Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fourier”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

System and method for high efficiency electrochemical desalination

The present disclosure relates to a capacitive deionization (CDI) system for desalinating salt water. The system may have a capacitor formed by spaced apart first and second electrodes, which enable a fluid flow containing salt water to pass either between them or through them. An input electrical power source is configured to generate an electrical forcing signal between the two electrodes. The electrical forcing signal represents a periodic signal including at least one of voltage or current, and which can be represented as a Fourier series. One component of the Fourier series is a constant, and a second component of the Fourier series is a sinusoidal wave of non-zero frequency which has the highest amplitude of the additive components of the Fourier series. The amplitude of the sinusoidal wave component is between 0.85 and 1.25 times the amplitude of the periodic signal.

Hawks, Steven↗
DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part II

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation ( i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Finally, two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Robust Automatic EXAFS First-Shell Fits

Extended X-ray absorption fine structure (EXAFS) is a widely used technique for atomic structure determination. Fourier transformation connects EXAFS in k space and R space. However, determining the appropriate k-range for the transformation can be challenging, but critical for the first-shell fit. In this study, we present an automatic method to determine the k-range using the Larch package and a Python program. The first step is to estimate spectral noise across a series of k-ranges with a fixed minimum value and identify the optimal maximum value in the k-range (k max ). The k max is determined by an empirical noise threshold that marks the point where the noise level in the Fourier transformed spectrum changes dramatically. Using the obtained k max value, the first shell is modeled to determine the minimum k value (k min ) by optimizing the background function through alignment of the spectrum with theory. The optimal k min corresponds to the point of the minimum R-factor, which quantifies the difference between the experimental and fitted spectrum. Our method was tested on various typical datasets and yielded suitable k-ranges for Fourier transformation and accurate first-shell fits. This approach helps avoid unreliable, irreproducible data analysis, especially for noisy data from diluted samples, and enables robust automatic first-shell EXAFS fitting.

EXAFS analysis↗
DOE OSTI2021

Emission spectroscopy with coded apertures for enhanced dimensionality

A coded aperture is used to demonstrate emission spectroscopy from multiple one-dimensional measurement locations simultaneously with a single camera. The coded aperture mask has several columns of periodic apertures, each with a unique spatial frequency. Light transmitted through all mask columns is detected through an imaging spectrometer. Dispersed light from the various mask columns overlaps on the spectrometer camera but is separated using Fourier-domain filtering using the known spatial frequencies of the mask. As the coded aperture is placed at an image plane, each Fourier-filtered spectrogram comes from a unique one-dimensional measurement location. This technique represents a significant increase in the amount of spatially and spectrally resolved emission data available using a single emission spectrometer and camera at the expense of some spatial resolution due to the Fourier filtering. This instrument is particularly useful for studying transient, non-repeating events. Megahertz-rate emission spectroscopy from five one-dimensional measurement locations is demonstrated with explosive fireballs using a single camera. Optical design parameters and instrument performance characteristics are discussed.

42 ENGINEERING↗
DOE OSTI2025

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗
DOE OSTI2020

Geometrical quasi-ballistic effects on thermal transport in nanostructured devices

In this work, we employ thermoreflectance thermal imaging to directly measure the steady-state two-dimensional (2D) temperature field generated by nanostructured heat sources deposited on silicon substrate with different geometrical configurations and characteristic sizes down to 400nm. The analysis of the results using Fourier’s law not only breaks down as size scales down, but it also fails to capture the impact of the geometry of the heat source. The substrate effective Fourier thermal conductivities fitted to wire-shaped and circular-shaped structures with identical characteristic lengths are found to display up to 40% mismatch. Remarkably, a hydrodynamic heat transport model reproduces the observed temperature fields for all device sizes and shapes using just intrinsic Si parameters, i.e., a geometry and size-independent thermal conductivity and nonlocal length scale. The hydrodynamic model provides insight into the observed thermal response and of the contradictory Fourier predictions. We discuss the substantial Silicon hydrodynamic behavior at room temperature and contrast it to InGaAs, which shows less hydrodynamic effects due to dominant phonon-impurity scattering.

42 ENGINEERING↗
DOE OSTI2022

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗
DOE OSTI2024

A FFT-based mesoscale continuum dislocation mechanics with defect energy: Applications to composites and polycrystals

A crystal plasticity elastoviscoplastic FFT (fast Fourier transform) formulation with a mesoscale continuum field dislocation mechanics model is presented, which incorporates a defect energy density that depends on GND densities and an associated material length scale. This allows to thermodynamically derive internal length scale dependent intra-crystalline backstress and Peach–Koehler force acting on GND densities. The model considers GND density evolution through a filtered numerical spectral approach, which is coupled with stress equilibrium through the elastoviscoplastic FFT algorithm. The discrete Fourier transform (DFT) method together with finite difference (FD) schemes is applied to solve both the backstress tensor and the Fourier–Green operator. Numerical results are first reported for two-phase laminate composites with plastic single crystal channels and elastic precipitates for shear loadings. Channel size effects are simulated and analyzed on the overall and local hardening behaviors during monotonous loadings. In addition, the evolutions of GND densities and the role of their associated backstress on size effects are examined during reversible shear loading. In a second part, the role of the defect energy internal length scale on polycrystal’s hardening during tension–compression is discussed. The results are compared to those obtained using FFT-based continuum field dislocation mechanics without defect energy.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at $E$ $beam$ / $A$ =1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. In conclusion, we find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Machine learning surrogate models for Landau fluid closure

The first result of applying the machine/deep learning technique to the fluid closure problem is presented in this letter. As a start, three different types of neural networks (multilayer perceptron (MLP), convolutional neural network (CNN) and two-layer discrete Fourier transform (DFT) network) were constructed and trained to learn the well-known Hammett-Perkins Landau fluid closure in configuration space. We found that in order to train a well-preformed network, a minimum size of training data set is needed; MLP also requires a minimum number of neurons in the hidden layers equals to the degrees of freedom in Fourier space despite training data is fed in configuration space. Out of three models DFT performs the best for the clean data most likely due to the existence of nice Fourier expression for Hammett-Perkins closure but it is least robust with respect to input noise. Overall, with appropriate tuning and optimization, all three neural networks are able to accurately predict Hammett-Perkins closure and reproduce the inherit nonlocal feature, suggesting a promising path to calculate more sophisticated closures with the machine/deep learning technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electron hopping heat transport in molecules

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier’s law. At molecular length scales, however, deviations from Fourier’s law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system’s thermal conductance commonly deviates from Fourier’s law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications

This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.

Nuclear science and engineering↗
DOE OSTI2025

HOD-dependent systematics for luminous red galaxies in the DESI 2024 BAO analysis

In this paper, we present the estimation of systematics related to the halo occupation distribution (HOD) modeling in the baryon acoustic oscillations (BAO) distance measurement of the Dark Energy Spectroscopic Instrument (DESI) 2024 analysis. This paper focuses on the study of HOD systematics for luminous red galaxies (LRG). We consider three different HOD models for LRGs, including the base 5-parameter vanilla model and two extensions to it, that we refer to as baseline and extended models. The baseline model is described by the 5 vanilla HOD parameters, an incompleteness factor and a velocity bias parameter, whereas the extended one also includes a galaxy assembly bias and a satellite profile parameter. We utilize the 25 dark matter simulations available in the AbacusSummit simulation suite at z=0.8 and generate mock catalogs for our different HOD models. To test the impact of the HOD modeling in the position of the BAO peak, we run BAO fits for all these sets of simulations and compare the best-fit BAO-scaling parameters α iso and α AP between every pair of HOD models. Furthermore, we do this for both Fourier and configuration spaces independently, using post-reconstruction measurements. We find a 3.3σ detection of HOD systematic for α AP in configuration space with an amplitude of 0.19%. For the other cases, we did not find a 3σ detection, and we decided to compute a conservative estimation of the systematic using the ensemble of shifts between all pairs of HOD models. By doing this, we quote a systematic with an amplitude of 0.07% in α iso for both Fourier and configuration spaces; and of 0.09% in α AP for Fourier space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An efficient method to propagate model uncertainty when inverting seismic data for time domain seismic moment tensors

SUMMARY We present a computationally efficient method to approximately propagate uncertainty when linearly inverting seismic data for point source, time variable moment tensor components. The method is based on the assumption that the data residual, given by the difference between the observed seismic data and the data predicated by a linear inversion, contains the effects of both data and model uncertainty. Our method uses a distribution of data residuals, added directly to the data, in a pseudo-Monte Carlo scheme. Using the assumption that the data residual is a stochastic process, we use the well-known Karhunen–Loève (KL) theorem to construct a distribution of data residuals, where the required basis functions are constructed using Fourier series. The Fourier series are scaled by a product of a random variable and the real-valued spectral amplitudes of the original data residual’s spectrum. Thus, the Fourier series and spectral amplitudes are eigenfunction-eigenvalue pairs used in the KL-based construction of data residual distribution. Using tests with synthetic data, we show that our method compares closely with a Finite Difference Monte Carlo (FDMC) method that we presented previously. More importantly, the method presented here is computationally several orders of magnitude faster than our previous FDMC method, and requires no a priori assumptions of model and/or data uncertainty.

Poppeliers, Christian (ORCID:0000000159526849)↗
DOE OSTI2023

Surface Merging Technique to Design GA-Optimized Heat Sinks

High-power density inverters require efficient and small heat dissipation systems. For liquid cooling systems, an effective heat sink design is important to enable higher heat transfer and keep the pressure drop within reasonable limits. A heat sink geometry generated from an extruded, 1D fast Fourier transform can achieve more even temperature distribution and improved heat transfer than a conventional heat sink. Building on this concept, this paper proposes a new heat sink geometry creation algorithm. Instead of one plane profile being extruded, multiple plane profiles, each created from the fast Fourier transform method, are subsequently merged by smooth surfaces along the flow direction of the heat sink. Thus, a 3D heat sink geometry is created that enables 3D coolant flow and efficient heat transfer. The volume of this design was reduced by 50% compared with pin fin heat sinks. Compared with extruded 1D fast Fourier transform heat sinks, the proposed design showed an approximately 5% device temperature reduction and a 20% pressure drop reduction.

Barua, Himel↗
DOE OSTI2021

Linear Grains

LIGR (Linear Grains) implements a linear (Fourier mode) analysis of a shock propagating through density perturbations. It has two primary capabilities. First, it calculates the shock front distortion and post-shock flow variables (density, velocity, pressure) for single Fourier mode pairs in two dimensions (a pair of x and y modes). Second, it calculates these same quantities for a grains-like pre-shock density perturbation, which consists of a sum of many Fourier modes. This grains-like perturbation is a periodic grid of rectangles at a specifiable density and size (the grains), separated by regions of a different specifiable size and density (interstitial spaces between the grains). The single-mode analysis is based on the work of Velikovich et al., Phys. Plasmas 14 072706 (2007).

Li, GraceJ↗
DOE OSTI2020

Synthetic-aperture radar (SAR) imaging with range-resolved reflection data

SAR imaging may be performed with range-resolved reflection data, where a spread-spectrum signal, such as a code division multiple access (CDMA) signal, is transmitted instead of a simple frequency chirp. The reflected spread-spectrum signal may be analyzed to gather range-resolved reflection data. Range-resolved reflection data may be gathered at each angular view. This data may be used to construct a more accurate approximation of the Fourier transform of the desired image than can be done by a conventional SAR approach. The image may be reconstructed from this Fourier transform using Fourier inversion techniques similar to those used in conventional SAR approaches. The range-resolved reflection scheme generally requires somewhat more processing to recover the image as compared with conventional SAR systems, but provides a significantly more stable image with less degradation from effects that plague conventional SAR systems. This can eliminate the need for phase coherency altogether and also eliminate “phase drift,” which leads to image distortion. This may be especially well suited for high resolution imaging of relatively large targets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Ultrahigh performance LC/FT-MS non-targeted screening for biomass burning organic aerosol with MZmine2 and MFAssignR

In recent years, ultrahigh performance liquid chromatography Fourier transform mass spectrometry (LC/FT-MS) based non-targeted screening (NTS) methods have become increasingly popular for comprehensive analysis of complex organic mixtures. However, applying these methods for environmental complex mixture analysis is challenging due to the extreme complexity of natural samples and a lack of standard samples or surrogates for environmental complex mixtures. Furthermore, limited molecular markers in the databases and insufficient data processing software workflows make the application of these methods more challenging for environmental complex mixtures. In this work, we implement a new NTS data processing workflow to process data collected from ultrahigh performance liquid chromatography and Fourier transform Orbitrap Elite Mass Spectrometry (LC/FT-MS) by combining MZmine2 and MFAssignR, two opensource data processing tools and commercial Mesquite liquid smoke as a surrogate for biomass burning organic aerosol. MZmine2.53 data extraction followed MFAssignR molecular formula assignment offered noise free and highly accurate 1733 individual molecular formulas presented in liquid smoke with 4906 molecular species, including isomers. The results of this new approach were consistent with the results of direct infusion FT-MS analysis confirming its reliability. Over 90% of the molecular formulas presented in mesquite liquid smoke were matched with the molecular formulas of ambient biomass burning organic aerosol. This suggests the potential use of commercial liquid smoke as a surrogate for biomass burning organic aerosol research. Furthermore, the presented method significantly improves the identification of the molecular composition of biomass burning organic aerosol by successfully addressing some of the limitations related to the data analysis and giving a semi quantitative insight into the analysis.

54 ENVIRONMENTAL SCIENCES↗