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NASA NTRS1992

Further investigations of the aeroelastic behavior of the AFW wind-tunnel model using transonic small disturbance theory

The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code, developed at the NASA Langley Research Center, is applied to the Active Flexible Wing wind-tunnel model for prediction of transonic aeroelastic behavior. A semi-span computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using CAP-TSD are computed. Dynamic (flutter) analyses then are performed as perturbations about the static aeroelastic deformations and presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motions and sensitivity to the modeling of the wing tip ballast stores also are presented and compared with experimental flutter results.

Silva, Walter A.↗

NASA NTRS2002

Intersymbol Interference Investigations Using a 3D Time-Dependent Traveling Wave Tube Model

For the first time, a time-dependent, physics-based computational model has been used to provide a direct description of the effects of the traveling wave tube amplifier (TWTA) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves. Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry and operating characteristics of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept- amplitude and/or swept-frequency data. First, the TWT model using the three dimensional (3D) electromagnetic code MAFIA is presented. Then, this comprehensive model is used to investigate approximations made in conventional TWT black-box models used in communication system level simulations. To quantitatively demonstrate the effects these approximations have on digital signal performance predictions, including intersymbol interference (ISI), the MAFIA results are compared to the system level analysis tool, Signal Processing Workstation (SPW), using high order modulation schemes including 16 and 64-QAM.

Kory, Carol L.↗

NASA NTRS2014

Comparison of Martian Surface Radiation Predictions to the Measurements of Mars Science Laboratory Radiation Assessment Detector (MSL/RAD)

For the analysis of radiation risks to astronauts and planning exploratory space missions, detailed knowledge of particle spectra is an important factor. Detailed measurements of the energetic particle radiation environment on the surface of Mars have been made by the Mars Science Laboratory Radiation Assessment Detector (MSL-RAD) on the Curiosity rover since August 2012, and particle fluxes for a wide range of ion species (up to several hundred MeV/u) and high energy neutrons (8 - 1000 MeV) have been available for the first 200 sols. Although the data obtained on the surface of Mars for 200 sols are limited in the narrow energy spectra, the simulation results using the Badhwar-O'Neill galactic cosmic ray (GCR) environment model and the high-charge and energy transport (HZETRN) code are compared to the data. For the nuclear interactions of primary GCR through Mars atmosphere and Curiosity rover, the quantum multiple scattering theory of nuclear fragmentation (QMSFRG) is used, which includes direct knockout, evaporation and nuclear coalescence. Daily atmospheric pressure measurements at Gale Crater by the MSL Rover Environmental Monitoring Station are implemented into transport calculations for describing the daily column depth of atmosphere. Particles impinging on top of the Martian atmosphere reach the RAD after traversing varying depths of atmosphere that depend on the slant angles, and the model accounts for shielding of the RAD by the rest of the instrument. Calculations of stopping particle spectra are in good agreement with the RAD measurements for the first 200 sols by accounting changing heliospheric conditions and atmospheric pressure. Detailed comparisons between model predictions and spectral data of various particle types provide the validation of radiation transport models, and thus increase the accuracy of the predictions of future radiation environments on Mars. These contributions lend support to the understanding of radiation health risks to astronauts for the planning of various mission scenarios.

Kim, Myung-Hee Y.↗

DOE OSTI2020

A Path to Zero Energy Ready Home Construction

This paper will be presented at the 5th Residential Building Design & Construction Conference in State College, Pennsylvania. While the number of zero energy homes constructed in the U.S. has grown dramatically, increasing nearly 400% since 2015, zero energy homes still accounted for less than 1% of all U.S. homes constructed as of December 2018. Concerns about high costs or implementation challenges have kept many builders from attempting zero energy home construction. However, builders participating in the U.S. Department of Energy’s Zero Energy Ready Home Program are showing that zero energy ready home construction can be achieved simply and cost effectively with off-the-shelf equipment and materials and common construction techniques. Construction methods used by builders in the DOE program are compared with those used in just-to-code new homes and existing homes for several key components, including wall assemblies and HVAC systems. Examples of cost-effective assemblies used in the Mid Atlantic states are provided.

U.S. Department of Energy Building Technologies Pr↗

DOE OSTI2022

Application of Dynamical System Scaling for Accelerated Fuel Qualification Efforts

There are considerable ongoing research and testing campaigns to qualify new fuel designs such as metallic fuels for advanced reactor designs and the Accident Tolerant Fuel (ATF) campaign for light water reactors (LWR). The typical research and development lifecycle needed to qualify a nuclear fuel design, under ideal conditions, can take up to 20-25 years which limits the ability for new fuels to make fast deployments into commercial, test, and research reactors. While there are several efforts to accelerate nuclear fuel qualification through advanced modeling coupled with state-of-the-art experiments, there is not yet a framework to methodically quantify and rank distortions occurring in experimental test specimens needed to validate nuclear fuel performance codes. This study uses the Dynamical System Scaling (DSS) methodology to quantify transient scaling distortions that occur over experiment and simulated transients. DSS analysis metrics provide a researcher with several tools and information embedded within test data to identify dominant phenomena, associated timescales, and quantify a transient?s overall dynamic distortion. This is demonstrated with separate analyses of the SETH-C and CHF-SERTTA thermal-hydraulic experiments in the TREAT facility at Idaho National Laboratory. The outcome of this work is a scaling and data analysis approach to account for the influence a scaled fuel test specimen?s geometric and temporal distortions have on its ability to be representative of the full-scale design.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Development and experimental qualification of a calculation scheme for the evaluation of gamma heating in experimental reactors. Application to MARIA and Jules Horowitz (JHR) MTR Reactors

Precise computational determination of nuclear heating which consists predominantly of gamma heating (more than 80 %) is one of the challenges in material testing reactor exploitation. Due to sophisticated construction and conditions of experimental programs planned in JHR it became essential to use most accurate and precise gamma heating model. Before the JHR starts to operate, gamma heating evaluation methods need to be developed and qualified in other experimental reactor facilities. This is done inter alia using OSIRIS, MINERVE or EOLE research reactors in France. Furthermore, MARIA - Polish material testing reactor - has been chosen to contribute to the qualification of gamma heating calculation schemes/tools. This reactor has some characteristics close to those of JHR (beryllium usage, fuel element geometry). To evaluate gamma heating in JHR and MARIA reactors, both simulation tools and experimental program have been developed and performed. For gamma heating simulation, new calculation scheme and gamma heating model of MARIA have been carried out using TRIPOLI4 and APOLLO2 codes. Calculation outcome has been verified by comparison to experimental measurements in MARIA reactor. To have more precise calculation results, model of MARIA in TRIPOLI4 has been made using the whole geometry of the core. This has been done for the first time in the history of MARIA reactor and was complex due to cut cone shape of all its elements. Material composition of burnt fuel elements has been implemented from APOLLO2 calculations. An experiment for nuclear heating measurements and calculation verification has been done in September 2014. This involved neutron, photon and nuclear heating measurements at selected locations in MARIA reactor using in particular Rh SPND, Ag SPND, Ionization Chamber (all three from CEA), KAROLINA calorimeter (NCBJ) and Gamma Thermometer (CEA/SCK CEN). Measurements were done in forty points using four channels. Maximal nuclear heating evaluated from measurements is of the order of 2.5 W/g at half of the possible MARIA power - 15 MW. The approach and the detailed program for experimental verification of calculations will be presented. The following points will be discussed: - Development of a gamma heating model of MARIA reactor with TRIPOLI 4 (coupled neutron-photon mode) and APOLLO2 model taking into account the key parameters like: configuration of the core, experimental loading, control rod location, reactor power, fuel depletion); - Design of specific measurement tools for MARIA experiments including for instance a new single-cell calorimeter called KAROLINA calorimeter; - MARIA experimental program description and a preliminary analysis of results; - Comparison of calculations for JHR and MARIA cores with experimental verification analysis, calculation behavior and n-γ 'environments'. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Application of BISON to UO 2 MiniFuel fission gas release analysis

There has been a recent push to accelerate fuel qualification by developing revolutionary capabilities to reduce irradiation periods, and thereby, reduce the time required to qualify a new fuel system. One such capability is the MiniFuel irradiation capsule designed to miniaturize fuel samples and irradiate “mini” fuel samples under isothermal temperature conditions. MiniFuel allows steady-state irradiations to decouple the traditionally coupled fission rate (i.e., power) and temperature parameters to understand and generate microstructures observed in fuel operated in a commercial reactor. Furthermore, this process offers the possibility to gather in situ data as well as postirradiation or transient data such as thermal conductivity, specific heat, fission gas diffusion and release, etc. However, accelerating fuel qualification is not solely reliant on generating large amounts of data but also on developing an informed test matrix designed to rapidly generate impactful data. Additionally, this process is reliant on fuel performance codes, such as BISON, to evaluate MiniFuel irradiations using existing material models. This process pinpoints model/data gaps, identifies desired irradiation conditions, and subsequently supports model validation and development. This work describes the use of BISON to perform a number of sensitivity studies designed to understand conditions that lead to fission gas release (FGR) under steady-state isothermal irradiation conditions and temperature transient conditions. The model is applied to a UO 2 MiniFuel example and shows an overall good qualitative agreement with experimental FGR annealing tests under different temperature conditions. It also accounts well for microstructural effects on FGR. When quantitatively compared with FGR data from previously irradiated 103 MWd/kgU UO 2 discs under thermal annealing, the model shows a less satisfactory agreement with the experimental data. Finally, a UO 2 MiniFuel test matrix is proposed to help to extend the model's operational range and validate the new FGR model capabilities to higher burnups and transient conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Reduced energetic particle transport models enable comprehensive time-dependent tokamak simulations

Time-dependent integrated simulations through codes such as TRANSP are becoming an indispensable tool for the interpretation of existing experiments and predictions of optimized scenarios. For many practical cases, quantitative simulations need to include the effect of plasma instabilities on the evolution of a tokamak discharge. An example is the degradation in energetic particle (EP) confinement induced by instabilities, which in turn affects important source terms for heating, non-inductive current, and momentum in a simulation. The reduced-physics "kick model" provides phase-space resolved transport probability matrices to TRANSP that are used to account for enhanced EP transport by instabilities in addition to neoclassical transport. The model has recovered the measured Alfvén eigenmode (AE) spectrum on NSTX, NSTX-U and DIII-D, and has reproduced details of phase-space resolved fast ion diagnostic data measured on DIII-D for EP-driven modes and tearing modes. In general, the kick model has proven the potential of phase-space resolved EP simulations to unravel details of EP transport for detailed theory/experiment comparison and for scenario planning based on optimization of Neutral Beam (NB) injection parameters. In this work, the extension of the kick model to low-frequency instabilities such as Tearing Modes and fishbones, in addition to AEs, is assessed. The goal is to enable TRANSP simulations that retain the main effects of multiple types of instabilities through a common framework. Results from the NSTX/NSTX-U and DIII-D tokamaks show that the extension to "multi-mode" scenarios can expand the range of applicability of the model for more reliable, quantitative integrated simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Notice of Illegal Foreign Pesticides Entering the United States: Information Bulletin v.01

This information bulletin is intended to generate a heightened awareness of illicit pesticide importation, distribution, and use in the United States. This bulletin focuses on solid, fumigant materials which are primarily used in the production of marijuana growth and cultivation. Exposure to illicit pesticides, fumigant fumes, or residual materials may pose a public health and officer safety concern. Many illegal fumigant pesticide products have been seized and determined to consist of a mixture of several pesticides and is often in contrast with the pesticide labelling. This information bulletin is not a complete account of all illegal pesticides found in country; it serves to highlight frequently encountered materials and present patterns in product presentation, packaging, and shipment containment which are intended to aid in identification and intervention. Other varieties of illegal pesticide fumigants are known to exist, and additional variations are expected to be encountered in policing intervention. This bulletin includes information on the presentation of illegal pesticides, label review recommendations, a field reference guide, which includes example photographs of seized pesticide/fumigants and their labels, and related United States federal regulation information, including relevant tariff code information for reference.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2001

Intersymbol Interference Investigations Using a 3D Time-Dependent Traveling Wave Tube Model

For the first time, a physics based computational model has been used to provide a direct description of the effects of the TWT (Traveling Wave Tube) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves. Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept amplitude and/or swept frequency data. The fully three-dimensional (3D), time-dependent, TWT interaction model using the electromagnetic code MAFIA is presented. This model is used to investigate assumptions made in TWT black box models used in communication system level simulations. In addition, digital signal performance, including intersymbol interference (ISI), is compared using direct data input into the MAFIA model and using the system level analysis tool, SPW (Signal Processing Worksystem).

Kory, Carol L.↗

NASA NTRS2002

Higher Order Modulation Intersymbol Interference Caused by Traveling-wave Tube Amplifiers

For the first time, a time-dependent, physics-based computational model has been used to provide a direct description of the effects of the traveling wave tube amplifier (TWTA) on modulated digital signals. The TWT model comprehensively takes into account the effects of frequency dependent AM/AM and AM/PM conversion; gain and phase ripple; drive-induced oscillations; harmonic generation; intermodulation products; and backward waves, Thus, signal integrity can be investigated in the presence of these sources of potential distortion as a function of the physical geometry and operating characteristics of the high power amplifier and the operational digital signal. This method promises superior predictive fidelity compared to methods using TWT models based on swept-amplitude and/or swept-frequency data. First, the TWT model using the three dimensional (3D) electromagnetic code MAFIA is presented. Then, this comprehensive model is used to investigate approximations made in conventional TWT black-box models used in communication system level simulations, To quantitatively demonstrate the effects these approximations have on digital signal performance predictions, including intersymbol interference (ISI), the MAFIA results are compared to the system level analysis tool, Signal Processing, Workstation (SPW), using high order modulation schemes including 16 and 64-QAM.

Kory, Carol L.↗

NASA NTRS2006

A Hybrid RANS/LES Approach for Predicting Jet Noise

Hybrid acoustic prediction methods have an important advantage over the current Reynolds averaged Navier-Stokes (RANS) based methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence. Unfortunately, they are unable to account for the high frequency sound generated by the turbulence in the initial mixing layers. This paper introduces an alternative approach that directly calculates the sound from a hybrid RANS/LES flow model (which can resolve the steep gradients in the initial mixing layers near the nozzle lip) and adopts modeling techniques similar to those used in current RANS based noise prediction methods to determine the unknown sources in the equations for the remaining unresolved components of the sound field. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid noise prediction methods.

Goldstein, Marvin E.↗

NASA NTRS2008

Reliability Assessment of Graphite Specimens under Multiaxial Stresses

An investigation was conducted to predict the failure strength response of IG-100 nuclear grade graphite exposed to multiaxial stresses. As part of this effort, a review of failure criteria accounting for the stochastic strength response is provided. The experimental work was performed in the early 1990s at the Oak Ridge National Laboratory (ORNL) on hollow graphite tubes under the action of axial tensile loading and internal pressurization. As part of the investigation, finite-element analysis (FEA) was performed and compared with results of FEA from the original ORNL report. The new analysis generally compared well with the original analysis, although some discrepancies in the location of peak stresses was noted. The Ceramics Analysis and Reliability Evaluation of Structures Life prediction code (CARES/Life) was used with the FEA results to predict the quadrants I (tensile-tensile) and quadrant IV (compression-tension) strength response of the graphite tubes for the principle of independent action (PIA), the Weibull normal stress averaging (NSA), and the Batdorf multiaxial failure theories. The CARES/Life reliability analysis showed that all three failure theories gave similar results in quadrant I but that in quadrant IV, the PIA and Weibull normal stress-averaging theories were not conservative, whereas the Batdorf theory was able to correlate well with experimental results. The conclusion of the study was that the Batdorf theory should generally be used to predict the reliability response of graphite and brittle materials in multiaxial loading situations.

Sookdeo, Steven↗

NASA NTRS2016

Feasibility of Varying Geo-Fence Around an Unmanned Aircraft Operation Based on Vehicle Performance and Wind

Managing trajectory separation is critical to ensuring accessibility, efficiency, and safety in the unmanned airspace. The notion of geo-fences is an emerging concept, where distance buffers enclose individual trajectories and areas of operation in order to manage the airspace. Currently, the Air Traffic Management system for commercial travel defines static distance buffers around the aircraft; however, commercial UASs are envisioned to operate in significantly closer proximity to other UAS requiring a geo-fence for spacing operations. The geo-fence size can be determined based on vehicle performance characteristics, state of the airspace, weather, and other unforeseen events such as emergency or disaster response. Calculation of the geo-fence size could be determined as part of pre-flight planning and during real-time operations. A largely non-homogeneous fleet of UASs will be operating in low altitude and will likely be commercially developed. Due to intellectual property concerns, the operators may not provide detailed specifications of the control system to UTM. In addition, the huge variety of UAS makes modeling each control system prohibitive and flight data for these vehicles may not exist. Therefore, a generalized, simple geo-fence sizing algorithm must be developed such that it does not rely on detailed knowledge of the vehicle control system, accounts for the presence of urban winds, and is sufficiently accurate. In this work, two simple models are investigated to determine its feasibility as an adequate means for calculating the geo-fence size. The vehicle data used in this work are provided by UAS manufactures who have partnered with NASA's UTM project and some publicly available websites. The first model utilizes wind data processed from the NOAA HRRR (Hourly Rapid Refresh) product and Sonar Annemometer data provided by San Jose State. The second model utilizes OpenFOAM which is a CFD code used to generate a wind field for flow around a single building. The key vehicle performance parameters can include UAS response time to disturbances, command to actuation latency, control system rate limits, time to recovery to desired path, and aerodynamics. It was found that the first model provides an initial understanding of geo-fence sizing, but does not provide enough accuracy to provide UTM with an efficient means of scheduling vehicles. The results of the second model reveal that modeling UAS controls systems with a linearized plant and gain scheduled PID controller does not allow capture the UAS flight dynamics within a significant envelope of the wind disturbances.

uncertainty↗

NASA NTRS2020

Marshall Space Flight Center Faculty Fellowship Program

This paper presents a multi-node model of autogenous pressurization of liquid nitrogen in a flight tank using the Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code developed at NASA/Marshall Space Flight Center. This study considers two different models: (a) pressurization of the tank by nitrogen gas from a supply tank and (b) pressurization of the tank by using the boil-off propellant through an IVF (Integrated Vehicle Fluids) loop. The tank pressurization model considers two different liquid fill-levels of the tank (a) 75% and (b) 45%. Heat and mass transfer between the liquid and vapor has been modeled at the liquid vapor interface. Heat transfer between wall and vapor at the ullage has been accounted for by assuming heat transfer occurs by natural convection. The model also accounts for heat leak to the tank through the insulation and metal wall by heat conduction. The predicted pressures and temperatures are compared with the measured data and good agreement has been observed. In the second case, the tank is pressurized by using the boil-off fluid that recirculates through an IVF loop. Preliminary results from this model are also reported.

N.F. Six↗

DOE OSTI2024

A new generation of effective core potentials: Selected lanthanides and heavy elements

Here, we construct correlation-consistent effective core potentials (ccECPs) for a selected set of heavy atoms and ƒ-elements that are of significant current interest in materials and chemical applications, including Y, Zr, Nb, Rh, Ta, Re, Pt, Gd, and Tb. As is customary, ccECPs consist of spin orbit averaged relativistic effective potential (AREP) and effective spin-orbit (SO) terms. For the AREP part, our constructions are carried out within a relativistic coupled-cluster framework while also taking into account objective function one-particle characteristics for improved convergence in optimizations. The transferability is adjusted using binding curves of hydride and oxide molecules. We address the difficulties encountered with ƒ-elements, such as the presence of large cores and multiple near-degeneracies of excited levels. For these elements, we construct ccECPs with core valence partitioning that includes 4ƒ-subshell in the valence space. The developed ccECPs achieve an excellent balance between accuracy, size of the valence space, and transferability and are also suitable to be used in plane wave codes with reasonable energy cutoffs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

TH-CD-207A-08: Simulated Real-Time Image Guidance for Lung SBRT Patients Using Scatter Imaging

Purpose: To develop a comprehensive Monte Carlo-based model for the acquisition of scatter images of patient anatomy in real-time, during lung SBRT treatment. Methods: During SBRT treatment, images of patient anatomy can be acquired from scattered radiation. To rigorously examine the utility of scatter images for image guidance, a model is developed using MCNP code to simulate scatter images of phantoms and lung cancer patients. The model is validated by comparing experimental and simulated images of phantoms of different complexity. The differentiation between tissue types is investigated by imaging objects of known compositions (water, lung, and bone equivalent). A lung tumor phantom, simulating materials and geometry encountered during lung SBRT treatments, is used to investigate image noise properties for various quantities of delivered radiation (monitor units(MU)). Patient scatter images are simulated using the validated simulation model. 4DCT patient data is converted to an MCNP input geometry accounting for different tissue composition and densities. Lung tumor phantom images acquired with decreasing imaging time (decreasing MU) are used to model the expected noise amplitude in patient scatter images, producing realistic simulated patient scatter images with varying temporal resolution. Results: Image intensity in simulated and experimental scatter images of tissue equivalent objects (water, lung, bone) match within the uncertainty (∼3%). Lung tumor phantom images agree as well. Specifically, tumor-to-lung contrast matches within the uncertainty. The addition of random noise approximating quantum noise in experimental images to simulated patient images shows that scatter images of lung tumors can provide images in as fast as 0.5 seconds with CNR∼2.7. Conclusions: A scatter imaging simulation model is developed and validated using experimental phantom scatter images. Following validation, lung cancer patient scatter images are simulated. These simulated patient images demonstrate the clinical utility of scatter imaging for real-time tumor tracking during lung SBRT.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

The correlation between metallicity and debris disk mass

We find that the initial dust masses in planetary debris disks are correlated with the metallicities of their central stars. We compiled a large sample of systems, including Spitzer, the Herschel DUNES and DEBRIS surveys, and WISE debris disk candidates. We also merged 33 metallicity catalogs to provide homogeneous [Fe/H] and σ{sub [Fe/H]} values. We analyzed this merged sample, including 222 detected disks (74 warm and 148 cold) around a total of 187 systems (some with multiple components) and 440 disks with only upper limits (125 warm and 315 cold) around a total of 360 systems. The disk dust masses at a common early evolutionary point in time were determined using our numerical disk evolutionary code, evolving a unique model for each of the 662 disks backward to an age of 1 Myr. We find that disk-bearing stars seldom have metallicities less than [Fe/H]=−0.2 and that the distribution of warm component masses lacks examples with large mass around stars of low metallicity ([Fe/H]<−0.085). Previous efforts to find a correlation have been largely unsuccessful; the primary improvements supporting our result are (1) basing the study on dust masses, not just infrared excess detections; (2) including upper limits on dust mass in a quantitative way; (3) accounting for the evolution of debris disk excesses as systems age; (4) accounting fully for the range of uncertainties in metallicity measurements; and (5) having a statistically large enough sample.

79 ASTRONOMY AND ASTROPHYSICS↗