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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

eddy Users Manual

eddy is a collection of tools - nonlinear solvers, meshing, post-processing, visualization, optimization, etc. - for performing scale-resolving simulations of multi-physics applications. The framework is designed to enable advanced R&D on a variety of topics by leveraging a mature capability for scale resolving simulations, and simultaneously be an appropriate tool for application analysis and support. Currently, eddy is at a relatively low technical readiness level (TRL), and users and developers should maintain appropriate expectations. The technical details behind eddy are outlined in several publications which can be consulted for more information [1–10]. The solvers are built around an unstructured high-order capability, and heavily utilize the tensor product sum-factorization approach for efficiency. The unsteady formulation utilizes a fully implicit space-time approach with a matrix-free Newton- Krylov method. A primitive steady-state solver is available for testing purposes, but is not expected to converge for all but simple verification cases. The Navier-Stokes fluid solvers do not support either RANS or hybrid-RANS capability, only LES and wall-modeled LES approaches. All of the solvers within eddy support three modes of operation: a primal solve of the full nonlinear problem, and two linearization approaches of the primal solve - the ad joint and the tangent solution. Details on how to select and use these three modes are outlined in Sec. 3.

Murman, Scott M.↗
NASA NTRS1979

Application of supersonic linear theory and hypersonic impact methods to three nonslender hypersonic airplane concepts at Mach numbers from 1.10 to 2.86

Aerodynamic predictions from supersonic linear theory and hypersonic impact theory were compared with experimental data for three hypersonic research airplane concepts over a Mach number range from 1.10 to 2.86. The linear theory gave good lift prediction and fair to good pitching-moment prediction over the Mach number (M) range. The tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone theory predictions were good for lift and fair to good for pitching moment for M more than or equal to 2.0. The combined tangent-cone/tangent-wedge method gave the least accurate prediction of lift and pitching moment. The zero-lift drag was overestimated, especially for M less than 2.0. The linear theory drag prediction was generally poor, with areas of good agreement only for M less than or equal to 1.2. For M more than or equal to 2.), the tangent-cone method predicted the zero-lift drag most accurately.

Pittman, J. L.↗
NASA NTRS1988

A method for determining crack opening load from load-displacement data

The fatigue crack opening load is determined as the tangent point on the ascending load-displacement data between the curved portion and the upper linear region. A model for the 'unzipping' behavior of the crack indicates that the curved portion of the load-deflection curve is second order. The opening load is determined by a nonlinear, least squares fit of the data to the model, which optimally locates the tangent point of the two curves. The method provided consistent results for determining opening load P(op) for 7475-T731 aluminum using data from a crack tip opening gage.

Carman, C. Davis↗
DOE OSTI2023

Generating accurate density matrices on the tangent space of a Grassmann manifold

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Chemistry↗
DOE OSTI2023

Quantum Kerr learning

Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity theory and physics, we demonstrate that a single Kerr mode can provide some 'quantum enhancements' when dealing with kernel-based methods. Using kernel properties, neural tangent kernel theory, first-order perturbation theory of the Kerr non-linearity, and non-perturbative numerical simulations, we show that quantum enhancements could happen in terms of convergence time and generalization error. Furthermore, we make explicit indications on how higher-dimensional input data could be considered. Finally, we propose an experimental protocol, that we call quantum Kerr learning, based on circuit QED.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Breaking of the first adiabatic invariants of charged particles in time-dependent magnetic fields - Computer simulations and theory

The mechanics of the first adiabatic invariant mu of nonrelativistic charged particles in time-dependent magnetic inductions B (t) are studied by means of computer simulations and analytic theory. Linear-ramp magnetic-induction profiles are utilized, as well as hyperbolic-tangent ramps and sine half-wave ramps. The change in mu that results from an induction change Delta B that occurs over a time Delta t is quantified for all values of Delta B and Delta t, as well as for all values of the particle position. It is found that the cases fall into two categories with very different mu behavior: cases in which the change in the magnetic induction occurs over a time Delta t that is exactly equal to an integer number of gyroperiods (textbook case) or cases in which the change in the induction occurs over a time Delta t that is not equal to an integer number of gyroperiods (more general case). In both categories mu is an adiabatic invariant, although the conservation of mu is much poorer in the latter category.

Borovsky, Joseph E.↗
NASA NTRS1993

Planar Cubics Through a Point in a Direction

It is shown that the planar cubics through three points and the associated tangent directions can be found by solving a cubic equation and a 2 x 2 system of linear equations. The result is combined with a previous published scheme to produce a better curve-fitting method.

Chou, J. J.↗
DOE OSTI2022

Deterministic Linear Time for Maximal Poisson‐Disk Sampling using Chocks without Rejection or Approximation

Abstract We show how to sample uniformly within the three‐sided region bounded by a circle, a radial ray, and a tangent, called a “chock.” By dividing a 2D planar rectangle into a background grid, and subtracting Poisson disks from grid squares, we are able to represent the available region for samples exactly using triangles and chocks. Uniform random samples are generated from chock areas precisely without rejection sampling. This provides the first implemented algorithm for precise maximal Poisson‐disk sampling in deterministic linear time. We prove O(n · M(b) log b), where n is the number of samples, b is the bits of numerical precision and M is the cost of multiplication. Prior methods have higher time complexity, take expected time, are non‐maximal, and/or are not Poisson‐disk distributions in the most precise mathematical sense. We fill this theoretical lacuna.

Mitchell, Scott A.↗
NASA NTRS1975

Space shuttle nonmetallic materials age life prediction

The chemiluminescence from samples of polybutadiene, Viton, Teflon, Silicone, PL 731 Adhesive, and SP 296 Boron-Epoxy composite was measured at temperatures from 25 to 150 C. Excellent correlations were obtained between chemiluminescence and temperature. These correlations serve to validate accelerated aging tests (at elevated temperatures) designed to predict service life at lower temperatures. In most cases, smooth or linear correlations were obtained between chemiluminescence and physical properties of purified polymer gums, including the tensile strength, viscosity, and loss tangent. The latter is a complex function of certain polymer properties. Data were obtained with far greater ease by the chemiluminescence technique than by the conventional methods of study. The chemiluminescence from the Teflon (Halon) samples was discovered to arise from trace amounts of impurities, which were undetectable by conventional, destructive analysis of the sample.

Mendenhall, G. D.↗
DOE OSTI2023

TwoFold: Highly accurate structure and affinity prediction for protein-ligand complexes from sequences

We describe our development of ab initio protein-ligand binding pose prediction models based on transformers and binding affinity prediction models based on the neural tangent kernel (NTK). Folding both protein and ligand, the TwoFold models achieve efficient and quality predictions matching state-of-the-art implementations while additionally reconstructing protein structures. In conclusion, solving NTK models points to a new use case for highly optimized linear solver benchmarking codes on HPC.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Stochastic symplectic reduced-order modeling for model-form uncertainty quantification in molecular dynamics simulations in various statistical ensembles

Here, this work focuses on the representation of model-form uncertainties in molecular dynamics simulations in various statistical ensembles. In prior contributions, the modeling of such uncertainties was formalized and applied to quantify the impact of, and the error generated by, pair-potential selection in the microcanonical ensemble (NVE). In this work, we extend this formulation and present a linear-subspace reduced-order model for the canonical (NVT) and isobaric (NPT) ensembles. The symplectic reduced-order basis is randomized on the tangent space of the Stiefel manifold to provide topological relationships and capture model-form uncertainty. Using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), we assess the relevance of these stochastic reduced-order atomistic models on canonical problems involving a Lennard-Jones fluid and an argon crystal melt.

42 ENGINEERING↗
NASA NTRS1989

Nonlinear and distributed parameter models of the mini-mast truss

Large spacecraft such as Space Station Freedom employ large trusses in their construction. The structural dynamics of such trusses often exhibit nonlinear behavior and little damping which can impact significantly the performance of control systems. The Mini-MAST truss was constructed to research such structural dynamics and control systems. The Mini-MAST truss is an object of study for the guest investigator program as part of NASA's controls-structures interaction program. The Mini-MAST truss is deployable and about 65 ft long. Although the bending characteristics of the Mini-MAST truss are essentially linear, the angular deflection under torsional loading has exhibited significant hysteresis and nonlinear stiffness. It is the purpose to develop nonlinear and distributed parameter models of the truss and to compare the model dynamics with actual measurements. Distributed parameter models have the advantage of requiring fewer model parameters. A tangent function is used to describe the nonlinear stiffness in torsion, partly because of the convenience of its easily expressed inverse. Hysteretic slip elements are introduced and extended to a continuum to account for the observed hysteresis in torsion. The contribution of slipping to the structural damping is analyzed and found to be strongly dependent on the applied loads. Because of the many factors which affect the damping and stiffness in a truss, it is risky to assume linearity.

Taylor, Lawrence W., Jr.↗
DOE OSTI2023

Using in-situ strain measurements to evaluate the accuracy of stress estimation procedures from fracture injection/shut-in tests

Fracture injection/shut-in tests are commonly used to measure the state of stress. Injection creates a hydraulic fracture (or in some cases, opens a preexisting fracture), and then the pressure after shut-in is monitored to identify fracture closure. Different interpretation procedures have been proposed for estimating closure, and the procedures sometimes yield significantly different results. In this study, direct, in-situ strain measurements are used to observe fracture reopening and closure. The tests were performed as part of the EGS Collab project, a mesoscale project performed at 1.25 and 1.5 km depth at the Sanford Underground Research Facility. The tests were instrumented with the SIMFIP tool, a double-packer probe with a high-resolution three-dimensional borehole displacement sensor. The measurements provide a direct observation of the fracture closure signature, enabling a high-fidelity estimate of the fracture closure stress (ie, the normal stress on the fracture). In two of the four tests, injection created an opening mode fracture, and so the closure stress can be interpreted as the minimum principal stress. In the other two tests, injection probably opened preexisting natural fractures, and so the closure stress can be interpreted as the normal stress on the fractures. The strain measurements are compared against different proposed methods for estimating closure stress from pressure transients. The shut-in transients are analyzed with two techniques that are widely used in the field of petroleum engineering – the ‘tangent’ method and the ‘compliance’ method. In three of the four tests, the tangent method significantly underestimates the closure stress. The compliance method is reasonably accurate in all four tests. Closure stress is also interpreted using two other commonly-used methods – ‘first deviation from linearity’ and the method of Hayashi and Haimson. In comparison with the SIMFIP data, these methods tend to overestimate the closure stress, evidently because they identify closure from early-time transient effects, such as near-wellbore tortuosity. In two of the tests, microseismic imaging provides an independent estimate of the size of the fracture created by injection. When combined with a simple mass balance calculation, the SIMFIP stress measurements yield predictions of fracture size that are reasonably consistent with the estimates from microseismic. In conclusion, the calculations imply an apparent fracture toughness 2-3x higher than typical laboratory-derived values.

58 GEOSCIENCES↗
NASA NTRS1986

A simple algorithm for computing canonical forms

It is well known that all linear time-invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consisting only of coordinate changes and linear feedback. However, the actual procedures for doing this have tended to be overly complex. The technique introduced here is envisioned as an on-line procedure and is inspired by George Meyer's tangent model for nonlinear systems. The process utilizes Meyer's block triangular form as an intermedicate step in going to Brunovsky form. The method also involves orthogonal matrices, thus eliminating the need for the computation of matrix inverses. In addition, the Kronecker indices can be computed as a by-product of this transformation so it is necessary to know them in advance.

Ford, H.↗
DOE OSTI2025

Feature learning and generalization in deep networks with orthogonal weights

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Local Synthesis and Tooth Contact Analysis of Face-Milled Spiral Bevel Gears

Computerized simulation of meshing and bearing contact for spiral bevel gears and hypoid gears is a significant achievement that could substantially improve the technology and the quality of the gears. An approach to the synthesis of face-milled spiral bevel gears and their tooth contact analysis is presented. The proposed approach is based on the following ideas: application of the principle of local synthesis that provides optimal conditions of meshing and contact at the mean contact point, M, and in the neighborhood of M; and application of relations between principle directions and curvatures for surfaces being in line contact or in point contact. The developed local synthesis of gears provides the following: (1) the required gear ratio at M; (2) a localized bearing contact with the desired direction of the tangent to the contact path on gear tooth surface and the desired length of the major axis of contact ellipse at M; (3) a predesigned parabolic function of a controlled level for transmission errors which enables absorption of linear functions of transmission errors caused by misalignment and reduces the level of vibrations. The proposed approach does not require either the tilt of the head-cutter for the process of generation or modified roll for the pinion generation. Improved conditions of meshing and contact of the gears can be achieved without the above mentioned parameters. A computer program for determination of basic machine-tool settings and tooth contact analysis for the designed gears is presented. The approach is illustrated with a numerical example.

Litvin, Faydor L.↗
NASA NTRS1975

A method for unique identification of relativistic /greater than 0.5/ magnetic monopoles with a fast film Cerenkov detector

A magnetic monopole traversing a dielectric medium at a velocity greater than the phase velocity of light in that medium, will give rise to Cerenkov radiation with the electric field tangent to the cone generated by the photon wave propagation vector, and the magnetic field normal to that surface. This is the opposite polarization to that encountered with an electric charge. It is proposed that either by inserting a linearly polarizing layer between the radiator and the photographic emulsion, or by selecting a linearly polarizing material as the radiator, one could directly observe the field polarization by examining the photographic image and thus uniquely identify a magnetic monopole. The ability of the detector is further enhanced by the index of refraction dependence of the Cerenkov output from a magnetic monopole.

Pinsky, L. S.↗