Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “magnitude”

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 127 records · Page 7

Satellite-derived cyanobacteria frequency and magnitude in headwaters & near-dam reservoir surface waters of the Southern U.S.

Reservoirs are dominant features of the modern hydrologic landscape and provide vital services. However, the unique morphology of reservoirs can create suitable conditions for excessive algae growth and associated cyanobacteria blooms in shallow in-flow reservoir locations by providing warm water environments with relatively high nutrient inputs, deposition, and nutrient storage. Cyanobacteria harmful algal blooms (cyanoHAB) are costly water management issues and bloom recurrence is associated with economic costs and negative impacts to human, animal, and environmental health. As cyanoHAB occurrence varies substantially within different regions of a water body, understanding in-lake cyanoHAB spatial dynamics is essential to guide reservoir monitoring and mitigate potential public exposure to cyanotoxins. Cloud-based computational processing power and high temporal frequency of satellites enables advanced pixel-based spatial analysis of cyanoHAB frequency and quantitative assessment of reservoir headwater in-flows compared to near-dam surface waters of individual reservoirs. Additionally, extensive spatial coverage of satellite imagery allows for evaluation of spatial trends across many dozens of reservoir sites. Surface water cyanobacteria concentrations for sixty reservoirs in the southern U.S. were estimated using 300m resolution European Space Agency (ESA) Ocean and Land Colour Instrument (OLCI) satellite sensor for a five year period (May 2016–April 2021). Of the reservoirs studied, spatial analysis of OLCI data revealed 98% had more frequent cyanoHAB occurrence above the concentration of >100,000 cells/mL in headwaters compared to near-dam surface waters (P < 0.001). Headwaters exhibited greater seasonal variability with more frequent and higher magnitude cyanoHABs occurring mid-summer to fall. Examination of reservoirs identified extremely high concentration cyanobacteria events (>1,000,000 cells/mL) occurring in 70% of headwater locations while only 30% of near-dam locations exceeded this threshold. Wilcoxon signed-rank tests of cyanoHAB magnitudes using paired-observations (dates with observations in both a reservoir's headwater and near-dam locations) confirmed significantly higher concentrations in headwater versus near-dam locations (p < 0.001).

cyanobacteria↗

On the Use of Smart Meter Data to Estimate the Voltage Magnitude on the Primary Side of Distribution Service Transformers: Preprint

This paper develops a novel method to estimate the voltage magnitude on the primary side of distribution service transformers. The proposed method relies exclusively on smart meters, and therefore it is fully data-driven. This is an important feature because electric utilities have detailed models of only the primary network--that is, the network between the distribution substation and the primary side of service transformers that are installed closer to end-customer sites. The network that connects the secondary side of service transformers to end-customer sites, referred to as the secondary network, is simply represented by a lumped load. For each secondary network, the proposed method uses data acquired from only 2 smart meters: the closest and the farthest--in the sense of electrical distance--from the service transformer. As a reference to this feature, the proposed method is named SM2Vp. To our knowledge, this is the first time a method is shown to provide actionable information for real-time operation and control of power distribution grids using only two smart meters per secondary network. This is important because utilities have experienced barriers in managing and using large data sets for real-time operation and control. SM2Vp is primarily intended to provide pseudo-measurements for distribution system state estimation, but it can also be used directly for voltage control schemes. The performance of SM2Vp is demonstrated by numerical simulations carried out on three secondary network synthetic models and by using field data provided by a utility partner serving customers in southwestern California. A maximum relative error of approximately 3.9% or less is observed for the primary voltage magnitude estimates in all numerical experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Aerogel Antennas Communications Study Using Error Vector Magnitude Measurements

This paper discusses an aerogel antennas communication study using error vector magnitude (EVM) measurements. The study was performed using 4x2 element polyimide (PI) aerogel-based phased arrays designed for operation at 5 GHz as transmit (Tx) and receive (Rx) antennas separated by a line of sight (LOS) distance of 8.5 meters. The results of the EVM measurements demonstrate that polyimide aerogel antennas work appropriately to support digital communication links with typically used modulation schemes such as QPSK and pi/4 DQPSK. As such, PI aerogel antennas with higher gain, larger bandwidth and lower mass than typically used microwave laminates could be suitable to enable aerospace-to-ground communication links with enough channel capacity to support voice, data and video links from cubesats, unmanned air vehicles (UAV), and commercial aircraft.

Aerogel Antennas↗

A Photoresponsive Receptor with a 10 5 Magnitude of Reversible Anion-Binding Switching

In a leap toward anion separation that uses only energy input for binding and release cycles, we report herein a new class of photoswitchable anion receptors featuring a diiminoguanidinium functionality that displays a change of more than five orders of magnitude in switched-off binding strength towards sulfate, a representative oxyanion, upon photoirradiation with UV light. Additionally, the (E,E)-2-pyridyl-diiminoguanidinium cation, synthesized as the triflate salt, binds sulfate with extraordinary strength in [D6]DMSO owing to its bidentate guanidinium hydrogen bonding, which can chelate the O-S-O edge of sulfate. Upon photoisomerization to the Z,Z isomer, the anion-binding site is essentially shut off by intramolecular hydrogen bonds to the 2-pyridyl substituents, as shown by anion-binding titrations, theoretical calculations, and X-ray structural analysis. This approach will allow the development of advanced anion-separation cycles that use only energy input and generate no chemical waste, and thus address challenging chemical separation problems in a more sustainable way.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interspecific variation in the timing and magnitude of hydraulic redistribution in a forest with distinct water sources

Trees regulate water availability among their rooting strata through a nocturnal, passive transference of water known as hydraulic redistribution (HR). This study investigates differences in HR and groundwater use among common canopy species in longleaf pine (Pinus palustris Mill., Pinaceae) woodlands and explores environmental factors influencing HR. HR was estimated by sap flux of lateral roots and main stems of three mature canopy species (P. palustris, Quercus laevis Walter., Fagaceae and Quercus margarettae Ashe., Fagaceae). We used δ18O and δD of xylem water, soil water, and groundwater to determine water source. Finally, we related HR to environmental factors (Temperature, VWC, VPD) to better understand controls of HR dynamics. Pinus palustris had higher water use than either Quercus species, and also redistributed significantly more water as a nocturnal subsidy. HR fluxes were inversely related with mean nightly temperature and independent of shallow soil moisture. Stable isotope mixing models, based on δ 18 O and δD, indicated that all species have access to groundwater, but utilized shallow soil water in differing amounts when available. In systems with strong water potential gradients among soil strata, any species with access to a groundwater source is likely capable of HR; however, the magnitude of HR varies significantly by species, even among closely related taxa.

54 ENVIRONMENTAL SCIENCES↗

Striving to translate shale physics across ten orders of magnitude: What have we learned?

Shales will play an important role in the successful transition of energy from fossil-based resources to renewables in the coming decades. Aside from being a significant source of low-carbon intensity fuels, like natural gas, they also serve as geologic seals of subsurface formations that may be used to isolate nuclear waste, sequester CO 2 , or store intermittent energy (e.g., solar hydrogen). Despite their importance, shales pose significant engineering and environmental challenges due to their nanoporous structure and extreme heterogeneity that spans at least ~10 orders of magnitude in spatial scale. Two challenges inhibit a system-level understanding: (1) the physics of fluid flow and phase behavior in shales are poorly understood due to the dominant molecular interactions between minerals and fluids under confinement, and (2) the apparent lack of scale separation that prevents a reliable (closed) description of the physics at any single scale of observation. In this review, we focus on the latter issue and discuss scale translation, which in its broadest sense is transforming data or simulations from one spatiotemporal scale to another. While effective scale translation is not exclusive to shales, but all geologic porous media, the need for it is especially acute in shales given their high degree of heterogeneity. Classical theories like homogenization, while indispensable, fail when scales are not separated. Other methods, like numerical upscaling, scale-translate in only one direction: small to large, but not the reverse, called downscaling. However, the confluence of advances in three areas are bringing challenging problems such as shales within reach: increased computational power and scalable algorithms; high-resolution imaging and multi-modal data acquisition; and machine learning to process massive amounts of data. While these advances equip geoscientists with a wide array of experimental and computational tools, no individual tool can probe the entire gamut of heterogeneity in shales. Their effective use, therefore, requires an ability to bridge between various data types obtained at different scales. The aim of this review is to present a coherent account of computational and experimental methods that may be used to achieve just that, i.e., to perform scale translation. We provide a broader definition of scale translation, one that transcends classical homogenization and upscaling methods, but is consistent with them and accommodates notions like downscaling and data translation. After a brief introduction to homogenization, we review hybrid methods, numerical upscaling and its recent extensions, multiscale computing, high-resolution imaging, and machine learning. We place particular emphasis on multiscale computing and propose an algorithmic framework to bridge between the pore (micro) and Darcy (macro) scales. Throughout the paper, we draw comparisons between the various methods and highlight their (often hidden) similarities, differences, benefits, and pitfalls. We finally conclude with two case studies on shales that exemplify some of the methods presented.

58 GEOSCIENCES↗

Investigating the relationship between radial pre-stress magnitude and ballistic projectile dwell in heavy confined ceramic targets

A series of bare silicon carbide ceramic armour disks were manufactured with high-strength steel containment to induce varying magnitudes of radial pre-stress. The induced radial stresses, ranging from 0 to 900 MPa, were measured via neutron diffraction and verified by comparison with numerical calculations. Four targets of each configuration, referred to as slip-fit, moderate pre-stress, and high pre-stress, were subject to ballistic testing with hemispherical-nose, tungsten heavy alloy long rod projectiles to determine the interface defeat transition velocity. In-situ diagnostics were unsuccessful in aiding the identification of interface defeat, necessitating a reliance on post-mortem assessment. A transition velocity of approx. 1000 m/s was identified for the unstressed target, increasing to approx. 1200 m/s for the pre-stressed configurations. No performance effect was discernible between the moderate (372 MPa) and high (899 MPa) pre-stress configurations, suggesting that an optimal performance may be achieved for lower pre-stress levels (i.e., <372 MPa). Additionally, the test results were compared with four semi-analytical predictions of interface defeat performance and good agreement was found, albeit with significant range in the model predictions.

42 ENGINEERING↗

Multi-modal imaging of a single mouse brain over five orders of magnitude of resolution

Mammalian neurons operate at length scales spanning six orders of magnitude; they project millimeters to centimeters across brain regions, are composed of micrometer-scale-diameter myelinated axons, and ultimately form nanometer scale synapses. Capturing these anatomical features across that breadth of scale has required imaging samples with multiple independent imaging modalities. Translating between the different modalities, however, requires imaging the same brain with each. Here, we imaged the same postmortem mouse brain over five orders of spatial resolution using MRI, whole brain micrometer-scale synchrotron x-ray tomography ($\mu$CT), and large volume automated serial electron microscopy. Using this pipeline, we can track individual myelinated axons previously relegated to axon bundles in diffusion tensor MRI or arbitrarily trace neurons and their processes brain-wide and identify individual synapses on them. This pipeline provides both an unprecedented look across a single brain's multi-scaled organization as well as a vehicle for studying the brain's multi-scale pathologies.

59 BASIC BIOLOGICAL SCIENCES↗

Ambient Synthesis for Fe(II) Polypyridyl Complexes with an Order of Magnitude Increase in Charge-Transfer Excited-State Lifetimes over [Fe(bpy) 3 ] 2+

Replacing precious metals with abundant metals is an important research focus in photochemical energy conversion and storage to meet global energy demands. However, transition metal complexes (TMCs) based on abundant 3d metals typically possess photochemical disadvantages─such as short charge-transfer excited-state lifetimes─and molecular modifications have focused on optimizing the interplay of structure, dynamics, and energetics to overcome their limitations. One strategy to do so is the use of bespoke ligands that can extend the lifetimes of chemically useful excited states. Here, in this study, we report the synthesis and characterization of novel Fe(II) complexes featuring lengthy polypyridyl ligands that can be readily synthesized. Steady-state and transient absorption spectroscopies indicate that these complexes have desirable properties and their excited metal-to-ligand charge-transfer states live an order of magnitude longer than in the benchmark [Fe(bpy) 3 ] 2+ . This lifetime is largely preserved in the heteroleptic complexes, thereby enabling the preparation of asymmetric complexes. Additionally, we apply nonradiative transition theory to explain the long-time decay kinetics. In light of their ease of preparation and reasonable excited-state lifetimes, we suggest the use of these complexes in Fe(II) dye-sensitized solar cells, where the rate of charge injection would be competitive with increased lifetime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Projecting Changes in the Frequency and Magnitude of Ozone Pollution Events Under Uncertain Climate Sensitivity

Abstract Climate change is projected to worsen ozone pollution over many populated regions, with larger impacts at higher concentrations. More intense and frequent ozone episodes risk setbacks to human health and environmental policy achievements. However, assessing these changes is complicated by uncertain climate sensitivity, closely related to climate model response, and internal variability in simulations projecting climate's influence on air quality. Here, leveraging a global modeling framework that one‐way couples a human activity model, an Earth system model of intermediate complexity, and an atmospheric chemistry model, we investigate the role of climate sensitivity in climate‐induced changes to high ozone pollution episodes in the United States using multiple greenhouse gas emissions scenarios, representations of climate sensitivity, and initial condition members. We bias correct and evaluate historical model simulations, identifying modeled and observed O 3 episodes using extreme value theory, and extend the approach to projections of mid‐ and end‐century climate impacts. Results show that the influence of climate sensitivity can be as significant as that of greenhouse gas emissions scenario absent precursor emissions changes. Climate change is projected to increase the magnitude of the highest annually occurring O 3 concentrations by over 2.3 ppb on average across the U.S. at mid‐century under a high climate sensitivity and moderate emissions scenario, but the increase is limited to less than 0.3 ppb under lower climate sensitivity. Further, we show that areas in the U.S. currently meeting air quality standards risk being pushed into non‐compliance due to a climate‐induced increase in frequency of high ozone days.

Environmental Sciences & Ecology↗

Small-Magnitude Seismic Swarms in Central Utah (US): Interactions of Regional Tectonics, Local Structures and Hydrothermal Systems

Swarms in Central Utah are situated in the complex transition between the Basin and Range (BR) province and the Colorado Plateau. Transecting transverse structures, volcanic deposits, and hydrothermal systems complicate the extensional BR horst and graben structures and provide a multitude of plausible triggering mechanisms. Revisiting the catalog of the University of Utah Seismograph Stations (1981–2022), we analyze spatio-temporal patterns and characteristic features of seismic sequences. Swarms with alternating seismicity rates, bursts, and longer swarms with persistent moment release exhibit a remarkable diversity in temporal evolution. Swarm durations do not scale with cumulative seismic moment: swarms lasting less than 1 day can have similar cumulative seismic moments as month-long swarms. Here, we observe stationary swarms re-occurring for years (e.g., Mineral Mountains), as well as singular swarms in low-seismicity areas (e.g., activating a local structure). The swarms show a pronounced heterogeneity in triggering and driving mechanisms, observed in the detailed analysis of exemplary sequences (detections, relocations, moment tensors, waveform-based clustering, and repeater analysis). The 2022 Sevier Valley sequence activated a BR-related normal fault, the first resolved fault plane in the valley since 1983. The 2011 Circleville sequence is interpreted as a swarm triggered by mainshock-aftershock activity characterized by increasing magnitudes, changing rupture mechanisms, and a concentration of highly similar events in the second part of the sequence. By jointly discussing exemplary sequences and catalog statistics, we draw a comprehensive picture of swarm activity and its relation to geothermal and tectonic activity.

58 GEOSCIENCES↗

Cascadia Subduction Zone Fault Heterogeneities From Newly Detected Small Magnitude Earthquakes

The Cascadia subduction zone (CSZ) is known to host M9 megathrust ruptures; however, no such event has occurred in historical observation. The distribution and characteristics of small- to moderate-sized earthquakes can be used to determine the behavior of the megathrust fault but are notably absent offshore the CSZ due to the distance from onshore seismometers. We use automated subspace detection coupled with an onshore-offshore seismic deployment to find small-magnitude earthquakes in the offshore seismogenic zone and analyze their locations in the context of interseismic locking and seismogenic zone extent. Here we detected and located 5,282 earthquakes, 4,096 of which had been previously undetected. We find that the downdip extent of the seismogenic zone as defined by interplate seismicity agrees with the 20% locking contour of the Schmalzle et al. (2014, https://doi.org/10.1002/2013GC005172) geodetic model and extends deeper than predicted by previous thermal models. We cannot determine the updip extent of the seismogenic zone; this may be due to a lack of templates for detection in the updip source area, stress shadows updip of asperity loading, and/or strong locking to the trench. We present a map of possible asperities determined by the small earthquakes in this study. Our asperity locations and extents show some, but not complete, agreement with the asperities modeled from the 1700 M9 rupture and geodetic locking models, and good agreement with the paleo-rupture extents determined from offshore turbidites and forearc basin-based asperity estimates. This highlights the need of continued offshore observations over time, and to elucidate fine-scale variation in locking.

58 GEOSCIENCES↗

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↗

New methodology for measuring electron density perturbations caused by plasma coherent modes using profile reflectometry: Magnitudes and radial profiles in DIII-D

New capabilities of fast-sweep frequency-modulated profile reflectometry are explored to measure electron density ne perturbation magnitudes and radial profiles due to plasma coherent modes in DIII-D. The first approach is based on the frequency analysis of phase perturbations associated with high frequency (~MHz) Alfvén eigenmodes (AEs). The measurement of ~5.5 MHz fast-ion-driven global Alfvén eigenmodes (GAEs) is demonstrated in a neutral beam-heated DIII-D plasma. The GAE induced a broad radial distribution of phase perturbations in the profile reflectometer data. Analysis of these data determined the effective cutoff location displacement and the estimated ne fluctuation profile. In the second approach, high resolution ne profiles are used directly to determine the radial structure of ne perturbations due to a neo-classical tearing mode. These new measurements broaden the application of profile reflectometry and advance the development of AE spectroscopy as a tool for non-invasive diagnosis of fast-ion-driven modes in DIII-D and burning plasmas such as ITER.

47 OTHER INSTRUMENTATION↗

Study of ablation and shock generation across three orders of magnitude of laser intensity with 100 ps laser pulses

The laser ablation and subsequent shock generation in solid targets plays an important role in a variety of research topics from equation of state models for materials to inertial confinement fusion. One of the long-standing issues is the knowledge of ablation depth in the picosecond time regime. Here, we report on a direct technique for determining the ablation depth in aluminum using x-ray diffraction data from Linac Coherent Light Source at the Stanford Linear Accelerator Center. This technique gives a direct measurement of the shock wave propagation in the bulk target, enabling an ability to discern early timescale physics from late timescale effects not available in postmortem analysis. We find that the ablation depths only vary by 0.2 μm across three orders of magnitude of laser intensity, while the pressure increased by a factor of 10 following a square root dependence on laser pulse energy. We further observe that the ablation depth in this intensity range (10 11 –10 13 W/cm 2 in intensity, corresponding to 0.8–80 J/cm 2 in fluence) cannot be modeled by a universal scaling law, given the complexity of the mechanisms governing laser ablation in this intensity regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cosmological constraints from H ii starburst galaxy apparent magnitude and other cosmological measurements

ABSTRACT We use H ii starburst galaxy apparent magnitude measurements to constrain cosmological parameters in six cosmological models. A joint analysis of H ii galaxy, quasar angular size, baryon acoustic oscillations peak length scale, and Hubble parameter measurements result in relatively model-independent and restrictive estimates of the current values of the non-relativistic matter density parameter $\Omega _{\rm m_0}$ and the Hubble constant H0. These estimates favour a 2.0–3.4σ (depending on cosmological model) lower H0 than what is measured from the local expansion rate. The combined data are consistent with dark energy being a cosmological constant and with flat spatial hypersurfaces, but do not strongly rule out mild dark energy dynamics or slightly non-flat spatial geometries.

79 ASTRONOMY AND ASTROPHYSICS↗

Unveiling the purely young star formation history of the SMC’s northeastern shell from colour–magnitude diagram fitting

ABSTRACT We obtain a quantitative star formation history (SFH) of a shell-like structure (‘shell’) located in the northeastern part of the Small Magellanic Cloud (SMC). We use the Survey of the MAgellanic Stellar History to derive colour–magnitude diagrams (CMDs), reaching below the oldest main-sequence turnoff, from which we compute the SFHs with CMD-fitting techniques. We present, for the first time, a novel technique that uses red clump (RC) stars from the CMDs to assess and account for the SMC’s line-of-sight depth effect present during the SFH derivation. We find that accounting for this effect recovers a more accurate SFH. We quantify an $\sim$7 kpc line-of-sight depth present in the CMDs, in good agreement with depth estimates from RC stars in the northeastern SMC. By isolating the stellar content of the northeastern shell and incorporating the line-of-sight depth into our calculations, we obtain an unprecedentedly detailed SFH. We find that the northeastern shell is primarily composed of stars younger than $\sim$500 Myr, with significant star formation enhancements around $\sim$250 and $\sim$450 Myr. These young stars are the main contributors to the shell’s structure. We show synchronicity between the northeastern shell’s SFH with the Large Magellanic Cloud’s (LMC) northern arm, which we attribute to the interaction history of the SMC with the LMC and the Milky Way (MW) over the past $\sim$500 Myr. Our results highlight the complex interplay of ram pressure stripping and the influence of the MW’s circumgalactic medium in shaping the SMC’s northeastern shell.

Sakowska, Joanna D. (ORCID:0000000215941466)↗

Calibrating the absolute magnitude of type Ia supernovae in nearby galaxies using [O II ] and implications for H 0

The present state of cosmology is facing a crisis where there is a fundamental disagreement in measurements of the Hubble constant ($H_{0}$), with significant tension between the early and late Universe methods. Type Ia supernovae (SNe Ia) are important to measuring $H_{0}$ through the astronomical distance ladder. However, there remains potential to better standardize SN Ia light curves by using known dependencies on host galaxy properties after the standard light curve width and colour corrections have been applied to the peak SN Ia luminosities. To explore this, we use the 5-yr photometrically identified SNe Ia sample obtained by the Dark Energy Survey, along with host galaxy spectra obtained by the Australian Dark Energy Survey. Using host galaxy spectroscopy, we find a significant trend with the equivalent width (EW) of the [O II ] $\lambda \lambda$ 3727, 29 doublet, a proxy for specific star formation rate, and Hubble residuals. We find that the correlation with [O II ] EW is a powerful alternative to the commonly used mass step after initial light-curve corrections. Applying this [O II ] EW correction to 20 SNe Ia in calibrator galaxies observed with WiFeS, we examined the impact on SN Ia absolute magnitudes and $H_{0}$. Our [O II ] EW corrections result in $H_{0}$ values ranging between 73.04 and 73.51 $km$ $s^{-1} \, Mpc^{-1}$, with a combined statistical and systematic uncertainty of $\sim 1.31$ $km$ $s^{-1} \, Mpc^{-1}$. However, even with this additional correction, the impact of host galaxy properties in standardizing SNe Ia appears limited in reducing the current tension ($\sim 5\sigma$) with the cosmic microwave background result for $H_{0}$.

79 ASTRONOMY AND ASTROPHYSICS↗