Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ERROR 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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Probing the carrier concentration profiles in phosphorus-implanted germanium using infrared spectroscopic ellipsometry

Spectroscopic ellipsometry with photon energy in the 0.045–0.65 eV range was used to investigate germanium samples implanted with 30 keV phosphorus ions and annealed at 700 °C. The infrared response of implanted layers is dominated by free carrier absorption which is modeled using a Drude oscillator. The carrier concentration profiles were modeled using an error function, and compared with those obtained by electrochemical capacitance-voltage profiling and secondary ion mass spectrometry. In the flat region of the carrier concentration profile, average carrier concentration and mobility of 1.40 × 10{sup 19} cm{sup −3} and 336 cm{sup 2}V{sup −1}s{sup −1}, respectively, were obtained. A phosphorus diffusivity of ∼1.2 × 10{sup −13} cm{sup 2}/s was obtained. The mobility versus carrier concentration relationships obtained for the implanted samples are close to the empirical relationship for bulk Ge.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Intermixing in Cu/Ni multilayers induced by cold rolling

Repeated cold rolling was performed on multilayers of Cu60/Ni40 and Cu40/Ni60 foil arrays to study the details of driven atomic scale interfacial mixing. With increasing deformation, there is a significant layer refinement down to the nm level that leads to the formation of a solid solution phase from the elemental end members. Intriguingly, the composition of the solid solution is revealed by an oscillation in the composition profile across the multilayers, which is different from the smoothly varying profile due to thermally activated diffusion. During the reaction, Cu mixed into Ni preferentially compared to Ni mixing into Cu, which is also in contrast to the thermal diffusion behavior. This is confirmed by observations from X-ray diffraction, electron energy loss spectrum and atom probe tomography. The diffusion coefficient induced by cold rolling is estimated as 1.7 × 10{sup −17} m{sup 2}/s, which cannot be attributed to any thermal effect. The effective temperature due to the deformation induced mixing is estimated as 1093 K and an intrinsic diffusivity d{sub b}, which quantifies the tendency towards equilibrium in the absence of thermal diffusion, is estimated as 6.38 × 10{sup −18} m{sup 2}/s. The fraction of the solid solution phase formed is illustrated by examining the layer thickness distribution and is described by using an error function representation. The evolution of mixing in the solid solution phase is described by a simplified sinusoid model, in which the amplitude decays with increased deformation level. The promoted diffusion coefficient could be related to the effective temperature concept, but the establishment of an oscillation in the composition profile is a characteristic behavior that develops due to deformation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A unified thermionic and thermionic-field emission (TE–TFE) model for ideal Schottky reverse-bias leakage current

We present a unified thermionic emission (TE) and thermionic-field emission (TFE) model for the ideal reverse-bias leakage current in Schottky junctions. The unified TE–TFE analytical model advances upon previous analytical TFE models by Murphy–Good and Padovani–Stratton, which are the two most widely adopted models by the community, in two major aspects: (i) the applicability of the TFE expression therein is extended to near-zero surface electric fields by an error-function correction, allowing for the calculation of the total current by a nontrivial sum of TE (over-the-barrier current) and TFE (below-the-barrier current) contributions; therefore, an accurate description of the TE-to-TFE transition region is captured analytically for the first time; (ii) image-force lowering is considered with much-simpler correction terms. Comparisons with the reference numerical model show that the unified TE–TFE model has excellent accuracy, as well as a 10 000× reduction in computation time. The unified model is further tested against experimental data from Schottky barrier diodes based on Si, 4H-SiC, GaN, and β-Ga 2 O 3 , revealing accurate extractions of barrier heights and correct descriptions of the ideal reverse leakage characteristics. With the extended applicable range, improved accuracy, and computational efficiency, the unified TE–TFE model is highly valuable for the design and analysis of devices based on Schottky junctions, as well as for potential integration in technology computer-aided design (TCAD) tools.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Continuum radiated power density $(P^{\textrm{C}}_{\textrm{rad}})$ and effective charge $(Z_{\textrm{eff}})$ estimates from multi-energy photon-counting measurements

Multi-energy soft x-ray pinhole cameras have been designed, built, calibrated, and operated at Madison symmetric Torus, Alcator C-Mod, and more recently at Tokamak a configuration variable and Tungsten Environment in Steady-State Tokamak (WEST), to measure plasma emission across multiple energy ranges. Here we describe a new methodology to estimate the local continuum radiated power density and the plasma effective charge (Z eff ) directly from photon-counting measurements of the line-free continuum emission (Bremsstrahlung and Radiative Recombination) in several energy bands between 11 and 18 keV. This capability is particularly valuable for confinement systems using metal plasma-facing components, where x-ray losses from interactions with the sputtered wall can represent a significant fraction of the total radiated power (P rad ). The approach leverages a well-characterized detector responsivity, modeled by a complementary error function, and interprets the differential multi-energy measurements between adjacent energy levels through the probability density function of a Gaussian distribution. The implementation of this diagnostic technique is currently under development on the WEST tokamak, aiming at the goal of providing real-time P rad and Z eff measurements during long-pulse operation (up to 1000 s) in the 2026 campaign.

WEST↗
DOE OSTI2024

Local step-flow dynamics in thin film growth with desorption

Desorption of deposited species plays a role in determining the evolution of surface morphology during crystal growth when the desorption time constant is short compared with the time to diffuse to a defect site, step edge, or kink. However, experiments to directly test the predictions of these effects are lacking. Novel techniques such as in situ coherent x-ray scattering can provide significant new information. Herein we present x-ray photon correlation spectroscopy (XPCS) measurements during diindenoperylene (DIP) vapor deposition on thermally oxidized silicon surfaces. DIP forms a nearly complete two-dimensional first layer over the range of temperatures studied (40–120 ⁢°C), followed by mounded growth during subsequent deposition. Local step flow within mounds was observed, and we find that there was a terrace-length-dependent behavior of the step edge dynamics. This led to unstable growth with rapid roughening (β>0.5) and deviation from a symmetric error-function-like height profile. At high temperatures, the grooves between the mounds tend to close up leading to nearly flat polycrystalline films. In conclusion, numerical analysis based on a (1+1)-dimensional model suggests that terrace-length dependent desorption of deposited ad-molecules is an essential cause of the step dynamics, and it influences the morphology evolution.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Evaluation of a coastal acoustic buoy for cetacean detections, bearing accuracy and exclusion zone monitoring

Abstract There is strong socio‐political support for offshore wind development in US territorial waters and construction is planned off several east coast states. Some of the planned development sites coincide with important habitat for critically endangered North Atlantic right whales. Both exclusion zones and passive acoustic monitoring are important tools for managing interactions between marine mammals and human activities. Understanding where animals are with respect to exclusion zones is important to avoid costly construction delays while minimizing the potential for negative impacts. Impact piling from construction of hundreds of offshore wind turbines likely require exclusion zones as large as 10 km. We have developed a three‐hydrophone passive acoustic monitoring system that provides bearing information along with marine mammal detections to allow for informed management decisions in real‐time. Multiple units form a monitoring system designed to determine whether marine mammal calls originate from inside or outside of an exclusion zone. In October 2021, we undertook a full system validation, with a focus on evaluating the detection range and bearing accuracy of the system with respect to right whale upcalls. Five units were deployed in Mid‐Atlantic waters and we played more than 3500 simulated right whale upcalls at known locations to characterize the detection function and bearing accuracy of each unit. The modelled results of the detection function error were then used to compare the effectiveness of a bearing‐based system to a single sensor that can only detect a signal but not ascertain directivity. Field trials indicated maximum detection ranges from 4–7.3 km depending on source and ambient noise levels. Simulations showed that incorporating bearing detections provide a substantial improvement in false alarm rates (6 to 12 times depending on number of units, placement and signal to noise conditions) for a small increase in the risk of missed detections inside of an exclusion zone (1%–3%). We show that the system can be used for monitoring exclusion zones and clearly highlight the value of including bearing estimation into exclusion zone monitoring plans while noting that placement and configuration of units should reflect anticipated ambient noise conditions.

17 WIND ENERGY↗
DOE OSTI2016

SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies have employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Oxygen diffusion in garnet: Experimental calibration and implications for timescales of metamorphic processes and retention of primary O isotopic signatures

Knowledge of oxygen diffusion in garnet is crucial for a correct interpretation of oxygen isotope signatures in natural samples. A series of experiments was undertaken to determine the diffusivity of oxygen in garnet, which remains poorly constrained. The first suite included high-pressure (HP), nominally dry experiments performed in piston-cylinder apparatus at: (1) T = 1050–1600 °C and P = 1.5 GPa and (2) T = 1500 °C and P = 2.5 GPa using yttrium aluminum garnet (YAG; Y3Al5O12) cubes. Second, HP H2O-saturated experiments were conducted at T = 900 °C and P = 1.0–1.5 GPa, wherein YAG crystals were packed into a YAG + Corundum powder, along with 18O-enriched H2O. Third, 1 atm experiments with YAG cubes were performed in a gas-mixing furnace at T = 1500–1600 °C under Ar flux. Finally, an experiment at T = 900 °C and P = 1.0 GPa was done using a pyrope cube embedded into pyrope powder and 18O-enriched H2O. Experiments using grossular were not successful. Profiles of 18O/(18O+16O) in the experimental charges were analyzed with three different secondary ion mass spectrometers (SIMS): sensitive high-resolution ion microprobe (SHRIMP II and SI), CAMECA IMS-1280, and NanoSIMS. Considering only the measured length of 18O diffusion profiles, similar results were obtained for YAG and pyrope annealed at 900 °C, suggesting limited effects of chemical composition on oxygen diffusivity. However, in both garnet types, several profiles deviate from the error function geometry, suggesting that the behavior of O in garnet cannot be fully described as simple concentration-independent diffusion, certainly in YAG and likely in natural pyrope as well. The experimental results are better described by invoking O diffusion via two distinct pathways with an inter-site reaction allowing O to move between these pathways. Modeling this process yields two diffusion coefficients (D values) for O, one of which is approximately two orders of magnitude higher than the other. Taken together, Arrhenius relationships are:logDm2s-1=-7.2(±1.3)+(-321(±32)kJmol-12.303RT) for the slow pathway, andlogDm2s-1=-5.4(±0.7)+(-321(±20)kJmol-12.303RT) for the fast pathway. We interpret the two pathways as representing diffusion following vacancy and inter-stitial mechanisms, respectively. Regardless, our new data suggest that the slow mechanism is prevalent in garnet with natural compositions, and thus is likely to control the retentivity of oxygen isotopic signatures in natural samples. The diffusivity of oxygen is similar to Fe-Mn diffusivity in garnet at 1000–1100 °C and Ca diffusivity at 850 °C. However, the activation energy for O diffusion is larger, leading to lower diffusivities at P-T conditions characterizing crustal metamorphism. Therefore, original O isotopic signatures can be retained in garnets showing major element zoning partially re-equilibrated by diffusion, with the uncertainty caveat of extrapolating the experimental data to lower temperature conditions.

Geochemistry & Geophysics↗
DOE OSTI2018

Long-term observations of cloud condensation nuclei over the Amazon rain forest - Part 2: Variability and characteristics of biomass burning, long-range transport, and pristine rain forest aerosols

For this study, size-resolved measurements of atmospheric aerosol and cloud condensation nuclei (CCN) concentrations and hygroscopicity were conducted over a full seasonal cycle at the remote Amazon Tall Tower Observatory (ATTO, March 2014–February 2015). In a preceding companion paper, we presented annually and seasonally averaged data and parametrizations (Part 1; Pöhlker et al., 2016a). In the present study (Part 2), we analyze key features and implications of aerosol and CCN properties for the following characteristic atmospheric conditions: Empirically pristine rain forest (PR) conditions, where no influence of pollution was detectable, as observed during parts of the wet season from March to May. The PR episodes are characterized by a bimodal aerosol size distribution (strong Aitken mode with D Ait ≈ 70nm and N Ait ≈ 160cm -3 , weak accumulation mode with D acc ≈ 160nm and N acc ≈ 90cm -3 ), a chemical composition dominated by organic compounds, and relatively low particle hygroscopicity (κ Ait ≈ 0.12, κ acc ≈ 0.18). Long-range-transport (LRT) events, which frequently bring Saharan dust, African biomass smoke, and sea spray aerosols into the Amazon Basin, mostly during February to April. The LRT episodes are characterized by a dominant accumulation mode ( DAit ≈ 80nm, N Ait ≈ 120cm -3 vs. D acc ≈ 180nm, N acc ≈ 310cm -3 ), an increased abundance of dust and salt, and relatively high hygroscopicity (κ Ait ≈ 0.18, κ acc ≈ 0.35). The coarse mode is also significantly enhanced during these events. Biomass burning (BB) conditions characteristic for the Amazonian dry season from August to November. The BB episodes show a very strong accumulation mode (D Ait ≈ 70nm, N Ait ≈ 140cm -3 vs. D acc ≈ 170nm, N acc ≈ 3400cm -3 ), very high organic mass fractions (~90%), and correspondingly low hygroscopicity (κ Ait ≈ 0.14, κ acc ≈ 0.17). Mixed-pollution (MPOL) conditions with a superposition of African and Amazonian aerosol emissions during the dry season. During the MPOL episode presented here as a case study, we observed African aerosols with a broad monomodal distribution (D ≈ 130nm, N CN, 10 ≈ 1300cm -3 ), with high sulfate mass fractions (~20%) from volcanic sources and correspondingly high hygroscopicity (κ < 100 nm ≈ 0.14, κ > 10 nm ≈ 0.22), which were periodically mixed with fresh smoke from nearby fires (D ≈ 110nm, N CN, 10 ≈ 2800cm -3 ) with an organic-dominated composition and sharply decreased hygroscopicity (κ < 150 nm ≈ 0.10, κ > 150 nm ≈ 0.20). Insights into the aerosol mixing state are provided by particle hygroscopicity (κ) distribution plots, which indicate largely internal mixing for the PR aerosols (narrow κ distribution) and more external mixing for the BB, LRT, and MPOL aerosols (broad κ distributions). The CCN spectra (CCN concentration plotted against water vapor supersaturation) obtained for the different case studies indicate distinctly different regimes of cloud formation and microphysics depending on aerosol properties and meteorological conditions. The measurement results suggest that CCN activation and droplet formation in convective clouds are mostly aerosol-limited under PR and LRT conditions and updraft-limited under BB and MPOL conditions. Normalized CCN efficiency spectra (CCN divided by aerosol number concentration plotted against water vapor supersaturation) and corresponding parameterizations (Gaussian error function fits) provide a basis for further analysis and model studies of aerosol–cloud interactions in the Amazon.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1967

Computer program for network synthesis by frequency response fit

Computer program synthesizes a passive network by minimizing the difference in desired and actual frequency response. The program solves for the critical points of the error function /weighted least squares fit between calculated and desired frequency response/ by the multivariable Newton-Raphson method with components constrained to an admissible region.

Green, S.↗
NASA NTRS1972

Effects of display format on pilot describing function and remnant

As part of a program to develop a comprehensive theory of manual control displays, six display formats were used by three instrument-rated pilots to regulate against random disturbances with a controlled element under both foveal and 10 deg parafoveal viewing conditions. The six display formats were: CRT line, CRT thermometer bar, 14-bar quantized on a CRT, a rotary dial and pointer, and two variations of a moving scale tape-drive. All were scaled to equivalent movement and apparent brightness. Measures included overall performance, describing functions, error remnant power spectra, critical instability scores, and subjective display ratings. The results show that the main effect of display format is on the loop closure properties. Less desirable displays induce lower bandwidth closures with consequent effects on the closed-loop remnant and performance.

Jex, H. R.↗
NASA NTRS1973

Quarantine constraints as applied to satellites

Plans for unmanned missions to planets beyond Mars in the 1970s include satellite encounters. Recently published observations of data for Titan, a satellite of Saturn, indicate that conditions may be hospitable for the growth of microorganisms. Therefore, the problem of satisfying possible quarantine constraints for outer planet satellites was investigated. This involved determining the probability of impacting a satellite of Jupiter or Saturn by a spacecraft for a planned satellite encounter during an outer planet mission. Mathematical procedures were formulated which determine the areas in the aim-plane that would result in trajectories that impact the satellite and provide a technique for numerically integrating the navigation error function over the impact area to obtain impact probabilities. The results indicate which of the planned spacecraft trajectory correction maneuvers are most critical in terms of satellite quarantine violation.

Hoffman, A. R.↗
NASA NTRS1973

Quarantine constraints as applied to satellites.

Plans for unmanned missions to planets beyond Mars in the 1970s include satellite encounters. Recently published observations of data for Titan, a satellite of Saturn, indicate that conditions may be hospitable for the growth of microorganisms. Therefore, the problem of satisfying possible quarantine constraints for outer planet satellites was investigated. This involved determining the probability of impacting a satellite of Jupiter or Saturn by a spacecraft for a planned satellite encounter during an outer planet mission. Mathematical procedures were formulated which (1) determine the areas in the aim-plane that would result in trajectories that impact the satellite and (2) provide a technique for numerically integrating the navigation error function over the impact area to obtain impact probabilities. The results indicate which of the planned spacecraft trajectory correction maneuvers are most critical in terms of satellite quarantine violation.

Hoffman, A. R.↗
NASA NTRS1976

Identification of natural frequencies and modal damping ratios of aerospace structures from response data

An analysis of one and multidegree of freedom systems with classical damping is presented. Definition and minimization of error functions for each system are discussed. Systems with classical and nonclassical normal modes are studied, and results for first order perturbation are given. An alternative method of matching power spectral densities is provided, and numerical results are reviewed.

Michalopoulos, C. D.↗
NASA NTRS1977

A new method for predicting response in complex linear systems. II

The paper describes convergence and response studies in the low frequency range of complex systems, particularly with low values of damping of different distributions, and reports on the modification of the relaxation procedure required under these conditions. A new method is presented for response estimation in complex lumped parameter linear systems under random or deterministic steady state excitation. The essence of the method is the use of relaxation procedures with a suitable error function to find the estimated response; natural frequencies and normal modes are not computed. For a 45 degree of freedom system, and two relaxation procedures, convergence studies and frequency response estimates were performed. The low frequency studies are considered in the framework of earlier studies (Kayser and Bogdanoff, 1975) involving the mid to high frequency range.

Bogdanoff, J. L.↗
NASA NTRS1979

Comparison of two flow surveys above stalled wings

A laser velocimeter (LV) surveyed the flow above two stalled wings. Each wing was tested in a different wind tunnel at different Mach numbers. The low-Mach-number test had an angle of attack of 19.4 deg, 0.15 Mach number, and 1 x 1,000,000 Reynolds number. The mean velocities above the reversed, separated flow were closely modeled by error function profiles. Thus, the flow resembled a turbulent free-shear layer. The high-Mach-number test had an angle of attack of 19.5 deg, 0.49 Mach number, and 1,400,000 Reynolds number. A series of strong, discrete vortices were shed from the airfoil crest at regular intervals. Both tests demonstrated the importance of the unsteady part of the velocities.

Young, W. H., Jr.↗
NASA NTRS1979

Geoid anomalies and the thickness of the lithosphere

By using accepted crustal density distributions and either error function or linear temperature distributions the difference in geoid height between stable continental areas and deep ocean basins has been determined as a function of the continental lithospheric thickness. If the continental lithosphere were greater than 200 km thick, the geoid anomaly over the continents would be systematically negative in relation to that over the ocean basins. By using the GEM 9 satellite geoid the mean geoid anomalies over ocean basins and stable continental areas have been obtained. No systematic difference between continental and oceanic geoids is observed. It is concluded that the thickness of the continental lithosphere is near 180 km. This is in good agreement with various interpretations of the surface heat flow observations.

Turcotte, D. L.↗