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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

In-situ fatigue monitoring procedure using nonlinear ultrasonic surface waves considering the nonlinear effects in the measurement system

Second harmonic generation using nonlinear ultrasonic waves have been shown to be an early indicator of possible fatigue damage in nuclear power plant components. This technique relies on measuring amplitudes, making it highly susceptible to variations in transducer coupling and instrumentation. This paper proposes an experimental procedure for in-situ surface wave nonlinear ultrasound measurements on specimen with permanently mounted transducers under high cycle fatigue loading without interrupting the experiment. It allows continuous monitoring and minimizes variation due to transducer coupling. Moreover, relations describing the effects of the measurement system nonlinearity including the effects of the material transfer function on the measured nonlinearity parameter are derived. An in-situ high cycle fatigue test was conducted using two 304 stainless steel specimens with two different excitation frequencies. A comprehensive analysis of the nonlinear sources, which result in variations in the measured nonlinearity parameters, was performed and the effects of the system nonlinearities are explained and identified. In both specimens, monotonic trend was observed in nonlinear parameter when the value of fundamental amplitude was not changing.

42 ENGINEERING↗
DOE OSTI2014

Nonlinear development of the two-plasmon decay instability in three dimensions

Most recent experiments on the excitation of the two plasmon-decay (TPD) instability involve a three-dimensional (3D) array of overlapping laser beams. Our recent two dimensional (2D) simulations suggested that Langmuir cavitation and collapse are important nonlinear saturation mechanisms for TPD. There are important quantitative differences in the Langmuir collapse process in 2D and 3D. To address these and other issues, we have developed a 3D Zakharov code. It has been applied to study the evolution of TPD from absolute instabilities (arising from 3D laser geometries) to the nonlinear state (J. Zhang et al., Phys. Rev. Lett. (submitted)). The present paper concentrates on the nonlinear saturated state excited by the collective action of two crossed laser beams with arbitrary polarizations. Remarkable agreement between 3D and 2D simulations is found for several averaged physical quantities when the beams are polarized in their common plane. As in the previous 2D simulations, we find: (a) the collective, initially convectively unstable triad modes dominate after a sub-picosecond burst, (b) Langmuir cavitation and collapse are important nonlinearities, and (c) that the statistics of intense cavitons are characteristic of a Gaussian random process. The 3D steady-state saturated Langmuir energy level is about 30% higher than in 2D. The auto-correlation functions of the Langmuir envelope field and of the low-frequency electron density field yield the spatial shape of the strongest collapsing cavitons which are 3D ellipsoids whose orientation depends on the laser polarizations. This tilting of the caviton's strongest electric field direction away from the normal to the target surface is a major new 3D result. This tilting may deflect the hot electron flux and thereby mitigate target preheat.

Vu, H. X.↗
DOE OSTI2015

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a one-waveguide array with either a cubic or quadratic nonlinearity.

Efremidis, Nikolaos K. (ORCID:0000000298300268)↗
DOE OSTI2015

Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from previous studies, we analyze turbulence dynamics in Fourier (k-) space to understand its sustenance. The linear growth of the MRI with the azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fourier space—the nonlinear transverse cascade—rather than the usual direct/inverse cascade. We demonstrate that the turbulence is sustained by the interplay of the linear transient growth of the MRI (which is the only energy supply for the turbulence) and the transverse cascade. These two processes operate at large length scales, comparable to the box size (disk scale height); the corresponding small wavenumber area, called the vital area in Fourier space, is crucial for the sustenance, while outside the vital area, direct cascade dominates. The interplay of the linear and nonlinear processes in Fourier space is generally too intertwined for a vivid schematization. Nevertheless, we reveal the basic subcycle of the sustenance that clearly shows the synergy of these processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered different aspect ratios of the simulation boxes. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universality of the sustenance mechanism of the MRI turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Nonlinear controller for nonlinear wave energy converters

The present invention is directed to a nonlinear controller for nonlinear wave energy converters (WECs). As an example of the invention, a nonlinear dynamic model is developed for a geometrically right-circular cylinder WEC design for the heave-only motion, or a single degree-of-freedom (DOF). The linear stiffness term is replaced by a nonlinear cubic hardening spring term to demonstrate the performance of a nonlinear WEC as compared to an optimized linear WEC. By exploiting the nonlinear physics in the nonlinear controller, equivalent power and energy capture, as well as simplified operational performance is observed for the nonlinear cubic hardening spring controller when compared to an optimized linear controller.

Wilson, David G.↗
DOE OSTI2018

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Nonlinear ultrasonic response of voids and Cu precipitates in body-centered cubic Fe

Interpreting nonlinear ultrasonic signals detected in nondestructive evaluation of radiation damage needs the knowledge of the correlation between defects and nonlinearity. In this work, molecular dynamics simulations are performed to study the effect of distributed vacancies, voids, Cu atoms, and Cu precipitates on nonlinear ultrasonic response in body-centered cubic (bcc) Fe. The nonlinearity parameter calculated from the second harmonic amplitude in the perfect lattice is 2.73. Vacancies are found to increase the nonlinearity. Surprisingly, clusters of vacancies in the form of spherical voids show an opposite effect. This finding can be used to conveniently distinguish vacancies from voids in the material. Unlike vacancies, individual Cu atoms decrease the nonlinearity. Clustering of Cu atoms into Cu precipitates further decrease the nonlinearity. Interestingly, precipitates with a diameter of 2 nm and larger exhibit a similar effect despite their different structure and coherency with the Fe matrix.

Setyawan, Wahyu↗
DOE OSTI2014

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins

This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Electron scattering and nonlinear trapping by oblique whistler waves: The critical wave intensity for nonlinear effects

In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonlinear parallel momentum transport in strong electrostatic turbulence

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux-〈v{sup ~}{sub r}n{sup ~}u{sup ~}{sub ∥}〉. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges

Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗