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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Refined Telluric Absorption Correction for Low-resolution Ground-based Spectroscopy: Resolution and Radial Velocity Effects in the O{sub 2}A-band for Exoplanets and K i Emission Lines

Telluric correction of spectroscopic observations is either performed via standard stars that are observed close in time and airmass along with the science target, or recently growing in importance, by theoretical telluric absorption modeling. Both approaches work fine when the telluric lines are resolved, i.e., at a spectral resolving power larger than about 10,000, and it is sufficient to facilitate the detection of spectral features at lower resolution. However, a meaningful quantitative analysis also requires the reliable recovery of line strengths. Here, we show for the Fraunhofer A-band of molecular O{sub 2} that the standard telluric correction approach fails in this at lower spectral resolutions, as an example for the general problem. Doppler-shift-dependent errors of the restored flux may arise, which can amount to more than 50% in extreme cases, depending on the line shapes of the target spectral features. Two applications are discussed: the recovery of the O{sub 2} band in the reflected light of an Earth analog atmosphere, as facilitated potentially in the future using an orbiting starshade and a ground-based extremely large telescope; and the recovery of the intrinsic ratio of the K i lines in the post-nova V4332 Sgr tracing the optical depth of the emitting region, to exemplify the relevance using present-day instrumentation. We show how one should derive correction functions for the compensation of the error in dependence of radial velocity shift, spectral resolution, and target line-profile function by use of high-resolution atmospheric transmission modeling, which has to be solved for the individual case.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Probing plasma physics with spectral index maps of accreting black holes on event horizon scales

The Event Horizon Telescope (EHT) collaboration has produced the first resolved images of the supermassive black holes at the centre of our galaxy and at the centre of the elliptical galaxy M87. As both technology and analysis pipelines improve, it will soon become possible to produce spectral index maps of black hole accretion flows on event horizon scales. Here, in this work, we predict spectral index maps of both M87* and Sgr A* by applying the general relativistic radiative transfer (GRRT) code IPOLE to a suite of general relativistic magnetohydrodynamic (GRMHD) simulations. We analytically show that the spectral index increases with increasing magnetic field strength, electron temperature, and optical depth. Consequently, spectral index maps grow more negative with increasing radius in almost all models, since all of these quantities tend to be maximized near the event horizon. Additionally, photon ring geodesics exhibit more positive spectral indices, since they sample the innermost regions of the accretion flow with the most extreme plasma conditions. Spectral index maps are sensitive to highly uncertain plasma heating prescriptions (the electron temperature and distribution function). However, if our understanding of these aspects of plasma physics can be tightened, even the spatially unresolved spectral index around 230 GHz can be used to discriminate between models. In particular, Standard and Normal Evolution (SANE) flows tend to exhibit more negative spectral indices than Magnetically Arrested Disc (MAD) flows due to differences in the characteristic magnetic field strength and temperature of emitting plasma.

(magnetohydrodynamics) MHD↗
DOE OSTI2024

Spectral Analysis of Regular Material Point Method and its Application to Study High Pressure Reverse Osmosis Membrane Compaction and Embossing

Material Point Method (MPM) is gaining widespread interest in applied continuum mechanics. The fact that all the continuum properties are stored on the particles (or material points) and the governing equations are solved on these material points makes MPM extremely suited to problems involving severe material deformations, such as crack propagation, soil movement, and fluid flows. Despite its popularity, only a few studies have focused on the numerical properties of MPM. This presentation introduces a global spectral analysis of the regular material point method. Contrary to previous studies, the analysis focuses on the numerical properties of the method in the spectral space. The amplification factor is derived as a function of the non- dimensional wave numbers. It provides insights into the stability and dissipative properties of the method for various CFL and Fourier numbers. The effect of the grid shape functions, number of particles per cell and their locations inside the grid cell are also analyzed. The EXAGOOP MPM solver (https://github.com/NREL/Exagoop.git) is developed at the National Renewable Energy Laboratory as a part of the NAWI UHPRO project and is based on the AMReX framework. A single-level, uniform cartesian grid is used as the background mesh, while the particle class in AMReX is used to manage the material point operations. Linear hat and B-splines are used as grid shape functions, while the time integration is performed using explicit Euler time integration. EXAGOOP is both CPU and GPU compatible and has been demonstrated to work well on multiple compute architectures. The performance of EXAGOOP on various computing architectures is presented along with its application to study compaction and embossing of high-pressure reverse osmosis membranes. The MPM solution accurately reproduces the membrane deformation. The deformed pore size and structure simulated using MPM also agree well with experimental SEM images.

material point method↗
DOE OSTI2021

Hybrid density functional study of band gap engineering of SrTi O 3 photocatalyst via doping for water splitting

Perovskite SrTiO 3 (STO) is an attractive photocatalyst for solar water splitting but suffers from a limited photoresponse in the visible spectral range due to its wide band gap. By means of hybrid density functional theory calculations, we systematically study engineering its band gap via doping 4$\textit{d}$ and 5$\textit{d}$ transition-metals $\textit{M}$ (M = Zr, Nb, Mo, Tc, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir, and Pt) and chalcogen elements $\textit{Y}$ ($\textit{Y}$ = S and Se).We find that transition-metal dopant M either has no effect on the STO band gap or introduces detrimental midgap states except for Pd and Pt that are able to reduce the STO band gap. In contrast, doping S and Se significantly reduces STO’s direct band gap, thus, leading to appreciable optical absorption transitions in the visible spectral range. In this work, our findings provide that Pd-, S-, and Se-doped STO are potential promising photocatalysts for water splitting under visible light irradiation thereby providing insightful theoretical guides for experiments to improve the photocatalytic activity of STO.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equations for the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f⁡(vy) or f⁡(v⊥). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. Further, the quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of PSL 2 (C) and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap λ 1 of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies λ 1 < 47.32. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.

Bonifacio, James [University of Mississippi, MS (U↗
DOE OSTI2022

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67

High-resolution spectroscopic surveys of the Milky Way have entered the Big Data regime and have opened avenues for solving outstanding questions in Galactic archeology. However, exploiting their full potential is limited by complex systematics, whose characterization has not received much attention in modern spectroscopic analyses. In this work, we present a novel method to disentangle the component of spectral data space intrinsic to the stars from that due to systematics. Using functional principal component analysis on a sample of 18,933 giant spectra from APOGEE, we find that the intrinsic structure above the level of observational uncertainties requires ≈10 functional principal components (FPCs). Our FPCs can reduce the dimensionality of spectra, remove systematics, and impute masked wavelengths, thereby enabling accurate studies of stellar populations. To demonstrate the applicability of our FPCs, we use them to infer stellar parameters and abundances of 28 giants in the open cluster M67. We employ Sequential Neural Likelihood, a simulation-based Bayesian inference method that learns likelihood functions using neural density estimators, to incorporate non-Gaussian effects in spectral likelihoods. By hierarchically combining the inferred abundances, we limit the spread of the following elements in M67: Fe ≲ 0.02 dex; C ≲ 0.03 dex; O, Mg, Si, Ni ≲ 0.04 dex; Ca ≲ 0.05 dex; N, Al ≲ 0.07 dex (at 68% confidence). Our constraints suggest a lack of self-pollution by core-collapse supernovae in M67, which has promising implications for the future of chemical tagging to understand the star formation history and dynamical evolution of the Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces

In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A new and alternative look at nonlinear Alfvénic states

The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Adjustments to the law of the wall above an Amazon forest explained by a spectral link

Modification to the law of the wall represented by a dimensionless correction function ϕ RSL (z/h) is derived using atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where z is the distance from the forest floor and h is the mean canopy height. The sites are the Amazon Tall Tower Observatory for z/h∈ [1,2.3] and the Green Ocean Amazon (GoAmazon) site for z/h∈ [1,1.4]. Here, a link between the vertical velocity spectrum E ww (k) (k is the longitudinal wavenumber) and ϕ RSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that ϕ RSL is determined by the ratio of two turbulent viscosities and is given as ν t,BL /ν t,RSL, where ν t,RSL = (1/A)∫$^{∞}_{0}$ τ(k)E ww (k)dk, ν t,BL = k v (z−d)u * , τ(k) is a scale-dependent decorrelation time scale between velocity components, A = C R /(1−C I ) = 4.5 is predicted from the Rotta constant C R = 1.8, and the isotropization of production constant C I = 3/5 given by rapid distortion theory, k v is the von Kármán constant, u * is the friction velocity at the canopy top, and d is the zero-plane displacement. Because the transfer of energy across scales is conserved in E ww (k) and is determined by the turbulent kinetic energy dissipation rate (ε), the CSB model also predicts that ϕ RSL scales with L BL /L d , where L BL is the length scale of attached eddies to z = d, and L d = u$_{*}^{3}$/ε is a macro-scale dissipation length.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

The Palomar Transient Factory Core-collapse Supernova Host-galaxy Sample. I. Host-galaxy Distribution Functions and Environment Dependence of Core-collapse Supernovae

Several thousand core-collapse supernovae (CCSNe) of different flavors have been discovered so far. However, identifying their progenitors has remained an outstanding open question in astrophysics. Studies of SN host galaxies have proven to be powerful in providing constraints on the progenitor populations. In this paper, we present all CCSNe detected between 2009 and 2017 by the Palomar Transient Factory. This sample includes 888 SNe of 12 distinct classes out to redshift z ≈ 1. We present the photometric properties of their host galaxies from the far-ultraviolet to the mid-infrared and model the host-galaxy spectral energy distributions to derive physical properties. The galaxy mass function of Type Ic, Ib, IIb, II, and IIn SNe ranges from 105 to 1011.5 M o˙, probing the entire mass range of star-forming galaxies down to the least-massive star-forming galaxies known. Moreover, the galaxy mass distributions are consistent with models of star-formation-weighted mass functions. Regular CCSNe are hence direct tracers of star formation. Small but notable differences exist between some of the SN classes. Type Ib/c SNe prefer galaxies with slightly higher masses (i.e., higher metallicities) and star formation rates than Type IIb and II SNe. These differences are less pronounced than previously thought. H-poor superluminous supernovae (SLSNe) and SNe Ic-BL are scarce in galaxies above 1010 M o˙. Their progenitors require environments with metallicities of < 0.4 and < 1 solar, respectively. In addition, the hosts of H-poor SLSNe are dominated by a younger stellar population than all other classes of CCSNe. Our findings corroborate the notion that low metallicity and young age play an important role in the formation of SLSN progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spectral Equivalence Properties of Higher-Order Tensor Product Finite Elements and Applications to Preconditioning

In this study, we present spectral equivalence results for higher-order tensor product edge-, face- and interior-based finite elements. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the higher-order elements are spectrally equivalent to those for an assembly of lowest-order elements on the associated Gauss-Lobatto-Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Solid state 59 Co NMR study of a Np(VII) compound

Np(VII) compounds with [Co(NH 3 ) 6 ] 3+ cations were synthesized and structurally examined using powder X-ray diffraction. Multiple phases were observed, consisting of octahedral [Co(NH 3 ) 6 ] 3+ cations, discrete tetragonal bipyramidal [NpO 4 (OH) 2 ] 3− anions, and waters of hydration. Electric field gradient tensors at Co sites were measured by solid state 59 Co nuclear magnetic resonance (NMR) spectroscopy and compared with theoretical calculations. The relative contributions of the chemical shift and electric field tensors to the NMR lineshape were determined by recording spectra at field strengths of 7.04 and 11.74 Tesla. Further, the evolution of structure and morphology as a function of sample age and the effects on NMR spectral parameters has also been investigated. These results demonstrate the use of NMR at multiple fields to expand understanding of the stability and electronic structure of high valent neptunium compounds.

heptavalent neptunium↗
DOE OSTI2023

Model-Free Approach for Profiling of Polydisperse Soft Matter Using Small Angle Scattering

A strategy for determining the size polydispersity of systems from their small angle coherent scattering is outlined. Here, using the method of moment expansion, we show that the various central moments representing the average particle size, variance of particle size, and skewness of size distribution function (SDF) for polydisperse systems can be extracted from spectral analysis without bias. When the degree of polydispersity is moderate, SDF can be further reconstructed based on the maximum entropy principle. Numerical benchmarking of a model study over a wide range of size nonuniformity demonstrates the validity of this analytical approach for quantifying the size distribution of general soft matter systems in a model-free manner. Furthermore, the efficacy of this method was validated by successfully applying it to the fitting of small-angle neutron scattering data obtained from L64 Pluronic micelles using various form factor models. The numerical and experimental verification underscores the reliability and versatility of this method in accurately characterizing the size distribution of complex soft matter systems.

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

Excitation Laser Energy Dependence of the Gap-Mode TERS Spectra of WS 2 and MoS 2 on Silver

In this work we present a systematic study of the dependence of the gap mode tip-enhanced Raman scattering (TERS) response of the mono- and bi-layer WS 2 and MoS 2 on silver as a function of the excitation laser energy in a broad spectral range from 473nm to 830 nm. For this purpose, we collected consecutive TERS maps of the same area in the sample containing mono-and bi-layer regions with the same TERS probe with 6 different excitation lasers. To decrease the number of collected TERS maps, we used for the first time to the best of our knowledge, concurrent excitation and collection with two lasers simultaneously. We found that the E 2g /A 1g peak intensity ratio for the bilayer WS 2 @Ag and the ratio of the A’/A 1g peak intensity of the out-of-plane mode for the mono- and the bilayer, change in a significantly non-monotonous way as the excitation laser energy is swept from 1.58 eV to 2.62 eV. The former ratio increases at energies corresponding to A and B excitons (~2.0 eV and 2.4 eV correspondingly) in bilayer WS 2 . The absolute intensity of the A’ peak in the monolayer, and correspondingly the A’/A 1g ratio, is surprisingly high at lower excitation energies, but dips dramatically at the energy corresponding to the A exciton, being restored partially in between A and B excitons, but still showing the descending trend as the excitation laser energy increases. A somewhat similar picture was observed in mono- and bi-layers of MoS 2 @Ag, though the existing set of excitation lasers did not match the excitonic profile of this material as nicely as for the case of WS 2 . We attribute the observed behavior to the presence of intermediate (Fano resonance) or strong (Rabi splitting) coupling between the excitons in transition metal dichalcogenides (TMDs) and the plasmons in the tip-substrate nanocavity. This is akin to the so-called Fano (Rabi) transparency experimentally observed in far field scattering from transition metal dichalcogenides between two plasmonic metals. The possibility of the formation of intermediate/strong coupling between the excitonic resonances in TMDs and the nanocavity re-evaluates the role of various resonances in the gap-mode TERS and should become an important factor to be considered by TERS practitioners during planning the experiments. Lastly, based on observed phenomena and its explanation, we propose the “ideal” substrate for efficient TERS and tip enhanced photoluminescence (TEPL) measurements.

Raman spectroscopy↗
DOE OSTI2020

Femtosecond photocurrents at the FeRh/Pt interface

Femtosecond laser excitations of FeRh/Pt bilayers launch an ultrafast pulse of electric photocurrents in the Pt-layer and subsequently result in the emission of electromagnetic radiation in the THz spectral range. Analysis of the THz emission as a function of the polarization of the femtosecond laser pulse, external magnetic field, sample temperature, and sample orientation shows that the photocurrent can emerge due to vertical spin pumping and photo-induced inverse spin–orbit torque at the FeRh/Pt interface. Additionally, the vertical spin pumping from FeRh into Pt does not depend on the polarization of light and originates from ultrafast laser-induced demagnetization of the ferromagnetic phase of FeRh. The photo-induced inverse spin–orbit torque at the FeRh/Pt interface can be described in terms of a helicity-dependent effect of circularly polarized light on the magnetization of the ferromagnetic FeRh and the subsequent generation of a photocurrent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Star cluster classification using deep transfer learning with PHANGS- HST

Currently available star cluster catalogues from the Hubble Space Telescope (HST) imaging of nearby galaxies heavily rely on visual inspection and classification of candidate clusters. Here, the time-consuming nature of this process has limited the production of reliable catalogues and thus also post-observation analysis. To address this problem, deep transfer learning has recently been used to create neural network models that accurately classify star cluster morphologies at production scale for nearby spiral galaxies (D ≲ 20 Mpc). Here, we use HST ultraviolet (UV)–optical imaging of over 20 000 sources in 23 galaxies from the Physics at High Angular resolution in Nearby GalaxieS (PHANGS) survey to train and evaluate two new sets of models: (i) distance-dependent models, based on cluster candidates binned by galaxy distance (9–12, 14–18, and 18–24 Mpc), and (ii) distance-independent models, based on the combined sample of candidates from all galaxies. We find that the overall accuracy of both sets of models is comparable to previous automated star cluster classification studies (~60–80 per cent) and shows improvement by a factor of 2 in classifying asymmetric and multipeaked clusters from PHANGS-HST. Somewhat surprisingly, while we observe a weak negative correlation between model accuracy and galactic distance, we find that training separate models for the three distance bins does not significantly improve classification accuracy. We also evaluate model accuracy as a function of cluster properties such as brightness, colour, and spectral energy distribution (SED)-fit age. Based on the success of these experiments, our models will provide classifications for the full set of PHANGS-HST candidate clusters (N ~ 200 000) for public release.

79 ASTRONOMY AND ASTROPHYSICS↗