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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Flux-split algorithms for the multi-dimensional Euler equations with real gases

Upwind algorithms are developed for the numerical solution of the multidimensional Euler equations for real gases. Flux-splitting methods are derived which account for a general equation of state. Approximations to the state equation based on physical arguments result in simplified algorithms which may be implemented into existing perfect-gas codes. Applications of the method to several high-Mach-number high-temperature flows are presented for two and three space dimensions.

Grossman, B.↗
DOE OSTI2024

Equation of State and Thermometry of the 2D SU ( N ) Fermi-Hubbard Model

We characterize the equation of state (EoS) of the SU ( N > 2 ) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N = 3 , 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU ( N ) FHM. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data

Significant advancement in Bayesian inference of nuclear equation of state (EOS) from gravitational wave and x-ray observations of neutron stars (NSs) has been made by the nuclear astrophysics community especially since GW170817. By extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not), we search for a data-driven and robust empirical formula for the radius 𝑅 1.4 of canonical NSs in terms of the characteristic EOS parameters (features). We also identify the single most important but currently poorly known EOS parameter for determining the 𝑅 1.4 . Using three regression-model-building methodologies: bidirectional stepwise feature selection, least absolute shrinkage selection operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding 𝑅 1.4 values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable 𝑅 1.4 formulas with varying statistical accuracy and technical complexity. Here, the most important EOS parameters for determining 𝑅 1.4 are found consistently in each of the feature selection processes to be (in order of decreasing importance): curvature 𝐾 sym , slope 𝐿, skewness 𝐽 sym of nuclear symmetry energy, skewness 𝐽 0 , incompressibility 𝐾 0 of symmetric nuclear matter, and the magnitude 𝐸 sym ⁡(𝜌 0 ) of symmetry energy at the saturation density 𝜌 0 of nuclear matter.

Bayesian methods↗
DOE OSTI2021

P–V–T Equation of State of Iridium Up to 80 GPa and 3100 K

In the present study, the high-pressure high-temperature equation of the state of iridium has been determined through a combination of in situ synchrotron X-ray diffraction experiments using laser-heating diamond-anvil cells (up to 48 GPa and 3100 K) and density-functional theory calculations (up to 80 GPa and 3000 K). The melting temperature of iridium at 40 GPa was also determined experimentally as being 4260 (200) K. The results obtained with the two different methods are fully consistent and agree with previous thermal expansion studies performed at ambient pressure. The resulting thermal equation of state can be described using a third-order Birch–Murnaghan formalism with a Berman thermal-expansion model. The present equation of the state of iridium can be used as a reliable primary pressure standard for static experiments up to 80 GPa and 3100 K. A comparison with gold, copper, platinum, niobium, rhenium, tantalum, and osmium is also presented. On top of that, the radial-distribution function of liquid iridium has been determined from experiments and calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

QCD Equation of State and Phase Diagram from Holographic Black Holes

By using the AdS/CFT correspondence, we construct an Einstein-Maxwell-Dilaton model to map the thermodynamics of strongly interacting matter. The holographic model, constrained to reproduce the lattice QCD equation of state at zero baryon chemical potential, predicts a critical end point and a first order phase transition line. We also obtain the equation of state of the model for a large region of the phase diagram. We characterize the crossover transition region by two lines, one associated to the inflection of the second order baryon susceptibility, and another one associated to the minimum of the square of the speed of sound along trajectories of constant entropy per baryon number. We observe that both lines merge at the critical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Direct nonparametric multimessenger constraints on the equation of state of cold dense nuclear matter

We utilize the now substantial amount of astrophysical observations of neutron stars (NSs), along with perturbative quantum chromodynamics (pQCD) calculations at high density, to directly constrain the NS equation of state (EOS). To this end, we construct nonparametric EOS priors by using Gaussian processes trained on 75 EOSs, which include models with either hadrons, hyperons, or quarks at high densities. We create a prior using the full EOS sample (model agnostic), and one prior for each EOS family to test model discrimination. We introduce a novel inference approach, which allows the simultaneous sampling of intrinsic and extrinsic parameters of binary NS mergers, as well as a nonparametric equation of state. We showcase this method in a Bayesian updating scheme by first performing a complete analysis of the binary NS merger event GW170817 with minimal assumptions, and sequentially adding information from x-ray and radio NS observations, along with pQCD calculations. Besides providing standard constraints, such as the pressure at twice nuclear saturation density 𝑝⁡(2⁢𝜌 sat ) = 4.3$^{+0.6}_{−0.6}$ × 10 34 dyne/cm 2 , at 95% confidence level, for the model agnostic prior, our methodology shows how the choice of EOS families used in conditioning changes the inferred astrophysical properties of the EOS, namely tidal deformability and maximum supported NS mass. We find hyperonic priors predicting higher tidal deformabilities for a 1.4⁢𝑀 ⊙ NS, and hadronic priors being preferred by the considered astrophysical data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Learning thermodynamically constrained equations of state with uncertainty

Numerical simulations of high energy-density experiments require equation of state (EOS) models that relate a material’s thermodynamic state variables—specifically pressure, volume/density, energy, and temperature. EOS models are typically constructed using a semi-empirical parametric methodology, which assumes a physics-informed functional form with many tunable parameters calibrated using experimental/simulation data. Since there are inherent uncertainties in the calibration data (parametric uncertainty) and the assumed functional EOS form (model uncertainty), it is essential to perform uncertainty quantification (UQ) to improve confidence in EOS predictions. Model uncertainty is challenging for UQ studies since it requires exploring the space of all possible physically consistent functional forms. Thus, it is often neglected in favor of parametric uncertainty, which is easier to quantify without violating thermodynamic laws. This work presents a data-driven machine learning approach to constructing EOS models that naturally captures model uncertainty while satisfying the necessary thermodynamic consistency and stability constraints. We propose a novel framework based on physics-informed Gaussian process regression (GPR) that automatically captures total uncertainty in the EOS and can be jointly trained on both simulation and experimental data sources. A GPR model for the shock Hugoniot is derived, and its uncertainties are quantified using the proposed framework. We apply the proposed model to learn the EOS for the diamond solid state of carbon using both density functional theory data and experimental shock Hugoniot data to train the model and show that the prediction uncertainty is reduced by considering thermodynamic constraints.

Sharma, Himanshu (ORCID:000900050235718X)↗
NASA NTRS1977

Equations of state and impact-induced shock-wave attenuation on the moon

Equation of state formulations are considered in a framework that permits comparison with one-dimensional impedance match solutions. The problem considered is the peak pressures attained along the impact symmetry axis when a sphere impacts with a half-space. The regimes of melting and vaporization - in particular, incipiently melted, completely melted, incipiently vaporized, and completely vaporized states - are examined, and the pressures at which critical isentropes intersect the Hugoniots of iron and gabbroic anorthosite are considered. A means of representing the spatial attenuation of shock pressure along the impact axis by two regimes is introduced, and results for the near-field and far-field regime are presented. It is thought that the treatment can be used to obtain quantitative bounds on the impact velocity of the meteorite.

Ahrens, T. J.↗
DOE OSTI2023

Parameterization of the β and γ phases of Tin using the Vinet and Mie-Grüneisen Equations of State

When testing new phase aware materials models, it is often not possible to use tabulated Equations of States for the phases since the model might only be available in a smaller specialized research code without capability to read in tables. These EOS parameterizations for two of the solid phases of Tin were developed for testing the Kinetic Phase Transition model by Carl Greeff, LANL. They are based on two isotherms per phase obtained from work in progress by Carl Greeff, and their phase boundary corresponds fairly well to SESAME 2162. A full machinery is applied for the parameterization of the Vinet EOSs while the Mie-Grüneisen parameterizations are translated from the Vinet EOSs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Sensitivity of magnetohydrodynamic simulations of Joule-heated conductors to the vaporization curve in equations of state

Magnetohydrodynamic (MHD) simulations of electrically exploded aluminum and copper rods demonstrate a technique to validate equations of state (EOS) for rapidly Joule-heated conductors. The balance of internal and magnetic forces at the conductor-insulator interface drives the metal there along the vaporization phase boundary. Variations between critical points and vaporization curves in existing models predict differing densities and temperatures in MHD simulations for these models. Here, the inclusion of Maxwell constructs in the liquid-vapor biphase region of the EOS caused the rod surface to vaporize earlier in time than unmodified tables with van der Waals loops. Velocimetry of recent experiments is used to validate the location of the vaporization curve in existing EOS models and differentiate between the vapor dome treatments. Dielectric coatings applied to the metal surface restricted the conductor’s expansion and diverted the metal into the warm dense matter regime.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The Equation of State of Neutron-Rich Matter at Fourth Order of Chiral Effective Field Theory and the Radius of a Medium-Mass Neutron Star

We report neutron star predictions based on our most recent equations of state. These are derived from chiral effective field theory, which allows for a systematic development of nuclear forces, order by order. We utilize high-quality two-nucleon interactions and include all three-nucleon forces up to fourth order in the chiral expansion. Our ab initio predictions are restricted to the domain of applicability of chiral effective field theory. However, stellar matter in the interior of neutron stars can be up to several times denser than normal nuclear matter at saturation, and its composition is essentially unknown. Following established practices, we extend our microscopic predictions to higher densities matching piecewise polytropes. The radius of the average-size neutron star, about 1.4 solar masses, is sensitive to the pressure at normal densities, and thus it is suitable to constrain ab initio theories of the equation of state. For this reason, we focus on the radius of medium-mass stars. We compare our results with other theoretical predictions and recent constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗
DOE OSTI2023

Impact of O4 future detections on the determination of the dense matter equations of state

Here, in view of the next LIGO-Virgo-KAGRA Observing period O4 (to start in Spring 2023), we address the question of the ability of the interferometers network to discriminate among different neutron stars equation of states better than what was possible with the observation of the binary neutron stars merger GW170817. We show that the observation of an event similar to GW170817 during O4 would allow us to resolve the dimensionless effective tidal deformability $\tilde{Λ}$ within an uncertainty 7 times better than the one obtained in O2. Thanks to the expected increase in sensitivities, we show that any GW170817-like single-event within a distance of 100 Mpc would imply significantly improved constraints of the neutron stars equations of state. We also illustrate the important impact of the noise in the analysis of the signal, showing how it can impact the effective tidal deformability probability density function for large signal-to-noise ratio.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

Cold equation of state in a strong magnetic field - Effects of inverse beta-decay

The influence of a high magnetic field (B is greater than 10 exp 12 G) on the degenerate matter equation of state appropriate to a neutron star is studied. The regime dominated by relativistic electrons up to the neutron drip density is highlighted. The equilibrium matter composition and equation of state, allowing for inverse beta-decay. Two different equilibrium models are determined: an ideal neutron-proton-electron (npe) gas and the more realistic model of Baym, Pethick, and Sutherland (1971) consisting of a Coulomb lattice of heavy nuclei embedded in an electron gas. For a sufficiently high field strength, the magnetic field has an appreciable effect, changing the adiabatic index of the matter and the nuclear transition densities. The influence of a strong field on some simple nonequilibrium processes, including beta-decay and inverse beta-decay (electron capture) is also considered. The effects produced by the magnetic field are mainly due to the changes in the transverse electron quantum orbits and the allowed electron phase space induced by the field.

Lai, Dong↗
DOE OSTI2021

Phase transitions and critical behavior in hadronic transport with a relativistic density functional equation of state

We develop a flexible, relativistically covariant parametrization of the dense nuclear matter equation of state suited for inclusion in computationally demanding hadronic transport simulations. Within an implementation in the hadronic transport code smash, we show that effects due to bulk thermodynamic behavior are reproduced in dynamic hadronic systems, demonstrating that hadronic transport can be used to study critical behavior in dense nuclear matter, both at and away from equilibrium. We also show that two-particle correlations calculated from hadronic transport simulation data follow theoretical expectations based on the second-order cumulant ratio, and constitute a clear signature of the crossover region above the critical point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Effect of the Nuclear Equation of State on Relativistic Turbulence-induced Core-collapse Supernovae

Abstract The nuclear equation of state (EOS) is an important component in the evolution of core-collapse supernovae. In this paper we make a survey of various EOSs in the literature and analyze their effect on spherical core-collapse models in which the effects of three-dimensional turbulence is modeled by a general relativistic formulation of Supernova Turbulence In Reduced-dimensionality (STIR). We show that the viability of the explosion is quite EOS dependent and that it best correlates with the early-time interior entropy density of the proto–neutron star. We check that this result is not progenitor dependent, although the lowest-mass progenitors show different explosion properties, due to the different pre-collapse nuclear composition. Larger central entropies also induce more vigorous proto–neutron star convection in our one-dimensional turbulence model, as well as a wider convective layer.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Equations of state and impact-induced shock-wave attenuation on the moon

Current equation of state formulations, used for finite difference cratering flow calculations, are cast into a framework permitting comparison of peak pressures attained upon impact of a sphere, with a half-space, along the impact symmetry axis, to one dimensional impedance match solutions. On the basis of this formulation and application of thermochemical data, the regimes of melting and vaporization are examined. For the purpose of identifying material which will, upon isentropic release from the impact-induced shock state, result in a solid just brought to its melting point, i.e., incipiently melted (IM); completely melted (CM); just brought to its boiling point, i.e., incipiently vaporized (IV); and completely vaporized (CV) state, the pressures at which the critical isentropes intersect the Hugoniots of iron and gabbroic anorthosite (GA) are examined in detail. The latter rock type is assumed to be representative of the lunar highlands. The Hugoniot pressures, for which IM, CM, IV, and CV will occur upon isentropic expansion, are calculated to be 2.2, 2.6, 4.2, and 16.8 Mbar, respectively.

Ahrens, T. J.↗
DOE OSTI2021

The Role of Strong Gravity and the Nuclear Equation of State on Neutron-star Common-envelope Accretion

Common-envelope evolution is important in the formation of neutron star binaries within the isolated binary formation channel. As a neutron star inspirals within the envelope of a primary massive star, it accretes and spins up. Because neutron stars are in the strong-gravity regime, they have a substantial relativistic mass deficit, i.e., their gravitational mass is less than their baryonic mass. This effect causes some fraction of the accreted baryonic mass to convert into neutron star binding energy. The relativistic mass deficit also depends on the nuclear equation of state, since more compact neutron stars will have larger binding energies. We model the mass growth and spin-up of neutron stars inspiraling within common-envelope environments and quantify how different initial binary conditions and hadronic equations of state affect the post-common-envelope neutron star's mass and spin. From these models, we find that neutron star mass growth is suppressed by ≈15%–30%. We also find that for a given amount of accreted baryonic mass, more compact neutron stars will spin-up faster while gaining less gravitational mass, and vice versa. Here, this work demonstrates that a neutron star's strong gravity and nuclear microphysics plays a role in neutron-star-common-envelope evolution, in addition to the macroscopic astrophysics of the envelope. Strong gravity and the nuclear equation of state may thus affect both the population properties of neutron star binaries and the cosmic double neutron star merger rate.

79 ASTRONOMY AND ASTROPHYSICS↗