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Results for “STEP 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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Rounded Approximate Step Functions For Interpolation

Rounded approximate step functions of form x(Sup m)/(x(Sup n) + 1) and 1/(x(Sup n) + 1) useful in interpolating between local steep slopes or abrupt changes in tabulated data varying more smoothly elsewhere. Used instead of polynomial curve fits. Interpolation formulas based on these functions implemented quickly and easily on computers. Used in real-time control computations to interpolate between tabulated data governing control responses.

Nunes, Arthur C., Jr.↗
NASA NTRS1959

Heat Transfer in a Liquid Metal Flowing Turbulently through a Channel with a Step Function Boundary Temperature

An analytical heat transfer solution is derived and evaluated for the general case of a turbulently flowing liquid metal which suddenly encounters a step-function boundary temperature in a channel system. Local Nusselt moduli, dimensionless mixed-mean fluid temperatures, and arithmetic-mean Nusselt moduli are given as functions of Reynolds and Prandtl moduli and a dimensionless axial-distance modulus. These solutions are compared with known solutions of more specific systems as well as with a set of experimental liquid-metal heat transfer data for a thermal entrance region.

Poppendiek, H. F.↗
NASA NTRS1990

Particle acceleration in step function shear flows - A microscopic analysis

The transport of energetic particles in a moving, scattering fluid, which has a large shear in its velocity over a distance small compared with the scattering mean free path is discussed. The analysis is complementary to an earlier paper by Earl, Jokipii, and Morfill (1988), which considered effects of more-gradual shear in the diffusion approximation. The case in which the scattering fluid undergoes a step function change in velocity, in the direction normal to the flow is considered. An analytical, approximate calculation and a Monte Carlo analysis of particle motion are presented. It is found that particles gain energy at a rate proportional to the square of the magnitude of the velocity change.

Jokipii, J. R.↗
NASA NTRS1990

Distorted-wave born approximation calculations for turbulence scattering in an upward-refracting atmosphere

Weiner and Keast observed that in an upward-refracting atmosphere, the relative sound pressure level versus range follows a characteristic 'step' function. The observed step function has recently been predicted qualitatively and quantitatively by including the effects of small-scale turbulence in a parabolic equation (PE) calculation. (Gilbert et al., J. Acoust. Soc. Am. 87, 2428-2437 (1990)). The PE results to single-scattering calculations based on the distorted-wave Born approximation (DWBA) are compared. The purpose is to obtain a better understanding of the physical mechanisms that produce the step-function. The PE calculations and DWBA calculations are compared to each other and to the data of Weiner and Keast for upwind propagation (strong upward refraction) and crosswind propagation (weak upward refraction) at frequencies of 424 Hz and 848 Hz. The DWBA calculations, which include only single scattering from turbulence, agree with the PE calculations and with the data in all cases except for upwind propagation at 848 Hz. Consequently, it appears that in all cases except one, the observed step function can be understood in terms of single scattering from an upward-refracted 'skywave' into the refractive shadow zone. For upwind propagation at 848 Hz, the DWBA calculation gives levels in the shadow zone that are much below both the PE and the data.

Gilbert, Kenneth E.↗
DOE OSTI2019

Determination of the N$_f$=12 step scaling function using Möbius domain wall fermions

We calculate the renormalized step scaling function for twelve fundamental flavors nonperturbatively by determining the gradient flow coupling on gauge field configurations generated with dynamical stout-smeared M\"obius domain wall fermions and Symanzik gauge action. Using Zeuthen, Symanzik, and Wilson flow we measure the energy density with three different operators. Our updated analysis is based on up to five volume pairs ranging from L 4 =8 4 up to 32 4 . Predictions for the infinite volume extrapolated step scaling function based on different flows and operators are mutually consistent. Our new results confirm the previously observed significant discrepancy with staggered fermion simulations in a wide range of the renormalized coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

BICEP/Keck XXI: Constraints on early-Universe parity violation from multipole-dependent birefringence

We present the first constraints on multipole-dependent cosmic birefringence using CMB polarization data from the BK18 dataset, which combines observations from BICEP2, Array, and BICEP3 at frequencies of 95, 150, and 220 GHz. Photon coupling to an axionlike field leads to the rotation of CMB polarization, inducing nonzero cross-correlations. We show that a multipole-dependent rotation imprints a distinct signature in the polarization spectra that can be constrained. Specifically, we consider an early dark energy (EDE) scenario in which a pseudoscalar field couples to photons through a Chern-Simons interaction, generating a polarization rotation with multipole dependence. We introduce a phenomenological as a step function, obtaining constraints on the step function size consistent with zero, with uncertainties less than (68% CL). In addition, using multi-frequency , , and cross spectra, along with robust BICEP/ foreground treatment and likelihood framework, we derive constraints on the axion-photon coupling amplitude for several choices of EDE parameters. For the baseline best-fit value from the 2018 analysis, we obtain (68% CL), consistent with previous limits.

Ade, P A R↗
NASA NTRS1999

Study of Flow of Superfluid He-II Very Near Tau(sub lambda)

We report here, preliminary data from an experiment studying flow of superfluid helium through a slit orifice (of sub-micron width) very close to T(sub lambda). Critical supercurrent (I(sub c)) data is obtained from a step function drive to the diaphragm in a Helmholtz resonator cell. The superfluid density (rho(sub s)) data can be obtained from the resonant frequency of the Helmholtz oscillator, as determined by transfer function of the resonator or from the free ringing after the step function excitation. Preliminary data shows that I(sub c) is proportional to (rho(sub s))(exp 1.27) and rho(sub s)) is proportional to tau(exp 0.73), where tau is the reduced temperature. However, the magnitude of I(sub c) is much larger than expected, indicating a possible parallel flow path. Further investigations are in progress. Keywords: superfluid; hydrodynamics; critical exponent

Mukharsky, Yury↗
DOE OSTI2021

Accuracy of environmental tracers and consequences for determining the Type Ia supernova magnitude step

Type Ia Supernovae (SNe Ia) are standardizable candles that allow us to measure the recent expansion rate of the Universe. Due to uncertainties in progenitor physics, potential astrophysical dependencies may bias cosmological measurements if not properly accounted for. The dependency of the intrinsic luminosity of SNe Ia with their host-galaxy environment is often used to standardize SNe Ia luminosity and is commonly parameterized as a step function. This functional form implicitly assumes two-populations of SNe Ia. In the literature, multiple environmental indicators have been considered, finding different, sometimes incompatible, step function amplitudes. We compare these indicators in the context of a two-populations model, based on their ability to distinguish the two populations. We show that local Hα-based specific star formation rate (lsSFR) and global stellar mass are better tracers than, for instance, host galaxy morphology. We show that tracer accuracy can explain the discrepancy between the observed SNe Ia step amplitudes found in the literature. Using lsSFR or global mass to identify the two populations can explain all other observations, though lsSFR is favoured. As lsSFR is strongly connected to age, our results favour a prompt and delayed population model. In any case, there exists two populations that differ in standardized magnitude by at least 0.121 ± 0.010 mag.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Calculation of the Thermodynamic Voltage Limit of CdSeTe Solar Cells

The first step to understand the origin of losses in any photovoltaic solar cell is to determine the fundamental thermodynamic efficiency and voltage limits of such a device. In this contribution, we detail techniques to calculate the voltage limit in the case of cadmium selenium telluride (CdSeTe) solar cells, and how approaches based on bandgap alone—i.e., the Shockley-Queisser approach with step-function absorptance—can overestimate the thermodynamic open-circuit voltage limit Voc,ideal . This is particularly true for arsenic-doped samples, which tend to exhibit below-bandgap absorptance.

absorptance↗
DOE OSTI2021

Soil enzymes as indicators of soil function: A step toward greater realism in microbial ecological modeling

Soil carbon (C) and nitrogen (N) cycles and their complex responses to environmental changes have received increasing attention. However, large uncertainties in model predictions remain, partially due to the lack of explicit representation and parameterization of microbial processes. One great challenge is to effectively integrate rich microbial functional traits into ecosystem modeling for better predictions. Here, using soil enzymes as indicators of soil function, we developed a competitive dynamic enzyme allocation scheme and detailed enzyme-mediated soil inorganic N processes in the Microbial-ENzyme Decomposition (MEND) model. We conducted a rigorous calibration and validation of MEND with diverse soil C-N fluxes, microbial C:N ratios, and functional gene abundances from a 12-year CO 2 × N grassland experiment (BioCON) in Minnesota, USA. In addition to accurately simulating soil CO 2 fluxes and multiple N variables, the model correctly predicted microbial C:N ratios and their negative response to enriched N supply. Model validation further showed that, compared to the changes in simulated enzyme concentrations and decomposition rates, the changes in simulated activities of eight C-N-associated enzymes were better explained by the measured gene abundances in responses to elevated atmospheric CO 2 concentration. In conclusion, our results demonstrated that using enzymes as indicators of soil function and validating model predictions with functional gene abundances in ecosystem modeling can provide a basis for testing hypotheses about microbially mediated biogeochemical processes in response to environmental changes. Further development and applications of the modeling framework presented here will enable microbial ecologists to address ecosystem-level questions beyond empirical observations, toward more predictive understanding, an ultimate goal of microbial ecology.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2011

Visual PEF Reader - VIPER

This software graphically displays all pertinent information from a Predicted Events File (PEF) using the Java Swing framework, which allows for multi-platform support. The PEF is hard to weed through when looking for specific information and it is a desire for the MRO (Mars Reconn aissance Orbiter) Mission Planning & Sequencing Team (MPST) to have a different way to visualize the data. This tool will provide the team with a visual way of reviewing and error-checking the sequence product. The front end of the tool contains much of the aesthetically appealing material for viewing. The time stamp is displayed in the top left corner, and highlighted details are displayed in the bottom left corner. The time bar stretches along the top of the window, and the rest of the space is allotted for blocks and step functions. A preferences window is used to control the layout of the sections along with the ability to choose color and size of the blocks. Double-clicking on a block will show information contained within the block. Zooming into a certain level will graphically display that information as an overlay on the block itself. Other functions include using hotkeys to navigate, an option to jump to a specific time, enabling a vertical line, and double-clicking to zoom in/out. The back end involves a configuration file that allows a more experienced user to pre-define the structure of a block, a single event, or a step function. The individual will have to determine what information is important within each block and what actually defines the beginning and end of a block. This gives the user much more flexibility in terms of what the tool is searching for. In addition to the configurability, all the settings in the preferences window are saved in the configuration file as well

Luo, Victor↗
DOE OSTI2018

Approximating Photo- z PDFs for Large Surveys

Modern galaxy surveys produce redshift probability density functions (PDFs) in addition to traditional photometric redshift (photo-z) point estimates. However, the storage of photo-z PDFs may present a challenge with increasingly large catalogs, as we face a trade-off between the accuracy of subsequent science measurements and the limitation of finite storage resources. This work presents qp, a Python package for manipulating parameterizations of one-dimensional PDFs, as suitable for photo-z PDF compression. We use qp to investigate the performance of three simple PDF storage formats (quantiles, samples, and step functions) as a function of the number of stored parameters on two realistic mock data sets, representative of upcoming surveys with different data qualities. We propose some best practices for choosing a photo-z PDF approximation scheme and demonstrate the approach on a science case using performance metrics on both ensembles of individual photo-z PDFs and an estimator of the overall redshift distribution function. We show that both the properties of the set of PDFs we wish to approximate and the fidelity metric(s) chosen affect the optimal parameterization. Additionally, we find that quantiles and samples outperform step functions, and we encourage further consideration of these formats for PDF approximation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Computational studies on scattering of radio frequency waves by density filaments in fusion plasmas

In modern magnetic fusion devices, such as tokamaks and stellarators, radio frequency (RF) waves are commonly used for plasma heating and current profile control, as well as for certain diagnostics. The frequencies of the RF waves range from ion cyclotron frequency to the electron cyclotron frequency. The RF waves are launched from structures, like waveguides and current straps, placed near the wall in a very low density, tenuous plasma region of a fusion device. The RF electromagnetic fields have to propagate through this scrape-off layer before coupling power to the core of the plasma. The scrape-off layer is characterized by turbulent plasmas fluctuations and by blobs and filaments. The variations in the edge density due to these fluctuations and filaments can affect the propagation characteristics of the RF waves—changes in density leading to regions with differing plasma permittivity. Analytical full-wave theories have shown that scattering by blobs and filaments can alter the RF power flow into the core of the plasma in a variety of ways, such as through reflection, refraction, diffraction, and shadowing [see, for example, Ram and Hizanidis, Phys. Plasmas 23, 022504 (2016), and references therein]. There are changes in the wave vectors and the distribution of power–scattering leading to coupling of the incident RF wave to other plasma waves, side-scattering, surface waves, and fragmentation of the Poynting flux in the direction towards the core. However, these theoretical models are somewhat idealized. In particular, it is assumed that there is step-function discontinuity in the density between the plasma inside the filament and the background plasma. In this paper, results from numerical simulations of RF scattering by filaments using a commercial full-wave code are described. The filaments are taken to be cylindrical with the axis of the cylinder aligned along the direction of the ambient magnetic field. The plasma inside and outside the filament is assumed to be cold. There are three primary objectives of these studies. The first objective is to validate the numerical simulations by comparing with the analytical results for the same plasma description—a step-function discontinuity in density. A detailed comparison of the Poynting flux shows that numerical simulations lead to the same results as those from the theoretical model. The second objective is to extend the simulations to take into account a smooth transition in density from the background plasma to the interior of the filament. The ensuing comparison shows that the deviations from the results of the theoretical model are quite small. The third objective is to consider the scattering process for situations well beyond a reasonable theoretical analysis. This includes scattering off multiple filaments with different densities and sizes. In conclusion, simulations for these complex arrangements of filaments show that, in spite of the obvious limitations, the essential physics of RF scattering is captured by the analytical theory for a single filament

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2001

Our Sun V: A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars

The relatively warm temperatures required on early Earth and Mars have been difficult to account for with warming from greenhouse gases. A slightly more massive young Sun would be brighter than predicted by the standard solar model, simultaneously resolving this problem for both Earth and Mars. We computed high-precision solar models with seven initial masses, from Mi = 1.01 to 1.07 solar mass - the latter being the maximum permitted if the early Earth is not to lose its water via a moist greenhouse effect. The relatively modest early mass loss that is required remains consistent with observational limits on mass loss from young stars and with estimates of the past solar wind obtained from lunar rocks. We considered three types of mass loss rates: (1) a reasonable choice of a simple exponential decline, (2) an extreme step-function case that gives the maximum effect consistent with observations, and (3) the radical case of a linear decline which is inconsistent with the solar wind mass loss estimates from lunar rocks. Our computations demonstrated that mass loss leaves a fingerprint oil the Sun's internal structure large enough to be detectable with helioseismic observations. All of our mass-losing solar models were consistent with the helioseismic observations; in fact, our preferred mass-losing cases were in marginally better agreement with the helioseismology than the standard solar model was, although this difference was smaller than the effects of other uncertainties in the input physics and in the solar composition. Mass loss has only a relatively minor effect on the predicted lithium depletion; the major portion of the solar lithium depletion must still be due to rotational mixing. Thus the modest mass loss cases considered here cannot be ruled out by observed lithium depletions. For the three mass loss types considered, the preferred initial masses were 1.07 solar mass for the exponential case and 1.04 solar mass for the step-function and linear cases; all of these provided high enough solar fluxes at Mars 3.8 Gyr ago to be consistent with the existence of liquid water. For a more massive early Sun, the planets would have had to be closer to the young Sun in order to end up in their present orbits; the orbital radii of the planets would vary inversely with the solar mass. Both of these effects contribute to the fact that the early solar flux at the planets would have been considerably higher than that of the standard solar model at that time. In fact, the 1.07 solar mass exponential case has a flux at birth 5% higher than the present solar flux, while the radical 1.04 solar mass linear case has a nearly constant flux over the first 3 Gyr only about 10% lower than at present. The early solar evolution would be in the opposite direction in the H-R diagram to that of the standard Sun.

Sackmann, I.-Juliana↗