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At least 1,549 records · Page 86

Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties

We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes negligibly small and the Hubbard bands are well separated. Using dynamical mean-field theory and the numerical renormalization group as real-frequency impurity solver, we identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities. Furthermore, These include ARPES-type spectra, the local self-energy, static local orbital and spin susceptibilities, resistivity, thermopower, and lattice and impurity entropies. Our detailed description of the behavior of these quantities within the context of a simple model Hamiltonian will be helpful for distinguishing Hundness from Mottness in experimental and theoretical studies of real materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Measurements and Model Improvement: Insight into NWP Model Error Using Doppler Lidar and Other WFIP2 Measurement Systems

Abstract Doppler-lidar wind-profile measurements at three sites were used to evaluate NWP model errors from two versions of NOAA’s 3-km-grid HRRR model, to see whether updates in the latest version 4 reduced errors when compared against the original version 1. Nested (750-m grid) versions of each were also tested to see how grid spacing affected forecast skill. The measurements were part of the field phase of the Second Wind Forecasting Improvement Project (WFIP2), an 18-month deployment into central Oregon–Washington, a major wind-energy-producing region. This study focuses on errors in simulating marine intrusions, a summertime, 600–800-m-deep, regional sea-breeze flow found to generate large errors. HRRR errors proved to be complex and site dependent. The most prominent error resulted from a premature drop in modeled marine-intrusion wind speeds after local midnight, when lidar-measured winds of greater than 8 m s −1 persisted through the next morning. These large negative errors were offset at low levels by positive errors due to excessive mixing, complicating the interpretation of model “improvement,” such that the updates to the full-scale versions produced mixed results, sometimes enhancing but sometimes degrading model skill. Nesting consistently improved model performance, with version 1’s nest producing the smallest errors overall. HRRR’s ability to represent the stages of sea-breeze forcing was evaluated using radiation budget, surface-energy balance, and near-surface temperature measurements available during WFIP2. The significant site-to-site differences in model error and the complex nature of these errors mean that field-measurement campaigns having dense arrays of profiling sensors are necessary to properly diagnose and characterize model errors, as part of a systematic approach to NWP model improvement. Significance Statement Dramatic increases in NWP model skill will be required over the coming decades. This paper describes the role of major deployments of accurate profiling sensors in achieving that goal and presents an example from the Second Wind Forecast Improvement Program (WFIP2). Wind-profile data from scanning Doppler lidars were used to evaluate two versions of HRRR, the original and an updated version, and nested versions of each. This study focuses on the ability of updated HRRR versions to improve upon predicting a regional sea-breeze flow, which was found to generate large errors by the original HRRR. Updates to the full-scale HRRR versions produced mixed results, but the finer-mesh versions consistently reduced model errors.

Meteorology & Atmospheric Sciences↗

Ion kinematics in a plasma focus.

The results of numerical integrations of three-dimensional equations of motion of ions subject to given electric and magnetic fields are presented. The fields represent those which may exist in the pinch phase of the plasma focus, although here they depend only on the radial coordinate. The ions initially have Maxwellian velocity distributions, and their trajectories are interpreted in terms of single-particle constants of the motion. Two models of the axial electric field Ez are considered. For strong Ez away from the axis, there is a cyclotron acceleration which leads to ion heating. For positive Ez on the axis, ions within a Larmor radius of the axis undergo very efficient acceleration; the results for this new model are in general agreement with experimental results.

Gary, S. P.↗

Structure and Energetics of Medium-scale Atmospheric Waves in the Southern Hemisphere Summer

The NMC analyses were used to study medium-scale waves during three Southern Hemisphere (SH) summers. The SH summer medium-scale waves are observed to exhibit remarkably regular eastward phase progression, and wave maxima can often be traced continuously around the globe. Frequent downstream development of existing wave patterns is observed. The medium-scale waves at times appear to be longitudinally localized features; at other times they resemble truly global-scale models. The time-mean wave structure is found to be consistent with basic-state propagation characteristics and the conservation of wave activity. There is a tendency for background wind structure to restrict wave propagation. From energetics studies it is found that wave-zonal-mean exchange is a valid concept for describing the SH summer circulation, and that the flow vacillated between periods of highly perturbed and zonally symmetric states. The medium-scale waves result from nonlinear baroclinic instabilities, and exhibit a well-defined life cycle of baroclinic growth, maturity, and barotropic decay.

Randel, W. J.↗

Surface scattering properties estimated from modeling ASAS multiple emission angle reflectance data over the lunar crater volcanic field, Nevada

ASAS multispectral data were acquired over Lunar Lake playa at 12 different lighting and viewing geometries. Atmospheric models and field-based data demonstrate that atmospheric contributions to ASAS data were relatively small and were thus ignored in analyses of surface photometric properties. ASAS data of an artificially roughened playa and cobble-strewn surfaces exhibit trends of increasing reflectance as phase angle decreases. The reflectance of a natural playa surface exhibits Lambertian scattering properties that cannot be replicated with the Hapke (1986) photometric function. The Hapke model does fit the rough and cobble-strewn playa data with single-scattering albedo, asymmetry factor, and roughness terms consistent with known properties of these surfaces. No published photometric model explains the reflectance variations of all three surfaces.

Guinness, Edward A.↗

Structure and dynamics of premixed flames in microgravity

In this report we describe the research performed at the Naval Research Laboratory in support of the NASA Microgravity Science and Applications Program over the past three years with emphasis on the work performed since February 1992, the beginning of the current project. The focus of our research has been on investigating fundamental combustion questions concerning the propagation and extinction of gas-phase flames in microgravity and earth-gravity environments. Our approach to resolving these fundamental questions has been to use detailed time-dependent, multidimensional numerical models to perform carefully designed computational experiments. The basic questions we have addressed, a general description of the numerical approach, and a summary of the results are described in this report. More detailed discussions are available in the papers published which are referenced herein.

Kailasanath, K.↗

Spectral representation of high-frequency Space Shuttle data

High frequency Space Shuttle liftoff data are treated by autoregressive (AR) and autoregressive-moving-average (ARMA) digital algorithms. These algorithms provide useful information on the spectral densities of the data. Further, they yield spectral models, which lend themeselves to incorporation into the concept of the random response spectrum. This concept yields a reasonably smooth power spectrum for the design of structural and mechanical systems when the available data bank is limited. Due to the nonstationary of the liftoff event, the pertinent data are split into three slices. Each of the slices is associated with a rather distinguished phase of the liftoff event, in which stationarity can be expected. The presented results are preliminary in nature; they aim to call attention to the availability of the discussed concepts and to the need to augment the Space Shuttle data bank as more flights are completed.

Spanos, P. D.↗

Internal Flow Simulation of Enhanced Performance Solid Rocket Booster for the Space Transportation System

An enhanced performance solid rocket booster concept for the space shuttle system has been proposed. The concept booster will have strong commonality with the existing, proven, reliable four-segment Space Shuttle Reusable Solid Rocket Motors (RSRM) with individual component design (nozzle, insulator, etc.) optimized for a five-segment configuration. Increased performance is desirable to further enhance safety/reliability and/or increase payload capability. Performance increase will be achieved by adding a fifth propellant segment to the current four-segment booster and opening the throat to accommodate the increased mass flow while maintaining current pressure levels. One development concept under consideration is the static test of a "standard" RSRM with a fifth propellant segment inserted and appropriate minimum motor modifications. Feasibility studies are being conducted to assess the potential for any significant departure in component performance/loading from the well-characterized RSRM. An area of concern is the aft motor (submerged nozzle inlet, aft dome, etc.) where the altered internal flow resulting from the performance enhancing features (25% increase in mass flow rate, higher Mach numbers, modified subsonic nozzle contour) may result in increased component erosion and char. To assess this issue and to define the minimum design changes required to successfully static test a fifth segment RSRM engineering test motor, internal flow studies have been initiated. Internal aero-thermal environments were quantified in terms of conventional convective heating and discrete phase alumina particle impact/concentration and accretion calculations via Computational Fluid Dynamics (CFD) simulation. Two sets of comparative CFD simulations of the RSRM and the five-segment (IBM) concept motor were conducted with CFD commercial code FLUENT. The first simulation involved a two-dimensional axi-symmetric model of the full motor, initial grain RSRM. The second set of analyses included three-dimensional models of the RSRM and FSM aft motors with four-degree vectored nozzles.

Ahmad, Rashid A.↗

Modular, Reconfigurable, High-Energy Technology Development

The Modular, Reconfigurable High-Energy (MRHE) Technology Demonstrator project was to have been a series of ground-based demonstrations to mature critical technologies needed for in-space assembly of a highpower high-voltage modular spacecraft in low Earth orbit, enabling the development of future modular solar-powered exploration cargo-transport vehicles and infrastructure. MRHE was a project in the High Energy Space Systems (HESS) Program, within NASA's Exploration Systems Research and Technology (ESR&T) Program. NASA participants included Marshall Space Flight Center (MSFC), the Jet Propulsion Laboratory (JPL), and Glenn Research Center (GRC). Contractor participants were the Boeing Phantom Works in Huntsville, AL, Lockheed Martin Advanced Technology Center in Palo Alto, CA, ENTECH, Inc. in Keller, TX, and the University of AL Huntsville (UAH). MRHE's technical objectives were to mature: (a) lightweight, efficient, high-voltage, radiation-resistant solar power generation (SPG) technologies; (b) innovative, lightweight, efficient thermal management systems; (c) efficient, 100kW-class, high-voltage power delivery systems from an SPG to an electric thruster system; (d) autonomous rendezvous and docking technology for in-space assembly of modular, reconfigurable spacecraft; (e) robotic assembly of modular space systems; and (f) modular, reconfigurable distributed avionics technologies. Maturation of these technologies was to be implemented through a series of increasingly-inclusive laboratory demonstrations that would have integrated and demonstrated two systems-of-systems: (a) the autonomous rendezvous and docking of modular spacecraft with deployable structures, robotic assembly, reconfiguration both during assembly and (b) the development and integration of an advanced thermal heat pipe and a high-voltage power delivery system with a representative lightweight high-voltage SPG array. In addition, an integrated simulation testbed would have been developed containing software models representing the technologies being matured in the laboratory demos. The testbed would have also included models for non-MRHE developed subsystems such as electric propulsion, so that end-to-end performance could have been assessed. This paper presents an overview of the MRHE Phase I activities at MSFC and its contractor partners. One of the major Phase I accomplishments is the assembly demonstration in the Lockheed Martin Advanced Technology Center (LMATC) Robot-Satellite facility, in which three robot-satellites successfully demonstrated rendezvous & docking, self-assembly, reconfiguration, adaptable GN&C, deployment, and interfaces between modules. Phase I technology maturation results from ENTECH include material recommendations for radiation hardened Stretched Lens Array (SLA) concentrator lenses, and a design concept and test results for a hi-voltage PV receiver. UAH's accomplishments include Supertube heatpipe test results, which support estimates of thermal conductivities at 30,000 times that of an equivalent silver rod. MSFC performed systems trades and developed a preliminary concept design for a 100kW-class modular reconfigurable solar electric propulsion transport vehicle, and Boeing Phantom Works in Huntsville performed assembly and rendezvous and docking trades. A concept animation video was produced by SAIC, wllich showed rendezvous and docking and SLA-square-rigger deployment in LEO.

Carrington, Connie↗

Electric Sail Design Sensitivities

Electric Sails (E-Sails) are a promising propulsion technology that seek to enable high characteristic propellentless acceleration for spacecraft to reach distant and/or difficult to reach orbits such as rapid transit to heliopause. The E-Sail system exchanges momentum by using positively charged electrostatic tethers to repel solar wind photons to push it through space. This concept was first theorized by Pekka Janhunen in 2004 with further developments occurring including a NASA Innovative Advanced Concepts Phase 1 and Phase 2 hosted out of NASA’s Marshall Space Flight Center (MSFC). These developments led to further maturation of the overall system, and this paper is designed to help identify different design sensitivities of an integrated Electric Sail system. To approach this, a small team at MSFC took an in-house developed three degrees of freedom (3DoF) simulation tool and a trajectory modelling tool to look at different design parameters and to determine a potential ideal E-Sail configuration. An E-Sail system has different design architectures including a barbell design, hub and spoke design, and a potential hybrid solution. The barbell design features two equally massed satellites that spin around a central point in the tether system. The hub and spoke design features a large central spacecraft with small end spacecraft to aid in formation control of the overall E-Sail system. Leveraging elements from both the hub and spoke, and barbell design, a hybrid option exists where one could have a larger central mass and one or two tethers extended to a smaller end mass [2]. In summary, the hub and spoke design is the ideal configuration for E-Sail with tethers spanning kilometers to achieve the designed design characteristic acceleration of at least one mm/s2 with this architecture being the focus of this study. Different key design parameters were varied as part of this study. These parameters include the total number of tethers, the length of the tethers, spin rate, relative spacecraft mass, tether voltage, inertia per tether, and impact of slew rate changes. These results started from an internal MSFC technology demonstration mission design and then the parameters were varied with engineering judgement to ensure that the results were consistent with expected results. These were varied in the MSFC 3DoF tool and compared to baseline results to generate a candidate ideal E-Sail design system. These results were then used to help inform the mission analysis design for the system. The 3DoF trajectory optimization was performed in the Astrodynamics and Space Science Enabling Toolbox (ASSET) and utilized collocation optimization of control vector pointing with the objective function being transfer duration. A representative model of the E-Sail force was derived as a function of the Sun-pointing vector direction. This model was initialized with a zero Sun Incidence Angle (SIA) trajectory for the initial guess generation, then with a portion of the mission optimized SIA time history for fast outbound transfers. After the trajectory is hyperbolic relative to a heliocentric frame, the SIA is maintained at 0 degrees except for any needed trajectory correction maneuvers. This trajectory optimization looked at different characteristic acceleration values to analyze the impact it had on mission performance. As a result of this study, the team can best inform mission designers and technology development efforts to mature the E-Sail system. This study will allow mission designers to have defined rules-of-thumb to design an E-Sail system to meet desired mission needs as well as providing several sample mission profiles. These design drivers will inform maturation efforts on which design requirements to consider for an integrated E-Sail design.

E-Sail↗

Electric thruster models for multimegawatt nuclear electric propulsion mission design

Three types of electric thrusters currently under development at JPL have potential to support future missions which utilize multimegawatt nuclear electric propulsion. These electric thrusters are the electron bombardment ion thruster, the magnetoplasmadynamic (MPD) thruster, and the electron-cyclotron-resonance (ECR) thruster. The electron bombardment ion thruster is a relatively mature technology which has been developed for operation at kilowatt power levels but will require new development for application in the multimegawatt regime. The MPD engine represents a technology which may be very well suited to steady-state multimegawatt applications but which has been limited to sub-scale (100's of kW) and pulsed (MW) testing thus far. The ECR plasma engine represents a class of very promising new concepts which are still in the basic research phase of development, but which may possess important fundamental advantages over other electric thruster technologies. Models of these thrusters are described and used to make projections of thrusters specific mass, efficiency, and power handling capacity for operation in the multimegawatt regime.

Leifer, Stephanie D.↗

Chemical Modeling of the Capture of Radioiodine Species

Iodine is a common fission product resulting from the transmutation of uranium fuel in nuclear power reactors. The short-lived radioactive isotope, 131 I, with a half-life of around eight days, would be a particular health concern if released into the environment. Capture materials, such as activated carbon, are used routinely in nuclear power plants and medical isotope production facilities to remove this hazard during normal operations to reduce emissions to acceptable levels. Iodine, unlike other common fission products such as noble gases, is challenging because of the wide range of molecular forms and oxidation states (from +VII in IF 7 to -I in iodide) that it displays, which can interconvert both in the gas phase and in the solution phase for example. The work in this project is focused on three computational tasks. In the first, we consider the binding of iodine-containing molecules of varying oxidation states to the major component of activated carbon – pristine graphene-like sheets. The second task focused on molecular binding and possible chemical transformations resulting from the reaction of molecular iodine with chemical functional groups on the edge of the graphene sheets or surface defects in the sheet itself. The final task was associated with radiolytic breakdown of 131 I to 131 Xe in iodine containing molecules and investigated the resulting molecular fragmentation process both in the gas phase and on the graphene-like surface. For each of the tasks, the intent was to learn about the thermodynamics and kinetics of the chemical transformations and use the calculations to provide parameters for input into kinetic models describing these processes for interpretation of experimental data in future work.

07 ISOTOPE AND RADIATION SOURCES↗

An ultrahigh-resolution E3SM land model simulation framework and its first application to the Seward Peninsula in Alaska

The availability of supercomputers and state-of-science datasets has made it possible to conduct large-scale land simulations at an ultrahigh-resolution. This study reported a computational framework for land surface simulation using the E3SM land model (ELM) at an unprecedented resolution (1 km x 1 km gridcell). The ultrahigh-resolution ELM (uELM) simulation framework includes three parts: (1) high-resolution atmospheric forcing and surface properties dataset generation, (2) massive gridcell-based simulation, and (3) large-scale simulation results analysis. Additionally, we implemented the uELM simulation framework and completed the first 1 km x 1 km terrestrial ecosystem simulation (from 1850 to 2014) over the Seward Peninsula in Alaska (78,000 km 2 ). The experiment contained two phases: a spin-up simulation and a transient simulation, and required five weeks of calculations using 320 cores in a 44-node Linux HPC computer. It created approximately 1.3 TB of data from the transient simulation alone (1850 - present). We selected sample results (monthly and daily simulation outputs) to illustrate the temporal and spatial variations of several variables in high-latitude Arctic ecosystems’ water, energy, and carbon cycles. At last, we summarized the lessons learned and proposed new developments for full-scale uELM simulations over the entire North American continent (approximately 22,000,000 km 2 ).

54 ENVIRONMENTAL SCIENCES↗

Continuous-Flow Centrifugal Solid/Liquid Separation for the Recovery of Rare-Earth Elements Containing Particles from Phosphoric Acid Sludge

Phosphoric acid sludge contains acid (~54% P 2 O 5 ) and solid precipitates including rare earth elements (REEs) at concentrations of ~2200 ppm. Low-cost recovery of valuable P 2 O 5 and simultaneous solid separation could be an economically feasible approach to recovering REEs while increasing the production of phosphoric acid. The sludge, however, is a complicated stream that cannot be separated by traditional technologies because of high viscosity and a large solid content (30–40%). Guided by a force balance model, an efficient solid/liquid separation method is demonstrated, using a continuous-flow centrifugal contactor. Additionally, the shear regime is bypassed by introducing the sludge directly into the rotor where a centrifugal force is exerted on the fluid, inducing phase separation. Solid particles are trapped in the contactor. High liquid recovery is demonstrated and the effects of process parameters on solid capture are investigated. Three contactors in series yield 94% recovery of solids containing 1500–2895 ppm of REEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Frustration-driven magnetic correlations in the spin-$\frac{5}{2}$ triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2

Here, a detailed study of the structural and magnetic properties of a spin-5/2 triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2 is presented using x-ray diffraction, magnetization, heat capacity, and 31 P nuclear magnetic resonance (NMR) experiments on a polycrystalline sample. The crystal structure features an equilateral triangular lattice of Fe 3+ ions. The thermodynamic measurements reveal the onset of a magnetic long-range order at 𝑇 N⁢1 ≃7.8K in zero field, followed by another low-temperature field-induced ordering at 𝑇 N⁢2 in higher fields. The transition at 𝑇 N⁢1 is further confirmed from the NMR spin lattice relaxation measurements. The value of the frustration ratio (𝑓≃7) implies moderate spin frustration in the compound. The 31 P NMR spectra exhibit two distinct spectral lines corresponding to two inequivalent phosphorus sites (P1 and P2), consistent with the crystal structure. The P1 site is strongly coupled with an isotropic hyperfine coupling of 𝐴$^{iso}_{hf}$ = 0.55⁢(2)⁢ T/𝜇 B while the P2 site is weakly coupled with 𝐴$^{iso}_{hf}$ = 0.25⁢(3)⁢ T/𝜇 B with the Fe 3+ ions. The magnetic susceptibility and NMR shift data are described well assuming a spin-5/2 isotropic triangular lattice antiferromagnetic model with an average exchange coupling of 𝐽/𝑘 B = 2.8⁢(2)⁢K. Below 𝑇 N⁢1 , the spectra evolve into a nearly rectangular powder pattern, indicating a commensurate antiferromagnetic type order. The 31 P spin-lattice relaxation rate well below 𝑇N⁢1 follows a 𝑇 3 temperature dependence, implying a two-magnon Raman scattering mechanism in the ordered state. Three well-defined phase regimes are clearly ascertained in the 𝐻−𝑇 phase diagram, reflecting a weak magnetic anisotropy in the compound.

Nagpal, V. [Indian Institute of Science Education ↗

Transport studies in a gate-tunable three-terminal Josephson junction

Josephson junctions with three or more superconducting leads have been predicted to exhibit topological effects in the presence of few conducting modes within the interstitial normal material. Such behavior, of relevance for topologically protected quantum bits, would lead to specific transport features measured between terminals, with topological phase transitions occurring as a function of phase and voltage bias. Although conventional, two-terminal Josephson junctions have been studied extensively, multiterminal devices have received relatively little attention to date. Motivated in part by the possibility to ultimately observe topological phenomena in multiterminal Josephson devices, as well as their potential for coupling gatemon qubits, here we describe the superconducting features of a top-gated mesoscopic three-terminal Josephson device. The device is based on an InAs two-dimensional electron gas proximitized by epitaxial aluminum. We map out the transport properties of the device as a function of bias currents, top gate voltage, and magnetic field. Finally, we find a very good agreement between the zero-field experimental phase diagram and a resistively and capacitively shunted junction computational model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Elliptic flow splittings in the Polyakov–Nambu–Jona-Lasinio transport model

To incorporate the effect of gluons on the evolution dynamics of the quark matter produced in relativistic heavy-ion collisions, we extend the three-flavor Nambu–Jona-Lasinio (NJL) transport model to include the contribution from the Polyakov loops. Imbedding the resulting pNJL partonic transport model in an extended multiphase transport (extended AMPT) model, we then study the elliptic flow splittings between particles and their antiparticles in relativistic heavy-ion collisions at beam energy scan energies. We find that a weak quark vector interaction in the partonic phase is able to describe the elliptic flow splitting between protons and antiprotons in heavy-ion collisions at √sNN=7.7 to 39 GeV. Knowledge of the quark vector interaction is useful for understanding the equation of state of quark matter at large baryon chemical potentials and thus the location of the critical point in the QCD phase diagram.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Gravitational-wave signature of core-collapse supernovae

Here, we calculate the gravitational-wave (GW) signatures of detailed 3D core-collapse supernova sim ulations spanning a range of massive stars. Most of the simulations are carried out to times late enough to capture more than 95% of the total GW emission. We find that the f/g-mode and f-mode of proto-neutron star oscillations carry away most of the GW power. The f-mode frequency inex orably rises as the proto-neutron star (PNS) core shrinks. We demonstrate that the GW emission is excited mostly by accretion plumes onto the PNS that energize modal oscillations and also high frequency (“haze”) emission correlated with the phase of violent accretion. The duration of the major phase of emission varies with exploding progenitor and there is a strong correlation between the total GW energy radiated and the compactness of the progenitor. Moreover, the total GW emissions vary by as much as three orders of magnitude from star to star. For black-hole formation, the GW signal tapers off slowly and does not manifest the haze seen for the exploding models. For such failed models, we also witness the emergence of a spiral shock motion that modulates the GW emission at a frequency near ~100 Hertz that slowly increases as the stalled shock sinks. We find significant angular anisotropy of both the high- and low-frequency (memory) GW emissions, though the latter have very little power.

79 ASTRONOMY AND ASTROPHYSICS↗