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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 271 records · Page 15

Can We Reconcile the TA Excess and Hotspot with Auger Observations?

The Telescope Array (TA) shows a 20° hotspot as well as an excess of ultra-high-energy cosmic-rays (UHECRs) above 50 EeV when compared with the Auger spectrum. We consider the possibility that both the TA excess and hotspot are due to a dominant source in the northern sky. We carry out detailed simulations of UHECR propagation in both the intergalactic medium and the Galaxy, using different values for the intergalactic magnetic field. We consider two general classes of sources: transients and steady, adopting a mixed UHECR composition that is consistent with the one found by Auger. The spatial location of the sources is drawn randomly. We generate Auger-like and TA-like data sets from which we determine the spectrum, the sky maps, and the level of anisotropy. We find that, while steady sources are favored over transients, it is unlikely to account for all the currently available observational data. While we reproduce fairly well the Auger spectrum for the vast majority of the simulated data sets, most of the simulated data sets with a spectrum compatible with that of TA (at most a few percent depending on density model tested) show a much stronger anisotropy than the one observed. We find that the rare cases in which both the spectrum and the anisotropy are consistent require a steady source within ∼10 Mpc, to account for the flux excess, and a strong extragalactic magnetic field ∼10 nG, to reduce the excessive anisotropy.

79 ASTRONOMY AND ASTROPHYSICS↗

Informing models through empirical relationships between foliar phosphorus, nitrogen and photosynthesis across diverse woody species in tropical forests of Panama

Here, our objective was to analyze and summarize data describing photosynthetic parameters and foliar nutrient concentrations from tropical forests in Panama to inform model representation of phosphorus (P) limitation of tropical forest productivity. Gas exchange and nutrient content data were collected from 144 observations of upper canopy leaves from at least 65 species at two forest sites in Panama, differing in species composition, rainfall and soil fertility. Photosynthetic parameters were derived from analysis of assimilation rate vs internal CO 2 concentration curves ( A/C i ), and relationships with foliar nitrogen (N) and P content were developed. The relationships between area-based photosynthetic parameters and nutrients were of similar strength for N and P and robust across diverse species and site conditions. The strongest relationship expressed maximum electron transport rate (J max ) as a multivariate function of both N and P, and this relationship was improved with the inclusion of independent data on wood density. Models that estimate photosynthesis from foliar N would be improved only modestly by including additional data on foliar P, but doing so may increase the capability of models to predict future conditions in P-limited tropical forests, especially when combined with data on edaphic conditions and other environmental drivers.

54 ENVIRONMENTAL SCIENCES↗

Aqueous-phase effects on ethanol decomposition over Ru-based catalysts

The effects of an aqueous phase on ethanol decomposition for hydrogen production over a Ru(0001) catalyst surface model have been investigated from first principles. Solvent effects on the reaction mechanism and kinetic parameters have been quantified with the help of a microkinetic reactor model, density functional theory, and an implicit solvation scheme (iSMS). Our calculations indicate that in both vapor- and aqueous-phase reaction environments, the ethanol decomposition starts with acetaldehyde formation on the surface, some of which further dehydrogenates to ketenyl species (CHCO), where the C–C bond cleaves to form methylidyne (CH) and CO. In the vapor phase, adsorbed CH gets hydrogenated to methane, and CO desorbs or undergoes methanation reducing the amount of hydrogen produced. In contrast, under aqueous phase reaction conditions, the methanation is inhibited, and the water–gas shift (WGS) reaction is accelerated, leading to complete conversion of CO to CO 2 and H 2 . Furthermore, calculations indicate that the observed reaction behavior under aqueous phase reforming conditions originates primarily from the higher water chemical potential, and implicit solvent models predict only a small solvation effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Venus gravity field - Pioneer Venus Orbiter navigation results

The gravity field of Venus has been modeled by a spherical harmonic expansion of the potential to degree and order seven. The estimates of these coeficients were obtained by combining information from 43 short arcs (4 hr) of line-of-sight Doppler data centered at periapsis. The data arcs were distributed in longitude and time over more than two circulations of Venus by the Pioneer Venus Orbiter subperiapsis point which was confined to the band of latitudes from 14 deg N to 17 deg N. Convergence of the solution has been assured by iterating upon the initial estimate. All estimates were performed with zero a priori information on the gravity coefficients. Since the altitude of periapsis for most of the orbits was within the sensible Venusian atmosphere, drag effects on the estimated harmonics have been removed using an exponential atmosphere density model. Estimates of the mass parameter (GM) of Venus using this dataset are also evaluated.

Williams, B. G.↗

Terrestrial Exospheric Dayside H-density Profile at 3 - 15 RE from UVIS/HDAC and TWINS Lyman-alpha Data Combined

Terrestrial ecliptic dayside observations of the exospheric Lyman-α column intensity between 3–15 Earth radii (RE) by UVIS/HDAC (UVIS – ultraviolet imaging spectrograph; HDAC – hydrogen-deuterium absorption cell) Lyman-α photometer at CASSINI have been analyzed to derive the neutral exospheric H-density profile at the Earth’s ecliptic dayside in this radial range. The data were measured during CASSINI’s swing-by maneuver at the Earth on 18 August 1999 and are published by Werner et al. (2004). In this study the dayside HDAC Lyman-α observations published by Werner et al. (2004) are compared to calculated Lyman-α intensities based on the 3D H-density model derived from TWINS (Two Wide-angle Imaging Neutral-atom Spectrometers) Lyman-α observations between 2008–2010 (Zoennchen et al., 2015). It was found that both Lyman-α profiles show a very similar radial dependence in particular between 3–8RE. Between 3.0–5.5RE impact distance Lyman-α observations of both TWINS and UVIS/HDAC exist at the ecliptic dayside. In this overlapping region the cross-calibration of the HDAC profile against the calculated TWINS profile was done, assuming that the exosphere there was similar for both due to comparable space weather conditions. As a result of the cross-calibration the conversion factor between counts per second and rayleigh, fc = 3.285 counts s−1R−1, is determined for these HDAC observations. Using this factor, the radial H-density profile for the Earth’s ecliptic dayside was derived from the UVIS/HDAC observations, which constrained the neutral H density there at 10RE to a value of 35 cm-3. Furthermore, a faster radial H-density decrease was found at distances above 8RE (≈r−2.37) compared to the lower distances of 3–7RE (≈r−2.37). This increased loss of neutral H above 8RE might indicate a higher rate of H ionization in the vicinity of the magnetopause at 9–11RE (near subsolar point) and beyond, because of increasing charge exchange interactions of exospheric H atoms with solar wind ions outside the magnetosphere.

Jochen H Zoennchen↗

Shuttle structural dynamics characteristics: The analysis and verification

The space shuttle introduced a new dimension in the complexity of the structural dynamics of a space vehicle. The four-body configuration exhibited structural frequencies as low as 2 hertz with a model density on the order of 10 modes per hertz. In the verification process, certain mode shapes and frequencies were identified by the users as more important than others and, as such, the test objectives were oriented toward experimentally extracting those modes and frequencies for analysis and test correlation purposes. To provide the necessary experimental data, a series of ground vibration tests (GVT's) was conducted using test articles ranging from the 1/4-scale structural replica of the space shuttle to the full-scale vehicle. The vibration test and analysis program revealed that the mode shapes and frequency correlations below 10 hertz were good. The quality of correlation of modes between 10 and 20 hertz ranged from good to fair and that of modes above 20 hertz ranged from poor to good. Since the most important modes, based on user preference, were below 10 hertz, it was judged that the shuttle structural dynamic models were adequate for flight certifications.

Modlin, C. T., Jr.↗

The role of excited-state ionization on the effective ionization of neutral neon using non-perturbative atomic data

With the aim of providing accurate atomic data for plasma edge temperature and density modeling with neutral neon, new non-perturbative R-Matrix with Pseudostates (RMPS) calculations are performed for both the electron-impact excitation and ionization of neutral neon. The new calculations agree well with past measurements and calculations for both electron-impact excitation and ionization. For ionization, the addition of pseudostates from $5\bar{d}$ to $12\bar{i}$ allows us to extract new cross sections and rate coefficients for all of the excited states through 2p 5 5p. The new RMPS ionization calculation gives a 20% increase in the cross section for the $2{p}^{5}5s$ ionization compared with previous non-perturbative calculations and shows classically-expected n 4 -scaled convergence for the np and nd valence shells. Ionization from these excited states contributes significantly to the effective ionization rate coefficient: a factor of three more than the ground-state ionization rate coefficient at an electron temperature of 25 eV and density of 1014 cm -3 . An accurate, non-perturbative set of atomic rates, both LS- and LSJ-resolved, for neutral neon across a wide range of temperatures and densities is compiled.

Optics↗

Analysis of Ice Mass Growth Over Time on the CRM65 Midspan Hybrid Model

The Aeronautics Research Mission Directorate at NASA is developing and applying tools to enable future technologies towards sustainable flight. Aircraft icing has been identified as a potential barrier to entry into service for innovative designs necessitating improvements to computational ice accretion tools. NASA is developing the Glenn Icing Computational Environment (GlennICE) to address deficiencies in the computational modeling capabilities of previously developed ice accretion solvers. To benchmark and improve the ability to model highly three-dimensional ice accretion, high quality validation data against experimental data is required. The CRM65 Midspan Hybrid geometry was previously tested at the NASA Icing Research Tunnel to generate experimental data for swept wing geometries typical for commercial transport aircraft. As a part of a 2018 icing test campaign, experimental data characterizing the relationship between ice accretion time and ice mass growth was obtained and can be leveraged for use in validation of computational tools. The desire for computational ice accretion solvers to predict ice shapes profiles accreted experimentally has often overshadowed the comparison to the mass and bulk volume of ice accreted. To address this deficiency, an analysis is presented in which GlennICE is applied to simulations of the CRM65 Midspan Hybrid model tested in the NASA Icing Research Tunnel. Results from the computational fluid dynamics simulations compared favorably to the experimental pressure coefficient data, thus validating the modeling setup. The experimental data showed excellent repeatability for the 15.0 minute accretion time. The comparisons between the experimental and computational ice mass over time showed good agreement up to 10.0 minutes after which the ice mass was underpredicted. The experimental ice mass was largely linear with some nonlinear data. The bulk volume of ice accreted experimentally compared well to GlennICE for the scanned ice shapes and mean combined cross section ice shapes, but was underpredicted for the maximum combined cross section ice shapes at longer accretion times. The experimental minimum combined cross section, mean combined cross section, and maximum combined cross section profiles when compared to GlennICE show good agreement for the mean combined cross section up to 15.0 minutes. The analyses show that with a single-shot method, GlennICE currently underpredicts the ice mass for longer accretion times, is not able to match the bulk volume of the maximum combined cross section due to dominating scallop features, and future work is required to generate a more generalized ice bulk density model.

Icing↗

Analysis of Ice Mass Growth Over Time on the CRM65 Midspan Hybrid Model

The Aeronautics Research Mission Directorate at NASA is developing and applying tools to enable future technologies towards sustainable flight. Aircraft icing has been identified as a potential barrier to entry into service for innovative designs necessitating improvements to computational ice accretion tools. NASA is developing the Glenn Icing Computational Environment (GlennICE) to address deficiencies in the computational modeling capabilities of previously developed ice accretion solvers. To benchmark and improve the ability to model highly three-dimensional ice accretion, high quality validation data against experimental data is required. The CRM65 Midspan Hybrid geometry was previously tested at the NASA Icing Research Tunnel to generate experimental data for swept wing geometries typical for commercial transport aircraft. As a part of a 2018 icing test campaign, experimental data characterizing the relationship between ice accretion time and ice mass growth was obtained and can be leveraged for use in validation of computational tools. The desire for computational ice accretion solvers to predict ice shapes profiles accreted experimentally has often overshadowed the comparison to the mass and bulk volume of ice accreted. To address this deficiency, an analysis is presented in which GlennICE is applied to simulations of the CRM65 Midspan Hybrid model tested in the NASA Icing Research Tunnel. Results from the computational fluid dynamics simulations compared favorably to the experimental pressure coefficient data, thus validating the modeling setup. The experimental data showed excellent repeatability for the 15.0 minute accretion time. The comparisons between the experimental and computational ice mass over time showed good agreement up to 10.0 minutes after which the ice mass was underpredicted. The experimental ice mass was largely linear with some nonlinear data. The bulk volume of ice accreted experimentally compared well to GlennICE for the scanned ice shapes and mean combined cross section ice shapes, but was underpredicted for the maximum combined cross section ice shapes at longer accretion times. The experimental minimum combined cross section, mean combined cross section, and maximum combined cross section profiles when compared to GlennICE show good agreement for the mean combined cross section up to 15.0 minutes. The analyses show that with a single-shot method, GlennICE currently underpredicts the ice mass for longer accretion times, is not able to match the bulk volume of the maximum combined cross section due to dominating scallop features, and future work is required to generate a more generalized ice bulk density model.

Icing↗

Charged-cell periodic DFT simulations via an impurity model based on density embedding: Application to the ionization potential of liquid water

Calculations of charged systems in periodic boundary conditions (PBC) are problematic because there are spurious interactions between the charges in different periodic images that can affect the physical picture. In addition, the intuitive limit of Coulomb interactions decaying to zero as the interacting charges are placed at infinite separation no longer applies, and for example total energies become undefined. Leveraging subsystem density functional theory (also known as density embedding) we define an impurity model that embeds a finite neutral or charged subsystem within an extended (infinite) surrounding subsystem. The combination of the impurity model and a consistent choice of the Coulomb reference provides us with an algorithm for evaluating the ionization potential (IP) in extended systems. Additionally, we demonstrate our approach in a pilot calculation of the IP of liquid water, based on a configuration from a prior ab initio molecular dynamics (AIMD) simulation of liquid water (Genova et al., J. Chem. Phys. 2016, 144, 234105). The calculations with the impurity model capture the broadening on the ionization energies introduced by the interactions between the water molecules. Furthermore, the calculated average IP value (10.5 eV) compare favorably to experiments (9.9-10.06 eV) and very recent simulations based on the GW approximation (10.55 eV), while at the same time outperforming density embedding calculations carried out with a naïve handling of the electrostatic interactions (about 7 eV).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Defect Thermodynamics and Transport Properties of Proton Conducting Perovskite Electrode and Electrolyte Materials Evaluated Based on Density Functional Theory Modeling

Both electron-rich and electron-poor perovskite oxides have been used in solid oxide cell applications as electrode and electrolyte materials. The rich oxygen defect chemistry and its coupling to temperature, hydrogen-steam or oxygen-steam gas pressure, or to the applied potentials creates enormous complexities for modeling performance and degradation of the materials. Herein, density functional theory-based thermodynamic modeling was carried out to describe the defect chemistry and transport properties of the proton-conducting electrolyte BaZr1-xYxO3-δ (x≤0.1) and of the triple-conducting perovskite (La,Ba)(Fe,M)O3-δ (M=Y and Zr). The defect thermodynamics of intrinsic point defects and the hydrogen-related defect reactions were solved in integrated defect models and further used to predict the Brouwer diagram and the transport properties of the functional perovskites. For the electron-poor electrolytes BaZr0.9Y0.1O3-δ, the developed model has been used to describe the experimental transport properties in the SOC operating conditions. Specifically, the roles played by the acceptor-bound holes and the intrinsic and hydrogen point defects upon the conductivities of holes, protons, and oxygen vacancies under the hydrogen-rich and oxygen-rich conditions at various humidity levels were demonstrated. A defect modeling tool was also developed for the triple-conducting perovskite (La,Ba)(Fe,M)O3-δ (M=Y and Zr) to examine magnetic effects and hydride defects in defect equilibria.

defect thermodynamics↗

Bridging confined phase behavior of CH 4 -CO 2 binary systems across scales

Phase behavior of confined fluids may deviate significantly from that of the bulk fluid due to the fluid-wall interactions being a significant portion of all intermolecular interactions under confinement. Despite recent advancements in understanding confined phase behavior of pure fluids, confined phase behavior of mixtures remains an understudied topic. In this work, we examine the confined phase behavior of a CH 4 -CO 2 binary system by combining Monte Carlo (MC) simulations, a cubic equation of state (EoS), and the lattice Boltzmann method (LBM). First, the effects of confinement on density and phase distribution in nano-size pores are established using Gibbs Ensemble MC calculations, which produce precise results of liquid and vapor confined pressures and account for the modification of the phase change location. By comparing the phase envelopes of bulk and confined mixtures at a fixed temperature, here it is observed that the phase envelopes shrink with reductions in pore size. Based on this observation, we extend a modified Peng-Robinson EoS, which was originally developed for pure fluids under confinement, to mixtures via van-der-Waals-type mixing rules and by accounting for shifts in the critical properties of confined CH 4 -CO 2 . The resulting phase envelopes are in good agreement with the MC data. In addition, a local density model is used in combination with the confined EoS to calculate adsorption isotherms of CH 4 -CO 2 mixtures and to characterize the behavior of confined matter in nanopores. Finally, we incorporate this EoS in a multicomponent multiphase LBM that uses a pseudopotential model to represent intermolecular forces. This workflow utilizes multiscale simulation techniques to bridge the behavior of multicomponent systems across scales and to shed light on the confined phase behavior of CH 4 -CO 2 binary systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-resolution lithospheric structure of continental China from joint inversion of surface wave and gravity data

The lithospheric structure of continental China has been previously determined by seismic travel time tomography, surface wave tomography, and joint inversion of body wave and surface wave data. However, due to the inherent limitations of seismic data, the lithospheric structure of continental China is still not well resolved in the shallow part and in some regions where the station coverage is relatively sparse. In this study, we aim at improving the lithospheric structure by joint inversion of seismic surface wave data and satellite gravity data to take advantage of the uniform distribution and complementary strength of the gravity data. Here, the empirical relationship between velocity and density is used as a bridge for joint inversion of surface wave and gravity data. The joint inversion shear-wave velocity Vs (density) model, named as USTClitho1.0g, can fit both surface wave and gravity data well. This high-resolution Vs model can better fit the active airgun source seismic arrival times and better delineate some features in continental China, such as the velocity contrast across the north–south gravity lineament (NSGL), the lithosphere thinning in eastern China, the crustal footprint of the Hainan mantle plume, the likely magma chamber beneath volcanos in northeast China, the middle-lower crust low velocity layer beneath the Tibetan plateau, and the tearing of subducted Indian mantle lithosphere. Our joint inversion Vs model can provide a reference model for geosciences in continental China and surrounding areas.

58 GEOSCIENCES↗

Multiresolution 3D-DenseNet for Chemical Shift Prediction in NMR Crystallography

We have developed a deep learning algorithm for chemical shift prediction for atoms in molecular crystals that utilizes an atom-centered Gaussian density model for the 3D data representation of a molecule. We define multiple channels that describe different spatial resolutions for each atom type that utilizes cropping, pooling, and concatenation to create a multiresolution 3D-DenseNet architecture (MR-3D-DenseNet). Because the training and testing time scale linearly with the number of samples, the MR-3D-DenseNet can exploit data augmentation that takes into account the property of rotational invariance of the chemical shifts, thereby also increasing the size of the training data set by an order of magnitude without additional cost. We obtain very good agreement for 13 C, 15 N, and 17 O chemical shifts when compared to ab initio quantum chemistry methods, with the highest accuracy found for 1 H chemical shifts that is comparable to the error between the ab initio results and experimental measurements. Principal component analysis (PCA) is used to both understand these greatly improved predictions for 1 H , as well as indicating that chemical shift prediction for 13 C, 15 N, and 17 O, which have far fewer training environments than the 1 H atom type, will improve once more unique training samples are made available to exploit the deep network architecture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dry Reforming of Methane on Single-Site Ni/MgO Catalysts: Importance of Site Confinement

Single-site catalysts (SSCs) have drawn considerable attention, because of their superior behaviors in catalysis. However, the origin of promoting the effect of a single site is not well understood. Here in this paper, we take the single-atom Ni1/Mg(100) and single-site Ni4/Mg(100) catalysts as a case study to elucidate their behaviors under the complex dry reforming of methane (DRM, CO 2 + CH 4 → 2CO + 2H 2 ) reaction by combining theoretical modeling (density functional theory and kinetic Monte Carlo simulation) and experimental studies. The synergy between single Ni atom and MgO is found to improve the binding property of MgO; yet, it is not enough to dissociate CO 2 and CH 4 . It can be achieved by the single-site Ni 4 /MgO(100) catalyst, enabling the formations of CO, H 2 , and H 2 O under the DRM conditions. During this process, coking, as observed for bulklike Ni particles, is eliminated. By confining the reaction to occur at the isolated Ni sites in the SSC, the Ni 4 /MgO(100) catalyst is able to balance the CO 2 and CH 4 activations, which is identified as the key for tuning the DRM activity and selectivity of Ni/MgO catalysts. The theory-identified promotion introduced by increasing the size of MgO-supported Ni clusters from Ni 1 to Ni 4 and the MgO-introduced site confinement of single-site catalysts are verified by corresponding experimental studies, highlighting the essential roles of confined sites in tuning the performance of SSCs during complex catalytic processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Single-Polymer–Particle Growth Kinetics with Molecular Catalyst Speciation and Single-Turnover Imaging

The dynamics of the local environments surrounding molecular polymerization catalysts plausibly impact turnover kinetics, but the impact of and nature of such dynamics have previously been obscured by ensemble averaging. With Grubbs’ second generation ruthenium metathesis catalyst and a precipitation polymerization system, studies at the single-particle and -turnover level establish that (1) an inverse correlation exists between rate and duration of single-polymer–particle growth of aggregates, consistent with a local environment density model for the time-variable kinetics; (2) cross-linking additives produced a small, but detectible, reduction in overall monomer incorporation; (3) total ruthenium quantity within the polymer particles (as characterized by energy dispersive X-ray spectroscopy) is differentiable from the quantity that is catalytically active (as characterized by in situ fluorescence microscopy), providing catalyst speciation information; and (4) time-resolved enyne metathesis reactions can be imaged, corresponding to single turnovers at individual molecular catalysts during polymer growth under synthetically relevant conditions. Here, these findings identify and characterize reactivity distributions likely arising from the dynamics of local environments. As such, these data provide reactivity information that is unavailable through traditional ensemble analytical methods that obscure this type of information through averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Validation of emission-line galaxies target selection algorithms for the Dark Energy Spectroscopic Instrument using the MMT Binospec

ABSTRACT The forthcoming Dark Energy Spectroscopic Instrument (DESI) experiment plans to measure the effects of dark energy on the expansion of the Universe and create a 3D map of the Universe using galaxies up to z ∼ 1.6 and QSOs up to z ∼ 3.5. In order to create this map, DESI will obtain spectroscopic redshifts of over 30 million objects; among them, a majority are [O ii] emitting star-forming galaxies known as emission-line galaxies (ELGs). These ELG targets will be pre-selected by drawing a selection region on the g − r versus r − z colour–colour plot, where high-redshift ELGs form a separate locus from the lower redshift ELGs and interlopers. In this paper, we study the efficiency of three ELG target selection algorithms – the Final Design Report (FDR) cut based on the DEEP2 photometry, Number Density Modelling (NDM) and Random Forest – to determine how the combination of these three algorithms can be best used to yield a simple selection boundary that will be best suited to meet DESI’s science goals. To do this, we selected 17 small patches in the DESI footprint where we run the three target selection algorithms to pre-select ELGs based on their photometry. We observed the pre-selected ELGs using the MMT Binospec, which is similar in functionality to the DESI instrument, to obtain their spectroscopic redshifts and fluxes of 1054 ELGs. By analysing the redshift and fluxing distribution of these galaxies, we find that although NDM performed the best, simple changes in the FDR definition would also yield sufficient performance.

79 ASTRONOMY AND ASTROPHYSICS↗

Double copy root of Hawking thermality

The Hawking radiation spectrum from a collapsing null shell can be derived via the double copy of a simpler gauge theory calculation. Analyzing the non-abelian Yang-Mills root of this process, we demonstrate that the radiation spectrum is thermal in the color charge eigenvalue 𝜆, not energy. Considering the 𝑆⁢𝑈⁡(𝑁 𝑐 ) gauge theory in the large 𝑁 𝑐 limit, we find the differential spectrum ⅆ⁢𝑁/ⅆ⁢𝜆 is a product of the gravitationally familiar Planck-like factor and the color phase space density, modeled here as the Wigner semicircle from random matrix theory. This reveals that apparent energy thermality in gravity is the direct dual of charge thermality in its underlying non-abelian gauge theory.

Carrasco, John Joseph M. [Northwestern University,↗