Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Maximization”

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 757 records · Page 42

Establishing the Role of Operating Potential and Mass Transfer in Multicarbon Product Generation for Photoelectrochemical CO 2 Reduction Cells Using a Cu Catalyst

There is increasing interest in the possibility of photoelectrochemical (PEC) reduction of CO 2 to C 2+ products; however, the criteria for maximizing PEC solar-to-C 2+ (STC 2+ ) rates are not well understood. We report here a continuum-scale model of PEC CO 2 reduction (CO 2 R) on Cu in 0.1 M CsHCO 3 and use it to optimize the design and operating conditions for generating C 2+ products. Furthermore, we demonstrate that the potential-dependent product distribution of CO 2 R on Cu requires operating near the potential that maximizes C 2+ generation rates ($V$ id ), unlike PEC water splitting, which desires operation at the maximum photocurrent density. Because of this requirement, the criterion for a high STC 2+ rate includes high-photocurrent semiconductors with photovoltages near $V$ id and low series resistance. The STC 2+ rate in these systems is enhanced by optimal CO 2 transport and exhibits low sensitivity to dirunal solar irradiance variations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantitative Determination of Biomass-derived Renewable Carbon in Fuels from Coprocessing of Bio-oils in Refinery Using a Stable Carbon Isotopic Approach

Increasing renewable carbon incorporation into conventional fuels through coprocessing with vacuum gas oil (VGO, a petroleum refining feedstock) is a critical step in biofuels development, scaling-up, adoption and associated GHG reduction. Optimization of the co-processing parameters maximizes incorporation of the renewable carbon in the fuel products. Quantitative determination of the renewable carbon content in the co-processed products provides direct evaluation of the parameters. The co-processing bio-oil with VGO through hydrocracking (HC) or fluid catalytic cracking (FCC) system resulted in carbon isotopic fractionation that prevented the direct use of the isotope mixing model for quantifying the renewable carbon. Here, we report an algorithm of using a stable carbon isotope approach to quantify the renewable carbon content in co-processing biofuel products through high-precision ?13C analysis. A controlled experiment carried out by blending a fossil diesel (-29.013‰) with a bio-diesel (-30.099‰) at various blending levels up to 98.0/2.0 wt% is presented and has demonstrated the applicability of this approach. The carbon isotope fractionation factors for the bio-oil co-processing were obtained by using a 14C-derived isotope-mixing model. The ?13C method was tested by co-processing 13C-labeled bio-crude and natural woody biomass-derived fast pyrolysis (FP) and catalytic fast pyrolysis (CFP) bio-oils with VGO. The results were verified by 14C accelerator mass spectrometry (AMS) method (ASTM-D6866) and compared with the yield mass balance (YMB) method. Strong agreement between d13C and 14C AMS methods demonstrated the applicability of the ?13C method to quantify renewable carbon content in co-processing fuel products and guide the co-processing optimization

Li, Zhenghua↗

Molecular Level Differences in Ionic Solvation and Transport Behavior in Ethylene Oxide-Based Homopolymer and Block Copolymer Electrolytes

Block copolymer electrolytes (BCE) such as polystyrene-block-poly(ethylene oxide) (SEO) blended with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) and composed of mechanically robust insulating and rubbery conducting nanodomains are promising solid-state electrolytes for Li batteries. Here, we compare ionic solvation, association, distribution, and conductivity in SEO-LiTFSI BCEs and their homopolymer PEO-LiTFSI analogs toward a fundamental understanding of the maximum in conductivity and transport mechanisms as a function of salt concentration. Ionic conductivity measurements reveal that SEO-LiTFSI and PEO-LiTFSI exhibit similar behaviors up to a Li/EO ratio of 1/12, where roughly half of the available solvation sites in the system are filled, and conductivity is maximized. As the Li/EO ratios increase to 1/5 the conductivity, of the PEO-LiTFSI drops nearly 3-fold, while the conductivity of SEO-LiTFSI remains constant. FTIR spectroscopy reveals that additional Li cations in the homopolymer electrolyte are complexed by additional EO units when the Li/EO ratio exceeds 1/12, while in the BCE, the proportion of complexed and uncomplexed EO units remains constant; Raman spectroscopy data at the same concentrations show that Li cations in the SEO-LiTFSI samples tend to coordinate more to their counteranions. Atomistic-scale molecular dynamics simulations corroborate these results and further show that associated ions tend to segregate to the SEO-LiTFSI domain interfaces. The opportunity for "excess" salt to be sequestered at BCE interfaces results in the retention of an optimum ratio of uncompleted and complexed PEO solvation sites in the middle of the conductive nanodomains of the BCE and maximized conductivity over a broad range of salt concentrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Influence of Cloud Types on Cloud–Radiative Forcing During DYNAMO/AMIE

Cloud-radiative feedback is known to be an important process for the Madden-Julian Oscillation (MJO) and its accurate representation in general circulation models. The MJO is known to have a stronger cloud-radiative feedback compared to higher frequency convectively coupled equatorial waves (CCEW), for reasons that remain unclear. The objective of this study is to use data from the Dynamics of the MJO/Atmospheric Radiation Measurement MJO Investigation Experiment field campaign to investigate how cloud type evolution and their associated cloud-radiative forcing (CRF) differ between the MJO and CCEWs and their application to MJO dynamics under moisture mode theory. This study finds that the amplitude of CRF is the largest within the MJO compared to the higher frequency CCEWs, and CRF maximizes after the maximum precipitation (enhanced phase) of the MJO. We suggest this delay in the timing of maximum CRF occurs because most cloud types (congestus, deep, anvil, and cirrus) simultaneously maximize in frequency after the enhanced phase of the MJO, which is not seen for the higher frequency CCEWs. These specific cloud types help maintain the MJO through their radiatively-driven moistening which acts to prolong the enhanced phase of the MJO. The decomposition of radiatively-driven moistening by cloud types shows that simultaneous moistening by deep, anvil, and congestus clouds are particularly responsible for the maintenance of the MJO under moisture mode theory. Further, this analysis suggests the importance of capturing the correct evolution of different cloud types and their associated radiative effects to better understand the thermodynamics of the MJO.

54 ENVIRONMENTAL SCIENCES↗

Quantum capacities of transducers

Abstract High-performance quantum transducers, which faithfully convert quantum information between disparate physical carriers, are essential in quantum science and technology. Different figures of merit, including efficiency, bandwidth, and added noise, are typically used to characterize the transducers’ ability to transfer quantum information. Here we utilize quantum capacity, the highest achievable qubit communication rate through a channel, to define a single metric that unifies various criteria of a desirable transducer. Using the continuous-time quantum capacities of bosonic pure-loss channels as benchmarks, we investigate the optimal designs of generic quantum transduction schemes implemented by transmitting external signals through a coupled bosonic chain. With physical constraints on the maximal coupling rate $${g}_{\max }$$ g max , the highest continuous-time quantum capacity $${Q}^{\max }\approx 31.4{g}_{\max }$$ Q max ≈ 31.4 g max is achieved by transducers with a maximally flat conversion frequency response, analogous to Butterworth electric filters. We further investigate the effect of thermal noise on the performance of transducers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Organizing principles for vegetation dynamics

Understanding vegetation dynamics is very challenging because of the multitude of contributing processes at 64widely different spatial and temporal scales. In this Perspective we propose that understanding of vegetation dynamics can be improved, permitting better predictions, based on organizing principles that constrain plant and ecosystem be haviour: natural selection, self-organization, and entropy maximization. Although these ideas are increasingly used,a limited common understanding of their theoretical basis has prevented their full potential to be realized. We explain the power of natural selection-based optimality to predict photosynthesis and carbon allocation responses to multiple environmental drivers, and how individual plasticity leads to the predictable self-organization of forest canopies. We show how models of natural selection acting on a few key traits can generate realistic plant communities, and how entropy maximization can distinguish between stochastic and deterministic drivers of vegetation patterns. In combination with empirical exploration of patterns in plant functional variation, these principles can accelerate the development of dynamic vegetation models as well as trait-based ecology resting on strengthened theoretical and empirical foundations.

Geosciences↗

Computational strategies for design and discovery of nanostructured thermoelectrics

Abstract The contribution of theoretical calculations and predictions in the development of advanced high-performance thermoelectrics has been increasingly significant and has successfully guided experiments to understand as well as achieve record-breaking results. In this review, recent developments in high-performance nanostructured bulk thermoelectric materials are discussed from the viewpoint of theoretical calculations. An effective emerging strategy for boosting thermoelectric performance involves minimizing electron scattering while maximizing heat-carrying phonon scattering on many length scales. We present several important strategies and key examples that highlight the contributions of first-principles-based calculations in revealing the intricate but tractable relationships for this synergistic optimization of thermoelectric performance. The integrated optimization approach results in a fourfold design strategy for improved materials: (1) a significant reduction of the lattice thermal conductivity through multiscale hierarchical architecturing, (2) a large enhancement of the Seebeck coefficient through intramatrix electronic band convergence engineering, (3) control of the carrier mobility through band alignment between the host and second phases, and (4) design of intrinsically low-thermal-conductivity materials by maximizing vibrational anharmonicity and acoustic-mode Gruneisen parameters. These combined effects serve to enhance the power factor while reducing the lattice thermal conductivity. This review provides an improved understanding of how theory is impacting the current state of this field and helps to guide the future search for high-performance thermoelectric materials.

36 MATERIALS SCIENCE↗

Continuous-wave upconverting nanoparticle microlasers

Reducing the size of lasers to microscale dimensions enables new technologies that are specifically tailored for operation in confined spaces ranging from ultra-high-speed microprocessors to live brain tissue. However, reduced cavity sizes increase optical losses and require greater input powers to reach lasing thresholds. Multiphoton-pumped lasers that have been miniaturized using nanomaterials such as lanthanide-doped upconverting nanoparticles (UCNPs) as lasing media require high pump intensities to achieve ultraviolet and visible emission and therefore operate under pulsed excitation schemes. Here, we make use of the recently described energy-looping excitation mechanism in Tm 3+ -doped UCNPs to achieve continuous-wave upconverted lasing action in stand-alone microcavities at excitation fluences as low as 14 kW cm -2 . Continuous-wave lasing is uninterrupted, maximizing signal and enabling modulation of optical interactions. By coupling energy-looping nanoparticles to whispering-gallery modes of polystyrene microspheres, we induce stable lasing for more than 5 h at blue and near-infrared wavelengths simultaneously. These microcavities are excited in the biologically transmissive second near-infrared (NIR-II) window and are small enough to be embedded in organisms, tissues or devices. The ability to produce continuous-wave lasing in microcavities immersed in blood serum highlights practical applications of these microscale lasers for sensing and illumination in complex biological environments.

47 OTHER INSTRUMENTATION↗

Closed-loop optimization of fast-charging protocols for batteries with machine learning

Simultaneously optimizing many design parameters in time-consuming experiments causes bottlenecks in a broad range of scientific and engineering disciplines. One such example is process and control optimization for lithium-ion batteries during materials selection, cell manufacturing and operation. A typical objective is to maximize battery lifetime; however, conducting even a single experiment to evaluate lifetime can take months to years. Furthermore, both large parameter spaces and high sampling variability necessitate a large number of experiments. As such, the key challenge is to reduce both the number and the duration of the experiments required. Here we develop and demonstrate a machine learning methodology to efficiently optimize a parameter space specifying the current and voltage profiles of six-step, ten-minute fast-charging protocols for maximizing battery cycle life, which can alleviate range anxiety for electric-vehicle users. We combine two key elements to reduce the optimization cost: an early-prediction model, which reduces the time per experiment by predicting the final cycle life using data from the first few cycles, and a Bayesian optimization algorithm, which reduces the number of experiments by balancing exploration and exploitation to efficiently probe the parameter space of charging protocols. Using this methodology, we rapidly identify high-cycle-life charging protocols among 224 candidates in 16 days (compared with over 500 days using exhaustive search without early prediction), and subsequently validate the accuracy and efficiency of our optimization approach. Our closed-loop methodology automatically incorporates feedback from past experiments to inform future decisions and can be generalized to other applications in battery design and, more broadly, other scientific domains that involve time-intensive experiments and multi-dimensional design spaces.

25 ENERGY STORAGE↗

Evaluation of entropy driven jet symmetry transitions

Here we determine whether entropy drives planar turbulent jets into round turbulent jets. Determining when a jet flow transitions from one symmetry to the next is an important but incompletely resolved problem. The constructal view argues that the transition between symmetries of jet flows is governed by the minimization or maximization of entropy. Here we explore whether entropy increases with the transition of a planar turbulent jet into a round turbulent jet and whether entropy maximization (or minimization) predicts the same location of symmetry transition as velocity matching. We find that entropy considerations presented do not predict this transition.

47 OTHER INSTRUMENTATION↗

Reduced methane recovery at high pressure due to methane trapping in shale nanopores

By 2050, shale gas production is expected to exceed three-quarters of total US natural gas production. However, current unconventional hydrocarbon gas recovery rates are only around 20%. Maximizing production of this natural resource thus necessitates improved understanding of the fundamental mechanisms underlying hydrocarbon retention within the nanoporous shale matrix. In this study, we integrated molecular simulation with high-pressure small-angle neutron scattering (SANS), an experimental technique uniquely capable of characterizing methane behavior in situ within shale nanopores at elevated pressures. Samples were created using Marcellus shale, a gas-generative formation comprising the largest natural gas field in the United States. Our results demonstrate that, contrary to the conventional wisdom that elevated drawdown pressure increases methane recovery, a higher peak pressure led to the trapping of dense, liquid-like methane in sub-2 nm radius nanopores, which comprise more than 90% of the measured nanopore volume, due to irreversible deformation of the kerogen matrix. These findings have critical implications for pressure management strategies to maximize hydrocarbon recovery, as well as broad implications for fluid behavior under confinement.

58 GEOSCIENCES↗

Dynamical insights into the mechanism of a droplet detachment from a fiber

Quantifying the detachment behavior of a droplet from a fiber is important in many applications such as fog harvesting, oil–water separation, or water management in fuel cells. When the droplets are forcibly removed from hydrophilic fibers, the ease of detachment strongly depends on droplet volume and the rate of the process controlled by the applied force. Experiments, conducted on a ferrofluid under magnetic force, as well as continuum level calculations from fluid mechanics have so far been unable to resolve the time-dependent dynamics of droplet detachment and, most importantly, to assess the role of the applied force as the key determinant of the volume of the droplet residue remaining on the fiber after detachment. In the present work, we study the mechanism of water droplet detachment and retention of residual water on smooth hydrophilic fibers using nonequilibrium molecular dynamics simulations. We investigate how the applied force affects the breakup of a droplet and how the minimal detaching force per unit mass decreases with droplet size. We extract scaling relations that allow extrapolation of our findings to larger length scales that are not directly accessible by molecular models. We find that the volume of the residue on a fiber varies nonmonotonically with the detaching force, reaching the maximal size at an intermediate force and associated detachment time. The strength of this force decreases with the size of the drop, while the maximal residue increases with the droplet volume, V, sub-linearly, in proportion to the V 2/3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Irradiance and temperature considerations in the design and deployment of high annual energy yield perovskite/CIGS tandems

The annual energy yields for metal halide perovskite/copper indium gallium diselenide (CIGS) tandem photovoltaics have been calculated for 16 different bandgap combinations, using both 2 terminal and 4 terminal device designs, with fixed-tilt mounting as well as 1- and 2-axis tracking. Measured complex index of refraction data were used for the materials comprising the devices, and hourly irradiance data were extracted from Version 3 of the National Solar Radiation Database. Simulations were performed for Toledo OH, Golden CO, Phoenix AZ, and New Orleans LA, and the effect of local temperature variation was also considered. The combination of irradiance and temperature variations throughout the year cause different devices to be optimal at different times of the year. Interestingly, devices constructed to maximize AM1.5 photoconversion efficiency do not necessarily maximize the annual energy yield. A detailed analysis of the monthly energy yields at the different locations reveals the interplay between the changing light and temperature conditions. Over the course of the year these effects average to some degree so that annual energy yields that are close to the maximum possible value can be achieved by several different tandem device designs. The conclusions are valid for devices made with relatively thin perovskite layers, such as those used in champion efficiency devices. When the perovskite layers are thicker, however, the device is less tolerant to variation. Our results show that close matching of bandgap pairs is not essential for the fabrication of high-performance tandems. These findings should allow manufacturing efforts to proceed without the need for precise compositional control during formation of the absorber layers.

14 SOLAR ENERGY↗

Leveraging the bioeconomy for carbon drawdown

Stringent climate change mitigation scenarios rely on large-scale drawdown of carbon dioxide from the atmosphere. Amongst drawdown technologies, bioenergy with carbon capture and sequestration (BECCS) has received considerable attention in the climate mitigation literature. Recently, attention has shifted further from a relatively narrow focus on BECCS to a broader focus on Biomass Carbon Removal and Storage (BiCRS). The concept of BiCRS has the potential to enable a future where the climate mitigation value of biomass resources is more valuable than the energy value, due to the potential to remove and sequester large quantities atmospheric CO2. This article provides a qualitative overview of prominent BiCRS technologies from which a set of the most promising technologies are assessed quantitively through life cycle assessment. There are numerous opportunities to incorporate carbon removal and management within the bioeconomy, but the majority of immediate carbon removal potential exists in four bioproducts: bioenergy, bioplastics, biochar, and wood products. We analyze the life cycle greenhouse gas emissions and disposition of sequestered carbon over 10 000 years for four bioproducts representative of each broader category: an advanced BECCS pathway, biopolyethylene, oriented strand board, and biochar soil amendment. We find that the BECCS pathway has the greatest magnitude and durability of CO2 storage over all time horizons. However, non-BECCS pathways achieve 34–64% of the drawdown magnitude relative to BECCS and retain 55–67% of their initial drawdown over 100 years (central estimate). We identify three engineering strategies for enhancing carbon drawdown: reducing biomass supply chain emissions, maximizing carbon stored in long-lived products, and extending the term of carbon storage. Finally, we highlight the need to characterize both the magnitude and permanence of carbon drawdown as a means for policymakers and technology developers to deploy limited biomass resources to maximize mitigation benefits.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anion chemical composition of poly(ethylene oxide)-based sulfonylimide and sulfonate lithium ionomers controls ion aggregation and conduction

Maximizing ion conduction in single-ion-conducting ionomers is essential for their application in energy-related technologies such as Li-ion batteries. Understanding the anion chemical composition impacts on ion conduction offers new perspectives to maximize ion transport, since the current approach of lowering T g has apparently reached a limit (lowest T g ~ 190 K, highest conductivity ~10 -5 –10 -4 S cm -1 ). Here, a series of random ionomers are synthesized by copolymerizing poly(ethylene glycol)methacrylate with either sulfonylimide lithium methacrylate (MTLi) or sulfonate lithium methacrylate (MSLi) using reversible addition–fragmentation chain transfer (RAFT) polymerization. Li-Ion conduction and self-diffusion coefficients (DLi+) of the ionomers are characterized with dielectric relaxation spectroscopy (DRS) and pulsed-field-gradient (PFG) NMR diffusometry, respectively. Increasing ion content decreases the Li-ion conductivity and D Li+ , as expected from the increased T g . Moreover, a considerably lower ionic conductivity and D Li+ are observed for MSLi compared to MTLi at constant ion content and T g /T. As revealed from X-ray scattering, strong ion aggregation in MSLi results in much lower conductivity and DLi+ compared with less aggregated MTLi based on the more delocalized sulfonylimide anion. These results emphasize the detrimental and molecularly specific role of ion aggregation in Li-ion conductivity, and highlight the necessity for minimizing ion aggregation via the rational choice of anion chemical composition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimizing microfluidic flow cell geometry for in situ resonant soft X-ray characterization of molecular nanostructures

Liquid-phase resonant soft X-ray scattering (LP-RSoXS) is an emerging label-free technique to probe chemically resolved nanostructures of molecular or hybrid materials in liquid environments. Still, quantitative analysis is hindered by the pressure-induced deformation of thin silicon nitride (SiN) membranes used as windows in microfluidic flow cells, which attenuates the signal in nonlinear ways, making experimental optimization difficult. Here, in this work, we directly characterize this deformation under experimental conditions for a variety of cell configurations. We use this to develop a predictive model that combines transmission effects of SiN bowing, incident X-ray beam profiles, and material-dependent resonant scattering cross sections to simulate the effective scattering intensity at the detector across the carbon K-edge. Maps of the total signal across the flow cell window reveal that increasing the window width and polymer concentration shifts the anisotropic intensity distributions from the center toward the edges of the window. It was determined that an optimal SiN thickness of 50 nm, with a window aperture of 104 μm, maximizes the total signal for typical solute concentrations and energies across the carbon K-edge. Our results overturn the assumption that corner regions dominate the scattering signal, offering explicit design guidelines for maximizing LP-RSoXS signals and significantly advancing the quantitative application of this technique to the characterization of molecular and hybrid nanostructured materials in liquids.

Grabner, Devin [Washington State Univ., Pullman, W↗

Sequential surface synthesis of dispersed sub-nanometer iridium on titanium nitride for acidic water oxidation

Maximizing iridium utilization while maintaining high oxygen evolution reaction (OER) performance remains a persistent challenge in acidic water electrolysis. Immobilizing Ir on conductive, acid-stable supports is promising, yet simultaneously achieving sub-nanometer size, high area coverage, and strong electronic coupling is difficult. Here, we report a sequential surface synthesis on titanium nitride (TiN) that yields uniformly distributed sub-nanometer Ir arrays (∼0.7 nm). Our method uses ethylenediaminetetraacetic acid (EDTA) as a temporal scaffold: it chemisorbs to TiN to install dense chelating sites, captures Ir 3+ ions, and confines Ir cluster growth. A subsequent thermal treatment at 500 °C in a reducing atmosphere removes the ligand shell, while preserving ultrasmall particle size and establishing direct Ir–TiN electronic coupling. The optimized catalyst exhibits mixed Ir 0 /Ir x+ coordination with low charge-transfer resistance (R ct = 19.2 Ω), delivering a mass activity of 342 A g Ir −1 at 1.54 V in acidic electrolyte. In situ X-ray absorption spectroscopy reveals irreversible surface oxidation as the primary stability-limiting factor. This stepwise strategy provides a general framework for supported catalysts that maximize precious metal utilization via sub-nanometer dispersion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TDCOSMO. XII. Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy

Strong-lensing time delays enable measurement of the Hubble constant ($H_{0}$) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the $H_0$ measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131$-$1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate $H_0$, effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy $D_{\rm d} = 865_{-81}^{+85}$ Mpc and the time-delay distance $D_{\Delta t} = 2180_{-271}^{+472}$ Mpc, giving $H_0 = 77.1_{-7.1}^{+7.3}$ km s$^{-1}$ Mpc$^{-1}$ - for a flat $\Lambda$ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the line-of-sight effects, and those related to the mass-anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ($H_0 = 78.3^{+3.4}_{-3.3}$ km s$^{-1}$ Mpc$^{-1}$) and for seven lenses ($H_0 = 74.2_{-1.6}^{+1.6}$ km s$^{-1}$ Mpc$^{-1}$), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ($H_0 = 73.3^{+5.8}_{-5.8}$ km s$^{-1}$ Mpc$^{-1}$). This agreement corroborates the methodology of time-delay cosmography.

79 ASTRONOMY AND ASTROPHYSICS↗