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NASA NTRS1994

Cosmic structure formation

This article reviews the prevailing paradigm for how galaxies and larger structures formed in the universe: gravitational instability. Basic observational facts are summarized to motivate the standard cosmological framework underlying most detailed investigations of structure formation. The observed univers approaches spatial uniformity on scales larger than about 10(exp 26) cm. On these scales gravitational dynamics is almost linear and therefore relatively easy to relate to observations of large-scale structure. On smaller scales cosmic structure is complicated not only by nonlinear gravitational clustering but also by nonlinear nongravitational gas dynamical processes. The complexity of these phenomena makes galaxy formation one of the grand challenge problems of the physical sciences. No fully satisfactory theory can presently account in detail for the observed cosmic structure. However, as this article summarizes, significant progress has been made during the last few years.

Bertschinger, Edumund↗

NASA NTRS1997

Overview of Recent Flight Flutter Testing Research at NASA Dryden

In response to the concerns of the aeroelastic community, NASA Dryden Flight Research Center, Edwards, California, is conducting research into improving the flight flutter (including aeroservoelasticity) test process with more accurate and automated techniques for stability boundary prediction. The important elements of this effort so far include the following: (1) excitation mechanisms for enhanced vibration data to reduce uncertainty levels in stability estimates; (2) investigation of a variety of frequency, time, and wavelet analysis techniques for signal processing, stability estimation, and nonlinear identification; and (3) robust flutter boundary prediction to substantially reduce the test matrix for flutter clearance. These are critical research topics addressing the concerns of a recent AGARD Specialists' Meeting on Advanced Aeroservoelastic Testing and Data Analysis. This paper addresses these items using flight test data from the F/A-18 Systems Research Aircraft and the F/A-18 High Alpha Research Vehicle.

Brenner, Martin J.↗

NASA NTRS1999

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗

NASA NTRS2003

Task I: A Computational Model for Short Wavelength Stall Inception and Development In Multi-Stage Compressors

A computational model is presented for simulating axial compressor stall inception and development via disturbances with length scales on the order of several (typically about three) blade pitches. The model was designed for multi-stage compressors in which stall is initiated by these short wavelength disturbances, also referred to as spikes. The inception process described is fundamentally nonlinear, in contrast to the essentially linear behavior seen in so-called modal stall inception . The model was able to capture the following experimentally observed phenomena: (1) development of rotating stall via short wavelength disturbances, (2) formation and evolution of localized short wavelength stall cells in the first stage of a mismatched compressor, (3) the switch from long to short wavelength stall inception resulting from the re-staggering of the inlet guide vane, (4) the occurrence of rotating stall inception on the negatively sloped portion of the compressor characteristic. Parametric investigations indicated that (1) short wavelength disturbances were supported by the rotor blade row, (2) the disturbance strength was attenuated within the stators, and (3) the reduction of inter-blade row gaps can suppress the growth of short wavelength disturbances. It is argued that each local component group (rotor plus neighboring stators) has its own instability point (i.e. conditions at which disturbances are sustained) for short wavelength disturbances, with the instability point for the compressor set by the most unstable component group.

Suder, Kenneth↗

NASA NTRS2006

Laboratory Study of Magnetorotational Instability and Hydrodynamic Stability at Large Reynolds Numbers

Two plausible mechanisms have been proposed to explain rapid angular momentum transport during accretion processes in astrophysical disks: nonlinear hydrodynamic instabilities and magnetorotational instability (MRI). A laboratory experiment in a short Taylor-Couette flow geometry has been constructed in Princeton to study both mechanisms, with novel features for better controls of the boundary-driven secondary flows (Ekman circulation). Initial results on hydrodynamic stability have shown negligible angular momentum transport in Keplerian-like flows with Reynolds numbers approaching one million, casting strong doubt on the viability of nonlinear hydrodynamic instability as a source for accretion disk turbulence.

Ji, H.↗

NASA NTRS1975

Empirical comparison of a linear and a nonlinear washout for motion simulators

The subjective opinions gathered from seven pilots in the process of comparing a linear and a nonlinear washout for motion simulators reveal an important advance in motion cue presentation. The advance is not in the increased cue provided by the nonlinear filter over a linear filter for the same amount of motion base travel, but rather in the elimination of false rotational rate cues presented by linear filters.

Parrish, R. V.↗

NASA NTRS1990

Theory on instability and transition

The fundamental fluid dynamics governing instability and transition to turbulence in boundary layers are considered, and attention is focused on the key aspects of nonlinear dynamics central to the transition process and to turbulent boundary-layer phenomena. Emphasis is placed on truly nonlinear theories, in which the boundary layer mean-flow profile is completely altered from its original form. Nonlinear TS transitions, Euler-stage interactions, and vortex/wave interactions are discussed, and compressible boundary layers are analyzed. Connections with experiments and computations are outlined, along with overall trends including the extension of the nonlinear theory and the advancement in the compressible and other flow regimes.

Smith, Frank T.↗

NASA NTRS1999

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗

NASA NTRS1996

Nonlinear Optical Properties of Organic and Polymeric Thin Film Materials of Potential for Microgravity Processing Studies

In this paper, we will take a closer look at the state of the art of polydiacetylene, and metal-free phthalocyanine films, in view of the microgravity impact on their optical properties, their nonlinear optical properties and their potential advantages for integrated optics. These materials have many attractive features with regard to their use in integrated optical circuits and optical switching. Thin films of these materials processed in microgravity environment show enhanced optical quality and better molecular alignment than those processed in unit gravity. Our studies of these materials indicate that microgravity can play a major role in integrated optics technology. Polydiacetylene films are produced by UV irradiation of monomer solution through an optical window. This novel technique of forming polydiacetylene thin films has been modified for constructing sophisticated micro-structure integrated optical patterns using a pre-programmed UV-Laser beam. Wave guiding through these thin films by the prism coupler technique has been demonstrated. The third order nonlinear parameters of these films have been evaluated. Metal-free phthalocyanine films of good optical quality are processed in our laboratories by vapor deposition technique. Initial studies on these films indicate that they have excellent chemical, laser, and environmental stability. They have large nonlinear optical parameters and show intrinsic optical bistability. This bistability is essential for optical logic gates and optical switching applications. Waveguiding and device making investigations of these materials are underway.

Abdeldayem, Hossin↗

NASA NTRS1985

Large eddy interactions in a turbulent channel flow

The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.

Hong, S. K.↗

DOE OSTI2023

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A beamline for ultrafast extreme ultraviolet magneto-optical spectroscopy in reflection near the shot noise limit

High harmonic generation (HHG) makes it possible to measure spin and charge dynamics in materials on femtosecond to attosecond timescales. However, the extreme nonlinear nature of the high harmonic process means that intensity fluctuations can limit measurement sensitivity. Here we present a noise-canceled, tabletop high harmonic beamline for time-resolved reflection mode spectroscopy of magnetic materials. We use a reference spectrometer to independently normalize the intensity fluctuations of each harmonic order and eliminate long term drift, allowing us to make spectroscopic measurements near the shot noise limit. Here, these improvements allow us to significantly reduce the integration time required for high signal-to-noise (SNR) measurements of element-specific spin dynamics. Looking forward, improvements in the HHG flux, optical coatings, and grating design can further reduce the acquisition time for high SNR measurements by 1–2 orders of magnitude, enabling dramatically improved sensitivity to spin, charge, and phonon dynamics in magnetic materials.

47 OTHER INSTRUMENTATION↗

NASA NTRS1992

Prediction of nonlinear optical properties of large organic molecules

The preparation of materials with large nonlinear responses usually requires involved synthetic processes. Thus, it is very advantageous for materials scientists to have a means of predicting nonlinear optical properties. The prediction of nonlinear optical properties has to be addressed first at the molecular level and then as bulk material. For relatively large molecules, two types of calculations may be used, which are the sum-over-states and the finite-field approach. The finite-field method was selected for this research, because this approach is better suited for larger molecules.

Cardelino, Beatriz H.↗

NASA NTRS1993

The evolution of strongly modulated, low-frequency, moderate-amplitude wave packets in a dispersive plasma

The evolution of strongly modulated wave packets in a dispersive plasma that propagate parallel to the magnetic field is studied. Modulation effects are shown to reduce significantly (about 30 percent) the rate of spreading from that due to dispersion alone. For fluidlike behavior, nonlinearity has its greatest impact on evolution when the linear sound speed and initial wave packet speeds are well matched, resulting in a strong coupling between the wave magnetic and sonic components. Ion kinetic processes reduce the impact of nonlinearity and cause the rate of spreading to approach that expected from dispersion alone as the ratio of ion and electron temperatures, Ti/Te approaches 4. For Beta equal to or greater than 1 and Ti/Te of about 1, the coupled waveforms correspond qualitatively to kinetic treatments of the derivative nonlinear Schroedinger equation.

Vasquez, Bernard J.↗

NASA NTRS1995

Some wave-particle effects on large-scale Alfven wave propagation and damping

Phase mixing can reduce greatly the torsional Alfven wave's dissipation length for propagation in complex magnetic field-line geometries. This phase mixing causes significant energy transfers from large to small scales where a conversion from ordered wave energy into a particle kinetic form occurs. This conversion during its initial stages is an entropy conserving process well described by Vlasov theory, Nonlinear stages of wave-particle resonance, particle trapping, and collisional resistivity are often invoked as processes eventually responsible for converting ordered wave motions into random thermal motion. Strictly speaking, this entropy producing phase cannot be described within Vlasov theory, and the large-scale effects of these microscopic events resides at the difficult frontier between generalized fluid and kinetic theories. We attempt to describe certain aspects of such resonances within the framework of fluid theory focusing on torsional Alfven wave energy transport and deposition within flux tubes.

Siregar, E.↗

DOE OSTI2024

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2003

Using High-Fidelity Analysis Methods and Experimental Results to Account for the Effects of Imperfections on the Buckling Response of Composite Shell Structures

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The analytical results include the effects of traditional and nontraditional initial imperfections and uncertainties in the values of selected shell parameters on the buckling loads of the shells. The nonlinear structural analysis results correlate very well with the experimental results. The high-fidelity nonlinear analysis procedure used to generate the analytical results can also be used to form the basis of a new shell design procedure that could reduce the traditional dependence on empirical results in the shell design process. KEYWORDS: high-fidelity nonlinear structural analysis, composite shells, shell stability, initial imperfections

Starnes, James H., Jr.↗

NASA NTRS1993

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗