Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Limit Branch”

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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Nuclear Structure and Decay Data for A=31 Isobars

Here, experimental nuclear spectroscopic data are evaluated for 11 known nuclides of mass 31 (F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K). Detailed evaluated information is presented for each reaction and decay experiment. Combining all the available data, recommended values are provided for energies, spins and parities, and half-lives of levels, with energies, branching ratios and multipolarities of γ radiations, and characteristics of β and α radiations in radioactive decays. 31 P is the most extensively studied one among all nuclides via various reactions and decays, followed by 31 S, 31 Si, 31 Mg and 31 Al. Information for excited states in 31 Ne, 31 Na, 31 Cl, 31 Ar and 31 K are limited; no excited states have yet been identified in 31 F, even its ground-state half-life is unknown. Significant new data have become available for the structure of 31 S, with its relevance to astrophysical applications. This work supersedes the earlier evaluation of A=31 by 2013Ou01, with literature cutoff date of Feb 15, 2013.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Validation of the GFS model for gyrokinetic stability of NSTX pedestal data

This study presents a large database validation of the gyro fluid system (GFS) model for linear gyrokinetic stability for high-mode (H-mode) edge transport barrier conditions in the national spherical torus experiment (NSTX) tokamak. The database of linear stability calculations with the CGYRO gyrokinetic code was produced using plasma profile measurements from NSTX discharges to identify kinetic ballooning modes (KBM), trapped electron modes (TEM), and micro-tearing modes (MTM) that limit the pressure profile gradient in the H-mode barrier. A novel Bayesian optimization approach determines optimal resolution parameters for GFS specifically for spherical tokamak pedestal conditions. Our results demonstrate that GFS, with optimized resolution, can achieve accurate linear stability analysis in NSTX pedestal conditions for reduced resolution compared to CGYRO. GFS can accurately find the KBM, TEM, and MTM instability branches. Parametric analysis reveals that GFS accuracy in this extreme pedestal parameter range is degraded for low magnetic shear and near the separatrix conditions. These findings establish GFS as a fast linear eigenmode solver for spherical tokamak pedestal gyrokinetic stability and demonstrate a systematic methodology for determining the optimum resolution settings.

Yang, Minglei [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2022

Radiative transfer in stars by feebly interacting bosons

Starting from first principles, we study radiative transfer by new feebly-interacting bosons (FIBs) such as axions, axion-like particles (ALPs), dark photons, and others. Our key simplification is to include only boson emission or absorption (including decay), but not scattering between different modes of the radiation field. Based on a given distribution of temperature and FIB absorption rate in a star, we derive explicit volume-integral expressions for the boson luminosity, reaching from the free-streaming to the strong-trapping limit. The latter is seen explicitly to correspond to quasi-thermal emission from a “FIB sphere” according to the Stefan-Boltzmann law. Our results supersede expressions and approximations found in the recent literature on FIB emission from a supernova core and, for radiatively unstable FIBs, provide explicit expressions for the nonlocal (“ballistic”) transfer of energy recently discussed in horizontal-branch stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Solid breeder material crystal structure evolution due to Li burn up–Loss of crystal stability

Solid breeder materials for fusion power plants are subjected to extreme conditions of radiation damage, high temperature and designed component burn-up. Here, the loss of lattice stability of Li 2 TiO 3 due to Li burn-up was investigated using first principles-based approaches to aid evaluation of upper limit of component lifetime. The lattice stability is analyzed using calculated phonon dispersion in the Li 2 TiO 3 supercell, while Li burn-up is modeled by the introduction of Li-vacancies. It has been determined that the studied ceramic can be structurally stable up to ~40% of Li atoms burn-up. At 50% burn-up, the negative frequency branch in the phonon dispersion spectrum appears indicating the loss of lattice dynamical stability. Moreover, the structure obtained by introduction of unstable frozen phonons with minima energy amplitude also results in a phonon dispersion with negative branches in the structure obtained. Therefore, the system completely loses stability when approximately half of Li atoms are consumed.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Design-controlled synthesis of IrO 2 sub-monolayers on Au nanoflowers: marrying plasmonic and electrocatalytic properties

We develop herein plasmonic–catalytic Au–IrO 2 nanostructures with a morphology optimized for efficient light harvesting and catalytic surface area; the nanoparticles have a nanoflower morphology, with closely spaced Au branches all partially covered by an ultrathin (1 nm) IrO 2 shell. This nanoparticle architecture optimizes optical features due to the interactions of closely spaced plasmonic branches forming electromagnetic hot spots, and the ultra-thin IrO 2 layer maximizes efficient use of this expensive catalyst. This concept was evaluated towards the enhancement of the electrocatalytic performances towards the oxygen evolution reaction (OER) as a model transformation. The OER can play a central role in meeting future energy demands but the performance of conventional electrocatalysts in this reaction is limited by the sluggish OER kinetics. We demonstrate an improvement of the OER performance for one of the most active OER catalysts, IrO 2 , by harvesting plasmonic effects from visible light illumination in multimetallic nanoparticles. We find that the OER activity for the Au–IrO 2 nanoflowers can be improved under LSPR excitation, matching best properties reported in the literature. Our simulations and electrocatalytic data demonstrate that the enhancement in OER activities can be attributed to an electronic interaction between Au and IrO 2 and to the activation of Ir–O bonds by LSPR excited hot holes, leading to a change in the reaction mechanism (rate-determinant step) under visible light illumination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Development of a machine learning model for polyethylene pyrolysis using a detailed reaction mechanism

Waste plastics have recently received significant attention as the issue of waste generation continues to increase. Thermal conversion processes, such as pyrolysis and gasification, are attractive potential technologies for utilizing waste plastics and reducing overall waste generation. Efficient utilization of plastics requires a detailed understanding of the conversion process such as pyrolysis and gasification. However, a mechanistic understanding of these processes lead to large and complex kinetic schemes that are not suited for large-scale and long-time simulation methods. Currently, most modeling approaches for pyrolysis and gasification rely on globally lumped, simplified kinetic schemes that provide results that are classified by their product type and not individual species, which limit the level of fidelity achieved via modeling. A machine learning (ML) model has been developed for the primary reactions of high-density polyethylene (HDPE) in an attempt to increase computational efficiency while still maintaining a high level of detail and accuracy. The ML model is trained on a detailed reaction mechanism containing 42 total species and 737 chemical reactions. A DeepONet branch and trunk architecture was adopted to train the model using time-steps relevant to computational fluid dynamics simulations. The ML used physics-informed loss functions to ensure mass conservation. The surrogate model has been deployed in simple MFiX CFD simulations, single particle and an experimental drop tube reactor, and has shown promising performance compared to the original scheme.

Houston, Ross↗
DOE OSTI2021

An Integrated View of Hydraulic Induced Fracture Geometry in Hydraulic Fracture Test Site 2

Until relatively recently, most of our understanding about the geometry of hydraulically induced fractures in unconventional reservoirs has been inferred by patterns observed via microseismic monitoring. Important information, such as fracture-azimuth, fracture-length, height-growth and other geometric data has been determined from microseismic “event clouds”, which in turn has been used to interpret a stimulated reservoir volume (SRV). It is important to note that relatively limited microseismic results have been acquired in conjunction with other diagnostics and validated in a consistent manner. The Hydraulic Fracture Test Site 2 (HFTS2) in the Permian Delaware Basin provides a unique opportunity to compare the frac geometry interpretations derived from multiple frac diagnostic tools and at multiple scales. The integrated view that emerges from all the frac diagnostic tools is that in HFTS2 the geometries of hydraulically induced fractures are not random and with a highly complex branching architecture. In fact, the fracs are mostly vertical, parallel plana domains, and both vertically and horizontally asymmetrical. The hydraulically induced fractures have a very consistent azimuth with a strike that matches SHmax. At the distance corresponding to the spacing between nearby wells in HFTS2, ~ 660 ft, the pattern of strain interceptions observed from Low Frequency Distributed Acoustic Sensing (LF-DAS) shows far-field dimensions that are consistent with the stage length dimensions at the stimulated well. In general, larger stages with higher number of clusters create larger number of interceptions and wider stimulated intervals than that of shorter stages with the same cluster to cluster spacing and fewer clusters. The hydraulically induced fractures also show a clear tendency to preferentially grow upwards as shown by the microseismic data, by the relative lower number of LF-DAS interceptions in nearby deeper wells and finally by the observed LF-DAS strain patterns in the vertical observation well. In the near field, the geometries of the fracture domains are also consistent. As shown by the distributed strain measurements obtained during production via the monitoring of Rayleigh Frequency Shift (RFS), each cluster has a separate, non-overlapping, frac-zone-domain that are generally centered around the locations of each perforation cluster. Overall, the hydraulically induced fractures in HFTS2 are interpreted as occurring in swarms associated with individual clusters, each with its own unique geometry but with similar predictable geometric and propagation tendencies. The comprehensive frac diagnostic program in HFTS2, the well-pad layout that permits the investigation of the Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/1-21URTC/D011S018R003/2477511/urtec-2021-5396-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5396 2 impact that nearby producing wells has on frac geometry, together with an innovative Design of Experiment (DofE) that includes sequential-fracing, consistent cluster-to-cluster distances and few single-perforation cluster stages, has allowed us to gain a unique perspective about the geometry of the induced hydraulic fractures on this pad. Finally, the HFTS2 dataset has also provided us with a better understanding of the applicability and limitations of the different diagnostic tools.

58 GEOSCIENCES↗
DOE OSTI2026

Global metagenomics reveals plastid diversity and unexplored algal lineages

Photosynthetic organelles in eukaryotes originated through primary endosymbiosis with a cyanobacterium, an event that profoundly shaped the evolutionary landscape of the eukaryotic tree of life. Primary plastids in Archaeplastida, especially in cultivable plants and algae, contribute most to known plastid diversity. Secondary and higher-order endosymbiosis, involving eukaryotic hosts and algal endosymbionts, further spread photosynthesis among protists within the CASH lineages (Cryptophyta, Alveolata, Stramenopila, and Haptophyta). Despite various hypotheses explaining secondary plastid evolution and distribution, empirical support remains limited. Here, we employ cultivation-independent global metagenomics to expand plastid diversity and investigate plastid origins. We capture 1,027 plastid sequences, including 300 novel sequences belonging to previously unsequenced plastids and representing yet-to-be described microeukaryotes. This includes a new lineage that offers insights into plastid evolution in haptophytes and cryptophytes. Our results confirm that Archaeplastida plastids originate from an early branching cyanobacterial lineage closely related to Gloeomargaritales and identify the closest extant relative of Paulinella plastids. Additionally, our findings suggest two independent origins of secondary red-algal plastids, contributing to plastid diversity in CASH lineages and challenging the prevailing model of single secondary plastid origin. Our study highlights the importance of metagenomic data in uncovering biological diversity and advancing understanding of plastid relationships across photosynthetic eukaryotes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Unified framework for B -anomalies, muon g – 2 and neutrino masses

We present a model of radiative neutrino masses which also resolves anomalies reported in B -meson decays, \( {R}_{D^{\left(\ast \right)}} \) and \( {R}_{K^{\left(\ast \right)}} \) , as well as in muon g – 2 measurement, Δ a μ . Neutrino masses arise in the model through loop diagrams involving TeV-scale leptoquark (LQ) scalars R 2 and S 3 . Fits to neutrino oscillation parameters are obtained satisfying all flavor constraints which also explain the anomalies in \( {R}_{D^{\left(\ast \right)}} \) , \( {R}_{K^{\left(\ast \right)}} \) and Δ a μ within 1 σ . An isospin-3/2 Higgs quadruplet plays a crucial role in generating neutrino masses; we point out that the doubly-charged scalar contained therein can be produced in the decays of the S 3 LQ, which enhances its reach to 1.1 (6.2) TeV at \( \sqrt{s} \) = 14 TeV high-luminosity LHC ( \( \sqrt{s} \) = 100 TeV FCC-hh). We also present flavor-dependent upper limits on the Yukawa couplings of the LQs to the first two family fermions, arising from non-resonant dilepton ( pp → ℓ + ℓ – ) processes mediated by t -channel LQ exchange, which for 1 TeV LQ mass, are found to be in the range (0 . 15 – 0 . 36). These limits preclude any explanation of \( {R}_{D^{\left(\ast \right)}} \) through LQ-mediated B -meson decays involving ν e or ν μ in the final state. We also find that the same Yukawa couplings responsible for the chirally-enhanced contribution to Δ a μ give rise to new contributions to the SM Higgs decays to muon and tau pairs, with the modifications to the corresponding branching ratios being at (2–6)% level, which could be tested at future hadron colliders, such as HL-LHC and FCC-hh.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Timelike form factor for the anomalous process γ⁎π → ππ

The form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) for the anomalous process 𝛾∗𝜋 → 𝜋𝜋 is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) using Dyson–Schwinger and Bethe–Salpeter equations. Beyond a quark interaction kernel representing gluon-mediated interactions, leading beyond-rainbow-ladder effects at low energies are incorporated by back-coupling pions as explicit degrees of freedom. Building upon an earlier calculation of the quark-photon vertex that captures the branch cut associated with the two-pion threshold and the ρ-meson resonance, the form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) is determined for timelike Mandelstam s. In particular, predictions are made for the kinematics relevant to the Primakoff reaction studied with COMPASS/AMBER at CERN.

Miramontes, Angel S. [Univ. of Valencia (Spain)] (↗
DOE OSTI2023

An Extensible High Energy Density Modeling Tool for Extreme Regimes

The overreaching goal of the project is to develop a simulation capability to model an entire High Energy Density (HED) target heated by an X-ray Free Electron Laser (XFEL) beam including the surrounding material with a focus on target material associated with subsequent shots. Our primary objective is to study target fratricide problems, where radiation/debris from the current shot degrade the target for subsequent shots. This work will have a large impact on research being conducted at HED facilities where the quality of data is directly related to the effective repetition rate of the driver, which is often limited by target fratricide problems. This project focuses on a stream of closely spaced droplet targets that are appropriate for new very high repetition rate sources such as the ~1 MHz LCLS-II upgraded XFEL. The capability of the PISALE (Pacific Island Structured-AMR with ALE) code is extended to model this class of problems. We summarize the capability and improvements made to the HED branch of the PISALE code. We discuss our simulations of target fratricide for small (5 micron) hydrogen droplets heated by an XFEL beam at SLAC. We also compare simulations of the initial dynamics of larger (50 micron) water droplets, heated by the same XFEL beam, with experimental data. We briefly discuss training, dissemination, and related activities associated with this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Subpicosecond HI elimination in the 266 nm photodissociation of branched iodoalkanes

Here, the 266 nm photodissociation dynamics of 1-iodopropane and 2-iodopropane were studied using photofragment translational energy spectroscopy using vacuum ultraviolet (VUV) photoionization and electron impact ionization detection of products. The photochemistry of 1-iodopropane was found to be similar to that of iodomethane and iodoethane, with dominant production of I*( 2 P 1/2 ), and no evidence (<0.21%) for HI + alkene formation. Significantly different behavior was observed for 2-iodopropane, with dominant production of ground state I( 2 P 3/2 ), and a HI yield >10.5%. The anisotropy (β) parameters for all channels approached the limiting value of 2.0, indicating that 1,2-HI elimination occurs on subpicosecond timescales, like direct C–I bond fission, following excitation to 3 Q 0 . The HI translational energy and angular distributions were similar to those for I( 2 P 3/2 ), suggesting that motion of the heavy I atom in HI is largely derived from the repulsive nature of the 1 Q 1 surface correlating to R + I with the light H atom picked up by ground state I late in the exit channel producing highly vibrationally excited HI.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Beta-delayed charged-particle spectroscopy using TexAT

β-delayed charged-particle emission is a sensitive probe of three-body decays in light nuclei. Time Projection Chambers (TPCs) offer a significant advantage over traditional charged-particle spectroscopy techniques due to a low-energy threshold and a high-geometric efficiency (≈ 4π) which are essential for use with radioactive ion beams where the beam intensities are limited. The technique for high-sensitivity spectroscopy of β-delayed charged-particle emission is shown to be possible using the Texas Active Target (TexAT) TPC in conjunction with the General Electronics for TPCs (GET) system. The benchmark case studied was that of 12 N β-decay to the first α-unbound state in 12 C, the Hoyle state. Here, half-life and branching ratio measurements are presented and are in good agreement with previous studies. The efficacy of using TPCs to study such a near-threshold state and disentangle the three-body dynamics of the decay products is demonstrated.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

First measurement in the Gamow window of a reaction for the γ-process in inverse kinematics: 76 Se(α,γ) 80 Kr

The p-nuclei are the few stable nuclei heavier than iron on the neutron-deficient side of the valley of stability that cannot be produced through astrophysical neutron-capture reactions. The limited experimental data on reactions through which the p-nuclei might be produced leaves the origin of their production largely unknown. This work presents the first cross section measurements of the 76 Se(α,γ) 80 Kr reaction. The rate of the time reversed reaction, 80 Kr(γ,α) 76 Se, is one of the most uncertain of possible reactions which can occur at the 80 Kr branching point on the ,-process photo-disintegration pathway. The reaction flow through 80 Kr will directly affect the final abundance of the p nuclide 78 Kr. Experimental cross sections at two astrophysically relevant energies are reported and compared to cross sections calculated using Hauser-Feshbach codes TALYS, NON-SMOKER, and SMARAGD. The success of these first (α,γ) cross section measurements performed in inverse kinematics in the energy region of the γ-process opens the door for future studies of reactions on radioactive γ-process nuclides.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Self-Supported Branched Poly(ethylenimine) Monoliths from Inverse Template 3D Printing for Direct Air Capture

3D-printed inverse templates are combined with ice templating to develop self-supported branched poly(ethylenimine) monoliths with regular channels of varying channel density and ordered macropores. A maximum uptake of 0.96 mmol of CO 2 /g of monolith from ambient air containing 45.5% RH is achieved from dynamic breakthrough experiments, which is a 31% increase compared to the CO 2 uptake from adsorption under dry conditions for the same duration. The breakthrough experiments show characteristics of internal mass-transfer limitations. The cyclic dynamic breakthrough experiments indicate stable operation without significant loss in CO 2 uptake across eight cycles. Moreover, the self-supported monolith shows minimal loss in adsorption capacity (7.7%) upon exposure to air containing 21% oxygen at 110 °C, in comparison to a conventional sorbent consisting of poly(ethylenimine) impregnated on Al 2 O 3 (18.9%). The monoliths exhibit good mechanical stability, contributed by elastic deformation, corresponding to up to 74% strain and lower pressure drop compared to many existing monoliths in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Thermodynamic, Kinetic, and Transport Contributions to Hydrogen Evolution Activity and Electrolyte-Stability Windows for Water-in-Salt Electrolytes

Concentrated water-in-salt electrolytes (WiSEs) are used in aqueous batteries and to control electrochemical reactions for fuel production. The hydrogen evolution reaction is a parasitic reaction at the negative electrode that limits cell voltage in WiSE batteries and leads to self-discharge, and affects selectivity for electrosynthesis. Mitigating and modulating these processes is hampered by a limited fundamental understanding of HER kinetics in WiSEs. Here, in this study, we quantitatively assess how thermodynamics, kinetics, and interface layers control the apparent HER activities in 20 m LiTFSI. When the LiTFSI concentration is increased from 1 to 20 m, an increase in proton activity causes a positive shift in the HER equilibrium potential of 71 mV. The exchange current density, i o , derived from the HER branch for 20 m LiTFSI in 98% purity (0.56 ± 0.05 μA/cm Pt 2 ), however, is 8 times lower than for 20 m LiTFSI in 99.95% (4.7 ± 0.2 μA/cm Pt 2 ) and 32 times lower than for 1 m LiTFSI in 98% purity (18 ± 1 μA/cm Pt 2 ), demonstrating that the WiSE's impurities and concentration are both central in significantly suppressing HER kinetics. The ability and applicability of the reported methods are extended by examining additional WiSEs formulations made of acetates and nitrates.

25 ENERGY STORAGE↗
DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

New superstrata from three-dimensional supergravity

We find a two-parameter family of generalized superstrata that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to SO(3). We also confirm that the other known families of microstrata are not supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗