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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 127 records · Page 7

Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits

Quantum bits, or qubits, are an example of coherent circuits envisioned for next-generation computers and detectors. A robust superconducting qubit with a coherent lifetime of O (100 µs) is the transmon: a Josephson junction functioning as a non-linear inductor shunted with a capacitor to form an anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap between neighboring circuits. Simply transplanting our recipe optimized for single, stand-alone devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer) initially resulted in global drifts in room-temperature tunneling resistance of ± 30%. Inferring a critical current variation from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in < 3.5% relative standard deviation (RSD) in critical current ( ) for 3000 Josephson junctions (both single-junctions and asymmetric SQUIDs) across an area of 49 cm 2 . Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown = 1.8% within 1x1 cm, on average, with a few 1x1 cm areas having < 1.0% (equivalent to < 0.5%). Such stability would drastically improve the yield of multi-junction chips with strict critical current requirements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multidimensional Numerical Modeling of Combustion Dynamics in a Non-Premixed Rotating Detonation Engine With Adaptive Mesh Refinement

In the present work, a novel computational fluid dynamics (CFD) methodology was developed to simulate full-scale non-premixed rotating detonation engines (RDEs). A unique feature of the modeling approach was the incorporation of adaptive mesh refinement (AMR) to achieve a good trade-off between model accuracy and computational expense. Here, unsteady Reynolds-averaged Navier–Stokes (RANS) simulations were performed for an Air Force Research Laboratory (AFRL) non-premixed RDE configuration with hydrogen as fuel and air as the oxidizer. The finite-rate chemistry model, along with a ten-species detailed kinetic mechanism, was employed to describe the H 2 -Air combustion chemistry. Three distinct operating conditions were simulated, corresponding to the same global equivalence ratio of unity but different fuel/air mass flowrates. For all conditions, the capability of the model to capture essential detonation wave dynamics was assessed. An exhaustive verification and validation study was performed against experimental data in terms of a number of waves, wave frequency, wave height, reactant fill height, oblique shock angle, axial pressure distribution in the channel, and fuel/air plenum pressure. The CFD model was demonstrated to accurately predict the sensitivity of these wave characteristics to the operating conditions, both qualitatively and quantitatively. A comprehensive heat release analysis was also conducted to quantify detonative versus deflagrative burning for the three simulated cases. The present CFD model offers a potential capability to perform rapid design space exploration and/or performance optimization studies for realistic full-scale RDE configurations.

42 ENGINEERING↗

Initial-site characterization of hydrogen migration following strong-field double-ionization of ethanol

Abstract An essential problem in photochemistry is understanding the coupling of electronic and nuclear dynamics in molecules, which manifests in processes such as hydrogen migration. Measurements of hydrogen migration in molecules that have more than two equivalent hydrogen sites, however, produce data that is difficult to compare with calculations because the initial hydrogen site is unknown. We demonstrate that coincidence ion-imaging measurements of a few deuterium-tagged isotopologues of ethanol can determine the contribution of each initial-site composition to hydrogen-rich fragments following strong-field double ionization. These site-specific probabilities produce benchmarks for calculations and answer outstanding questions about photofragmentation of ethanol dications; e.g., establishing that the central two hydrogen atoms are 15 times more likely to abstract the hydroxyl proton than a methyl-group proton to form H $${}_{3}^{+}$$ 3 + and that hydrogen scrambling, involving the exchange of hydrogen between different sites, is important in H 2 O + formation. The technique extends to dynamic variables and could, in principle, be applied to larger non-cyclic hydrocarbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enabling microbial electrolysis cell scale-up via electrochemistry-, hydrodynamic-, and microbial ecology-informed framework

Microbial electrolysis cells (MECs) can produce green hydrogen while removing organic contaminants from liquid waste streams by leveraging the metabolic activity of electroactive microorganisms. Despite their potential in a sustainable, circular economy, large-scale MECs that can treat relevant volumes of wastewater have failed to deliver performance proportional to their lab-scale counterparts. The reason behind this lower performance at scale remains unclear. Here, in this study, we developed a combined electrochemistry-, hydrodynamic-, and microbial ecology-informed framework to analyze and optimize MEC performance during scale-up, enabling accurate quantification of major limitations and the identification of strategies to overcome them, ultimately facilitating equivalent performance at scale. Applying this framework to the scale-up of a zero-gap MEC from 9 cm 2 electrode area to 100 cm 2 electrode area, resulted in similar maximum current densities in a 100 cm 2 MEC (21.7 ± 1.1 A/m 2 ) compared to a 9 cm 2 system (25.1 ± 2.7 A/m 2 ), as well as equivalent hydrogen production rates of 69.3 L/L-d (100 cm 2 ) and 67.7 ± 2.4 L/L-d (9 cm 2 ). COMSOL flow dynamics simulations were used to scale up the reactor configuration without negatively affecting electrolyte velocity and distribution in the cell, minimizing the increase in internal resistances during scale-up (11.7 ± 0.5 mΩm 2 at 9 cm 2 ; 19.7 ± 1.3 mΩm 2 at 100 cm 2 ). Microbial community structures were assessed at both scales using high-throughput sequencing, highlighting the differences of populations across electrode dimensions and operational parameters. The framework presented here accelerates the development of effective strategies toward the scale-up of MECs by furthering the understanding of how electrochemical, hydrodynamic, and microbial ecology parameters change as the reactor dimension is increased. Ultimately, this approach contributes to advancing electrochemical biotechnology toward practical deployment in energy-efficient wastewater treatment systems.

Flow path↗

FATES crown damage simulation outputs 2022

This dataset contains outputs from the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) and accompanies the paper "Needham, J.F., Arellano, A., Davies, S.J., Fisher, R.A., Hammer, V., Knox, R., Mitre, D., Muller-Landau, H.C., Zuleta, D., Koven, C.D. Tree crown damage and its effects on forest carbon cycling in a tropical forest, 2022, Global Change Biology". Data are unprocessed netcdf file outputs from simulations that were run to test the effect of a new crown damage module in FATES. Specifically, this data package contains a sensitivity analysis to the carbon cushion parameter damage_Ccushion_ensemble_e1b5bd9_bf013ef_2021-09-02.h0.ensemble.sofar.nc, a sensitivity analysis to the root nitrogen stoichiometry parameter damage_Nstoich_ensemble_e1b5bd9_bf013ef_2021-09-02.h0.ensemble.sofar.nc, a sensitivity analysis to parameters controlling crown damage and recovery damage_recovery_ensemble_e1b5bd9_354f0b0_2021-09-02.h0.ensemble.sofar.nc, and a sensitivity analysis to the number of crown damage bins elm_fates_bci_*_damagebins.Eac53ccb80b-F8f994c29.2022-04-19.elm.h0.fullrun.nc. This data package also contains a high root nitrogen configuration of FATES, including both a control, and a crown damage simulation high_root_N_control_e1b5bd9_354f0b0_2021-09-02.clm2.h0.fullrun.nc and high_root_N_damage_e1b5bd9_354f0b0_2021-09-02.clm2.h0.fullrun.nc. There is an analogous low root nitrogen configuration of FATES, including a control, low_root_N_control_e1b5bd9_bf013ef_2021-09-02.clm2.h0.fullrun.nc a damage only simulation low_root_N_damageonly_e1b5bd9_bf013ef_2021-09-02.clm2.h0.fullrun.nc, a damage plus mortality simulation low_root_N_damage_mort_e1b5bd9_bf013ef_2021-09-02.clm2.h0.fullrun.nc, and a mortality only simulation low_root_N_mort_only_e1b5bd9_ef845c8_2021-09-02.clm2.h0.fullrun.nc. Finally, there is a two PFT simulation in which we test the effect of recovery on competitive dynamics, low_root_N_damage_two_pfts_stoichastic_e1b5bd9_bf013ef_2021-09-10.clm2.h0.fullrun.nc. These simulations test the effect of representing crown damage in FATES, compared with simulations that have an equivalent increase in mortality. Jupyter notebooks to analyse these files can be found at https://github.com/JessicaNeedham/Needham_etal_GCB_2022_FATES_crown_damage.

54 ENVIRONMENTAL SCIENCES↗

The Impact of Operated Window Shading on Visual Comfort, Non-Visual Health, and Energy Demand from Electric Lighting

This paper introduces a simulation-based workflow to assess annual circadian lighting performance, glare risk and energy demand for an array of seated view positions under operated shading and electric lighting conditions. This workflow uses a combination of 9-band and 81-band simulations to represent daylight and electric lighting respectively. Annual daylight-driven calculations rely on a python-based code provided in the LARK simulation engine which was used to run 180-degree high dynamic range (HDR) renderings with 9-bands of spectral resolution. The results reveal the impact of shading systems on equivalent melanopic lux (EML) and daylight glare probability (DGP) over time and the energy demand (kWh) from electric lighting systems to supplement eye-level recommendations from the WELL v2 Building Standard.

Rockcastle, Siobhan↗

Microscopic Origins of the Nonlinear Behavior of Particle-Filled Rubber Probed with Dynamic Strain XPCS

The underlying microscopic response of filler networks in reinforced rubber to dynamic strain is not well understood due to the experimental difficulty of directly measuring filler network behavior in samples undergoing dynamic strain. This difficulty can be overcome with in situ X-ray photon correlation spectroscopy (XPCS) measurements. The contrast between the silica filler and the rubber matrix for X-ray scattering allows us to isolate the filler network behavior from the overall response of the rubber. This in situ XPCS technique probes the microscopic breakdown and reforming of the filler network structure, which are responsible for the nonlinear dependence of modulus on strain, known in the rubber science community as the Payne effect. These microscopic changes in the filler network structure have consequences for the macroscopic material performance, especially for the fuel efficiency of tire tread compounds. In this work, we elucidate the behavior with in situ dynamic strain XPCS experiments on industrially relevant, vulcanized rubbers filled (13 vol %) with novel air-milled silica of ultrahigh-surface area (UHSA) (250 m 2 /g). The addition of a silane coupling agent to rubber containing this silica causes an unexpected and counterintuitive increase in the Payne effect and decrease in energy dissipation. For this rubber, we observe a nearly two-fold enhancement of the storage modulus and virtually equivalent loss tangent compared to a rubber containing a coupling agent and conventional silica. Interpretation of our in situ XPCS results simultaneously with interpretation of traditional dynamic mechanical analysis (DMA) strain sweep experiments reveals that the debonding or yielding of bridged bound rubber layers is key to understanding the behavior of rubber formulations containing the silane coupling agent and high-surface area silica. These results demonstrate that the combination of XPCS and DMA is a powerful method for unraveling the microscale filler response to strain which dictates the dynamic mechanical properties of reinforced soft matter composites. With this combination of techniques, we have elucidated the great promise of UHSA silica when used in concert with a silane coupling agent in filled rubber. Such composites simultaneously exhibit large moduli and low hysteresis under dynamic strain.

36 MATERIALS SCIENCE↗

Accelerating charge estimation in molecular dynamics simulations using physics-informed neural networks: corrosion applications

Molecular Dynamics (MD) simulations are used to understand the effects of corrosion on metallic materials in salt brine. Reactive force fields in classical MD enable accurate modeling of bond formation and breakage in the aqueous medium and at the metal-electrolyte interface, while also facilitating dynamic partial charge equilibration. However, MD simulations are computationally intensive and unsuitable for modeling the long time scales characteristic of corrosive phenomena. To address this, we develop reduced-order machine learning models that provide accurate and efficient predictions of charge density in corrosive environments. Specifically, we use Long Short-Term Memory (LSTM) networks to forecast charge density evolution based on atomic environments represented by Smooth Overlap of Atomic Positions (SOAP) descriptors. A physics-informed loss function enforces charge neutrality and electronegativity equivalence. The atomic charges predicted by the deep learning model trained on this work were obtained two orders of magnitude faster than those from molecular dynamics (MD) simulations, with an error of less than 3% compared to the MD-obtained charges, even in extrapolative scenarios, while adhering to physical constraints. This demonstrates the excellent accuracy, computational efficiency, and validity of the developed model. Lastly, even though developed for corrosion, these protocols are formulated in a phenomenon-agnostic manner, allowing application to various variable-charge interatomic potentials and related fields.

Atomistic models↗

Quantum field theory, worldline theory, and spin magnitude change in orbital evolution

A previous paper [Z. Bern et al., Binary dynamics through the fifth power of spin at 𝑂⁡(𝐺 2 ), Phys. Rev. Lett. 130, 201402 (2023)] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through 𝒪⁡(𝛼 2 ) and 𝒪⁡(𝑆 2 ), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity.

classical black holes↗

Analysis of Transformer Magnetizing Reactance Using Describing Function in Direct Power Control of Back-to-Back Modular Multilevel Converter with Advanced Grid Support

This paper presents a Port Controlled Hamiltonian based direct power control architecture for a back-to-back modular multilevel converter system connecting two ac sources at different frequencies. The system features advanced grid support functionalities based on IEEE 1547-2018, implemented on the inverter side. The rectifier side controller ensures reference following for active and/or reactive powers and maintains the commanded dc bus voltage. The inverter side controller ensures power command following for active and reactive powers.The proposed control architecture is designed to suppress second harmonic oscillations in powers during unbalanced grid voltage sags by dynamically adjusting the currents on each ac side. This also ensures effective elimination of any second harmonic oscillations in the equivalent dc bus voltage. Validation is performed on an OPAL-RT real-time platform with case studies on unbalanced and balanced sags, demonstrating the controller's effectiveness during real time implementation. A reduced-scale laboratory prototype further verifies these case studies, with experimental results for balanced sags due to grid simulator limitations. The results confirm the robustness and efficiency of the proposed control strategy in ensuring stable and reliable operation under various grid conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Characterization of Flex-Fuel Prechamber Enabled Mixing-Controlled Combustion With Gasoline/Ethanol Blends at High Load

This numerical study focuses on the characterization of prechamber-enabled mixing-controlled combustion (PC-MCC) at ~18 bar brake mean effective pressure (BMEP) and 2200 rpm with 10% by volume ethanol-gasoline blend (E10) and pure ethanol (E100). Computational fluid dynamic (CFD) simulations of a stock and prechamber retrofitted single-cylinder Caterpillar C9.3B are carried out using CONVERGE. Prechamber equivalence ratio at spark timing, prechamber spark timing advance, and main chamber injection strategy are assessed with respect to their impact on ignition assistance performance and emissions characteristics relative to a diesel baseline at the same boundary conditions. Simulation results indicate that PC-MCC is flex-fuel capable and operates well for both E10 and E100 at the operating conditions considered. The results demonstrate that the use of a pilot-main injection strategy enables spark timing in the prechamber to be advanced and thus reduces spark plug firing pressure while maintaining robust ignition assistance. Results also indicate that the rich prechamber operation is favored for improved ignition assistance capabilities. Furthermore, the findings of this work suggest that a heavy-duty vehicle using a PC-MCC engine can utilize any blend of gasoline and ethanol, up to including pure ethanol, with no major sacrifices in performance relative to the diesel engine.

33 ADVANCED PROPULSION SYSTEMS↗

High-Efficiency, Low-Cost III-V Solar Cells by Dynamic Hydride Vapor Phase Epitaxy Coupled with Rapid, Polishing-Free Wafer Reuse through Orientation-Optimized (110) Spalling

We demonstrated (110) GaAs solar cells grown by D-HVPE with equivalent performance and material quality relative to (100) devices. Also, we developed a procedure for repeatable wafer-scale spalling of (110) GaAs. Spalled surfaces were free of the facets founds in (100) GaAs spalling, the large arrest lines found in (100) Ge spalling, and surface features greater than 3 µm in peak-to-valley height, which can otherwise degrade the efficiency of regrown III-V devices. A sub-µm step-terrace morphology was discovered on the post-spall wafer surface, resulting from the restricted cleavage system of GaAs, but we developed understanding of the factors that determine the resulting morphology, enabling ample opportunity for optimization of morphologies suitable for device growth and spall depth waste minimization on (110) GaAs. Lastly, we demonstrated a device grown on a previously spalled surface with only 8% relative efficiency difference to a cell grown on a new unspalled wafer. Significant optimization of the substrate regrowth conditions are required to enable higher efficiency, but these results highlight the promise of (110)-oriented devices coupled with substrate reuse by spalling as a pathway for low-cost III-V photovoltaics.

14 SOLAR ENERGY↗

Understanding curing dynamics of arylacetylene and phthalonitrile thermoset blends

Tetrakis(phenylethynyl)benzene (TPEB), a high char yield arylacetylene resin, was blended with a resorcinol-based PEEK™-like oligomeric phthalonitrile resin (Res). Here, we observed the influence of each polymer precursor on the structural changes and material dynamics of different mixtures of these resins during thermal curing to produce thermosets with high char retention. We provide insight to help understand fundamental processes that control and tune this complex thermally driven curing mechanism, which, to date, has not been well understood. We show that an equivalent blend of Res and TPEB mitigates the exothermic curing process and exhibits a low viscosity, which may facilitate processing of these thermosetting blends for composite manufacturing. To obtain a more comprehensive overview of the different dynamics of these polymers during curing, we correlated thermodynamic changes with rheology, materials characterization, and molecular dynamics derived from neutron scattering. Our efforts shed more light on the thermally driven chemical changes, physical transformation, and gelation dynamics that drive or accompany softening and curing of these two distinct crosslinking resin groups.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Geometric decoherence time in Lindbladian dynamics

The onset of decoherence in open many-body systems lacks a dynamical timescale grounded in the loss of bipartite entanglement. Here, we introduce the geometric decoherence time, defined as the earliest moment the monotone relation between logarithmic negativity and Rényi-$\frac{1}{2}$ entropy—exactly equal across any bipartition for pure states—breaks down under open-system evolution, signaling entropy growth without accompanying entanglement growth. We establish this criterion in both single-particle Gaussian dynamics and many-body Lindbladian evolution. We show that quantum mutual information provides a complementary long-time diagnostic: Its asymptotic vanishing is equivalent to factorization of the steady state across the bipartition, a condition strictly stronger than separability, and whenever a product steady state is approached exponentially in trace norm, negativity and mutual information share the same decay rate. In the presence of a strong symmetry, this tracking can fail—residual classical correlations can survive after entanglement has vanished. In the Kitaev chain with balanced gain and loss, we derive a closed-form solution and show that the topological phase sustains longer coherence times than the trivial phase at identical dissipation, with a local minimum at the chiral-symmetric point. In the interacting XXZ chain, exact many-body evolution shows that local 𝑍 dephasing preserves residual classical correlations, whereas gain and loss restore the mutual-information tracking of negativity. Furthermore, our results establish the geometric decoherence time as a dynamical scale tracking the onset of decoherence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Command of active and responsive elastomers by topological defects and patterns

The project resulted in the development of stimuli-responsive elastomer coatings formed by photopolymerized liquid crystal molecules. The molecular orientation of the liquid crystal elastomers is coupled to rubber-like elasticity. The project developed an approach to produce complex patterns of molecular orientation in elastomers by employing photopatterning technique based on plasmonic metamasks that convert unpolarized incoming light into a transmitted light beam with spatially-varying linear polarization. The polarization-modulated light beam aligns the film of azodye molecules, which serves as the substrate for liquid crystal elastomer coating. The alignment of the azodye molecules follows the polarization pattern with a phase shift of the alignment direction by 90 degrees. The azodye substrate imposes orientation of molecules in the adjacent liquid crystal layer which is preserved after the monomers are polymerized into a liquid crystal elastomer. By using differently aligned substrates one could produce various patterns of molecular orientation in the elastomer, which dictate the mechanical properties of the elastomers and their response to external stimuli such as temperature, humidity, and ultraviolet irradiation. In particular, the predesigned molecular orientation produces deterministically defined topography response of the liquid crystal coatings, in which their free surface changes from flat to either locally elevated or locally compressed, depending on whether the pre-inscribed molecular orientation is predesigned with a splay or bend deformation. The research established that the mechanism of this deterministic relation between the dynamic topography and pre-inscribed molecular orientation is rooted in the change of the tensorial order parameter that characterizes the degree of orientational order, and in the contraction/expansion of polymer molecules in response to the order parameter changes. In particular, lowering the order causes contraction of polymer globules. The work demonstrated that the dynamic topography of elastomer coatings with three-dimensional pattern of orientational order includes up and down motion of the material (along the normal to the coating) and also shifts in lateral directions. We demonstrate that the deterministic relationship between the orientational patterns and variations of coatings’ profile is caused by forces that are mathematically equivalent to active forces in the system of “pullers” or “pushers” in active matter, demonstrating universality of the out-of-equilibrium behavior. The project resulted in theoretical models that predictively describe the dynamic response of coatings. The topography of liquid crystal elastomers is sensitive to stimuli such as temperature, ultraviolet irradiation, and humidity. The applicability of the patterned approach to produce dynamic coatings was expanded from nematic elastomers to their smectic counterparts. The project combined a battery of imaging techniques to unveil the dynamic properties of the coatings, ranging from the state-of-the-art dynamic holographic microscopy to fluorescent confocal polarizing microscopy and polscope microscopy. The research uncovered potential applications of dynamic elastomer coatings, such as control placement of colloidal particles, engineering of living tissues with alignment patterns of cells that follow the orientational order of elastomer coatings. The approach developed in the project can be used to design programmable dynamic coatings with functionalities that mimic biological tissues such as skin.

36 MATERIALS SCIENCE↗

Average nonlinear dynamics of particles in gravitational pulses: Effective Hamiltonian, secular acceleration, and gravitational susceptibility

Particles interacting with a prescribed quasimonochromatic gravitational wave (GW) exhibit secular (average) nonlinear dynamics that can be described by Hamilton’s equations. We derive the Hamiltonian of this “ponderomotive” dynamics to the second order in the GW amplitude for a general background metric. For the special case of vacuum GWs, we show that our Hamiltonian is equivalent to that of a free particle in an effective metric, which we calculate explicitly. We also show that already a linear GW pulse displaces a particle from its unperturbed trajectory by a finite distance that is independent of the GW phase and proportional to the integral of the pulse intensity.This effect is independent from the nonlinear memory effects that has been known. We calculate the particle displacement analytically and show that our result is in agreement with numerical simulations. We also show how the Hamiltonian of the nonlinear averaged dynamics naturally leads to the concept of the linear gravitational susceptibility of a particle gas with an arbitrary phase-space distribution. We calculate this susceptibility explicitly to apply it, in a follow-up paper, toward studying self-consistent GWs in inhomogeneous media within the geometrical-optics approximation

79 ASTRONOMY AND ASTROPHYSICS↗