply it to the time period of Carrington rotation 1913 (1996 August 22 to September 18). The form of the coronal heating term strongly affects the plasma density and temperature of the solutions. We perform our calculation for three different empirical heating models: (1) a heating function exponentially decreasing in radius; (2) the model of Schrijver et al.; and (3) a model reproducing the heating properties of the quiet Sun and active regions. We produce synthetic emission images from the density and temperature calculated with these three heating functions and quantitatively compare them with observations from E W Imaging Telescope on the Solar and Heliospheric Observatory and the soft X-ray telescope on Yohkoh. Although none of the heating models provide a perfect match, heating models 2 and 3 provide a reasonable match to the observations.

Lionello, Roberto↗
DOE OSTI2016

Investigation of liquid cloud microphysical properties of deep convective systems: 1. Parameterization raindrop size distribution and its application for stratiform rain estimation

Abstract To investigate liquid‐phase ( T > 3°C) cloud and precipitation microphysical properties within Deep Convective Systems (DCSs), eight DCS cases sampled by the University of North Dakota Citation II research aircraft during Midlatitude Continental Convective Clouds Experiment were selected. A full spectrum of raindrop size distribution (DSD) was constructed from 120 µm to 4000 µm through a combination of two‐dimensional cloud probe (120 to 900 µm) and High Volume Precipitation Spectrometer (900 to 4000 µm) data sets. A total of 1126 five second DSDs have been used to fit to Gamma and Exponential functions within the stratiform rain (SR) regions of DCSs. The Gamma shape μ Γ and slope λ Γ parameters are then compared with those derived from surface disdrometer measurements. The similar μ Γ ‐ λ Γ relationships but different μ Γ and λ Γ value ranges from two independent platforms at different elevations may represent the real nature of DSD shape information in clouds and at the surface. To apply the exponentially fitted DSD parameters to precipitation estimation using Next Generation Weather Radar (NEXRAD) radar reflectivity factor Z e , the terms N 0 E and λ E have been parameterized as a function of Z e using an empirical N 0 E ‐ λ E relationship. The averaged SR rain rate retrieved from this study is almost identical to the surface measurements, while the NEXRAD Q2 precipitation is twice as large. The comparisons indicate that the new DSD parameterization scheme is robust, while the Q2 SR precipitation estimation based on Marshall‐Palmer Z‐R relationship, where a constant DSD intercept parameter ( N 0 E ) was assumed, needs to be improved for heavy precipitation cases.

Wang, Jingyu↗
NASA NTRS1975

Turbulence in a gaseous hydrogen-liquid oxygen rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a LOX-GH2 rocket combustion chamber was determined from experimental measurements of tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and a numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber, and an exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the value of the intensity of turbulence reaches a maximum of 14% at a location about 7" downstream from the injector. The Lagrangian correlation coefficient associated with this value is given by the above exponential expression where alpha = 10,000/sec.

Lebas, J.↗
DOE OSTI2025

Predicting Pulsed-Laser Deposition SrTiO 3 Homoepitaxy Growth Dynamics Using High-Speed Reflection High-Energy Electron Diffraction

Pulsed-laser deposition (PLD) is a powerful technique for growing complex oxides with controlled stoichiometry. To understand growth dynamics therein, it is common to leverage in situ spectroscopies, such as reflection high-energy electron diffraction (RHEED), to monitor surface crystallinity. Most commercial systems rely on video-rate cameras operating at 60-120 Hz that lack sufficient temporal resolution to capture growth dynamics at practical deposition frequencies. Here, a high-speed platform to record in situ dynamics via RHEED at >500 Hz is implemented. An open-source analysis package is designed to fit diffraction spots to 2D Gaussians, allowing single-pulse surface reconstruction kinetics extraction. Using homoepitaxially deposited (001)-oriented SrTiO 3 as a model system, we demonstrate how high-speed RHEED can provide real-time insight into growth processes obscured by slower acquisition systems. By fitting the single-pulse intensity to a set of exponential functions, we observe changes in the characteristic decay time and mechanism correlated to the substrate step width and surface termination. We observe distinct surface effects, with diffraction intensity decaying on lower-energy TiO 2 -terminated surfaces and stabilizing on SrO- or mixed-terminated surfaces. Similarly, using an exponential model, the extracted characteristic time of adatom deposition decreases with increased density of bonding sites associated with mixed termination and narrower step widths. Ultimately, this work shows how increasing RHEED temporal resolution can uncover new insights into growth processes, with practical implications for the design and control of PLD processes. This experimental platform provides new capabilities to enable data-driven machine learning analysis and autonomous control systems to enhance the complexity and fecundity of PLD.

(SrO)↗
DOE OSTI2023

Investigating the vertical distribution of the disk as a function of radial action

As heating processes can broaden the distributions of radial actions and the vertical distributions of the Galactic disks, we investigate the vertical distribution of the Galactic disks as a function of radial action based on Apache Point Observatory Galactic Evolution Experiment (APOGEE) and Gaia data in order to deepen our understanding of the formation and heating history of the Galactic disks. The vertical distributions of the thin and thick Galactic disks defined in the chemical plane were fitted with a simple exponential function with a free parameter of scale height in different radial action ranges. Therefore, we were able to analyze the scale height as a function of radial action for different disk populations. We find that the distributions of radial action for both the thin and thick disks can be approximately described by pseudo-isothermal distributions, which give a statistical measurement for the temperature of the disk as indicated by the mean radial action of the star sample. Estimations of the scale heights in different radial action ranges for these pseudo-isothermal distributions of the disks seem to show fixed relationships between radial action J R and scale height h. We describe these relationships with a two-parameter function of h = √(J R /a)+b, where a and b are free parameters. When testing with a three-parameter function of h = α √(J R /a)+b, we find that this two-parameter function describes the thin disk well, but we note the function should be used with care for the thick disk. When comparing the best-fit relationships between the inner and outer disk for both of the thin and thick disks, we find that the relationships are nearly the same for the thin disks but are different for the thick disks. The inner thick disk shows a nearly flattened relationship, while the outer thick disk presents a gradually increasing relationship. This work highlights an alternative way to unveil the heating history of the disks by investigating the relationship between scale height and radial action, as these relationships encode the formation and heating history of the Galactic disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Self-Diffusivity Measurement of Eutectic F 7 LiNaK with and without Additives Using Quasi-Elastic Neutron Scattering

The atomic scale relaxation dynamics of eutectic F 7 LiNaK (46.5 LiF–11.5 NaF–42 KF mol %, Li-7 enriched) were measured using quasi-elastic neutron scattering (QENS) over a temperature range of 500–750 °C. Here, the effect of adding 0.988 mol % cerium, 0.499 mol % cesium, and 1.21 mol % zirconium individually to the dynamics of F 7 LiNaK was also investigated. The relaxation process in both pure and doped F 7 LiNaK molten salts was fit with a stretched exponential function and the temperature dependence follows an Arrhenius behavior over a wavevector transfer range of 0.4 Å –1 < Q < 0.9 Å –1 . The measured activation energy for self-diffusion is E a = 0.77 ± 0.02 eV/atom for pure molten F 7 LiNaK. The QENS response with additives added to F 7 LiNaK was also fit with a stretched exponential and the associated Arrhenius behavior was characterized with activation energies of E a = 0.88 ± 0.01 eV/atom for zirconium (1.21 mol %), E a = 1.02 ± 0.02 eV/atom for cerium (0.988 mol %), and E a = 0.71 ± 0.03 eV/atom for cesium (0.499 mol %). The measured diffusivities are compared to those simulated with a neural network force field model by Lee et al. [Lee, S.-C. Comparative Studies of the Structural and Transport Properties of Molten Salt FLiNaK Using the Machine-Learned Neural Network and Reparametrized Classical Forcefields. J. Phys. Chem. B 2021, 125(37), 10562–10570].

FLiNaK↗
DOE OSTI2014

A new approach to investigate leakage current mechanisms in infrared photodiodes from illuminated current-voltage characteristics

This paper presents a new approach to investigate leakage current mechanisms in infrared photodiodes from the illuminated current–voltage characteristics. The example of mid-wave mercury cadmium telluride photodiodes is presented to illustrate the new approach. The new method is suitable for evaluating diodes in an array environment as advance knowledge of any of the material or device parameters are not required. The thermal saturation current is estimated from the observed open circuit voltage and zero-bias current (photo-current) of the diode. The ohmic shunt resistance is estimated from the observed maximum dynamic impedance of the diode. The experimentally observed reverse bias diode current in excess of thermal current, photo-current, and ohmic shunt current is reported to be best described by an exponential function of the type, I{sub excess} = I{sub r0} + K{sub 1} exp (K{sub 2} V), where I{sub r0}, K{sub 1}, and K{sub 2} are fitting parameters and V is the applied bias voltage. Our investigations reveal a close link between the excess current and the sources of ohmic currents in the diode. Exponential growth of excess current with the applied bias voltage has been interpreted as an indication of soft breakdown of the diodes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗