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Results for “Complete equation 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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Development of the functional simulator for the Galileo attitude and articulation control system

A simulation program for verifying and checking the performance of the Galileo Spacecraft's Attitude and Articulation Control Subsystem's (AACS) flight software is discussed. The program, which is called Functional Simulator (FUNSIM), provides a simple method of interfacing user-supplied mathematical models coded in FORTRAN which describes spacecraft dynamics, sensors, and actuators; this is done with the AACS flight software, coded in HAL/S (High-level Advanced Language/Shuttle). It is thus able to simulate the AACS flight software accurately to the HAL/S statement level in the environment of a mainframe computer system. FUNSIM also has a command and data subsystem (CDS) simulator. It is noted that the input/output data and timing are simulated with the same precision as the flight microprocessor. FUNSIM uses a variable stepsize numerical integration algorithm complete with individual error bound control on the state variable to solve the equations of motion. The program has been designed to provide both line printer and matrix dot plotting of the variables requested in the run section and to provide error diagnostics.

Namiri, M. K.↗
NASA NTRS2013

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Modeling↗
DOE OSTI2020

Indirect methods in nuclear astrophysics with relativistic radioactive beams

Reactions with radioactive nuclear beams at relativistic energies have opened new doors to clarify the mechanisms of stellar evolution and cataclysmic events involving stars and during the big bang epoch. Numerous nuclear reactions of astrophysical interest cannot be assessed directly in laboratory experiments. Ironically, some of the information needed to describe such reactions, at extremely low energies (e.g., keVs), can only be studied on Earth by using relativistic collisions between heavy ions at GeV energies. In this contribution, we make a short review of experiments with relativistic radioactive beams and of the theoretical methods needed to understand the physics of stars, adding to the knowledge inferred from astronomical observations. We continue by introducing a more detailed description of how the use of relativistic radioactive beams can help to solve astrophysical puzzles and several successful experimental methods. State-of-the-art theories are discussed at some length with the purpose of helping us understand the experimental results reported. The review is not complete and we have focused most of it to traditional methods aiming at the determination of the equation of state of symmetric and asymmetric nuclear matter and the role of the symmetry energy. Whenever possible, under the limitations of our present understanding of experimental data and theory, we try to pinpoint the information still missing to further understand how stars evolve, explode, and how their internal structure might be. We try to convey the idea that in order to improve microscopic theories for many-body calculations, nuclear structure, nuclear reactions, and astrophysics, and in order to constrain and allow for convergence of our understanding of stars, we still need considerable improvements in terms of accuracy of experiments and the development of new and dedicated nuclear facilities to study relativistic reactions with radioactive beams.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation

Here we present a Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfield equation. Instead of full-scale coarse-graining, this approximation only truncates terms in the Redfield equation that average out over a time-scale typical of the quantum system. The first step in this approximation is to properly renormalize the system Hamiltonian, to symmetrize the gains and losses of the state due to the environmental coupling. In the second step, we swap out an arithmetic mean of the spectral density with a geometric one, in these gains and losses, thereby restoring complete positivity. This completely positive approximation, GAME (geometric-arithmetic master equation), is adaptable between its time-independent, time-dependent, and Floquet form. In the exactly solvable, three-level, Jaynes-Cummings model, we find that the error of the approximate state is almost an order of magnitude lower than that obtained by solving the coarse-grained stochastic master equation. As a test-bed, we use a ferromagnetic Heisenberg spin-chain with long-range dipole-dipole coupling between up to 25-spins, and study the differences between various master equations. We find that GAME has the highest accuracy per computational resource.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Phase stability of a eutectic high entropy alloy under extremes of pressures and temperatures

Additively manufactured high-entropy alloys are of interest because of their unique combination of high yield strength and large ductility achieved with far-from-equilibrium crystalline phases and micro/nanostructure morphology. We report on the phase transformation and thermal equation of state of the eutectic high-entropy alloy (EHEA) Al 18 Co 20 Cr 10 Fe 10 Ni 40 W 2 , produced by laser powder-bed fusion (L-PBF). The EHEA was studied in a large-volume Paris–Edinburgh cell using energy-dispersive x-ray diffraction to a pressure of 5.5 GPa and a temperature of 1723 K. Static compression studies in diamond anvil cells using angle-dispersive x-ray diffraction extended the high-pressure structural data to 317 GPa at ambient temperature. The initial dual-phase nanolamellar face-centered cubic (FCC) and body-centered cubic (BCC) structure of Al 18 Co 20 Cr 10 Fe 10 Ni 40 W 2 transforms into a single FCC phase under high pressure, with the BCC-to-FCC phase transformation completing at 9 ± 2 GPa. The FCC phase remained stable up to the highest pressure of 317 GPa. The measured thermal equation of state for the FCC phase of Al 18 Co 20 Cr 10 Fe 10 Ni 40 W 2 is presented up to 5.5 GPa and 1473 K. We observed melting of the EHEA at 1698 ± 25 K at a pressure of 5.5 GPa, and the recrystallized sample shows an increased fraction of the CsCl-type (B2) phase at ambient conditions following release from the high-pressure high-temperature state. The BCC-to-FCC phase transition completion pressure is correlated with the nanolamellae thickness of the BCC layer in this diffusion-less transformation at ambient temperature.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Improved solar models constructed with a formulation of convection for stellar structure and evolution calculations without the mixing-length theory approximations

We have updated a previous attempt to incorporate within a solar model a treatment of convection based upon numerical simulations of convection rather than mixing-length theory (MLT). We have modified our formulation of convection for a better treatment of the kinetic energy flux. Our solar model has been updated to include a complete range of OPAL opacities, the Debye-Hueckel correction to the equation of state, helium diffusion due to gravitational settling, and atmospheres by Kurucz. We construct a series of models using both MLT and our revised formulation of convection and the compared results to measurements of the solar radius, the solar luminosity, and the depth of the solar convection zone as inferred from helioseismology. We find X(solar) = 0.702 +/- 0.005, Y(solar) = 0.278 +/- 0.005, and Z(solar) = 0.0193 +/- 0.0005.

Lydon, Thomas J.↗
NASA NTRS1975

A new approach to radiative transfer theory using Jones's vectors. I Fundamentals

Radiative transfer of partially polarized radiation in an anisotropically scattering, inhomogeneous atmosphere containing an arbitrary polydispersion of particles is described using Jones's (1941) amplitude vectors and matrices. This approach exploits the close analogy between the quantum-mechanical states of spin 1/2 systems and the polarization states of electromagnetic radiation described by Jones's vector. The complete equivalence between the transport equation for Jones's vectors and the classical radiative-transfer equation for Stokes's intensity vectors is demonstrated in two independent ways after deriving the transport equations for the polarization coherency matrices and for the quaternions corresponding to the Jones's vectors. A compact-operator formulation of the theory is provided and used to derive the necessary equations for both a local and a global description of the transport of Jones's vectors. The integro-differential equations for the amplitude reflection and transmission matrices are derived and related to the usual corresponding equations.

Fymat, A. L.↗
NASA NTRS1980

A magnetohydrodynamic model for corotating interplanetary structures

A model is developed which treats interplanetary structures as a small-scale incompressible Alfvenic fluctuation superposed on a large-scale background flow, and uses the complete magnetohydrodynamic equations and the full energy equation to describe the interplanetary structures. For steady-state corotating structures the model assumes the background flow to be field aligned, and the nonlinear system is treated as being composed of two subsets: one dealing with the expansion of the solar wind in stream tubes, the other with the interaction between neighboring stream tubes. The expansion subset has a singularity at Parker's critical radius, and the interaction subset has a singularity at the Alfvenic point. Concerning the region where the flow velocity is super-Alfvenic, the characteristic equation is derived, and a general method of numerical solution for the three-dimensional problems based on the characteristics theory is discussed. In addition, a viscous WKB solution of the microscale system is presented.

Whang, Y. C.↗
NASA NTRS1994

Convergence acceleration of an aeroelastic Navier-Stokes solver

New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.

Obayashi, S.↗
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 OSTI2025

Suppression of Composition g -modes in Chemically Equilibrating Warm Neutron Stars

We investigate the impact of chemical equilibration and the resulting bulk viscosity on nonradial oscillation modes of warm neutron stars at temperatures up to T ≈ 5 MeV, relevant for protoneutron stars and neutron star postmerger remnants. In this regime, the relaxation rate of weak interactions becomes comparable to the characteristic frequencies of composition g-modes in the core, resulting in resonant damping. To capture this effect, we introduce the dynamical sound speed, a complex, frequency-dependent generalization of the adiabatic sound speed that encodes both the restoring force and the dissipative effects of bulk compression. Using realistic weak reaction rates and three representative equations of state, we compute the complex frequencies of composition g-modes with finite-temperature profiles. We find that bulk viscous damping becomes increasingly significant with temperature and can completely suppress composition g-modes. In contrast, the f-mode remains largely unaffected by bulk viscosity due to its nearly divergence-free character. Our results highlight the sensitivity of g-mode behavior to thermal structure, weak reaction rates, and the equation of state, and establish the dynamical sound speed as a valuable descriptor characterizing oscillation properties in dissipative neutron star matter.

Neutron stars↗
NASA NTRS1976

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of nonlinear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead lag, elastic bending in flap and lead-lag blade root torsion and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.

Shamie, J.↗
NASA NTRS1985

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Antar, B. N.↗
NASA NTRS2016

The XXL Survey I. Scientific Motivations - Xmm-Newton Observing Plan - Follow-up Observations and Simulation Programme

The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have supported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey; it comes at a time when the Planck mission results are being finalized. Aims. We present the XXL Survey, the largest XMM programme totaling some 6.9 Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25 deg2 each at a point-source sensitivity of approx. 5 x 10(exp 15) erg/s/sq cm in the [0.5-2] keV band (completeness limit). The surveys main goals are to provide constraints on the dark energy equation of state from the space-time-distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programs. Methods. We describe the 542 XMM observations along with the associated multi- and numerical simulation programmes. We give a detailed account of the X-ray processing steps and describe innovative tools being developed for the cosmological analysis. Results. The paper provides a thorough evaluation of the X-ray data, including quality controls, photon statistics, exposure and background maps, and sky coverage. Source catalogue construction and multi-associations are briefly described. This material will be the basis for the calculation of the cluster and AGN selection functions, critical elements of the cosmological and science analyses. Conclusions. The XXL multi- data set will have a unique lasting legacy value for cosmological and extragalactic studies and will serve asa calibration resource for future dark energy studies with clusters and other X-ray selected sources. With the present article, we release the XMM XXL photon and smoothed images along with the corresponding exposure maps.

X-rays: general – large-scale structure of Unive↗
DOE OSTI2021

Non-Markovian dynamics of open quantum system with memory

Highlights: • Non-Markovian master equation for open quantum system with power-law memory is proposed. • Non-Markovian dynamics of two-level quantum system with memory is described. • Solutions of non-Markovian quantum master equations are derived. • Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. • Exact solution of non-Markovian equations of system with memory is proposed. In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.

Shamie, J.↗
NASA NTRS1991

On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

A complete potential based framework using internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive while the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, i.e., the Compliance operator, is defined which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached, is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the used forms, to restore the complete potential structure.

Arnold, S. M.↗