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DOE OSTI2024

Self-Assembled TiN-Metal Nanocomposites Integrated on Flexible Mica Substrates towards Flexible Devices

The integration of nanocomposite thin films with combined multifunctionalities on flexible substrates is desired for flexible device design and applications. For example, combined plasmonic and magnetic properties could lead to unique optical switchable magnetic devices and sensors. In this work, a multiphase TiN-Au-Ni nanocomposite system with core–shell-like Au-Ni nanopillars embedded in a TiN matrix has been demonstrated on flexible mica substrates. The three-phase nanocomposite film has been compared with its single metal nanocomposite counterparts, i.e., TiN-Au and TiN-Ni. Magnetic measurement results suggest that both TiN-Au-Ni/mica and TiN-Ni/mica present room-temperature ferromagnetic property. Tunable plasmonic property has been achieved by varying the metallic component of the nanocomposite films. The cyclic bending test was performed to verify the property reliability of the flexible nanocomposite thin films upon bending. This work opens a new path for integrating complex nitride-based nanocomposite designs on mica towards multifunctional flexible nanodevice applications.

42 ENGINEERING↗

DOE OSTI2021

Deep Learning with Quantized Neural Networks for Gravitational-wave Forecasting of Eccentric Compact Binary Coalescence

We present the first application of deep learning forecasting for binary neutron stars, neutron star–black hole systems, and binary black hole mergers that span an eccentricity range e ≤ 0.9. In this work, we train neural networks that describe these astrophysical populations, and then test their performance by injecting simulated eccentric signals in advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) noise available at the Gravitational Wave Open Science Center to (1) quantify how fast neural networks identify these signals before the binary components merge; (2) quantify how accurately neural networks estimate the time to merger once gravitational waves are identified; and (3) estimate the time-dependent sky localization of these events from early detection to merger. Our findings show that deep learning can identify eccentric signals from a few seconds (for binary black holes) up to tens of seconds (for binary neutron stars) prior to merger. A quantized version of our neural networks achieves 4× reduction in model size, and up to 2.5× inference speedup. These novel algorithms may be used to facilitate time-sensitive multimessenger astrophysics observations of compact binaries in dense stellar environments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

RR Lyrae Mid-infrared Period–Luminosity–Metallicity and Period–Wesenheit–Metallicity Relations Based on Gaia DR3 Parallaxes

We present new empirical infrared period–luminosity–metallicity (PLZ) and period–Wesenheit–metallicity (PWZ) relations for RR Lyae based on the latest Gaia Early Data Release 3 (EDR3) parallaxes. The relations are provided in the Wide-field Infrared Survey Explorer (WISE) W1 and W2 bands, as well as in the W(W1, V - W1) and W(W2, V - W2) Wesenheit magnitudes. The relations are calibrated using a very large sample of Galactic halo field RR Lyrae stars with homogeneous spectroscopic [Fe/H] abundances (over 1000 stars in the W1 band), covering a broad range of metallicities (-2.5 ≲ [Fe/H] ≲ 0.0). We test the performance of our PLZ and PWZ relations by determining the distance moduli of both galactic and extragalactic stellar associations: the Sculptor dwarf spheroidal galaxy in the Local Group (finding ${\bar{\mu }}_{0}=19.47\pm 0.06$ ), the Galactic globular clusters M4 (${\bar{\mu }}_{0}=11.16\pm 0.05$ ), and the Reticulum globular cluster in the Large Magellanic Cloud (${\bar{\mu }}_{0}=18.23\pm 0.06$ ). The distance moduli determined through all our relations are internally self-consistent (within ≲0.05 mag) but are systematically smaller (by ~2–3σ) than previous literature measurements taken from a variety of methods/anchors. However, a comparison with similar recent RR Lyrae empirical relations anchored with EDR3 likewise shows, to varying extents, a systematically smaller distance modulus for PLZ/PWZ RR Lyrae relations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

The LSST AGN Data Challenge: Selection Methods

Abstract Development of the Rubin Observatory Legacy Survey of Space and Time (LSST) includes a series of Data Challenges (DCs) arranged by various LSST Scientific Collaborations that are taking place during the project's preoperational phase. The AGN Science Collaboration Data Challenge (AGNSC-DC) is a partial prototype of the expected LSST data on active galactic nuclei (AGNs), aimed at validating machine learning approaches for AGN selection and characterization in large surveys like LSST. The AGNSC-DC took place in 2021, focusing on accuracy, robustness, and scalability. The training and the blinded data sets were constructed to mimic the future LSST release catalogs using the data from the Sloan Digital Sky Survey Stripe 82 region and the XMM-Newton Large Scale Structure Survey region. Data features were divided into astrometry, photometry, color, morphology, redshift, and class label with the addition of variability features and images. We present the results of four submitted solutions to DCs using both classical and machine learning methods. We systematically test the performance of supervised models (support vector machine, random forest, extreme gradient boosting, artificial neural network, convolutional neural network) and unsupervised ones (deep embedding clustering) when applied to the problem of classifying/clustering sources as stars, galaxies, or AGNs. We obtained classification accuracy of 97.5% for supervised models and clustering accuracy of 96.0% for unsupervised ones and 95.0% with a classic approach for a blinded data set. We find that variability features significantly improve the accuracy of the trained models, and correlation analysis among different bands enables a fast and inexpensive first-order selection of quasar candidates.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

HAWC Detection of a TeV Halo Candidate Surrounding a Radio-quiet Pulsar

Extended very-high-energy (VHE; 0.1–100 TeV) γ-ray emission has been observed around several middle-aged pulsars and referred to as "TeV halos." Their formation mechanism remains under debate. It is also unknown whether they are ubiquitous or related to a certain subgroup of pulsars. With 2321 days of observation, the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory detected VHE γ-ray emission at the location of the radio-quiet pulsar PSR J0359+5414 with >6σ significance. By performing likelihood tests with different spectral and spatial models and comparing the TeV spectrum with multiwavelength observations of nearby sources, we show that this excess is consistent with a TeV halo associated with PSR J0359+5414, though future observation of HAWC and multiwavelength follow-ups are needed to confirm this nature. This new halo candidate is located in a noncrowded region in the outer galaxy. It shares similar properties to the other halos but its pulsar is younger and radio-quiet. Our observation implies that TeV halos could commonly exist around pulsars and their formation does not depend on the configuration of the pulsar magnetosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Bayesian chain graph models to characterize microbe-environment dynamics

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data.

compositional data↗

DOE OSTI2024

Uncertainty Propagation within Chained Models for Machine Learning Reconstruction of Neutrino-LAr Interactions

Sequential or chained models are increasingly prevalent in machine learning for scientific applications, due to their flexibility and ease of development. Chained models are particularly useful when a task is separable into distinct steps with a hierarchy of meaningful intermediate representations. In reliability-critical tasks, it is important to quantify the confidence of model inferences. However, chained models pose an additional challenge for uncertainty quantification, especially when input uncertainties need to be propagated. In such cases, a fully uncertainty-aware chain of models is required, where each step accepts a probability distribution over the input space, and produces a probability distribution over the output space. In this work, we present a case study for adapting a single model within an existing chain, designed for reconstruction within neutrino-Argon interactions, developed for neutrino oscillation experiments such as MicroBooNE, ICARUS, and the future DUNE experiment. We test the performance of an input uncertainty-enabled model against an uncertainty-blinded model using a method for generating synthetic noise. By comparing these two, we assess the increase in inference quality achieved by exposing models to upstream uncertainty estimates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A new biogeochemical modelling framework (FLaMe-v1.0) for lake methane emissions on the regional scale: development and application to the European domain

This study presents a new physical-biogeochemical modelling framework for simulating lake methane (CH 4 ) emissions at regional scales. The new model, FLaMe-v1.0 (Fluxes of Lake Methane), rests on an innovative, computationally efficient lake clustering approach that enables the simulation of CH 4 emissions across a large number of lakes. Building on the Canadian Small Lake Model (CSLM) that simulates the lake physics, we develop a suite of biogeochemical modules to simulate transient dynamics of organic Carbon (C), Oxygen (O 2 ), and CH 4 . We first test the performance of FLaMe-v1.0 by analyzing physical and biogeochemical processes in two theoretical lakes with characteristics that can be considered representative for many lakes (an oligotrophic, deep lake driven by cold climate versus a eutrophic, shallow lake driven by warm climate). Next, we evaluate the model by comparing simulated and observed timeseries of CH 4 emissions in four well-surveyed lakes. We then apply FLaMe-v1.0 at the European scale to evaluate simulated diffusive and ebullitive lake CH 4 fluxes against in-situ measurements in both boreal and central European regions. Finally, we provide a first assessment of the spatio-temporal variability in CH 4 emissions from European lakes with a surface area comprised between 0.1–1000 km 2 (n= 108 407, total area = 1.33 × 105 km 2 ), indicating a total emission of 0.97 ± 0.23 Tg CH 4 yr −1 , with the uncertainty constrained by combining FLaMe-v1.0 and machine learning techniques. Moreover, 30 % and 70 % of these CH 4 emissions are through diffusive and ebullitive pathways, respectively. Annually averaged CH 4 emission rates per unit lake area during 2010–2016 have a South-to-North decreasing gradient, resulting in a mean over the European domain as 7.39 g CH 4 m −2 yr −1 . Our simulations reveal a strong seasonality (with ice-blocking effects accounted for) in European lake CH 4 emissions, with nearly ten times higher emissions during late summer than during winter. This pronounced seasonal variation highlights the importance of accounting for the sub-annual variability in CH 4 emissions to accurately constrain regional CH 4 budgets. In the future, FLaMe-v1.0 could be embedded into Earth System Models to investigate the feedback between climate warming and global lake CH 4 emissions.

Maisonnier, Manon [Free Univ. of Brussels (Belgium↗

DOE OSTI2024

Merged Observatory Data Files (MODFs): an integrated observational data product supporting process-oriented investigations and diagnostics

A large and ever-growing body of geophysical information is measured in campaigns and at specialized observatories as a part of scientific expeditions and experiments. These collections of observed data include many essential climate variables (as defined by the Global Climate Observing System) but are often distinguished by a wide range of additional non-routine measurements that are designed to not only document the state of the environment but also the drivers that contribute to that state. These field data are used not only to further understand environmental processes through observation-based studies but also to provide baseline data to test model performance and to codify understanding to improve predictive capabilities. To address the considerable barriers and difficulty in utilizing these diverse and complex data for observation–model research, the Merged Observatory Data File (MODF) concept has been developed. A MODF combines measurements from multiple instruments into a single file that complies with well-established data format and metadata practices and has been designed to parallel the development of corresponding Merged Model Data Files (MMDFs). Using the MODF and MMDF protocols will facilitate the evolution of model intercomparison projects into model intercomparison and improvement projects by putting observation and model data “on the same page” in a timely manner. The MODF concept was developed especially for weather forecast model studies in the Arctic. The surprisingly complex process of implementing MODFs in that context refined the concept itself. Thus, this article explains the concept of MODFs by providing details on the issues that were revealed and resolved during that first specific implementation. Detailed instructions are provided on how to make MODFs, and this article can be considered a MODF creation manual.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

A graph neural network (GNN) approach to basin-scale river network learning: the role of physics-based connectivity and data fusion

Abstract. Rivers and river habitats around the world are under sustained pressure from human activities and the changing global environment. Our ability to quantify and manage the river states in a timely manner is critical for protecting the public safety and natural resources. In recent years, vector-based river network models have enabled modeling of large river basins at increasingly fine resolutions, but are computationally demanding. This work presents a multistage, physics-guided, graph neural network (GNN) approach for basin-scale river network learning and streamflow forecasting. During training, we train a GNN model to approximate outputs of a high-resolution vector-based river network model; we then fine-tune the pretrained GNN model with streamflow observations. We further apply a graph-based, data-fusion step to correct prediction biases. The GNN-based framework is first demonstrated over a snow-dominated watershed in the western United States. A series of experiments are performed to test different training and imputation strategies. Results show that the trained GNN model can effectively serve as a surrogate of the process-based model with high accuracy, with median Kling–Gupta efficiency (KGE) greater than 0.97. Application of the graph-based data fusion further reduces mismatch between the GNN model and observations, with as much as 50 % KGE improvement over some cross-validation gages. To improve scalability, a graph-coarsening procedure is introduced and is demonstrated over a much larger basin. Results show that graph coarsening achieves comparable prediction skills at only a fraction of training cost, thus providing important insights into the degree of physical realism needed for developing large-scale GNN-based river network models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

New methods to improve the vertical extrapolation of near-surface offshore wind speeds

Accurate characterization of the offshore wind resource has been hindered by a sparsity of wind speed observations that span offshore wind turbine rotor-swept heights. Although public availability of floating lidar data is increasing, most offshore wind speed observations continue to come from buoy-based and satellite-based near-surface measurements. The aim of this study is to develop and validate novel vertical extrapolation methods that can accurately estimate wind speed time series across rotor-swept heights using these near-surface measurements. We contrast the conventional logarithmic profile against three novel approaches: a logarithmic profile with a long-term stability correction, a single-column model, and a machine-learning model. These models are developed and validated using 1 year of observations from two floating lidars deployed in US Atlantic offshore wind energy areas. We find that the machine-learning model significantly outperforms all other models across all stability regimes, seasons, and times of day. Machine-learning model performance is considerably improved by including the air–sea temperature difference, which provides some accounting for offshore atmospheric stability. Finally, we find no degradation in machine-learning model performance when tested 83 km from its training location, suggesting promising future applications in extrapolating 10 m wind speeds from spatially resolved satellite-based wind atlases.

17 WIND ENERGY↗

DOE OSTI2020

Production and characterization of extracellular cellulases from a native strain of Trichoderma harzianum using wheat straw from the Mexicali valley as the carbon source. Producción y caracterización de celulasas Extracelulares a partir de cepa nativa de Trichoderma harzianum usando como fuente de Carbono paja de trigo del valle de Mexicali

The purpose of this study was to produce cellulase enzyme from a native strain Trichoderma harzianum, isolated from crop soil. Cellulase production was carried out by two different methods of fermentation, submerging and solid state fermentation. Mandels mineral medium was used as a source of nitrogen and ammonium sulfate. Dry and ground wheat straw was used in fermentation as a carbon source. Cellulase activity was determined using the 3,5-dinitrosalicylic acid (DNS) method. The results showed that wheat straw has the potential to be used as a substrate in the production of cellulases. Trichoderma harzianum showed enzymatic activity of 0.125 FPU / ml (filter paper units) and 1. 35 U / ml CMC (carboxymethyl cellulose units) by solid state fermentation (FSS) after 96 hours of fermentation. The optimum pH for the two substrates was determined by testing with citrate buffers (pH 4 to 6), phosphates (pH 6 to 7) and tris-HCL (pH 8 to 9). To determine the optimum temperature the range of 30 ° C to 80 ° C was investigated. Storage tests were performed every seven days over a period of 6 weeks. The optimum activity pH on paper and CMC was found to be 6. The optimum activity temperature is 70 ° C for PF and 80 ° C for CMC. El propósito de este estudio fue producir enzima celulasa a partir de una cepa nativa Trichoderma harzianum, aislada de suelo de cultivo. La producción de celulasa se realizó por dos métodos diferentes de fermentación, sumergida y fermentación en estado sólido. Se utilizó medio mineral Mandels y como fuentes de nitrógeno urea y sulfato de amonio. Se utilizó paja de trigo seca y molida en las fermentaciones como fuente de carbono. La actividad de la celulasa se determinó por medición de azúcares reductores al papel filtro y a la carboximetilcelulosa usando el método del ácido 3,5- dinitrosalicílico (DNS). Los resultados mostraron que la paja de trigo tiene el potencial para usarse como sustrato en la producción de celulasas. Trichoderma harzianum mostró actividad enzimática de 0.125 FPU/ml (unidades de papel filtro) y 1.35 U/ml a la CMC (unidades de carboximetilcelulosa) por fermentación en estado sólido (FSS) después de 96 horas de fermentación. El pH óptimo para los dos sustratos se determinó realizando pruebas con buffers de citratos (pH 4 a 6), de fosfatos (pH 6 a 7) y tris- HCL (pH 8 a 9). Para la determinación de la temperatura óptima se manejó el rango de 30°C a 80°C. Las pruebas de almacenamiento se realizaron cada siete días en un periodo de 6 semanas. Se encontró que el pH óptimo de actividad en papel y CMC es de 6. La temperatura óptima de actividad es de 70°C para PF y de 80°C para CMC.

09 BIOMASS FUELS↗

DOE OSTI2020

Development of Two-Phase Dense Fluid Expander for Advanced Cryogenic Air Separation and Low-Grade Heat Recovery

Cryogenic air separation represents the state-of-the-art technology to produce oxygen to feed coal gasification units. Given the maturity of this technology, it is difficult to identify opportunities to improve process efficiency and reduce the cost of the oxygen produced. However, Air Products conducted research and a feasibility investigation into the use of a two-phase (liquid-vapor) dense fluid expander (DFE) to improve the overall efficiency of cryogenic air separation. Demonstration of this novel concept was intended to allow two important process improvements: 1) elimination of the need for the DFE discharge to be single phase 2) expansion of the operating region of expanders in ASU service. Expanding the scope of turboexpander application beyond current application limits and traditional device designs would allow an increase in power recovery, and application of refrigeration and power recovery at new locations in process cycles would also enable the implementation of new process concepts. These new process concepts include power recovery from compression waste heat and refrigeration extraction and power recovery by replacing let-down valves with two-phase DFEs. Considering the maturity of cryogenic air separation, these new process options could represent a step change in power reduction and provide significant savings in operating costs. These new concepts would be particularly well-suited to large-scale oxygen production by cryogenic air separation and would enhance the economics of producing oxygen for use in coal gasification processes. Rotoflow, an Air Products business unit, manufactures dense fluid expanders in Pennsylvania for sites around the world. This project was executed in two phases, which are illustrated in Figure 1 below. Phase 1 consisted of a feasibility investigation of multiple applications of two-phase DFEs. In Phase 2, devices were identified, designed, fabricated and tested to explore the feasibility of commercial applications of DFEs operating in two-phase service. Engineering and testing were performed by personnel in Air Products’ Rotoflow business unit, with coordination with other Air Products business units.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Refrigerator Door-in-Door Opening Controller

Door-in-door refrigerators are becoming increasingly popular on the market. To save energy, items that are most frequently used are stored between doors. Thus only the outer door needs to be opened for access. This invention is used for standard energy performance laboratory tests for these kinds of refrigerators. In conjunction with an automated refrigerator door opener, it allows the refrigerator door opener to open either the outer door only or both inner and outer doors together.

Wang, Duo↗

DOE OSTI2021

Shear Assisted Processing and Extrusion of Aluminum Alloy 7075 Tubing at High Speed

Conventional extrusion of aluminum alloy 7075 is limited to 1-2 meters per minute in order to avoid surface tearing and cracking. An emerging technique called Shear Assisted Processing and Extrusion (ShAPE) was used to extrude aluminum alloy 7075 tubing at a speed of 7.4 meters per minute without inducing surface defects. The faster extrusion speed is attributed to the unique flow characteristics inherent to the ShAPE process compared to conventional extrusion. Tubes with an inner diameter of 10 mm, outer diameter of 12 mm, and length of 2 meters were extruded at temperatures ranging from 340°C to 466°C. Tensile testing was performed per ASTM B557-15 with strain measured using digital image correlation. An ultimate tensile strength of 565 ± 4.6 MPa, yield strength of 496 ± 8.7 MPa, and elongation of 16.4 ± 1.0 % were measured for extrusion made at 362°C and heat treated to the T6 condition.

Shear Assisted Processing and Extrusion, Friction ↗

DOE OSTI2021

Sr and Co Vapor-Phase Transport from LSCF Cathodes

A series of tests were performed to differentiate between surface diffusion and vapor-phase diffusion of chemical species from LSCF cathode material at typical sintering temperatures (up to 1100°C) in SOFC production. A GDC source substrate was printed with LSCF and separated by an air gap from a YSZ target substrate. Various geometries with long surface paths were employed to reduce the possibility of surface transport. Sr and Co were detected on the target substrates via energy dispersive spectroscopy (EDS) and x-ray photoelectron spectroscopy (XPS), including spatially resolved XPS. These results support a vapor-phase transport mechanism for Sr and Co. Sintering conditions and barrier layer requirements may need to be revisited to prevent the formation of undesired strontium zirconate at cathode/electrolyte interface due to vapor-phase transport.

vapor phase transport, SOFC cathode, Sr transport↗

DOE OSTI2021

Impact of Blockchain Delay on Grid-Tied Solar Inverter Performance: Preprint

This paper investigates the impact of the delay resulting from a blockchain, a promising security measure, for a hierarchical control system of inverters connected to the grid. The blockchain communication network is designed at the secondary control layer for resilience against cyberattacks. To represent the latency in the communication channel, a model is developed based on the complexity of the blockchain framework. Taking this model into account, this work evaluates the plant’s performance subject to communication delays, introduced by the blockchain, among the hierarchical control agents. In addition, this article considers an optimal model-based control strategy that performs the system’s internal control loop. The work shows that the blockchain’s delay size influences the convergence of the power supplied by the inverter to the reference at the point of common coupling. In the results section, real-time simulations on OPAL-RT are performed to test the resilience of two parallel inverters with increasing blockchain complexity.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2021

Dark Energy Survey Year 3 Results: Constraints on cosmological parameters and galaxy bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

We constrain cosmological parameters and galaxy-bias parameters using the combination of galaxy clustering and galaxy-galaxy lensing measurements from the Dark Energy Survey Year-3 data. We describe our modeling framework and choice of scales analyzed, validating their robustness to theoretical uncertainties in small-scale clustering by analyzing simulated data. Using a linear galaxy bias model and redMaGiC galaxy sample, we obtain constraints on the matter content of the universe to be $\Omega_{\rm m} = 0.325^{+0.033}_{-0.034}$. We also implement a non-linear galaxy bias model to probe smaller scales that includes parameterizations based on hybrid perturbation theory, and find that it leads to a 17% gain in cosmological constraining power. Using the redMaGiC galaxy sample as foreground lens galaxies, we find the galaxy clustering and galaxy-galaxy lensing measurements to exhibit significant signals akin to decorrelation between galaxies and mass on large scales, which is not expected in any current models. This likely systematic measurement error biases our constraints on galaxy bias and the $S_8$ parameter. We find that a scale-, redshift- and sky-area-independent phenomenological decorrelation parameter can effectively capture this inconsistency between the galaxy clustering and galaxy-galaxy lensing. We perform robustness tests of our methodology pipeline and demonstrate stability of the constraints to changes in the theory model. After accounting for this decorrelation, we infer the constraints on the mean host halo mass of the redMaGiC galaxies from the large-scale bias constraints, finding the galaxies occupy halos of mass approximately $1.5 \times 10^{13} M_{\odot}/h$.

79 ASTRONOMY AND ASTROPHYSICS↗