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At least 379 records · Page 21

Antifoam Development for Eliminating Flammability Hazards and Decreasing Cycle Time in the Defense Waste Processing Facility

The Savannah River National Laboratory (SRNL) was requested to develop a new antifoam control method for the Defense Waste Processing Facility’s (DWPF) Chemical Process Cell (CPC). SRNL completed testing of both chemical and nonchemical foam controls. The nonchemical foam controls were either ineffective (or worse, created more foam) or impractical (a water spray can control foam, but excessive water is needed). As a result, the focus of this study was on finding a superwetter or commercial antifoam for controlling foam. Thirty potential antifoams were tested as part of this study. A series of tests were developed to help screen out ineffective alternatives including: 1. Spreading testing of superspreaders, 2. Foam column testing with physical simulants, 3. Boiling testing with physical and chemical simulants, 4. Days-only Sludge Receipt and Adjustment Tank (SRAT) process simulations with sludge (containing noble metals and mercury), Precipitate Reactor Feed Tank (PRFT), and Slurry Mix Evaporator Feed Tank (SEFT) simulants in the RC1 Reaction Calorimeter (purchased for antifoam testing), and 5. Around-the-clock SRAT and Slurry Mix Evaporator (SME) process simulations with sludge(containing noble metals and mercury), PRFT, and SEFT simulants in the RC1 Reaction Calorimeter. Evonik Surfynol® MD20, a commercially available defoamer, was relatively effective in controlling foam, while remaining chemically stable in SRAT and SME processing across the pH range of 4 to 13. No degradation products were detected in the offgas, in the condensate or in the SRAT and SME products. In nitric-glycolic acid flowsheet testing, 250 mg/kg Evonik Surfynol® MD20 was needed for foam control compared to 1,625 mg/kg for Antifoam 747, DWPF’s current antifoam. In nitric-formic acid flowsheet testing, 1,125 mg/kg of Evonik Surfynol® MD20 was needed to control foam throughout the SRAT and SME cycles. The commercially available superspreader Momentive™ Y-17112 was even more effective than Evonik Surfynol® MD20 as both a defoamer and an antifoam. Not only was the foam destroyed upon addition but also was less persistent between additions. It was the most effective antifoam in testing using both the nitric-glycolic acid flowsheet and the nitric-formic acid flowsheet. In nitric-glycolic acid flowsheet testing, only 100 mg/kg Momentive™ Y-17112 was needed to control foam throughout the SRAT and SME cycles. In nitric-formic acid flowsheet testing, 300 mg/kg Momentive™ Y-17112 was needed to control foam throughout the SRAT and SME cycles. Momentive™ Y-17112 is also resistant to hydrolysis as demonstrated by its chemical stability in SRAT and SME processing across the pH range of 4 to 13 and lack of degradation products in offgas or condensate. Both candidates were effective as potential replacements for Antifoam 747, with Y-17112 demonstrating superior foam control. During nitric-glycolic flowsheet testing 50% less antifoam was needed when using Momentive™ Y-17112 compared to MD20. During nitric-formic flowsheet testing 75% less antifoam was needed when using Momentive™ Y-17112 compared to MD20. Foam remediated with Momentive™ Y-17112 was less persistent throughout testing. In addition, no degradation products were detected in the offgas, in the condensate or in the SRAT and SME products. Based on this testing, Momentive™ Y-17112 is clearly superior to Evonik Surfynol® MD20 and Antifoam 747, especially for the nitric-formic acid flowsheet processing; it is recommended that Momentive™ Y-17112 replace Antifoam 747 in DWPF. An antifoam addition strategy is recommended for both the nitric-glycolic acid flowsheet and the nitric-formic acid flowsheet. Implementation of Momentive™ Y-17112 is expected to decrease SRAT and SME boiling times by up to 50%, eliminate the issues resulting from Antifoam 747 degradation products, and minimize foamovers. To validate the effectiveness of these defoaming agents, SRNL recommends irradiation of a SRAT or SME product simulant containing fresh antifoam. The goal of this testing is to determine whether the irradiation causes decomposition of the antifoam that would make it less effective or produce new species in the offgas or slurry. This testing began in April 2020. An evaluation should be completed to determine the thermolytic hydrogen and methane generation rate in downstream equipment, including the High-Level Waste evaporators.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Heating and Acceleration of Solar Wind by Parametric Decay Instability Mediated Turbulence

One of the main goals of this project to understand the origin of density fluctuations in the solar winds, as revealed by the NASA’s Flagship satellite Parker Solar Probe (PSP) measurements, which motivates us to simulate and analyze magnetohydrodynamic (MHD) turbulence in the compressible regime. To achieve this goal, we have developed a set of sophisticated turbulence driving methods to study how MHD turbulence will develop under different time-correlated fluctuations at large-scales. Another key advance is that we have developed a new 3+1 (three spatial plus time domain) 4D FFT analysis of simulation data-cubes so that we can perform the spatio-temporal spectrum and mode decomposition studies on MHD turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

Performance of methods for SARS-CoV-2 variant detection and abundance estimation within mixed population samples

The accurate identification of SARS-CoV-2 (SC2) variants and estimation of their abundance in mixed population samples (e.g., air or wastewater) is imperative for successful surveillance of community level trends. Assessing the performance of SC2 variant composition estimators (VCEs) should improve our confidence in public health decision making. Here, we introduce a linear regression based VCE and compare its performance to four other VCEs: two re-purposed DNA sequence read classifiers (Kallisto and Kraken2), a maximum-likelihood based method (Lineage deComposition for Sars-Cov-2 pooled samples (LCS)), and a regression based method (Freyja). We simulated DNA sequence datasets of known variant composition from both Illumina and Oxford Nanopore Technologies (ONT) platforms and assessed the performance of each VCE. We also evaluated VCEs performance using publicly available empirical wastewater samples collected for SC2 surveillance efforts. Bioinformatic analyses were performed with a custom NextFlow workflow (C-WAP, CFSAN Wastewater Analysis Pipeline). Relative root mean squared error (RRMSE) was used as a measure of performance with respect to the known abundance and concordance correlation coefficient (CCC) was used to measure agreement between pairs of estimators. Based on our results from simulated data, Kallisto was the most accurate estimator as it had the lowest RRMSE, followed by Freyja. Kallisto and Freyja had the most similar predictions, reflected by the highest CCC metrics. We also found that accuracy was platform and amplicon panel dependent. For example, the accuracy of Freyja was significantly higher with Illumina data compared to ONT data; performance of Kallisto was best with ARTICv4. However, when analyzing empirical data there was poor agreement among methods and variations in the number of variants detected (e.g., Freyja ARTICv4 had a mean of 2.2 variants while Kallisto ARTICv4 had a mean of 10.1 variants). This work provides an understanding of the differences in performance of a number of VCEs and how accurate they are in capturing the relative abundance of SC2 variants within a mixed sample (e.g., wastewater). Such information should help officials gauge the confidence they can have in such data for informing public health decisions.

60 APPLIED LIFE SCIENCES↗

The Thermal Stability of Unsymmetrical Dimethylhydrazine

The thermal stability of unsymmetrical dimethylhydrazine was investigated in a static system simulating conditions in an almost-empty fuel tank. The self-ignition temperature and spontaneous decomposition temperature of the pure fuel were determined at atmospheric pressure to be 454 and 740 F. respectively, with the larger (740 F) value, obtained in an inert atmosphere of nitrogen, representing the minimum temperature that would cause a rapid exothermic reaction. The addition of 40 weight percent dimethylenetriamine to unsymmetrical dimethylhydrazine did not significantly affect these properties.

Spakowski, Adolph E.↗

Alternative Modal Basis Selection Procedures For Reduced-Order Nonlinear Random Response Simulation

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of a computationally taxing full-order analysis in physical degrees of freedom are taken as the benchmark for comparison with the results from the three reduced-order analyses. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Przekop, Adam↗

Multiscale Simulations of Magnetic Island Coalescence

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Dorelli, John C.↗

Extension of the high-resolution thermal-hydraulics code ESCOT to hexagonal core geometries for multi-physics calculations

The extension of the capabilities of the pin-level nuclear reactor core thermal-hydraulics (T/H) code ESCOT to analyze hexagonal fueled cores and its performance are presented. ESCOT is an accurate yet fast core thermal-hydraulics solution aiming at high-fidelity and high-resolution multi-physics core analysis in the framework of massively parallel computing platforms. Its algorithm solution is based on the four-equation drift-flux model for two-phase calculations, these are numerically solved by applying the Finite Volume Method (FVM) and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE)-like algorithm in a staggered grid system. Constitutive models such as turbulent mixing, pressure drop, and vapor generation are employed to simulate key phenomena in subchannel-scale analysis. ESCOT is parallelized by a double (radial and axial) domain decomposition that enables its highly parallelized execution. The coupling of the code with the neutronics whole core solver for hexagonal geometries nTRACER is described. The newly implemented ESCOT features are validated by comparing single assembly and full core steady state nTRACER-ESCOT solutions with nTRACER standalone internal one-dimensional T/H solver results. The validation problems are based on the VVER 440 and VVER 1000 cores. ESCOT results show differences within an acceptable range with respect to the simple 1D nTRACER built-in solver. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Loading Capacity and Dilute Nitric Acid Rinse of Diglycolamide Resin for the Recovery of Transplutonium and Rare Earth Elements from Mark-18A Targets

N,N,N′,N′-tetraoctyldiglycolamide (TODGA) as a resin (“DGA resin”) produced by Eichrom Technologies will be used by Savannah River National Laboratory for the indiscriminate extraction of trivalent actinides and rare earth elements with the intent of recovering Cm and Am from dissolved irradiated 242 Pu Mark-18A targets in 7 to 9 M nitric acid. The extracted constituents will be recovered as an oxide by direct thermal decomposition of the loaded resin followed by calcination of the resultant residue. The characteristics of DGA resin with non-radiological feed simulant representative of the anticipated feed in the Mark-18A process, with Sm and Nd as surrogates for Cm and Am, respectively, including breakthrough point and saturation capacity were evaluated in this work. Additionally, this work examined the losses from the loaded resin by rinsing the resin bed with dilute acid to reduce the nitrate concentration in the resin bed prior to thermal decomposition operations to improve the safety posture of the process. A resin loading profile was developed, and the resin was determined to have a trivalent metal saturation capacity of 74 μmol/mL resin under the experimental conditions evaluated. Following a wash of the loaded resin bed with fresh 8 M HNO 3 , the trivalent metals retained was reduced to 68 μmol/mL resin, which represents the practical capacity of the resin for the Mark-18A process. Lighter lanthanides breakthrough the resin well before the saturation capacity is reached. Rinsing the saturated resin bed with 0.26 M HNO 3 was found to result in a rapid reduction in retention of rare earth elements by the resin. After 2.8 bed volumes of dilute acid rinse, the mean resin bed free acid concentration was reduced to 0.28 M and 3.1 bed volumes of dilute acid rinse resulted in a reduction of the cumulative rare earth element retention to 52 μmol/mL of resin.

Transplutonium separations↗

Development, Verification and Use of Gust Modeling in the NASA Computational Fluid Dynamics Code FUN3D

This paper presents the implementation of gust modeling capability in the CFD code FUN3D. The gust capability is verified by computing the response of an airfoil to a sharp edged gust. This result is compared with the theoretical result. The present simulations will be compared with other CFD gust simulations. This paper also serves as a users manual for FUN3D gust analyses using a variety of gust profiles. Finally, the development of an Auto-Regressive Moving-Average (ARMA) reduced order gust model using a gust with a Gaussian profile in the FUN3D code is presented. ARMA simulated results of a sequence of one-minus-cosine gusts is shown to compare well with the same gust profile computed with FUN3D. Proper Orthogonal Decomposition (POD) is combined with the ARMA modeling technique to predict the time varying pressure coefficient increment distribution due to a novel gust profile. The aeroelastic response of a pitch/plunge airfoil to a gust environment is computed with a reduced order model, and compared with a direct simulation of the system in the FUN3D code. The two results are found to agree very well.

Bartels, Robert E.↗

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamic mode decomposition of nonequilibrium electron-phonon dynamics: accelerating the first-principles real-time Boltzmann equation

Abstract Nonequilibrium dynamics governed by electron–phonon ( e -ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport equation (rt-BTE) with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations (phonons). Yet, a bottleneck of these simulations is the calculation of e –ph scattering integrals on dense momentum grids at each time step. Here we show a data-driven approach based on dynamic mode decomposition (DMD) that can accelerate the time propagation of the rt-BTE and identify dominant electronic processes. We apply this approach to two case studies, high-field charge transport and ultrafast excited electron relaxation. In both cases, simulating only a short time window of ~10% of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD extrapolation. Analysis of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or equilibrium. The combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials.

36 MATERIALS SCIENCE↗

Computational Performance Bounds Prediction in Quantum Computing With Unstable Noise

Quantum computing has significantly advanced in recent years, boasting devices with hundreds of quantum bits (qubits), hinting at its potential quantum advantage over classical computing. Yet, noise in quantum devices poses significant barriers to realizing this supremacy. Understanding noise’s impact is crucial for reproducibility and application reuse; moreover, the next-generation quantum-centric supercomputing essentially requires efficient and accurate noise characterization to support system management (e.g., job scheduling), where ensuring correct functional performance (i.e., fidelity) of jobs on available quantum devices can even be higher-priority than traditional objectives. However, noise fluctuates over time, even on the same quantum device, which makes predicting the computational bounds for on-the-fly noise is vital. Noisy quantum simulation can offer insights but faces efficiency and scalability issues. Here, in this work, we propose a data-driven workflow, namely QuBound, to predict computational performance bounds. It decomposes historical performance traces to isolate noise sources and devises a novel encoder to embed circuit and noise information processed by a Long Short-Term Memory (LSTM) network. For evaluation, we compare QuBound with a state-of-the-art learning-based predictor, which only generates a single performance value instead of a bound. Experimental results show that the result of the existing approach falls outside of performance bounds, while all predictions from our QuBound with the assistance of performance decomposition better fit the bounds. Moreover, QuBound can efficiently produce practical bounds for various circuits with over 106 speedup over simulation; in addition, the range from QuBound is over 10× narrower than the state-of-the-art analytical approach.

Li, Jinyang [George Mason Univ., Fairfax, VA (Unit↗

Precipitation and nitrogen application stimulate soil nitrous oxide emission

Precipitation and nitrogen (N) fertilization are the two most important drivers for soil nitrous oxide (N 2 O) emission. However, the effects of changes in N fertilization and precipitation patterns (i.e., precipitation intensity and frequency) on N 2 O emissions in agricultural fields are still unclear. In this study, we simulated soil N 2 O emission under different precipitation patterns (6 precipitation intensities, and 12 precipitation frequencies by either merging or splitting precipitation events) and N fertilization rates (low, typical, and high N fertilization) in a cornfield using the DeNitrification-DeComposition model. The model was parameterized and validated using meteorological data and N experimental measurements in Nashville, Tennessee, USA. Results showed that soil water filled pore space (WFPS) and simulated soil N 2 O emission increased as precipitation intensity increased. Less frequent but high intensity precipitation treatments reduced the soil WFPS by 25.2% and stimulated soil N 2 O emission by 45.3%, while more frequent but low intensity precipitation treatments increased soil WFPS by 9.0% and reduced soil N 2 O emission by 23.9%. Compared to typical N fertilization, the sensitivity of soil N 2 O emission to precipitation was higher under high N than low N fertilization treatments, and the response ratios were 50.0% and 40.1%, respectively. There was significant interactive effect of precipitation intensity and N fertilization on soil N 2 O emission. Furthermore, these findings improved our understanding of precipitation and N impacts on soil N 2 O emissions and provided useful knowledge for irrigation and N fertilizer management in agriculture to mitigate greenhouse gas emissions.

54 ENVIRONMENTAL SCIENCES↗

A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data

Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.

Astronomy & Astrophysics↗

Shock compression response of an insensitive high explosive single crystal: 1,1-diamino-2,2-dinitroethene (FOX-7)

Insensitive high explosives (IHEs) – that do not compromise performance – are of immense interest as a safer alternative to conventional high explosives, such as pentaerythritol tetranitrate (PETN) and cyclotrimethylenetrinitramine (RDX). Despite the strong interest in using IHEs, shock compression experiments on IHE single crystals have not been reported. To address this need, plate impact experiments were conducted to measure wave profiles in 1,1-diamino-2,2-dinitroethene (FOX-7) single crystals – a representative IHE crystal – shocked to 21 GPa longitudinal stress. Particle velocity histories, measured using laser interferometry, show a clear two-wave structure (elastic-inelastic response) at modest stresses (<3.8 GPa). Wave profiles at higher stresses show a single (overdriven) wave. Measured shock velocities and wave profiles provide accurate Hugoniot data to 21 GPa. The measured wave profiles to 21 GPa show no sign of energy release due to chemical decomposition and constitute the first demonstration of an IHE single crystal insensitivity under plane shock compression. Numerical simulations using a phenomenological material model developed for FOX-7 showed good agreement with the measured wave profiles. The experimental results and continuum simulations presented here constitute a significant first step in gaining insight into the shock compression response of IHE single crystals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Photoinduced electronic excitations drive polymerization of carbon monoxide: A first-principles study

Under pressure, carbon monoxide (CO) transforms into a polymer that can be recovered to ambient conditions. While this transformation can occur without additional stimuli, experimental observations have shown that laser irradiation can induce a similar transformation at reduced pressure. The resulting polymeric phase, which is metastable under ambient conditions, releases energy through decomposition into more stable configurations. Using time-dependent density functional theory and Born–Oppenheimer molecular dynamics simulations, we investigate the mechanism by which electronic excitation facilitates CO polymerization. Our calculations reveal that electronic excitation enhances carbon–carbon bonding, enabling polymerization at pressures significantly lower than those required by conventional compression methods. In conclusion, these findings suggest that a photo-assisted approach could be employed to synthesize novel, potentially energetic materials under less demanding pressure conditions.

Born-Oppenheimer molecular dynamics↗

Monte Carlo Tree Search for Integrated Planning, Learning, and Execution in Nondeterministic Python

We present a novel use of Monte Carlo Tree Search (MCTS),adapted to explore a search space produced by the choice points embedded in Python code. The choice points are non-deterministic assignment statements and subroutine calls. We present MCTS extensions required for doing tree search in this context which includes control constructs like hierarchical decomposition (subroutine calls), iterative while loops and conditional statements. We demonstrate how the system works in a simulated rideshare scenario in an urban setting, and present preliminary experiments as a proof of concept.

Automatic planning↗

A New Window into the Baryon Cycle at Cosmic Noon with Line Intensity Mapping: Forecasts for auto- and cross-correlations in [CII]-158$μ$m, HI 21 cm, CO$_{J+1\rightarrow J}$, and H$α$ galaxies

Across the peak of cosmic star formation at $z\sim1-2$, inflow, processing, and feedback drive rapid changes in the spatial distribution and chemical composition of baryons in galaxies and surrounding reservoirs; this baryon cycle can be tomographically mapped by line intensity mapping (LIM) of atomic hydrogen, ionized carbon, and carbon monoxide. We present a simulation-based forecasting framework for detecting auto- and cross-power spectra between spectroscopic surveys of four such tracers at $z\sim0.5-1.7$ mapping the same deep field - TIM, EoRSpec/FYST, MeerKAT, & Euclid. We forward-model 3-D distributions for these tracers from magnetohydrodynamic simulations, directly capturing the two-halo, one-halo, and shot statistics without relying on analytical decompositions. We further detail a signal-to-noise formalism, tailored to LIM surveys with highly anisotropic geometries and Fourier-space coverage. We demonstrate that galaxy cross-correlations will be the dominant discovery channel for current-generation surveys. These instruments will detect the auto-spectra for CO and HI 21 cm and the CO $\times$ 21 cm cross-spectrum at modest S/N $\sim 1-10$, while placing upper limits on the [CII]-158$μ$m signals. [CII], CO, and HI LIM will be $\sim3-30\times$ ($0.5-1.5$ dex) more sensitive to cross-correlation with the Euclid survey, however, than their respective auto-correlations, constraining all three models of line emission at high significance (S/N $\sim 10-40$) within this decade. Finally, we formulate a staged instrumental trajectory with planned or reasonable improvements, including the as-proposed SKA-Mid. We forecast advancing the per-$k$-mode sensitivities of each auto-, galaxy-line, and line-line spectrum by several orders of magnitude, enabling new percent- and sub-percent level constraints on cosmology and the redshift evolution of star formation and the baryon cycle.

Agrawal, Shubh [Pennsylvania U., Dept. Math.]↗