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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Harmonic analysis of 2d CFT partition functions

We apply the theory of harmonic analysis on the fundamental domain of SL(2, Z) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space H/SL(2, Z), and of target space moduli space O(c, c; Z)\O(c, c; R)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Harmonic Analysis of Common-mode Reduction Modulation for Three-level Inverter

This paper presents harmonic analysis of common-mode reduction (CMR) modulation for three-level voltage source inverters. The analytical model to calculate the harmonics of CMR modulation with arbitrary PWM sequence is developed. The impact of alternative PWM sequences of CMR modulation on harmonics is investigated. New three-state and four-state PWM sequences of CMR are proposed which spread the energy centered in the carrier frequency in the conventional CMR, and thus reduce the voltage peaks in frequency domain. Experiments are conducted on a three-level neutral point clamped inverter. Experiment results verify the developed analytical model and harmonic analysis.

Chen, Ruirui↗
DOE OSTI2019

Harmonic analysis and mean field theory

We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and “seed” operators in 4d, and MFT for currents and stress-tensors in 3d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Harmonic analysis of discrete tracers of large-scale structure

It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an angular power spectrum) using a pixelized map one has to deal with aliasing of small-scale power and pixel window functions. We compare and contrast the approaches to this problem taken in the cosmic microwave background and large-scale structure communities, and advocate for a direct approach that avoids pixelization. We describe a method for performing a pseudo-spectrum analysis of a galaxy data set and show that it can be implemented efficiently using well-known algorithms for special functions that are suited to acceleration by graphics processing units (GPUs). The method returns the same spectra as the more traditional map-based approach if in the latter the number of pixels is taken to be sufficiently large and the mask is well sampled. The method is readily generalizable to cross-spectra and higher-order functions. It also provides a convenient route for distributing the information in a galaxy catalog directly in harmonic space, as a complement to releasing the configuration-space positions and weights, and a route to spectral apodization. Finally, we make public a code enabling the application of our method to existing and upcoming datasets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

On extraction of twist-two Compton form factors from DVCS observables through harmonic analysis

We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) {$\mathcal{H,E,\tilde H,\tilde E}$} which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + y. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t,x b , y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Impacts of Experimentally Obtained Harmonic Spectrums of Residential Appliances on Distribution Feeder

Owing to the increased use of power electronic based appliances and energy-efficient home equipment such as modern lighting loads, the percentage of nonlinear loads has increased in the distribution system, which can impact system performance, loss, and stability. Thus a comprehensive knowledge of their power quality and harmonic analysis is essential to improve the load models, voltage stability assessment, determination of possible interactions at harmonic frequencies, protection planning, and the effect of system impedance. This paper focuses on harmonic load flow analysis for multiple residential load types to determine the expected impacts on an modeled distribution secondary. For this study, the household appliances include lighting, power electronic, resistive, and motor loads with a nominal supply voltage of 120 V single-phase or 240 V split phase at a nominal frequency of 60 Hz. The harmonic spectrums, as obtained from the experimental evaluation of real loads, are used to inform the harmonic load flow for a detailed secondary network, including the distribution service transformer extracted from a real distribution feeder's model. Additionally, the impact of voltage harmonics on a three-phase test load is presented with experimental results. The harmonic data of the transformer terminal voltage, as obtained from the former load flow study, are scaled to generate the source voltage for the three-phase configuration of the grid simulator to make the test setup very similar to a typical secondary design in the U.S.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗
DOE OSTI2023

Analysis of harmonically seeded Free-Electron Laser

We revisit Free-Electron Laser (FEL) equations in the presence of a planar undulator to investigate effects on longitudinal FEL dynamics upon seeding by a harmonic for both low-gain and high-gain cases. Then, we extend the FEL equations in 3D to include electron beam emittance and radiation diffraction effects.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Magnetic Designs of New First Target Beamline Magnets for the ORNL SNS Upgrade

The Spallation Neutron Source (SNS) at ORNL currently is being upgraded from 1.0 GeV to 1.3 GeV. Several water-cooled magnets should be upgraded to transport 30% of higher beam energy. New chicane, injection/extraction septum, and Lambertson magnets were designed. Designing the magnets was a challenging task because the new magnets required good combined integrated field quality and needed to occupy the old magnets space but with about 20% greater integrated magnetic field. Additional strong requirements applied to the magnets fringe field do not disturb the circulating beam. The special field profiles had to be provided in foil areas between magnets. The analysis described here was based on OPERA3D simulations. A special technique was used for analyzing the integrated field harmonics. Initially, the particle track was simulated, and integrated field components were calculated along this track for the reference radius, which were used for the harmonics analysis. In addition, 3D field maps were provided for beam optics simulations. The final beamline analysis confirmed good beam transmission and low losses.

3d field maps↗
DOE OSTI2023

Analyzing Distribution Transformer Degradation with Increased Power Electronic Loads

The influx of non-linear power electronic loads into the distribution network has the potential to disrupt the existing distribution transformer operations. They were not designed to mediate the excessive heating losses generated from the harmonics. To have a good understanding of current standing challenges, a knowledge of the generation and load mix as well as the current harmonic estimations are essential for designing transformers and evaluating their performance. In this paper, we investigate a mixture of essential power electronic loads for a household designed in PSCAD/EMTdc and their potential impacts on transformer eddy current losses and derating using harmonic analysis. Our findings reveal that in the presence of high power electronic loads (especially third harmonics), increasing PV generation may worsen transformer degradation. However, with a low amount of power electronic loads, additional PV generation helps to reduce the harmonic content in the current and improve transformer performance.

eddy current, harmonics, PV, THD, power transforme↗
DOE OSTI2020

Impacts of Experimentally Obtained Harmonic Spectrums of Residential Appliances on Distribution Feeder: Preprint

This paper focuses on the harmonic load flow study for a set of residential loads and the impacts of the harmonic contents on the distribution feeder. Owing to the increased use of the power electronic based appliances and energy efficient home equipment like the lighting loads, the percentage of non-linear loads has increased in the distribution system which can impact the system performance, loss, and stability. Thus a comprehensive knowledge of their power quality and harmonic analysis is essential to improve the load models, voltage stability assessment, determining possible interactions at harmonic frequencies, protection planning, and the effect of the system impedance. For this study, the household appliances include the lighting, power electronics, resistive, and motor loads with a nominal supply voltage of 120 V single-phase or 240 V split-phase at a nominal frequency of 60 Hz. The harmonic spectrum as obtained from the experimental data is used to solve the harmonic load flow for a detailed secondary network including the distribution transformer extracted from a real distribution feeder's model. Additionally, the impact of the voltage harmonic on a three phase test load is presented through experimental results. The harmonic data of the transformer terminal voltage as obtained from the former load flow study is scaled to generate the source voltage for the three phase configuration of the grid simulator to make the test setup very similar to a real scenario.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Minkowski conformal blocks and the Regge limit for Sachdev-Ye-Kitaev-like models

We discuss scattering in a conformal field theory (CFT) via the conformal partial-wave analysis and the Regge limit. The focus of this paper is on understanding an operator product expansion (OPE) with Minkowski conformal blocks. Starting with a t-channel OPE, it leads to an expansion for an s-channel scattering amplitude in terms of t-channel exchanges. By contrasting with Euclidean conformal blocks we see a precise relationship between conformal blocks in the two limits without preforming an explicit analytic continuation. We discuss a generic feature for a CFT correlation function having singular F (M) (u,v) ~ u –δ , δ > 0, in the limit u → 0 and v → 1. Here, δ = (ℓ eff – 1)/2, with ℓ eff serving as an effective spin and it can be determined through an OPE. In particular, it is bounded from above, ℓ eff ≤ 2, for all CFTs with a gravity dual, and it can be associated with string modes interpolating the graviton in AdS. This singularity is historically referred to as the Pomeron. This bound is nearly saturated by SYK-like effective d = 1 CFT, and its stringy and thermal corrections have piqued current interests. Our analysis has been facilitated by dealing with Wightman functions. We provide a direct treatment in diagonalizing dynamical equations via harmonic analysis over physical scattering regions. As an example these methods are applied to the SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

On the Impact of High-Order Harmonic Generation in Electrical Distribution Systems

The modern power grid has seen a rise in the integration of non-linear loads, presenting a significant concern for operators. These loads introduce unwanted harmonics, leading to potential issues such as overheating and improper functioning of circuit breakers. In pursuing a more sustainable grid, the adoption of electric vehicles (EVs) and photovoltaic (PV) systems in residential networks has increased. Understanding and examining the effects of high-order harmonic frequencies beyond $1.5$ kHz is crucial to understanding their impact on the operation and planning of electrical distribution systems under varying nonlinear loading conditions. This study investigates a diverse set of critical power electronic loads within a household modeled using PSCAD/EMTdc, analyzing their unique harmonic spectra. This information is utilized to run the time-series harmonic analysis program in OpenDSS on a modified IEEE 34 bus test system model. The impact of high-order harmonics is quantified using metrics that evaluate total harmonic distortion (THD), transformer harmonic-driven eddy current loss component, and propagation of harmonics from the source to the substation transformer.

Peerzada, Aaqib A. [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2020

A one-loop test of the near-AdS 2 /near-CFT 1 correspondence

We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS 2 to show that the logarithmic corrections to the partition function are determined entirely by quadratic holomorphic differentials, even when conformal symmetry is broken and harmonic modes are no longer true zero modes. Our quantum-corrected partition function agrees precisely with the SYK result. We argue that our effective quantum field theory methods and results generalize to other theories of two-dimensional dilaton gravity.

2D Gravity↗
DOE OSTI2025

Can Restoring Tidal Wetlands Reduce Estuarine Nuisance Flooding of Coasts Under Future Sea‐Level Rise?

Wetland restoration is an increasingly popular nature‐based method for flood risk mitigation in coastal communities. In this study, we present a novel method using hydrodynamic modeling and harmonic analysis to quantify wetlands' ability to reduce future nuisance flooding. The method leverages a hydrodynamic model calibrated to present day data and was run for a range of future sea‐level rise (SLR) and wetland restoration scenarios to quantify changes to tidal harmonic amplitudes and phases. The harmonic constituents are used to generate water surface elevations over a time period of interest (e.g., one year) and compared to critical exceedance thresholds such as levee elevations. Then, changes to nuisance flooding are calculated by counting the number of hours critical thresholds are exceeded under different SLR and wetland restoration scenarios. We applied the method to Coos Bay, Oregon, USA as a test case. We found restoration reduces the number of hours nuisance flooding occurs in downtown Coos Bay from 15 hr (present day conditions) to 0 hr (fully restored condition) under median SLR (82 cm by 2100). Restoration had spatially variable impacts on reducing peak flood elevations with minimal impacts near the estuary mouth and greatest impact 32 km inland. The effectiveness of restoration was heavily dependent on future SLR. Restoration was maximally effective in 2050 under all SLR scenarios, less effective in 2100 under median SLR, and not effective under high SLR. Modeling results suggest increased tidal prism and accommodation space are driving restoration‐associated reductions in tidal amplitudes.

Brand, Matthew W. [Louisiana State Univ., Baton Ro↗