Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Performance Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46

Nonlinear dynamics, bifurcations, and multi-stability in a vibro-impact system with geometric and multi-segmented freeplay nonlinearities

Freeplay is a common type of piecewise-smooth nonlinearity in dynamical systems, and it can cause discontinuity-induced bifurcations and other behaviors that may bring about undesirable and potentially damaging responses. Prior research has focused on piecewise-smooth systems with two or three distinct regions, but less attention is devoted to systems with more regions (i.e., multi-segmented systems). In this work, numerical analysis is performed on a dynamical system with multi-segmented freeplay, in which there are four stiffness transitions and five distinct regions in the phase space. Here, the effects of the multi-segmented parameters are studied through bifurcation diagram evolution along with induced multi-stable behavior and different bifurcations. These phenomena are interrogated through various tools, such as harmonic balance, basins of attraction, phase planes, and Poincaré section analysis. Results show that among the three multi-segmented parameters, the asymmetry has the strongest effect on the response of the system.

42 ENGINEERING↗

Community-Scale Energy Efficiency Assessment for Zero Net Energy Using the URBANopt Simulation Platform: Preprint

This project explored an innovative modeling approach for assessing the energy efficiency potential of the existing low-income Oceano neighborhood, in unincorporated San Luis Obispo County, and its effects on renewable generation requirements for achieving zero net energy (ZNE). One particular challenge faced was ascertaining the technical energy savings potential across a large neighborhood in a timely manner. The project overcame this challenge through the use of the URBANopt simulation platform, developed at the National Renewable Energy Laboratory. URBANopt manages the automated model creation, simulation, and result aggregation for different design scenarios of existing or candidate buildings in a large neighborhood. Customized energy efficiency packages considered for the residential and commercial sector in the neighborhood included lighting, HVAC, plug load, water heating, envelope, and energy education measures. As a result of the analysis for the Oceano community, energy efficiency measures that are available through incentive programs may provide a 7.4% reduction in the required distributed energy resource (DER) size, corresponding to a 25,000 ft2 decrease in PV array area, to achieve ZNE. Through this work, a computational tool was developed and is being leveraged by the County of San Luis Obispo (CoSLO). The tool has enabled the CoSLO staff to perform similar analysis of the technical potential for energy efficiency, and an understanding of the DER asset requirements and potential savings in other communities within the county.

building energy modeling↗

An Integrated Assessment of a G3 GMD Event on Large-Scale Power Grids: From Magnetometer Data to Geomagnetically Induced Current Analysis

Solar activities can cause geomagnetic disturbances (GMDs) that give rise to geomagnetically induced currents (GICs) which may compromise the reliability of the power system. In order to build more reliable models representing GMD interactions with the power grid, the power system’s detailed electrical model must be considered along with fluctuations in the earth’s magnetic and induced surface electric fields. Here, this study investigates the impact of incorporating spatially varying magnetic fields into surface electric field models on GMD risk metrics. A spatially independent magnetic field model and a spatially varying model are compared through simulations. To perform this analysis, the earth’s magnetic field disturbances are transformed into surface electric fields using respective one-dimensional earth conductivity models. Then, the modeling impact of these electric fields is studied using a 2,000-bus grid for Texas and a 25,000-bus grid for the northeast and mid- Atlantic regions of the United States. Simulation results reveal that the inclusion of spatially varying magnetic fields results in considerable differences in GMD risk metrics, highlighting the importance of accounting for spatial variability when assessing GMD risks in the power system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The first two chromosome‐scale genome assemblies of American hazelnut enable comparative genomic analysis of the genus Corylus

Summary The native, perennial shrub American hazelnut ( Corylus americana ) is cultivated in the Midwestern United States for its significant ecological benefits, as well as its high‐value nut crop. Implementation of modern breeding methods and quantitative genetic analyses of C. americana requires high‐quality reference genomes, a resource that is currently lacking. We therefore developed the first chromosome‐scale assemblies for this species using the accessions ‘Rush’ and ‘Winkler’. Genomes were assembled using HiFi PacBio reads and Arima Hi‐C data, and Oxford Nanopore reads and a high‐density genetic map were used to perform error correction. N50 scores are 31.9 Mb and 35.3 Mb, with 90.2% and 97.1% of the total genome assembled into the 11 pseudomolecules, for ‘Rush’ and ‘Winkler’, respectively. Gene prediction was performed using custom RNAseq libraries and protein homology data. ‘Rush’ has a BUSCO score of 99.0 for its assembly and 99.0 for its annotation, while ‘Winkler’ had corresponding scores of 96.9 and 96.5, indicating high‐quality assemblies. These two independent assemblies enable unbiased assessment of structural variation within C. americana , as well as patterns of syntenic relationships across the Corylus genus. Furthermore, we identified high‐density SNP marker sets from genotyping‐by‐sequencing data using 1343 C. americana , C. avellana and C. americana × C. avellana hybrids, in order to assess population structure in natural and breeding populations. Finally, the transcriptomes of these assemblies, as well as several other recently published Corylus genomes, were utilized to perform phylogenetic analysis of sporophytic self‐incompatibility (SSI) in hazelnut, providing evidence of unique molecular pathways governing self‐incompatibility in Corylus .

54 ENVIRONMENTAL SCIENCES↗

Technical and economic feasibility of molten chloride salt thermal energy storage systems

A techno-economic study is performed to assess the feasibility of molten chloride salt thermal energy storage (TES) systems for next generation concentrating solar power. Refractory liners internally insulate tanks to allow tank shells to be constructed from carbon steel. The liner must not be wetted by salt to maintain predictable thermal properties and manageable heat loss out of the tank. The commercial scale tank liner is an anchored brick and mortar design with expansion joints to accommodate thermal expansion. Furthermore, finite element analysis is performed to optimize the thermal and mechanical profile of the tank. Equalizing the shell temperature between the water-cooled foundation and the shell wall is necessary to minimize differential thermomechanical stress and lower overall stress values below industrial allowable limits. The cost of the TES system is estimated to be $60/kWhth, which is four times greater than Department of Energy targets. Solutions to reduce system cost and overall risk are proposed.

14 SOLAR ENERGY↗

The importance of localized modes spectral contribution to thermal conductivity in amorphous polymers

Abstract Polymers are a unique class of materials from the perspective of normal mode analysis. Polymers consist of individual chains with repeating units and strong intra-chain covalent bonds, and amorphous arrangements among chains with weak inter-chain van der Waals and for some polymers also electrostatic interactions. Intuitively, this strong heterogeneity in bond strength can give rise to special features in the constituent phonons, but such effects have not been studied deeply before. Here, we use lattice dynamics and molecular dynamics to perform modal analysis of the thermal conductivity in amorphous polymers. We find an abnormally large population of localized modes in amorphous polymers, which is fundamentally different from amorphous inorganic materials. Contrary to the common picture of thermal transport, localized modes in amorphous polymers are found to be the dominant contributors to thermal conductivity. We find that a significant portion of the localization happens within individual chains, but heat is dominantly conducted when localized modes involve two chains. These results suggest localized modes generally play a key role in thermal transport for different polymers. The results provide an alternative perspective on why polymer thermal conductivity is generally quite low and gives insight into how to potentially change it.

36 MATERIALS SCIENCE↗

ANTARES: a new IRSN computational chain for safety analysis

Since some years, the IRSN has developed a new project to simulate accurately the interaction between neutronic and thermal hydraulic phenomena. This project called ANTARES (Advanced Neutronics and Thermal-hydraulic for the Analysis of Reactor Safety) couples the thermal hydraulic code CATHARE-3 with the 3D neutronic nodal code PARCS. The purpose of this project is to take the advantage of the complementary of these 2 codes, by the knowledge of the 3D core power distribution in CATHARE-3 (computed by PARCS) and improving the thermal hydraulic boundaries conditions in PARCS. In this way, the IRSN diversifies and enlarges its available tools to perform safety analysis with improved accuracy. The current technique usually adopted in France for the safety demonstrations for Reactivity Insertion Accident (RIA) is the so-called 'conservative' approach, which consists of reducing all the feedback (Doppler and moderator effects) and in modifying some physical quantities in such a way to increase a power peak. For this reason, these facilities ('penalties') have been implemented in ANTARES. In this paper we will give two examples of accidental transients that can be simulated with ANTARES: a Main Steam Line Break (MSLB) and an inadvertent boron dilution event. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗

stochprop Documentation (Release 1.0)

Simulations of infrasonic propagation in the atmosphere typically utilize a single atmospheric specification describing the acoustic sound speed, ambient winds, and density as a function of altitude. Due to the dynamic and sparsely sampled nature of the atmosphere, there is a notable amount of uncertainty in the atmospheric state at a given location and time so that a more robust analysis of infrasonic propagation requires inclusion of this uncertainty. This Python library, stochprop, has been implemented using methods developed jointly by infrasound scientists at Los Alamos National Laboratory (LANL) and the University of Mississippi’s National Center for Physical Acoustics (NCPA). This software library includes methods to quantify variability in the atmospheric state, identify typical seasonal variability in the atmospheric state and generate suites of representative atmospheric states during a given season, as well as perform uncertainty analysis on a specified atmospheric state given some level of uncertainty. These methods have been designed to interface between propagation modeling capabilities such as InfraGA/GeoAc and NCPAprop and signal analysis methods in the LANL InfraPy tool.

58 GEOSCIENCES↗

Process Modeling of Aerosol‐Cloud Interaction in Summertime Precipitating Shallow Cumulus Over the Western North Atlantic

Abstract Process modeling of Aerosol‐cloud interaction (ACI) is essential to bridging gaps between observational analysis and climate modeling of aerosol effects in the Earth system and eventually reducing climate projection uncertainties. In this study, we examine ACI in summertime precipitating shallow cumuli observed during the Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE). Aerosols and precipitating shallow cumuli were extensively observed with in‐situ and remote‐sensing instruments during two research flight cases on 02 June and 07 June, respectively, during the ACTIVATE summer 2021 deployment phase. We perform observational analysis and large‐eddy simulation (LES) of aerosol effect on precipitating cumulus in these two cases. Given the measured aerosol size distributions and meteorological conditions, LES is able to reproduce the observed cloud properties by aircraft such as liquid water content (LWC), cloud droplet number concentration ( N c ) and effective radius r eff . However, it produces smaller liquid water path (LWP) and larger N c compared to the satellite retrievals. Both 02 and 07 June cases are over warm waters of the Gulf Stream and have a cloud top height over 3 km, but the 07 June case is more polluted and has larger LWC. We find that the N a ‐induced LWP adjustment is dominated by precipitation feedback for the 2 June precipitating case and there is no clear entrainment feedback in both cases. An increase of cloud fraction due to a decrease of aerosol number concentration is also shown in the simulations for the 02 June case.

54 ENVIRONMENTAL SCIENCES↗

Reconstructing phase-resolved hysteresis loops from first-order reversal curves

The first order reversal curve (FORC) method is a magnetometry based technique used to capture nanoscale magnetic phase separation and interactions with macroscopic measurements using minor hysteresis loop analysis. This makes the FORC technique a powerful tool in the analysis of complex systems which cannot be effectively probed using localized techniques. However, recovering quantitative details about the identified phases which can be compared to traditionally measured metrics remains an enigmatic challenge. We demonstrate a technique to reconstruct phase-resolved magnetic hysteresis loops by selectively integrating the measured FORC distribution. From these minor loops, the traditional metrics—including the coercivity and saturation field, and the remanent and saturation magnetization—can be determined. In order to perform this analysis, special consideration must be paid to the accurate quantitative management of the so-called reversible features. This technique is demonstrated on three representative materials systems, high anisotropy FeCuPt thin-films, Fe nanodots, and SmCo/Fe exchange spring magnet films, and shows excellent agreement with the direct measured major loop, as well as the phase separated loops.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

X-ray Computed Tomography as a Metrology Technique for the Analysis of Additively Manufactured Material

X-ray computed tomography (X-ray CT) is an analytical technique used in materials science to non-destructively characterize features in a variety materials like polymer, metals, composites, and explosives. It also has the capability of imaging additively manufacture, machine and assembled parts. The non-destructive imaging allows for the analysis of features (voids and cracks), which give a fundamental understanding of the material characteristics. Additionally, X-ray CT can obtain accurate measurements of dimensional and topographic variations due to different stimuli and assess the accuracy of material production. This study focuses on parts manufactured via metal additive manufacturing (AM). Although AM produces parts faster and easier, the printing process can produce defects (pores and surface roughness) that undermine the part’s mechanical properties and performance. The analysis of 3D printed objects has an asset in that the material has an STL file from which the item was printed, which is not available in many manufactured materials (i.e., foams) due to stochastic structures. For this study, the print accuracy of four additively manufactured cylinders will be assessed via X-ray CTto approximate the surface roughness and visualize any major morphological changes to assess the dimensional accuracy of complex additively manufactured parts. It was concluded that using X-ray CT to measure surface roughness was affective because reasonable surface roughness values were measured. Additionally, itwas determined that small-scale features can be produced via additive manufacturing with strong dimensional accuracy so long as the features are highly complex with sharp grooves.

36 MATERIALS SCIENCE↗

Field Measurement and Analysis of Frequency and RoCoF for Low-Inertia Power Systems

The frequency measurement and rate of change of frequency (RoCoF) calculations are important for active power, frequency control, and frequency-related protection in power system operations. With the rapid decrease in inertia under modern power systems, however, multiple power variations introduced by variable renewable energy bring large RoCoF and introduce oscillations in frequency measurements. To shed light on this issue, this article proposes a frequency measurement and RoCoF analysis technology, as well as the sensitivity analysis for the real low-inertia power grid. First, a real-world event in an island power grid is analyzed as an example, and an event numerical model is estimated considering four uncertainties, including event RoCoF, oscillation magnitude, oscillation frequency, and underfrequency load-shedding threshold. Then, a sensitivity analysis is performed using the Sobol indices method and quasi-Monte Carlo simulations to identify the dominant uncertainties based on the event model. Here, the dominant uncertainties are compared to provide a guideline for the frequency estimation algorithm selection under different event cases. This algorithm is compared with an enhanced zero-crossing algorithm and gives a 3.41% better RoCoF error rate. Finally, an experiment is conducted using universal grid analyzers to validate the simulation results and the theoretical analysis.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Design optimization of an ethanol heavy-duty engine using design of experiments and bayesian optimization

Diesel-fueled engines still hold a large market share in the medium and heavy-duty transportation sector. However, the increase in fossil fuel prices and the strict emission regulations are leading engine manufacturers to seek cleaner alternatives without a compromise in performance. Alcohol-based fuels, such as ethanol, offer a promising alternative to diesel fuel in meeting regulatory demands. Ethanol provides cleaner combustion and lower levels of soot due to its chemical properties, in particular its lower level of carbon content. In addition, the stoichiometric operating conditions of alcohol fueled engines enable the mitigation of NOx emissions in aftertreatment stage. With the promise of retrofitting diesel engines to run on ethanol to reduce emissions, the thermal efficiency of these engines remains the primary optimization target. In order to find the optimal ethanol-fueled engine design that maximizes the thermal efficiency, a large design space needs to be investigated using engineering tools. In this study, previous research by the authors on optimizing the design of a single-cylinder ethanol-fueled engine was extended to explore the design space for a heavy-duty multi-cylinder engine configuration. A heavy-duty engine setup with multiple operating conditions at different engine speeds and loads were considered. A design optimization analysis was performed to identify the potential designs that maximize the indicated thermal efficiency in an ethanol-fueled compression ignition engine. First, a computational fluid dynamics (CFD) model of the engine was validated using experimental data for four drive cycle points. Using a design of experiments (DoE) approach and a parameterized piston bowl geometry, the model was then exercised to explore the relationship among geometric features of the piston bowl and spray targeting angle and indicated thermal efficiency across all tested operating conditions. After evaluating 165~candidate designs, a piston bowl geometry was identified that yielded an increase between 1.3 to 2.2 percentage points in indicated thermal efficiency for all tested conditions, while satisfying the operational design constraints for peak pressure and maximum pressure rise rate. The increased performance was attributed to enhanced mixing that led to the formation of a more homogeneous distribution of in-cylinder temperature and equivalence ratio, higher combustion temperatures, and shorter combustion duration. Finally, a Bayesian optimization (BOpt) analysis was employed to find the optimal piston bowl geometry with a fixed spray injector angle for one of the operating conditions. Using BOpt, a piston candidate was identified that resulted in a 1.9~percentage point increase in thermal efficiency from the baseline design, yet only required 65\% of the design samples investigated using the DoE approach.

Tekgul, Bulut↗

Limitations of cetane number to predict transient combustion phenomena in high-pressure fuel sprays

Fundamental understanding of in-cylinder processes in diesel engines is important to screen emerging biofuels and advanced combustion modes that can reduce greenhouse gas emissions and regulated pollutants including soot. In this study, the role of fuel properties on spray development and combustion is investigated by systematically isolating chemical and thermophysical effects. Three different fuels are considered, two with similar chemical properties and two with similar thermophysical properties with one fuel common to both groups. Experiments are performed in a constant-pressure flow chamber de-signed to provide stable test conditions and facilitate acquisition of at least 150 injections in quick succession for each fuel under reacting conditions at high-pressure, high-temperature ambient conditions using a modified conventional diesel engine injector. Further, high speed optical diagnostics including rainbow schlieren deflectometry, OH* chemiluminescence, and a two-color pyrometry system are employed to simultaneously image the transient spray and reacting jets. Image analysis is performed to determine liquid length, vapor penetration length, timing and location of first stage and main ignition events, lift-off location, total soot mass, and more. Results show that fuels with similar chemical properties or cetane number (CN) exhibit similar delay times for first stage and main ignition events as may be expected, but very different liquid length, first stage and main ignition locations, lift-off length, apparent turbulent flame speed, and soot formation. As such, the ability to characterize candidate biofuels with CN or other parameters derived from simple flame configurations is called into question. In this study, thermo-physical properties controlling the liquid length are identified as the main contributing factor for the observed differences.

33 ADVANCED PROPULSION SYSTEMS↗

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗

Proteogenomic characterization of difficult-to-treat breast cancer with tumor cells enriched through laser microdissection

Abstract Background Breast cancer (BC) is the most commonly diagnosed cancer and the leading cause of cancer death among women globally. Despite advances, there is considerable variation in clinical outcomes for patients with non-luminal A tumors, classified as difficult-to-treat breast cancers (DTBC). This study aims to delineate the proteogenomic landscape of DTBC tumors compared to luminal A (LumA) tumors. Methods We retrospectively collected a total of 117 untreated primary breast tumor specimens, focusing on DTBC subtypes. Breast tumors were processed by laser microdissection (LMD) to enrich tumor cells. DNA, RNA, and protein were simultaneously extracted from each tumor preparation, followed by whole genome sequencing, paired-end RNA sequencing, global proteomics and phosphoproteomics. Differential feature analysis, pathway analysis and survival analysis were performed to better understand DTBC and investigate biomarkers. Results We observed distinct variations in gene mutations, structural variations, and chromosomal alterations between DTBC and LumA breast tumors. DTBC tumors predominantly had more mutations inTP53,PLXNB3, Zinc finger genes, and fewer mutations inSDC2,CDH1,PIK3CA,SVIL, andPTEN. Notably, Cytoband 1q21, which contains numerous cell proliferation-related genes, was significantly amplified in the DTBC tumors. LMD successfully minimized stromal components and increased RNA–protein concordance, as evidenced by stromal score comparisons and proteomic analysis. Distinct DTBC and LumA-enriched clusters were observed by proteomic and phosphoproteomic clustering analysis, some with survival differences. Phosphoproteomics identified two distinct phosphoproteomic profiles for high relapse-risk and low relapse-risk basal-like tumors, involving several genes known to be associated with breast cancer oncogenesis and progression, includingKIAA1522,DCK,FOXO3,MYO9B,ARID1A,EPRS,ZC3HAV1, andRBM14. Lastly, an integrated pathway analysis of multi-omics data highlighted a robust enrichment of proliferation pathways in DTBC tumors. Conclusions This study provides an integrated proteogenomic characterization of DTBC vs LumA with tumor cells enriched through laser microdissection. We identified many common features of DTBC tumors and the phosphopeptides that could serve as potential biomarkers for high/low relapse-risk basal-like BC and possibly guide treatment selections.

Oncology↗

Velocity reconstruction in the era of DESI and Rubin/LSST. I. Exploring spectroscopic, photometric, and hybrid samples

Peculiar velocities of galaxies and halos can be reconstructed from their spatial distribution alone. This technique is analogous to the baryon acoustic oscillations reconstruction, using the continuity equation to connect density and velocity fields. The resulting reconstructed velocities can be used to measure imprints of galaxy velocities on the cosmic microwave background like the kinematic Sunyaev-Zel’dovich effect or the moving lens effect. As the precision of these measurements increases, characterizing the performance of the velocity reconstruction becomes crucial to allow unbiased and statistically optimal inference. In this paper, we quantify the relevant performance metrics: the variance of the reconstructed velocities and their correlation coefficient with the true velocities. We show that the relevant velocities to reconstruct for kSZ and moving lens are actually the halo—rather than galaxy—velocities. We quantify the impact of redshift-space distortions, photometric redshift errors, satellite galaxy fraction, incorrect cosmological parameter assumptions and smoothing scale on the reconstruction performance. Here, we also investigate hybrid reconstruction methods, where velocities inferred from spectroscopic samples are evaluated at the positions of denser photometric samples. We find that using exclusively the photometric sample is better than performing a hybrid analysis. The 2 Gpc/ℎ length simulations from abacussummit with realistic galaxy samples for DESI and Rubin LSST allow us to perform this analysis in a controlled setting. In the companion paper [B. Hadzhiyska, S. Ferraro, B. Ried Guachalla, and E. Schaan, companion paper, Phys. Rev. D 109, 103534 (2024).], we further include the effects of evolution along the light cone and give realistic performance estimates for DESI luminous red galaxies, emission line galaxies, and Rubin LSST-like samples.

79 ASTRONOMY AND ASTROPHYSICS↗