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NASA NTRSDate not supplied

Nanoflare Heating Frequency of an X-ray Bright Point Observed by MaGIXS

Nanoflares have been considered to be one of the most likely candidates for heating the solar corona to multi-million kelvin temperatures. Individual nanoflares are difficult to detect with today's instruments, but their presence may be established by comparing simulated nanoflare-heated plasma emissions to observed emissions. We present a simulation of emission from an X-ray Bright Point (XBP) detected by the MaGIXS, as well as simultaneous observations from SDO/AIA and Hinode/XRT. To simulate the XBP loops, we utilize the HYDRAD code. The length and magnetic field strength of these loops are determined using potential field extrapolation of SDO/HMI's observed photospheric magnetogram. Each loop is considered to be heated by random nanoflares, the amplitude and frequency of which are governed by the length of the loop and the strength of the magnetic field. The simulated outputs are used to estimate the intensity of spectrally pure maps of Fe-18, Fe-17, Ne-9, O-8, O-9, Ne-9, and so on, which is then compared to the intensity determined from MaGIXS observations. In addition, we derived the intensity maps obtained by AIA and XRT and compared them to the observed data. The composite distribution of the delay time of the nanoflares for which the simulated loops morphology and intensities match with observation shows a peak at 200s-500s, indicating that most of the nanoflares have a high/intermediate frequency.

coronal heating↗
NASA NTRS2006

Exploring the Production of NOx by Lightning and Its Impact on Tropospheric Ozone

Our quantitative understanding of free tropospheric (FT) chemistry is quite poor. State-of-the-art regional air quality models (e.g., US EPA's CMAQ) perform very poorly in simulating FT chemistry, with Uniform ozone around 70 ppb throughout the FT in summer, while ozonesonde data show much higher levels of ozone and much spatial-temporal structure. Such models completely neglect lightning-NOx (LNOx) emissions (the most significant source of NOx in the FT), and also contain large uncertainties in the specifications of intercontinental transport, stratosphere-troposphere exchange (STE) and PBLFT exchange (PFTE). Global air chemistry models include LNOx, but in very crude fashion, with the frequency and distribution of lightning being based on modeled cloud parameters (hence large uncertainty), lightning energetics being assumed to be constant for all flashes (literature value, while in reality there is at least a two-orders of magnitude variability from flash-to-flash), and the production of NOx in the surrounding heated air, per Joule of heating, being assumed to be constant also (literature value, while in fact it is a non-linear function of the dissipated heat and local air density, p). This situation is commonly blamed on paucity of pertinent observational data, but for the USA, there is now a wealth of surface- and satellite-based data of lightning available to permit much improved observation-based estimation of LNOx emissions. In the FT, such NOx has a long residence time, and also the ozone production efficiency from NOx there is considerably higher than in the PBL. It is, therefore, of critical importance in FT chemistry. This paper will describe the approach and data products of an ongoing NSSTC project aimed at a much-improved quantification of not only LNOx production on the scale of continental USA based on local and regional lightning observations, but also of intercontinental transport, STE and PFTE, all in upgraded simulations of tropospheric transport and chemistry. In our approach for LNOx, (a) we utilize continuous observed lightning information from the NLDN ground network and from satellite imagers (OTD and LIS) to quantify lightning frequency and distribution at the spatial-temporal scales of models such as CMAQ; (b) we develop new methodologies to quantify flash-specific lightning energy dissipation as heat (epsilon) using data from the research-grade lightning measurement facility at NASA-KSC, and to parameterize epsilon based on regional lightning monitoring data (ground- and satellite-based); and, (c) we develop a new parameterization of NOx production as a function of epsilon and rho. Based on such observation-based information, we are working to develop a gridded, episodic LNOx emissions inventory for the USA for use in models like CMAQ. We are also developing approaches for global(MOZART)- regional(CMAQ) chemistry coupling to improve intercontinental transport and STE. Finally, we are developing new methodologies for assimilation of satellite-observed (GOES) clouds into meteorological modeling (MM5), to improve PFTE and to optimize co-location of cloud convection and observed lightning. We will incorporate these improvements in CMAQ simulations over the USA to better understand FT processes and chemistry, and its impact on ground-level ozone.

Gillani, Noor↗
DOE OSTI2020

Earth as an Exoplanet. I. Time Variable Thermal Emission Using Spatially Resolved Moderate Imaging Spectroradiometer Data

Among the more than 4000 exoplanets known today, some terrestrial planets have been detected in the so-called habitable zone of their host stars and their number is expected to increase in the near future, energizing a drive to understand and interpret the eagerly awaited wealth of data to identify signs of life beyond our solar system. So far, Earth remains the best and only example of a habitable (and inhabited) world. Although, it seems extremely unlikely that any other exoplanets will be true Earth twins, it is important to explore and understand the full range of spectral signatures and variability of Earth in order to inform the design of future instruments and missions, and understand their diagnostic power as well as potential limitations. In this work we use Earth observation data collected by the MODIS instrument aboard the Aqua satellite. The complete data set comprises 15 years of thermal emission observations in the 3.66–14.40 μm range for five different locations on Earth (Amazon Rainforest, Antarctica, Arctic, Indian Ocean, and the Sahara Desert). We then determine flux levels and variations as a function of wavelength and surface type (i.e., climate zone and surface thermal properties) and investigate whether periodic signals indicating Earth’s tilted rotation axis can be detected. Our findings suggest that (1) viewing geometry plays an important role when thermal emission data is analyzed as Earth’s spectrum varies by a factor of three and more depending on the dominant surface type underneath; (2) typically strong absorption bands from CO 2 (15 μm) and O 3 (9.65 μm) are significantly less pronounced and partially absent in data from the polar regions implying that estimating correct abundance levels for these molecules might be challenging in these cases; and (3) the time-resolved thermal emission spectrum encodes information about seasons/planetary obliquity, but the significance depends on the viewing geometry and spectral band considered.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Constraining the range of Yukawa gravity interaction from S2 star orbits II: bounds on graviton mass

Recently LIGO collaboration discovered gravitational waves [1] predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting about the discovery, the joint LIGO and VIRGO team presented an upper limit on graviton mass such as m {sub g} < 1.2 × 10{sup −22} eV [2] (see also more details in another LIGO paper [3] dedicated to a data analysis to obtain such a small constraint on a graviton mass). Since the graviton mass limit is so small the authors concluded that their observational data do not show violations of classical general relativity. We consider another opportunity to evaluate a graviton mass from phenomenological consequences of massive gravity and show that an analysis of bright star trajectories could bound graviton mass with a comparable accuracy with accuracies reached with gravitational wave interferometers and expected with forthcoming pulsar timing observations for gravitational wave detection. It gives an opportunity to treat observations of bright stars near the Galactic Center as a wonderful tool not only for an evaluation specific parameters of the black hole but also to obtain constraints on the fundamental gravity law such as a modifications of Newton gravity law in a weak field approximation. In particular, we obtain bounds on a graviton mass based on a potential reconstruction at the Galactic Center.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Meteor velocity distribution and an optimum monitoring mathematical model

At present, there are a great number of radio meteor, ionosphere and rocket observation data for the altitude range of 80 to 100 km which indicate the existence of large scale circulation systems in the mesopause to low thermosphere range which change regularly with season and latitude. But the existing observation network and observation programs are not optimal for revealing the main factors forming the circulation mode at these altitudes. A generalized optimum monitoring mathematical model is offered for consideration. The model input data are distribution density, response function, individual measurement root mean square uncertainty and detection effectiveness function. The model makes it possible to obtain the observation distribution density, the minimal possible dispersion and optimized system effectiveness.

Volkov, N. G.↗
NASA NTRS1989

The next 40 years in space standards

Methods used in producing, introducing, and using standards for civilian space research are examined, with special consideration given to the recommendations of the Consultative Committee for Space Data Systems (CCSDS) as an example of a set of standards best coordinated through the International Standard Organization (ISO). The paper uses an example of earth-observation data as a CCSDS application for an international coordination effort within the ISO and describes progress in achieving this objective. Lists of CCDSD member agencies and CCSDS observer agencies are included.

Sheetz, H. J.↗
NASA NTRS1997

Observations and Modeling of the Transient General Circulation of the North Pacific Basin

The objective of this study was to clarify the role that interstellar-cloud chemistry played in forming the population of organic molecules presently found in carbonaceous meteorites. This goal was to be achieved by means of defining the isotopic components present in organic and related phases in the meteorites and thereby identify the processes and source reservoirs involved in organic synthesis in the early solar system. Isotopic analysis of separated amino acids from the Murchison meteorite yielded results that are complex and not fully interpretable at this time. Substantial inter-acid variability in D/H ratio was observed, some but not all of which could be attributed to exchange with terrestrial hydrogen. Pronounced, though smaller, variability was also found for N-15/N-14 ratios. For both D/H and N-15/N-14 data, observed meteoritic values were substantially greater than found in terrestrial materials, providing a robust constraint on degrees of possible terrestrial contamination. Also, C-13/C-12 ratios, though falling within the range of data found on earth, significantly exceeded those characteristic of naturally occurring terrestrial amino acids. Inter-acid variability in C-13/C-12 ratios was muted relative to that observed for D/H and N-15/N-14 but still lay well outside of experimental uncertainty. No systematic relationship could be observed between variations in H, C and N isotopes. Two anomalous components were also found during the course of this study. A highly (greater than 6% relative to terrestrial) N-15-depleted, N-rich compound, which has not yet been identified, co-eluted with some amino acids. Clearly the Murchison meteorite sampled nitrogen from a number of highly diverse isotopic reservoirs. In fact, from this and related studies, it is now apparent that the distribution of nitrogen isotopes in the primitive solar system was extremely inhomogeneous. The second anomalous result obtained in the present study was for an extract of 'ammonia' from Murchison. It should be noted that this sample consisted of ammonia that was probably derived from a number of different compounds present in the meteorite itself, possibly including amines and amides, as well as ammonia sensu strictu and ammonium slats. However, the significance of this analysis is that the N-15/N-14 ratio measured was much lower than those found for the meteoritic amino acids (+2% vs around + 9% relative to terrestrial). This raises an important question concerning the source of the ammonia that was involved in synthesis of the amino acids. This issue needs to be explored further.

Kerridge, John F.↗
NASA NTRS1993

Porosity and the ecology of icy satellites

The case for a significant role for porosity in the structure and evolution of icy bodies in the Solar System has been difficult to establish. We present a relevant new data set and a series of structure models including a mechanical compression, not thermal creep, model for porosity that accounts satisfactorily for observed densities, moments of inertia, geologic activity, and sizes of tectonic features on icy satellites. Several types of observational data sets have been used to infer significant porosity, but until recently, alternative explanations have been preferred. Our first area of concern is the occurrence of cryovolcanism as a function of satellite radius; simple radiogenic heating models of icy satellites suggest minimum radii for melting and surface cryovolcanism to be 400 to 500 km, yet inferred melt deposits are seen on satellites half that size. One possible explanation is a deep, low conductivity regolith which lowers conductivity and raises internal temperatures, but other possibilities include tidal heating or crustal compositions of low conductivity. Our second area of concern is the occurrence and magnitude of tectonic strain; tectonic structures have been seen on icy satellites as small as Mimas and Proteus. The structures are almost exclusively extensional, with only a few possible compression Al features, and inferred global strains are on the order of 1 percent expansion. Expansions of this order in small bodies like Mimas and prevention of late compressional tectonics due to formation of ice mantles in larger bodies like Rhea are attained only in structure models including low-conductivity, and thus possibly high porosity, crusts. Thirdly, inferred moments of inertia less than 0.4 in Mimas and Tethys can be explained by high-porosity crusts, but also by differentiation of a high density core. Finally, the relatively low densities of smaller satellites like Mimas and Miranda relative to larger neighbors can be explained by deep porosity, but also by bulk compositional differences. Recent work has strengthened the case for significant porosity. Halley's nucleus was found to have a density near 0.6 g/cu cm, Janus and Epimethus were proposed to have densities near 0.7 g/cu cm, densities almost certainly due to high porosity. The irregular-spherical shape transition of icy satellites was quantitatively explained by low conductivity regoliths. A creative structure/thermal history model for Mimas simultaneously accounts quantitatively for Mimas' low density and moment of inertia by invoking initial high-porosity and subsequent compaction in the deep interior by thermal creep. The main problem with this promising model is that approximately 7 percent predicts a reduction in Mimas' radius, implying significant compressional failure and prevention of extensional tectonics, in contradiction to the observed extensional features and inferred 1 percent expansion in radius.

Croft, Steven K.↗
DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Some recent developments in the interpretation of MST radar returns from clear air (keynote paper), part 2

Mesosphere-stratosphere-troposphere (MST) radar returns from clear air come about through the interaction of electromagnetic waves with the inhomogeneous structures of refractive index in the atmosphere. In order to interpret the data correctly to obtain information concerning the dynamics of the atmosphere, one must first know how the various refractive index structures can affect the propagation and scattering of the radio waves. This can be achieved through theoretical and model studies. On the other hand, in order to carry out realistic theoretical studies, realistic models of the inhomogeneous structures of the atmospheric refractive index are needed. These are available only through observational data. Therefore the close interplays between theoretical and observational investigations are essential in making progress in this area. Some results on certain aspects of the problem are presented with emphasis on those aspects that may lead to new developments.

Liu, C. H.↗
DOE OSTI2020

Variations of the physical parameters of the blazar Mrk 421 based on analysis of the spectral energy distributions

Abstract We report on the variations of the physical parameters of the jet observed in the blazar Mrk 421, and discuss the origin of X-ray flares in the jet, based on analysis of several spectral energy distributions (SEDs). The SEDs are modeled using the one-zone synchrotron self-Compton model, its parameters determined using a Markov chain Monte Carlo method. The lack of data at TeV energies means many of the parameters cannot be uniquely determined and are correlated. These are studied in detail. We find that the optimal solution can be uniquely determined only when we apply a constraint to one of four parameters: the magnetic field (B), the Doppler factor, the size of the emitting region, and the normalization factor of the electron energy distribution. We used 31 sets of SEDs from 2009 to 2014 with optical–UV data observed with UVOT/Swift and the Kanata telescope, X-ray data with XRT/Swift, and γ-ray data with the Fermi Large Area Telescope. The result of our SED analysis suggests that, in the X-ray faint state, the emission occurs in a relatively small area (∼1016 cm) with a relatively strong magnetic field (B ∼ 10−1 G). The X-ray bright state shows a tendency opposite to that of the faint state, that is, a large emitting area (∼1018 cm), probably downstream of the jet, and a weak magnetic field (B ∼ 10−3 G). The high X-ray flux was due to an increase in the maximum energy of electrons. On the other hand, the presence of two kinds of emitting areas implies that the one-zone model is unsuitable for reproducing at least part of the observed SEDs.

Yamada, Yurika↗
DOE OSTI2024

Including the parallel mass flow in calculating the steady-state solutions and stability of the momentum balance equations for a quasisymmetric stellarator

The Helically Symmetric Experiment (HSX) is a quasisymmetric stellarator with minimal parallel viscous damping in a helical direction. The parallel flow (Vǁ) along the magnetic field is similarly weakly damped by viscosity. In this paper, the self-consistent steady-state parallel and poloidal momentum balance equations are used to show that a large Vǁ on the order of the ion thermal velocity can increase the ion resonant radial electric field (Er) beyond the value calculated using the typical approximation that Vǁ is zero. By altering the damping of Vǁ, either by degrading the quasisymmetry or varying the neutral density, the ion resonant Er can shift in a controllable fashion. It is shown explicitly that there exist stable and unstable steady-state solutions in the two-dimensional space of Vǁ and Er. A stability analysis of each solution is performed by calculating the eigenvalues and eigenvectors of the Jacobian. The unstable solution corresponds to a saddle point in which the eigenvalues have opposite signs. The analysis leads to the conclusion that unstable solutions occur when the derivative of the total poloidal damping with respect to Er is positive. A hysteresis in Er and Vǁ is observed when the radial current density is linearly increased to a maximum and then decreased back to zero. Jumps in the radial electric field and the parallel flow are observed as the radial current density drives the evolution from one stable point to the next. This result is similar to experimental data observed on several devices.

Physics↗
DOE OSTI2023

Deep Learning Parameterization of Vertical Wind Velocity Variability via Constrained Adversarial Training

Atmospheric models with typical resolution in the tenths of kilometers cannot resolve the dynamics of air parcel ascent, which varies on scales ranging from tens to hundreds of meters. Small-scale wind fluctuations are thus characterized by a subgrid distribution of vertical wind velocity W with standard deviation σ W . The parameterization of σ W is fundamental to the representation of aerosol–cloud interactions, yet it is poorly constrained. Using a novel deep learning technique, this work develops a new parameterization for σ W merging data from global storm-resolving model simulations, high-frequency retrievals of W , and climate reanalysis products. The parameterization reproduces the observed statistics of σ W and leverages learned physical relations from the model simulations to guide extrapolation beyond the observed domain. Incorporating observational data during the training phase was found to be critical for its performance. The parameterization can be applied online within large-scale atmospheric models, or offline using output from weather forecasting and reanalysis products.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Models, data, and scripts associated with “Prediction of Distributed River Sediment Respiration Rates using Community-Generated Data and Machine Learning”

This data package is associated with the publication “Prediction of Distributed River Sediment Respiration Rates using Community-Generated Data and Machine Learning’’ submitted to the Journal of Geophysical Research: Machine Learning and Computation (Scheibe et al. 2024). River sediment respiration observations are expensive and labor intensive to obtain and there is no physical model for predicting this quantity. The Worldwide Hydrobiogeochemisty Observation Network for Dynamic River Systems (WHONDRS) observational data set (Goldman et al.; 2020) is used to train machine learning (ML) models to predict respiration rates at unsampled sites. This repository archives training data, ML models, predictions, and model evaluation results for the purposes of reproducibility of the results in the associated manuscript and community reuse of the ML models trained in this project. One of the key challenges in this work was to find an optimum configuration for machine learning models to work with this feature-rich (i.e. 100+ possible input variables) data set. Here, we used a two-tiered approach to managing the analysis of this complex data set: 1) a stacked ensemble of ML models that can automatically optimize hyperparameters to accelerate the process of model selection and tuning and 2) feature permutation importance to iteratively select the most important features (i.e. inputs) to the ML models. The major elements of this ML workflow are modular, portable, open, and cloud-based, thus making this implementation a potential template for other applications. This data package is associated with the GitHub repository found at Please see the file level metadata (flmd; “sl-archive-whondrs_flmd.csv”) for a list of all files contained in this data package and descriptions for each. Please see the data dictionary (dd; “sl-archive-whondrs_dd.csv”) for a list of all column headers contained within comma separated value (csv) files in this data package and descriptions for each. The GitHub repository is organized into five top-level directories: (1) “input_data” holds the training data for the ML models; (2) “ml_models” holds machine learning models trained on the data in “input_data”; (3) “scripts” contains data preprocessing and postprocessing scripts and intermediate results specific to this data set that bookend the ML workflow; (4) “examples” contains the visualization of the results in this repository including plotting scripts for the manuscript (e.g., model evaluation, FPI results) and scripts for running predictions with the ML models (i.e., reusing the trained ML models); (5) “output_data” holds the overall results of the ML model on that branch. Each trained ML model resides on its own branch in the repository; this means that inputs and outputs can be different branch-to-branch. Furthermore, depending on the number of features used to train the ML models, the preprocessing and postprocessing scripts, and their intermediate results, can also be different branch-to-branch. The “main-*” branches are meant to be starting points (i.e. trunks) for each model branch (i.e. sprouts). Please see the Branch Navigation section in the top-level README.md in the GitHub repository for more details. There is also one hidden directory “.github/workflows”. This hidden directory contains information for how to run the ML workflow as an end-to-end automated GitHub Action but it is not needed for reusing the ML models archived here. Please the top-level README.md in the GitHub repository for more details on the automation.

13C↗
DOE OSTI2020

Weak Lensing And Cosmology In The Dark Energy Survey

In this PhD Thesis, we present studies which aim at understanding and testing the fundamental assumptions of the $\Lambda$CDM cosmological model. We initially show that weak gravitational lensing can be derived as a consequence of General Relativity, and that it can be applied to astronomical data from the Dark Energy Survey (DES) in order to constrain the amplitude of matter fluctuations in the universe. This constraint can be used as an end-to-end cosmological test when it is compared to inferences from the Cosmic Microwave Background. We further extend the cosmological model to account for non-standard parameters which can point to novel physics, and use DES data to assess their statistical significance. We finally show that the Cold Dark Matter (CDM) paradigm can also be fundamentally tested with observational data using morphological signatures of disk galaxies in cluster environments if CDM is self-interacting.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Recurrent brief X-ray bursts from the globular cluster NGC 6624

Observational data are presented on ten brief X-ray bursts, recurrent at nearly equal time intervals, recorded during a two-day observation of 3U 1820-30 in the globular cluster NGC 6624 with the wide-field modulation collimator detectors on the SAS-3 X-ray observatory. The occurrence times were fitted by least squares to a linear sequence with an rms deviation of 621 sec, corresponding to a phase jitter of 3.9%. The bursts were observed in two energy channels. For a sequence of five of the most clearly observed bursts, the 2-6 keV rate rose to its peak value in about 1 sec and then decayed to preburst level in about 10 sec. The 6-11 keV rate rose more slowly and decayed similarly. The smooth decay of their averaged light curve suggests the temporal evolution may have a geometrical origin, where Compton scattering in a surrounding cloud of hot plasma stretches the pulse out and causes a progressive hardening of the spectrum.

Clark, G. W.↗
NASA NTRS1979

Transfer of solar radiation in the atmosphere

Current needs in the field of atmospheric radiative transfer include the development and validation of fast but accurate calculation techniques for use in climate modeling. Progress toward meeting these needs can be made by application of existing computational techniques and use of observational data for radiation transfer across the earth-atmosphere system boundaries. In this study radiative transfer model simulations are compared to satellite observations of reflected solar radiation. Calculations are presented from both detailed and approximate transfer models for the solar radiation reflected from the earth-atmosphere system. These calculations are compared with the measurements made by the Earth Radiation Budget (ERB) experiment on Nimbus 6 in August 1975. Results show good agreement between simulations and observations.

Suttles, J. T.↗
NASA NTRS1979

Scale covariance and G-varying cosmology. III - The /m, z/, /theta sub m, z/, /theta sub i, z/, and /N/m/, m/ tests

The Einstein gravitational equations in atomic units are fully solved for a matter-dominated universe in the context of a recently proposed scale-covariant cosmology. The magnitude-redshift relation for elliptical galaxies is studied, the evolutionary parameter used in such a study is derived, and the relation between isophotal angular diameters and redshifts is investigated, along with the relation between metric angular diameters and redshifts, the N(m)-magnitude relation for QSOs, and the magnitude-redshift relation for QSOs. Results are presented for four gauges (i.e., relations between G and the scale function beta (t)), and no contradictions are found between the proposed theory and the observational data. It is shown that only an open universe can fit the data if certain gauges suggested by a recent analysis of the time variation of the moon's period are selected and that observations made with atomic instruments do not necessarily yield geometrical parameters unless specific assumptions are made regarding the relation between atomic and gravitational dynamics.

Canuto, V. M.↗