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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Noise Constraints on Sensitivity Scaling in Quantum Nonlinear Metrology

Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource 𝑁 (e.g., particle number or energy) from 1/√𝑁 to 1/𝑁. Through the use of nonlinear effects, Roy and Braunstein [Exponentially enhanced quantum metrology, Phys. Rev. Lett. 100, 220501 (2008)] derived a 1/𝑁 2 scaling. However, later works argued this exponential improvement is unphysical and that even modest gains, like 1/𝑁 2 , may vanish under noise. We show that, in the presence of small errors, the nonlinear interactions enabling metrological enhancement induce emergent errors. Here, the errors propagate through the sensing protocol and are magnified proportional to any intended nonlinear enhancement. We identify a critical value of the parameter to be estimated, for a fixed error, below which the emergent errors can be avoided.

Quantum Fisher information↗
DOE OSTI2022

Mid-Infrared Nonlinear Frequency Conversion Using Monolithic Barium Titanate on Silicon-on-Insulator

In this work, efficient nonlinear frequency conversion in the mid-infrared (mid-IR) region was demonstrated by a barium titanate (BTO) on a silicon-on-insulator (SOI) substrate. The BTO thin film was epitaxially grown by pulsed-laser deposition (PLD). The tensorial second order optical nonlinearity and the ferroelectric domain property of the BTO were characterized by the polarimetric mid-IR second harmonic generation (SHG) measurements. Azimuthal-dependent polarized SHG was modeled at different combinations of the nonlinear coefficient $d_{ij}$ and the domain fraction factor $ΔD^Y/ΔD^X$. Strong SHG intensity was experimentally observed over a broad spectrum at λ = 3.1 μm - 3.7 μm. A characteristic linear dependence between the SHG signal and the square of the pumping laser intensity was observed. The monolithic integration between the epitaxial BTO and the Si provides a compact platform for efficient on-chip light generation and quantum photonic technologies.

25 ENERGY STORAGE↗
DOE OSTI2024

Robust PID Control Against Nonlinear Uncertainties in Modern Power Systems with Microgrids

This paper investigates the problem of robust PID control for nonlinear power systems with uncertainties. In this paper, we analyze the challenges posed by nonlinearities and uncertainties in power systems, as well as the limitations of traditional linearization methods. On this basis, a PID control design method is proposed, which utilizes only the Lipschitz constant information of the nonlinear uncertainties to achieve global stability control for the power systems. The paper provides a rigorous mathematical foundation to demonstrate the effectiveness and robustness of the controller. Finally, simulation studies are conducted to validate and evaluate the performance of the proposed model, algorithm, and controller design.

Yuan, Shuo↗
DOE OSTI2017

Nonlinear Model Reduction in Power Systems by Balancing of Empirical Controllability and Observability Covariances

Abstract: In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods, the external system does not need to be linearized but is directly dealt with as a nonlinear system. A transformation is found to balance the controllability and observability covariances in order to determine which states have the greatest contribution to the input-output behavior. The original system model is then reduced by Galerkin projection based on this transformation. The proposed method is tested and validated on a system comprised of a 16-machine 68-bus system and an IEEE 50-machine 145-bus system. The results show that by using the proposed model reduction the calculation efficiency can be greatly improved; at the same time, the obtained state trajectories are close to those for directly simulating the whole system or partitioning the system while not performing reduction. Compared with the balanced truncation method based on a linearized model, the proposed nonlinear model reduction method can guarantee higher accuracy and similar calculation efficiency. It is shown that the proposed method is not sensitive to the choice of the matrices for calculating the empirical covariances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Bayesian High-Rank Hankel Matrix Completion for Nonlinear Synchrophasor Data Recovery

Phasor measurement units (PMUs) provide high temporal-resolution synchrophasor measurements for power system monitoring and control. The frequent data quality issues, such as missing and bad data, prevent the incorporation of synchrophasor data in real-time operations. Most existing data-driven data recovery methods assume the power system dynamics can be approximated by a linear dynamical system, and the recovery performance degrades significantly when the power system is experiencing nonlinear dynamics during significant events. Here, this paper proposes a data-driven Bayesian nonlinear synchrophasor data recovery method (Ba-NSDR) that can recover a consecutive time period of simultaneous data losses or errors across all channels, even when the underlying system is highly nonlinear. The idea is to lift the Hankel matrix of the spatial-temporal synchrophasor data to a higher dimension such that the lifted Hankel matrix is low-rank in that space and can be processed with the kernel trick. Our proposed Bayesian method then infers the probabilistic distributions of synchrophasor from the partial observations. Some distinctive features of Ba-NSDR include an uncertainty index to measure the accuracy of the recovery result and the robustness to parameter selections. Our method is verified on both synthetic and recorded event datasets.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2017

A unified materials approach to mitigating optical nonlinearities in optical fiber. III. Canonical examples and materials road map

Abstract This paper, Part III in the Trilogy (Ballato, Cavillon, Dragic, 2018; Dragic, Cavillon, Ballato, et al ., 2018a,b), provides a road map for the development of simple core/clad optical fibers whose enhanced performance—in particular, marked reductions in optical nonlinearities—is achieved materially and not through the more conventional present routes of geometrically complex fiber design. More specifically, the material properties that give rise to Brillouin, Raman and Rayleigh scattering, transverse mode instabilities ( TMI ), and n 2 ‐mediated nonlinear effects are compiled and results on a wide range of optical fibers are discussed with a focus on trends in performance with glass composition. Furthermore, optical power scaling estimations as well as binary and ternary property diagrams associated with Rayleigh scattering, the Brillouin gain coefficient ( BGC ) and the thermo‐optic coefficient (d n /d T ) are developed and employed to graphically represent general trends with composition along with compositional targets for a single intrinsically low nonlinearity, silica‐based optical fiber that can achieve the power scaling goals of future high energy fiber laser applications. A foundational finding of this work is that the high‐silica content optical fibers fabricated using conventional chemical vapor deposition methods will not suffice to meet the power scaling demands of future high‐power and high‐energy fiber lasers.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Passive Suppression Mechanisms in Laminar Vortex-Induced Vibration of a Sprung Cylinder With a Strongly Nonlinear, Dissipative Oscillator

We study cross-flow vortex-induced vibration (VIV) of a linearly sprung circular cylinder equipped with a dissipative oscillator with cubic stiffness nonlinearity, restrained to move in the direction of travel of the cylinder. The dissipative, essentially nonlinear coupling between the cylinder and the oscillator allows for targeted energy transfer (TET) from the former to the latter, whereby the oscillator acts as a nonlinear energy sink (NES) capable of passively suppressing cylinder oscillations. For fixed values of the Reynolds number (Re = 48, slightly above the fixed-cylinder Hopf bifurcation), cylinder-to-fluid density ratio, and dimensionless cylinder spring constant, spectral-element simulations of the Navier–Stokes equations coupled to the rigid-body motion show that different combinations of NES parameters lead to different long-time attractors of the dynamics. We identify four such attractors which do not coexist at any given point in the parameter space, three of which lead to at least partial VIV suppression. We construct a reduced-order model (ROM) of the fluid–structure interaction (FSI) based on a wake oscillator to analytically study those four mechanisms seen in the high-fidelity simulations and determine their respective regions of existence in the parameter space. Asymptotic analysis of the ROM relies on complexification-averaging (CX-A) and slow–fast partition of the transient dynamics and predicts the existence of complete and partial VIV-suppression mechanisms, relaxation cycles, and Hopf and Shilnikov bifurcations. These outcomes are confirmed by numerical integration of the ROM and comparisons with spectral-element simulations of the full system.

Blanchard, Antoine↗
DOE OSTI2013

Assessing the Importance of Nonlinearities in the Development of a Substructure Model for the Wind Turbine CAE Tool FAST: Preprint

Design and analysis of wind turbines are performed using aero-servo-elastic tools that account for the nonlinear coupling between aerodynamics, controls, and structural response. The NREL-developed computer-aided engineering (CAE) tool FAST also resolves the hydrodynamics of fixed-bottom structures and floating platforms for offshore wind applications. This paper outlines the implementation of a structural-dynamics module (SubDyn) for offshore wind turbines with space-frame substructures into the current FAST framework, and focuses on the initial assessment of the importance of structural nonlinearities. Nonlinear effects include: large displacements, axial shortening due to bending, cross-sectional transverse shear effects, etc.

17 WIND ENERGY↗
DOE OSTI2012

A nonlinear lag correction algorithm for a-Si flat-panel x-ray detectors

Purpose: Detector lag, or residual signal, in a-Si flat-panel (FP) detectors can cause significant shading artifacts in cone-beam computed tomography reconstructions. To date, most correction models have assumed a linear, time-invariant (LTI) model and correct lag by deconvolution with an impulse response function (IRF). However, the lag correction is sensitive to both the exposure intensity and the technique used for determining the IRF. Even when the LTI correction that produces the minimum error is found, residual artifact remains. A new non-LTI method was developed to take into account the IRF measurement technique and exposure dependencies. Methods: First, a multiexponential (N = 4) LTI model was implemented for lag correction. Next, a non-LTI lag correction, known as the nonlinear consistent stored charge (NLCSC) method, was developed based on the LTI multiexponential method. It differs from other nonlinear lag correction algorithms in that it maintains a consistent estimate of the amount of charge stored in the FP and it does not require intimate knowledge of the semiconductor parameters specific to the FP. For the NLCSC method, all coefficients of the IRF are functions of exposure intensity. Another nonlinear lag correction method that only used an intensity weighting of the IRF was also compared. The correction algorithms were applied to step-response projection data and CT acquisitions of a large pelvic phantom and an acrylic head phantom. The authors collected rising and falling edge step-response data on a Varian 4030CB a-Si FP detector operating in dynamic gain mode at 15 fps at nine incident exposures (2.0%-92% of the detector saturation exposure). For projection data, 1st and 50th frame lag were measured before and after correction. For the CT reconstructions, five pairs of ROIs were defined and the maximum and mean signal differences within a pair were calculated for the different exposures and step-response edge techniques. Results: The LTI corrections left residual 1st and 50th frame lag up to 1.4% and 0.48%, while the NLCSC lag correction reduced 1st and 50th frame residual lags to less than 0.29% and 0.0052%. For CT reconstructions, the NLCSC lag correction gave an average error of 11 HU for the pelvic phantom and 3 HU for the head phantom, compared to 14-19 HU and 2-11 HU for the LTI corrections and 15 HU and 9 HU for the intensity weighted non-LTI algorithm. The maximum ROI error was always smallest for the NLCSC correction. The NLCSC correction was also superior to the intensity weighting algorithm. Conclusions: The NLCSC lag algorithm corrected for the exposure dependence of lag, provided superior image improvement for the pelvic phantom reconstruction, and gave similar results to the best case LTI results for the head phantom. The blurred ring artifact that is left over in the LTI corrections was better removed by the NLCSC correction in all cases.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Assessment of volumetric noise and resolution performance for linear and nonlinear CT reconstruction methods

Purpose: For nonlinear iterative image reconstructions (IR), the computed tomography (CT) noise and resolution properties can depend on the specific imaging conditions, such as lesion contrast and image noise level. Therefore, it is imperative to develop a reliable method to measure the noise and resolution properties under clinically relevant conditions. This study aimed to develop a robust methodology to measure the three-dimensional CT noise and resolution properties under such conditions and to provide guidelines to achieve desirable levels of accuracy and precision. Methods: The methodology was developed based on a previously reported CT image quality phantom. In this methodology, CT noise properties are measured in the uniform region of the phantom in terms of a task-based 3D noise-power spectrum (NPS{sub task}). The in-plane resolution properties are measured in terms of the task transfer function (TTF) by applying a radial edge technique to the rod inserts in the phantom. The z-direction resolution properties are measured from a supplemental phantom, also in terms of the TTF. To account for the possible nonlinearity of IR, the NPS{sub task} is measured with respect to the noise magnitude, and the TTF with respect to noise magnitude and edge contrast. To determine the accuracy and precision of the methodology, images of known noise and resolution properties were simulated. The NPS{sub task} and TTF were measured on the simulated images and compared to the truth, with criteria established to achieve NPS{sub task} and TTF measurements with <10% error. To demonstrate the utility of this methodology, measurements were performed on a commercial CT system using five dose levels, two slice thicknesses, and three reconstruction algorithms (filtered backprojection, FBP; iterative reconstruction in imaging space, IRIS; and sinogram affirmed iterative reconstruction with strengths of 5, SAFIRE5). Results: To achieve NPS{sub task} measurements with <10% error, the number of regions of interest needed to be greater than 65. To achieve TTF measurements with <10% error, the contrast-to-noise ratio of the edge needed to be ≥15, achievable by averaging multiple slices across the same edge. The NPS{sub task} measured on a commercial CT system showed IR's reduced noise (IRIS, 30% and SAFIRE5, 55%) and “waxier” texture (peak frequencies: FBP, 0.25 mm{sup −1}; IRIS, 0.23 mm{sup −1}; and SAFIRE5, 0.16 mm{sup −1}). The TTF measured within the axial plane showed improved in-plane resolution with SAFIRE5 at the TTF 50% frequency, f{sub 50} (FBP, 0.36–0.41 mm{sup −1}; SAFIRE5, 0.37–0.46 mm{sup −1}). The TTF measured along the axial direction showed improved z-direction resolution with thinner slice thickness (f{sub 50}: 0.6 mm, 0.35–0.79 mm{sup −1}; 1.5 mm, 0.22–0.3 mm{sup −1}) and with SAFIRE5 (f{sub 50}: FBP, 0.35–0.52 mm{sup −1}; SAFIRE5, 0.42–0.79 mm{sup −1}). Both in-plane and z-direction resolution of SAFIRE5 showed strong dependency on contrast, reflecting SAFIRE5's nonlinearity. Conclusions: A methodology was developed to measure three-dimensional CT noise and resolution properties for iterative reconstruction, especially at challenging measurement conditions with low contrast and high image noise. The methodology also demonstrated its utility for evaluating commercial CT systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Thermal modulation of nonlinear ultrasonic wave for concrete damage evaluation

A nonlinear ultrasonic test is proposed for material damage evaluation using thermal modulation. Temperature change excites and modulates nonlinear behavior of ultrasonic waves in concrete. Coda wave interferometry was used to analyze the relative velocity change of ultrasonic wave with temperature variations. On concrete samples with different levels of thermal damage, experimental results indicate that the samples with a higher damage level demonstrated higher sensitivity to temperature variations. In addition, a slow dynamics nonlinear behavior was observed. When the temperature changed and then remained constant, the wave velocity gradually approached to its equilibrium value.

Acoustic spectroscopy↗
DOE OSTI2021

Nonlinear ultrasonic technique for the characterization of microstructure in additive materials

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

42 ENGINEERING↗
DOE OSTI2023

Disordered topological graphs enhancing nonlinear phenomena

Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to preserve the response of systems in the presence of disorder. We propose and demonstrate topological structurally disordered systems with a modal structure that enhances nonlinear phenomena in the topological channels by inhibiting the ultrafast leakage of energy from edge modes to bulk modes. We present the construction of the graph and show that its dynamics enhances the topologically protected photon pair generation rate by an order of magnitude. Disordered nonlinear topological graphs will enable advanced quantum interconnects, efficient nonlinear sources, and light-based information processing for artificial intelligence.

42 ENGINEERING↗
DOE OSTI2023

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, in this paper, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi 2 Te 4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2020

Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in $\mathrm {PbPb}$ collisions at $\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$ and 5.02$\,\text {TeV}$

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in $\mathrm {PbPb}$ collisions at nucleon-nucleon center-of-mass energies $\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$ and 5.02$\,\text {TeV}$ with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗