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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Building bases of loop integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all ‘leading-(transcendental-)weight’ contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory — for generic helicities and arbitrary multiplicity.

1/NExpansion↗
NASA NTRS2012

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C0-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite elements provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Tessler, Alexander↗
NASA NTRS2012

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C(sup 0)-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite element approximations thus provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Tessler, Alexander↗
NASA NTRS1947

Preliminary Tests in the Supersonic Sphere

This report presents preliminary data obtained in the Langley supersonic sphere. The supersonic sphere is essentially a whirling mechanism enclosed in a steel shell which can be filled with either air or Freon gas. The test models for two-dimensional study are of propeller form having the same plan form and diameter but varying only in the airfoil shape and thickness ratio. Torque coefficients for the 16-006, 65-110, and the 15 percent thick ellipse models are presented, as well as pressure distributions on a circular-arc supersonic airfoil section having a maximum thickness of 10 percent chord at the 1/3-chord position. Torque coefficients were measured in both Freon and air on the 15 percent thick ellipse, and the data obtained in air and Freon are found to be in close agreement. The torque coefficients for the three previously mentioned models showed large differences in magnitude at tip Mach numbers above 1, the model with the thickest airfoil section having the largest torque coefficient. Pressure distribution on the previously mentioned circular-arc airfoil section are presented at Mach numbers of 0.69, 1.26, and 1.42. At Mach numbers of 1.26 and 1.42 the test section is in the mixed flow region where both subsonic and supersonic speeds occur on the airfoil. No adequate theory has been developed for this condition of mixed flow, but the experimental data have been compared with values of pressure based on Ackeret's theory. The experimental data obtained at a Mach number of 1.26 on the rear portion of the airfoil section agree fairly well with the values calculated by Ackeret's theory. At a Mach number of 1.42 a larger percentage of the airfoil is in supersonic flow, and the experimental data for the entire airfoil agree fairly well with the values obtained using Ackeret's theory.

Baker, John E.↗
NASA NTRS1974

On the theory of H2 rotational excitation

A number of mechanisms for exciting higher-J states in the ground vibrational level are considered. Attention is given to collisions with H atoms and electrons. Other mechanisms involve a cascading down from upper vibrational levels, following absorption and reemission of photons in the Lyman and Werner bands, or a cascading down from upper vibrational levels, following formation of hydrogen molecules in excited vibrational and rotational levels. Theoretical population densities of rotational levels are shown in a graph.

Spitzer, L., Jr.↗
NASA NTRS1989

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.↗
NASA NTRS1990

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Van Dommelen, Leon L.↗
NASA NTRS1946

Comparison of Several Methods of Predicting the Pressure Loss at Altitude Across a Baffled Aircraft-Engine Cylinder

Several methods of predicting the compressible-flow pressure loss across a baffled aircraft-engine cylinder were analytically related and were experimentally investigated on a typical air-cooled aircraft-engine cylinder. Tests with and without heat transfer covered a wide range of cooling-air flows and simulated altitudes from sea level to 40,000 feet. Both the analysis and the test results showed that the method based on the density determined by the static pressure and the stagnation temperature at the baffle exit gave results comparable with those obtained from methods derived by one-dimensional-flow theory. The method based on a characteristic Mach number, although related analytically to one-dimensional-flow theory, was found impractical in the present tests because of the difficulty encountered in defining the proper characteristic state of the cooling air. Accurate predictions of altitude pressure loss can apparently be made by these methods, provided that they are based on the results of sea-level tests with heat transfer.

Neustein, Joseph↗
DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1983

Large numbers hypothesis. II - Electromagnetic radiation

This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.

Adams, P. J.↗
DOE OSTI2024

Dynamic density functional theory of polymers with salt in electric fields

Here we present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager’s transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Gradient Technique Theory: Tracing Magnetic Field and Obtaining Magnetic Field Strength

Abstract The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfvén Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfvén Mach number M A . We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Theoretical and experimental study of twisted and cambered delta wings designed for a Mach number of 3.5

Data are provided for the evaluation of the aerodynamic performance of a series of twisted and cambered delta wings designed for a Mach number of 3.5. Systematic force and pressure data are also presented for comparison with theory. Force tests were made at Mach numbers of 2.3, 3.0, 3.5, 4.0, and 4.6. Design lift coefficients of 0.0 and 0.1 were employed on the 55 deg and 68 deg sweep wings, and design lift coefficients of 0.0, 0.05, and 0.1 were employed on the 76 deg sweep wings. Pressure tests were conducted on the 55 deg and 76 deg sweep flat wings and on the 0.1 design lift coefficient 76 deg sweep wing. The results indicate that for the sweep angles tested, an increase in the zero-lift pitching-moment coefficient is the primary benefit of twist and camber at a Mach number of 3.5. Comparison of the experimental results with results obtained from several lift theories indicates that the Carlson-Middleton linear theory method gave the best overall agreement. The pressure data indicate, however, that there is a cancellation of error at high angle of attack where the lower surface pressures are significantly underpredicted over the inboard region of the wing and where the upper and lower surface pressures are overpredicted over the outboard region of the wing.

Sorrells, R. B., III↗
NASA NTRS1984

Magnetohydrodynamic and gasdynamic theories for planetary bow waves

The observed properties of bow waves and the associated plasma flows are outlined, along with those features identified that can be described by a continuum magnetohydrodynamic flow theory as opposed to a more detailed multicomponent particle and field plasma theory. The primary objectives are to provide an account of the fundamental concepts and current status of the magnetohydrodynamic and gas dynamic theories for solar wind flow past planetary bodies. This includes a critical examination of: (1) the fundamental assumptions of the theories; (2) the various simplifying approximations introduced to obtain tractable mathematical problems; (3) the limitations they impose on the results; and (4) the relationship between the results of the simpler gas dynamic-frozen field theory and the more accurate but less completely worked out magnetohydrodynamic theory. Representative results of the various theories are presented and compared. A number of deficiencies, ambiguities, and suggestions for improvements are discussed, and several significant extensions of the theory required to provide comparable results for all planets, their satellites, and comets are noted.

Spreiter, J. R.↗
NASA NTRS1992

Low Mach number two-dimensional hydrodynamic turbulence - Energy budgets and density fluctuations in a polytropic fluid

Theory suggests that three distinct types of turbulence can occur in the low Mach number limit of polytropic flow: nearly incompressible flows dominated by vorticity, nearly pure acoustic turbulence dominated by compression, and flows characterized by near statistical equipartition of vorticity and compressions. Distinctions between these kinds of turbulence are investigated here by direct numerical simulation of two-dimensional compressible hydrodynamic turbulence. Dynamical scalings of density fluctuations, examination of the ratio of transverse to longitudinal velocity fluctuations, and spectral decomposition of the fluctuations are employed to distinguish the nature of these low Mach number solutions. A strong dependence on the initial data is observed, as well as a tendency for enhanced effects of compressibility at later times and at higher wave numbers, as suggested by theories of nearly incompressible flows.

Ghosh, S.↗
DOE OSTI2020

$T\overline{T}$, black holes and negative strings

String theory on AdS 3 has a solvable single-trace irrelevant deformation that is closely related to $T\overline{T}$. For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum. For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states. Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity. We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture. The singularity does not give rise to a hard ultraviolet wall for excitations -one must include the region beyond it to understand the theory. The size of black holes diverges as their energy approaches the upper bound, as does the location of the singularity. Fundamental strings pass smoothly through the singularity, but if their energy is above the upper bound, their trajectories are singular. From the point of view of the boundary at infinity, this background can be thought of as a vacuum of Little String Theory which contains a large number of negative strings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗