Search NASA⌕ Search

SEARCH · Search NASA

Results for “Kinetics Parameters”

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

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

At least 1,045 records · Page 58

State switching kinetics for quasi-one-dimensional nanosystems: Effects of Finite length and irradiation

The state switching in an extended quasi-one-dimensional material is modeled by the stochastic formation of local new-state nuclei and their subsequent growth along the system axis. An analytical approach is developed to describe the influence of defects, dividing a sample into an ensemble of finite-length segments, on its state switching kinetics. As applied to magnetic systems, the method makes it possible to calculate magnetization curves for different defect concentrations and parameters of material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Single-Well Push–Pull Tracer Test Analyses to Determine Aquifer Reactive Transport Parameters at a Former Uranium Mill Site (Grand Junction, Colorado)

At a former uranium mill site where tailings have been removed, prior work has determined several potential ongoing secondary uranium sources. These include locations with uranium sorbed to organic carbon, uranium in the unsaturated zone, and uranium associated with the presence of gypsum. To better understand uranium mobility controls at the site, four single-well push–pull tests (with a drift phase) were completed with the goal of deriving aquifer flow and contaminant transport parameters for inclusion in a future sitewide reactive transport model. This goes beyond the traditional use of a constant sorption distribution coefficient (K d ) and allows for the evaluation of alternative remedial injection fluids, which can produce variable K d values. Dispersion was first removed from the resulting data to determine possible reactions before conducting reactive transport simulations. These initial analyses indicated the potential need to include cation exchange, uranium sorption, and gypsum dissolution. A reactive transport model using multiple layers to account for partially penetrating wells was completed using the PHT-USG reactive transport modeling code and calibrated using PEST. The model results quantify the hydraulic conductivity and dispersion parameters using the injected tracer concentrations. Uranium sorption, cation exchange, and gypsum dissolution parameters were quantified by comparing the simulated versus observed geochemistry. All simulations required some cation exchange and calcite equilibrium, and one simulation required gypsum dissolution to improve the model fit for calcium and sulfate. Uranium sorption parameters were not strongly influenced by the other parameter values but were highly influenced by uranium concentrations during the drift phase, with possible kinetic rate limitations. Thus, a future recommendation for such push–pull tests is to collect more geochemical data during the drift phase. The final uranium sorption parameters were within the range of values determined from prior column testing. The flow and transport parameters derived from these single-well push–pull tests will provide initial parameters for any future sitewide reactive transport model.

54 ENVIRONMENTAL SCIENCES↗

Tuning Porosity and Surface Area in Mesoporous Silicon for Application in Li-Ion Battery Electrodes

This work aims to improve the poor cycle lifetime of silicon-based anodes for Li-ion batteries by tuning microstructural parameters such as pore size, pore volume, and specific surface area in chemically synthesized mesoporous silicon. In this paper, we have specifically produced two different mesoporous silicon samples from the magnesiothermic reduction of ordered mesoporous silica in either argon or forming gas. In situ X-ray diffraction studies indicate that samples made in Ar proceed through a Mg 2 Si intermediate, and this results in samples with larger pores (diameter ≈ 90 nm), modest total porosity (34%), and modest specific surface area (50 m 2 g –1 ). Reduction in forming gas, by contrast, results in direct conversion of silica to silicon, and this produces samples with smaller pores (diameter ≈ 40 nm), higher porosity (41%), and a larger specific surface area (70 m 2 g –1 ). The material with smaller pores outperforms the one with larger pores, delivering a capacity of 1121 mAh g –1 at 10 A g –1 and retains 1292 mAh g –1 at 5 A g –1 after 500 cycles. For comparison, the sample with larger pores delivers a capacity of 731 mAh g –1 at 10 A g –1 and retains 845 mAh g –1 at 5 A g –1 after 500 cycles. The dependence of capacity retention and charge storage kinetics on the nanoscale architecture clearly suggests that these microstructural parameters significantly impact the performance of mesoporous alloy type anodes. Our work is therefore expected to contribute to the design and synthesis of optimal mesoporous architectures for advanced Li-ion battery anodes.

25 ENERGY STORAGE↗

A deep learning approach to fast analysis of collective Thomson scattering spectra

Fast analysis of collective Thomson scattering ion acoustic wave features using a deep convolutional neural network model is presented. The network was trained from spectra to predict the plasma parameters, including ion velocities, population fractions, and ion and electron temperatures. A fully kinetic particle-in-cell simulation was used to model a laboratory astrophysics experiment and simulate a diagnostic image of the ion acoustic wave feature. Network predictions were compared with Bayesian inference of the plasma model parameters for both the simulated and experimentally measured images. Both approaches were fairly accurate predicting the simulated image and the network predictions matched a good portion of the Bayesian results for the experimentally measured image. The Bayesian approach is more robust to noise and motivates future work to train deep learning models with realistic noise. The advantage of the deep learning model is making thousands of predictions in a few hundred milliseconds, compared to a few seconds to minutes per prediction for the optimization and Bayesian approaches presented here. The results demonstrate promising capabilities of deep learning models to analyze Thomson data orders of magnitude faster than conventional methods when using the neural network for standalone analysis. If more rigorous analysis is needed, neural network predictions can be used to quickly initialize other optimization methods and increase chances of success. This is especially useful when the dataset becomes very large or highly dimensional and manually refining initial conditions for the entire dataset are no longer tractable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Unsteady Crystal Growth Due to Step-Bunch Cascading

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

Vekilov, Peter G.↗

Observationally Constrained Modeling of the Reactive Uptake of Isoprene-Derived Epoxydiols under Elevated Relative Humidity and Varying Acidity of Seed Aerosol Conditions

Isoprene is the non-methane volatile organic compound (VOC) emitted in largest amounts to the atmosphere, and it is a significant source of secondary organic aerosol (SOA) mass. The uptake of isoprene oxidation products followed by multiphase chemistry in fine particles is the key pathway to form isoprene epoxydiol-derived SOA (IEPOX-SOA). However, many parameters that relate to diffusion and reaction of IEPOX in the particle phase remain uncertain, since reaction kinetics previously measured in bulk aqueous phase solutions might be different from atmospheric aerosols. Here, we use simultaneous environmental chamber measurements of multiple parameters governing IEPOX-SOA formation at timescales of ~hours: particle size distribution, composition, and volatility of IEPOX-SOA to constrain the key parameters governing IE-POX-SOA formation under humid (i.e., 50% relative humidity, RH) and varying seed aerosol acidity conditions. Reducing the 2-methyltetrol (tetrol) reaction rate constants by a factor of 4 brings the model predictions in agreement with the IEPOX-SOA measurements with acidified ammonium bisulfate seed aerosols. For less acidic ammonium sulfate aerosols both the organo-sulfate (OS) and tetrol reaction rate constants need to be reduced to bring model predictions closer to chamber observations. Using the measured non-volatile content of IEPOX-SOA we constrain the oligomerization timescale of 2-methyltetrols. We find that the oligomerization timescale is 4 hours with acidified seed aerosols, but a much longer time scale of 24 hours is needed for non-acidified seed aerosols, indicating that the aerosol acidity greatly affects the oligomerization rate of tetrols. Here we show that the actual kinetics of IEPOX-SOA formation rate on aerosol seeds consisting of both ammonium bisulfate and ammonium sulfate are a factor of 4~5 slower under 50-60% RH conditions compared to their application in previous models, which were based on bulk aqueous solution measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Skyrmion lattice formation and destruction mechanisms probed with TR-SANS

Magnetic skyrmions are topologically protected, nanoscale whirls of the spin configuration that tend to form hexagonally ordered arrays. As a topologically non-trivial structure, the nucleation and annihilation of the skyrmion, as well as the interaction between skyrmions, varies from conventional magnetic systems. Recent works have suggested that the ordering kinetics in these materials occur over millisecond or longer timescales, which is unusually slow for magnetic dynamics. The current work investigates the skyrmion ordering kinetics, particularly during lattice formation and destruction, using time-resolved small angle neutron scattering (TR-SANS). Evaluating the time-resolved structure and intensity of the neutron diffraction pattern reveals the evolving real-space structure of the skyrmion lattice and the timeframe of the formation. Measurements were performed on three prototypical skyrmion materials: MnSi, (Fe,Co)Si, and Cu 2 OSeO 3 . To probe lattice formation and destruction kinetics, the systems were prepared in the stable skyrmion state, and then a square-wave magnetic field modulation was applied. The measurements show that the skyrmions quickly form ordered domains, with a significant distribution in lattice parameters, which then converge to the final structure; the results confirm the slow kinetics, with formation times between 10 ms and 99 ms. Comparisons are made between the measured formation times and the fundamental material properties, suggesting the ordering temperature, saturation magnetization and magnetocrystalline anisotropy may be driving the timeframes. Micromagnetic simulations were also performed and support a scaling of the kinetics with sample volume, a behavior which is caused by the reconciling of misaligned domains.

Liyanage, W. L. N. C.↗

The Superluminous Supernova SN 2017egm in the Nearby Galaxy NGC 3191: A Metal-rich Environment Can Support a Typical SLSN Evolution

At redshift z = 0.03, the recently discovered SN 2017egm is the nearest Type I superluminous supernova (SLSN) to date and first near the center of a massive spiral galaxy (NGC 3191). Using SDSS spectra of NGC 3191, we find a metallicity ∼2 Z{sub ⊙} at the nucleus and ∼1.3 Z{sub ⊙} for a star-forming region at a radial offset similar to SN 2017egm. Archival radio-to-UV photometry reveals a star formation rate of ∼15 M{sub ⊙} yr{sup −1} (with ∼70% dust obscured), which can account for a Swift X-ray detection and a stellar mass of ∼10{sup 10.7} M{sub ⊙}. We model the early UV–optical light curves with a magnetar central-engine model, using the Bayesian light curve fitting tool MOSFiT. The fits indicate an ejecta mass of 2–4 M{sub ⊙}, a spin period of 4–6 ms, a magnetic field of (0.7--1.7)×10{sup 14} G, and a kinetic energy of 1--2×10{sup 51} erg. These parameters are consistent with the overall distributions for SLSNe, modeled by Nicholl et al., although the derived mass and spin are toward the low end, possibly indicating an enhanced loss of mass and angular momentum before explosion. This has two implications: (i) SLSNe can occur at solar metallicity, although with a low fraction of ∼10%, and (ii) metallicity has at most a modest effect on their properties. Both conclusions are in line with results for long gamma-ray bursts. Assuming a monotonic rise gives an explosion date of MJD 57889 ± 1. However, a short-lived excess in the data relative to the best-fitting models may indicate an early-time “bump.” If confirmed, SN 2017egm would be the first SLSN with a spectrum during the bump phase; this shows the same O ii lines seen at maximum light, which may be an important clue for explaining these bumps.

79 ASTRONOMY AND ASTROPHYSICS↗

Sensitivity Analysis of Cf-252 (sf) Neutron and Gamma Observables in CGMF

CGMF is a Monte Carlo code that simulates the decay of primary fission fragments by emission of neutrons and gamma rays, according to the Hauser-Feshbach equations. As the CGMF code was recently integrated into the MCNP6.2 transport code, great emphasis has been placed on providing optimal parameters to CGMF such that many different observables are accurately represented. Of these observables, the prompt neutron spectrum, prompt neutron multiplicity, prompt gamma spectrum, and prompt gamma multiplicity are crucial for accurate transport simulations of criticality and nonproliferation applications. This contribution to the ongoing efforts to improve CGMF presents a study of the sensitivity of various neutron and gamma observables to several input parameters for Californium-252 spontaneous fission. Among the most influential parameters are those that affect the input yield distributions in fragment mass and total kinetic energy (TKE). A new scheme for representing Y(A,TKE) was implemented in CGMF using three fission modes, S1, S2 and SL. The sensitivity profiles were calculated for 17 total parameters, which show that the neutron multiplicity distribution is strongly affected by the TKE distribution of the fragments. The total excitation energy (TXE) of the fragments is shared according to a parameter RT, which is defined as the ratio of the light to heavy initial temperatures. The sensitivity profile of the neutron multiplicity shows a second order effect of RT on the mean neutron multiplicity. A final sensitivity profile was produced for the parameter alpha, which affects the spin of the fragments. Higher values of alpha lead to higher fragment spins, which inhibit the emission of neutrons. Understanding the sensitivity of the prompt neutron and gamma observables to the many CGMF input parameters provides a platform for the optimization of these parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The role of energy transfer and competing bimolecular reactions in characterizing the unimolecular dissociations of allylic radicals

Resonantly stabilized radicals (RSR's) such as allylic radicals typically have bond energies exceeding 45 kcal/mol and are therefore reasonably long-lived up to quite high temperatures. Consequently, kinetics of the unimolecular dissociations and bimolecular reactions of these long-lived RSR's assume significance in high temperature chemically reacting systems such as in flames. Our recent analyses (J. Cho et al., Proc. Comb. Inst., 2022) of the uncertainty propagated by the energy transfer parameters for 1-methylallyl (1MA) dissociation to the laminar flame speed, indicates an intricate coupling between the kinetics of 1MA dissociation (chain propagation) and its reaction with H-atoms (chain-termination). Here, this work extends such analyses to other C 3 – C 5 allylic radicals: allyl, 2-methylallyl, 1,1-dimethylallyl, 1,2-dimethylallyl, and 1,3-dimethylallyl. Theoretical kinetics for the C 3 – C 4 allylic radicals were taken from prior literature studies (J.A. Miller et al., J. Phys. Chem., 2008; J. Cho et al., Proc. Comb. Inst., 2022; R.S. Tranter et al., Proc. Comb. Inst., 2017). Potential energy surfaces were newly computed for the dissociations of the larger C5 allylic radicals and the reactions of these radicals with H-atoms. These PES's were then used to calculate rate constants for the relevant unimolecular and bimolecular reactions. Energy transfer has a crucial role to play in these pressure-dependent reactions and therefore the present kinetics calculations relied on a-priori predictions of collisional energy transfer parameters to best characterize the branching between chain propagating unimolecular dissociations of these allylic radicals and chain terminating bimolecular reactions of these RSR's with H-atoms. Prompt dissociations are now established to be a universal feature of free radical dissociations. Here we have also characterized the propensity for prompt dissociations in these more-stable allylic RSR's and their role in combustion simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Physical and dynamical conditions in interstellar clouds

Techniques for measuring the local and global parameters that describe molecular clouds are presented and illustrated by selected results. The local parameters which characterize a given location in a cloud are gas kinetic temperature, dust temperature, total density, magnetic field strength, abundance of species i, volume cooling and heating rates for gas and dust, and the thermal and turbulent velocities. Global properties which characterize the cloud as a whole include the size expressed as a length or area, the orientation and shape, the mass, and the integrated heating and cooling rates. If the cloud as a whole is collapsing or rotating, then the collapse velocity and the rotational velocity or angular momentum are global properties. An intermediate class of parameters which shares features of local and global properties includes the column density of species i, the total column density, and the average density.

Evans, N. J., II↗

Gravitational wave and CMB probes of axion kination

Rotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scaling of the detonation product state with reactant kinetic energy

Chemical explosives provide one of the most high-power and energy-dense storage materials available. During detonation, transfer of this energy to adjacent materials is governed by the detonation product equation of state. No accurate methodology exists for prediction of this thermodynamic relationship and equation-of-state data continues to be experimentally characterized for each new formulation or charge density. Here we present a universal detonation product equation of state derived from several newly discovered empirical correlations in prior condensed-phase detonation product measurements. This model depends only on initial charge density and detonation velocity as inputs, dramatically simplifying the calibration process relative to existing models, which require measurement of up to seven formulation-specific parameters. This new result implies the product energy density scales with reactant kinetic energy density, which is the product of the explosive initial density and detonation velocity squared, for all condensed-phase energetic materials and that explosive microstructural or chemical details only influence the product energy density though these two parameters.

25 ENERGY STORAGE↗

Transport properties in dilute UN ( X ) solid solutions ( X = Xe , Kr )

Uranium nitride (UN) is a candidate fuel for current GEN III fission reactors, for which it is investigated as an accident-tolerant fuel, as well as for future GEN IV reactors. In this study, we investigate the kinetic properties of gas fission products (Xe and Kr) in UN. Binding and migration energies are obtained using density functional theory, with an added Hubbard correlation to model f electrons, and the occupation matrix control scheme to avoid metastable states. These energies are then used as input for the self-consistent mean field method which enables to determine transport coefficients for vacancy-mediated diffusion of Xe and Kr on the U sublattice. The magnetic ordering of the UN structure is explicitly taken into account, for both energetic and transport properties. Solute diffusivities are compared with experimental measurements and the effect of various parameters on the theoretical model is carefully investigated. We find that kinetic correlations are very strong in this system, and that despite atomic migration anisotropy, macroscopic solute diffusivities show limited anisotropy. Our model indicates that the discrepancy between experimental measurements probably results from different irradiation conditions, and hence different defect concentrations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

This article addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A novel parameter to describe the glass-forming ability of alloys

In this paper, we propose a new parameter for glass-forming ability (GFA) based on the combination of thermodynamic (stability of stable and metastable liquids by ΔT{sub m} = T{sub m}{sup mix} − T{sub l} and ΔT{sub x} = T{sub x} − T{sub g}, respectively) and kinetic (resistance to crystallization by T{sub x}) aspects for glass formation. The parameter is defined as ε = (ΔT{sub m} + ΔT{sub x} + T{sub x})/T{sub m}{sup mix} without directly adding T{sub g} while considering the whole temperature range for glass formation up to T{sub m}{sup mix}, which reflects the relative position of crystallization curve in continuous cooling transformation diagram. The relationship between the ε parameter and critical cooling rate (R{sub c}) or maximum section thickness for glass formation (Z{sub max}) clearly confirms that the ε parameter exhibits a better correlation with GFA than other commonly used GFA parameters, such as ΔT{sub x} (=T{sub x} − T{sub g}), K (=[T{sub x} − T{sub g}]/[T{sub l} − T{sub x}]), ΔT*(=(T{sub m}{sup mix} − T{sub l})/T{sub m}{sup mix}), T{sub rg} (=T{sub g}/T{sub l}), and γ (=[T{sub x}]/[T{sub l} + T{sub g}]). The relationship between the ε parameter and R{sub c} or Z{sub max} is also formulated and evaluated in the study. The results suggest that the ε parameter can effectively predict R{sub c} and Z{sub max} for various glass-forming alloys, which would permit more widespread uses of these paradigm-shifting materials in a variety of industries.

36 MATERIALS SCIENCE↗

The ilmenite/titano-magnetite assemblage - Kinetics of re-equilibration

The petrogenesis of igneous and metamorphic rocks is a function of several parameters. Of these, temperature and pressure are of particular importance. Information concerning these two parameters is obtained through the use of mineral indicators. One such commonly used geothermometer/oxybarometer is that involving ilmenite/titano-magnetite. Anomalously low temperatures have been reported in cases in which the geothermometer/oxybarometer was employed. The studies suggest that low temperatures result from slow cooling rates which allows the Fe-Ti oxides to re-equilibrate. The current investigation is mainly concerned with the kinetics of the reduction of ilmenite-hematite solid solution, since this is the slower and, consequently, rate-controlling step in the re-equilibration process. The reaction rates determined for the reduction of ilmenites in the investigation are geologically rapid and must be considered when applying the considered geothermometer/oxybarometer.

Hammond, P. A.↗

Ohm’s Law, the Reconnection Rate, and Energy Conversion in Collisionless Magnetic Reconnection

Magnetic reconnection is a ubiquitous plasma process that transforms magnetic energy into particle energy during eruptive events throughout the universe. Reconnection not only converts energy during solar flares and geomagnetic substorms that drive space weather near Earth, but it may also play critical roles in the high energy emissions from the magnetospheres of neutron stars and black holes. In this review article, we focus on collisionless plasmas that are most relevant to reconnection in many space and astrophysical plasmas. Guided by first-principles kinetic simulations and spaceborne in-situ observations, we highlight the most recent progress in understanding this fundamental plasma process. We start by discussing the non-ideal electric field in the generalized Ohm’s law that breaks the frozen-in flux condition in ideal magnetohydrodynamics and allows magnetic reconnection to occur. We point out that this same reconnection electric field also plays an important role in sustaining the current and pressure in the current sheet and then discuss the determination of its magnitude (i.e., the reconnection rate), based on force balance and energy conservation. This approach to determining the reconnection rate is applied to kinetic current sheets with a wide variety of magnetic geometries, parameters, and background conditions. We also briefly review the key diagnostics and modeling of energy conversion around the reconnection diffusion region, seeking insights from recently developed theories. Finally, future prospects and open questions are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗