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DOE OSTI2021

Correlations of azimuthal anisotropy Fourier harmonics with subevent cumulants in p Pb collisions at s N N = 8.16 TeV

Event-by-event long-range correlations of azimuthal anisotropy Fourier coefficients ($v_n$) in 8.16 TeV p Pb data, collected by the CMS experiment at the CERN Large Hadron Collider, are extracted using a subevent four-particle cumulant technique applied to very low multiplicity events. Each combination of four charged particles is selected from either two, three, or four distinct subevent regions of a pseudorapidity range from -2.4 to 2.4 of the CMS tracker, and with transverse momentum between 0.3 and 3.0 GeV. Using the subevent cumulant technique, correlations between $v_n$ of different orders are measured as functions of particle multiplicity and compared to the standard cumulant method without subevents over a wide event multiplicity range. At high multiplicities, the $v_2$ and $v_3$ coefficients exhibit an anticorrelation; this behavior is observed consistently using various methods. The $v_2$ and $v_4$ correlation strength is found to depend on the number of subevents used in the calculation. As the event multiplicity decreases, the results from different subevent methods diverge because of different contributions of noncollective or few-particle correlations. Correlations extracted with the four-subevent method exhibit a tendency to diminish monotonically toward the lowest multiplicity region (about 20 charged tracks) investigated. These findings extend previous studies to a significantly lower event multiplicity range and establish the evidence for the onset of long-range collective multiparticle correlations in small system collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Measurements of second-harmonic Fourier coefficients from azimuthal anisotropies in p + p , p + Au , d + Au , and He 3 + Au collisions at s N N = 200 GeV

Recently, the PHENIX Collaboration has published second- and third-harmonic Fourier coefficients v 2 and v 3 for midrapidity (|η|< 0.35 ) charged hadrons in 0%–5% central p+Au, d+Au, and 3 He+Au collisions at $\sqrt{s_{NN}}$= 200 GeV, utilizing three sets of two-particle correlations for two detector combinations with different pseudorapidity acceptance [Acharya et al., Phys. Rev. C 105, 024901 (2022)]. Here, this paper extends these measurements of v 2 to all centralities in p+Au, d+Au, and 3 He+Au collisions, as well as p+p collisions, as a function of transverse momentum (p T ) and event multiplicity. The kinematic dependence of v 2 is quantified as the ratio R of v 2 between the two detector combinations as a function of event multiplicity for 0.5 < p T <1 and 2 T < 2.5 GeV/c. A multiphase-transport (AMPT) model can reproduce the observed v 2 in most-central to midcentral d Au and 3 He+Au collisions. However, the AMPT model systematically overestimates the measurements in p+p, p+Au, and peripheral d+Au and 3 He+Au collisions, indicating a higher nonflow contribution in the AMPT model than in the experimental data. The AMPT model fails to describe the observed R for 0.5 < p T < 1 GeV/c , but there is qualitative agreement with the measurements for 2 < p T < 2.5 GeV/c.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Fourier coefficients of noninterdependent collective motions in heavy-ion collisions

Here, we present a scenario in heavy-ion collisions where different modes of collective motions are noninterdependent, driven by factorized actions in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously. If the probability of particle emission is modulated by each nondependent collective motion with a single-harmonic Fourier expansion, the particle azimuthal distribution should be the product of all these expansions. Consequently, nonleading cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop separately, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving insights into searches for the CME, we also propose feasible experimental tests based on conventional flow harmonics, and demonstrate the emergence of nonleading cross terms with a multiphase transport model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Simple nonparametric reconstruction of parton distributions from limited Fourier information

Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem using a Gaussian process as a Bayesian prior. We propose to fix the hyperparameters of the prior in a meaningful physical fashion, offering a simple implementation, great numerical efficiency, and allowing us to understand and keep control easily of the uncertainty of the reconstruction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

tomoCAM : fast model-based iterative reconstruction via GPU acceleration and non-uniform fast Fourier transforms

X-ray-based computed tomography is a well established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the brightness and detector technology of tomography instruments at synchrotron sources. These advancements have led to the emergence of new observations and discoveries, with improved capabilities such as faster frame rates, larger fields of view, higher resolution and higher dimensionality. These advancements have enabled the material science community to expand the scope of tomographic measurements towards increasingly in situ and in operando measurements. In these new experiments, samples can be rapidly evolving, have complex geometries and restrictions on the field of view, limiting the number of projections that can be collected. In such cases, standard filtered back-projection often results in poor quality reconstructions. Iterative reconstruction algorithms, such as model-based iterative reconstructions (MBIR), have demonstrated considerable success in producing high-quality reconstructions under such restrictions, but typically require high-performance computing resources with hundreds of compute nodes to solve the problem in a reasonable time. Here, tomoCAM , is introduced, a new GPU-accelerated implementation of model-based iterative reconstruction that leverages non-uniform fast Fourier transforms to efficiently compute Radon and back-projection operators and asynchronous memory transfers to maximize the throughput to the GPU memory. The resulting code is significantly faster than traditional MBIR codes and delivers the reconstructive improvement offered by MBIR with affordable computing time and resources. tomoCAM has a Python front-end, allowing access from Jupyter -based frameworks, providing straightforward integration into existing workflows at synchrotron facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Fourier Analysis-Based Evolutionary Multi-Objective Multiphysics Optimization of Liquid-Cooled Heat Sinks

Optimal heat dissipation in power modules can significantly increase their power density. Removing the generated heat is critical for capturing the benefits of advanced semiconductor materials and improving the reliability of the device operation. This article proposes a design optimization method for liquid-cooled heat sinks that use a Fourier analysis-based tool and an evolutionary optimization algorithm to optimize the heat sink geometry for specified objectives. The optimized heat sink geometry is then compared with state-of-the-art solutions in literature based on finite element analysis of different designs. The proposed methodology can develop complex geometries that outperform the conventional heat sink geometries.

Sahu, Raj↗

DOE OSTI2020

Model-less Source Location for Forced Oscillation based on Synchrophasor and Moving Fast Fourier Transformation

Forced oscillations in power systems occur when the grid is driven by an external and periodic force. To quickly detect and locate the source of the forced oscillation is critical in terms of ensuring the reliability of an interconnected power grid. This paper explores the electromechanical wave propagation theory and the Fast Fourier Transformation to analyze the forced oscillations. It proposes a model-less, adaptive, fast, and accurate source location algorithm. The proposed algorithm is extensively evaluated through simulation data from a 70k-bus U.S. Eastern Interconnection test system and field-collected synchrophasor data from the distribution-level wide-area monitoring system, FNET/GridEye. The evaluation results demonstrate the correctness and effectiveness of the proposed model-less forced oscillation source location algorithm.

Wang, Weikang↗

DOE OSTI2025

Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform

Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leveraged digital quantum resources, such as discrete-variable (DV) systems like qubits, rather than analog quantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals—specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.

42 ENGINEERING↗

DOE OSTI2025

Spatio-temporal Fourier Transformer for Long-term Dynamics Prediction (StFT) v1.0

We propose a novel machine learning model spatio-temporal Fourier transformer (StFT) to emulate long-term dynamics of multi-scale and multi-physics systems. Our method StFT overcomes the limitations of rapid error accumulation, particularly in long-term forecasting of systems characterized by complex and coupled dynamics. StFT achieves outstanding accuracy and computational efficiency by effectively capturing multi-scale interactions, and quantify the uncertainties inherent in the predictions. Our model leverages a structured hierarchy of StFT blocks, and explicitly captures dynamics across both macro- and micro- spatial scales. Evaluations conducted on three benchmark datasets (plasma, fluid, and atmospheric dynamics) demonstrate the advantages of our approach over state-of-the-art ML methods.

Bai, Zhe [Lawrence Berkeley National Laboratory (L↗

DOE OSTI2023

High-bandwidth image-based predictive laser stabilization via optimized Fourier filters

Controlling the delivery of kHz-class pulsed lasers is of interest in a variety of industrial and scientific applications, from next-generation laser-plasma acceleration to laser-based x-ray emission and high-precision manufacturing. The transverse position of the laser pulse train on the application target is often subject to fluctuations by external drivers (e.g., room cooling and heating systems, motorized optics stages and mounts, vacuum systems, chillers, and/or ground vibrations). For typical situations where the disturbance spectrum exhibits discrete peaks on top of a broad-bandwidth lower-frequency background, traditional PID (proportional-integral-derivative) controllers may struggle, since as a general rule PID controllers can be used to suppress vibrations up to only about 5%–10% of the sampling frequency. Here, a predictive feed-forward algorithm is presented that significantly enhances the stabilization bandwidth in such laser systems (up to the Nyquist limit at half the sampling frequency) by online identification and filtering of one or a few discrete frequencies using optimized Fourier filters. Furthermore, the system architecture demonstrated here uses off-the-shelf CMOS cameras and piezo-electric actuated mirrors connected to a standard PC to process the alignment images and implement the algorithm. To avoid high-end, high-cost components, a machine-learning-based model of the piezo mirror’s dynamics was integrated into the system, which enables high-precision positioning by compensating for hysteresis and other hardware-induced effects. A successful demonstration of the method was performed on a 1 kHz laser pulse train, where externally-induced vibrations of up to 400 Hz were attenuated by a factor of five, far exceeding what could be done with a standard PID scheme.

Natal, Joseph↗

DOE OSTI2022

Fourier-method beam analysis for coherent vertical cavity surface emitting laser arrays

Effective engineering and exploitation of coherently coupled vertical cavity surface emitting laser arrays will benefit from simple and fast characterization of the optical coupling and coherence. We propose a Fourier method of analyzing beam profiles as an alternative to the prior beam visibility analysis and show that the mode suppression ratio and phase between a pair of supermodes can be extracted. Our analysis enables fast quantitative determination of the array coherence and supermode characteristics.

Strzebonski, Pawel (ORCID:0000000156286296)↗

DOE OSTI2021

Lifetime-resolved photon-correlation Fourier spectroscopy

The excited state population of single solid-state emitters is subjected to energy fluctuations around the equilibrium driven by the bath and relaxation through the emission of phonons or photons. Simultaneous measurement of the associated spectral dynamics requires a technique with a high spectral and temporal resolution with an additionally high temporal dynamic range. We propose a pulsed excitation-laser analog of photon-correlation Fourier spectroscopy (PCFS), which extracts the linewidth and spectral diffusion dynamics along the emission lifetime trajectory of the emitter, effectively discriminating spectral dynamics from relaxation and bath fluctuations . This lifetime-resolved PCFS correlates photon-pairs at the output arm of a Michelson interferometer in both their time-delay between laser-excitation and photon-detection T and the time-delay between two photons τ . We propose the utility of the technique for systems with changing relative contributions to the emission from multiple states, for example, quantum emitters exhibiting phonon-mediated exchange between different fine-structure states.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Maskless Fourier transform holography

Fourier transform holography is a lensless imaging technique that retrieves an object's exit-wave function with high fidelity. It has been used to study nanoscale phenomena and spatio-temporal dynamics in solids, with sensitivity to the phase component of electronic and magnetic textures. However, the method requires an invasive and labor-intensive nanopatterning of a holography mask directly onto the sample, which can alter the sample properties, forces a fixed field-of-view, and leads to a low signal-to-noise ratio at high resolution. In this work, we propose using wavefront-shaping diffractive optics to create a structured probe with full control of its phase at the sample plane, circumventing the need for a mask. We demonstrate in silico that the method can image nanostructures and magnetic textures and validate our approach with a visible light-based experiment. The method enables investigation of a plethora of phenomena at the nanoscale including magnetic and electronic phase coexistence in solids, with further uses in soft and biological matter research.

Keskinbora, Kahraman↗

DOE OSTI2022

High-dimensional discrete Fourier transform gates with a quantum frequency processor

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this article, we show that d -point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d . We verify gate fidelity F W > 0.9997 and success probability P W > 0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multistage Training

The recent development of neural operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this article, we use the Fourier neural operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground-motion simulations on different frequencies and show the frequency bias of the FNO model, that is, it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multistage FNO training, that is, after training a stage 1 FNO model for estimating the ground motion, we use a second FNO model as the stage 2 to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multistage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground-motion simulations. Thus the multistage training FNO improves the accuracy and realism of the ground-motion simulations.

earthquakes↗

DOE OSTI2020

The Connection of Adiabaticity to the Fourier Transform

This is probably the first thing I’d suggest anyone learns about adiabatic transitions because it tells you how a linear system reacts to an arbitrary forcing function. Not all systems are linear but they are usually locally linear near their stable fixed point. I think Scott Berg pointed out the relation to the Fourier transform to me and there’s probably literature about this under generic dynamical systems.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Feasibility of Using Fourier Neural Operators for 3D Elastic Seismic Simulations

Seismic simulations in three-dimensional (3D) Earth models are important in many of the seismological applications related to our lab’s mission, however, accurate high-fidelity simulations are computationally costly. We investigated the capabilities of the newly developed Fourier Neural Operator (FNO) to solve the 3D elastic wave equations for seismic simulations. We generated simulation data for training the FNO model, and analyzed its performance on various test cases, such as the performance with different number of training data, different resolutions, and on more canonical structures. We found the FNO model can reproduce 3D seismic simulations with high accuracy and ~169 times faster on a small spatial grid size of 16 x 16 x16. When applied on higher resolution data, we found that transfer learning with fine-tuning on a small amount of data achieves reasonable results. This feasibility study showed promising results for using FNO’s for 3D seismic simulations and represents the foundation of further research to develop this into a more mature approach for different seismological applications. The potential impact of this project will provide techniques for large-scale or real-time applications of solving PEDs in support of national lab’s programs.

58 GEOSCIENCES↗

DOE OSTI2024

Optimal Control for Fourier Transform on Qudits

In this work, we develop a protocol to find the optimal control pulse for implementing the Quantum Fourier Transform (QFT) on qudit-based hardware. We focus on two types of controls: (1) qubit-qudit dispersive coupling with qubit and qudit drives, and (2) qubit-qudit system with tunable coupling and qubit drive. We observe that for both systems, the minimum gate time grows linearly as a function of the size of the logical space. We find that the latter system supports faster pulses, requiring 45% shorter pulse time.

Ha, Triet↗