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Results for “STATE EQUATION”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Chiral condensate and the equation of state at nonzero baryon density from the hadron resonance gas model with a repulsive mean field

We study the QCD equation of state and the chiral condensate using the hadron resonance gas model with repulsive mean-field interactions. We find that the repulsive interactions improve the agreement with the lattice results on the derivatives of the pressure with respect to the baryon chemical potential up to eighth order. From the temperature dependence of the chiral condensate we estimate the crossover temperature as a function of baryon chemical potential, T p c ( μ B ) . We find that the chiral crossover line starts to deviate significantly from the chemical freeze-out line already for μ B > 400 MeV . Furthermore, we find that the chiral pseudocritical line can be parametrized as T p c ( μ B ) / T p c ( 0 ) = 1 − κ 2 [ μ B / T p c ( 0 ) ] 2 − κ 4 [ μ B / T p c ( 0 ) ] 4 with κ 2 = 0.0150 ( 2 ) and κ 4 = 3.1 ( 6 ) × 10 − 5 , which are in agreement with lattice QCD results for small values of μ B . For the first time we find a tiny but nonzero value of κ 4 in our study. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

JCZ3: An Equation of State Based on the Exponential-Six Intermolecular Potential – Update: Formulation

This report presents a comprehensive analysis of the JCZ3 equation of state (EOS) as implemented in the TIGER code, focusing on its thermodynamic framework, mathematical formulations, and implications for modeling gas phase behavior under varying conditions. Overall, the report affirms the TIGER code's foundational robustness and its potential as a valuable tool for simulating high-pressure, high-temperature gas mixtures, while also highlighting areas for further refinement and validation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Solar oscillations and the equation of state

The dependence of frequencies of solar oscillations on the thermodynamic state of the sun is considered. On the basis of an analysis of the equations of stellar structure, as well as the relevant aspects of the properties of the oscillations, it is argued that in the convection zone, information about the equation of state which is relatively unaffected by other uncertainties in the physics of the solar interior can be isolated. The different treatments that have been employed to describe the thermodynamics of stellar plasmas are reviewed. Through application of several of these treatments to the computation of models of the solar envelope, it is demonstrated that the sensitivity of the observed frequencies is in fact sufficient to distinguish even quite subtle features of the physics of solar matter.

Christensen-Dalsgaard, Jorgen↗
NASA NTRS2004

State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

Beeler, Scott C.↗
NASA NTRS1973

An equation of state for oxygen and nitrogen

Recent measurements of thermodynamic properties of oxygen and nitrogen have provided data necessary for development of a single equation of state for both fluids. Data are available in summary report and two-part detailed study on thermodynamic properties of oxygen and nitrogen. Same data are used to develop vapor-pressure equation and heat-capacity equation.

Jacobsen, R. T.↗
DOE OSTI2026

Microscopic constraints for the equation of state and structure of neutron stars: A Bayesian model mixing framework

Bayesian model mixing (BMM) is a statistical technique that can combine constraints from different regions of an input space in a principled way. Here we extend our BMM framework for the equation of state (EOS) of strongly interacting matter from symmetric nuclear matter to asymmetric matter, specifically focusing on zero-temperature, charge-neutral, 𝛽-equilibrated matter. We use Gaussian processes (GPs) to infer constraints on the neutron-star matter EOS at intermediate densities from two different microscopic theories: chiral effective-field theory (𝜒⁢EFT) at baryon densities around nuclear saturation, 𝑛 𝐵 ∼ 𝑛 0 , and perturbative QCD at asymptotically high baryon densities, 𝑛 𝐵 ⩾ 20⁢𝑛 0 . The uncertainties of the 𝜒⁢EFT and pQCD EOSs are obtained using the BUQEYE truncation error model. We demonstrate the flexibility of our framework through the use of two categories of GP kernels: conventional stationary kernels and a nonstationary changepoint kernel. We use the latter to explore potential constraints on the dense matter EOS by including exogenous data representing theory predictions and heavy-ion collision measurements at densities ⩾ 2⁢𝑛 0 . We also use our EOSs to obtain neutron-star mass-radius relations and their uncertainties. Finally, our framework, whose implementation will be available through a GitHub repository, provides a prior distribution for the EOS that can be used in large-scale neutron-star inference frameworks.

Bayesian methods↗
NASA NTRS1985

Parametrized equation of state for electron liquids in the Singwi-Tosi-Land-Sjolander aproximation

Results are reported of a theoretical study of an equation of state for electron liquids (one-component plasmas of electrons embedded in a uniform neutralizing background of positive charges), where there is an interplay between the strong Coulomb-coupling effect and the degrees of Fermi degeneracy. Calculations are based on the Singwi-Tosi-Land-Sjolander approximation (1968). The calculated results are parametrized in the form of analytic formulas for the interaction and excess free energies, which are applicable over a wide range of parameters as long as the electrons are in a paramagnetic fluid state. Unlike the present study, earlier studies concentrated on plasmas where the Fermi degeneracy parameter tended either to zero or to infinity, thus excluding many actual plasmas (stellar interiors, heavy planets such as Jupiter, plasmas in projected inertial confinement fusion experiments, and the liquid metals).

Tanaka, S.↗
DOE OSTI2025

Unified nonparametric equation-of-state inference from the neutron-star crust to perturbative-QCD densities

Perturbative quantum chromodynamics (pQCD), while valid only at densities exceeding those found in the cores of neutron stars, could provide constraints on the dense-matter equation of state (EOS). Here, in this work, we examine the impact of pQCD information on the inference of the EOS using a nonparametric framework based on Gaussian processes (GPs). We examine the application of pQCD constraints through a ``pQCD likelihood,'' and verify the findings of previous works; namely, a softening of the EOS at the central densities of the most massive neutron stars and a reduction in the maximum neutron-star mass. Although the pQCD likelihood can be easily integrated into existing EOS inference frameworks, this approach requires an arbitrary selection of the density at which the constraints are applied. The EOS behavior is also treated differently on either side of the chosen density. To mitigate these issues, we extend the EOS model to higher densities, thereby constructing a ``unified'' description of the EOS from the neutron-star crust to densities relevant for pQCD. In this approach the pQCD constraints effectively become part of the prior. Since the EOS is unconstrained by any calculation or data between the densities applicable to neutron stars and pQCD, we argue for maximum modeling flexibility in that regime. We compare the unified EOS with the traditional pQCD likelihood, and although we confirm the EOS softening, we do not see a reduction in the maximum neutron-star mass or any impact on macroscopic observables. Though residual model dependence cannot be ruled out, we find that pQCD suggests the speed of sound in the densest neutron-star cores has already started decreasing toward the asymptotic limit; we find that the speed of sound squared at the center of the most massive neutron star has an upper bound of $\sim 0.5$ at the 90% level.

equations of state of nuclear matter↗
DOE OSTI2025

General features of the stellar matter equation of state from microscopic theory, new maximum-mass constraints, and causality

The profile of a neutron star probes a very large range of densities, from the density of iron up to several times the density of saturated nuclear matter, and thus no theory of hadrons can be considered reliable if extended to those regions. We emphasize the importance of taking contemporary ab initio theories of nuclear and neutron matter as the baseline for any extension method, which will unavoidably involve some degree of phenomenology. We discuss how microscopic theory, on the one end, with causality and maximum-mass constraints, on the other, set strong boundaries to the high-density equation of state. We present our latest neutron star predictions where we combine polytropic extensions and parametrizations guided by speed of sound considerations. The predictions we show include our baseline neutron star cooling curves.

chiral effective field theory↗
NASA NTRS1980

Anorthite - Thermal equation of state to high pressures

New shock-wave data are presented for anorthite from which a full high-temperature, high-pressure equation of state is derived. Whereas anorthite has relatively low values of thermal expansion and Grueneisen parameter at zero pressure, it is found that these attain relatively high values in the high density state corresponding to the high-pressure phase Hugoniot but decrease upon compression as expected. It is noted that higher order anharmonic contributions decrease more rapidly with pressure and that the thermal expansion therefore saturates to a high temperature value at pressures above about 100 GPa. Reduction of the Hugoniot data permits shock temperatures to be calculated; it also yields a principal adiabat for the high pressure branch of the Hugoniot. The initial bulk modulus of this adiabat is essentially identical to that of anorthite, whereas the initial density is about 3.40 Mg/cu m.

Jeanloz, R.↗
NASA NTRS1986

Temperature effects on the universal equation of state of solids

Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus; (2)it P=0 pressure derivative; (3) the P=0 volume; and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.

Vinet, P.↗
NASA NTRS1987

Temperature effects on the universal equation of state of solids

Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P = 0) isothermal bulk modulus; (2) its P = 0 pressure derivative; (3) the P = 0 volume; and (4) the P = 0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.

Vinet, Pascal↗
DOE OSTI2026

Calculating shock Hugoniot and isentropes using multiphase equation of state tables and application to shock and release of diamond ablators in inertial confinement fusion implosions

Advances in shock and ramp compression techniques now allow experimental access to unprecedented extreme conditions of pressure and temperature, providing a means to test theoretical models. Here, we describe a simple methodology to compute multi-phase shock Hugoniot and isentropes using multiphase equation of state tables. We treat explicitly the phase coexistence along the phase boundary to reveal the evolution of the sample as it undergoes the phase transformation in adiabatic conditions. We illustrate the method by calculating the predicted shock and shock-and-release behavior of diamond at conditions relevant for the initial stage of inertial confinement fusion implosions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Equation-of-state measured via x-ray phase contrast imaging for Epon 828/DEA epoxy

Epoxies are a broad class of polymer materials often used as adhesive, structural or binding materials. Epon 828 is an epoxy resin that can be polymerized with a variety of curing agents with the choice of curing agent potentially having an effect on the resulting epoxy polymer’s material properties. In this study, the dynamic behavior of Epon 828 epoxy resin cured with diethanolamine (DEA) is investigated through a series of tamped Richtmyer-Meshkov instability (RMI) experiments measured with x-ray phase-contrast imaging. The measured shock and particle velocities are combined with data in the literature to calibrate Mie-Grüneisen equations-of-state (EOS) for portions and combinations of the collective dataset. The calibrated Mie-Grüneisen EOS are validated against particle velocity profiles extracted from published literature using the Eulerian hydrocode CTH. Here, the Mie-Grüneisen EOS fit to only the tamped RMI experimental data presented here most closely follows the particle velocity profile in the published literature.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Equation of state measurement of detonation carbon condensates using optical microscopy and interferometry

Thermochemical models of detonation that estimate performance (e.g., detonation velocity, energy delivery, etc.), are based on assumptions that carbon condensates (soot) formed during detonation is largely similar to bulk carbon. However, soot constituents can range from amorphous carbon to nanodiamond and include other material phases. Since thermodynamic properties of the soot such as compressibility are imperative for accurate thermochemical modeling of detonation reaction chemistry, experimental measurements of the equation of state (EOS) which determine the compressibility are vital. Due to the mixed-phase nature of detonation soot, typical methods to measure the EOS (e.g., x-ray diffraction) are untenable. In this study, the high-pressure EOS up to 20 GPa was determined for detonation soot collected from PBX 9502, Composition B (Comp B), Hexanitrostilbene (HNS), and LX-21 high explosives by employing a direct volume technique using optical microscopy and interferometry in a diamond anvil cell. Comp B soot was determined to be the least compressible [K 0 = 57.9(17) GPa] with HNS soot [K 0 = 53.7(15) GPa], LX-21 soot [K 0 = 45.8(51) GPa], and PBX 9502 soot [K 0 = 28.2(27) GPa] being more compressible, likely due to differences in nanodiamond content as compared to amorphous carbon and graphite content.

Amorphous materials↗
DOE OSTI2026

Direct inference of nuclear equation-of-state parameters from gravitational-wave observations

The observation of neutron star mergers with gravitational waves (GWs) has provided a new method to constrain the dense-matter equation of state (EOS) and to better understand its nuclear physics. However, inferring nuclear microphysics from GW observations necessitates the sampling of EOS model parameters that serve as input for each EOS used during the GW data analysis. The sampling of the EOS parameters requires solving the Tolman–Oppenheimer–Volkoff (TOV) equations a large number of times—a process that slows down each likelihood evaluation in the analysis on the order of a few seconds. Here, we employ emulators for the TOV equations built using multilayer perceptron neural networks to enable direct inference of nuclear EOS parameters from GW strain data. Our emulators allow us to rapidly solve the TOV equations, taking in EOS parameters and outputting the associated tidal deformability of a neutron star in only a few tens of milliseconds. We implement these emulators in PyCBC to directly infer the EOS parameters using the event GW170817, providing posteriors on these parameters informed solely by GWs. We benchmark these runs against analyses performed using the full TOV solver and find that the emulators achieve speed ups of nearly two orders of magnitude, with negligible differences in the recovered posteriors. Additionally, we constrain the slope and curvature of the symmetry energy at the 90% upper credible interval to be $L$ sym ≲ 106 MeV and $K$ sym ≲ 26 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1974

Robot arm dynamics and control

Variations in total inertia and gravity loads at the joint outputs are treated along with the relative importance of gravity and acceleration-generated reaction torques or forces versus inertia torques or forces. The relation between the dynamical state equations in explicit terms and servoing the manipulator is briefly discussed in the framework of state variable feedback control which also forms the basis of adaptive manipulator control. Exact state equations were determined for total inertia and gravity loads at the joint outputs as a function of joint variables, using the constant inertial and geometric parameters of the individual links defined in the respective link coordinate frames. The range of maximum variations in total inertia and gravity loads at the joint outputs was calculated for both no load and load in the hand. The main result is the construction of a set of greatly simplified state equations which describe the total inertia and gravity load variations at the output of the six joints with an average error of less than 5%.

Bejczy, A. K.↗