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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗
NASA NTRS1957

Linearized Lifting-Surface and Lifting-line Evaluations of Sidewash Behind Rolling Triangular Wings at Supersonic Speeds

The lifting-surface sidewash behind rolling triangular wings has been derived for a range of supersonic Mach numbers for which the wing leading edges remain swept behind the mark cone emanating from the wing apex. Variations of the sidewash with longitudinal distance in the vertical plane of symmetry are presented in graphical form. An approximate expression for the sidewash has been developed by means of an approach using a horseshoe-vortex approximate-lifting-line theory. By use of this approximate expression, sidewash may be computed for wings of arbitrary plan form and span loading. A comparison of the sidewash computed by lifting-surface and lifting-line expressions for the triangular wing showed good agreement except in the vicinity of the trailing edge when the leading edge approached the sonic condition. An illustrative calculation has been made of the force induced by the wing sidewash on a vertical tail located in various longitudinal positions.

Bobbitt, Percy J↗
DOE OSTI2025

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗
NASA NTRS1976

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.

Chandra, N.↗
NASA NTRS1983

Approximation in control of flexible structures, theory and application

The sense in which the feedback control law based on an approximate finite dimensional model of a continuous structure approximates a control law which is optimal for the distributed, or infinite dimensional, model of the structure is studied. From the analysis of the various control and stability issues associated with this basis question, useful information for designing finite dimensional compensators which produce near-optimal performance in infinite dimensional systems is gained. Some of the important predictions that can be made about large-order finite dimensional control laws, using the theory of infinite dimensional Riccati equations are indicated.

Gibson, J. S.↗
NASA NTRS1972

A gas-dynamic calculation of type 2 shock propagation through the corona

An approximate analytic theory of acoustic shock propagation in nonuniform media is used to determine the motion of a flare-generated shock wave in the corona. The shock is followed from the time it strikes the chromosphere-corona transition region (density interface) out to 5 solar radii under the assumption that the corona in this region is approximately in hydrostatic equilibrium. The strength of the shock incident on the transition region from below determines the ejection velocity of eruptive prominence material, as well as the initial velocity of the coronal shock. The calculation is applied to one well-documented case of a related flare spray, moving type 4 isolated source, and type 2 burst. It is shown that a chromospheric shock of the appropriate strength to produce the observed prominence and type 4 velocities strengthens as it moves out in the corona by an amount sufficient to account for the observed high velocity of the type 2 burst.

Kopp, R. A.↗
NASA NTRS1975

Velocity and rolling-moment measurements in the wake of a swept-wing model in the 40 by 80 foot wind tunnel

Measurements were made in the wake of a swept wing model to study the structure of lift generated vortex wakes shed by conventional span loadings and by several span loadings designed to reduce wake velocities. Variations in the span loading on the swept wing generator were obtained by deflecting seven flap segments on each side by amounts determined by vortex lattice theory to approximate the desired span loadings. The resulting wakes were probed with a three component, hot wire probe to measure velocity, and with a wing to measure the rolling moment that would be induced on a following aircraft. The experimental techniques are described herein, and the measured velocity and rolling moments are presented, along with some comparisons with the applicable theories.

Rossow, V. J.↗
NASA NTRS1988

Transport of low- and medium-energy electron and ion beams in seawater and its vapors

A general theory of stopping power for electrons and ions in a target medium (gas, liquid, or thin solid foil) containing neutral as well as positive and negative ions is developed. The approach is quite accurate in the low- and medium-energy range (less than 1 MeV), where the Bethe stopping-power cross section is inaccurate. The energy transfer during individual collisions is treated by the binary-encounter approximation. The theory is applied to determine the stopping power of seawater, whose major components are H2O molecules and Na(+) and Cl(-) ions. The stopping-power cross sections for low- and medium-energy protons in water show excellent agreement with existing measurements.

Erwin, Daniel A.↗
NASA NTRS1991

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.↗
NASA NTRS2005

Surface Collisions Involving Particles and Moisture (SCIP'M)

Experiments were performed on the collision of a solid sphere with a nearly horizontal flat surface covered with a thin layer of viscous liquid. High-speed collisions were obtained by dropping the ball onto the surface from various heights, using gravitational acceleration. Low-speed collisions were obtained using pendulums with long strings or by launching the balls at low velocities in the reduced-gravity environment of parabolic flight. The sphere bounces only when the impact velocity exceeds a critical value. The coefficient of restitution (ratio of rebound velocity to impact velocity) increases with increasing impact velocity above the critical value, indicating the increasing relative importance of elastic deformation to viscous dissipation. The critical impact velocity increases, and the coefficient of restitution decreases, with increasing viscosity or thickness of the liquid layer and with decreasing density or size of the sphere. The ratio of the wet and dry coefficients is expressed as a function of the Stokes number (ratio of particle inertia and viscous forces), showing good agreement between theory and experiment. Similar experiments were performed with the flat surface inclined at various angles to the approaching sphere. A modified Stokes number, which is a measure of the ratio of inertia of the sphere in the normal direction to the viscous forces exerted by the fluid layer, was used for the analysis of oblique collisions. Even for these oblique collisions, it was found that no rebound of the ball was observed below a certain critical Stokes number. The coefficient of normal restitution, defined as a ratio of normal rebound velocity to normal approach velocity, was found to increase beyond the critical Stokes number and even out as it approaches the value for dry restitution at high Stokes numbers. It was also found that, for smooth spheres like steel, the normal restitution at the same modified Stokes number is independent of the angle of impact. The tangential coefficient of restitution, defined as the ratio of tangential rebound velocity to tangential approach velocity, is found to be nearly unity, except for very low approach velocities. Thus, as a first approximation, the theories that predict the coefficient of restitution for head-on wet collisions can be extended to predict the coefficient of normal restitution for oblique wet collisions. Additional experiments were performed with soft surfaces in which a porous cloth or sponge layer was placed over the hard, flat surface. In these experiments, the coefficient of restitution was found to decrease with increasing impact velocity, due to inelastic losses in the soft material. A model combining inelastic deformation and flow through porous media was developed to describe these findings.

Davis, Robert H.↗
DOE OSTI2025

Theory and numerics of subspace approximation of eigenvalue problems

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to mitigate the computational burden associated with high-fidelity systems. Furthermore, we provide general error estimates under non-simple eigenvalue conditions, establishing some theoretical foundations for understanding the convergence behavior of subspace approximations. Numerical examples, including problems with one-dimensional to three-dimensional spatial domain and one-dimensional to two-dimensional parameter domain, are presented to demonstrate the efficacy of reduced basis method in handling parametric variations in boundary conditions and coefficient fields to achieve significant computational savings while maintaining high accuracy, making them promising tools for practical applications in large-scale eigenvalue computations.

Eigenvalue problems↗
DOE OSTI2026

Role of electron correlation on the adenine dimer interaction for non-equilibrium geometries: a benchmark Quantum Monte Carlo study

The accurate description of non-covalent interactions is critical for understanding the structure, dynamics, and eventual function of biomolecules. The adenine dimer serves as a benchmark system for computational methods due to its role in nucleic acid structures and its rich conformational landscape. In this study, we employ benchmark diffusion quantum Monte Carlo (DMC) methods to investigate the relative energies and role of electron correlation on a set of adenine dimer conformations generated via a search of the potential energy landscape using the global optimizer algorithm. Relative DMC energies are compared against a wide range of density functional theory (DFT) approximation results. We find that although most of the DFT functionals perform well for low-energy structures, their accuracy varies significantly for higher-energy conformations, including stacked and T-shaped structures. A large fraction of the variation is due to the treatment of the van der Waals interaction. BLYP, B3LYP, and PBE0 significantly improve with added D4 dispersion, while the recent r2SCAN-D4 and ωB97M-V functionals show the least scatter and closest agreement with the DMC. These findings highlight the delicate nature of these interactions in biomolecular systems and provide guidance for simulations of their structure and dynamics and for the development of machine learned interatomic potentials.

Washburn, Laurel [ORNL] (ORCID:0000000324179335)↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Microstructure development during rapid alloy solidification

Abstract Solidification processing of structural alloys can take place over an extremely wide range of solid–liquid interface velocities spanning six orders of magnitude, from the low-velocity constitutional supercooling limit of microns/s to the high-velocity absolute stability limit of m/s. In between these two limits, the solid–liquid interface is morphologically unstable and typically forms cellular-dendritic microstructures, but also other microstructures that remain elusive. Rapid developments in additive manufacturing have renewed the interest in modeling the high-velocity range, where approximate analytical theories provide limited predictions. In this article, we discuss recent advances in phase-field modeling of rapid solidification of metallic alloys, including a brief description of state-of-the-art experiments used for model validation. We describe how phase-field models can cope with the dual challenge of carrying out simulations on experimentally relevant length- and time scales and incorporating nonequilibrium effects at the solid–liquid interface that become dominant at rapid rates. We present selected results, illustrating how phase-field simulations have yielded unprecedented insights into high-velocity interface dynamics, shedding new light on both the absolute stability limit and the formation of banded microstructures that are a hallmark of rapid alloy solidification near this limit. We also discuss state-of-the-art experiments used to validate those insights. Graphical abstract

36 MATERIALS SCIENCE↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Near optimum digital phase locked loops.

Near optimum digital phase locked loops are derived utilizing nonlinear estimation theory. Nonlinear approximations are employed to yield realizable loop structures. Baseband equivalent loop gains are derived which under high signal to noise ratio conditions may be calculated off-line. Additional simplifications are made which permit the application of the Kalman filter algorithms to determine the optimum loop filter. Performance is evaluated by a theoretical analysis and by simulation. Theoretical and simulated results are discussed and a comparison to analog results is made.

Polk, D. R.↗
NASA NTRS1972

Shock waves in the solar system.

Review of the role of gasdynamic processes involving shock waves in the transfer of solar material and energy to the earth and elsewhere in the solar system. The role of shock waves in maintaining the high temperature of the solar corona and in establishing the steady-state solar wind is discussed. An approximate hydromagnetic theory is developed to explain the flow of a supersonic solar wind past planets and the moon. Data concerning the passage of interplanetary shock waves and the ability of a solar flare to produce such a wave are reviewed, and some terrestrial consequences of solar activity are cited.

Spreiter, J. R.↗