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NASA NTRS2002

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Powers, Lynn M.↗

DOE OSTI2021

Exact results for nonlinear Drude weights in the spin-1/2 XXZ chain

Nonlinear Drude weight (NLDW) is a generalization of the linear Drude weight, which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-1/2 XXZ chain in the critical regime. The effects of the Dzyaloshinskii-Moriya interaction and an external magnetic field are also studied. Solving the Bethe equations numerically, we obtain these weights for very large system sizes and identify parameter regimes where the weights diverge in the thermodynamic limit. These divergences appear in all the orders studied in this Letter and can be regarded as a generic feature of the NLDWs. We study the origin of these divergences and reveal that they result from nonanalytic finite-size corrections to the ground-state energy. As a result, we compute closed-form expressions for several weights in the thermodynamic limit and find excellent agreement with the numerical results.

1-dimensional systems↗

NASA NTRS2000

Wormhole Formation in RSRM Nozzle Joint Backfill

The RSRM nozzle uses a barrier of RTV rubber upstream of the nozzle O-ring seals. Post flight inspection of the RSRM nozzle continues to reveal occurrence of "wormholes" into the RTV backfill. The term "wormholes", sometimes called "gas paths", indicates a gas flow path not caused by pre-existing voids, but by a little-understood internal failure mode of the material during motor operation. Fundamental understanding of the mechanics of the RSRM nozzle joints during motor operation, nonlinear viscoelastic characterization of the RTV backfill material, identification of the conditions that predispose the RTV to form wormholes, and screening of candidate replacement materials is being pursued by a joint effort between Thiokol Propulsion, NASA, and the Army Propulsion & Structures Directorate at Redstone Arsenal. The performance of the RTV backfill in the joint is controlled by the joint environment. Joint movement, which applies a tension and shear load on the material, coupled with the introduction of high pressure gas in combination create an environment that exceeds the capability of the material to withstand the wormhole effect. Little data exists to evaluate why the material fails under the modeled joint conditions, so an effort to characterize and evaluate the material under these conditions was undertaken. Viscoelastic property data from characterization testing will anchor structural analysis models. Data over a range of temperatures, environmental pressures, and strain rates was used to develop a nonlinear viscoelastic model to predict material performance, develop criteria for replacement materials, and quantify material properties influencing wormhole growth. Three joint simulation analogs were developed to analyze and validate joint thermal barrier (backfill) material performance. Two exploratory tests focus on detection of wormhole failure under specific motor operating conditions. A "validation" test system provides data to "validate" computer models and predictions. Finally, two candidate replacement materials are being screened and "validated" using the developed test systems.

Stevens, J.↗

DOE OSTI2023

Accelerator Physics at NSLS-II: Research Accomplishments in 2023

NSLS-II accelerator physicists provided operation support for user operations and machine start-ups, carried out routine lattice characterization, and produced regular reports on beam dynamics. The commissioning of a superconducting wiggler for the HEX beamline is complete, and the wiggler effects on beam dynamics have been studied. A Facility Improvement Project for absolute lattice characterization has been approved and funded. We implemented and tested a new orbit-based technique of lattice characterization and correction. We developed a theory to calculate the beam-induced power in ceramic vacuum chambers and a new convergence map technique for nonlinear lattice characterization. We continued working on the NSLS-II upgrade including lattice development, commissioning a low-energy complex bend prototype, analyzing beam sensitivity to various errors, implementing higher-harmonic RF cavities, studying collective effects, and assessing FEL options. We also supported lattice optimization and beam diagnostics development for the EIC project. Main research accomplishments achieved in 2023, are summarized in this report.

43 PARTICLE ACCELERATORS↗

NASA NTRS1994

Channel to energy calibration results for the BATSE large area detectors

Continuum 16 channel spectra obtained from in flight data are used to identify and correct for nonlinearities in the channel-to-energy conversion algorithm for the BATSE large area detectors. The Crab Nebula spectra obtained by the BATSE earth occultation technique are used to characterize any nonlinearities inherent in the low energy channel bin widths on a detector by detector basis. The bin widths are optimized to remove distortions from observed gamma ray spectra. The recalibrated bin edges are used in an analysis of Crab Pulsar data to verify the improvements in the calibration.

Pendleton, Geoffrey N.↗

DOE OSTI2024

Time-resolved biphase signatures of quadratic nonlinearity observed in coupled Alfvén eigenmodes on the DIII-D tokamak

We report the detection of nonstationary quadratic coupling between toroidicity-induced Alfvén eigenmodes (TAEs) on sub-millisecond time scales. Identification of phase coherency between multiple TAEs and nonlinearly generated modes is facilitated by wavelet-based bicoherence analysis of time-series from inductive coils, taken from a DIII-D discharge heated by neutral beam injection (NBI). Characterization of nonlinear three-wave interaction is inferred by stationary local bispectrum phase (biphase) and confirmed via bandpass filtering. Biphase dynamics associated with prominent bispectral features are well-resolved in time and consistent with transient quadratic coupling. Onset and duration of nonlinearity are correlated with enhanced amplitude of participating TAEs; coincident changes in amplitude are observed for modes at difference frequency |f TAE,1 - f TAE,2 |.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Demonstration of the DC-Kerr effect in silicon-rich nitride

We demonstrate the DC-Kerr effect in plasma enhanced chemical vapor deposition (PECVD) silicon-rich nitride (SRN) and use it to demonstrate a third order nonlinear susceptibility, χ (3) , as high as (6 ± 0.58) × 10 -19 m 2 /V 2 . We employ spectral shift versus applied voltage measurements in a racetrack resonator as a tool to characterize the nonlinear susceptibilities of these films. In doing so, we demonstrate a χ (3) larger than that of silicon and argue that PECVD SRN can provide a versatile platform for employing optical phase shifters while maintaining a low thermal budget using a deposition technique readily available in CMOS process flows.

42 ENGINEERING↗

DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗

NASA NTRS1991

Formulation of the linear model from the nonlinear simulation for the F18 HARV

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

Hall, Charles E., Jr.↗

DOE OSTI2021

Nonlinear signal distortion corrections through quantum sensing

Having accurate gate generation is essential for precise control of a quantum system. The generated gate usually suffers from linear and nonlinear distortion. Previous works have demonstrated how to use a qubit to correct linear frequency distortions but have not commented on how to handle nonlinear distortions. This is an important issue as we show that nonlinear amplitude distortions from the RF electronics can affect Rabi pulses by as much as 10%. We present work that demonstrates how a transmon qubit can be used as a highly sensitive cryogenic detector to characterize these nonlinear amplitude distortions. We show that a correction can drive these errors down to <1% over a 700 MHz range. The correction technique provides a method to minimize the effects of signal distortions and can be easily applied to broadband control pulses to produce higher fidelity arbitrary quantum gates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Characterizing non-polarization-maintaining highly nonlinear fiber toward squeezed-light generation

Squeezed light, which is easily degraded by loss, could benefit from generation directly in optical fiber. Furthermore, highly nonlinear fiber could offer more efficient generation with lower pump power and shorter fiber lengths than standard single-mode fiber. We investigate non-polarization-maintaining highly nonlinear fiber (HNLF) for squeezed-light generation by characterizing possible sources of excess noise, including its zero-dispersion wavelength (ZDW) variation and polarization noise. We find significant ZDW variation and excess polarization noise. We believe the polarization noise is from non-linear polarization-mode dispersion. We model this polarization noise and find that it is likely to degrade Kerr squeezing but not squeezing from four-wave mixing.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗

DOE OSTI2026

Ultrasonic Resonance Techniques for Materials Research

Mechanical resonances are directly related to the physical behavior of a system at the bulk and microscopic levels. In materials science, resonant ultrasound spectroscopy (RUS) has long been a preferred nondestructive method to study mechanical resonances of solids and precisely measure quantitative material properties, namely elasticity. In recent years, advances in computational power and hardware have enabled RUS to be relevant for an increasing range of applications, such as advanced manufacturing. An extension of this technique, nonlinear RUS (NRUS), has been demonstrated to provide unmatched sensitivity to early-stage damage. NRUS was originally developed to probe geologic materials but has become a vital tool in nondestructive evaluation and materials research, offering a powerful means of quantifying and characterizing microstructural nonlinearity in a broad range of materials. This review summarizes recent developments and growth opportunities in RUS and NRUS techniques, modeling, and applications across a wide range of material systems including metals, composites, geomaterials, and explosives.

36 MATERIALS SCIENCE↗

NASA NTRS2007

Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver

A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.

Kuruvila, Geojoe↗

NASA NTRS1990

Tensile stress acoustic constants of unidirectional graphite/epoxy composites

Previously, the stress acoustic constants (SACs) of unidirectional graphite/epoxy composites were measured to determine the nonlinear moduli of this material. These measurements were made under compressive loading in order to obtain the sufficient number of values needed to calculate these moduli. However, because their strength in tension along fiber directions can be several times greater, most composites are used under tensile loading. Thus, it is important to characterize the nonlinear properties of these materials in tension as well. The SACs which are defined as the slope of the normalized change in ultrasonic 'natural' velocity as a function of stress were measured in a unidirectional laminate of T300/5208 graphite/epoxy. Tensile load was applied along the fiber axis with the ultrasonic waves propagating perpendicular to the fiber direction. Changes in velocity were measured using a pulsed phase locked loop ultrasonic interferometer with the nominal frequency of the ultrasonic waves being 2.25 MHz.

Prosser, W. H.↗

NASA NTRS1990

Tensile Stress Acoustic Constants of Unidirectional Graphite/Epoxy Composites

Previously, the stress acoustic constants (SAC's) of unidirectional graphite/epoxy composites were measured to determine the nonlinear moduli of this material. These measurements were made under compressive loading in order to obtain the sufficient number of values needed to calculate these moduli. However, because their strength in tension along fiber directions can be several times greater, most composites are used under tensile loading. Thus, it is important to characterize the nonlinear properties of these materials in tension as well. The SAC's which are defined as the slope of the normalized change in ultrasonic "natural" velocity as a function of stress were measured in a unidirectional laminate of T300/5208 graphite/epoxy. Tensile load was applied along the fiber axis with the ultrasonic waves propagating perpendicular to the fiber direction. Changes in velocity were measured using a pulsed phase locked loop ultrasonic interferometer with the nominal frequency of the ultrasonic waves being 2.25 MHz.

Prosser, W. H.↗

NASA NTRS2011

Assessment of MODIS Thermal Emissive Band On-Orbit Calibration

Sixteen Moderate Resolution Imaging Spectroradiometer thermal emissive bands (TEBs) cover the wavelength from 3.75 to 14.24 m. TEB calibration uses data collected from the detector responses to the onboard blackbody (BB) and space view. The BB was designed to operate either at a constant temperature for detector linear gain calibration or at temperatures varying from ambient ( 270 K) to 315 K for on-orbit characterization of nonlinear coefficients. In this paper, we assess TEB on-orbit calibration performance in two aspects: One is to review the calibration trending on the orbital, daily, and multiyear timescales, and the other is to analyze the on-orbit calibration radiance uncertainty and its impact on the calibration. The calibration trending confirms the detector response dependence on the instrument temperature. The temperature trending and prelaunch characterization provide the basis for determining the calibration radiance source temperature range and uncertainties. An analytical approach was used to assess the impacts of onboard radiance uncertainties. The BB emission uncertainty, resulting from the temperature measurement error and emissivity uncertainty, causes a calibration uncertainty up to 0.3%, a value decreasing with the band wavelength. The BB nonblackness effect is analyzed and found to be insignificant. For the band with the lowest BB emissivity, the nonblackness affects the calibration radiance by less than 0.08%. The cavity emission uncertainty and the scan-mirror emission uncertainty both cause a less than 0.1% calibration uncertainty. The analysis of the nonlinear calibration coefficient uncertainty shows that its effect on the low Earth-view brightness-temperature range varies by band and is generally insignificant.

Chang, Tiejun↗

NASA NTRS1993

On acoustic radiation from a vibrating panel

An experimental and numerical study of the response and radiation from an acoustically loaded aircraft panel is presented. In the experiment, the panel is excited by a normally incident, harmonic wave. Measurements of the panel response and the resulting transmitted pressure are made in both the near- and acoustic far-fields. The numerical computations model the experiment and in particular account for the full coupling between the panel and the surrounding three dimensional acoustic fluid. The results demonstrate that for a sufficiently high excitation level, the panel response becomes nonlinear. The nonlinearity is characterized by the appearance of harmonics and subharmonics in the power spectral densities of the panel motion and consequently in the resulting acoustic radiation. The primary characteristic of the far-field acoustic radiation is the increase in harmonic content relative to the fundamental and subharmonics with increasing distance from the panel. This is shown to be a result of linear and weakly nonlinear wave propagation effects. The numerical results show that the radiated far-field pressure is strongly dependent on the position of the measurement point with respect to the panel center. The experimental and numerical results are in good qualitative agreement.

Frendi, Abdelkader↗