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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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DOE OSTI2024

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

An ICP-OES method for the precise and accurate quantification of rare earth elements in natural water: A comparative study from mine waste sites in New Mexico, USA

Inductively coupled plasma techniques such as ICP-OES and ICP-MS are routinely used to determine the concentrations of rare earth elements (REE) in water samples. However, their performance for the determination of REE concentration in mine drainage waters from epithermal vein and porphyry copper mining districts has not been evaluated extensively. In this work, we develop an REE analysis method on an Agilent 5900 ICP-OES instrument and assess the accuracy and precision for the quantification of REE in the natural waters collected from mine adits and an acid seep of mine sites in the Steeple Rock and Hillsboro mining districts, New Mexico, USA. The total REE concentrations in the water samples were measured using the methods we developed for both ICP-OES and ICP-MS. The power of the new ICP-OES method lies in routine analysis of μg/L level concentrations normally analyzed using ICP-MS, including a U.S. Geological Survey standard reference sample, laboratory blank samples spiked with a National Institute of Standards and Technology traceable standard, and surface water samples from mine waste sites. This ICP-OES method achieves low quantification limits ranging from 0.2 to 5 μg/L and excellent analytical accuracy and precision for REE analysis. The precision of light (La-Gd) and heavy (Tb-Lu) REE analysis using this method are better than 5% at average concentrations above 5 ± 4 μg/L and 3 ± 2 μg/L, respectively, and 3% at average concentrations above 10 ± 9 μg/L and 5 ± 4 μg/L, respectively. This method also shows excellent sensitivity and reproducibility for our laboratory and field samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

An In Situ , Automated High-Explosives Aging Method Utilizing Two-Dimensional Gas Chromatography–Mass Spectrometry

Understanding chemical changes that occur in high explosives as they age is of great importance to the safe employment and storage of these compounds. Traditional methods of aging high explosives even under accelerated aging conditions are time intensive with durations on the order of months to years. The nature of traditional aging analyses reduces each sample to a snapshot data point often separated widely in time, requiring many assumptions as to how the degradation products develop. Further complicating matters, several analytical techniques are typically employed for each sample analysis in order to ascertain an entire picture of the decomposition pathways. To address these shortcomings with existing methods, a new method of accelerated aging of high explosives utilizing comprehensive two-dimensional gas chromatography coupled to high-resolution mass spectrometry (GC × GC-HRMS) was developed using 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) as a model compound for method development. This in situ automated method reduces the time scale of aging to a matter of hours using the inlet of the GC × GC as the aging vessel. GC × GC in combination with HRMS allowed for the collection of both evolved gases and other decomposition products produced during the entire aging process in real time with HRMS providing far greater certainty in identification of explosives aging products. Additionally, this method allowed for a higher throughput of samples with greatly simplified sample preparation. Chemometric analysis of the GC × GC-HRMS data set via the alteration analysis (ALA) enabled discovery of statistically significant chemical changes providing insight into the variation of decomposition pathways with varying aging temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Advancing density functional tight-binding method for large organic molecules through equivariant neural networks

Semi-empirical quantum-mechanical (QM) methods have become valuable tools for studying complex (bio)molecular systems due to their balance between computational efficiency and accuracy. A key aspect of these methods is their parameterization, which not only governs the reliability of the results but also provides an opportunity to enhance their overall performance. In our previous work [J. Phys. Chem. Lett., 2021, 11, 16], we advanced the third-order semi-empirical density functional tight-binding (DFTB3) method for computing multiple properties of small molecules by developing the machine learning (ML) potential NN rep to bridge the gap between DFTB3 electronic components and those of the hybrid DFT-PBE0 functional. To overcome the limitations of NN rep , we introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks (NN) to parameterize scalable and transferable many-body Δ TB potentials, replacing the standard pairwise DFTB repulsive potential. This advancement extends the applicability of our ML-corrected DFTB approach to larger molecules and non-covalent systems (including only C, N, O, and H atoms), going beyond the chemical space represented in the training QM datasets. The enhanced performance of EquiDTB over the standard TB methods is demonstrated by the accurate computation of the atomic forces of S66x8 molecular dimers, as well as their interaction energies. Moreover, EquiDTB can be effectively employed to explore the potential energy surfaces of large and flexible drug-like molecules—for example, to determine the minimum energy path between isomers, analyze structural transitions during dynamical simulations, compute vibrational modes, and investigate energetic rankings. The performance for single molecules slightly decreases when the DFTB electronic energy is reduced to first-order but remains superior to standard TB methods. Our work thus demonstrates that an optimal integration of an equivariant NN with QM datasets can advance the DFTB method while maintaining high efficiency, paving the way for reliable (bio)molecular simulations.

Medrano Sandonas, Leonardo [Technische Universität↗
DOE OSTI2026

Calculations of enrichment cascade performance using enrichment probabilities – a new method

A new method for calculating the performance of uranium enrichment cascades is presented. The method assigns a unique “enrichment probability” for each isotope to move up or down from the basic enrichment unit, allowing independent material balance calculations for each isotope. The formulation is much simpler than previous methods, which rely on isotopic ratios, and this method can be used when previous methods fail. This method gives the same results as published cases for 235 U enrichment and also gives good agreement with published data on minor isotopes. Some comparisons with measured data and other calculations are given. One case shows that the maximum 235 U enrichment that can be obtained by enrichment of reprocessed uranium (0.02% 234 U initial) is 82%. Another example shows a large difference in the minor isotopic content of material enriched in batches compared to continuous enrichment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Sensitivity of magnetic islands in permanent magnet stellarators using the gradient and Hessian methods

Stellarator plasmas are known to be very sensitive to perturbations in the magnetic field. The permanent magnet stellarator was in part developed as a solution to high machining tolerances placed on the shape properties of electromagnetic coils in traditional stellarators. However, as a consequence of this high sensitivity to the field structure, sensitivities of permanent magnet stellarator plasmas to perturbations of permanent magnet properties must necessarily be well-understood. The gradient and Hessian matrix methods have been previously demonstrated to be useful sensitivity analysis methods for modular coils. We apply these two methods to the study of island width sensitivities in both the MUSE and PM4STELL permanent magnet stellarator projects. These sensitivity methods were used to determine the relative impacts of permanent magnet parameter perturbations on island widths in the vacuum field approximation of both stellarator equilibria. The square of resonant magnetic field perturbation is used here as a proxy for island width. In particular, gradients of magnetizations of individual magnets were examined in MUSE, as well as gradients of magnet group displacements informed by device design. Three different forms of permanent magnet magnetization perturbations are investigated for MUSE, and the flux surface response to perturbations is demonstrated. The Hessian matrix method is applied to PM4STELL, illustrating the sensitivity of dominant island widths to displacements of toroidal wedge structures. These methods allow for selective direction of experimental resources toward regions of heightened sensitivity, while constraints on less impactful permanent magnet parameters can be relaxed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Recent evolution of risk analyses in atomic bomb survivor studies: new methods and applications

Abstract Several decades ago a dramatic leap forward occurred in the development and application of statistical methods for modeling radiation risk at the Radiation Effects Research Foundation (RERF). Poisson regression analysis for grouped person-year cohort data and the linear excess relative risk model were introduced, and subsequently a devoted software system, Epicure® (https://www.hirosoft.com), was developed by researchers at RERF and at the U.S. National Cancer Institute. Numerous advancements in understanding radiation effects on humans were made possible with these methods, which are still the state-of-the-art for risk assessment at RERF and have remained part of the standard toolbox for radiation—and other environmental—epidemiological studies worldwide. Nevertheless, as our understanding of radiation risk has increased, so have the breadth and depth of questions that require answers based on emerging data that are not amenable to these conventional methods. This overview briefly recounts the conventional methods and then describes our recent diversification into the use or development of new statistical approaches to meet the challenges of burgeoning biological data and emerging mechanistic information. We briefly discuss the development and application of new methods, current and planned, that are part of the RERF Statistics Department’s role in supporting institution-wide research, especially in our collaborations involving the Life Span Study, Adult Health Study, and First-generation Offspring Clinical Study. Some approaches to modeling and assessing radiation risk with newer methods mentioned herein have already been published, while some are still in development or are only beginning at the proposal stage.

Oncology↗
DOE OSTI2024

The seventh blind test of crystal structure prediction: structure ranking methods

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol −1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

Chemistry↗
DOE OSTI2025

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Divide and conquer: using RhizoVision Explorer to aggregate data from multiple root scans using image concatenation and statistical methods

Roots are important in agricultural and natural systems for determining plant productivity and soil carbon inputs. Sometimes, the amount of roots in a sample is too much to fit into a single scanned image, so the sample is divided among several scans, and there is no standard method to aggregate the data. Here, we describe and validate two methods for standardizing measurements across multiple scans: image concatenation and statistical aggregation. We developed a Python script that identifies which images belong to the same sample and returns a single, larger concatenated image. These concatenated images and the original images were processed with RhizoVision Explorer, a free and open-source software. An R script was developed, which identifies rows of data belonging to the same sample and applies correct statistical methods to return a single data row for each sample. These two methods were compared using example images from switchgrass, poplar, and various tree and ericaceous shrub species from a northern peatland and the Arctic. Most root measurements were nearly identical between the two methods except median diameter, which cannot be accurately computed by statistical aggregation. We believe the availability of these methods will be useful to the root biology community.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials

Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adapting Traditional Hazards Analysis Methods to Address Cyber Risks

Traditional hazards analysis (HA) methods, originally developed to address physical and operational risks, often fall short when it comes to identifying and mitigating cyber threats. These cyber threats pose unique and evolving risks to critical infrastructure and industrial control systems (ICS). This report explores the integration of Cyber-Informed Engineering (CIE) principles into existing HA methods to enhance their ability to address cyber-induced risks. CIE provides organizations with a practical, cost-effective approach to closing the gap between traditional HA methods and the need for cyber risk mitigation. By leveraging existing safety processes and controls, CIE allows users to examine and mitigate cyber vulnerabilities without overhauling existing HA methods. This report identifies areas where HA and CIE naturally align and where their approaches diverge. It emphasizes how CIE principles can be used to adapt HA methods, broadening their scope to include cyber risks and enabling the mitigation of cyber- induced impacts alongside traditional hazards and failure scenarios. This report examines how CIE can be applied across various HA methods—such as Hazard and Operability Studies (HAZOP), Probabilistic Risk Assessment (PRA), Failure Modes and Effects Analysis (FMEA), Systems-Theoretic Process Analysis (STPA), Hazard and Consequence Analysis for Digital Systems (HAZCADS), and Layers of Protection Analysis (LOPA). It provides strategies for integrating CIE to strengthen the identification, assessment, and mitigation of cyber-induced risks. The findings offer a structured entry point for organizations to embed CIE concepts into hazards and safety analyses, as well as broader engineering processes, ultimately supporting the design and operation of a more resilient infrastructure.

42 ENGINEERING↗
DOE OSTI2025

Adapting Traditional Hazards Analysis Methods to Address Cyber Risks

Traditional hazards analysis (HA) methods, originally developed to address physical and operational risks, often fall short when it comes to identifying and mitigating cyber threats. These cyber threats pose unique and evolving risks to critical infrastructure and industrial control systems (ICS). This report explores the integration of Cyber-Informed Engineering (CIE) principles into existing HA methods to enhance their ability to address cyber-induced risks. CIE provides organizations with a practical, cost-effective approach to closing the gap between traditional HA methods and the need for cyber risk mitigation. By leveraging existing safety processes and controls, CIE allows users to examine and mitigate cyber vulnerabilities without overhauling existing HA methods. This report identifies areas where HA and CIE naturally align and where their approaches diverge. It emphasizes how CIE principles can be used to adapt HA methods, broadening their scope to include cyber risks and enabling the mitigation of cyber- induced impacts alongside traditional hazards and failure scenarios. This report examines how CIE can be applied across various HA methods—such as Hazard and Operability Studies (HAZOP), Probabilistic Risk Assessment (PRA), Failure Modes and Effects Analysis (FMEA), Systems-Theoretic Process Analysis (STPA), Hazard and Consequence Analysis for Digital Systems (HAZCADS), and Layers of Protection Analysis (LOPA). It provides strategies for integrating CIE to strengthen the identification, assessment, and mitigation of cyber-induced risks. The findings offer a structured entry point for organizations to embed CIE concepts into hazards and safety analyses, as well as broader engineering processes, ultimately supporting the design and operation of a more resilient infrastructure.

42 - ENGINEERING↗
DOE OSTI2026

Methods for safely sharing dual-use genetic data

Background: Some genetic data has dual-use potential. Sharing pathogen data has shown tremendous value. For example therapeutic development and lineage tracking during the COVID pandemic. This data sharing is complicated by the fact that these data have the potential to be used for harm. The genome sequence of a pathogen can be used to enable malicious genetic engineering approaches or to recreate the pathogen from synthetic DNA. Standard data security methods can be applied to genetic data, but when data is shared between institutions, ensuring appropriate security can be difficult. Sensitive data that is shared internationally among a wide array of institutions can be especially difficult to control. Methods for securely storing and sharing genetic data with potential for dual-use are needed to mitigate this potential harm.Results: Here we propose new methods that allow genetic data to be shared in a data format that prevents a nefarious actor from accessing sensitive aspects of the data. Our methods obfuscate raw sequence data by pooling reads from different samples. This approach can ensure that data is secure while stored and during electronic transfer. We demonstrate that by pooling raw sequence data from multiple samples of the same organism, the ability to fully reconstruct any individual sample is prevented. In the pooled data, most genomic information remains, but reads or mutations cannot be directly attributed to any individual sample. To further restrict access to information, regions of a genome can be removed from the reads.Conclusion: Our methods obscure genomic information within raw sequence reads. This method can allow genetic data to be stored and shared while preventing a nefarious actor from being able to perfectly reconstruct an organism. Broad-scale sequence information remains, while fine scale details about specific samples are difficult or impossible to reconstruct. Our software is available at https://github.com/Geneinfosec-Inc/ReadMixer.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Methods for Incorporating Model Uncertainty into Exoplanet Atmospheric Analysis

A key goal of exoplanet spectroscopy is to measure atmospheric properties, such as abundances of chemical species, in order to connect them to our understanding of atmospheric physics and planet formation. In this new era of high-quality JWST data, it is paramount that these measurement methods are robust. When comparing atmospheric models to observations, multiple candidate models may produce reasonable fits to the data. Typically, conclusions are reached by selecting the best-performing model according to some metric. This ignores model uncertainty in favor of specific model assumptions, potentially leading to measured atmospheric properties that are overconfident and/or incorrect. In this paper, we compare three ensemble methods for addressing model uncertainty by combining posterior distributions from multiple analyses: Bayesian model averaging, a variant of Bayesian model averaging using leave-one-out predictive densities, and stacking of predictive distributions. We demonstrate these methods by fitting the Hubble Space Telescope (HST) + Spitzer transmission spectrum of the hot Jupiter HD 209458b using models with different cloud and haze prescriptions. All of our ensemble methods lead to uncertainties on retrieved parameters that are larger but more realistic and consistent with physical and chemical expectations. Since they have not typically accounted for model uncertainty, uncertainties of retrieved parameters from HST spectra have likely been underreported. We recommend stacking as the most robust model combination method. Our methods can be used to combine results from independent retrieval codes and from different models within one code. They are also widely applicable to other exoplanet analysis processes, such as combining results from different data reductions.

79 ASTRONOMY AND ASTROPHYSICS↗