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At least 19 records

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

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)]↗

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↗

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↗

Generalized Circuit Representation for a Synchronous Machine

In this letter, a generalized circuit representation for a synchronous machine is presented. This circuit represents voltage and current relationship and can be used for dynamic and harmonic analysis. A distinct feature of the circuit is the use of Laplace transform variable s , which simplifies both calculus and frame conversion. Two derivation approaches are presented. Here, the first approach starts from a steady-state circuit representation, while the second approach starts from the dq-frame dynamic model of a synchronous generator. Both arrive at the same representation.

42 ENGINEERING↗

Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using #SHAARP package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, here we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.

complex systems↗

Implementing Superresolution of Nonstationary Tides with Wavelets: An Introduction to CWT_Multi

Abstract Tides are often nonstationary due to nonastronomical influences. Investigating variable tidal properties implies a trade-off between separating adjacent frequencies (using long analysis windows) and resolving their time variations (short analysis windows). Previous continuous wavelet transform (CWT) tidal methods resolved tidal species. Here, we present CWT_Multi, a MATLAB code that 1) uses CWT linearity (via the “response coefficient method”) to implement superresolution, i.e., resolving tidal constituents beyond the Rayleigh criterion; 2) provides a Munk–Hasselmann constituent selection criterion appropriate for superresolution; and 3) introduces an objective, time-variable form of inference (“dynamic inference”) based on time-varying data properties. CWT_Multi resolves tidal species on time scales of days, and multiple constituents per species with fortnightly filters. It outputs astronomical phase lags and admittances, analyzes multiple records, and provides power spectra of the signal(s), residual(s), and reconstruction(s); confidence limits; and signal-to-noise ratios. Artificial data and water levels from the Lower Columbia River Estuary (LCRE) and San Francisco Bay Delta (SFBD) are used to test CWT_Multi and compare it to harmonic analysis programs NS_Tide and UTide. CWT_Multi provides superior reconstruction, detiding, dynamic analysis utility, and time resolution of constituents (but with broader confidence limits). Dynamic inference resolves closely spaced constituents (like K 1 , S 1 , and P 1 ) on fortnightly time scales, quantifying impacts of diel power peaking (with a 24-h period, like S 1 ) on water levels in the LCRE. CWT_Multi also helps quantify the impacts of high flows and a salt barrier closing on tidal properties in the SFBD. On the other hand, CWT_Multi does not excel at prediction, and results depend on analysis details, as for any method applied to nonstationary data. Significance Statement Ocean tides, especially in coastal and estuarine systems, are often nonstationary, in the sense that the mean and standard deviation of tidal properties vary over time, usually in response to some nontidal process. We introduce here a MATLAB code, CWT_Multi, that uses wavelet transforms to resolve both tidal species and constituents on time scales from a few days to months. Our code accommodates multiple scalar time series and has typical tidal analysis features like constituent selection and inference, plus two forms of uncertainty analyses. It is flexible, allowing the user to adapt analysis properties to diverse datasets. CWT_Multi is applicable to many problems involving time-variable tides, including sea level rise, compound flooding, sediment transport, and wetland habitat analyses. Application to vector data is a straightforward extension, but further development of our uncertainty analysis is merited. Because nonstationary tidal analysis is rapidly advancing, we also define the features of a “well-formed” analysis code.

Lobo, Matthew↗

The inversion formula and 6j symbol for 3d fermions

In this work we study the 6 j symbol of the 3 d conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning 6 j symbols to the simpler 6 j symbol for four scalar operators. As one application we use these techniques to compute 3 d mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scalar modular bootstrap and zeros of the Riemann zeta function

Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗