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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗
DOE OSTI2019

Evaluating next-generation intensity–duration–frequency curves for design flood estimates in the snow-dominated western United States

Civil infrastructure such as culverts and bridges are commonly designed using precipitation-based intensity-duration-frequency (PREC-IDF) curves, which assume that the occurrence of precipitation is in the form of rainfall and immediately available for the rainfall-runoff process. In snow-dominated regions, where most winter precipitation occurs as snow that melts during spring to early summer, the use of standard PREC-IDF curves may lead to substantial underestimation of design floods and high failure risk of infrastructure. In this context, we developed next-generation IDF (NG-IDF) curves that characterize the actual water reaching the land surface (i.e., rainfall plus snowmelt) to enhance standard infrastructure design in snow-dominated regions. This study evaluates the performance of NG-IDF curves coupled with U.S. Department of Agriculture Technical Release 55 hydrologic model in estimating design floods for 246 snowy locations in different hydroclimate regimes of the western United States. Design flood estimates from a well-validated continuous simulation using a physics-based hydrologic model, the Distributed Hydrology Soil Vegetation Model (DHSVM), were used as the performance benchmark. Compared with the benchmark estimates, the standard PREC-IDF curves led to substantial errors in design flood estimates while the NG-IDF curves significantly reduced these errors. For example, the averaged error in the 50-year design flood estimates over the 246 locations was reduced from 31% with the use of PREC-IDF curves to 12% with the use of NG-IDF curves. Despite the different model structures, the single-event NG-IDF approach versus the continuous simulation DHSVM did not exhibit statistically significant differences in 91% of the 246 locations for the 50-year design flood estimates. We find this indicates a satisfactory performance of NG-IDF curves to estimate design flow under the conditions tested in the snow-dominated western United States. This article also presents technical suggestions and the limitations of infrastructure design using NG-IDF curves for regulatory agencies and practicing engineers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A Semi-supervised Hybrid Machine Learning Framework for the Qualification of Resistance Spot Welds

• Industries requiring high structural integrity, including automotive, aerospace, and construction, place considerable significance on weld quality classification. • The inspection normally involves human expertise through predefined quality metrics that are subjective, error-prone, and time-intensive • The challenge to classification model development is the scarcity of labeled data and imbalanced distributions in the data that are labeled. • This work develops a new hybrid methodology that achieves clustering using KMeans++ together with supervised classification to overcome these challenges. • The ensemble-based classifiers were identified as optimal, with accuracy enhancements of up to 8% using the pseudo-labeled dataset. • The work provides practical insight into feature engineering and machine learning integration in industrial quality assurance applications.

Rogers, Jeremy K. [Savannah River National Laborat↗
DOE OSTI2020

A Physical Model for Understanding the Activation of MoS 2 Basal-plane Sulfur Atoms for the Hydrogen Evolution Reaction

All the DFT calculations are done with the Vienna Ab Initio Simulation Package (VASP) using the projector augmented wave method. The Bayesian error estimation exchange-correlation functionals (BEEF) with van der Waals interactions are employed. A plane-wave cutoff energy of 400 eV is used together with PAW-PBE potentials where semi core p states are treated as valence. All the calculations allow for spin-polarization. The structures are relaxed until the force is converged to < 0.01 eV/Å. The lattice parameter of MoS 2 unit cell, optimized with this functional, is 3.19 Å. A (4×4) supercell is used to model all the transition metal doped MoS 2 systems studied here, including those with S vacancies. For calculations in the initial dopant structure exploration, the Brillouin zone is sampled with a 3x3x1 Monkhorst-Pack k-point mesh. A 6×6×1 Monkhorst-Pack k-point mesh is used for the H binding energy and density of states calculations. In all calculations, the vacuum layer is set as 15 Å to eliminate periodic interaction perpendicular to the basal plane.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
NASA NTRS2010

NASA's New Orbital Debris Engineering Model, ORDEM2010

This paper describes the functionality and use of ORDEM2010, which replaces ORDEM2000, as the NASA Orbital Debris Program Office (ODPO) debris engineering model. Like its predecessor, ORDEM2010 serves the ODPO mission of providing spacecraft designers/operators and debris observers with a publicly available model to calculate orbital debris flux by current-state-of-knowledge methods. The key advance in ORDEM2010 is the input file structure of the yearly debris populations from 1995-2035 of sizes 10 micron - 1 m. These files include debris from low-Earth orbits (LEO) through geosynchronous orbits (GEO). Stable orbital elements (i.e., those that do not randomize on a sub-year timescale) are included in the files as are debris size, debris number, material density, random error and population error. Material density is implemented from ground-test data into the NASA breakup model and assigned to debris fragments accordingly. The random and population errors are due to machine error and uncertainties in debris sizes. These high-fidelity population files call for a much higher-level model analysis than what was possible with the populations of ORDEM2000. Population analysis in the ORDEM2010 model consists of mapping matrices that convert the debris population elements to debris fluxes. One output mode results in a spacecraft encompassing 3-D igloo of debris flux, compartmentalized by debris size, velocity, pitch, and yaw with respect to spacecraft ram direction. The second output mode provides debris flux through an Earth-based telescope/radar beam from LEO through GEO. This paper compares the new ORDEM2010 with ORDEM2000 in terms of processes and results with examples of specific orbits.

Krisko, Paula H.↗
DOE OSTI2022

Learning in continuous action space for developing high dimensional potential energy models

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a “window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The impact of curation errors in the PDBBind Database on machine learning predictions of protein–protein binding affinity

The PDBBind database has been widely utilized for the computational prediction of protein–protein binding affinities. While the accuracy of the PDBBind-curated equilibrium dissociation constants (K D ) has been reported for the protein–ligand subset of the PDBBind database, the curation accuracy has not been reported for the protein–protein subset. Here, we present a detailed manual analysis for the subset of PDBBind records with PubMed Central Open Access primary publications and find that ~19% of these records had K D values that were not supported by their primary publications. The impact of these putative curation errors on the machine learning-based prediction of K D from experimental protein–protein 3D structures was evaluated and correcting the curation errors improved the Pearson correlation coefficient between measured and random forest-predicted log 10 (K D ) values by ~8 percentage points. This finding underscores the importance of dataset accuracy for computational modelling and highlights the need for more stringent curation processes when extracting information from the scientific literature.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Reliability Analysis for Unreliable FSM Computations

Finite State Machines (FSMs) are fundamental in both hardware design and software development. However, the reliability of FSM computations remains poorly understood. This becomes increasingly critical as the technology scaling becomes more aggressive. Existing reliability analyses are mainly designed for generic computations and are unaware of the special error tolerance characteristics in FSM computations. In this work, we introduce RelyFSM – a state-level reliability analysis framework for FSM computations. By qualitatively reasoning about the transition structures in FSM computations, RelyFSM can precisely capture their inherent error tolerance. Basically, RelyFSM takes an FSM specification as input and analyzes its reliability for a specific execution. At the core of the analysis is a set of mathematical models that accurately define the behaviors of unreliable FSM executions. Our evaluation with a spectrum of FSM benchmarks confirms the accuracy and efficiency of RelyFSM in analyzing the reliability of real-world FSM computations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Variations in Transport Derived from Satellite Altimeter Data over the Gulf Stream

Variations in total change of sea surface height (delta h) across the Gulf Stream are observed using Seasat radar altimeter data. The sea surface height is related to transport within the stream by a two layer model. Variations in delta h are compared with previously observed changes in transport found to increase with distance downstream. No such increase is apparent since the satellite transports show no significant dependence on distance. Though most discrepancies are less than 50 percent, a few cases differ by about 100 percent and more. Several possible reasons for these discrepancies are advanced, including geoid error, but only two oceanographic contributions to the variability are examined, namely, limitations in the two layer model and meanders in the current. It is concluded that some of the discrepancies could be explained as changes in the density structure not accounted for by the two layer model.

Molinelli, Eugene↗
NASA NTRS1984

Minimum time slew of the SCOLE configuration

The motivation was to develop a control design and analysis methodology directly applicable to design concepts of flexible spacecraft of interest the the U.S. Navy and to provide a testbed for the evaluation of large space structure control techniques developed at the Naval Research Laboratory. The topics covered include the following: (1) a list of key concepts; (2) evaluation of the Spacecraft Control Laboratory Experiment (SCOLE) model with DISCOS; (3) baseline results, line of sight error vs. time; (4) general formulation of optimization; (5) geometric interpretation, projected eigenaxis; (6) closed loop control law; and (7) future directions.

Fisher, S.↗
NASA NTRSDate not supplied

The Impact of All-Sky Hyperspectral Infrared Radiance Assimilation on the Simulation and Forecast of Hurricane Sally in GEOS

Hyperspectral infrared (IR) radiance observations have been one of the major data sources assimilated in the data assimilation system over the last 20 years. However, observations peaking in the lower and mid-troposphere are underutilized in clear-sky radiance data assimilation as the quality control procedure removes a significant portion of cloud-affected observations from the assimilation. To include these cloud-affected observations, one approach is to assimilate them directly under all-sky conditions. The framework for all-sky assimilation of hyperspectral IR radiance observations has been developed in GEOS. The preliminary evaluation of simulated cloud-affected IR observations has been conducted, along with the corresponding sensitivities with respect to all hydrometeors. The symmetric cloud effect has been used as a cloud proxy in the observation error modeling, providing a balanced representation that mitigates the discrepancies between observations and model simulations for IR all-sky assimilation. The observation errors vary for different cloud conditions and have been modeled as cloud amount dependent and inter-channel correlated. Preliminary evaluation of model simulations for IR all-sky assimilation indicates that the simulated brightness temperature tends to have broader structures and lacks small-scale details. Excessive clouds generated by the model are also observed. To address this issue, Hurricane Sally (2020), which formed near the Bahamas, is used as a case study. Several cloud overlap schemes and cloud lookup tables (LUTs), along with other important aspects of all-sky IR radiance assimilation, will be evaluated and tested, aiming to improve the impact on Hurricane Sally's simulation and forecast.

Wei Gu↗
DOE OSTI2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: anisotropic clustering analysis in configuration space

We explore the cosmological implications of anisotropic clustering measurements of the quasar sample from Data Release 14 (DR14) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) in configuration space. The similar to 147000 quasar sample observed by eBOSS offers a direct tracer of the density field and bridges the gap of previous baryon acoustic oscillation measurements between redshift 0.8 < z < 2.2. By analysing the two-point correlation function characterized by clustering wedges xi(wi)(s) and multipolesi xi(l)(S), we measure the angular diameter distance, Hubble parameter, and cosmic structure growth rate. We define a systematic error budget for our measurements based on the analysis of N-body simulations and mock catalogues. Based on the DR14 large-scale structure quasar sample at the effective redshift z(eff) = 1.52, we find the growth rate of cosmic structure f sigma(8)(z(eff)) = 0.396 +/- 0.079, and the geometric parameters Dv(z)/r(d) = 26.47 +/- 1.23, and F-AP(Z) = 2.53 +/- 0.22, where the uncertainties include both statistical and systematic errors. These values are in excellent agreement with the best-fitting standard A cold dark matter model to the latest cosmic microwave background data from Planck.

cosmology↗
DOE OSTI2019

A method for the characterization of intra-pixel response of infrared sensor

Due to the response variations within a pixel, response of sensor varies with the positions of the point target. The accurate measurement of intra-pixel response of the sensor is the key to high-precision centroid estimation and radiometric calibration. In this paper, we establish an intra-pixel response model based on the pixel structure and use Gauss function to describe the beam spot profile. We further calculate the full width at half maximum (FWHM) of the Gauss function and the fill factor of the infrared sensor using the grid search algorithm. Experimental results show that the Gauss function FWHM differences among different pixels using the same radius could be less than 6%. The fill factors are not constant in different pixels because of errors in the process of manufacture and assembly, and the error between model and measured values is less than 3.6%. This work could be useful for stellar calibration and centroid estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2015

A Vehicle Management End-to-End Testing and Analysis Platform for Validation of Mission and Fault Management Algorithms to Reduce Risk for NASA's Space Launch System

The engineering development of the new Space Launch System (SLS) launch vehicle requires cross discipline teams with extensive knowledge of launch vehicle subsystems, information theory, and autonomous algorithms dealing with all operations from pre-launch through on orbit operations. The characteristics of these spacecraft systems must be matched with the autonomous algorithm monitoring and mitigation capabilities for accurate control and response to abnormal conditions throughout all vehicle mission flight phases, including precipitating safing actions and crew aborts. This presents a large and complex system engineering challenge, which is being addressed in part by focusing on the specific subsystems involved in the handling of off-nominal mission and fault tolerance with response management. Using traditional model based system and software engineering design principles from the Unified Modeling Language (UML) and Systems Modeling Language (SysML), the Mission and Fault Management (M&FM) algorithms for the vehicle are crafted and vetted in specialized Integrated Development Teams (IDTs) composed of multiple development disciplines such as Systems Engineering (SE), Flight Software (FSW), Safety and Mission Assurance (S&MA) and the major subsystems and vehicle elements such as Main Propulsion Systems (MPS), boosters, avionics, Guidance, Navigation, and Control (GNC), Thrust Vector Control (TVC), and liquid engines. These model based algorithms and their development lifecycle from inception through Flight Software certification are an important focus of this development effort to further insure reliable detection and response to off-nominal vehicle states during all phases of vehicle operation from pre-launch through end of flight. NASA formed a dedicated M&FM team for addressing fault management early in the development lifecycle for the SLS initiative. As part of the development of the M&FM capabilities, this team has developed a dedicated testbed that integrates specific M&FM algorithms, specialized nominal and off-nominal test cases, and vendor-supplied physics-based launch vehicle subsystem models. Additionally, the team has developed processes for implementing and validating these algorithms for concept validation and risk reduction for the SLS program. The flexibility of the Vehicle Management End-to-end Testbed (VMET) enables thorough testing of the M&FM algorithms by providing configurable suites of both nominal and off-nominal test cases to validate the developed algorithms utilizing actual subsystem models such as MPS. The intent of VMET is to validate the M&FM algorithms and substantiate them with performance baselines for each of the target vehicle subsystems in an independent platform exterior to the flight software development infrastructure and its related testing entities. In any software development process there is inherent risk in the interpretation and implementation of concepts into software through requirements and test cases into flight software compounded with potential human errors throughout the development lifecycle. Risk reduction is addressed by the M&FM analysis group working with other organizations such as S&MA, Structures and Environments, GNC, Orion, the Crew Office, Flight Operations, and Ground Operations by assessing performance of the M&FM algorithms in terms of their ability to reduce Loss of Mission and Loss of Crew probabilities. In addition, through state machine and diagnostic modeling, analysis efforts investigate a broader suite of failure effects and associated detection and responses that can be tested in VMET to ensure that failures can be detected, and confirm that responses do not create additional risks or cause undesired states through interactive dynamic effects with other algorithms and systems. VMET further contributes to risk reduction by prototyping and exercising the M&FM algorithms early in their implementation and without any inherent hindrances such as meeting FSW processor scheduling constraints due to their target platform - ARINC 653 partitioned OS, resource limitations, and other factors related to integration with other subsystems not directly involved with M&FM such as telemetry packing and processing. The baseline plan for use of VMET encompasses testing the original M&FM algorithms coded in the same C++ language and state machine architectural concepts as that used by Flight Software. This enables the development of performance standards and test cases to characterize the M&FM algorithms and sets a benchmark from which to measure the effectiveness of M&FM algorithms performance in the FSW development and test processes.

Trevino, Luis↗
DOE OSTI2020

Monte Carlo control loops for cosmic shear cosmology with DES Year 1 data

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. Monte Carlo control loops (MCCL) is a forward modeling method designed to tackle this problem. It relies on the ultra fast image generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. Here, we present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_ℓ$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, point spread function (PSF), an approximate Bayesian computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and a fast method to estimate the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a nontomographic setting, we derive a set of $C_ℓ$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $Ω_m$, $σ_8$, and intrinsic alignment amplitude $A_{IA}$, defined as $S_8D_{IA}=σ_8(Ω_m/0.3)^{0.5}D_{IA}$, where $D_{IA}=1-0.11(A_{IA}-1)$. We find $S_8D_{IA}=0.8954_{-0.039}^{+0.054}$, where systematics are at the level of roughly 60% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Quantification of modeling uncertainty in the Rayleigh damping model

Understanding and accurately characterizing energy dissipation mechanisms in civil structures during earthquakes is an important element of seismic assessment and design. The most commonly used model is attributed to Rayleigh. This paper proposes a systematic approach to quantify the uncertainty associated with Rayleigh's damping model. Bayesian calibration with embedded model error is employed to treat the coefficients of the Rayleigh model as random variables using modal damping ratios. Through a numerical example, we illustrate how this approach works and how the calibrated model can address modeling uncertainty associated with the Rayleigh damping model.

42 ENGINEERING↗
DOE OSTI2022

Comparing Model Representations of Physiological Limits on Transpiration at a Semi-arid Ponderosa Pine Site

Mechanistic representations of biogeochemical processes in ecosystem models are rapidly advancing, requiring advancements in model evaluation approaches. Here we quantify multiple aspects of model functional performance to evaluate improved process representations in ecosystem models. We compare semi-empirical stomatal models with hydraulic constraints against more mechanistic representations of stomatal and hydraulic functioning at a semi-arid pine site using a suite of metrics and analytical tools. We find that models generally perform similarly under unstressed conditions, but performance diverges under atmospheric and soil drought. The more empirical models better capture synergistic information flows between soil water potential and vapor pressure deficit to transpiration, while the more mechanistic models are overly deterministic. Although models can be parameterized to yield similar functional performance, alternate parameterizations could not overcome structural model constraints that underestimate the unique information contained in soil water potential about transpiration. Additionally, both multilayer canopy and big-leaf models were unable to capture the magnitude of canopy temperature divergence from air temperature, and we demonstrate that errors in leaf temperature can propagate to considerable error in simulated transpiration. This study demonstrates the value of merging underutilized observational data streams with emerging analytical tools to characterize ecosystem function and discriminate among model process representations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

KiDS-1000 cosmology: Combined second- and third-order shear statistics

Aims.In this work, we perform the first cosmological parameter analysis of the fourth release of Kilo Degree Survey (KiDS-1000) data with second- and third-order shear statistics. This paper builds on a series of studies aimed at describing the roadmap to third-order shear statistics. Methods.We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics 〈ℳ ap 3 〉 in a tomographic set-up. We validated our pipeline withN-body mock simulations of the KiDS-1000 data release. To model the second- and third-order statistics, we used the latest version of HMCODE2020 for the power spectrum and BIHALOFITfor the bispectrum. Furthermore, we used an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the 〈ℳ ap 3 〉 part of the data vector. This makes it possible to carry out a data analysis of the KiDS-1000 data release using a combined analysis of COSEBIs and third-order shear statistics. Results.We first validated the accuracy of our modelling by analysing a noise-free mock data vector, assuming the KiDS-1000 error budget, finding a shift in the maximum of the posterior distribution of the matter density parameter, ΔΩ m < 0.02 σ Ω m , and of the structure growth parameter, ΔS 8 < 0.05 σ S 8 . Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained Ω m = 0.248 −0.055 +0.062 andS 8 = σ 8 √(Ω m /0.3 )= 0.772 ± 0.022. The geometric average on the errors of Ω m andS 8 of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.

Astronomy & Astrophysics↗