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At least 253 records · Page 14

Intuitive reasoning about abstract and familiar physics problems

Previous research has demonstrated that many people have misconceptions about basic properties of motion. Two experiments examined whether people are more likely to produce dynamically correct predictions about basic motion problems involving situations with which they are familiar, and whether solving such problems enhances performance on a subsequent abstract problem. In experiment 1, college students were asked to predict the trajectories of objects exiting a curved tube. Subjects were more accurate on the familiar version of the problem, and there was no evidence of transfer to the abstract problem. In experiment 2, two familiar problems were provided in an attempt to enhance subjects' tendency to extract the general structure of the problems. Once again, they gave more correct responses to the familiar problems but failed to generalize to the abstract problem. Formal physics training was associated with correct predictions for the abstract problem but was unrelated to performance on the familiar problems.

Kaiser, Mary Kister↗

Light-curve solutions for S Cancri and TT Hydrae with rapid rotation

Physical model light- and velocity-curve solutions for S Cancri and TT Hydrae are obtained, and analyses with incorporation of asynchronous rotation are carried out. A photometric rotation rate for the primary star of TT Hya is determined, and excellent agreement with results from spectral line profiles is found. Both separate light- and velocity-curve solutions and simultaneous light-velocity solutions are listed. The photometric rotation for S Cnc from existing light curves is indeterminate, but is compatible with line profile measures. Evidence for third light from the light curves of S Cnc is found. An explanation for the apparent conflict between the rotational states and mass-transfer activities of the two binaries is suggested.

Van Hamme, W.↗

Revealing the role of redox reaction selectivity and mass transfer in current–voltage predictions for ensembles of photocatalysts

Photocatalysts are conceptually simple reaction units where nanoscale semiconductors integrated with catalysts drive a pair of redox reactions on illumination. However, the proximity of reaction sites performing cathodic and anodic reactions poses dire challenges to realize large light-to-fuel conversion efficiencies. In this study, a powerful, yet straightforward, equivalent-circuit detail-balance modeling framework is developed and applied to evaluate the performance of photocatalytic systems featuring multiple light absorbers. Specifically, low bandgap iridium-doped strontium titanate is modeled as a Z-scheme photocatalyst to achieve desirable hydrogen evolution and iron-based redox shuttle oxidation reactions. Our model has unique capabilities to simulate competing redox reactions and address mass-transfer limitations. In a significant departure from state-of-the-art circuit models, our study develops tools to perform load-line analyses by incorporating a net electrochemical load curve that includes both desired and competing redox reactions. Consequently, reaction selectivity is predicted from equivalent circuit models for photocatalytic and photoelectrochemical systems. Our investigation into ensembles comprised of multiple, semi-transparent light absorbers reveals their potential to outperform a single, optically thick light absorber, particularly when operated under mass-transfer-limited conditions. However, this outcome hinges on minimizing mass-transfer rates of select redox species to prevent undesired reactions of hydrogen oxidation and/or redox shuttle reduction. Our findings demonstrate that reaction selectivity can be achieved by tuning asymmetry in redox species mass-transfer even with perfectly symmetric electrocatalytic charge-transfer coefficients. The influences of various kinetic, mass-transfer, and thermodynamic parameters are explored to offer crucial insights for synthesis of the next-generation of photocatalysts and selective coatings, and reactor designs.

25 ENERGY STORAGE↗

LLNL measurements of thermally irradiated HEU sample and saltwater-matrixed HEU sample

Two scintillation vials, kindly provided by the PNNL team, were received in the LLNL radiochemistry building on June 10, 2024; one containing approximately 2 mL dissolved thermally-irradiated HEU, and the other containing dried salt from irradiated seawater. A quick, semiquantitative screening count of the salt showed that the activation product activities were very low, with the highest activity being ~1 Bq 24 Na. The dissolved HEU solution was transferred to a Prindle vial (LLNL standard counting geometry) and weighed. Approximately 2 mL 3 M HNO 3 was added so that the solution completely covered the bottom of the vial and Gamanal software would be able to accurately generate an efficiency curve. This sample, called “PNNLFP24” is the irradiated HEU solution received, gravimetrically diluted by a factor of 1.7356 ± 0.0003, and was sent for quick gamma counting prior to further modification. Meanwhile the salt was quantitatively transferred to a 250 mL polyethylene bottle and dissolved in 160 mL 3 M HNO 3 . After counting, 50 µL PNNLFP24 was aliquoted for Resonance Ionization Mass Spectrometry (RIMS) analysis, and then 10.0 mL of the salt solution (6.03% of the total salt, gravimetrically) was added to the remaining PNNLFP24 solution to make “PNNLFPSW24”. After weighing, two 100 µL aliquots were removed for RIMS and DES, and 3 mL was aliquoted for microfluidic chemistry. The remaining “PNNLFPSW24” solution was weighed and proceeded for singles and coincidence counting on the MCBOS system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of the early spectra and light curve of SN 1987A

Numerical modeling of supernova spectra, light curves, and hydrodynamics requires physical inputs, numerical techniques, approximations, and assumptions which must be thoroughly understood in order to study the details of supernova explosions. Here, we discuss some of these in the context of the early evolution of supernova 1987A. Gray radiation-hydrodynamics is used to calculate the bolometric light curve and the hydrodynamic evolution of the supernova. Synthetic spectra are then obtained for the resulting density and velocity structure. The spectrum calculations are performed using a special-relativistic treatment of the radiative transfer equation in the comoving frame, line blanketing by about 10(exp 5) spectral lines, and departures from local thermodynamic equilibrium (LTE) for H I, He I, Mg II, and Ca II. We find that we are able to simultaneously fit the early light curve and spectra reasonably well, using a progenitor model from Arnett (1991a), without fine-tuning the free parameters. Temperature structures and radiative equilibrium, non-LTE effects, homologous expansion, and mean opacities are discussed.

Hauschildt, Peter H.↗

Laminar Heat-Transfer and Pressure Measurements at a Mach Number of 6 on Sharp and Blunt 15 deg Half-Angle Cones at Angles of Attack Up to 90 deg

Two circular conical configurations having 15 deg half-angles were tested in laminar boundary layer at a Mach number of 6 and angles of attack up to 90 deg. One cone had a sharp nose and a fineness ratio of 1.87 and the other had a spherically blunted nose with a bluntness ratio of 0.1428 and a fineness ratio of 1.66. Pressure measurements and schlieren pictures of the flow showed that near-conical flow existed up to an angle of attack of approximately 60 deg. At angles of attack above 70 deg high-pressure areas were present near the base and the bow shock wave was considerably curved. Comparison of the results with simply applied theories showed that on the stagnation line pressures may be predicted by Newtonian theory, and heat transfer by local yawed-cylinder theory based on the yaw angle of the windward generator and the local radius of the cone. Base effects increased the heat transfer in a region extending forward approximately 15 to 30 percent of the windward generator. Circumferential pressure distributions were higher than the corresponding Newtonian distribution and a better prediction was obtained by modifying the theory to match the pressure at 90 deg from the windward generator to that on the surface of the cone at an angle of attack of 0 deg. Circumferential heat-transfer distributions were predicted satisfactorily up to about 60 deg from the stagnation line by using Lees' heat-flux distribution based on the Newtonian pressure. The effects of nose bluntness at large angles of attack were very small in the region beyond two nose radii from the point of tangency.

Conti, Raul J.↗

GC/MS Method Development for Separating Lunar Volatile Ice Simulant Headspace Gases

Various investigators propose the lunar surface contains widely distributed volatiles, especially water- like species, i.e. OH and H2O. Surface volatiles are theorized to exist as a hydrated regolith layer, concentrated in extremely cold polar permanently shadowed regions (PSR), and/or solar wind implantation reservoirs in lunar glasses. The proposed sources of lunar surface volatiles range from cometary impacts, solar wind, or a supply present during moon formation. Future Artemis missions aim to collect and return the samples containing volatiles collected near lunar polar craters or PSRs. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving returned sample integrity as much as possible. Pristine volatile-bearing samples are invaluable to the scientific community seeking to unravel the history of the solar system. Realistically, a sample will experience alteration during collection, transportation back to earth, and storage. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on high-fidelity volatile-containing regolith simulants, the foundation for the future of cold curation. This abstract outlines the separation, identification, and quantification of headspace gases over volatile ice feed stock material using gas chromatography/mass spectrometry (GC/MS). Preliminary objectives concentrated on sample handling, reproducibility, and understanding the elution characteristics for each analyte. Initial GC/MS method development experiments utilized diluted static headspace sample preparation. Diluted samples were used because sampling headspace gases directly from a vial containing liquid analyte resulted in overloading of the column and detector. Overloading is evident based on chromatogram peak shapes and instrument contamination, or carry over, between experiments. A mixture of three alcohols were used for a majority of the sample handling and reproducibility studies. Reproducibility was tested via multiple users, calibration curves, and check standards. Stock solutions of condensed lunar volatile analytes included methanol, ammonia in methanol, hydrogen sulfide in water, and an equal volume mixture of methanol, ethanol, and isopropanol. Current samples use room air as the headspace sample matrix, however future experiments will incorporate an inert purge gas, such as argon or nitrogen. Three mL of each analyte solution were capped in separate 20 mL crimp top GC vials. Dilutions were carried out by removing an aliquot of headspace gases with a calibrated 1 mL gastight syringe and immediately transferring to a 20 mL capped crimp top vial. The GC/MS is a Thermo Fisher Trace 1310/ISQ 7000 with a TriPlus RSH autosampler and split/splitless injector module. The experiments outlined in this abstract use the following hardware: a 2.5 mL gastight headspace syringe tool, 1 mm ID x 78.5 mm length ultra-inert straight injection liner, and a TG-BondQ 30 m × 0.32 mm × 10 μm column. Various parameters, such as hardware selection and the temperature, pressure, and split ratio set points, continue to evolve as the overall experiment is refined. Diluted headspace chromatograms were collected for the individual stock solutions. Retention times, peak shapes, and mass spectra were evaluated and added to the data processing method for each molecule of interest. Figure 1 shows the total ion chromatograms for the three major lunar volatile simulant stock solutions: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. Tailing peak shapes for ammonia (2.98 min rt) and water (4.06 min rt) indicate the molecules are not properly eluting from the selected column with the current separation method. Additionally, hydrogen sulfide and ammonia have overlapping peak windows, which could impact quantification. Ongoing experiments aim to address the peak shape and overlapping via the separation method and hardware selection. Sample preparation reproducibility experiments used stock solution containing equal volumes of a non- interactive mixture of methanol, ethanol, and isopropanol. Mass spectrum ion traces were used to identify and quantify all three alcohols. Peaks were automatically detected, identified, and integrated through the mass spectra detection and processing parameters. Calibration response curves and check standards were used to evaluate the validity of the sample preparation procedure. Figure 2 shows the methanol chromatogram peak area versus total headspace dilution volume transferred from the alcohol mixture vial. The calibration response curves and check standards validate sample preparation procedure. Continuing data analysis efforts are working towards correlating the peak area and instrument response factor to the headspace analyte concentration and condensed phase composition. Static headspace gas chromatography theory relies on Dalton’s law, Raoult’s law, Henry’s Law, and the Kolb and Ettre equation to associate peak area to the analyte composition in a non-ideal solution. Equation 1 is a simplified expression derived from the aforementioned theories. Future experiments involve liquid injections of the individual stock solutions, liquid and headspace analysis of various stock solution combinations, and the addition of regolith simulants to the mixtures. Temperature is another variable expected to affect reaction rates and will be explored.

Cecilia L. Amick↗

Planetary spectra for anisotropic scattering

Some effects on planetary spectra that would be produced by departures from isotropic scattering are examined. The phase function is the simplest departure to handle analytically and the only phase function, other than the isotropic one, that can be incorporated into a Chandrasekhar first approximation. This approach has the advantage of illustrating effects resulting from anisotropies while retaining the simplicity that yields analytic solutions. The curve of growth is the sine qua non of planetary spectroscopy. The discussion emphasizes the difficulties and importance of ascertaining curves of growth as functions of observing geometry. A plea is made to observers to analyze their empirical curves of growth, whenever it seems feasible, in terms of coefficients of which are the leading terms in radiative-transfer analysis. An algebraic solution to the two sets of anisotropic H functions is developed which gives emergent intensities accurate to 0.3%.

Chamberlain, J. W.↗

Solar panel acceptance testing using a pulsed solar simulator

Utilizing specific parameters as area of an individual cell, number in series and parallel, and established coefficient of current and voltage temperature dependence, a solar array irradiated with one solar constant at AMO and at ambient temperature can be characterized by a current-voltage curve for different intensities, temperatures, and even different configurations. Calibration techniques include: uniformity in area, depth and time, absolute and transfer irradiance standards, dynamic and functional check out procedures. Typical data are given for individual cell (2x2 cm) to complete flat solar array (5x5 feet) with 2660 cells and on cylindrical test items with up to 10,000 cells. The time and energy saving of such testing techniques are emphasized.

Hershey, T. L.↗

On the interweaving of partial cross sections of different parity

Partial cross sections of definite parity, calculated for electronic-rotational energy transfer in the F +H2 collision system, interweave with increasing total angular momentum J. An explanation, in terms of diabatic curve crossings induced by the centrifugal potential in the body-fixed coordinate system, predicts the interweaving to occur only in systems having half-integer J.

Devries, P. L.↗

Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis

To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1 %) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucteotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.

Weber, Arthur L.↗

Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis

To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1%) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucleotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.

Weber, Arthur L.↗

Optimized Highly Efficient SSCB Using Organic Substrate Packaging for Electric Vehicle Applications

Solid State Circuit Breakers (SSCBs) are an attractive protection solution for their arcless current interruption and fast actuation speeds over mechanical breakers. This paper proposes a Bidirectional SSCB (BSSCB) with a thermally defined and digitally controlled current time profile for fault protection in EV and other low-voltage DC systems. The paper proposes an organic packaging approach utilizing flex circuitry to develop a reliable, cost-effective power module for BSSCBs. The paper studies transient heat transfer in the power modules using finite element analysis (FEA). An RC themal ladder network is extracted to define a fusing curve. To demonstrate and verify the design, a 1kV/50 A SiC MOSFET BSSCB prototype is fabricated and tested, having a power density of 60 W/cm3 and 4x reduction in form factor over presently researched breakers. Also, given are results for 750 V/150 A operation showing interruption in 2.4 μs.

organic power packaging↗

Prediction of error rates in dose-imprinted memories on board CRRES by two different methods

An analysis of the expected space radiation effects on the single event upset (SEU) properties of CMOS/bulk memories onboard the Combined Release and Radiation Effects Satellite (CRRES) is presented. Dose-imprint data from ground test irradiations of identical devices are applied to the predictions of cosmic-ray-induced space upset rates in the memories onboard the spacecraft. The calculations take into account the effect of total dose on the SEU sensitivity of the devices as the dose accumulates in orbit. Estimates of error rates, which involved an arbitrary selection of a single pair of threshold linear energy transfer (LET) and asymptotic cross-section values, were compared to the results of an integration over the cross-section curves versus LET. The integration gave lower upset rates than the use of the selected values of the SEU parameters. Since the integration approach is more accurate and eliminates the need for an arbitrary definition of threshold LET and asymptotic cross section, it is recommended for all error rate predictions where experimental sigma-versus-LET curves are available.

Brucker, G. J.↗

PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Prediction

Understanding protein structure-function relationships is a key challenge in computational biology, with applications across the biotechnology and pharmaceutical industries. While it is known that protein structure directly impacts protein function, many functional prediction tasks use only protein sequence. In this work, we isolate protein structure to make functional annotations for proteins in the Protein Data Bank in order to study the expressiveness of different structure-based prediction schemes. We present PersGNN - an end-to-end trainable deep learning model that combines graph representation learning with topological data analysis to capture a complex set of both local and global structural features. While variations of these techniques have been successfully applied to proteins before, we demonstrate that our hybridized approach, PersGNN, outperforms either method on its own as well as a baseline neural network that learns from the same information. PersGNN achieves a 9.3% boost in area under the precision recall curve (AUPR) compared to the best individual model, as well as high F1 scores across different gene ontology categories, indicating the transferability of this approach.

Swenson, Nicolas↗

Accretion onto a Supermassive Black Hole Binary before Merger

While supermassive binary black holes (SMBBHs) inspiral toward merger they may also accrete matter from a surrounding disk. To study the dynamics of this system requires simultaneously describing the evolving spacetime and the magnetized plasma. We present the first relativistic calculation simulating two equal-mass, nonspinning black holes as they inspiral from a 20 M (G = c = 1) initial separation almost to merger. Our results imply important observational consequences: for instance, the accretion rate $\dot{M}$ onto the black holes first decreases and then plateaus, dropping by only a factor of ~3 despite the rapid inspiral. An estimated bolometric light curve follows the same profile, suggesting some merging SMBBHs may be significantly luminous past the predicted circumbinary disk decoupling. The minidisks are nonstandard: Reynolds, not Maxwell, stresses dominate, and they oscillate between two states. In one part of the cycle, "sloshing" streams transfer mass between minidisks, carrying kinetic energy at a rate sometimes as high as the peak minidisk bolometric luminosity. We also discover that episodic accretion drives time-varying minidisk tilts. These complex dynamics all contribute to unique cyclical behavior in the light curves of late-time inspiraling SMBBHs. The poloidal magnetic flux on the black holes is roughly constant at a dimensionless level $\phi$ ~ 2–3, but doubles just before merger; for significant black hole spin, this flux predicts powerful jets with variability driven by binary dynamics, another potentially unique electromagnetic signature. This simulation is the first to employ our multipatch infrastructure PATCHWORK MHD, decreasing the computational expense to ~3% of conventional single-grid methods' cost.

79 ASTRONOMY AND ASTROPHYSICS↗

Bio-inspired alula-based winglet design for enhanced heat transfer in high temperature fin-and-tube heat exchangers

Fin-and-tube heat exchangers (FTHEs) are widely used for high-temperature flue-gas heat recovery, but their performance is often limited by wake regions and non-uniform fin-surface temperatures. This study proposes and numerically evaluates four bio-inspired longitudinal vortex generator (VG) configurations in a high-temperature FTHE with flue-gas inlet temperature ∼1230 K: double-delta, curved double-delta, alula, and a new curved-alula geometry. The reference fin is not hydraulically plain; it already incorporates leading-edge separation columns and convex protrusions, so the alula-type winglets are assessed as downstream add-ons acting on a strongly disturbed flow. In a second step, perforations (one, two and three circular holes) are introduced into the curved-alula VGs to further tailor the flow field. Three-dimensional simulations with the Shear Stress Transpor (SST) $k - ω$ model, temperature-dependent flue-gas properties and conjugate conduction are carried out for gas-side Reynolds numbers $Re_g ≈ 8.0$ x $10^2 - 3.6$ x $10^3$ (mass flow rates 0.5 – 2.5 g/s), and the designs are compared in terms of surface heat flux, Nusselt number, friction factor and hydrothermal performance factor (HTPF). For this already-promoted fin, the additional downstream winglets provide moderate, incremental hydrothermal gains. At the highest Reynolds number, the best non-perforated design (curved-alula) increases surface heat flux from 1630.9 to 1794.7 kW/m² (∼ 10 % gain) and the Nusselt number from 227.6 to 242.6 (∼ 7 % gain), while the friction factor rises from 0.26 to about 0.30, yielding HTPF values close to unity (∼ 0.9 – 1.0). Introducing circular perforations into the curved-alula winglets acts mainly as a wake-bleeding refinement: the three-hole configuration provides a heat flux of 1824.7 kW/m² and a pressure drop of 127.9 Pa, with HTPF in the range ∼ 1.03 – 1.14 and a small (∼ 1 – 3 %) improvement over the solid curved-alula design. Flow-field analysis shows that the perforated curved-alula VGs shrink tube-wake regions, thin the thermal boundary layer and homogenize the fin-surface temperature (outlet-gas temperature ∼ 510 – 520 K and fin-surface temperature ∼ 420 – 421 K for the three-hole case). An optimal flue-gas mass flow rate of ∼ 1 g/s ($Re_g ≈ 1.5$ x $10^3$) is identified, beyond which additional heat-transfer gains are offset by rapidly increasing pressure losses. Overall, the results highlight that initial fin geometry and VG placement are as important as VG shape: alula-based winglets are expected to yield larger relative gains on simpler flat-fin layouts or when positioned closer to the fin leading edge and tube

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Axisymmetric Radiative Transfer Models of Kilonovae

The detailed observations of GW170817 proved for the first time directly that neutron star mergers are a major production site of heavy elements. The observations could be fit by a number of simulations that qualitatively agree, but can quantitatively differ (e.g., in total r-process mass) by an order of magnitude. We categorize kilonova ejecta into several typical morphologies motivated by numerical simulations, and apply a radiative transfer Monte Carlo code to study how the geometric distribution of the ejecta shapes the emitted radiation. We find major impacts on both spectra and light curves. The peak bolometric luminosity can vary by two orders of magnitude and the timing of its peak by a factor of five. These findings provide the crucial implication that the ejecta masses inferred from observations around the peak brightness are uncertain by at least an order of magnitude. Mixed two-component models with lanthanide-rich ejecta are particularly sensitive to geometric distribution. A subset of mixed models shows very strong viewing angle dependence due to lanthanide "curtaining," which persists even if the relative mass of lanthanide-rich component is small. The angular dependence is weak in the rest of our models, but different geometric combinations of the two components lead to a highly diverse set of light curves. We identify geometry-dependent P Cygni features in late spectra that directly map out strong lines in the simulated opacity of neodymium, which can help to constrain the ejecta geometry and to directly probe the r-process abundances.

79 ASTRONOMY AND ASTROPHYSICS↗