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Results for “INTEGRAL FUNCTION”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Expansion series of integral functions occurring in unsteady aerodynamics

Attention is given to two real integral functions which occur in the kernel of singular integral equations for subsonic unsteady lifting surfaces. The arguments k, r, and X of the functions correspond to the reduced frequency, spanwise distance, and modified coordinate in the flow direction, respectively. The value of the parameter nu in the functions depends on geometrical conditions. The considered investigation has the objective to present a series for general values of the nonnegative integer nu in order to compute efficiently the integral functions. The approach makes it possible to avoid any approximation or numerical quadrature.

Ueda, T.↗
DOE OSTI2025

Toward extracting scattering phase shift from integrated correlation functions. III. Coupled channels

The formalism developed in the preceding papers that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped nonrelativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by a exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications. Published by the American Physical Society 2025

Guo, Peng (ORCID:0000000265660881)↗
DOE OSTI2025

Background-field Method and QCD Factorization

One method for deriving a factorization for QCD processes is to use successive integration over fields in the functional integral. In this approach, we separate the fields into two categories: dynamical fields with momenta above a relevant cutoff, and background fields with momenta below the cutoff. The dynamical fields are then integrated out in the background of the low-momentum background fields. This strategy works well at tree level, allowing us to quickly derive QCD factorization formulas at leading order. However, to extend the approach to higher loops, it is necessary to rigorously define the functional integral over dynamical fields in an arbitrary background field. This framework was carefully developed for the calculation of the effective action in a background field at the two-loop level in the classic paper by Abbott «The Background Field Method Beyond One Loop», Nucl. Phys. B 185 , 189 (1981). Building on this work, I specify the renormalized background-field Lagrangian and define the notion of the quantum average of an operator in a background field, consistent with the “separation of scales” scheme mentioned earlier. As examples, I discuss the evolution of the twist-2 gluon light-ray operator and the one-loop gluon propagator in a background field near the light cone.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1976

The implementation of fail-operative functions in integrated digital avionics systems

System architectures which incorporate fail operative flight guidance functions within a total integrated avionics complex are described. It is shown that the mixture of flight critical and nonflight critical functions within a common computer complex is an efficient solution to the integration of navigation, guidance, flight control, display, and flight management. Interfacing subsystems retain autonomous capability to avoid vulnerability to total avionics system shutdown as a result of only a few failures.

Osoer, S. S.↗
NASA NTRS1958

Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics

Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.

Legendre, Robert↗
DOE OSTI2024

Formation of functionally graded steel by laser powder bed fusion via in-situ carbon doping

Additive Manufacturing (AM) enables functional integration by combining multiple components into a single part to shorten assembly time, reduce weight, and improve performance. Laser Powder Bed Fusion (LPBF) is an important AM method due to excellent spatial resolution, surface finish, and material properties without the need for extensive post-processing. Functional integration could be enhanced by spatial tuning of properties, but LPBF cannot readily vary material composition. Here, this paper addresses a method to add spatial composition control by printing small quantities of dopants via liquid carrier prior to laser fusion. The impact of carbon black suspension added to select regions of a Stainless Steel 316 L powder bed on melt pool dimension, hardness, and porosity is reported. The distribution of the carbon between the doped and plain layers and the resulting spatial variation in hardness is measured. Optical microscopy and composition analysis show that the carbon dispersed uniformly within the layer of deposition and diffused as little as 50 μm in the build direction. Keyhole conditions dramatically increase the inter-layer transport of the dopant. The added carbon increased hardness by >50 %. Porosity increased in doped regions but remained below 1.5 % for the best processing parameters. These results demonstrate that the composition of LPBF parts could be controlled in 3-dimensions using a dopant that is soluble in the melt pool. Additional work will be required to evaluate different dopant materials and optimize processing conditions for full density, but microalloying with soluble dopants appears to be a plausible solution to enhance functional integration with LPBF.

36 MATERIALS SCIENCE↗
NASA NTRS1975

A cost effective data management subsystem for the LST

The paper outlines the approach used in developing DMS (Data Management Subsystem) alternatives for the LST (Large Space Telescope) and in selecting the concept considered to be the most cost effective means of implementing the LST DMS requirements. Two candidate DMS concepts are discussed: a functionally integrated and a functionally separated one. For the single vehicle LST program, separation of the DMS functions best provides high reliability, operations flexibility, minimal interface complexity, and the least complex software development and verification task. The use of available hardware and NASA standard components is stressed.

Dougherty, J. A.↗
NASA NTRS1982

Exact triple integrals of beam functions

Definite triple integrals encountered in applying the Galerkin method to the problem of heat and mass transfer across rectangular enclosures are discussed. Rather than evaluating them numerically, the technique described by Reid and Harris (1958) was extended to obtain the exact solution of the integrals. In the process, four linear simultaneous equations with triple integrals as unknowns were obtained. These equations were then solved exactly to obtain the closed form solution. Since closed form representations of this type have been shown to be useful in solving nonlinear hydrodynamic problems by series expansion, the integrals are presented here in general form.

Jhaveri, B. S.↗
NASA NTRS1968

Computation and analysis

Direct summation of series involving higher transcendental functions, integrals of confluent hypergeometric functions, and computer methods for approximating continuous functions

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