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Results for “asymptotic analysis”

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At least 199 records · Page 11

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NASA NTRS1990

Initial postbuckling response of an unsymmetrically laminated rectangular plate

It was shown that anisotropic plates can have unstable postbuckling behavior resulting in potential imperfection sensitivity. The degree of instability for rectangular, simply-supported, cross-ply laminated plates is quantified. The analysis is based on asymptotic Koiter-type expansion of postbuckling response. The degree of postbuckling instability is quantified in terms of the reduction in load carrying capacity in the immediate postbuckling range. For graphite-epoxy plates it is found that this measure of instability is very small. Only a low aspect ratio plate with a high degree of anisotropy can have any significant reduction in its buckling load.

Haftka, Raphael T.↗

NASA NTRS1992

Initial postbuckling response of anisotropic laminated rectangular plates

It has been shown that anisotropic plates can have unstable postbuckling behavior resulting in potential imperfection sensitivity. The present paper quantifies the degree of instability for rectangular, simply supported asymmetrically laminated plates. The analysis is based on asymptotic Koiter-type expansion of postbuckling response. The degree of postbuckling instability is quantified in terms of the reduction in load carrying capacity in the immediate postbuckling range. For graphite-epoxy plates it is found that this measure of instability is very small unless the lamination asymmetry is very pronounced.

Johnson, Eric R.↗

NASA NTRS1989

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked.

Burkholder, R. J.↗

NASA NTRS1994

Asymptotic forms for the energy of force-free magnetic field ion figurations of translational symmetry

It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.

Sturrock, P. A.↗

NASA NTRS1992

Application of the variational-asymptotical method to composite plates

A method is developed for the 3D analysis of laminated plate deformation which is an extension of a variational-asymptotical method by Atilgan and Hodges (1991). Both methods are based on the treatment of plate deformation by splitting the 3D analysis into linear through-the-thickness analysis and 2D plate analysis. Whereas the first technique tackles transverse shear deformation in the second asymptotical approximation, the present method simplifies its treatment and restricts it to the first approximation. Both analytical techniques are applied to the linear cylindrical bending problem, and the strain and stress distributions are derived and compared with those of the exact solution. The present theory provides more accurate results than those of the classical laminated-plate theory for the transverse displacement of 2-, 3-, and 4-layer cross-ply laminated plates. The method can give reliable estimates of the in-plane strain and displacement distributions.

Hodges, Dewey H.↗

DOE OSTI2026

Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis

The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.

Computational methods↗

DOE OSTI2022

Novel nonwetting solid-infused surfaces for superior fouling mitigation

Fouling is a ubiquitous issue in several environmental and energy applications. Here we introduce novel nonwetting solid-infused surfaces (SIS) with superior anti-fouling characteristics that are durable than conventional nonwetting surfaces in a dynamic flow environment. A systematic study is presented to elucidate the fouling mitigation performance of SIS in comparison to lubricant-infused surface (LIS) and conventional smooth surface. Copper tubes with SIS, LIS or smooth inner walls are fabricated and subjected to accelerated calcium sulfate fouling in a flow fouling experimental setup. Fouling on the various surface types is quantified in terms of asymptotic fouling resistance, and the fundamental morphological differences in the interactions of the foulant and the various surface types are analyzed. Based on a systematic sweep of the parameter combinations using design of experiments and Taguchi analysis, an analytical dependence of asymptotic fouling resistance on the governing parameters namely, Reynolds number, foulant concentration and temperature is derived. The analytical model is shown to predict the asymptotic fouling resistance to within 20% accuracy with a 95% confidence. In addition, for the first time, the effects of shear durability on the fouling mitigation performance of LIS vis-à-vis SIS are studied. It is shown that the novel nonwetting SIS offers a robust option for superior fouling mitigation over LIS in the long run.

42 ENGINEERING↗

NASA NTRS1993

Temporal model of an optically pumped co-doped solid state laser

Currently, research is being conducted on the optical properties of materials associated with the development of solid state lasers in the two micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are attained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

Wangler, T. G.↗

NASA NTRS2025

Line List for the A 2 Π−X 2 Σ + and the B 2 Σ + −X 2 Σ + Band Systems of CaF

The spectral analysis of molecule-rich asymptotic giant branch (AGB) stars is challenging. Although other calcium and fluorine bearing molecules are observed in the microwave and in the visible spectrum of AGB stars, CaF has never been detected, despite favorable chemical equilibrium predictions. Yet, measuring the CaF abundance could give more insight into the fluorine budget of AGB stars and allow better simulation of stellar spectra. In this work, we present an analysis of the visible spectrum of CaF obtained with a Fourier transform spectrometer. CaF A 2 Π−X 2 Σ + and the B 2 Σ + −X 2 Σ + band systems were excited with a hollow cathode discharge. Using previous fluorescence spectroscopy measurements, highly accurate ground state constants, and reasonable extrapolation schemes, the strongest features of CaF in the visible spectrum can be accurately modeled for both band systems. Spectroscopic constants are determined for A 2 Π with v ≤ 16 and for B 2 Σ + with v ≤ 20. Ab initio transition dipole moment curves of both transitions were calculated and scaled, and we provide a line list with Einstein A coefficients and oscillator strengths. This line list can be used to simulate spectra of CaF at temperatures and pressures relevant to astrophysical environments.

Léo Lavy↗

NASA NTRS1981

Shock development in sound transmitted through a nearly choked flow

A nonlinear quasi-one dimensional theory of sound transmitted through a converging-diverging duct section is extended to the case where the acoustical source is located well downstream of the throat, at a point where the flow Mach number is low. The development and subsequent effects of shocks in the acoustic quantities are of primary consideration. The analysis uses a method of matched asymptotic expansions, yielding a set of inner equations of motion and shock conditions valid in the near-sonic throat region. The analysis leads to a generalization of the 'equal area' relation of weak shock theory. The manner in which nonlinear effects increase with source strength, frequency, and throat Mach number is illustrated by the numerical results and corresponding graphs. The shock waves are shown to cause significant dissipation in acoustic power.

Myers, M. K.↗

NASA NTRS1992

The structure of premixed particle-cloud flames

The structure of premixed flames propagating in combustible systems, containing uniformly distributed volatile fuel particles, in an oxidizing gas mixture, is analyzed. It is presumed that the fuel particles vaporize first to yield a gaseous fuel of known chemical structure, which is subsequently oxidized in the gas phase. The analysis is performed in the asymptotic limit, where the value of the characteristic Zeldovich number, based on the gas-phase oxidation of the gaseous fuel is large, and for values of phi(u) greater than or equal to 1.0, where phi(u) is the equivalence ratio based on the fuel available in the fuel particles. The structure of the flame is presumed to consist of a preheat vaporization zone where the rate of the gas-phase chemical reaction is small, a reaction zone where convection and the rate of vaporization of the fuel particles are small and a convection zone where diffusive terms in the conservation equations are small. For given values phi(u) the analysis yields results for the burning velocity and phi(g) where phi(g) is the effective equivalence ratio in the reaction zone. The analysis shows that even though phi(u) greater than or equal to 1.0, for certain cases the calculated value of phi(g) is less than unity. This prediction is in agreement with experimental observations.

Seshadri, K.↗

NASA NTRS1987

Evolution of a localized thermal explosion in a reactive gas

Experimental observations of ignition in premixed gaseous reactants indicate that perfectly homogeneous initiation is practically unrealizable. Instead, combustion first sets in, as a rule, at small, discrete sites where inherent inhomogeneities cause chemical activity to proceed preferentially and lead to localized explosions. Combustion waves propagating away from these hot spots or reaction centers eventually envelop the remaining bulk. This study examines the spatial structure and temporal evolution of a hot spot for a model involving Arrhenius kinetics. The hot spot, characterized by peaks in pressure and temperature with little diminution in local density, is shown to have one of two possible self-similar structures. The analysis employs a combination of asymptotics and numerics, and terminates when pressure and temperature in the explosion have peaked.

Jackson, T. L.↗

NASA NTRS1988

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Wen, John T.↗

NASA NTRS1989

Evolution of a reaction center in an explosive material

Consideration is given to the spatial structure and temporal evolution of a reaction center for a model involving Arrhenius kinetics. The center, which is characterized by peaks in pressure and temperature with little diminution in local density, is found to have one of two possible self-similar structures. The analysis uses a combination of asymptotics and numerics and terminates when pressure and temperature in the reaction center have peaked.

Jackson, T. L.↗

NASA NTRS1991

Resonant Triad in Boundary-Layer Stability: Composite Solution and Comparison with Observations - Part 2

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Mankbadi, Reda R.↗

NASA NTRS1990

The performance of trellis-coded MDPSK with multiple symbol detection

The idea of using a multiple (more than two) symbol observation interval to improve error probability performance is applied to differential detection of trellis-coded multiple phase-shift keying (MPSK) over an additive white Gaussian noise (AWGN) channel. An equivalent Euclidean distance measure per trellis branch is determined for this detection scheme. This is used to define an augmented (larger multiplicity) trellis code whose distance measure is the conventional squared Euclidean distance typical of conventional trellis-coded modulation on the AWGN. Such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis. Results are obtained by a combination of analysis (upper Chernoff bounds and asymptotic large-SNR approximations) and computer simulation. It is shown that only a slight increase (e.g., one symbol) in the length of the observation interval will provide a significant improvement in bit error probability performance.

Divsalar, Dariush↗

NASA NTRS1990

Particle acceleration by electromagnetic ion cyclotron turbulence

The LF EM-turbulence which furnishes energy for the acceleration of ions in various regions of the earth's magnetosphere efficiently accomplishes its transfer of energy from waves to particles through ion cyclotron resonance (ICR) with the left-hand polarized component of the turbulence; the result of this interaction is a heating of the particle distribution. A general theoretical treatment of ICR heating in a weakly inhomogeneous magnetic geometry is presented, en route to a more detailed examination of auroral ion conics' formation. A substantial simplification of the analysis of the altitude-asymptotic form of the conic distribution is obtained via the similarity transformation introduced into the properties of the electric field spectral density and the earth's dipolar magnetic field.

Crew, G. B.↗

NASA NTRS1989

Near Zone: Basic scattering code user's manual with space station applications

The Electromagnetic Code - Basic Scattering Code, Version 3, is a user oriented computer code to analyze near and far zone patterns of antennas in the presence of scattering structures, to provide coupling between antennas in a complex environment, and to determine radiation hazard calculations at UHF and above. The analysis is based on uniform asymptotic techniques formulated in terms of the Uniform Geometrical Theory of Diffraction (UTD). Complicated structures can be simulated by arbitrarily oriented flat plates and an infinite ground plane that can be perfectly conducting or dielectric. Also, perfectly conducting finite elliptic cylinder, elliptic cone frustum sections, and finite composite ellipsoids can be used to model the superstructure of a ship, the body of a truck, and airplane, a satellite, etc. This manual gives special consideration to space station modeling applications. This is a user manual designed to give an overall view of the operation of the computer code, to instruct a user in how to model structures, and to show the validity of the code by comparing various computed results against measured and alternative calculations such as method of moments whenever available.

Marhefka, R. J.↗