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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is widely used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the $\chi^2$ used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum $\chi^2$-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A multi-chord, two-color interferometer using Hilbert transform phase detection for measuring electron density in spheromak plasmas

A new, four-chord, CO 2 /He–Ne heterodyne interferometer has been designed and built for measuring line-averaged plasma density in the HIT-SI3 and subsequent HIT-SIU sustained spheromak devices. The two-color system successfully eliminates vibration-induced errors caused by mirrors that are secured to the vacuum chamber and is able to resolve electron densities ne in the full operating range of 10 18 –10 20 m –3 in both experiments with an integrated error of 4.7 × 10 17 m –2 . Here, data are presented from high toroidal current plasma discharges, showing the time evolution of electron densities n e and j Φ /n e along multiple chords.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Real-Time Wave Energy Converter Control Using Instantaneous Frequency

Wave Energy Converters (WECs) rely on effective Power Take-Off (PTO) control strategies to maximize energy absorption under dynamic sea conditions. Traditional hydrodynamic modeling techniques may require computationally intensive convolution calculations, making real-time control implementation challenging. This paper presents an alternative approach by leveraging instantaneous frequency estimation to dynamically adjust PTO damping in response to varying wave frequencies. Two real-time frequency estimation methods are explored: the Hilbert Transform (HT) and Phase-Locked Loop (PLL). The Hilbert Transform method provides accurate frequency tracking but introduces a delayed response due to its dependence on causal data. Conversely, the PLL approach demonstrates strong potential in frequency tracking but requires careful gain tuning, particularly in complex sea states. Comparative evaluations across multiple test cases—including sinusoidal variations, amplitude steps, frequency step changes, and real-world JONSWAP spectrum waves—highlight the strengths and limitations of each method. The two different PTO control techniques across the various frequency estimation methods were tested under real-sea states using a state-space model of a point-absorbing Wave Energy Converter. The Capture Width Ratio (CWR) is used as a performance metric, with results showing that the HT achieves a 10.6% improvement, while the PLL estimation yields a 0.9% improvement relative to the fixed parameter control baseline. These results highlight the effectiveness of real-time frequency estimation in improving energy absorption compared to static control parameters.

WEC control↗
DOE OSTI2024

IoT-Enabled Traveling Wave Microgrid Protection

Traveling Wave Protection based on the Internet of Things (TWP-IoT) is developed to enable ultra-resilient microgrids. TWP-IoT adopts a directional traveling wave approach that utilizes the voltage and current modal components obtained from Discrete Hilbert Transform to identify the fault features via ultra-lightweight IoT hardware. Furthermore, the main contributions of this work include (1) a novel TWP-IoT for microgrid and distribution networks that can achieve the time-of-arrival fault detection and localization with composite wave impedance and conductance using Discrete Hilbert Transform, (2) a cost-effective smart IoT prototype with functionalities outperforming commercial relays, and (3) a real-time hardware-in-the-loop prototype based on RTDS that verifies the robustness and efficacy of TWP-IoT subject to a diverse set of working conditions. TWP-IoT is found to have excellent performance under a wide spectrum of internal and external fault conditions across a myriad of microgrid locations, which is unattainable by today’s TWP products.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

BCARS Simulated Phantom Dataset for Evaluation of Processing Pipelines

Broadband coherent anti-Stokes Raman scattering (BCARS) microscopy is a powerful label-free biological imaging technique, but the raw signal requires careful processing. The vibrationally resonant (Raman) fingerprint signal is usually small compared with instrumental noise sources and the nonresonant background (NRB) inherent in the BCARS signal. Fortunately, the NRB exhibits a systematic phase relationship with the coherent Raman response, acting as a heterodyne amplifier for the weak fingerprint signal. Due to this heterodyne effect, the Raman response can be recovered quantitatively and invariantly across different instruments, provided the NRB shape is known. Even with heterodyne amplification, the amplitudes of fingerprint signal components are often comparable to system noise. Singular value decomposition (SVD), which utilizes spatial information, is often employed for additional noise filtering. Consequently, finding optimal processing parameters to properly distinguish the NRB and Raman responses and suppress noise in the complex BCARS signal requires a reference system that realistically represents the spectral and spatial properties of BCARS signals obtained from biological samples. We present a digital tissue phantom that meets these criteria as a tool for testing candidate signal processing pipelines. The digital phantom is generated with simulated hyperspectral Raman images having system-specific noise and background characteristics. Here, we analyze phantom datasets with differing background and signal-to-noise conditions to evaluate their impact on the performance of multiple signal processing pipelines. Specifically, we investigate the application of a Butterworth filter-based routine to directly estimate the NRB from the BCARS signal. Additionally, we evaluate a Lorentzian wavelet transform as an alternative to the Hilbert transform for extracting the Raman spectrum from the BCARS signal. While we demonstrate this phantom for BCARS, it can be used for any spectroscopic Raman imaging approach.

Dixon, Jessica Z. [Georgia Institute of Technology↗
DOE OSTI2021

Vector elastic deconvolution migration with dual wavefield decomposition

Here, we report elastic-wave imaging using multicomponent data can provide more useful subsurface information than acoustic-wave imaging, but it is usually algorithmically challenging. We have developed a vector elastic deconvolution migration method for high-resolution imaging of subsurface structures in isotropic and anisotropic elastic media. Our new method uses a vector deconvolution imaging condition based on dual wavefield decomposition, including an explicit directional wavefield separation using the Hilbert transform and a P/S vector wavefield decomposition using the low-rank decomposition method. Using three elastic models, we numerically determine that our new method produces notably higher resolution and more amplitude-balanced elastic images compared with a crosscorrelation-based vector elastic reverse time migration method.

58 GEOSCIENCES↗
DOE OSTI2021

Spatially Quasi-Periodic Water Waves of Infinite Depth

Abstract We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Wilkening, Jon (ORCID:0000000327827596)↗
DOE OSTI2021

Quasi-periodic travelling gravity–capillary waves

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Investigation of Causal Relationships of the Cross‐Scale Wave Coupling Through Information Theoretical Approach

On 2015 October 2, MMS spacecraft observed an electron micro-injection event near the southern hemispheric high-altitude cusp, coinciding with intense wave activity across several frequency bands. Here, we investigated the MMS magnetic field and plasma during this event to explore cross-scale coupling among the wave modes. Employing the Hilbert-Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross-scale wave coupling phenomena.

Rivera, Elmer C. [Andrews University, Berrien Spri↗
DOE OSTI2021

Hybrid Data-Driven Based HVdc Ancillary Control for Multiple Frequency Data Attacks

The high voltage direct current (HVdc) intertie has been applied to provide ancillary-services for ac grids, utilizing the real-time feedback from phasor measurement units (PMUs). However, PMU data communication is vulnerable to false data injection attacks (FDIA) due to protocol defects, thus the HVdc ancillary control and system stability will be threatened. To address this issue, this article proposes a novel HVdc control strategy based on a hybrid data-driven (HDD) methodology. In this work, the HDD methodology is first proposed to detect the types and duration time of multiple frequency attacks. Specifically, the Hilbert Huang transform (HHT) is used to decompose the frequency data, using variational mode decomposition instead of the traditional empirical mode decomposition, to extract data features. Second, a multikernel support vector machine is proposed to classify the attacked data based on the designed distinctive features from HHT. Meanwhile, the attacking duration time is decided using an unsupervised technique. Third, an HDD-based HVdc ancillary control strategy is established to eliminate the effect of FDIAs on the HVdc frequency response. Comprehensive experiments of HDD-based HVdc ancillary controls under different FDIAs suggest that the proposed HDD could fast and accurately classify the FDIAs, and the HDD-based HVdc ancillary control strategy could significantly suppress the impact of the FDIAs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mechanisms of Low-Level Jet Formation in the U.S. Mid-Atlantic Offshore

Abstract Low-level jets (LLJs), in which the wind speed attains a local maximum at low altitudes, have been found to occur in the U.S. mid-Atlantic offshore, a region of active wind energy deployment as of 2023. In contrast to widely studied regions such as the U.S. southern Great Plains and the California coastline, the mechanisms that underlie LLJs in the U.S. mid-Atlantic are poorly understood. This work analyzes floating lidar data from buoys deployed in the New York Bight to understand the characteristics and causes of coastal LLJs in the region. Application of the Hilbert–Huang transform, a frequency analysis technique, to LLJ case studies reveals that mid-Atlantic jets frequently occur during times of adjustment in synoptic-scale motions, such as large-scale temperature and pressure gradients or frontal passages, and that they do not coincide with motions at the native inertial oscillation frequency. Subsequent analysis with theoretical models of inertial oscillation and thermal winds further reveals that these jets can form in the stationary geostrophic wind profile from horizontal temperature gradients alone—in contrast to canonical LLJs, which arise from low-level inertial motions. Here, inertial oscillation can further modulate the intensity and altitude of the wind speed maximum. Statistical evidence indicates that these oscillations arise from stable stratification and the associated frictional decoupling due to warmer air flowing over a cold sea surface during the springtime land–sea breeze. These results improve our conceptual understanding of mid-Atlantic jets and may be used to better predict low-level wind speed maxima. Significance Statement The purpose of this work is to identify and characterize the atmospheric mechanisms that result in an occasional low-level maximum in the wind speed off the U.S. mid-Atlantic coastline. Our findings show that these low-level jets form due to horizontal temperature gradients arising from fronts and synoptic systems, as well as from the land–sea breeze that forces warmer air over the cold ocean surface. This work aids predictability of such jets, improves our understanding of this coastal environment, and has implications for future deployment of offshore wind energy in this region.

17 WIND ENERGY↗
DOE OSTI2021

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as U(1) gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. Here, we briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Generalized Wigner theorem for noninvertible symmetries

In this article, we establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probabilities under the application of symmetries mandates that all non-invertible symmetries may only correspond to projective unitary or antiunitary transformations, i.e., partial isometries. This extends the notion of physical states beyond conventional rays in Hilbert space to equivalence classes in an extended, gauged Hilbert space, thereby broadening the traditional understanding of symmetry transformations in quantum theory. Our generalized theorem applies irrespective of the origin of the (non)invertible symmetry, holds in arbitrary spatial dimensions, and is independent of the Hamiltonian or action. We explore its physical consequences and, using simple model systems, illustrate how the distinction between invertible and non-invertible symmetries can sometimes be tied to the choice of boundary conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Gravitational Contact Interactions and the Physical Equivalence of Weyl Transformations in Effective Field Theory

Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +F(\phi) )R +L(\phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim F(\phi) T_\mu^\mu(\phi)/M_P^2$ and $F(\phi)\partial^2 F(\phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗