Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “equations of state”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Progress in Developing a New Field-theoretical Crossover Equation-of-State

A new field-theoretical crossover equation-of-state model is being developed. This model of a liquid-gas critical point provides a bridge between the asymptotic equation-of-state behavior close to the transition, obtained by the Guida and Zinn-Justin parametric model [J. Phys. A: Math. Gen. 31, 8103 (1998)], and the expected mean field behavior farther away. The crossover is based on the beta function for the renormalized fourth-order coupling constant and incorporates the correct crossover exponents and critical amplitude ratios in both regimes. A crossover model is now being developed that is consistent with predictions along the critical isochore and along the coexistence curve of the minimal subtraction renormalization approach developed by Dohm and co-workers and recently applied to the O(1) universality class [Phys. Rev. E, 67, 021106 (2003)]. Experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve near the He-3 critical point are being compared to the predictions of this model. The results of these comparisons will be presented.

Rudnick, Joseph↗
DOE OSTI2022

Hot and dense matter equation of state probability distributions for astrophysical simulations

We add an ensemble of nuclei to the equation of state for homogeneous nucleonic matter to generate a new set of models suitable for astrophysical simulations of core-collapse supernovae and neutron star mergers. We implement empirical constraints from (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. Our model is also guided by microscopic many-body theory calculations based on realistic nuclear forces, including the zero-temperature neutron matter equation of state from quantum Monte Carlo simulations and thermal contributions to the free energy from finite-temperature many-body perturbation theory. We ensure that the parameters of our model can be varied while preserving thermodynamic consistency and the connection to experimental or observational data, thus providing a probability distribution of the astrophysical hot and dense matter equation of state. Furthermore, we compare our results with those obtained from other available equations of state. While our probability distributions indeed represent a large number of possible equations of state, we cannot yet claim to have fully explored all of the uncertainties, especially with regard to the structure of nuclei in the hot and dense medium.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Neural network reconstruction of the dense matter equation of state from neutron star observables

The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. Here, in this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of ~1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations. We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Dense nuclear matter equation of state from heavy-ion collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. Furthermore, this white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Sesame Equation of State for Nickel

A new Sesame equation of state table for nickel has been created and released for testing. The material ID is 83103. Of note the new table incorporates a magnetic contribution based on specific heat data and a melt curve based on experimental data to 100 GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Prospects for a Precise Equation of State Measurement from Advanced LIGO and Cosmic Explorer

Gravitational-wave observations of neutron star mergers can probe the nuclear equation of state by measuring the imprint of the neutron star's tidal deformability on the signal. We investigate the ability of future gravitational-wave observations to produce a precise measurement of the equation of state from binary neutron star inspirals. Because measurability of the tidal effect depends on the equation of state, we explore several equations of state that span current observational constraints. We generate a population of binary neutron stars as seen by a simulated Advanced LIGO–Virgo network, as well as by a planned Cosmic Explorer observatory. We perform Bayesian inference to measure the parameters of each signal, and we combine measurements across each population to determine R 1.4 , the radius of a 1.4 M ⊙ neutron star. We find that, with 321 signals, the LIGO–Virgo network is able to measure R 1.4 to better than 2% precision for all equations of state we consider; however, we also find that achieving this precision could take decades of observation, depending on the equation of state and the merger rate. On the other hand, we find that with one year of observation, Cosmic Explorer will measure R 1.4 to better than 0.6% precision. In both cases, we find that systematic biases, such as from an incorrect mass prior, can significantly impact measurement accuracy, and efforts will be required to mitigate these effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Sensitivity of an integrated experiment to uncertainty in the high explosive equations of state

Traditionally, hydrodynamics simulations are performed with a single equation-of-state (EOS) to describe each material. These EOSs typically have a physics-informed functional form with adjustable parameters that are calibrated in order to replicate small-scale data. However, because the calibration data have uncertainty and there are typically inherent degeneracies in fitting the EOS, there are actually multiple EOSs that might be consistent with calibration data. In this work, we perform uncertainty quantification (UQ) for the reactant and product equations of state for the high explosive PBX 9501 to yield an ensemble of EOSs that match the uncertain small-scale calibration data. We then simulate an experiment of an explosively formed penetrator repeatedly with different EOSs to both validate the UQ analysis and determine the effects of EOS uncertainty on the prediction of quantities of interest in the experiment. In general, we find good agreement between the simulation predictions and the experimental measurements, and we identify an EOS variable that contributes most directly to the spread in the predictions as the EOSs are varied.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Continuum shock mixture models for Ni+Al multilayers: Individual layers and bulk equations of state

Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni x Al y ⁠, as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni x Al y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.

36 MATERIALS SCIENCE↗
NASA NTRS1971

Equation of state for porous metals under strong shock compression.

An equation of state is developed for metals in the high-pressure high-temperature region that can be extended in a thermodynamically consistent manner to the vapor phase. The constants are obtained from observed thermodynamic properties and are specified for Al, Fe, Cu, Ni, Pb, and W. This equation of state was checked against experimental data by computing the Hugoniot curves for normal and porous samples for cases where experimental data are available. Also, the velocity of sound and release isentropes were computed for various shock conditions.

Naumann, R. J.↗
DOE OSTI2022

Thermal Pressure in the Thermal Equation of State for Solid and a Proposed Substitute

Abstract The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state, P ( V , T ) = P ( V , T 0 ) + P th ( V , T ), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1989

Equation Of State With Temperature Effects For Solids

Behavior at high temperature predicted from only four parameters. Equations derived to express thermodynamical properties of compressed solids at high temperatures. New equations based on fundamental considerations of thermodynamics, isothermal equation of state, and assumption thermal pressure independent of volume and varies linearly with temperature near and about Debye temperature. Using only four parameters (three are those of isothermal equation of state), new equations describe thermodynamic behavior of material over range of temperatures from approximately Debye temperature to melting point.

Vinet, Pascal↗
DOE OSTI2026

Machine-learned quantum molecular dynamics calculations of warm dense equation of state and ionic transport coefficients of deuterated water

White dwarf models require accurate equations of state and ionic transport coefficients in the warm dense matter regime, where kinetic theory models and tabulated equations of state are often inaccurate. In this work, spectral-partitioned density functional theory and machine-learned interatomic potentials are combined to perform large-scale, first-principles quantum molecular dynamics simulations of deuterated water (D 2 O) near the principal Hugoniot. This approach retains Kohn-Sham accuracy while achieving orders-of-magnitude speedup, yielding converged equation of state and transport properties over a broad pressure and temperature range. The results reveal the thermodynamic conditions under which ionic transport models for interdiffusivity and shear viscosity converge and identify those in closest agreement with density functional theory benchmarks at temperatures in the warm dense matter regime. The present framework extends first-principles transport calculations to higher temperatures than previously achieved, and provides an efficient, scalable, and general approach for studying transport properties in complex multicomponent mixtures.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2002

Test of a new field-theoretical crossover equation-of-state

A new field-theoretical crossover equation-of-state model provides a bridge between the asymptotic behavior close to a liquid-gas critical point and the expected mean field behavior farther away.

equation-of-state critical phenomena liquid-gas cr↗
DOE OSTI2023

The equations of state of statically compressed palladium and rhodium

Here, the pressure–volume equations of state of palladium and rhodium statically compressed in neon are presented. Vinet fits give parameters for palladium: V0=58.678(73) Å 3 , B 0 =189.3(30) GPa, B' 0 =5.473(63), and rhodium: V 0 =55.062(63) Å3, B 0 =241.3(65) GPa, B' 0 =5.34(24). Both metals are observed to react with hydrocarbons under pressure to form hydrides. Existing equations of state are discussed with regard to potential inadvertent hydrogen contamination as a source for discrepancies and anomalous fitted parameters.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Astrophysical Applications of Quantum Corrections to the Equation of State of a Plasma

The quantum electrodynamic correction to the equation of state of a plasma at finite temperature is applied to the areas of solar physics and cosmology. A previously neglected, purely quantum term in the correction is found to change the equation of state in the solar core by -0.37%, which is roughly estimated to decrease the calculated high energy neutrino flux by about 2.2%. We also show that a previous calculation of the effect of this correction on big bang nucleosynthesis is incomplete, and we estimate the correction to the primordial helium abundance Y to be Delta A= 1.4 x 10(exp -4). A physical explanation for the correction is found in terms of corrections to the dispersion relation of the electron, positron, and photon.

Heckler, Andrew F.↗
DOE OSTI2023

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

Here, this paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature including problems with composite waves.

97 MATHEMATICS AND COMPUTING↗