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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 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Are continuum predictions of clustering chaotic?

Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ 1 ≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a direct consequence of the fundamental kinematic instability, but requires a secondary (inherently multidimensional) instability. Granular matter is a collection of discrete, interacting solid particles which, like classic (molecular) matter, can be generally classified into one of three states:1 (i) under static conditions granular heaps or piles can sustain gravity-induced stress and behave like a solid; (ii) dense granular flows characterized by enduring and multi-particle contacts behave similarly to a fluid; and (iii) rapid granular flows characterized by instantaneous contacts described as a granular gas. However, it is worth noting that all three granular states are only superficially similar to their molecular counterparts due to the dissipative nature of particle-particle contacts (inelasticity, friction, etc.). In industrial operations, rapid (collision-dominated) granular flows are often encountered in devices in which the particles are fluidized by a gas; such gas-solid flows are the focus of this work. Rapid gas-solid flows are prone to an instability termed clustering in which particles tend to form spatially inhomogeneous patterns of high and low concentrations. Continuum or two-fluid models (TFM) have long been known to be able to predict the qualitative nature of the clustering instability and more recent quantitative assessments have also shown promising results. However, it is yet unknown whether or not such predictions are chaotic. We take a first step in answering this question by simulating fluidization in an unbounded domain and calculating a positive largest Lyapunov exponent (LLE), thereby indicating that continuum predictions of clustering are in fact chaotic. Further, we show that chaotic behavior may be reduced to periodic behavior by constraining the dimensionality of the system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes

In this work, we develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Bayesian optimization of the Community Land Model simulated biosphere-atmosphere exchange using CO 2 observations from a dense tower network and aircraft campaigns over Oregon

Here, the vast forests and natural areas of the Pacific Northwest comprise one of the most productive ecosystems in the northern hemisphere. The heterogeneous landscape of Oregon poses a particular challenge to ecosystem models. We present a framework using a scaling factor Bayesian inversion to improve the modeled atmosphere-biosphere exchange of carbon dioxide. Observations from 5 CO/CO 2 towers, eddy covariance towers, and airborne campaigns were used to constrain the Community Land Model CLM4.5 simulated terrestrial CO 2 exchange at a high spatial and temporal resolution (1/24°, 3-hourly). To balance aggregation errors and the degrees of freedom in the inverse modeling system, we applied an unsupervised clustering approach for the spatial structuring of our model domain. Data from flight campaigns were used to quantify the uncertainty introduced by the Lagrangian particle dispersion model that was applied for the inversions. The average annual statewide net ecosystem productivity (NEP) was increased by 32% to 29.7 TgC per year by assimilating the tropospheric mixing ratio data. The associated uncertainty was decreased by 28.4% to 29%, on average over the entire Oregon model domain with the lowest uncertainties of 11% in western Oregon. The largest differences between posterior and prior CO 2 fluxes were found for the Coast Range ecoregion of Oregon that also exhibits the highest availability of atmospheric observations and associated footprints. In this area, covered by highly productive Douglas-fir forest, the differences between the prior and posterior estimate of NEP averaged 3.84 TgC per year during the study period from 2012 through 2014.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr 2 Cu 2.75 Mo 0.25 O 7.54 (T c =84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO 2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO 2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2006

A comparison of global estimates of marine primary production from ocean color

The third primary production algorithm round robin (PPARR3) compares output from 24 models that estimate depth-integrated primary production from satellite measurements of ocean color, as well as seven general circulation models (GCMs) coupled with ecosystem or biogeochemical models. Here we compare the global primary production fields corresponding to eight months of 1998 and 1999 as estimated from common input fields of photosynthetically-available radiation (PAR), sea-surface temperature (SST), mixed-layer depth, and chlorophyll concentration. We also quantify the sensitivity of the ocean-color-based models to perturbations in their input variables. The pair-wise correlation between ocean-color models was used to cluster them into groups or related output, which reflect the regions and environmental conditions under which they respond differently. The groups do not follow model complexity with regards to wavelength or depth dependence, though they are related to the manner in which temperature is used to parameterize photosynthesis. Global average PP varies by a factor of two between models. The models diverged the most for the Southern Ocean, SST under 10 C, and chlorophyll concentration exceeding 1mg Chlm-3. Based on the conditions under which the model results diverge most, we conclude that current ocean-color-based models are challenged by high-nutrient low-chlorophyll conditions, and extreme temperatures or chlorophyll concentrations. The GCM-based models predict comparable primary production to those based on ocean color: they estimate higher values in the Southern Ocean, at low SST, and in the equatorial band, while they estimate lower values in eutrophic regions (probably because the area of high chlorophyll concentrations is smaller in the GCMs). Further progress in primary production modeling requires improved understanding of the effect of temperature on photosynthesis and better parameterization of the maximum photosynthetic rate.

Yamanaka, Yasuhiro↗
DOE OSTI2013

COSMOLOGICAL CONSTRAINTS FROM SUNYAEV-ZEL'DOVICH-SELECTED CLUSTERS WITH X-RAY OBSERVATIONS IN THE FIRST 178 deg{sup 2} OF THE SOUTH POLE TELESCOPE SURVEY

We use measurements from the South Pole Telescope (SPT) Sunyaev-Zel'dovich (SZ) cluster survey in combination with X-ray measurements to constrain cosmological parameters. We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology. The method is generalizable to multiple cluster observables, and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints. We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg{sup 2} of the 2500 deg{sup 2} SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM-Newton. Assuming a spatially flat {Lambda}CDM cosmological model, we find the SPT cluster sample constrains {sigma}{sub 8}({Omega} {sub m}/0.25){sup 0.30} = 0.785 {+-} 0.037. In combination with measurements of the cosmic microwave background (CMB) power spectrum from the SPT and the seven-year Wilkinson Microwave Anisotropy Probe data, the SPT cluster sample constrains {sigma}{sub 8} = 0.795 {+-} 0.016 and {Omega} {sub m} = 0.255 {+-} 0.016, a factor of 1.5 improvement on each parameter over the CMB data alone. We consider several extensions beyond the {Lambda}CDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses ({Sigma}m {sub {nu}}), the effective number of relativistic species (N {sub eff}), and a primordial non-Gaussianity (f {sub NL}). We find that adding the SPT cluster data significantly improves the constraints on w and {Sigma}m {sub {nu}} beyond those found when using measurements of the CMB, supernovae, baryon acoustic oscillations, and the Hubble constant. Considering each extension independently, we best constrain w = -0.973 {+-} 0.063 and the sum of neutrino masses {Sigma}m {sub {nu}} < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 improvement, respectively, over the constraints without clusters. Assuming a {Lambda}CDM model with a free N {sub eff} and {Sigma}m {sub {nu}}, we measure N {sub eff} = 3.91 {+-} 0.42 and constrain {Sigma}m {sub {nu}} < 0.63 eV at 95% confidence. We also use the SPT cluster sample to constrain f {sub NL} = -220 {+-} 317, consistent with zero primordial non-Gaussianity. Finally, we discuss the current systematic limitations due to the cluster mass calibration, and future improvements for the recently completed 2500 deg{sup 2} SPT-SZ survey. The survey has detected {approx}500 clusters with a median redshift of {approx}0.5 and a median mass of {approx}2.3 Multiplication-Sign 10{sup 14} M {sub Sun} h {sup -1} and, when combined with an improved cluster mass calibration and existing external cosmological data sets will significantly improve constraints on w.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Intertwined spin, charge, and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit

Significance The high-temperature superconducting cuprates are governed by intertwined striped magnetic and charge orders, in addition to superconductivity. Remarkably similar behavior has also been seen in numerical calculations for the Hubbard model describing the copper–oxygen layers in these materials. Finite-cluster methods typically find that spin- and charge-stripe order dominates, while embedded quantum-cluster methods, which access the thermodynamic limit, often conclude that superconductivity does. Here, we report the observation of fluctuating spin and charge stripes in an embedded cluster calculation for the Hubbard model. This discovery demonstrates that striped states survive in the thermodynamic limit and allows us to study their influence on the model’s superconducting properties, where we find evidence for pair-density-wave correlations intertwined with the stripe correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Spectroscopic Characterization of redMaPPer Galaxy Clusters with DESI

Optical galaxy cluster identification algorithms such as redMaPPer promise to enable an array of astrophysical and cosmological studies, but suffer from biases whereby galaxies in front of and behind a galaxy cluster are mistakenly associated with the primary cluster halo. These projection effects caused by irreducible photometric redshift uncertainty must be quantified to facilitate the use of optical cluster catalogues. We present measurements of galaxy cluster projection effects and velocity dispersion using spectroscopy from the Dark Energy Spectroscopic Instrument. Our findings are as follows: we confirm that the fraction of redMaPPer putative member galaxies mistakenly associated with cluster haloes is richness dependent, being more than twice as large at low richness than high richness; we present the first spectroscopic evidence of an increase in projection effects with increasing redshift, by as much as 25 per cent from $z\sim 0.1$ to $z\sim 0.2$; moreover, we find qualitative evidence for luminosity dependence in projection effects, with fainter galaxies being more commonly far behind clusters than their bright counterparts; finally, we fit the scaling relation between measured mean spectroscopic richness and velocity dispersion, finding an implied linear scaling between spectroscopic richness and halo mass. We discuss further directions for the application of spectroscopic data sets to improve use of optically selected clusters to test cosmological models.

clusters↗
DOE OSTI2026

Constraints on the normal branch of DGP gravity from SPT galaxy clusters with DES and HST weak-lensing mass calibration and from P l a n c k PR4 CMB anisotropies

We present constraints on the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld gravity model from the abundance of massive galaxy clusters. On scales below the nDGP crossover scale r c , the nDGP model features an effective gravitylike fifth force that alters the growth of structure, leading to an enhancement of the halo mass function (HMF) on cluster scales. The enhanced cluster abundance allows for constraints on the nDGP model using cluster samples. We employ the South Pole Telescope (SPT) cluster sample, selected through the thermal Sunyaev-Zel’dovich effect with the SPT and with mass calibration using weak-lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample contains 1,005 clusters with redshifts 0.25 < z < 1.78 , which are confirmed with the multicomponent matched filter algorithm using optical and near-infrared data. Weak-lensing data from DES and HST enable a robust mass measurement of the cluster sample. We use DES Year 3 data for 688 clusters with redshifts z < 0.95 , and HST data for 39 clusters with redshifts 0.6 < z < 1.7 . We account for the enhancement in the HMF through a semi-analytic correction factor to the standard cosmology HMF derived from the spherical collapse model in the nDGP model. We then further calibrate this model using N -body simulations. In addition, for the first time, we analyze the primary CMB temperature and polarization anisotropy measurements from Planck PR4 within the nDGP model. We obtain a competitive constraint from the joint analysis of the SPT cluster abundance with the Planck PR4 data, and report an upper bound of 1 / H 0 r c < 1.41 at 95% when assuming a cosmology with massive neutrinos.

Vogt, S. M.L. [Munich U. Observ.; LMU Munich (main↗
DOE OSTI2017

Coupled Cluster Studies of Ionization Potentials and Electron Affinities of Single-Walled Carbon Nanotubes

In this paper we apply equation-of-motion coupled cluster (EOMCC) methods in studies of vertical ionization potentials (IP) and electron affinities (EA) for sin- gled walled carbon nanotubes. EOMCC formulations for ionization potentials and electron affinities employing excitation manifolds spanned by single and double ex- citations (IP/EA-EOMCCSD) are used to study IPs and EAs of nanotubes as a function of nanotube length. Several armchair nanotubes corresponding to C20nH20 models with n = 2 - 6 have been used in benchmark calculations. In agreement with previous studies, we demonstrate that the electronegativity of C20nH20 systems remains, to a large extent, independent of nanotube length. We also compare IP/EA- EOMCCSD results with those obtained with the coupled cluster models with single and double excitations corrected by perturbative triples, CCSD(T), and density func- tional theory (DFT) using global and range-separated hybrid exchange-correlation functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Magnon heat transport in a two-dimensional Mott insulator

Whether or not anomalies in the thermal conductivity in insulating cuprates can be attributed to antiferromagnetic order and magnons in a 2D Mott insulator remains an intriguing open question. To shed light on this issue, we investigate the thermal conductivity $\kappa$ and its relationship with the specific heat $c_v$ in the half-filled 2D single-band Hubbard model, using the numerically exact determinant quantum Monte Carlo algorithm and maximum entropy analytic continuation. At low temperatures where the charge degrees of freedom are gapped-out and $c_v$ exhibits a clear magnon peak, we observe that thermal conductivity $\kappa$ also tends to form a peak at similar temperatures. Reducing temperature further produces a sharp upturn in $\kappa$, associated with an increasing mean-free path. Here we identify this as the high-temperature side of the anomalous peak in insulating cuprates, where the mean-free path eventually is cut-off by other scattering effects, including phonons, disorder, and physical size. Different scattering effects in our model are identified and analyzed in the thermal diffusivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Systematics of E 2 strength in the s d shell with the valence-space in-medium similarity renormalization group

Recent developments in ab initio nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, E2, strength associated with collectivity. The valence-space in-medium similarity renormalization group (VS-IMSRG) is a particularly powerful method for accessing medium- and high-mass nuclei but has been found to underpredict E2 strengths. The purpose of this work is to evaluate the isospin dependence of this underprediction. We perform a systematic comparison of VS-IMSRG calculations with available literature. We make use of isoscalar and isovector contributions to the E2 matrix elements to assess isoscalar and isovector contributions to the missing strength. It is found that the E2 strength is consistent throughout T z =|12|, T z =|1|, T z =|32|, and T z =2 pairs within the sd shell. Furthermore, no isovector contribution to the deficiency is identified. A comparison with toy-models and coupled-cluster calculations is used to discuss potential origins of the missing strength, which arises from missing many-particle, many-hole excitations out of the model space. The absence of any significant isovector contribution to the missing E2 strength indicates that the E2 strength discrepancy, and therefore any correction, is largely independent of the isospin of the nuclei in question.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

MixSim : An R Package for Simulating Data to Study Performance of Clustering Algorithms

The R package MixSim is a new tool that allows simulating mixtures of Gaussian distributions with different levels of overlap between mixture components. Pairwise overlap, defined as a sum of two misclassification probabilities, measures the degree of interaction between components and can be readily employed to control the clustering complexity of datasets simulated from mixtures. These datasets can then be used for systematic performance investigation of clustering and finite mixture modeling algorithms. Among other capabilities of MixSim, there are computing the exact overlap for Gaussian mixtures, simulating Gaussian and non-Gaussian data, simulating outliers and noise variables, calculating various measures of agreement between two partitionings, and constructing parallel distribution plots for the graphical display of finite mixture models. All features of the package are illustrated in great detail. The utility of the package is highlighted through a small comparison study of several popular clustering algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Cluster Sampling Filters for Non-Gaussian Data Assimilation

This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the &ldquo;cluster sampling filter&rdquo;, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using a Gaussian Mixture Model (GMM). Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a GMM to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled following an MCMC approach. Four versions of the proposed filter, namely C ℓ MCMC , C ℓ HMC , MC- C ℓ HMC , and MC- C ℓ HMC are presented. C ℓ MCMC uses a Gaussian proposal density to sample the posterior, and C ℓ HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C ℓ MCMC and MC- C ℓ HMC are multi-chain versions of the cluster sampling filters C ℓ MCMC and C ℓ HMC respectively. The multi-chain versions are proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a simple one-dimensional example, and a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Here, numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Buzzard to Cardinal: Improved Mock Catalogs for Large Galaxy Surveys

Abstract We present the Cardinal mock galaxy catalogs, a new version of the Buzzard simulation that has been updated to support ongoing and future cosmological surveys, including the Dark Energy Survey (DES), DESI, and LSST. These catalogs are based on a one-quarter sky simulation populated with galaxies out to a redshift of z = 2.35 to a depth of m r = 27. Compared to the Buzzard mocks, the Cardinal mocks include an updated subhalo abundance matching model that considers orphan galaxies and includes mass-dependent scatter between galaxy luminosity and halo properties. This model can simultaneously fit galaxy clustering and group–galaxy cross-correlations measured in three different luminosity threshold samples. The Cardinal mocks also feature a new color assignment model that can simultaneously fit color-dependent galaxy clustering in three different luminosity bins. We have developed an algorithm that uses photometric data to further improve the color assignment model and have also developed a novel method to improve small-scale lensing below the ray-tracing resolution. These improvements enable the Cardinal mocks to accurately reproduce the abundance of galaxy clusters and the properties of lens galaxies in the DES data. As such, these simulations will be a valuable tool for future cosmological analyses based on large sky surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Comparative hazard analysis and toxicological modeling of diverse nanomaterials using the embryonic zebrafish (EZ) metric of toxicity

The integration of rapid assays, large data sets, informatics and modeling can overcome current barriers in understanding nanomaterial structure-toxicity relationships by providing a weight-of-the-evidence mechanism to generate hazard rankings for nanomaterials. Here we present the use of a rapid, low-cost assay to perform screening-level toxicity evaluations of nanomaterials in vivo. Calculated EZ Metric scores, a combined measure of morbidity and mortality, were established at realistic exposure levels and used to develop a predictive model of nanomaterial toxicity. Hazard ranking and clustering analysis of 68 diverse nanomaterials revealed distinct patterns of toxicity related to both core composition and outermost surface chemistry of nanomaterials. The resulting clusters guided the development of a predictive model of gold nanoparticle toxicity to embryonic zebrafish. In addition, our findings suggest that risk assessments based on the size and core composition of nanomaterials alone may be wholly inappropriate, especially when considering complex engineered nanomaterials. These findings reveal the need to expeditiously increase the availability of quantitative measures of nanomaterial hazard and broaden the sharing of that data and knowledge to support predictive modeling. In addition, research should continue to focus on methodologies for developing predictive models of nanomaterial hazard based on sub-lethal responses to low dose exposures.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Model independent dark matter properties from cosmic growth

Dark matter dominates the matter budget of the universe but its nature is unknown. Deviations from the standard model, where dark matter clusters with the same gravitational strength as baryons, and has the same pressureless equation of state as baryons, can be tested by cosmic growth measurements. We take a model independent approach, allowing deviations in bins of redshift, and compute the constraints enabled by ongoing cosmic structure surveys through redshift space distortions and peculiar velocities. These can produce constraints at the 3-14% level in four independent redshift bins over z = [0,4].

79 ASTRONOMY AND ASTROPHYSICS↗