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NASA NTRS1990

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Scargle, Jeffrey D.↗

NASA NTRS1985

Turbulence and wave particle interactions in solar-terrestrial plasmas

Activities in the following study areas are reported: (1) particle and wave processes in solar flares; (2) solar convection zone turbulence; and (3) solar radiation emission. To investigate the amplification of cyclotron maser radiation in solar flares, a radio frequency. (RF) heating model was developed for the corona surrounding the energy release site. Then nonlinear simulations of compressible convection display prominent penetration by plumes into regions of stable stratification at the base of the solar convection zone, leading to the excitation of internal gravity waves there. Lastly, linear saturation of electron-beam-driven Langmuir waves by ambient density fluctuations, nonlinear saturation by strong turbulence processes, and radiation emission mechanisms are examined. An additional section discusses solar magnetic fields and hydromagnetic waves in inhomogeneous media, and the effect of magnetic fields on stellar oscillation.

Dulk, G. A.↗

DOE OSTI2022

A resistive MHD model and simulation on plasma flow evolution in the presence of resonant magnetic perturbation in a tokamak

Nonaxisymmetric magnetic fields such as the intrinsic error field and the externally applied resonant magnetic perturbation (RMP) in a tokamak are known to influence the plasma momentum transport and flow evolution through plasma response, which itself strongly depends on the plasma flow as well. The nonlinear interaction between plasma response and flow has been previously modeled in the conventional error field theory with the “no-slip” condition, which has been recently extended to allow the “free-slip” condition. In this work, we further target this specific process and numerically simulate the nonlinear plasma response and flow evolution in the presence of a single-helicity RMP in a circular-shaped model tokamak configuration, based on the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel (to k) flow or “slip frequency” profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Here, k is the wave vector of the propagating island. Good agreement with the extended theory with free-slip condition has been achieved for the parallel flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the no-slip condition tends to diminish as the plasma resistivity approaches zero.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

Image restoration and superresolution as probes of small scale far-IR structure in star forming regions

Far-infrared continuum studies from the Kuiper Airborne Observatory are described that are designed to fully exploit the small-scale spatial information that this facility can provide. This work gives the clearest picture to data on the structure of galactic and extragalactic star forming regions in the far infrared. Work is presently being done with slit scans taken simultaneously at 50 and 100 microns, yielding one-dimensional data. Scans of sources in different directions have been used to get certain information on two dimensional structure. Planned work with linear arrays will allow us to generalize our techniques to two dimensional image restoration. For faint sources, spatial information at the diffraction limit of the telescope is obtained, while for brighter sources, nonlinear deconvolution techniques have allowed us to improve over the diffraction limit by as much as a factor of four. Information on the details of the color temperature distribution is derived as well. This is made possible by the accuracy with which the instrumental point-source profile (PSP) is determined at both wavelengths. While these two PSPs are different, data at different wavelengths can be compared by proper spatial filtering. Considerable effort has been devoted to implementing deconvolution algorithms. Nonlinear deconvolution methods offer the potential of superresolution -- that is, inference of power at spatial frequencies that exceed D lambda. This potential is made possible by the implicit assumption by the algorithm of positivity of the deconvolved data, a universally justifiable constraint for photon processes. We have tested two nonlinear deconvolution algorithms on our data; the Richardson-Lucy (R-L) method and the Maximum Entropy Method (MEM). The limits of image deconvolution techniques for achieving spatial resolution are addressed.

Lester, D. F.↗

DOE OSTI2025

Transfer learning nonlinear plasma dynamic transitions in low dimensional embeddings via deep neural networks

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel, data-driven model reduction methods, coupled with detection of abnormal modes with plasma physics, opens a unique opportunity to identify plasma instabilities through automated construction of parsimonious models that can be tuned to balance accuracy and cost. Our fusion transfer learning (FTL) model demonstrates success in rapidly reconstructing nonlinear kink mode structures by learning from a limited amount of nonlinear simulation data. The knowledge transfer process leverages a pre-trained neural encoder–decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL’s capacity to capture transitional behaviors and dynamical features in plasma dynamics—a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Smith, F. T.↗

NASA NTRS1980

Flutter analysis of an airplane with multiple structural nonlinearities in the control system

Experience has shown that the flutter prediction process for airplanes can be greatly affected by strong concentrated nonlinearities which may be localized in the linking elements of the control mechanism, in the pivot joints of variable-sweep-wing systems, and in the connecting points between wing and pylon-mounted external stores. The principle of equivalent linearization offers an efficent possibility for solving the related nonlinear flutter equations in the frequency domain as a complement to the well-known time domain procedures. Taking as an example an airplane with nonlinear control characteristics, it is demonstrated how the equivalent linearization approach can be extended to rather complicated systems with multiple sets of strongly interacting, concentrated nonlinearities.

Breitbach, E. J.↗

DOE OSTI2022

A CONDUCTION-BASED HEAT PIPE MODEL FOR ANALYZING THE ENTIRE PROCESS OF LIQUID-METAL HEAT PIPE STARTUP

The Heat Pipe-cooled Microreactor (HPM) is one of the micro nuclear reactor designs under active study at the U.S. Idaho National Laboratory. Among the major concerns of HPM research is to understand the startup behavior of the heat pipe-cooled system associated with the startup of the liquid-metal heat pipes initialing from frozen state. The startup of liquid-metal heat pipes typically involves a number of nonlinear mass and heat transport processes including the phase change from solid to liquid and vapor. Hence, it is still a huge challenge to simulate the liquid-metal heat pipe startup using conventional CFD methods and software. The major difficulties of numerical CFD modeling come from the phase-change process, multiphase interaction, microporous wick flow, and compressible gas dynamics that occur during startup of the liquid-metal heat pipes. This paper proposes a simplified conduction-based method to provide practical insights into the entire startup process of the liquid-metal heat pipes while mitigating the challenges of addressing all the complex physics. We discuss the theoretical basis and modeling assumptions to analyze the liquid-metal heat pipe startup from frozen state based solely on heat-conduction equations. Then, the proposed model is implemented into the commercial CFD software to verify the model performance. The model prediction results are discussed via the comparison with the experimental data obtained from sodium heat-pipe startup experiments.

42 ENGINEERING↗

NASA NTRS1975

NASTRAN nonlinear vibration analysis of beam and frame structures

A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.

Mei, C.↗

NASA NTRS2002

Acoustically Enhanced Electroplating Being Developed

In cooperation with the NASA Glenn Research Center, Alchemitron Corp. is developing the Acoustically Enhanced Electroplating Process (AEEP), a new technique of employing nonlinear ultrasonics to enhance electroplating. The applications range from electroplating full-panel electronic circuit boards to electroplating microelectronics and microelectromechanical systems (MEMS) devices. In a conventional plating process, the surface area to be plated is separated from the nonplated areas by a temporary mask. The mask may take many forms, from a cured liquid coating to a simple tape. Generally, the mask is discarded when the plating is complete, creating a solid waste product that is often an environmental hazard. The labor and materials involved with the layout, fabrication, and tooling of masks is a primary source of recurring and nonrecurring production costs. The objective of this joint effort, therefore, is to reduce or eliminate the need for masks. AEEP improves selective plating processes by using directed beams of high-intensity acoustic waves to create nonlinear effects that alter the fluid dynamic and thermodynamic behavior of the plating process. It relies on two effects: acoustic streaming and acoustic heating. Acoustic streaming is observed when a high-intensity acoustic beam creates a liquid current within the beam. The liquid current can be directed as the beam is directed and, thus, users can move liquid around as desired without using pumps and nozzles. The current of the electroplating electrolyte, therefore, can be directed at distinct target areas where electroplating is desired. The current delivers fresh electrolyte to the target area while flushing away the spent electrolyte. This dramatically increases the plating rate in the target area. In addition, acoustic heating of both the liquid in the beam and the target surface increases the chemical reaction rate, which further increases the plating rate. The combined effects of acoustic streaming and heating accelerate the deposition of plating in that area and, thus, provide an effect similar to a mask but without the costs of masking. AEEP further improves the plating process by clearing debris and bubbles from the surface by acoustic radiation pressure and acoustic streaming.

Oeftering, Richard C.↗

NASA NTRS1985

Evolution and interaction of large interplanetary streams

A computer simulation for the evolution and interaction of large interplanetary streams based on multi-spacecraft observations and an unsteady, one-dimensional MHD model is presented. Two events, each observed by two or more spacecraft separated by a distance of the order of 10 AU, were studied. The first simulation is based on the plasma and magnetic field observations made by two radially-aligned spacecraft. The second simulation is based on an event observed first by Helios-1 in May 1980 near 0.6 AU and later by Voyager-1 in June 1980 at 8.1 AU. These examples show that the dynamical evolution of large-scale solar wind structures is dominated by the shock process, including the formation, collision, and merging of shocks. The interaction of shocks with stream structures also causes a drastic decrease in the amplitude of the solar wind speed variation with increasing heliocentric distance, and as a result of interactions there is a large variation of shock-strengths and shock-speeds. The simulation results shed light on the interpretation for the interaction and evolution of large interplanetary streams. Observations were made along a few limited trajectories, but simulation results can supplement these by providing the detailed evolution process for large-scale solar wind structures in the vast region not directly observed. The use of a quantitative nonlinear simulation model including shock merging process is crucial in the interpretation of data obtained in the outer heliosphere.

Whang, Y. C.↗

NASA NTRS1975

Vaporization response of evaporating drops with finite thermal conductivity

A numerical computing procedure was developed for calculating vaporization histories of evaporating drops in a combustor in which travelling transverse oscillations occurred. The liquid drop was assumed to have a finite thermal conductivity. The system of equations was solved by using a finite difference method programmed for solution on a high speed digital computer. Oscillations in the ratio of vaporization of an array of repetitivity injected drops in the combustor were obtained from summation of individual drop histories. A nonlinear in-phase frequency response factor for the entire vaporization process to oscillations in pressure was evaluated. A nonlinear out-of-phase response factor, in-phase and out-of-phase harmonic response factors, and a Princeton type 'n' and 'tau' were determined. The resulting data was correlated and is presented in graphical format. Qualitative agreement with the open literature is obtained in the behavior of the in-phase response factor. Quantitatively the results of the present finite conductivity spray analysis do not correlate with the results of a single drop model.

Agosta, V. D.↗

NASA NTRS1973

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

Shih, C. C.↗

NASA NTRS1979

Amplification of Reynolds number dependent processes by wave distortion

The amplification of a Reynolds number dependent process by wave distortion and the possibility of applying the results to other similar Reynolds number dependent processes were investigated. The process investigated was that associated with the operation of a constant-temperature hot-wire anemometer. The application of vaporization limited combustion, the type of combustion typically associated with liquid propellant rocket engines, was studied. A series of experiments were carried out to determine the effect of wave distortion on a Reynolds number dependent process and to establish the analogy between the anemometer process and the combustion process. Parametric trends, behavior common to different chamber geometries, and stability boundaries were identified. The results indicate a high degree of similarity between the two processes and the possibility of using the anemometer system to investigate combustion instability. The nonlinear aspects of a Reynolds number dependent process appear to be the dominant mechanisms controlling instability.

Ventrice, M.↗

DOE OSTI2025

Exciton dressing by extreme nonlinear magnons in a layered semiconductor

Collective excitations presenting nonlinear dynamics are fundamental phenomena with broad applications. A prime example is nonlinear optics, where diverse frequency mixing processes are central to communication, sensing, wavelength conversion, and attosecond physics. Leveraging recent progress in van der Waals magnetic semiconductors, we demonstrate nonlinear opto-magnonic coupling by presenting exciton states dressed by up to 20 harmonics of magnons, resulting from their nonlinearities, in the layered antiferromagnetic semiconductor CrSBr. We also create tunable optical side bands from sum- and difference-frequency generation between two optically bright magnon modes under symmetry breaking magnetic fields. Moreover, the observed difference-frequency generation mode can be continuously tuned into resonance with one of the fundamental magnons, resulting in parametric amplification of magnons. These findings realize the modulation of the optical frequency exciton with the extreme nonlinearity of magnons at microwave frequencies, which could find applications in magnonics and hybrid quantum systems, and provide new avenues for implementing opto-magnonic devices.

Diederich, Geoffrey M.↗

DOE OSTI2023

Plasmonic Nonlinear Energy Transfer Enhanced Second Harmonic Generation Nanoscopy

Nonlinear optical response is a fingerprint of various physicochemical properties of materials related to symmetry, including crystallography, interfacial configuration, and carrier dynamics. However, the intrinsically weak nonlinear optical susceptibility and the diffraction limit of far-field optics restrict probing deep-subwavelength-scale nonlinear optics with measurable signal-to-noise ratio. Here, we propose an alternative approach toward efficient second harmonic generation (SHG) nanoscopy for SHG-active sample (zinc oxide nanowire; ZnO NW) using an SHG-active plasmonic nanotip. Our full-wave simulation suggests that the experimentally observed high near-field SHG contrast is possible when the nonlinear response of ZnO NW is enhanced and/or that of the tip is suppressed. Here, this result suggests possible evidence of quantum mechanical nonlinear energy transfer between the tip and the sample, modifying the nonlinear optical susceptibility. Further, this process probes the nanoscale corrosion of ZnO NW, demonstrating potential use in studying various physicochemical phenomena in nanoscale resolution.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Magnetic Energy Conversion in Magnetohydrodynamics: Curvature Relaxation and Perpendicular Expansion of Magnetic Fields

Abstract The mechanisms and pathways of magnetic energy conversion are an important subject for many laboratory, space, and astrophysical systems. Here, we present a perspective on magnetic energy conversion in magnetohydrodynamics through magnetic field curvature relaxation (CR) and perpendicular expansion (PE) due to magnetic pressure gradients, and quantify their relative importance in two representative cases, namely 3D magnetic reconnection and 3D kink-driven instability in an astrophysical jet. We find that the CR and PE processes have different temporal and spatial evolutions in these systems. The relative importance of the two processes tends to reverse as the system enters the nonlinear stage from the instability growth stage. Overall, the two processes make comparable contributions to magnetic energy conversion, with the PE process somewhat stronger than the CR process. We further explore how these energy conversion terms can be related to particle energization in these systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Space-Charge Aberrations in Single-Shot Time-Resolved Transmission Electron Microscopy

In this paper, we discuss effects of space-charge fields on imaging performance in a single-shot time-resolved transmission electron microscope. Using a Green’s function perturbation method, we derive analytical estimates for the effects of space-charge nonlinearity on the image formation process and the associated aberration coefficients. The dependence of these coefficients on the initial beam phase space distribution is elucidated. The results are validated by particle tracking simulations and provide fundamental scaling laws for the trade-off between temporal and spatial resolutions in single-shot time-resolved transmission electron microscopy.

43 PARTICLE ACCELERATORS↗