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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

High frequency scattering by a smooth coated cylinder simulated with generalized impedance boundary conditions

Rigorous uniform geometrical theory of diffraction (UGTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristic to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. As usual, the diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Syed, Hasnain H.↗
NASA NTRS1991

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

Syed, H. H.↗
NASA NTRS1993

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Steely, Sidney L.↗
NASA NTRS1983

The effects of laminate thickness on the fracture behavior of composite laminates

The relationship between both fracture toughness and the development of crack-tip damage as a function of specimen thickness was investigated. Fracture toughness was determined experimentally using center-cracked tension specimens for (0/plus or minus 45/90)ns and (0/90)ns laminates, where ns means multiple layers with the same repeated sequence and symmetric about the midplane. Laminate thicknesses ranged from 8 plies to 96 plies. As with isotropic metals, fracture toughness was found to decrease with increasing specimen thickness and asymptotically approached a lower bound. The crack tip damage in the (0/plus or minus 45/90)ns laminate does not appear to be a function of thickness. However, there are differences in the damage of the (0/90)2s and (0/90)8s laminates and associated differences in fracture toughness.

Harris, C. E.↗
NASA NTRS1985

Fracture of thick graphite/epoxy laminates with part-through surface flaws

Fracture behavior of tensile specimens containing through-the-thickness flaws and part-through semi-elliptic surface flaws was investigated. The material was T300/5208 graphite/epoxy, with a stacking sequence 0/+ or - 45/90 sub ns. Laminate thicknesses ranged from 8 to 120 plies. Fracture toughness for specimens with through-the-thickness flaws was a function of laminate thickness. Fracture toughness was also independent of crack size. Fracture toughness for the thick laminates was also independent of specimen geometry (center-cracked tension specimen, compact tension specimen, and three-point bend specimen). Using the asymptotic value of facture toughness and linear elastic isotropic fracture mechanics, the notched strength of tensile specimens with semi-elliptic surface flaws was predicted. The strength ratio is a function of the flaw depth (a/t) and flaw aspect (a/c) ratios. Comparisons between predicted and experimental strengths are good for large values of a/t. The notched strength of filament wound graphite/epoxy tensile specimens with part-through surface flaws was also predicted.

Morris, D. H.↗
NASA NTRS1986

Fracture of thick graphite/epoxy laminates with part-through surface flaws

Fracture behavior of tensile specimens containing through-the-thickness flaws and part-through semi-elliptic surface flaws was investigated. The material was T300/5208 graphite/epoxy, with a stacking sequence 0/+ or - 45/90 sub ns. Laminate thicknesses ranged from 8 to 120 plies. Fracture toughness for specimens with through-the-thickness flaws was a function of laminate thickness. Fracture toughness was also independent of crack size. Fracture toughness for the thick laminates was also independent of specimen geometry (center-cracked tension specimen, compact tension specimen, and three-point bend specimen). Using the asymptotic value of fracture toughness and linear elastic isotropic fracture mechanics, the notched strength of tensile specimens with semi-elliptic surface flaws was predicted. The strength ratio is a function of the flaw depth (a/t) and flaw aspect (a/c) ratios. Comparisons between predicted and experimental strengths are good for large values of a/t. The notched strength of filament wound graphite/epoxy tensile specimens with part-through surface flaws was also predicted.

Harris, C. E.↗
NASA NTRS1990

Verification of floating-point software

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Hoover, Doug N.↗
DOE OSTI2024

Tidal Love numbers and Green’s functions in black hole spacetimes

Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include tidal Love numbers, describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four space-time dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the retarded Green’s function provides the complete description of the behavior of dynamical systems. Here, in this work we investigate the relation between Love numbers and Green’s functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss Banados-Teitelboim-Zanelli black holes, where the absence of radiative modes allows us to make a direct link between them.

classical black holes↗
DOE OSTI2024

An Asymptotic Preserving Discontinuous Galerkin Method for a Linear Boltzmann Semiconductor Model

A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f$ = $f$ ($x, v, t$) converges to an isotropic function $M (v)$$ρ$$(x, t)$, called the drift-diffusion limit, where $M$ is a Maxwellian and the physical density $ρ$ satisfies a second-order parabolic PDE known as the drift-diffusion equation. Numerical approximations that mirror this property are said to be asymptotic preserving. In this paper we build a discontinuous Galerkin method to the semiconductor model, and we show this scheme is both uniformly stable in $ε$, where 1/$ε$ is the scale of the collision frequency, and asymptotic preserving. Here in particular, we discuss what properties the discrete Maxwellian must satisfy in order for the schemes to converge in $ε$ to an accurate $h$-approximation of the drift-diffusion limit. Discrete versions of the drift-diffusion equation and error estimates in several norms with respect to $ε$ and the spacial resolution are also included.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Stability of uncertain systems

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Blankenship, G. L.↗
NASA NTRS1974

A comparison of computational methods and algorithms for the complex gamma function

A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries.

Ng, E. W.↗
NASA NTRS1981

Coherent detection of frequency-hopped quadrature modulations in the presence of jamming. I - QPSK and QASK modulations

This paper examines the performance of coherent QPSK and QASK systems combined with FH or FH/PN spread spectrum techniques in the presence of partial-band multitone or noise jamming. The worst-case jammer and worst-case performance are determined as functions of the signal-to-background noise ratio (SNR) and signal-to-jammer power ratio (SJR). Asymptotic results for high SNR are shown to have a linear dependence between the jammer's optimal power allocation and the system error probability performance.

Simon, M. K.↗
NASA NTRS1982

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Yahsi, O. S.↗
NASA NTRS1983

A cylindrical shell with an arbitrarily oriented crack

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

Yahsi, O. S.↗
NASA NTRS1987

Quantized synchrotron radiation in strong magnetic fields

Spectra from electrons making synchrotron transitions in high magnetic fields are calculated using the exact quantum transition rates for Landau states up to n = 500, and the results are compared with spectra calculated from the classical formula and the asymptotic quantum formula. The behavior of the transition rates are examined at low and high harmonics as a function of the spin state of the electron. The calculations confirm those of Herold, Ruder, and Wunner (1982) for low Landau states, extending them to higher states and individual spin state transitions. The results also confirm the dominance of ground-state transitions at high field strengths noted by White (1976). Single particle emissivities for electrons with both spin-up and spin-down in the initial state are calculated using these transition rates. Spectra for thermal electron distributions at transrelativistic temperatures and for steady state injection of monoenergetic electrons with isotropic pitch angles are also presented.

Harding, Alice K.↗
NASA NTRS1989

A nonlinear investigation of the stationary modes of instability of the three-dimensional compressible boundary layer due to a rotating disc

The effects of compressibility on a stationary mode of instability of the 3-D boundary layer due to a rotating disc are investigated. The aim is to determine whether this mode will be important in the finite amplitude destabilization of the boundary layer. This stationary mode is characterized by the effective velocity profile having zero shear stress at the wall. Triple-deck solutions are presented for an adiabatic wall and an isothermal wall. It is found that this stationary mode is only possible over a finite range of Mach numbers. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of these modes as functions of the local Mach number. The effects of nonlinearity are investigated allowing the finite amplitude growth of a disturbance close to the neutral location to be described.

Seddougui, Sharon O.↗
NASA NTRS1989

A comparison of predicted and measured strengths of thick notched graphite/epoxy laminates

The effect of thickness on the notched strength of three graphite/epoxy laminates is studied. The strength of the laminates is shown to be a function of laminate thickness. The notched strength of (0/+ or - 45/90)ns and (0/90)ns laminates decreased toward asymptotic values with increasing laminate thickness, while that of the (0/+ or - 45)ns laminate increased toward an asymptotic value with increasing laminate thickness. For all three laminate types, the notched strength decreased with increasing notch size, regardless of thickness. The fracture of the thick laminates was essentially uniform and self-similar with the notch. The 'universal' value of the general toughness parameter developed by Poe (1981) successfully predicts the notched strength of the thick laminates.

Harris, C. E.↗
NASA NTRS1990

A nonlinear investigation of the stationary modes of instability of the three-dimensional compressible boundary layer due to a rotating disc

The effects of compressibility on a stationary mode of instability of the 3D boundary layer due to a rotating disk are investigated. The aim is to determine whether this mode will be important in the finite amplitude destabilization of the boundary layer. This stationary mode is characterized by the effective velocity profile having zero shear stress at the wall. Triple-deck solutions are presented for an adiabatic wall and an isothermal wall. It is found that this stationary mode is only possible over a finite range of Mach numbers. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of these modes as functions of the local Mach number. The effects of nonlinearity are investigated allowing the finite amplitude growth of a disturbance close to the neutral location to be described.

Seddougui, Sharon O.↗