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Results for “theory of computation”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Geometry program for aerodynamic lifting surface theory

A computer program that provides the geometry and boundary conditions appropriate for an analysis of a lifting, thin wing with control surfaces in linearized, subsonic, steady flow is presented. The kernel function method lifting surface theory is applied. The data which is generated by the program is stored on disk files or tapes for later use by programs which calculate an influence matrix, plot the wing planform, and evaluate the loads on the wing. In addition to processing data for subsequent use in a lifting surface analysis, the program is useful for computing area and mean geometric chords of the wing and control surfaces.

Medan, R. T.↗
NASA NTRS1992

Studies of a flat wake rotor theory

A computer code was developed at Princeton University to calculate the velocity components in the flow field near a lifting rotor. The induced velocity components in the rotor flow field predicted by this theory are compared with experiment. It appears that on balance, this relatively simple theory gives a reasonable prediction of the average induced velocities in a rotor flow and is quite suitable for such applications as estimating the influence of the rotor wake on the tail surfaces of rotorcraft. The theory predicts that significant induced velocity components are present in all three flow directions in the wake at a lifting rotor. It should be noted , however, that there are a few experimental measurements of the longitudinal and lateral induced velocity components in the rotor wake. This theory, known as the flat wake theory, is essentially the rotary wing analog of Prandtl's lifting line theory. The theory is described in this report. Calculations based on the theory are presented and compared with a modern free wake theory.

Curtiss, H. C., Jr.↗
DOE OSTI2025

Thermal relaxation and the complete set of second-order transport coefficients for the unitary Fermi gas from kinetic theory

We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an 𝑠 -wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate 𝜏 𝜅 = 𝜅⁢𝑚/(𝑐 𝑃 ⁢𝑇) even if the full collision kernel is taken into account. Furthermore, 𝜅 is the thermal conductivity, 𝑚 is the mass of the particles, 𝑐𝑃 is the specific heat at constant pressure, and 𝑇 is the temperature.

Kinetic theory↗
NASA NTRS1974

Electromagnetic diffraction efficiencies for plane reflection diffraction gratings

The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.

Marathay, A. S.↗
NASA NTRS1990

A collision-selection rule for a particle simulation method suited to vector computers

A theory is developed for a selection rule governing collisions in a particle simulation of rarefied gas-dynamic flows. The selection rule leads to an algorithmic form highly compatible with fine grain parallel decomposition, allowing for efficient utilization of supercomputers having vector or massively parallel single instruction multiple data architectures. A comparison of shock-wave profiles obtained using both the selection rule and Bird's direct simulation Monte Carlo (DSMC) method show excellent agreement. The equation on which the selection rule is based is shown to be directly related to the time-counter procedure in the DSMC method. The results of several example simulations of representative rarefied flows are presented, for which the number of particles used ranged from 10 to the 6th to 10 to the 7th demonstrating the greatly improved computational efficiency of the method.

Baganoff, D.↗
DOE OSTI2020

Two-loop HTL-resummed thermodynamics for $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory

We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using only simple vacuum energy, gluon mass, scalar mass, and quark mass counter terms. The HTL mass parameters m D , M D , and m q are then determined self-consistently using a variational prescription which results in a set of coupled gap equations. Based on this, we obtain the two-loop HTL-resummed thermodynamic functions of \( \mathcal{N} \) = 4 SYM. We compare our final result with known results obtained in the weak- and strong-coupling limits. We also compare to previously obtained approximately self-consistent HTL resummations and Padé approximants. We find that the two-loop HTL resummed results for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2 and is in agreement with previous approximately self-consistent HTL resummation results for λ ≲ 6.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1984

Irradiance from stars based on blackbody theory

A computer program which calculates a theoretical backbody curve for a star when given only the star's temperature and visual magnitude is presented. The program was written to produce approximate stellar spectra to be used in the design of the Space Telescope Fine Guidance System (FGS). In addition to the blackbody curve, the program calculates the number of photons tht would be received by the Space Telescope per 25 MSEC interval in wavelength increments of 0.2 microns. The equations used for the computations work best for stars that emit primarily in the range of near infrared to ultraviolet.

Jacobs, W. A.↗
NASA NTRS1989

Transient response of lattice structures based on exact member theory

The computer program BUNVIS-RG, which treats vibration and buckling of lattice structures using exact member stiffness matrices, has been extended to calculate the exact modal mass and stiffness quantities that can be used in a conventional transient response analysis based on modes. The exact nature of the development allows inclusion of local member response without introduction of any interior member nodes. Results are given for several problems in which significant interaction between local and global response occurs.

Anderson, Melvin S.↗
NASA NTRS1992

Further investigations of the aeroelastic behavior of the AFW wind-tunnel model using transonic small disturbance theory

The Computational Aeroelasticity Program-Transonic Small Disturbance (CAP-TSD) code, developed at LaRC, is applied to the active flexible wing wind-tunnel model for prediction of transonic aeroelastic behavior. A semi-span computational model is used for evaluation of symmetric motions, and a full-span model is used for evaluation of antisymmetric motions, and a full-span model is used for evaluation of antisymmetric motions. Static aeroelastic solutions using CAP-TSD are computed. Dynamic deformations are presented as flutter boundaries in terms of Mach number and dynamic pressure. Flutter boundaries that take into account modal refinements, vorticity and entropy corrections, antisymmetric motion, and sensitivity to the modeling of the wing tip ballast stores are also presented with experimental flutter results.

Silva, Walter A.↗
DOE OSTI2021

Indexed improvements for real-time trotter evolution of a (1 + 1) field theory using NISQ quantum computers

Today's quantum computers offer the possibility of performing real-time calculations for quantum field theory scattering processes motivated by high energy physics. In order to follow the successful roadmap which has been established for the calculation of static properties at Euclidean time, it is crucial to develop new algorithmic methods to deal with the limitations of current noisy intermediate-scale quantum (NISQ) devices and to establish quantitative measures of the progress made with different devices. In this paper, we report recent progress in these directions. We show that nonlinear aspects of the trotter errors allow us to take much larger step then suggested by low-order analysis. This is crucial to reach physically relevant time scales with today's NISQ technology. We propose to use an index averaging absolute values of the difference between the accurately calculated trotter evolution of site occupations and their actual measurements on NISQ machines (G index) as a measure to compare results that have been obtained from different hardware platforms. Using the transverse Ising model in one spatial dimension with four sites we apply this metric across several hardware platforms. We study the results including readout mitigation and Richardson extrapolations and show that the mitigated measurements are very effective based on the analysis of the trotter step size modifications. Furthermore, we discuss how this advance in the trotter step size procedures can improve quantum computing physics scattering results and how this technical advance can be applied to other machines and noise mitigation methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum embedding theories to simulate condensed systems on quantum computers.

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.

Vorwerk, Christian↗
NASA NTRS1993

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗
NASA NTRSDate not supplied

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition↗
DOE OSTI2022

IMPROVING THE ACCURACY OF COMPOSITE METHODS: A G4MP2 METHOD WITH G4-LIKE ACCURACY AND IMPLICATIONS FOR MACHINE LEARNING

G4MP2 theory has proven to be a reliable and accurate quantum chemical composite method for the calculation of molecular energies using an approximation based on second-order perturbation theory to lower computational costs compared to G4 theory. However, it has been found to have significantly increased errors when applied to larger organic molecules with 10 or more nonhydrogen atoms. We report here on an investigation of the cause of the failure of G4MP2 theory for such larger molecules. One source of error is found to be the "higher-level correction (HLC)", which is meant to correct for deficiencies in correlation contributions to the calculated energies. This is because the HLC assumes that the contribution is independent of the element and the type of bonding involved, both of which become more important with larger molecules. We address this problem by adding an atom-specific correction, dependent on atom type but not bond type, to the higher-level correction. We find that a G4MP2 method that incorporates this modification of the higher-level correction, referred to as G4MP2A, becomes as accurate as G4 theory (for computing enthalpies of formation) for a test set of molecules with less than 10 nonhydrogen atoms as well as a set with 10-14 such atoms, the set of molecules considered here, with a much lower computational cost. The G4MP2A method is also found to significantly improve ionization potentials and electron affinities. Finally, we implemented the G4MP2A energies in a machine learning method to predict molecular energies.

Dandu, Naveen↗