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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Merging neutron stars. 1. Initial results for coalescence of noncorotating systems

We present three-dimensional Newtonian simulations of the coalescence of two neutron stars, using a smoothed particle hydrodynamics (SPH) code. We begin the simulations with the two stars in a hard, circular binary, and have them spiral together as angular momentum is lost through gravitational radiation at the rate predicted by modeling the system as two point masses. We model the neutron stars as hard polytropes (gamma = 2.4) of equal mass, and investigate the effect of the initial spin of the two stars on the coalescence. The process of coalescence, from initial contact to the formation of an axially symmetric object, takes only a few orbital periods. Some of the material from the two neutron stars is shed, forming a thick disk around the central, coalesced object. The mass of this disk is dependent on the initial neutron star spins; higher spin rates result in greater mass loss and thus more massive disks. For spin rates that are most likely to be applicable to real systems, the central coalesced object has a mass of 2.4 solar mass, which is tantalizingly close to the maximum mass allowed by any neutron star equation of state for an object that is supported in part by rotation. Using a realistic nuclear equation of state, we estimate the temperature of the material after the coalescence. We find that the central object is at a temperature of approximately 10 MeV, while the disk is heated by shocks to a temperature of 2 to 4 MeV.

Davies, M. B.↗
DOE OSTI2025

Distinguishing prompt-collapse binary neutron star mergers from binary black Holes: Tidal effects and remnant properties

We study the properties of remnants formed in prompt-collapse binary neutron star mergers. We consider nonspinning neutron star binaries over a range of total masses and mass ratios across a set of 22 equations of state, totaling 107 numerical relativity simulations. We report the final mass and spin of the systems (including the accretion disk and ejecta) to be constrained in a narrow range—0.98 ≲ 𝑀 𝑓 /𝑀 ≲ 0.99 for the mass and 0.85 ≲ 𝑎 𝑓 ≲ 0.95 for the dimensionless spin—regardless of the binary configuration and matter effects. This sets them apart from binary black hole merger remnants. We assess the detectability of the postmerger signal in a future 40 km Cosmic Explorer observatory and find that the signal-to-noise ratio in the postmerger of an optimally located and oriented binary at a distance of 100 Mpc can range from <1 to 8, depending on the binary configuration and equation of state, with a majority of them greater than 4 in the set of simulations that we consider. We also consider the distinguishability between prompt-collapse binary neutron star and binary black hole mergers with the same masses and spins. We find that Cosmic Explorer will be able to distinguish such systems primarily via the measurement of tidal effects in the late inspiral. Neutron star binaries with reduced tidal deformability $\tilde{Λ}$ as small as ∼ 3.5 can be identified up to a distance of 100 Mpc, while neutron star binaries with $\tilde{Λ}$ ∼ 22 can be identified to distances greater than 250 Mpc. This is larger than the distance up to which the postmerger will be visible. Finally, we discuss the possible implications of our findings for the equation of state of neutron stars from the gravitational wave event GW230529.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1988

An upwind-differencing scheme for the incompressible Navier-Stokes equations

The steady state incompressible Navier-Stokes equations in 2-D are solved numerically using the artificial compressibility formulation. The convective terms are upwind-differenced using a flux difference split approach that has uniformly high accuracy throughout the interior grid points. The viscous fluxes are differenced using second order accurate central differences. The numerical system of equations is solved using an implicit line relaxation scheme. Although the current study is limited to steady state problems, it is shown that this entire formulation can be used for solving unsteady problems. Characteristic boundary conditions are formulated and used in the solution procedure. The overall scheme is capable of being run at extremely large pseudotime steps, leading to fast convergence. Three test cases are presented to demonstrate the accuracy and robustness of the code. These are the flow in a square-driven cavity, flow over a backward facing step, and flow around a 2-D circular cylinder.

Rogers, Stuart E.↗
DOE OSTI2024

Towards Exascale Astrophysics of Mergers and Supernovae (TEAMS)

The major goals of the TEAMS project are (i) to improve the modeling of many of the suggested astrophysical sites of the r‐process, as well as some potential p‐process sites, (ii) to use our models to support and guide the experimental efforts at FRIB and similar facilities, and (iii) to use our tools to cement our understanding of the roles that massive stars play in galactic chemical evolution. As part of the TEAMS project, Mezzacappa (UTK, Reddy (UW), Surman (ND), and Steiner (UTK) are (i) generating equations of state and neutrino opacities for simulations of core‐collapse supernovae and neutron star mergers which are more faithful to current understanding of the nucleon‐nucleon interaction, (ii) integrating those new equations of state and neutrino opacities into new simulation codes being developed, (iii) performing detailed nuclear reaction network post‐processing to determine abundances from simulations and (iv) quantifying the impact of nuclear physics uncertainties on r‐process abundances.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Measurements of the inert Hugoniot and observation of mechanical ignition in Ni(V) + Al reactive multilayers via x-ray diffraction

This study investigates the inert Hugoniot response, mechanical ignition, and reaction dynamics of Ni(V)+Al multilayers during longitudinal, laser-driven shock compression experiments. Ni(V)+Al multilayers, known for their self-propagating exothermic reactions, were subjected to longitudinal stresses exceeding 50 GPa using the laser shock facility within the Dynamic Compression Sector (DCS) at the Advanced Photon Source (APS). In situ x-ray diffraction (XRD) revealed that Ni(V) and Al were not in equilibrium during compression, with stress discrepancies attributed to twinning, grain structure effects, and/or dislocation density. However, the measured inert Hugoniot closely matched prior experimental and computational studies, confirming the utility of XRD for measuring the equation of state of thin, complex materials. Additionally, reaction was observed at significantly higher stresses than reported previously using laser-launched flyers. This discrepancy suggests a strong influence of externally imposed shear stress on reaction thresholds, which likely arose from deviations in flyer planarity during past experiments. Full reaction of the multilayer occurred within 40 ns after shock-wave passage, evidenced by complete melting of the constituents. Eulerian hydrocode simulations replicated experimental conditions, providing insights into equilibrium dynamics and experimental artifacts. The results highlight how even small shear forces facilitate ignition in Ni(V)+Al multilayers at lower stresses.

Crystallography↗
DOE OSTI2022

Kinetically driven ekpyrosis

We explore the possibility of a scalar field driving ekpyrotic contraction through a noncanonical kinetic energy density rather than a negative potential. We find that this kinetically driven ekpyrosis (“k-ekpyrosis”) can be achieved in a variety of models, including scalar field theories with power-law, polynomial, or Dirac-Born-Infeld (DBI-)like kinetic terms in the action. Of these examples, the ekpyrotic phase is best sustained in power-law models, which can generate large and constant equation-of-state parameters, followed by DBI-like models, which can exhibit dynamical attractors toward similarly large equations of state. Here we show that for a broad class of theories including these examples, phases of k-ekpyrosis are accompanied by preceding or concurrent phases of superluminality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Systematic study on the phase transition of confined fluid mixture up to the critical region

Systematic experimental study on the phase transition of confined fluids up to the critical region has been performed, in which many new insights have been obtained. For confined pure fluids, compared to the bulk phase, the critical point shifts to lower pressure and temperature, but the relative shift of critical pressure is much larger than that of critical temperature. The behavior of the shift, i.e., the shift as a function of pore size, is dependent on the pore type. For confined fluid mixtures, compared to the bulk phase, the critical point also shifts to lower pressure and temperature, and the relative shift of critical pressure is also much larger than that of critical temperature. Confined fluid mixture behaves similarly to confined pure fluid, i.e., it exhibits hysteresis at lower temperature range and does not exhibit phase coexistence or phase envelope. An equation of state for confined pure fluids, based on the Generalized van der Waals partition function, has also been developed and demonstrated to accurately predict the capillary condensation of simple molecules in MCM-41. The parameters of the equation of state are derived from experimental critical point.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2024

Exploring toroidal anvil profiles for larger sample volumes above 4 Mbar

Abstract With the advent of toroidal and double-stage diamond anvil cells (DACs), pressures between 4 and 10 Mbar can be achieved under static compression, however, the ability to explore diverse sample assemblies is limited on these micron-scale anvils. Adapting the toroidal DAC to support larger sample volumes offers expanded capabilities in physics, chemistry, and planetary science: including, characterizing materials in soft pressure media to multi-megabar pressures, synthesizing novel phases, and probing planetary assemblages at the interior pressures and temperatures of super-Earths and sub-Neptunes. Here we have continued the exploration of larger toroidal DAC profiles by iteratively testing various torus and shoulder depths with central culet diameters in the 30–50 µm range. We present a 30 µm culet profile that reached a maximum pressure of 414(1) GPa based on a Pt scale. The 300 K equations of state fit to our P–V data collected on gold and rhenium are compatible with extrapolated hydrostatic equations of state within 1% up to 4 Mbar. This work validates the performance of these large-culet toroidal anvils to > 4 Mbar and provides a promising foundation to develop toroidal DACs for diverse sample loading and laser heating.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1987

Constraints on the mass-radius relation for the neutron star in the X-ray burst source 4U/MXB 1820-30 located in the globular cluster NGC 6624

From the spectral evolution of seven X-ray bursts observed from 4U/MXB 1820-30 (Haberl et al., 1986) during the phases of photospheric expansion and cooling, constraints are derived on the mass-radius relation of the neutron star in this system. Taking into account the uncertainty in the source distance and the possible anisotropy of the burst emission. If during bursts with radius expansion the outer layers of the neutron star are of a hydrogen-poor composition, none of the current equations of state of high-density matter is excluded. For a hydrogen-rich composition, only very soft equations of state are allowed.

Van Paradijs, J.↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
DOE OSTI2025

Exploiting Synergies Between Lensing and BAO Surveys for Improved Cosmological Constraints

Pinning down the nature of dark energy is one of the most pressing questions in modern physics and is one of the five key science drivers identified in the P5 report [P514]. Dark energy is thought to be either a cosmological constant with an equation of state w = P/ρ = −1 which remains constant at all times, a new type of fluid with an equation of state that varies with time (w ̸= constant), or dark energy might indicate a breakdown of Einstein’s Theory of General Relativity (GR). It is of critical importance to distinguish between these three scenarios. This can only be accomplished by ambitious and demanding measurements of both the expansion rate of the universe (to track the time evolution of dark energy) together with measurements of the rate at which cosmic structures, such as galaxies and clusters of galaxies, grow with time (the “growth rate”). Because of the challenging nature of such observations, and because no single probe simultaneously measures both expansion and growth, the Dark Energy Task Force [A+06] emphasized the importance of using multiple distinct methods to characterize dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Heat Equation Neural Simulation

This code solves a steady state heat equation problem on a wire with random walks implemented using a spiking neural algorithm. SAND2020-12194 M

Reeder, Leah↗
DOE OSTI2025

Linking the Spin Transition of Ferric Iron in δ‐(Al,Fe)OOH to Water Storage in the Lower Mantle

As the most massive geochemical reservoir, the lower mantle affects the Earth's budget of volatile elements, including hydrogen or H 2 O. The properties of minerals in the lower mantle are further affected by changes in the electronic configurations of iron cations, that is, by spin transitions. The feedback between spin transitions and potential storage of H 2 O in solid hydrous phases in the lower mantle, however, remains unexplored. By combining high‐pressure nuclear resonant inelastic X‐ray scattering and high‐pressure high‐temperature X‐ray diffraction experiments, we constrained the thermal equation of state of δ‐(Al,Fe)OOH, a member of the phase H solid solution. Based on the derived thermal equation of state of δ‐(Al,Fe)OOH and the underlying thermodynamic model, we calculate the excess Gibbs free energy that arises from the spin transition of ferric iron in this compound and evaluate the effect on phase equilibria. The results of our analysis show that the spin transition of ferric iron in phase H may significantly reduce the thermodynamic activity and hence the concentration of H 2 O in a coexisting hydrous melt. As a consequence, nominally anhydrous minerals of the lower mantle may become dehydrated in the presence of phase H. Our analysis further suggests that, under certain conditions, the spin transition may expand the thermal stability of Fe 3+ ‐bearing phase H and create a geochemical link between the storage of H 2 O in phase H and ferric iron in the lower mantle.

Buchen, Johannes [Univ. of Bayreuth (Germany); Cal↗
DOE OSTI2025

DESI 2024 VI: cosmological constraints from the measurements of baryon acoustic oscillations

We present cosmological results from the measurement of baryon acoustic oscillations (BAO) in galaxy, quasar and Lyman-α forest tracers from the first year of observations from the Dark Energy Spectroscopic Instrument (DESI), to be released in the DESI Data Release 1. DESI BAO provide robust measurements of the transverse comoving distance and Hubble rate, or their combination, relative to the sound horizon, in seven redshift bins from over 6 million extragalactic objects in the redshift range 0.1 < z < 4.2. To mitigate confirmation bias, a blind analysis was implemented to measure the BAO scales. DESI BAO data alone are consistent with the standard flat ΛCDM cosmological model with a matter density Ω m =0.295±0.015. Paired with a baryon density prior from Big Bang Nucleosynthesis and the robustly measured acoustic angular scale from the cosmic microwave background (CMB), DESI requires H 0 =(68.52±0.62) km s -1 Mpc -1 . In conjunction with CMB anisotropies from Planck and CMB lensing data from Planck and ACT, we find Ω m =0.307± 0.005 and H 0 =(67.97±0.38) km s -1 Mpc -1 . Extending the baseline model with a constant dark energy equation of state parameter w, DESI BAO alone requirew=-0.99 +0.15 -0.13 . In models with a time-varying dark energy equation of state parametrised by w 0 and w a , combinations of DESI with CMB or with type Ia supernovae (SN Ia) individually prefer w 0 > -1 and w a < 0. This preference is 2.6σ for the DESI+CMB combination, and persists or grows when SN Ia are added in, giving results discrepant with the ΛCDM model at the 2.5σ, 3.5σ or 3.9σ levels for the addition of the Pantheon+, Union3, or DES-SN5YR supernova datasets respectively. For the flat ΛCDM model with the sum of neutrino mass ∑ m ν free, combining the DESI and CMB data yields an upper limit ∑ m ν < 0.072 (0.113) eV at 95% confidence for a ∑ m ν > 0 (∑ m ν > 0.059) eV prior. These neutrino-mass constraints are substantially relaxed if the background dynamics are allowed to deviate from flat ΛCDM.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

The thermodynamic properties of oxygen and nitrogen

The development of a single equation of state for oxygen and nitrogen based on the thermodynamic properties of the gases is described. The coefficients of the equation of state were determined by simultaneous least squares fits to values of isochoric heat capacity and saturation density values used to define the criteria for phase equilibrium. Tables of data for the conditions of both gases are included.

Stewart, R. B.↗
NASA NTRS1983

Closed-form solutions for a class of optimal quadratic tracking problems

Closed-form solutions are derived for a class of tracking problems including a linear optimal regulator and a prefilter for a time-invariant plant. The solutions for the prefilter equation and state trajectory coupled by the Riccati equation are exponentially related to the stability matrix of the plant. A computational procedure is presented in recursive form when the desired output state dynamics is assumed linear and time-invariant. Several examples are given for illustration.

Turner, J. D.↗
NASA NTRS1975

Design and application of squeeze film dampers for turbomachinery stabilization

The steady-state transient response of the squeeze film damper bearing was investigated. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived; the steady-state equations were used to determine the damper equivalent stiffness and damping coefficients. These coefficients are used to find the damper configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The effects of end seals and cavitated fluid film are included. The transient analysis of rotor-bearing systems was conducted by coupling the damping and rotor equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed.

Gunter, E. J.↗