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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.

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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Semi-supervised machine-learning classification of materials synthesis procedures

Digitizing large collections of scientific literature can enable new informatics approaches for scientific analysis and meta-analysis. However, most content in the scientific literature is locked-up in written natural language, which is difficult to parse into databases using explicitly hard-coded classification rules. In this work, we demonstrate a semi-supervised machine-learning method to classify inorganic materials synthesis procedures from written natural language. Without any human input, latent Dirichlet allocation can cluster keywords into topics corresponding to specific experimental materials synthesis steps, such as “grinding” and “heating”, “dissolving” and “centrifuging”, etc. Guided by a modest amount of annotation, a random forest classifier can then associate these steps with different categories of materials synthesis, such as solid-state or hydrothermal synthesis. Finally, we show that a Markov chain representation of the order of experimental steps accurately reconstructs a flowchart of possible synthesis procedures. Our machine-learning approach enables a scalable approach to unlock the large amount of inorganic materials synthesis information from the literature and to process it into a standardized, machine-readable database.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Machine learning-based discovery of vibrationally stable materials

The identification of the ground state phases of a chemical space in the convex hull analysis is a key determinant of the synthesizability of materials. Online material databases have been instrumental in exploring one aspect of the synthesizability of many materials, namely thermodynamic stability. However, the vibrational stability, which is another aspect of synthesizability, of new materials is not known. Applying first principles approaches to calculate the vibrational spectra of materials in online material databases is computationally intractable. Here, a dataset of vibrational stability for ~3100 materials is used to train a machine learning classifier that can accurately distinguish between vibrationally stable and unstable materials. This classifier has the potential to be further developed as an essential filtering tool for online material databases that can inform the material science community of the vibrational stability or instability of the materials queried in convex hulls.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Machine learning of high dimensional data on a noisy quantum processor

Abstract Quantum kernel methods show promise for accelerating data analysis by efficiently learning relationships between input data points that have been encoded into an exponentially large Hilbert space. While this technique has been used successfully in small-scale experiments on synthetic datasets, the practical challenges of scaling to large circuits on noisy hardware have not been thoroughly addressed. Here, we present our findings from experimentally implementing a quantum kernel classifier on real high-dimensional data taken from the domain of cosmology using Google’s universal quantum processor, Sycamore. We construct a circuit ansatz that preserves kernel magnitudes that typically otherwise vanish due to an exponentially growing Hilbert space, and implement error mitigation specific to the task of computing quantum kernels on near-term hardware. Our experiment utilizes 17 qubits to classify uncompressed 67 dimensional data resulting in classification accuracy on a test set that is comparable to noiseless simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Permutable SOS (symmetry operational similarity)

Abstract Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type and discuss their symmetry operational similarity (SOS) relationships, which are often permutable. A number of recent experimental observations, including current-induced magnetization in polar or chiral conductors, non-linear Hall effect in polar conductors, spin-polarization of tunneling current to chiral conductors, and ferro-rotational domain imaging with linear gyration are discussed in terms of (permutable) SOS. In addition, based on (permutable) SOS, we predict a large number of new phenomena in low symmetry materials that can be experimentally verified in the future.

Materials Science↗
DOE OSTI2018

Climate sensitive size-dependent survival in tropical trees

Survival rates of large trees determine forest biomass dynamics. Survival rates of small trees are linked to mechanisms that maintain biodiversity across tropical forests. How species survival rates change with size offers insight into the links between biodiversity and ecosystem function across tropical forests. We tested patterns of size-dependent tree survival across the tropics using data from 1781 species and over two million individuals to assess whether tropical forests can be characterized by size-dependent life-history survival strategies. We found species were classifiable into four “survival modes” that explain life-history variation that shapes carbon-cycling and the relative abundances within forests. Frequently collected functional traits, such as wood density, leaf mass per area, and seed mass, were not generally predictive of species’ survival modes. Mean annual temperature and cumulative water deficit predicted the proportion of biomass of survival modes, indicating important links between evolutionary strategies, climate, and carbon cycling. The application of survival modes in demographic simulations predicted biomass change across forest sites. Our results reveal globally identifiable size-dependent survival strategies that differ across diverse systems in a consistent way. The abundance of survival modes and interaction with climate ultimately determine forest structure, carbon storage in biomass, and future forest trajectories.

Johnson, Daniel J.↗
DOE OSTI2019

Data-driven prediction of battery cycle life before capacity degradation

Accurately predicting the lifetime of complex, nonlinear systems such as lithium-ion batteries is critical for accelerating technology development. However, diverse aging mechanisms, significant device variability and dynamic operating conditions have remained major challenges. We generate a comprehensive dataset consisting of 124 commercial lithium iron phosphate/graphite cells cycled under fast-charging conditions, with widely varying cycle lives ranging from 150 to 2,300 cycles. Using discharge voltage curves from early cycles yet to exhibit capacity degradation, we apply machine-learning tools to both predict and classify cells by cycle life. Our best models achieve 9.1% test error for quantitatively predicting cycle life using the first 100 cycles (exhibiting a median increase of 0.2% from initial capacity) and 4.9% test error using the first 5 cycles for classifying cycle life into two groups. This work highlights the promise of combining deliberate data generation with data-driven modelling to predict the behaviour of complex dynamical systems.

25 ENERGY STORAGE↗
DOE OSTI2019

Evolutionary characteristics of intergenic transcribed regions indicate rare novel genes and widespread noisy transcription in the Poaceae

Abstract Extensive transcriptional activity occurring in intergenic regions of genomes has raised the question whether intergenic transcription represents the activity of novel genes or noisy expression. To address this, we evaluated cross-species and post-duplication sequence and expression conservation of intergenic transcribed regions (ITRs) in four Poaceae species. Among 43,301 ITRs across the four species, 34,460 (80%) are species-specific. ITRs found across species tend to be more divergent in expression and have more recent duplicates compared to annotated genes. To assess if ITRs are functional (under selection), machine learning models were established in Oryza sativa (rice) that could accurately distinguish between phenotype genes and pseudogenes (area under curve-receiver operating characteristic = 0.94). Based on the models, 584 (8%) and 4391 (61%) rice ITRs are classified as likely functional and nonfunctional with high confidence, respectively. ITRs with conserved expression and ancient retained duplicates, features that were not part of the model, are frequently classified as likely-functional, suggesting these characteristics could serve as pragmatic rules of thumb for identifying candidate sequences likely to be under selection. This study also provides a framework to identify novel genes using comparative transcriptomic data to improve genome annotation that is fundamental for connecting genotype to phenotype in crop and model systems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets

Advanced materials characterization techniques with ever-growing data acquisition speed and storage capabilities represent a challenge in modern materials science, and new procedures to quickly assess and analyze the data are needed. Machine learning approaches are effective in reducing the complexity of data and rapidly homing in on the underlying trend in multi-dimensional data. Here, we show that by employing an algorithm called the mean shift theory to a large amount of diffraction data in high-throughput experimentation, one can streamline the process of delineating the structural evolution across compositional variations mapped on combinatorial libraries with minimal computational cost. Data collected at a synchrotron beamline are analyzed on the fly, and by integrating experimental data with the inorganic crystal structure database (ICSD), we can substantially enhance the accuracy in classifying the structural phases across ternary phase spaces. We have used this approach to identify a novel magnetic phase with enhanced magnetic anisotropy which is a candidate for rare-earth free permanent magnet.

Kusne, AG↗
DOE OSTI2015

Classification of octet AB-type binary compounds using dynamical charges: A materials informatics perspective

The role of dynamical (or Born effective) charges in classification of octet AB-type binary compounds between four-fold (zincblende/wurtzite crystal structures) and six-fold (rocksalt crystal structure) coordinated systems is discussed. We show that the difference in the dynamical charges of the fourfold and sixfold coordinated structures, in combination with Harrison’s polarity, serves as an excellent feature to classify the coordination of 82 sp–bonded binary octet compounds. We use a support vector machine classifier to estimate the average classification accuracy and the associated variance in our model where a decision boundary is learned in a supervised manner. Lastly, we compare the out-of-sample classification accuracy achieved by our feature pair with those reported previously.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Antimicrobial resistance prediction in PATRIC and RAST

The emergence and spread of antimicrobial resistance (AMR) mechanisms in bacterial pathogens, coupled with the dwindling number of effective antibiotics, has created a global health crisis. Being able to identify the genetic mechanisms of AMR and predict the resistance phenotypes of bacterial pathogens prior to culturing could inform clinical decision-making and improve reaction time. At PATRIC (http://patricbrc.org/), we have been collecting bacterial genomes with AMR metadata for several years. In order to advance phenotype prediction and the identification of genomic regions relating to AMR, we have updated the PATRIC FTP server to enable access to genomes that are binned by their AMR phenotypes, as well as metadata including minimum inhibitory concentrations. Using this infrastructure, we custom built AdaBoost (adaptive boosting) machine learning classifiers for identifying carbapenem resistance in Acinetobacter baumannii , methicillin resistance in Staphylococcus aureus , and beta-lactam and co-trimoxazole resistance in Streptococcus pneumoniae with accuracies ranging from 88–99%. We also did this for isoniazid, kanamycin, ofloxacin, rifampicin, and streptomycin resistance in Mycobacterium tuberculosis , achieving accuracies ranging from 71–88%. Lastly, this set of classifiers has been used to provide an initial framework for species-specific AMR phenotype and genomic feature prediction in the RAST and PATRIC annotation services.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Understanding, quantifying, and controlling the molecular ordering of semiconducting polymers: from novices to experts and amorphous to perfect crystals

Molecular packing and texture of semiconducting polymers are often critical to the performance of devices using these materials. Although frameworks exist to quantify the ordering, interpretations are often just qualitative, resulting in imprecise use of terminology. Here, we reemphasize the significance of quantifying molecular ordering in terms of degree of crystallinity (volume fractions that are ordered) and quality of ordering and their relation to the size scale of an ordered region. We are motivated in part by our own imprecise and inconsistent use of terminology in the past, as well as the need to have a primer or tutorial reference to teach new group members. We strive to develop and use consistent terminology with regards to crystallinity, semicrystallinity, paracrystallinity, and related characteristics. To account for vastly different quality of ordering along different directions, we classify paracrystals into 2D and 3D paracrystals and use paracrystallite to describe the spatial extent of molecular ordering in 1–10 nm. We show that a deeper understanding of molecular ordering can be achieved by combining grazing-incidence wide-angle X-ray scattering and differential scanning calorimetry, even though not all aspects of these measurements are consistent, and some classification appears to be method dependent. We classify a broad range of representative polymers under common processing conditions into five categories based on the quantitative analysis of the paracrystalline disorder parameter (g) and thermal transitions. A small database is presented for 13 representative conjugated and insulating polymers ranging from amorphous to semi-paracrystalline. Lastly, we outline the challenges to rationally design more perfect polymer crystals and propose a new molecular design approach that envisions conceptual molecular grafting that is akin to strained and unstrained hetero-epitaxy in classic (compound) semiconductors thin film growth.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Creating ground truth for nanocrystal morphology: a fully automated pipeline for unbiased transmission electron microscopy analysis

Control over colloidal nanocrystal morphology (size, size distribution, and shape) is important for tailoring the functionality of individual nanocrystals and their ensemble behavior. Despite this, traditional methods to quantify nanocrystal morphology are laborious. New developments in automated morphology classification will accelerate these analyses but the assessment of machine learning models is limited by human accuracy for ground truth, causing even unsupervised machine learning models to have inherent bias. Herein, we introduce synthetic image rendering to solve the ground truth problem of nanocrystal morphology classification. By simulating 2D images of nanocrystal shapes via a function of high-dimensional parameter space, we trained a convolutional neural network to link unique morphologies to their simulated parameters, defining nanocrystal morphology quantitatively rather than qualitatively. An automated pipeline then processes, quantitatively defines, and classifies nanocrystal morphology from experimental transmission electron microscopy (TEM) images. Using improved computer vision techniques, 42,650 nanocrystals were identified, assessed, and labeled with quantitative parameters, offering a 600-fold improvement in efficiency over best-practice manual measurements. Further, a classification algorithm was trained with a prediction accuracy of 99.5%, which can successfully analyze a range of concave, convex, and irregular nanocrystal shapes. The resulting pipeline was applied to differentiating two syntheses of nominally cuboidal CsPbBr 3 nanocrystals and uniquely classifying binary nickel sulfide nanocrystal phase based on morphology. This pipeline provides a simple, efficient, and unbiased method to quantify nanocrystal morphology and represents a practical route to construct large datasets with an absolute ground truth for training unbiased morphology-based machine learning algorithms.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Identification of linearised RMS-voltage dip patterns based on clustering in renewable plants

Generation units connected to the grid are currently required to meet low-voltage ride-through (LVRT) requirements. In most developed countries, these requirements also apply to renewable sources, mainly wind power plants and photovoltaic installations connected to the grid. This study proposes an alternative characterisation solution to classify and visualise a large number of collected events in light of current limits and requirements. The authors' approach is based on linearised root-mean-square-(RMS)-voltage trajectories, taking into account LRVT requirements, and a clustering process to identify the most likely pattern trajectories. The proposed solution gives extensive information on an event's severity by providing a simple but complete visualisation of the linearised RMS-voltage patterns. In addition, these patterns are compared to current LVRT requirements to determine similarities or discrepancies. A large number of collected events can then be automatically classified and visualised for comparative purposes. Real disturbances collected from renewable sources in Spain are used to assess the proposed solution. Extensive results and discussions are also included in this study.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Hybrid approach for estimating dynamic states of synchronous generators

Accurate and robust estimation of dynamic states is essential for monitoring and controlling a power grid. To achieve higher accuracy and robustness, this paper proposes a hybrid estimation approach to estimate the dynamic states of synchronous generators using multiple models, classified into a set of local models and a wide-area model. The proposed estimation approach, first, estimates dynamic states using the extended Kalman filter (EKF) based on a local model and a wide-area model. Then, at each time step, probability indexes, which quantify the likelihood of both local and wide-area models, are determined using hypothesis testing based on measurements innovations. Finally, using the weighted fix approach, the states estimated from the local and wide-area models are combined based on their probability indexes. Simulation studies using the two-area four-machine system shows that the proposed approach can improve estimation accuracy and increase robustness against model errors.

Akhlaghi, Shahrokh↗
DOE OSTI2015

PESSTO: survey description and products from the first data release by the Public ESO Spectroscopic Survey of Transient Objects

Context. The Public European Southern Observatory Spectroscopic Survey of Transient Objects (PESSTO) began as a public spectroscopic survey in April 2012. PESSTO classifies transients from publicly available sources and wide-field surveys, and selects science targets for detailed spectroscopic and photometric follow-up. PESSTO runs for nine months of the year, January - April and August - December inclusive, and typically has allocations of 10 nights per month. Aims. We describe the data reduction strategy and data products that are publicly available through the ESO archive as the Spectroscopic Survey data release 1 (SSDR1). Methods. PESSTO uses the New Technology Telescope with the instruments EFOSC2 and SOFI to provide optical and NIR spectroscopy and imaging. We target supernovae and optical transients brighter than 20.5m for classification. Science targets are selected for follow-up based on the PESSTO science goal of extending knowledge of the extremes of the supernova population. We use standard EFOSC2 set-ups providing spectra with resolutions of 13-18 Å between 3345-9995 Å. A subset of the brighter science targets are selected for SOFI spectroscopy with the blue and red grisms (0.935-2.53 μm and resolutions 23-33 Å) and imaging with broadband JHKs filters. Results. This first data release (SSDR1) contains flux calibrated spectra from the first year (April 2012-2013). A total of 221 confirmed supernovae were classified, and we released calibrated optical spectra and classifications publicly within 24 h of the data being taken (via WISeREP). The data in SSDR1 replace those released spectra. They have more reliable and quantifiable flux calibrations, correction for telluric absorption, and are made available in standard ESO Phase 3 formats. We estimate the absolute accuracy of the flux calibrations for EFOSC2 across the whole survey in SSDR1 to be typically ~15%, although a number of spectra will have less reliable absolute flux calibration because of weather and slit losses. Acquisition images for each spectrum are available which, in principle, can allow the user to refine the absolute flux calibration. The standard NIR reduction process does not produce high accuracy absolute spectrophotometry but synthetic photometry with accompanying JHKs imaging can improve this. Whenever possible, reduced SOFI images are provided to allow this. Conclusions. Future data releases will focus on improving the automated flux calibration of the data products. The rapid turnaround between discovery and classification and access to reliable pipeline processed data products has allowed early science papers in the first few months of the survey.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

PTF12os and iPTF13bvn: Two stripped-envelope supernovae from low-mass progenitors in NGC 5806

Context. In this paper, we investigate two stripped-envelope supernovae (SNe) discovered in the nearby galaxy NGC 5806 by the (intermediate) Palomar Transient Factory [(i)PTF]. These SNe, designated PTF12os/SN 2012P and iPTF13bvn, exploded within ~520 days of one another at a similar distance from the host-galaxy center. We classify PTF12os as a Type IIb SN based on our spectral sequence; iPTF13bvn has previously been classified as Type Ib having a likely progenitor with zero age main sequence (ZAMS) mass below ~17 M ⊙ . Because of the shared and nearby host, we are presented with a unique opportunity to compare these two SNe. Aims. Our main objective is to constrain the explosion parameters of iPTF12os and iPTF13bvn, and to put constraints on the SN progenitors. We also aim to spatially map the metallicity in the host galaxy, and to investigate the presence of hydrogen in early-time spectra of both SNe. Methods. We present comprehensive datasets collected on PTF12os and iPTF13bvn, and introduce a new automatic reference-subtraction photometry pipeline (FPipe) currently in use by the iPTF. We perform a detailed study of the light curves (LCs) and spectral evolution of the SNe. The bolometric LCs are modeled using the hydrodynamical code hyde. We analyze early spectra of both SNe to investigate the presence of hydrogen; for iPTF13bvn we also investigate the regions of the Paschen lines in infrared spectra. We perform spectral line analysis of helium and iron lines to map the ejecta structure of both SNe. We use nebular models and late-time spectroscopy to constrain the ZAMS mass of the progenitors. We also perform image registration of ground-based images of PTF12os to archival HST images of NGC 5806 to identify a potential progenitor candidate. Results. We find that our nebular spectroscopy of iPTF13bvn remains consistent with a low-mass progenitor, likely having a ZAMS mass of ~12M ⊙ . Our late-time spectroscopy of PTF12os is consistent with a ZAMS mass of ~15M ⊙ . We successfully identify a source in pre-explosion HST images coincident with PTF12os. The colors and absolute magnitude of this object are consistent between pre-explosion and late-time HST images, implying it is a cluster of massive stars. Our hydrodynamical modeling suggests that the progenitor of PTF12os had a compact He core with a mass of 3.25 + 0.77 -0.56 M ⊙ at the time of the explosion, which had a total kinetic energy of 0.54 + 0.41 -0.25 × 10 51 erg and synthesized 0.063 + 0.020 -0.011 M ⊙ of strongly mixed 56 Ni. Spectral comparisons to the Type IIb SN 2011dh indicate that the progenitor of PTF12os was surrounded by a thin hydrogen envelope with a mass lower than 0.02M ⊙ . We also find tentative evidence that the progenitor of iPTF13bvn could have been surrounded by a small amount of hydrogen prior to the explosion. Finally, this result is supported by possible weak signals of hydrogen in both optical and infrared spectra.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Abell 1430: A merging cluster with exceptional diffuse radio emission

Diffuse radio emission has been found in many galaxy clusters, predominantly in massive systems which are in the state of merging. The radio emission can usually be classified as relic or halo emission, which are believed to be related to merger shocks or volume-filling turbulence, respectively. Recent observations have revealed radio bridges for some pairs of very close galaxy clusters. The mechanisms that may allow one to explain the high specific density of relativistic electrons, which are necessary to explain the radio luminosity of these bridge regions, have been poorly explored until now. When inspecting the first data release of the LOFAR Two-Metre Sky Survey (LoTSS), we discovered diffuse radio emission in the galaxy cluster Abell 1430. Here, for this work, we aim to determine the dynamical state of the cluster and characterise the diffuse radio emission. We analysed the LoTSS data in detail and complemented them with recent Karl G. Jansky Very Large Array observations in the L-band. To study the dynamical state of the cluster, we analysed XMM-Newton data, Chandra data, and Sloan Digital Sky Survey data. Moreover, we compared our results to clusters extracted from THE THREE HUNDRED PROJECT cosmological simulation. We find that Abell 1430 consists of two components, namely A1430-A and A1430-B, with a mass ratio of about 2:1. The massive component shows diffuse radio emission which can be classified as radio halo which shows a low radio power at 1.4 GHz with respect to the mass of the cluster. Most interestingly, there is extended diffuse radio emission in the following dubbed as the ‘Pillow’ according to its morphology, which is apparently related to A1430-B and which is neither typical halo nor typical relic emission. The origin of this emission is puzzling. We speculate that the two components of Abell 1430 undergo an off-axis merger. In this scenario, A1430-B is moving towards the main cluster component and may have compressed and stirred the medium in the filament between the two cluster components. We have discovered evidence for diffuse radio emission related to the low-density intracluster or intergalactic medium in Abell 1430. To date, only a few examples of emission originating from such regions are known. These discoveries are crucial to constrain possible acceleration mechanisms which may allow us to explain the presence of relativistic electrons in these regions. In particular, our results indicate a spectral index of α 144 MHz 1.5 GHz = -1.4±0.5 for the Pillow. If upcoming observations confirm a slope as flat as -1.4 or even flatter, this would pose a challenge for the electron acceleration scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Disturbed, diffuse, or just missing? A global study of the H I content of Hickson compact groups

Hickson compact groups (HCGs) are dense configurations of four to ten galaxies, whose H I morphology appears to follow an evolutionary sequence of three phases, with gas initially confined to galaxies, then significant amounts spread throughout the intra-group medium, and finally with almost no gas remaining in the galaxies themselves. It has also been suggested that several groups may harbour a diffuse H I component that is resolved out by interferometric observations. The H I deficiency of HCGs is expected to increase as the H I morphological phase progresses along the evolutionary sequence. If this is the case, H I deficiency would be a rough proxy for the age and evolutionary state of a HCG. We aim to test this hypothesis for the first time using a large sample of HCGs and to investigate the evidence for diffuse H I in HCGs. We performed a uniform reduction of all publicly available VLA H I observations (38 HCGs) with a purpose-built pipeline that also maximises the reproducibility of this study. The resulting H I data cubes were then analysed with the latest software tools to perform a manual separation of emission features into those belonging to galaxies and those extending into the intra-group medium. We thereby classified the H I morphological phase of each group as well as quantified their H I deficiency compared to galaxies in isolation. We find little evidence that H I deficiency can be used as a proxy for the evolutionary phase of a compact group in either of the first two phases, with the distribution of H I deficiency being consistent in both. However, for the final phase, the distribution clearly shifts to high H I deficiencies, with more than 90% of the expected H I content typically missing. Across all HCGs studied, we identify a few cases where there is strong evidence for a diffuse gas component in the intra-group medium, which might be detectable with improved observations. We also classify a new sub-phase where groups contain a lone H I -bearing galaxy, but are otherwise devoid of gas. The new morphological phase we have identified is likely the result of an evolved, gas-poor group acquiring a new, gas-rich member. The large spread of H I deficiencies in the first two morphological phases suggests that there is a broad range of initial H I content in HCGs, which is perhaps influenced by large-scale environment, and that the timescale for morphological changes is, in general, considerably shorter than the timescale for the destruction or consumption of neutral gas in these systems.

79 ASTRONOMY AND ASTROPHYSICS↗