Search NASA⌕ Search

SEARCH · Search NASA

Results for “data ordering”

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 721 records · Page 40

CMLM (Co-Optimized Machine-Learned Manifolds) [SWR-23-41]

Co-optimized Machine-Learned Manifolds (CMLM) is a data-driven approach for developing reduced-order manifold models for high-dimensional chemically reacting systems. It involves a specially designed neural network, the training of which simultaneously optimizes linear combinations of species that define the manifold, nonlinear mapping to outputs of interest such as reaction rates, and (optionally) subfilter closure for large eddy simulation. This software package provides an implementation of the CMLM approach in Python using the PyTorch machine learning library. A few example cases are included, showing how the tool can be applied to different types of data from 0D and 1D reacting simulations performed using Cantera. The neural networks can be saved in a format that is readable by the Pele suite of combustion solvers for use in reacting computational fluid dynamics simulations. This software repository contains several python scripts to perform various tasks associated with the Co-optimized Machine Learned Manifolds (CMLM) model, which is described in Perry, Henry de Frahan, and Yellapantula, CNF, 2022 (https://doi.org/10.1016/j.combustflame.2022.112286). This includes not only the code that defines the CMLM model, but also scripts to generate suitable training data, scripts to pre-process the data, scripts to train the CMLM model, and scripts to plot the output, as well as various other helper files. The scripts depend on several commonly used python libraries for data analysis and chemical reaction computations. The trained models that result from this tool are designed to work with the an interface being implemented in the Pele suite of reacting flow solvers (https://github.com/AMReX-Combustion).

Perry, Bruce↗

Bridging the Gap between Cosmological Simulations with Graph Neural Networks and Domain Adaptation

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross dataset tasks (up to 28% better relative error and up to almost an order of magnitude better χ 2 ). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

97 MATHEMATICS AND COMPUTING↗

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks (up to $28\%$ better relative error and up to almost an order of magnitude better $\chi^2$). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

Data Science Meets Physical Organic Chemistry

At the heart of synthetic chemistry is the holy grail of predictable catalyst design. In particular, researchers involved in reaction development in asymmetric catalysis have pursued a variety of strategies toward this goal. This is driven by both the pragmatic need to achieve high selectivities and the inability to readily identify why a certain catalyst is effective for a given reaction. While empiricism and intuition have dominated the field of asymmetric catalysis since its inception, enantioselectivity offers a mechanistically rich platform to interrogate catalyst-structure response patterns that explain the performance of a particular catalyst or substrate. In the early stages of an asymmetric reaction development campaign, the overarching mechanism of the reaction, catalyst speciation, the turnover limiting step, and many other details are unknown or posited based on related reactions. Considering the unclear details leading to a successful reaction, initial enantioselectivity data are often used to intuitively guide the ultimate direction of optimization. However, if the conditions of the Curtin-Hammett principle are satisfied, then measured enantioselectivity can be directly connected to the ensemble of diastereomeric transition states (TSs) that lead to the enantiomeric products, and the associated free energy difference between competing TSs (ΔΔ G ‡ = - RT ln[( S )/( R )], where ( S ) and ( R ) represent the concentrations of the enantiomeric products). We, and others, speculated that this important piece of information can be leveraged to guide reaction optimization in a quantitative way. Although traditional linear free energy relationships (LFERs), such as Hammett plots, have been used to illuminate important mechanistic features, we sought to develop data science derived tools to expand the power of LFERs in order to describe complex reactions frequently encountered in modern asymmetric catalysis. Specifically, we investigated whether enantioselectivity data from a reaction can be quantitatively connected to the attributes of reaction components, such as catalyst and substrate structural features, to harness data for asymmetric catalyst design. In this context, we developed a workflow to relate computationally derived features of reaction components to enantioselectivity using data science tools. The mathematical representation of molecules can incorporate many aspects of a transformation, such as molecular features from substrate, product, catalyst, and proposed transition states. Statistical models relating these features to reaction outputs can be used for various tasks, such as performance prediction of untested molecules. Perhaps most importantly, statistical models can guide the generation of mechanistic hypotheses that are embedded within complex patterns of reaction responses. Overall, merging traditional physical organic experiments with statistical modeling techniques creates a feedback loop that enables both evaluation of multiple mechanistic hypotheses and future catalyst design. In this Account, we highlight the evolution and application of this approach in the context of a collaborative program based on chiral phosphoric acid catalysts (CPAs) in asymmetric catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NOMAD total scattering dataset for SMC data challenge

The data provided for this challenge was measured using the Nanoscale-Ordered Materials Diffractometer (NOMAD) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. The data is stored in a hdf5 file following the NeXus standard and can be read with tools built for either. While the NeXus format is self-describing, there is benefit to explaining some details. The data is stored in 4 NXentries in the file. The NXentries that begin with 'amorphous_SiO2' are for the amorphous data, and the NXentries that begin with 'crystalbolite_SiO2' are for the crystalline material. Solutions that were produced by the scientist are in the entries that end with '_byhand'. Each of the NXdata groups are the plottable data with the 'signal', axes, and (in the case of by-hand components) 'auxiliary_signals' describing which fields should be used. The by-hand component ranges are listed in a 'component' attribute of the various signals. The filtered Sr data is the Fourier transform of the combined components. The data can be quickly viewed using tools such as Nexpy or HDFview. Most languages have libraries that can work with HDF5 (eg. H5py for python) a partial list is provided at https://manual.nexusformat.org/utilities.html The data can be quickly viewed using tools such as Nexpy or HDFview. https://neutrons.ornl.gov/nomad https://www.hdfgroup.org/solutions/hdf5 https://www.nexusformat.org/

36 MATERIALS SCIENCE↗

Perovskite Sorbent Oxygen Separation Modeling with MFiX

This document chronicles the development and implementation of computational kinetic rate models that capture absorption and desorption characteristics of the National Energy Technology Laboratory (NETL) developed perovskite, Sr 1-x Ca x FeO 3-δ . Two paths to create accurate kinetic rates were followed: (1) an isothermal rate approach where thermogravimetric (TGA) data are recast as oxygen capacities through a pseudo-second order Lagergren equation (He et al., 2009); and (2) a more traditional Arrhenius approach where experimental data are fit with a power law model to derive associate activation energies (Bulfin et al., 2020a). For reference, the mathematics and associate experimental strategies that support these derivations are included in this report. In addition, computational fluid dynamics (CFD) models were developed to utilize both kinetic rate formulations and applied to simulate oxygen uptake and release in small scale scenarios. The program Multiphase Flow with interphase eXchanges (MFiX) was used to create: (1) discrete element method (DEM) simulations of a single tube of granular perovskite experiencing isothermal O 2 -absorption; and desorption and (2) two-fluid-model (TFM) non-isothermal simulations of perovskite O 2 -absorption and desorption tubes that share a wall. Conjugate heat transfer between steel walled tubes and the perovskite bed were managed with user-defined functions. As the project moves to simulating larger scale devices that will require more robust conjugate heat transfer methods, developed kinetic rates and associate methodologies have been recast for use in the ANSYS Fluent CFD program.

36 MATERIALS SCIENCE↗

Topaz, a Potential Volatile-Carrier in Cold Subduction Zone: Constraint from Synchrotron X-ray Diffraction and Raman Spectroscopy at High Temperature and High Pressure

The equation of state and stability of topaz at high-pressure/high-temperature conditions have been investigated by in situ synchrotron X-ray diffraction (XRD) and Raman spectroscopy in this study. No phase transition occurs on topaz over the experimental pressure–temperature ($P-T$) range. The pressure–volume data were fitted by the third-order Birch–Murnaghan equation of state (EoS) with the zero-pressure unit–cell volume V 0 = 343.86 (9) Å 3 , the zero-pressure bulk modulus K 0 = 172 (3) GPa, and its pressure derivative K’ 0 = 1.3 (4), while the obtained K 0 = 155 (2) GPa when fixed K’ 0 = 4. In the pressure range of 0–24.4 GPa, the vibration modes of in-plane bending OH-groups for topaz show non-linear changes with the increase in pressure, while the other vibration modes show linear changes. Moreover, the temperature–volume data were fitted by Fei’s thermal equation with the thermal expansion coefficient α 300 = 1.9 (1) × 10 –5 K –1 at 300 K. Finally, the $P-T$ stability of topaz was studied by a synchrotron-based single-crystal XRD at simultaneously high $P-T$ conditions up to ~10.9 GPa and 700 K, which shows that topaz may maintain a metastable state at depths above 370 km in the upper mantle along the coldest subducting slab geotherm. Thus, topaz may be a potential volatile-carrier in the cold subduction zone. It can carry hydrogen and fluorine elements into the deep upper mantle and further affect the geochemical behavior of the upper mantle.

36 MATERIALS SCIENCE↗

Searching for Gravitational Waves from Cosmological Phase Transitions with the NANOGrav 12.5-Year Dataset

We search for a first-order phase transition gravitational wave signal in 45 pulsars from the NANOGrav 12.5-year dataset. We find that the data can be modeled in terms of a strong first order phase transition taking place at temperatures below the electroweak scale. However, we do not observe any strong preference for a phase-transition interpretation of the signal over the standard astrophysical interpretation in terms of supermassive black hole mergers; but we expect to gain additional discriminating power with future datasets, improving the signal to noise ratio and extending the sensitivity window to lower frequencies. An interesting open question is how well gravitational wave observatories could separate such signals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evidence of Mass Ordering of Charm and Bottom Quark Energy Loss in Au+Au Collisions at RHIC

Abstract Partons traversing the strongly interacting medium produced in heavy-ion collisions are expected to lose energy depending on their color charge and mass. We measure the nuclear modification factors for charm- and bottom-decay electrons, defined as the ratio of yields, divided by the number of binary nucleon–nucleon collisions, in $$\sqrt{s_{\textrm{NN}}}=200$$ s NN = 200 GeV Au+Au collisions to p + p collisions ( $$R_{\textrm{AA}}$$ R AA ), or in central to peripheral Au+Au collisions ( $$R_{\textrm{CP}}$$ R CP ). We find the bottom-decay electron $$R_{\textrm{AA}}$$ R AA and $$R_{\textrm{CP}}$$ R CP to be significantly higher than those of charm-decay electrons. Model calculations including mass-dependent parton energy loss in a strongly coupled medium are consistent with the measured data. These observations provide evidence of mass ordering of charm and bottom quark energy loss when traversing through the strongly coupled medium created in heavy-ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scientific Discovery with Physics-Informed System Identification (Abbreviated Report)

My fellowship research focused on making physics-based simulations faster and more useful through machine learning. Many problems in science and engineering are governed by partial differential equations, but high-fidelity simulations are often too expensive to run repeatedly. I worked on improving Latent Space Dynamics Identification (LaSDI), a reduced-order modeling framework that compresses large simulation data sets into a smaller representation and then learns how that representation evolves over time. The motivation was to develop reduced models that remain accurate for more challenging systems, especially when predictions must remain reliable over long time intervals or when the underlying dynamics are more complicated than standard methods can easily handle. I also contributed to related work on Quandary, a high-performance software effort for simulation and control of open quantum systems, before focusing primarily on Latent Space Dynamics Identification methods. The main outcomes of the fellowship were two new algorithms (both of which were published), Rollout-LaSDI and Higher-Order LaSDI, together with supporting work on multi-stage Latent Space Dynamics Identification. Rollout-LaSDI improved long-term prediction by training the model to stay accurate over extended time horizons, and Higher-Order LaSDI broadened the method so it could model systems with higher-order time dynamics. My contributions to multistage Latent Space Dynamics Identification also helped show that its later training stages could be simplified without losing effectiveness, and that this behavior held across different model architectures and training strategies. Taken together, these advances improved the accuracy, flexibility, and practical value of reduced-order modeling tools for computational science.

97 MATHEMATICS AND COMPUTING↗

Implementation of an Experimental Setup Based on the Three-Omega Method for Thermal Conductivity Measurements of Molten Salts

Molten salt reactors (MSRs) are one of the most promising next-generation nuclear reactor designs which use molten salts as the fuel and coolant. To design, model, predict, license, and operate MSRs, the behavior of the fuel and coolant must be understood as a function of temperature and irradiation, i.e., burnup. Of particular importance and complexity is the reliable and reproducible measurement of thermal conductivity of molten salts at high temperatures (> 500 °C). Thermal conductivity provides information on the rate at which heat passes through a specified material and is dependent on chemical composition. Currently, in the national laboratory complex, several methods for measuring thermal conductivity on molten salt systems are under development, however, to date, consistent data have not been produced. Typically, thermal conductivity measurements of high-temperature melts have been conducted by using the Transient Hot Wire (THW) method where thermal conductivity is determined by the change in temperature over time at a certain distance from a heating wire. Another time-dependent technique is the laser flash method, commonly used for solid samples. Laser flash requires prior measurements of density and heat capacity to calculate the thermal conductivity of the sample, introducing additional measurement errors. Steady state and time-dependent measurements such as THW and laser flash have errors from convection and ambient temperature fluctuations (heat radiation). In order to produce high fidelity thermal conductivity data, a measurement technique needs to be developed that will reduce the effect of convection at high temperatures by measuring in a very fast time window. In addition, to measure on actinide and irradiated salts the sample size should be small. Therefore, this project aims to develop a frequency-domain technique based on the three-omega (3?) method, previously proven to work on solids, nanofluids and low temperature solar salts (25 to 250 °C). If the 3?-device can be designed with materials that can withstand high temperatures (>500 °C) and can be configured to reduce errors due to convection, then it would prove to be a valuable technique for ensuring thermal conductivity on molten salt systems needed for MSR development. For this proposal, the 3? instrument will be designed, assembled, and tested on non-radioactive salts before being used on actinide bearing salts. In addition, a thermal model will be developed to determine the thermal conductivity of the sample from the measured thermal oscillation of the sensor. Because 3? is a direct method that requires a small volume of sample and works in a very fast time window, it will aid in suppressing the interference due to convection which is ideal when working with high temperature liquid samples.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Magnetic properties of Tm 3+ in layered triangular lattices

Rare-earth chalcogenides, ARCh 2 (A = alkali metal or monovalent ion; R = rare-earth elements; Ch = O, S, and Se), have been identified as promising candidates for exploring a variety of novel frustrated quantum magnetic phenomena. Tm-based series, ATmCh 2 , where Tm 3+ ions are arranged on various frustrated geometric lattices, provide a platform for investigating the competitions among spin–orbit coupling, crystal field effects, and magnetic exchange interactions in the context of geometric frustration. In this study, we present how the crystallographic structures of newly synthesized ATmSe 2 (A = Li and Na) influence their frustrated magnetic behaviors. Both NaTmSe 2 and LiTmSe 2 adopt a delafossite-type structure with a two-dimensional (2D) triangular lattice, but LiTmSe 2 has a much shorter c-axis parameter compared to this in NaTmSe 2 . Both heat capacity and magnetic susceptibility measurements confirm the absence of long-range magnetic order in either compound. However, magnetic measurements data reveals the differences in magnetic interactions: NaTmSe 2 exhibits features of low-dimensional magnetism, likely driven by its layered crystal structure, compared to LiTmSe 2 .

Crystal field theory↗

Flaring Stars in a Non-targeted mm-wave Survey with SPT-3G

We present a flare star catalog from four years of non-targeted millimeter-wave survey data from the South Pole Telescope (SPT). The data were taken with the SPT-3G camera and cover a 1500-square-degree region of the sky from $20^{h}40^{m}0^{s}$ to $3^{h}20^{m}0^{s}$ in right ascension and $-42^{\circ}$ to $-70^{\circ}$ in declination. This region was observed on a nearly daily cadence from 2019-2022 and chosen to avoid the plane of the galaxy. A short-duration transient search of this survey yields 111 flaring events from 66 stars, increasing the number of both flaring events and detected flare stars by an order of magnitude from the previous SPT-3G data release. We provide cross-matching to Gaia DR3, as well as matches to X-ray point sources found in the second ROSAT all-sky survey. We have detected flaring stars across the main sequence, from early-type A stars to M dwarfs, as well as a large population of evolved stars. These stars are mostly nearby, spanning 10 to 1000 parsecs in distance. Most of the flare spectral indices are constant or gently rising as a function of frequency at 95/150/220 GHz. The timescale of these events can range from minutes to hours, and the peak $\nu L_{\nu}$ luminosities range from $10^{27}$ to $10^{31}$ erg s$^{-1}$ in the SPT-3G frequency bands.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗

Finite-temperature many-body perturbation theory in the canonical ensemble

Benchmark data are presented for the zeroth- through third-order many-body perturbation corrections to the electronic Helmholtz energy, internal energy, and entropy in the canonical ensemble in a wide range of temperature. They are determined as numerical λ-derivatives of the respective quantities computed by thermal full configuration interaction with a perturbation-scaled Hamiltonian, $\hat{H} = \hat{H}_0 + λ\hat{V}$. Sum-over-states analytical formulas for up to the third-order corrections to these properties are also derived as analytical λ-derivatives. These formulas, which are verified by exact numerical agreement with the benchmark data, are given in terms of the Hirschfelder–Certain degenerate perturbation energies and should be valid for both degenerate and nondegenerate reference states at any temperature down to zero. Further, the results in the canonical ensemble are compared with the same in the grand canonical ensemble.

74 ATOMIC AND MOLECULAR PHYSICS↗

Analysis of Persistent Soiling Losses: Cooperative Research and Development (Final Report)

The Contractor will analyze data from sensors and equipment provided by Participant in order to provide the basis for understanding of the processes and rates for the formation of 'persistent' soiling (soiling not removed by rain). The resulting, data, technical report, and publications will provide the basis for Participant to improve it's predictive soiling model.

14 SOLAR ENERGY↗

Hydraulic Properties Data Package for the E-Area Soils, Cementitious Materials, and Waste Zones–Update

Hydraulic property estimates for the soils, cementitious materials, and waste zones associated with the E-Area low-level radioactive waste disposal units have been provided to support the Performance Assessments (PA) for the E-Area Low-Level Waste Facility (LLWF). Nominal or “best estimate” hydraulic property values for use in the deterministic modeling are provided along with representations of the hydraulic property value uncertainty for use in sensitivity and uncertainty modeling. The hydraulic properties provided for each of the E-Area materials include: porosity ( η ), dry bulk density ( ρ b ), particle density (ρ p ), saturated hydraulic conductivity ( K sat ), characteristic curves (suction head, saturation, and relative permeability), and effective diffusion coefficient ( D e ). A representation of the uncertainty associated with each property, except for the characteristic curves, is provided for each material, except for the E-Area waste zones. These nominal parameter values for each of the E-Area soils, cementitious materials, and waste zones, and, where indicated, parameter uncertainty representations, are based upon the following in order of priority: Site-specific field data, Site-specific laboratory data, Similarity to material with site-specific field or laboratory data, and Literature data. Additionally, a methodology to represent long-term concrete degradation is provided. Finally, because much of the nominal hydraulic property values and uncertainty representations for the E-Area soils, cementitious materials, and waste zones are based on similarity to other materials or literature data, a methodology to prioritize additional work to better define these values and representations is outlined. Prioritization should be based on the importance of the material and/or property to the results of deterministic, sensitivity, and uncertainty modeling. This prioritization should be established through a process of sensitivity modeling. This report supersedes the previous hydraulic properties data package. Revision 1 contains clarifications, updates and corrections to text, figures and tables in a number of places in the report along with some minor editing.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

High Resolution Data Analysis: Plans and Prospects [Book Chapter]

Herein, a report on the progress on the high resolution data analysis of the ADMX experimental results is presented. In this paper, tools are developed and tested on a blind injection mimicking a Maxwellian like signal in the frequency domain. This blind injection will be used as a test bed which can be later implemented on all the high resolution data. The high resolution data is stored in the Fermilab server. In this analysis a PostgreSQL query was made to ensure the blind injection is in the middle of the frequency spectrum and 19 such files were found. The time series data is read using a c++ program. An apodization function is applied on the time series data and zero filled to reduce the frequency spacing in order to achieve a better interpolation. A FFTW header is used to compute the Fourier transform of the time series data. A Savitzky–Golay filter is applied on the unnormalized power which then can be used to remove the spectral shape. Each frequency spectrum has a bandwidth of 50 kHz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗