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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 271 records · Page 15

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NASA NTRS1976

Numerical computation of space shuttle heating and surface streamlines

Exact inviscid flow-field codes are used together with a quasi-three-dimensional boundary-layer analysis to provide estimates of the windward surface heating and streamline patterns of the shuttle orbiter vehicle. The accuracy and limitations of the methods are established by comparison with available wind-tunnel experiments and with more exact numerical solutions for simple flows. Flight predictions are presented showing the effects of finite-rate (nonequilibrium) chemical reactions, and the effects of varying boundary-layer edge conditions due to the growth of the boundary-layer into the inviscid flow (entropy layer swallowing). Differences between flow-field predictions at wind-tunnel and nominal flight conditions are discussed.

Rakich, J. V.↗

NASA NTRS1982

The baroclinic instability of highly structured one-dimensional basic states

A frictionless, adiabatic, quasi-geostrophic model on a beta-plane was employed to examine the baroclinic instability of highly structured one-dimensional basic states. Definitions of the model eigenvalue equation, the boundary conditions, and the fluxes and energetics are provided, and highly structured average wind speed and temperature profiles were selected to represent a wide range of latitudes. Attention was given to the instability source, wavelength, growth rate, phase velocity, steering levels, and the vertical structure of their amplitude, phase, meridional entropy transport, and conversion of potential-to-kinetic energy. Green modes, Charney-Eady modes, and the modes defined in the paper are examined in connection with the highly structured profiles. The eigenvalue approach is shown to be superior to the numerical time integration approach and necessary conditions for instabilities are defined.

Fullmer, J. W. A.↗

NASA NTRS2000

Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

Tam, Christopher K. W.↗

DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗

DOE OSTI2025

Superheating gold beyond the predicted entropy catastrophe threshold

In their landmark study, Fecht and Johnson unveiled a phenomenon that they termed the ‘entropy catastrophe’, a critical point where the entropy of superheated crystals equates to that of their liquid counterparts. This point marks the uppermost stability boundary for solids at temperatures typically around three times their melting point. Despite the theoretical prediction of this ultimate stability threshold, its practical exploration has been prevented by numerous intermediate destabilizing events, colloquially known as a hierarchy of catastrophes, which occur at far lower temperatures. Here we experimentally test this limit under ultrafast heating conditions, directly tracking the lattice temperature by using high-resolution inelastic X-ray scattering. Our gold samples are heated to temperatures over 14 times their melting point while retaining their crystalline structure, far surpassing the predicted threshold and suggesting a substantially higher or potentially no limit for superheating. We point to the inability of our samples to expand on these very short timescales as an important difference from previous estimates. These observations provide insights into the dynamics of melting under extreme conditions.

Laser-produced plasmas↗

NASA NTRS1972

Thermal elastoplastic structural analysis of non-metallic thermal protection systems

An incremental theory and numerical procedure to analyze a three-dimensional thermoelastoplastic structure subjected to high temperature, surface heat flux, and volume heat supply as well as mechanical loadings are presented. Heat conduction equations and equilibrium equations are derived by assuming a specific form of incremental free energy, entropy, stresses and heat flux together with the first and second laws of thermodynamics, von Mises yield criteria and Prandtl-Reuss flow rule. The finite element discretization using the linear isotropic three-dimensional element for the space domain and a difference operator corresponding to a linear variation of temperature within a small time increment for the time domain lead to systematic solutions of temperature distribution and displacement and stress fields. Various boundary conditions such as insulated surfaces and convection through uninsulated surface can be easily treated. To demonstrate effectiveness of the present formulation a number of example problems are presented.

Chung, T. J.↗

NASA NTRS1988

Entropy and vorticity corrections for transonic flows

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non-uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.

Hafez, M.↗

NASA NTRS1989

Conservation equations and physical models for hypersonic air flows over the aeroassist flight experiment vehicle

The code development and application program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), with emphasis directed toward support of the Aeroassist Flight Experiment (AFE) in the near term and Aeroassisted Space Transfer Vehicle (ASTV) design in the long term is reviewed. LAURA is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3-D, viscous, hypersonic flows in chemical and thermal nonequilibrium. The algorithm is derived using a finite volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over an AFE wind tunnel model. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium over the full scale AFE configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗

DOE OSTI2023

Entanglement between valence and sea quarks in hadrons of 1+1 dimensional QCD

The conceptual interpretation of valence- and sea-quark separation, which is a key aspect of the parton model and of an intuitive picture of hadron structure, becomes obscured by quantum effects in QCD. This suggests that there may be measures of entanglement between quark degrees of freedom that are present in QCD, but absent in the intuitive picture with a clear valence-sea (VS) separation. In this paper, we define the first rigorous measure of VS entanglement in QCD in an attempt to bring conceptual clarity to this issue, and, potentially, to find a measure of the applicability of the parton model to QCD bound states. This VS entanglement vanishes in the large-N c limit, and it remains low when finite-N c states resemble their large-N c counterparts. We perform a numerical study of VS entanglement in 1 + 1 dimensional discrete light-cone quantized QCD, and in the process develop a method for building the color-singlet basis of 1 + 1d QCD that is manifestly complete and orthogonal by construction. We calculate this VS entanglement entropy for the first time and find that it is relatively low for the first few excited states of both mesons and baryons compared to all other states in the spectrum, with the VS entropy of ground state hadrons providing a minimum. We also see that for ground state mesons the entropy is well described in the 1/N c approximation. These results suggest that low energy hadrons may be the only QCD bound states for which the large-N c expansion, and perhaps the parton model, provide an accurate description. This work also provides the first evidence that the VS entanglement entropy of QCD in 3 + 1d, which would likely serve as an order parameter for the transition between quark and hadron degrees of freedom, may be perturbatively accessible through a large-N c expansion.

1+1 dimensional QCD↗

NASA NTRS1944

The numerical solution of compressible fluid flow problems

Numerical methods have been developed for obtaining the steady, adiabatic flow field of a frictionless, perfect gas about arbitrary two-dimensional bodies. The solutions include the subsonic velocity regions, the supersonic velocity regions, and the transition compression shocks, if required. Furthermore, the rotational motion and entropy changes following shocks are taken into account. Extensive use is made of the relaxation method. In this report the details of the methods of solution are emphasized so as to permit others to solve similar problems. Solutions already obtained are mentioned only by way of illustrating the possibilities of the methods described. The methods can be applied directly to wind tunnel and free air tests of arbitrary airfoil shapes at subsonic, sonic, and supersonic speeds.

Emmons, Howard W↗

DOE OSTI2023

Cross Entropy Benchmark for Measurement-Induced Phase Transitions

Here, we investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy χ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and χ = 1. In the area law phase χ < 1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O⁢(1/ϵ 2 ) trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the “classical” side can be simulated efficiently, while simulating the “quantum” side is still classically hard.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Entropy Stable Conservative Flux Form Neural Networks

We propose an entropy-stable conservative flux form neural network (CFN) to predict the dynamics of unknown governing conservation laws. The design of the network is based on the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN, hereafter referred to as ESCFN, uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Importantly, our method is designed to predict long term dynamics of the unknown conservation law exclusively from a short temporal window of observed data, that is, without oracle knowledge of the PDE or later-time solution profiles. Numerical experiments demonstrate that the ESCFN achieves both stability and conservation while maintaining accuracy over extended time domains, and successfully predicts shock propagation speeds in long-term simulations. Furthermore, it is also robust to both noisy and sparse data environments.

Hyperbolic conservation laws↗

DOE OSTI2023

Theory and Implementation of the Spectacular Nonlinear Viscoelastic Constitutive Model

This report is a comprehensive guide to the nonlinear viscoelastic Spectacular model, which is an isotropic, thermo-rheologically simple constitutive model for glass-forming materials, such as amorphous polymers. Spectacular is intermediate in complexity to the previous PEC and SPEC models (Potential Energy Clock and Simplified Potential Energy Clock models, respectively). The model form consists of two parts: a Helmholtz free energy functional and a nonlinear material clock that controls the rate of viscoelastic relaxation. The Helmholtz free energy is derived from a series expansion about a reference state. Expressions for the stress and entropy functionals are derived from the Helmholtz free energy following the Rational Mechanics approach. The material clock depends on a simplified expression for the potential energy, which itself is a functional of the temperature and strain histories. This report describes the thermo-mechanical theory of Spectacular, the numerical methods for time-integrating the model, model verification for its implementation in LAMÉ, a user guide for its implementation in LAMÉ, and ideas for future work. A number of appendices provide supplementary mathematical details and a description of the procedure used to derive the simplified potential energy from the full expression for the potential energy. The goal of this report is create a convenient point-of-entry for engineers who wish to learn more about Spectacular, but also to serve as a reference manual for advanced users of the model.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Thermodynamics of the near-extremal Kerr spacetime

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as Z ~ T$\frac{3}{2}$ e S 0 +c log S 0 , with S 0 the classical degeneracy and c a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient c. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1986

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Deshpande, S. M.↗

NASA NTRS1992

Point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Gnoffo, P. A.↗

DOE OSTI2022

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗