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DOE OSTI2022

Beware of fake ν ’s: The effect of massive neutrinos on the nonlinear evolution of cosmic structure

Massive neutrinos suppress the growth of cosmic structure on small, nonlinear scales. It is thus often proposed that using statistics beyond the power spectrum can tighten constraints on the neutrino mass by extracting additional information from these nonlinear scales. We study the information content regarding neutrino mass at the field level, quantifying how much of this information arises from the difference in nonlinear evolution between a cosmology with one fluid [cold dark matter (CDM)] and two fluids ( CDM + neutrinos ). We do so by running two N -body simulations, one with and one without massive neutrinos, both with the same phases, and matching their linear power spectrum at a given low redshift. This effectively isolates the information encoded in the linear initial conditions from the nonlinear cosmic evolution. We demonstrate that, for k ≲ 1 h / Mpc , and for a single redshift, there is negligible difference in the real-space CDM field between the two simulations. This suggests that all the information regarding neutrino mass is in the linear power spectrum set by the initial conditions. Thus, any probe based on the CDM field alone will have negligible constraining power beyond that which exists at the linear level over the same range of scales. Consequently, any probe based on the halo field will contain little information beyond the linear power. We find similar results for the matter field responsible for weak lensing. We also demonstrate that there may be much information beyond the power spectrum in the 3D matter field; however, this is not observable in modern surveys via dark matter halos or weak lensing. Finally, we show that there is additional information to be found in redshift space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Optical tweezer measurements of asymptotic nonlinearities in complex fluids

This article presents micro-medium-amplitude oscillatory shear (μMAOS), a method to measure the frequency-dependent micromechanical properties of soft materials in the asymptotically nonlinear regime using optical tweezers. For this work, we have developed a theoretical framework to extract these nonlinear mechanical properties of the material from experimental measurements and also proposed a physical interpretation of the third-order nonlinearities measured in single-tone oscillatory tests. We validate the method using a well-characterized surfactant solution of wormlike micelles, and subsequently employ this technique to demonstrate that the cytoplasm of a living cell undergoes strain softening and shear thinning when locally subjected to weakly nonlinear oscillatory deformations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Nonlinear Thomson scattering with ponderomotive control

In nonlinear Thomson scattering, a relativistic electron re-radiates the photons of a laser pulse, converting optical light to x rays or beyond. While this extreme frequency conversion offers a promising source for probing high-energy-density materials and driving uncharted regimes of nonlinear quantum electrodynamics, conventional nonlinear Thomson scattering has inherent tradeoffs in its scaling with laser intensity. Here we discover that the ponderomotive control afforded by spatiotemporal pulse shaping enables novel regimes of nonlinear Thomson scattering that substantially enhance the scaling of the radiated power, emission angle, and frequency with laser intensity. By appropriately setting the velocity of the intensity peak, a spatiotemporally shaped pulse can increase the power radiated by orders of magnitude. Here, the enhanced scaling with laser intensity allows for operation at significantly lower electron energies or intensities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonlinear resonances and antiresonances of a forced sonic vacuum

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Enhancement of Second-Order Nonlinear-Optical Signals by Optical Stimulation

Second-order nonlinear optical interactions such as sum- and difference-frequency generation are widely used for bioimaging and as selective probes of interfacial environments. However, inefficient nonlinear optical conversion often leads to poor signal-to-noise ratio and long signal acquisition times. We demonstrate the dramatic enhancement of weak second-order nonlinear optical signals via stimulated sum- and difference-frequency generation. We present a conceptual framework to quantitatively describe the interaction and show that the process is highly sensitive to the relative optical phase of the stimulating field. To emphasize the utility of the technique, we demonstrate stimulated enhancement of second harmonic generation (SHG) from bovine collagen-I fibrils. Using a stimulating pulse fluence of only $3\text{ }\text{ }\mathrm{nJ}/{\mathrm{cm}}^{2}$, we obtain an SHG enhancement >${10}^{4}$ relative to the spontaneous signal. The stimulation enhancement is greatest in situations where spontaneous signals are the weakest—such as low laser power, small sample volume, and weak nonlinear susceptibility—emphasizing the potential for this technique to improve signal-to-noise ratios in biological imaging and interfacial spectroscopy.

42 ENGINEERING↗
DOE OSTI2019

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges

We report the first experimental observation of nonlinear standing waves excited by plasma-series-resonance-enhanced harmonics in low pressure, very high frequency, parallel plate, capacitively coupled plasmas. Furthermore, spatial structures of the harmonics of the magnetic field, measured by a magnetic probe, are in very good agreement with simulations based on a nonlinear electromagnetics model. At relatively low pressure, the nonlinear sheath motion generates high-order harmonics that can be strongly enhanced near the series resonance frequencies. Satisfying certain conditions, such nonlinear harmonics induce radial standing waves, with voltage and current maxima on axis, resulting in center-high plasma density. Excitation of higher harmonics is suppressed at higher pressures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Truncated Nonlinear Interferometry for Quantum-Enhanced Atomic Force Microscopy

Nonlinear interferometers that replace beam splitters in Mach-Zehnder interferometers with nonlinear amplifiers for quantum-enhanced phase measurements have drawn increasing interest in recent years, but practical quantum sensors based on nonlinear interferometry remain an outstanding challenge. Here, we demonstrate the first practical application of nonlinear interferometry by measuring the displacement of an atomic force microscope microcantilever with quantum noise reduction of up to 3 dB below the standard quantum limit, corresponding to a quantum-enhanced measurement of beam displacement of 1.7 fm/√Hz. Further, we minimize photon backaction noise while taking advantage of quantum noise reduction by transducing the cantilever displacement signal with a weak squeezed state while using dual homodyne detection with a higher power local oscillator. This approach may enable quantum-enhanced broadband, high-speed scanning probe microscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Effect of directed aging on nonlinear elasticity and memory formation in a material

Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to modify dramatically the elastic properties of our systems in the nonlinear regime. Using simulations, we study two models for the microscopic evolution of properties of such a material; the first considers changes in the material strength, while the second considers distortions in the microscopic geometry. Both models capture different aspects of the experiments including the encoding of memories of the aging history of the system and the dramatic effects on the material’s nonlinear elastic properties. Our results demonstrate how aging can be used to create complex elastic behavior in the nonlinear regime.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A new route to obtain fluorescence X-ray absorption spectra of compounds and to remove the self-absorption induced nonlinearity in the spectra

A new route to obtain fluorescence X-ray absorption spectra of compounds and to remove the self-absorption induced nonlinearity in the spectra is described. The fluorescent intensity If is linearly proportional to the absorption coefficient μ. For studies of surface structures around an element (κ) the fluorescence detection is often the mode of choice. However, the measurement may suffer from a self-absorption (SA) effect which nonlinearly distorts the spectra. The effect is severe when κ is concentrated or the measurements are carried out in certain geometries. Here, the correlations among emission events in compounds are examined following resonance X-ray core-electron excitation within κ. Under conditions leading to SA, If emitted from κ apparently has a conjugated relationship with the fluorescent intensities simultaneously emitted from other elements (ξ). Normalizing the former (κ) by the latter (ξ) will largely remove SA effects and reduce this nonlinear problem to a tractable linear problem. This does result in a moderate reduction of the spectral amplitude due to the so-called secondary emission from ξ excited by the emission from κ. Nonetheless, the resulting spectra will allow one to accurately determine bond distances and disorder and, in some respects, can be superior to spectra obtained via the absorption channel. For μξ < μκ and grazing incidence geometry, the amplitude reduction can be small and simple normalization is sufficient to restore the spectral integrity with remarkable accuracy. This has been instrumental in unravelling the surface and subsurface structures around cations in amorphous Ga–In–O and Zn–Sn–O films which are otherwise inaccessible due to severe SA effects. This method has also been applied to several samples with μξ ≃ μκ to examine its applicability. For these samples, the amplitude reduction is 12 ± 4% versus their standards for the data measured with the classical 45°/45° geometry. This experimental method is easy to implement. Since If from κ and ξ are measured by the same detector system, it is also superior to other methods in removing systematic errors such as detector system nonlinearity, electronic noise, and some beam instabilities, and in removing spectral imperfections due to, for example, SA effects, diffraction effects and sample inhomogeneity. The distortions resulting from the latter can be severe in the spectra measured in transmission mode.

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

Hierarchical Network Partitioning for Solution of Potential-Driven, Steady-State Nonlinear Network Flow Equations

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends on the network topology, and in general, there is no numerical algorithm that offers guaranteed convergence to the solution (assuming a solution exists). Some methods offer guarantees in cases where the network topology satisfies certain assumptions, but these methods fail for larger networks. On the other hand, the Newton-Raphson algorithm offers a convergence guarantee if the starting point lies close to the (unknown) solution. It would be advantageous to compute the solution of the large nonlinear system through the solution of smaller nonlinear sub-systems wherein the solution algorithms (Newton-Raphson or otherwise) are more likely to succeed. Here, this letter proposes and describes such a procedure, a hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.

42 ENGINEERING↗
DOE OSTI2019

Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs

This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.

Unscented Kalman filter, unbiased minimumvariance ↗
DOE OSTI2018

A Multi-Step Adaptive Interpolation Approach to Mitigating the Impact of Nonlinearity on Dynamic State Estimation

Accurate estimation of dynamic states (such as synchronous machine rotor angle and speed) is critical for monitoring and controlling transient stability. Extended Kalman filter (EKF)--based approaches have been developed for estimating dynamic states. In order to improve the EKF's performance in estimating dynamic states of a synchronous machine, this paper proposes a multi-step adaptive interpolation (MSAI) approach to achieve balance between estimation accuracy and computational time. This approach consists of three major steps. First, two indexes are calculated to quantify the nonlinearity of the state transition function and measurement function, respectively. Second, based on the nonlinearity indexes, the interpolation factor is determined using a finite state machine model. And finally, to mitigate the negative impact of nonlinearity on the estimation accuracy, pseudo-measurements are added between consecutive measurements through linear interpolation. A simple example is used to validate the proposed nonlinear indexes. The two-area four-machine system and 16-machine 68-bus system are used to evaluate the effectiveness of the proposed MSAI approach. It is shown through the Monte-Carlo method that the estimation accuracy can be improved through interpolation. In addition, a good trade-off between estimation accuracy and computational time can be achieved effectively through the proposed MSAI approach.

Dynamic State Estimation, extended Kalman filter (↗
DOE OSTI2022

Surrogate Modeling of Nonlinear Dynamic Systems: A Comparative Study

Surrogate models play a vital role in overcoming the computational challenge in designing and analyzing nonlinear dynamic systems, especially in the presence of uncertainty. This paper presents a comparative study of different surrogate modeling techniques for nonlinear dynamic systems. Four surrogate modeling methods, namely, Gaussian process (GP) regression, a long short-term memory (LSTM) network, a convolutional neural network (CNN) with LSTM (CNN-LSTM), and a CNN with bidirectional LSTM (CNN-BLSTM), are studied and compared. All these model types can predict the future behavior of dynamic systems over long periods based on training data from relatively short periods. The multi-dimensional inputs of surrogate models are organized in a nonlinear autoregressive exogenous model (NARX) scheme to enable recursive prediction over long periods, where current predictions replace inputs from the previous time window. Three numerical examples, including one mathematical example and two nonlinear engineering analysis models, are used to compare the performance of the four surrogate modeling techniques. The results show that the GP-NARX surrogate model tends to have more stable performance than the other three deep learning (DL)-based methods for the three particular examples studied. The tuning effort of GP-NARX is also much lower than its deep learning-based counterparts.

42 ENGINEERING↗
DOE OSTI2024

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗
DOE OSTI2018

Three-dimensional modeling and numerical predictions of multimodal nonlinear behavior in damaged concrete blocks

In this work, the multimodal nonlinear elastic behavior of concrete, which is representative of a consolidated granular material, is modeled numerically. Starting from a local three-dimensional softening law, the initial stiffness properties are re-estimated according to the local strain field. The experiments deal with samples of thermally damaged concrete blocks successively excited around their first three modes of vibration. The geometry of these samples cannot be described by a one-dimensional approximation in these experiments where compressional and shear motions are strongly coupled. Despite this added complexity, the nonlinear behavior for the three modes of vibration of the samples is well captured by the simulations using a single scalar nonlinear parameter appropriately integrated into the elasticity equations. Finally, it is shown that without sufficient attention paid to the latter, the conclusions would have brought erroneous statements such as nonlinearity dispersion or strain type dependence.

58 GEOSCIENCES↗
DOE OSTI2014

The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear

We use a fourth-order fluid expansion to make general predictions for asymptotically nonlinear material functions in oscillatory shear, a characterization protocol sometimes known as medium-amplitude oscillatory shear. The calculation applies to any viscoelastic fluid in the terminal regime defined by the limit of Deborah number much less than one. Two viscous nonlinearities appear at third order, with shear stress scaling as ω 3 , and are interrelated by a constant multiplicative factor. Two elastic nonlinearities appear at fourth order, with shear stress scaling as ω 4 , and are also interrelated by a constant multiplicative factor. These nonlinear measures are decoupled from the linear material functions G' and G" because they depend on different expansion coefficients. Experimental measurements are presented for all four asymptotic shear material functions using a linear and well-entangled homopolymer of polyisoprene. Here, the experimental observations are consistent with both the predicted frequency scaling and the predicted interrelations in the terminal regime. Signs and magnitudes cannot be universally predicted, leaving these as free parameters that depend on the specifics of the material microstructure or constitutive model. These general results explain previous observations involving different materials and constitutive models, and provide an important reference for future experiments, analytical results, and numerical computations of these rheological fingerprints.

42 ENGINEERING↗
DOE OSTI2025

Quantum critical electro-optic and piezo-electric nonlinearities

Although electro-optic (EO) nonlinearities are essential for many quantum and classical photonics applications, a major challenge is inefficient modulation in cryogenic environments. Guided by the connection between phase transitions and nonlinearity, we identify the quantum paraelectric perovskite SrTiO 3 as a strong cryogenic EO [>500 picometers per volt (pm/V)] and piezo-electric material (>90 picocoulombs per newton) at T = 5 K, at frequencies to at least 1 megahertz. Furthermore, by tuning SrTiO 3 toward quantum criticality, we more than double the EO and piezo-electric effects, demonstrating a linear Pockels coefficient above 1000 pm/V. Furthermore, our results probe the link between quantum phase transitions, dielectric susceptibility, and nonlinearity, unlocking opportunities in cryogenic optical and mechanical systems and providing a framework for discovering new nonlinear materials.

Anderson, Christopher P. [Stanford University, CA ↗
DOE OSTI2016

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗