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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Coordinated time variability of multi-phase ultra-fast outflows in J132216.25 + 052446.3

ABSTRACT We present a time variability analysis of broad absorption lines (BAL; spread over the velocity range of 5800–29 000 km s−1) seen in the spectrum of J132216.25 + 052446.3 (zem = 2.04806) at ten different epochs spanning over 19 yr. The strongest absorption component (BAL-A; spread over 5800–9900 km s−1) is made up of several narrow components having velocity separations close to C iv doublet splitting. The C iv, N v, and Si iv absorption from BAL-A show correlated optical depth variability without major changes in the velocity structure. A very broad and shallow absorption (BAL-C; spread over the velocity range 15 000–29 000 km s−1) emerged during our monitoring period coinciding with a dimming episode of J1322 + 0524. All the identified absorption lines show correlated variability with the equivalent widths increasing with decreasing flux. This together with the C iv emission line variability is consistent with ionization being the main driver of the correlated variability. The observed UV-continuum variations are weaker than what is required by the photoionization models. This together with a scatter in the C iv equivalent width at a given continuum flux can be understood if variations of the C iv ionizing photons are much larger than that of the UV continuum, the variations in the ionizing photon and UV fluxes are not correlated and/or the covering factor of the flow varies continuously. We suggest BAL-A is produced by a stable clumpy outflow located beyond the broad emission line region and BAL-C is a newly formed wind component located near the accretion disc and both respond to changes in the ionizing continuum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

XRISM high-resolution X-ray spectroscopy of Cygnus X-1: Orbital and short-term variability of iron absorption

We present the first high-resolution spectroscopy of the black hole high-mass X-ray binary Cygnus X-1 with XRISM, including orbital-phase-resolved analyses and tentative evidence of short-term variability in the Fe K band on second timescales. Using data from the Performance Verification phase in 2024 April, we analyzed spectral variability across orbital phases with the Resolve microcalorimeter and the Xtend CCD imager. The unprecedented resolution of Resolve reveals variability in highly ionized Fe absorption lines. The absorption features show orbital-phase-dependent variability in column density, ionization state, and blueshifted velocity, suggesting structural variations in the focused stellar wind along the line of sight. We also find indications of subtle broadening of the neutral Fe emission profile. In addition, intensity-sorted spectroscopy during dip phases suggests possible variability on timescales of a few seconds in the absorption features, consistent with cooler, denser, and lower-ionized gas clumps. Although the statistical significance is limited, these results hint that the stellar wind and the X-rays from the accretion disk around the black hole may interact on timescales as short as a few seconds. These XRISM results constrain wind-fed accretion in Cyg X-1 and highlight Resolve’s capability to probe plasma environments in high-mass X-ray binaries.

Astronomy and AstroPhysics↗
DOE OSTI2022

Training data selection for event classification in a highly variable environment

A problem of interest for nuclear nonproliferation is monitoring activities at nuclear facilities, where proliferation events may only take place a few times and often under variable conditions. Machine learning has revolutionized data analytics by enabling the use of measurable signatures to generate predictive models of facility operations. However, traditional methods for training these models require large, reliable data sets with labeled observations, a challenge for nonproliferation. Highly variable conditions further complicate this as events from training data may have occurred in conditions quite different from the event of interest. Our hypothesis is that when events occur in a highly variable environment, careful training data selection for each test event could outperform the standard approach of using all available training data. We developed a method to optimize training data selection for the given test event and applied it to predicting the power level of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. In this study, the reactor startup exhibits variability between occurrences due to natural variability in environmental conditions and operational procedures. Using a combination of analysis techniques, a similitude assessment was performed on data collected from HFIR to isolate clusters that were optimal for training a predictive model. Concepts such as dynamic time warping and Jaccard similarity were used in conjunction with clustering analysis. In order to validate this approach, the model was trained on every combination of unique training events and the predictive performance was compared to the performance using a subset of the training data selected by isolated clusters found through the similitude assessment.

Iyer, A↗
DOE OSTI2021

Changes in Future Precipitation Mean and Variability across Scales

Changes in precipitation variability can have large societal consequences, whether at the short time scales of flash floods or the longer time scales of multiyear droughts. Recent studies have suggested that in future climate projections, precipitation variability rises more steeply than does its mean, leading to concerns about societal impacts. Here we evaluate changes in mean precipitation over a broad range of spatial and temporal scales using a range of models from high-resolution regional simulations to millennial-scale global simulations. Results show that changes depend on the scale of aggregation and involve strong regional differences. On local scales that resolve individual rainfall events (hours and tens of kilometers), changes in precipitation distributions are complex and variances rise substantially more than means, as is required given the well-known disproportionate rise in precipitation intensity. On scales that aggregate across many events, distributional changes become simpler and variability changes smaller. At regional scale, future precipitation distributions can be largely reproduced by a simple transformation of present-day precipitation involving a multiplicative shift and a small additive term. The “extra” broadening is negatively correlated with changes in mean precipitation: in strongly “wetting” areas, distributions broaden less than expected from a simple multiplicative mean change; in “drying” areas, distributions narrow less. Precipitation variability changes are therefore of especial concern in the subtropics, which tend to dry under climate change. Outside the tropics, variability changes are similar on time scales from days to decades (i.e., show little frequency dependence). This behavior is highly robust across models, suggesting it may stem from some fundamental constraint.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

First Measurement of Differential Charged Current Quasielastic-like $\nu_\mu$–Argon Scattering Cross Sections In Kinematic Imbalance Variables With The MicroBooNE Detector

We report the first measurement of flux-integrated multi-differential cross sections for charged-current events with muon neutrinos scattering on argon with solely a muon and a single proton in the final state as a function of kinematic imbalance variables. The measurement was carried out using the Booster Neutrino Beam at Fermi National Accelerator Laboratory within the MicroBooNE Liquid Argon Time Projection Chamber detector with an exposure of 6.79 × 10 20 protons on target. Events were selected to enhance the contribution of charged-current mesonless interactions with one proton detected in the final state. The data discussed here are reported in terms of multidifferential cross sections in kinematic imbalance variables, which are generally sensitive to nuclear effects. The double-differential results in these variables can provide an excellent handle to disentagle specific nuclear aspects not easily isolated via single differential cross sections. Our results pave a path towards identifying regions of the phase-space where future interaction modeling development and Monte Carlo neutrino generator tuning efforts should concentrate. EVENT SELECTION Neutrino oscillation measurements aim to extract neutrino mixing angles, mass differences, the value of the chargeparity violating phase in the lepton sector, and to search for new physics beyond the Standard Model [1, 2]. For that to be achieved, an unprecedented understanding of neutrino-argon interactions is of utmost importance since a growing number of neutrino oscillation experiments employ Liquid Argon Time Projector Chamber (LArTPC) neutrino detectors [3–6]. The accuracy to which these experiments can extract neutrino oscillation parameters requires a good understanding of the neutrino energy. Experimentally, this energy is deduced from the measured kinetic energies of particles that are emitted following the neutrino interaction in the detector. The kinematic properties of such finalstate particles reflect complex dynamics due to nuclear and initial-state effects of the interaction [7]. However, certain categories of nuclear effects can be isolated by variables built specifically to characterize the degeneracy between such effects [8–10]. This note reports cross sections in kinematic variables sensitive to nuclear effects using events with one detected muon with momentum 0.1 < pµ < 1.2 GeV/c, and exactly one proton with 0.3 < pp < 1 GeV/c. This signal definition includes events with any number of protons below 300 MeV/c, neutrons at any momenta, and charged pions with momentum lower than 70 MeV/c. This choice is guided by the fact that their experimental signature of correlated muon-proton pairs is fairly straightforward to reconstruct [11–22]. Such events primarily originate from chargedcurrent (CC) neutrino-nucleon quasielastic (QE) scattering interactions where the neutrino removes a single intact nucleon from the nucleus without producing any additional particles. This definition can also include contributions from interactions that lead to the production of additional particles that are absent from the final state due to nuclear effects, such as pion absorption, or have momenta that are below the experimental detection threshold.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Design and Operation of Energy Systems with Large Amounts of Variable Generation: IEA Wind TCP Task 25 (Final Summary Report)

This report summarizes findings on wind integration from the 17 countries or sponsors participating in the International Energy Agency Wind Technology Collaboration Program (IEA Wind TCP) Task 25 from 2006-2020. Both real experience and studies are reported. Many wind integration studies incorporate solar energy, and most of the results discussed here are valid for other variable renewables in addition to wind. The national case studies address several impacts of wind power on electric power systems. In this report, they are grouped under long-term planning issues and short-term operational impacts. Long-term planning issues include grid planning and capacity adequacy. Short-term operational impacts include reliability, stability, reserves, and maximizing the value of wind in operational timescales (balancing related issues). The first section presents the variability and uncertainty of power system-wide wind power, and the last section presents recent studies toward 100% shares of renewables. The appendix provides a summary of ongoing research in the national projects contributing to Task 25 for 2021-2024. The design and operation of power and energy systems is an evolving field. As ambitious targets toward net-zero carbon energy systems are announced globally, many scenarios are being made regarding how to reach these future decarbonized energy systems, most of them involving large amounts of variable renewables, mainly wind and solar energy. The secure operation of power systems is increasingly challenging, and the impacts of variable renewables, new electrification loads together with increased distribution system resources will lead to somewhat different challenges for different systems. Tools and methods to study future power and energy systems also need to evolve, and both short-term operational aspects (such as power system stability) and long-term aspects (such as resource adequacy) will probably see new paradigms of operation and design. The experience of operating and planning systems with large amounts of variable generation is accumulating, and research to tackle the challenges of inverter-based, nonsynchronous generation is on the way. Energy transition and digitalization also bring new flexibility opportunities, both short and long term.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Wave resource spatial and temporal variability dependence on WEC size

As the wave energy sector grows and looks to the Blue Economy for commercialization opportunities, there is a distinct and pressing need to clearly understand and quantify the coupled impacts of wave energy converter (WEC) size and wave resource characteristics on the annual energy production, spatial variability and temporal variability. Utilizing generic frequency domain representations of the Oscilla Power Triton WEC and spectral wave conditions at PacWave (Oregon), Los Angeles (California) and WETS (Hawaii), a series of interesting results emerge. Firstly, the ‘optimal’ WEC size, from an energy standpoint, is fundamentally dependent on the frequency distribution of the incoming wave variance density spectrum. Secondly, and from a seasonality perspective, the seasonal WEC energy generation doesn’t necessarily follow the seasonal distribution of gross wave power. Finally, from an hourly power variability perspective, a reduction in WEC size generally decreases variability. However, for each of the locations investigated, there appears to be a WEC size threshold; a threshold where further reducing WEC size results in increased power variability.

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Spectral Variability of VHS J1256–1257b from 1 to 5 μm

Multiwavelength time-resolved observations of rotationally modulated variability from brown dwarfs and giant exoplanets are the most effective method for constraining their heterogeneous atmospheric structures. In a companion paper, we reported the discovery of strong near-infrared variability in HST/WFC3/G141 light curves of the very red L-dwarf companion VHS J1256–1257b. In this paper, we present a follow-up 36 hr Spitzer/IRAC Channel 2 light curve together with an in-depth analysis of the Hubble space telescope (HST) and the Spitzer data. The combined data set provides time-resolved light curves of VHS1256b sampling 1.1 to 4.5 μm. The Spitzer light curve is best fit with a single sine wave with a period of 22.04 ± 0.05 hr and a peak-to-peak amplitude of 5.76 ± 0.04%. Combining the period with a previously measured projected rotational velocity (v sin i), we find that VHS1256b is most consistent with equatorial viewing geometry. The HST/G141+Spitzer spectral energy distribution favors a model with a T{sub eff} of 1000 K and low surface gravity with disequilibrium chemistry. The spectral variability of VHS1256b is consistent with predictions from partly cloudy models, suggesting that heterogeneous clouds are the dominant source of the observed modulations. We find evidence at the 3.3σ level for amplitude variations within the 1.67 μm CH{sub 4} band, which is the first such detection for a variable L-dwarf. We compare the HST/G141 time-resolved spectra of three red L-dwarfs with high-amplitude near-infrared rotational modulations and find that although their time-averaged spectra are similar, their spectroscopic variabilities exhibit notable differences. This diversity reinforces the advantage of time-resolved spectroscopic observations for understanding the atmospheres of brown dwarfs and directly imaged exoplanets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Near-infrared Census of RR Lyrae Variables in the Messier 3 Globular Cluster and the Period–Luminosity Relations

We present new near-infrared (NIR), JHK {sub s}, time-series observations of RR Lyrae variables in the Messier 3 (NGC 5272) globular cluster using the WIRCam instrument at the 3.6 m Canada–France–Hawaii Telescope. Our observations cover a sky area of ∼21′ × 21′ around the cluster center and provide an average of 20 epochs of homogeneous JHK {sub s}-band photometry. New homogeneous photometry is used to estimate robust mean magnitudes for 175 fundamental-mode (RRab), 47 overtone-mode (RRc), and 11 mixed-mode (RRd) variables. Our sample of 233 RR Lyrae variables is the largest thus far obtained in a single cluster with time-resolved, multiband NIR photometry. NIR-to-optical amplitude ratios for RR Lyrae in Messier 3 exhibit a systematic increase moving from RRc to short-period (P < 0.6 day) and long-period (P ≳ 0.6 day) RRab variables. We derive JHK {sub s}-band period–luminosity relations for RRab, RRc, and the combined sample of variables. Absolute calibrations based on the theoretically predicted period–luminosity–metallicity relations for RR Lyrae stars yield a distance modulus, μ=15.041±0.017 (statistical)±0.036 (systematic) mag, to Messier 3. When anchored to trigonometric parallaxes for nearby RR Lyrae stars from the Hubble Space Telescope and the Gaia mission, our distance estimates are consistent with those resulting from the theoretical calibrations, albeit with relatively larger systematic uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations

Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.

Fagin, Joshua [City Univ. of New York (CUNY), NY (↗
DOE OSTI2022

First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass

In this paper we quantify the temporal variability and image morphology of the horizon-scale emission from Sgr A*, as observed by the EHT in 2017 April at a wavelength of 1.3 mm. We find that the Sgr A* data exhibit variability that exceeds what can be explained by the uncertainties in the data or by the effects of interstellar scattering. The magnitude of this variability can be a substantial fraction of the correlated flux density, reaching ~100% on some baselines. Through an exploration of simple geometric source models, we demonstrate that ring-like morphologies provide better fits to the Sgr A* data than do other morphologies with comparable complexity. We develop two strategies for fitting static geometric ring models to the time-variable Sgr A* data; one strategy fits models to short segments of data over which the source is static and averages these independent fits, while the other fits models to the full data set using a parametric model for the structural variability power spectrum around the average source structure. Both geometric modeling and image-domain feature extraction techniques determine the ring diameter to be 51.8 ± 2.3 μas (68% credible intervals), with the ring thickness constrained to have an FWHM between ~30% and 50% of the ring diameter. To bring the diameter measurements to a common physical scale, we calibrate them using synthetic data generated from GRMHD simulations. This calibration constrains the angular size of the gravitational radius to be ${4.8}_{-0.7}^{+1.4}$ μas, which we combine with an independent distance measurement from maser parallaxes to determine the mass of Sgr A* to be ${4.0}_{-0.6}^{+1.1}\times {10}^{6}$ M⊙.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

The relative importance of wind and hydroclimate drivers in modulating the interannual variability of dust emissions in Earth system models

Windblown dust emissions are controlled by near-surface wind speed and sediment erodibility, the latter modulated by hydroclimate and land-use conditions. Accurate representations of these drivers are critical for reproducing historical dust variability and projecting future dust changes in Earth system models (ESMs). This study examines the discrepancies among 21 ESMs in the relative importance of wind speed versus five hydroclimate drivers in explaining the historical (1980–2014) variability of dust emissions from global drylands. In hyperarid areas, models show poor agreement in the simulated dust variability, with only 9 % out of 210 inter-model comparisons exhibiting significant positive correlations. In contrast, arid and semiarid areas exhibit a dual pattern driven by a “double-edged sword” effect of land surface memory: models with coherent hydroclimate variability show better agreement, whereas those with divergent hydroclimate representations show larger disagreement. While the ESMs capture the dominant role of wind speed in hyperarid areas, they diverge markedly in the relative contributions of wind and hydroclimate drivers in arid and semiarid areas. Replacing the Zender et al. (2003) dust scheme with the Kok et al. (2014) scheme in CESM and E3SM generally strengthens hydroclimate influences while reducing wind speed contributions to simulated dust variability. MERRA-2 reanalysis produces stronger wind influences than most ESMs across all dryland regions. These results underscore the need for improved near-surface wind simulations in hyperarid areas and more realistic land surface and hydroclimate representations in arid and semiarid areas to reduce uncertainties in global dust emission simulations.

Li, Xinzhu [Michigan Technological University, Hou↗
DOE OSTI2021

The interpretation of temperature and salinity variables in numerical ocean model output and the calculation of heat fluxes and heat content

Abstract. The international Thermodynamic Equation of Seawater 2010 (TEOS-10) defined the enthalpy and entropy of seawater, thus enabling the global ocean heat content to be calculated as the volume integral of the product of in situ density, ρ, and potential enthalpy, h0 (with reference sea pressure of 0 dbar). In terms of Conservative Temperature, Θ, ocean heat content is the volume integral of ρcp0Θ, where cp0 is a constant “isobaric heat capacity”. However, many ocean models in the Coupled Model Intercomparison Project Phase 6 (CMIP6) as well as all models that contributed to earlier phases, such as CMIP5, CMIP3, CMIP2, and CMIP1, used EOS-80 (Equation of State – 1980) rather than the updated TEOS-10, so the question arises of how the salinity and temperature variables in these models should be physically interpreted, with a particular focus on comparison to TEOS-10-compliant observations. In this article we address how heat content, surface heat fluxes, and the meridional heat transport are best calculated using output from these models and how these quantities should be compared with those calculated from corresponding observations. We conclude that even though a model uses the EOS-80, which expects potential temperature as its input temperature, the most appropriate interpretation of the model's temperature variable is actually Conservative Temperature. This perhaps unexpected interpretation is needed to ensure that the air–sea heat flux that leaves and arrives in atmosphere and sea ice models is the same as that which arrives in and leaves the ocean model. We also show that the salinity variable carried by present TEOS-10-based models is Preformed Salinity, while the salinity variable of EOS-80-based models is also proportional to Preformed Salinity. These interpretations of the salinity and temperature variables in ocean models are an update on the comprehensive Griffies et al. (2016) paper that discusses the interpretation of many aspects of coupled Earth system models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Benchmarking soil moisture and its relationship to ecohydrologic variables in Earth System Models

Soil moisture (SM) is a key regulator of ecosystem biogeophysics, influencing plant water relations and land-atmosphere energy exchanges. We evaluate the representation of SM in 16 Earth System Models from the Coupled Model Intercomparison Project Phase 6 (CMIP6) using the International Land Model Benchmarking (ILAMB) framework, focusing on surface (0–5, 0–10 cm) and rootzone (0–100 cm) depths, as well as key ecohydrological variables like gross primary productivity (GPP), leaf area index (LAI), and evapotranspiration (ET), and their coupling. Models are benchmarked against multiple observational and assimilated datasets to assess both state variables and cross-variable relationships. Surface SM is generally well represented (r > 0.87), while rootzone SM variability is systematically overestimated (normalized standard deviation > 1). ET shows strong agreement with observations (r > 0.9), whereas GPP and LAI exhibit larger inter-model spread. Skill in individual variables does not guarantee realistic SM–ecohydrology coupling, which varies strongly across models and depends on the reference dataset. Köppen-based regional analyses reveal strong regime dependence, with several models performing well in Tropical and Temperate regions but degrading in Continental (high-latitude) zones. Across both global and regional benchmarks, models cluster by land surface framework, indicating that structural choices in soil hydrology and soil–plant coupling exert a first-order control on performance. These results provide process-relevant benchmarks and suggest that improving the representation of vertical soil structure, rooting depth distributions, and soil–plant hydraulic coupling will be central to advancing soil moisture realism in next-generation Earth system models.

CMIP6↗
DOE OSTI2025

Biomass for Carbon Removal and Storage (BiCRS) Variables Matrices

The Biomass for Carbon Removal and Storage (BiCRS) Variables Matrices provide insights related to measured, monitored, reported and verified (MMRV) components (variables) across a BiCRS value chain. Suggested variable values and components to be measured with literature references and context obtained from industry and scientists are provided for several biomass sources, conversion routes and storage scenarios. The Variables Matrices are meant to support life cycle assessment and MMRV efforts for BiCRS projects. These variables and insights may need to be updated in the future as additional information, scientific advancements, and data become available (Version 1 issued in 2025).

09 BIOMASS FUELS↗
NASA NTRS1956

An Engineering Approach to the Variable Fluid Property Problem in Free Convection

An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Gregg, J. L.↗
NASA NTRS1975

On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

Broucke, R.↗