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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Effect of Grain Shape and Relative Humidity on the Nonlinear Elastic Properties of Granular Media

Abstract This study focuses on unraveling the microphysical origins of the nonlinear elastic effects, which are pervasive in the Earth's crust. Here, we examine the influence of grain shape on the elastic nonlinearity of granular assemblies. We find that the elastic nonlinearity of angular sand particles is of the same order of magnitude as that previously measured in spherical glass beads. However, while the elastic nonlinearity of glass beads increases by an order of magnitude with RH that of sand particles is rather RH independent. We attribute this difference to the angularity of sand particles: absorbed water on the spherical grains weakens the junctions making them more nonlinear, while no such effect occurs in sand due to grain interlocking. Additionally, for one of the nonlinear parameters that likely arises from shearing/partial slip of the grain junctions, we observe a sharp amplitude threshold in sand which is not observed in glass beads.

58 GEOSCIENCES↗
DOE OSTI2024

Why Do Oceanic Nonlinearities Contribute Only Weakly to Extreme El Niño Events?

Abstract Extreme El Niño events have outsized global impacts and control the El Niño Southern Oscillation (ENSO) warm/cold phases asymmetries. Yet, a consensus regarding the relative contributions of atmospheric and oceanic nonlinearities to their genesis remains elusive. Here, we isolate the contribution of oceanic nonlinearities by conducting paired experiments forced with opposite wind stress anomalies in an oceanic general circulation model, which realistically simulates extreme El Niño events and oceanic nonlinearities thought to contribute to ENSO skewness (Tropical Instability Waves (TIWs), Nonlinear Dynamical Heating (NDH)). Our findings indicate a weak contribution of oceanic nonlinearities to extreme El Niño events in the eastern Pacific, owing to compensatory effects between lateral (NDH and TIWs) and vertical processes. These results hold across different vertical mixing schemes and modifications of the upper‐ocean heat budget mixed layer criterion. Our study reinforces previous research underscoring the pivotal role of atmospheric nonlinearities in shaping extreme El Niño events.

Geology↗
DOE OSTI2022

Enhancing high-fidelity nonlinear solver with reduced order model

Abstract We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM’s prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards’ equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM’s accuracy while speeding up nonlinear solver by 18–73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM’s prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM’s accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Determination of acoustic nonlinearity parameters using thermal modulation of ultrasonic waves

This study presents a test method and its theoretical framework to determine the acoustic nonlinearity parameters (α, β, δ) of material using thermal modulation of ultrasonic waves. Temperature change-induced thermal strain excites the nonlinear response of the material and modulates the ultrasonic wave propagating in it. Experimental results showed a strong correlation between the relative wave velocity change and the temperature change. With a quadratic polynomial model, the acoustic nonlinearity parameters were obtained from the polynomial coefficients by curve fitting the experimental data. Their effects on thermal-induced velocity change were discussed. The parameters α, β, and δ govern the hysteretic gap, average slope, and curvature of the correlation curve, respectively. The proposed theory was validated on aluminum, steel, intact and damaged concrete samples. The obtained nonlinear parameters show reasonable agreement with values reported in the literature. Compared to other nonlinear acoustic methods using vibration or acoustic excitation, the thermal modulation method generates more uniform, slow changing, and larger strain field in the test sample. Employing the thermal effect as the driving force for nonlinearity instead of an undesired influencing factor, this method can measure the absolute values of α, β, and δ with good accuracy using a simple ultrasonic test setup.

Physics↗
DOE OSTI2022

Effect of relative humidity on the nonlinear elastic response of granular media

We study the influence of relative humidity (RH) on the nonlinear elastic response of granular media. Previous work has shown that the nonlinear elastic response of consolidated granular media like rocks likely arises from two distinct mechanisms; however, we do not have a clear understanding of their physical origins at the microscopic scale. Here, we conduct dynamic acousto-elastic testing (DAET) on samples of glass beads under dry (~10%), ambient (~60%), and humid (~100%) conditions at room temperature and a constant static stress of 4 MPa. DAET allows us to retrieve the full nonlinear elastic response, including transient softening and hysteretic effects. We find that the elastic nonlinearity of humid samples is an order of magnitude larger than dry samples. Moreover, we find that all extracted nonlinear parameters increase with RH. This overall increase in nonlinearity is consistent with findings from previous studies and with the hypothesis that water adsorption on the grains makes the contact junctions weaker and prone to greater disturbances when subjected to dynamic stressing. Our results also suggest that, if indeed both mechanisms coexist, they are affected in a similar fashion in these glass bead samples and cannot be distinguished by varying RH.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Cross-beam energy transfer in direct-drive ICF. I. Nonlinear and kinetic effects

Results are presented from a series of simulations examining the susceptibility of the cross-beam energy transfer (CBET) instability to nonlinear processes in the context of direct-drive inertial confinement fusion experiments on the OMEGA laser facility. These form the basis for the second paper of this series [A. G. Seaton, L. Yin, R. Follett, B. J. Albright, and A. Le, “Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth,” Phys. Plasmas 29, 042707 (2022)], where we examine the efficacy of increases in laser bandwidth at suppressing CBET. We choose laser and plasma conditions for the simulations that are favorable to CBET and promote nonlinearity. Through a comparison of outputs from the particle-in-cell code vector particle in cell (VPIC) and the linearized fluid code laser-plasma simulation environment (LPSE), a series of nonlinear effects have been identified in the kinetic simulations that include particle trapping, the two-ion wave decay, and ion-acoustic wave self-focusing. These effects produce time-dependent energy transfer, in contrast to the linearized fluid simulations in which a steady state is reached after an initial transient. Ion trapping is shown to allow for increased energy transfer relative to fluid simulations, with the remaining nonlinear processes acting to reduce the energy transfer. Nonlinear dynamics is contrasted for low- and high-intensity beams as well as between speckled and planar beams. For the parameters under consideration, beam profile has a significant effect on nonlinear dynamics, though the greatest sensitivity is to beam intensity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer

The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Nonlinear simulations of GAEs in NSTX-U

A set of nonlinear simulations has been performed in order to study the nonlinear evolution of unstable global Alfvén eigenmodes in the National Spherical Torus Experiment-Upgrade (NSTX-U). Results of the single toroidal mode number, n, simulations are compared with a full nonlinear simulation (all toroidal harmonics included). In single-n simulations, the conservation of two integrals of motion of a particle in a cyclotron resonance with a monochromatic wave is demonstrated, resulting in a one-dimensional evolution of the particle distribution in (E,μ,pϕ) phase-space. Nonlinear simulations (both single-n and full nonlinear) show a significant redistribution of the resonant fast ions, especially in the pitch parameter. Thus, the changes in the resonant particle's parallel and perpendicular energies can be several times larger than the total particle energy change, with only a small fraction transferring into the excitation of the mode itself. This implies that even a relatively small amplitude mode can significantly modify the beam distribution in the resonant region. For the NSTX-U case considered, the single-n simulation results are close to full nonlinear simulation only for the most unstable mode, in which case the saturation amplitudes and changes in the fast ion distribution are comparable. In contrast, peak amplitudes of subdominant modes in all-n simulations are smaller by a factor of 3–10 compared to single-n runs due to the flattening of the beam ion distribution by the fastest growing mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Similarity properties in capacitive radio frequency plasmas with nonlinear collision processes

Abstract Similarity laws (SL) are essential for correlating the characteristics of plasmas at different dimensional scales, which have been validated for radio frequency (rf) discharges at low pressure but under limited conditions. In this work, we evaluate the effects of nonlinear collisions (e.g. stepwise ionization) on the similarity properties in capacitive rf discharges in argon across a wide range of pressure regimes via fully kinetic particle-in-cell simulations. The SL scalings of fundamental discharge parameters, e.g. the electron power absorption and electron energy probability function, are examined with and without nonlinear collisions, respectively. Without the nonlinear collisions, the similarity scalings are found to be rigorously valid. When the nonlinear collisions are considered, the similarity properties in rf discharges still exist approximately, which indicates that the violations caused by the nonlinear collisions are still minor in the studied cases. The reasons for the effectiveness of SL scalings with nonlinear collision processes are also discussed. The results from this study confirmed the validity of similarity transformations with more complex reaction kinetics, which may promote the applicability of the SL scalings for the design and fabrications of plasma devices.

Physics↗
DOE OSTI2025

Improved bound on nonlinear quantum mechanics using a cryogenic radio frequency experiment

There are strong arguments that quantum mechanics may be nonlinear in its dynamics. A discovery of nonlinearity would hint at a novel understanding of the interplay between gravity and quantum field theory, for example. As such, experiments searching for potential nonlinear effects in the electromagnetic sector are important. Here, in this study, we outline such an experiment, consisting of a stream of random bits (which were generated using Rigetti’s Aspen-M-3 chip) as input to an rf signal generator coupled to a cryogenic detector. Projective measurements of the qubit state, which is originally prepared in an equal superposition, serve as the random binary output of a signal generator. Thereafter, spectral analysis of the rf detector would yield a detectable excess signal predicted to arise from such a nonlinear effect. A comparison between the projective measurements of the quantum bits vs the classical baseline showed no power excess. This sets a new limit on the electromagnetic nonlinearity parameter |ε| ⪅ 1.15 x 10 -12 , at a 90.0% confidence level. This is the most stringent limit on nonlinear quantum mechanics thus far and an improvement by nearly a factor of 50 over the previous experimental limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Adaptive nonlinear wavefront shaping in layered TMDs

Two-dimensional transition metal dichalcogenides are promising candidates for nonlinear photonics applications, offering strong nonlinear susceptibility and compatibility with integrated platforms. Although considerable effort has been devoted to manipulating second harmonic generation in these materials, the dynamic control of nonlinear wavefronts remains largely unexplored. Metasurfaces have enabled significant progress in nonlinear beam engineering, yet their practical implementation is limited by low conversion efficiencies and restricted design flexibility. In this work, we employ feedback-based wavefront shaping using spatial light modulators to enhance SHG from pyramid-like WS 2 multilayer structures by over three orders of magnitude in selected spatial regions. This approach allows us to program nonlinear holograms and dynamically shape the SHG signal through phase-only modulation, opening new possibilities for nonlinear imaging, optical information processing, and data communication.

Mavian, Alex [Rensselaer Polytechnic Inst., Troy, ↗
DOE OSTI2024

Ultrafast temporal phase-resolved nonlinear optical spectroscopy in the molecular frame

In an ultrafast nonlinear optical interaction, the electric field of the emitted nonlinear signal provides direct access to the induced nonlinear transient polarization or transient currents and thus carries signatures of ultrafast dynamics in a medium. Measurement of the electric field of such signals offers sensitive observables to track ultrafast electron dynamics in various systems. In this work, we resolve the real-time phase of the electric field of a femtosecond third-order nonlinear optical signal in the molecular frame. The electric field emitted from impulsively pre-aligned gas-phase molecules at room temperature, in a degenerate four-wave mixing scheme, is measured using a spectral interferometry technique. The nonlinear signal is measured around a rotational revival to extract its molecular-frame angle dependence from pump-probe time-delay scans. By comparing these measurements for two linear molecules, carbon dioxide and nitrogen, we show that the measured second-order phase parameter (temporal chirp) of the signal is sensitive to the valence electronic symmetry of the molecules, whereas the amplitude of the signal does not show such sensitivity. We compare measurements to theoretical calculations of the chirp observable in the molecular frame. This work is an important step towards using electric field measurements in nonlinear optical spectroscopy to study ultrafast dynamics of electronically excited molecules in the molecular frame.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets

Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2022

Focusing Ions at Atmospheric Pressure using Nonlinear DC Voltage Sequences Applied to a Stacked Ring Ion Guide

Many modern ion mobility (IM) and mass spectrometers (MS) operate under low pressure (= 10 Torr) and employ high voltage radiofrequencies (RF) to provide ion confinement. Unfortunately, RF effectiveness drastically decreases as pressure increases, and few techniques for focusing ions at elevated pressures exist. Here we demonstrate a new approach for focusing ions at atmospheric pressure (AP) by applying nonlinear DC voltage sequences following quadratic and power (exponential) functions to a stacked ring ion guide. We used ion trajectory simulations to rigorously explore how ions react to nonlinear electric fields and validate the simulations with a set of ion current measurements performed at AP. Ion trajectory simulations show that ions initially defocus near the entrance of the device but then become intensely focused as they travel through the device. Contour plots for both nonlinear voltage sequences show electric field lines that increasingly curve inwards as a function of distance, resulting in spatial ion focusing. Experimental ion current and spot size measurements were performed at AP using a 10-cm stacked ring ion guide and a segmented Faraday cup detector. Quadratic sequences produced ~5% smaller spot sizes (~22.8 mm) and ~25% higher ion current compared to a linear voltage sequence (~24.0 mm). Alternatively, power sequences produced ~64% smaller spot sizes (~8.7 mm), albeit with ~10x lower ion current. However, both nonlinear voltage sequences produced similar ion currents at the center of the Faraday cup detector, indicating that higher ion densities are achieved when using nonlinear voltage gradients. These results demonstrate a new way to focus ions at AP, and the capabilities demonstrated here provide fundamental insights on how to keep ions inside analytical devices at elevated pressures without RF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2026

Nonlinear viscoelastic response of silicone additively manufactured direct ink write (DIW) foams under repetitive compression

To investigate dynamic fatigue behavior of foam in military protective applications, such as helmets, additively manufactured (AM) foams were compressively strained into the plateau region using a reduced design of experiments. A simple power law was found to govern the decline in dynamic stiffness (complex modulus) as the foams underwent the purchase order requirement of 10,000 cycles of small deformation in the plateau region. This rate of decline was newly found to correlate with the degree of nonlinearity in the material’s deformation, quantified using total harmonic distortion. Materials with low nonlinearity exhibited relatively stable stiffness across cycles, while those with high nonlinearity experienced greater losses. The observed nonlinearity depended on both applied stress and strain rate. A strong linear correlation (R 2 = 0.78) was identified between second-order nonlinearity and the time-dependent stiffness response. Two lattice structures were examined: face-centered tetragonal (FCT) and simple cubic (SC). The SC material exhibited higher total harmonic distortion (5%) and lower stiffness retention than the FCT (2%). In conclusion, these results suggest that for cyclic compression applications in a wide variety of industries such as packaging, personal protective equipment, or aerospace, selecting materials with lower stress and greater structural uniformity can enhance the stability of dynamic performance.

42 ENGINEERING↗
DOE OSTI2024

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗