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Results for “Principal Component Analysis”

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.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Probing the Hydrogen Enhanced Near-Field Emission of ITO without a Vacuum-Gap

In-situ monitoring of the multi-component gas streams in high temperature energy conversion devices offer the promises to higher efficiency via improved understanding of the chemical environments during device operation. While conventional resistive based metal oxide semiconductor gas sensors suffer from strong cross-sensitivity, optical sensing approaches offer intrinsic advantages to achieve gas selectivity based on wavelength specific interactions. This manuscript describes a novel method to achieve multicomponent gas sensing during gas exposure of H2, CO2, CH4and CO in humid high temperature environments. A single sensor element comprised of a perovskite La0.3Sr0.7TiO3(LSTO) oxide thin film layer coated on silica optical fiber was used. The sensing responses consisted of two wavelength-specific near infrared (NIR) mechanisms, namely broadband absorption associated with the metal oxide layer, and wavelength localized thermal emission responses associated with the hydroxyl defects within the silica fiber. Principal component analysis (PCA) was applied to couple the two mechanisms to achieve selective gas identification. Successful discrimination of H2and CO2on a single fiber sensor was achieved, where the results are both stable and reversible. This design demonstrates that by coupling multiple optical mechanisms on a single oxide coated fiber sensor, simple platforms can also achieve multi-component sensing functionality without the added complexity of a sensor array. Thus, it suggests a new approach to construct simple, robust and functional sensor designs capable of gas discrimination and quantification in multi-component gas streams.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2017

Multi-mode humidity sensing with water-soluble copper phthalocyanine for increased sensitivity and dynamic range

Aqueous solubility of copper phthalocyanine-3,4',4',4"'-tetrasulfonic acid tetrasodium salt (CuPcTs) enables fabrication of flexible electronic devices by low cost inkjet printing. We (1) investigate water adsorption kinetics on CuPcTs for better understanding the effects of relative humidity (RH) on hydrophilic phthalocyanines, and (2) assess CuPcTs as a humidity-sensing material. Reaction models show that H 2 O undergoes 2-site adsorption which can be represented by a pair of sequentially-occurring pseudo-first order reactions. Using high frequency (300–700 THz) and low frequency (1–8 MHz) dielectric spectroscopy combined with gravimetric measurements and principal component analysis, we observe that significant opto-electrical changes in CuPcTs occur at RH ≈ 60%. The results suggest that rapid H 2 O adsorption takes place at hydrophilic sulfonyl/salt groups on domain surfaces at low RH, while slow adsorption and diffusion of H 2 O into CuPcTs crystallites leads to a mixed CuPcTs-H 2 O phase at RH > 60%, resulting in high frequency dielectric screening of the film by water and dissociation of Na+ from CuPc(SO 3 -) 4 ions. Lastly, the CuPcTs-H 2 O interaction can be tracked using a combination of gravimetric, optical, and electrical sensing modes, enabling accurate ( ± 2.5%) sensing in the ~0–95% RH range with a detection limit of less than 0.1% RH.

36 MATERIALS SCIENCE↗
DOE OSTI2020

In situ molecular imaging of adsorbed protein films in water indicating hydrophobicity and hydrophilicity

Abstract In situ molecular imaging of protein films adsorbed on a solid surface in water was realized by using a vacuum compatible microfluidic interface and time-of-flight secondary ion mass spectrometry (ToF-SIMS). Amino acid fragments from such hydrated protein films are observed and identified in the positive ion mode and the results are in agreement with reported works on dry protein films. Moreover, water clusters from the hydrated protein films have been observed and identified in both the positive and negative ion mode for a series protein films. Thus, the detailed composition of amino acids and water molecules in the hydrated protein films can be characterized, and the protein water microstructures can be revealed by the distinct three-dimensional spatial distribution reconstructed from in situ liquid ToF-SIMS molecular imaging. Furthermore, spectral principal component analysis of amino acid fragment peaks and water cluster peaks provides unique insights into the water cluster distribution, hydrophilicity, and hydrophobicity of hydrated adsorbed protein films in water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unsupervised learning-enabled pulsed infrared thermographic microscopy of subsurface defects in stainless steel

Metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing method (AM) frequently contain microscopic porosity defects, with typical approximate size distribution from one to 100 microns. Presence of such defects could lead to premature failure of the structure. In principle, structural integrity assessment of LPBF metals can be accomplished with nondestructive evaluation (NDE). Pulsed infrared thermography (PIT) is a non-contact, one-sided NDE method that allows for imaging of internal defects in arbitrary size and shape metallic structures using heat transfer. PIT imaging is performed using compact instrumentation consisting of a flash lamp for deposition of a heat pulse, and a fast frame infrared (IR) camera for measuring surface temperature transients. However, limitations of imaging resolution with PIT include blurring due to heat diffusion, sensitivity limit of the IR camera. We demonstrate enhancement of PIT imaging capability with unsupervised learning (UL), which enables PIT microscopy of subsurface defects in high strength corrosion resistant stainless steel 316 alloy. PIT images were processed with UL spatial–temporal separation-based clustering segmentation (STSCS) algorithm, refined by morphology image processing methods to enhance visibility of defects. The STSCS algorithm starts with wavelet decomposition to spatially de-noise thermograms, followed by UL principal component analysis (PCA), fine-tuning optimization, and neural learning-based independent component analysis (ICA) algorithms to temporally compress de-noised thermograms. The compressed thermograms were further processed with UL-based graph thresholding K-means clustering algorithm for defects segmentation. The STSCS algorithm also includes online learning feature for efficient re-training of the model with new data. For this study, metallic specimens with calibrated microscopic flat bottom hole defects, with diameters in the range from 203 to 76 µm, were produced using electro discharge machining (EDM) drilling. While the raw thermograms do not show any material defects, using STSCS algorithm to process PIT images reveals defects as small as 101 µm in diameter. To the best of our knowledge, this is the smallest reported size of a sub-surface defect in a metal imaged with PIT, which demonstrates the PIT capability of detecting defects in the size range relevant to quality control requirements of LPBF-printed high-strength metals.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Raman chemical imaging of the rhizosphere bacterium Pantoea sp. YR343 and its co-culture with Arabidopsis thaliana

Chemical imaging of plant-bacteria co-cultures renders it possible to characterize bacterial populations and behaviors and their interactions with proximal organisms, under conditions closest to the environment in the rhizosphere. Here Raman micro-spectroscopy and confocal Raman imaging are used as minimally invasive probes to study the rhizosphere bacterial isolate, Pantoea sp. YR343, and its co-culture with model plant Arabidopsis thaliana by combining enhanced Raman spectroscopies with electron microscopy and principal component analysis (PCA). In this work, the presence of carotenoid pigments in the wild type Pantoea sp. YR343 was characterized using resonance Raman scattering, which was also used to confirm successful disruption of the crtB gene in an engineered carotenoid mutant strain. Other components of the Pantoea sp. YR343 cells were imaged in the presence of resonantly enhanced pigments using a combination of surface enhanced Raman imaging and PCA. Pantoea sp. YR343 cells decorated with Ag colloid synthesized ex situ gave spectra dominated by carotenoid scattering, whereas colloids synthesized in situ produced spectral signatures characteristic of flavins in the cell membrane. Scanning electron microscopy (SEM) of whole cells and transmission electron microscopy (TEM) images of thinly sliced cross-sections were used to assess structural integrity of the coated cells and to establish the origin of spectral signatures based on the position of Ag nanoparticles in the cells. Finally, raman imaging was also used to characterize senescent green Arabidopsis thaliana plant roots inoculated with Pantoea sp. YR343, and PCA was used to distinguish spectral contributions from plant and bacterial cells, thereby establishing the potential of Raman imaging to visualize the distribution of rhizobacteria on plant roots.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Induced polarization restricts the conformational distribution of a light-harvesting molecular triad in the ground state

The light-harvesting molecular triad consisting of carotenoid polyene (C), diaryl-porphyrin (P) and pyrrole-fullerene (C60) is a donor–acceptor molecule capable of absorbing incident light in the visible range. Its ability to convert solar energy to electrical excitation and charge separation energy suggests a great potential in real-world applications. The ensemble of its conformations under ambient conditions varies widely according to its electronic state. In previous work, we applied a non-polarizable model to study the conformational distribution of the molecular triad in the ground and charge separated states. However, due to the lack of polarization, which imparts subtle changes in the charge distribution on atoms, molecular simulations fail to produce accurate average dipole moments. We developed the first polarizable model for a molecular triad to investigate the structural and dynamic properties of a molecular triad in the ground state in an explicit organic solvent, tetrahydrofuran (THF). We performed first-principles electronic structure calculations of the individual components in the triad as well as THF and then fit the partial atomic charges to the electrostatic potential using the i-RESP methodology. We validated these force field parameters by comparing the thermodynamic and dynamic properties obtained from molecular dynamics simulations with those from experiments. We enhanced the sampling of the triad conformations with replica exchange molecular dynamics simulations. We characterized the effects of induced polarization on the structural stability of the triad by analyzing the free energy landscapes constructed with polarizable force fields. Furthermore, by using principal component analysis, we found that the molecular triad conformations adopted a small range of torsional angles with induced polarization. The triad conformation solvated in polar solvent with a polarizable force field qualitatively agrees with that obtained from nuclear magnetic resonance spectroscopy.

Starovoytov, Oleg N.↗
DOE OSTI2019

Experiments and computations of microfluidic liquid–liquid flow patterns

We study two-phase liquid–liquid flow patterns in a 500 μm capillary microchannel for four biphasic systems: ethyl acetate/water, 2-pentanol/water, methyl isobutyl ketone/water, and heptane/water. Flow visualization experiments using laser induced fluorescence (LIF) reveal a total of 7 different flow patterns for all solvent pairs, namely slug flow, droplet flow, slug-droplet flow, parallel, annular, dispersed, and irregular flow. A map of different flow patterns was built to delineate the origin of their formation. We find conventional dimensionless groups are insufficient to uniquely identify the flow patterns. Computational fluid dynamics (CFD) modeling in OpenFOAM shows agreement with the experimental flow patterns for most of the two-phase flows. Principal component analysis reduces the dimensionality of potential descriptors of flow patterns and, unlike prior work using two dimensionless numbers, determines six important features that describe >95% of the variance of the experimental flow patterns. These include the total flow rate, the flow rate ratio between the two phases, the capillary and Ohnesorge numbers of the aqueous phase, and the Weber number and velocity of the organic phase. Lastly, we build a decision-tree model to further regress the data and identify the critical features and demonstrate an accuracy in predicting the flow patterns of up to 93%.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Reductive catalytic fractionation of agricultural residue and energy crop lignin and application of lignin oil as antimicrobials

Cheap and abundant waste from bioethanol and agricultural processing industries are an alluring alternative feedstock for biorefineries. In this work, we employ reductive catalytic fractionation (RCF) to depolymerize, over Ru/C powder and Ru/Al 2 O 3 pellets, five herbaceous biomass feedstocks, namely corn stover, miscanthus, switchgrass, sugarcane bagasse, and wheat straw into phenolic monomers with high yields (~40 wt.% based on total (Klason + acid soluble) lignin and > 50 wt.% when stabilized using aldehydes), leaving behind a carbohydrate pulp residue. Interestingly, a polar solvent is sufficient to solubilize and fragment the lignin polymer into monomers without any catalyst. Here, contrary to woody biomass, where the monomer yields are positively correlated with the S-content of lignin, principal component analysis indicates that the monomer yields from herbaceous biomass depend on the content of lignin crosslinker – ferulate. Using NMR, we further identify α – 6 C-C linked oligomers formed from condensation reactions, explaining the unexpected low monomer yields of high β-O-4 herbaceous biomass. Recyclability experiments indicate that catalyst deactivation occurs through sintering, leaching, and fouling. Lignin oil from herbaceous biomass exhibits bacteriostatic effects against Staphylococcus aureus, highlighting a potential application in functional food development and as food or feed preservative.

09 BIOMASS FUELS↗
DOE OSTI2020

Combined Plasmonic Au-nanoparticle and Conducting Metal Oxide High-temperature Optical Sensing with LSTO

<span style="color: rgba(0, 0, 0, 0.79); font-family: &quot;Source Sans Pro&quot;, source-sans-pro, museo_sans300, museo-sans, Arial, sans-serif; font-size: 16px; background-color: rgb(255, 255, 255);">Fiber optic sensor technology offers several advantages for harsh-environment applications. However, the development of optical gas sensing layers that are stable under harsh environmental conditions is an ongoing research challenge. In this work, electronically conducting metal oxide lanthanum-doped strontium titanate (LSTO) films embedded with gold nanoparticles are examined as a sensing layer for application in reducing gas flows at high temperature (600–800 °C). A strong localized surface plasmon resonance (LSPR) based response to hydrogen is demonstrated in the visible region of the spectrum, while a Drude free electron-based response is observed in the near-IR. Characteristics of these responses are studied both on planar glass substrates and on silica fibers. Charge transfer between the oxide film and the gold nanoparticles is explored as a possible mechanism governing the Au LSPR response and is considered in terms of the corresponding properties of the conducting metal oxide-based matrix phase. Principal component analysis is applied to the combined plasmonic and free-carrier based response over a range of temperatures and hydrogen concentrations. It is demonstrated that the combined visible and near-IR response of these films provides improved versatility for multiwavelength interrogation, as well as improved discrimination of important process parameters (concentration and temperature) through application of multivariate analysis techniques.</span>

Wuenschell, Jeffrey K.↗
DOE OSTI2020

Active Learning-driven Quantitative Synthesis-Structure-Property Relations for Improving Performance and Revealing Active Sites of Nitrogen-Doped Carbon for the Hydrogen Evolution Reaction

While quantitative structure-properties relations (QSPRs) have been developed successfully in multiple fields, catalyst synthesis affects structure and in turn performance, making simple QSPRs inadequate. Furthermore, catalysts often have multiple active sites preventing one from obtaining insights into structure-property relations. Here, we develop a data-driven quantitative synthesis-structure-property relation (QS2PRs) methodology to elucidate correlations between catalyst synthesis conditions, structural properties as well as observed performance and to provide fundamental insights into active sites and a systematic way to optimize practical catalysts. Here, we demonstrate the approach to the synthesis of nitrogen-doped catalysts (NDC) made via pyrolysis for the performance of the electrochemical hydrogen evolution reaction (HER), quantified by the onset potential and the current density. We determine crystallinity, nitrogen species type and fraction, surface area, and pore structure of the NDC’s using XRD, XPS, and BET characterization. We demonstrated that an active learning-based optimization combined with various elementary machine learning tools (regression, principal component analysis, partial least squares) can efficiently identify optimum pyrolysis conditions to tune structural characteristics and performance with concomitant savings in materials and experimental time. Unlike previous reports on the importance of pyridinic or graphitic nitrogen, we discover that the electrochemical performance is not driven by a single catalyst property; rather, it arises from a multivariate influence of nitrogen dopants, pore structure and disorder in the NDC materials. Identification of active sites can help mechanistic understanding and further catalyst improvement.

42 ENGINEERING↗
DOE OSTI2021

Molecular imaging of plant-microbe interactions on the Brachypodium seed surface

Plant growth-promoting rhizobacteria (PGPR) play a crucial role in biological control and pathogenic defense on and with-in plant tissues, however the mechanism(s) by which plants associate with PGPR to elicit such beneficial effects needs further study. Here, we present high mass resolution time-of-flight secondary ion mass spectrometry (ToF-SIMS) imaging of Brachypodium distachyon (Brachypodium) seeds with and without exposure to two model PGPR, i.e., Gram-negative Pseudomonas fluorescens SBW25::GFP (P.) and Gram-positive Arthrobacter chlorophenolicus A6::GFP (A.). Delayed image extraction was used to image PGPB-treated seed sections to reveal morphological changes. ToF-SIMS spectral compari-son, principal component analysis (PCA), and two-dimensional (2D) imaging show that the selected PGPR have different effects on the host seed surface, resulting in changes in chemical composition and morphology. Metabolite prod-ucts and biomarkers, such as flavonoids, phenolic com-pounds, fatty acids, and indole-3-acetic acid (IAA), were ob-served on the PGPR-treated seed surfaces. These compounds had different distributions on the Brachypodium seed surface for the two PGPR, indicating that the different bacteria elicited distinct responses from the host. Our results illustrate that ToF-SIMS is an effective tool to study plant-microbe interac-tions and to provide insightful information with submicrome-ter lateral resolution of the chemical distributions associated with morphological features, potentially offering a new way to study the mechanisms underlying beneficial roles of PGPR.

PGPR, Brachypodium distachyon, ToF-SIMS, metabolit↗
DOE OSTI2021

Unsupervised machine learning for unbiased chemical classification in X-ray absorption spectroscopy and X-ray emission spectroscopy

Here we report a comprehensive computational study of unsupervised machine learning for extraction of chemically relevant information in X-ray absorption near edge structure (XANES) and in valence-to-core X-ray emission spectra (VtC-XES) for classification of a broad ensemble of sulphorganic molecules. By progressively decreasing the constraining assumptions of the unsupervised machine learning algorithm, moving from principal component analysis (PCA) to a variational autoencoder (VAE) to t-distributed stochastic neighbour embedding (t-SNE), we find improved sensitivity to steadily more refined chemical information. Surprisingly, when embedding the ensemble of spectra in merely two dimensions, t-SNE distinguishes not just oxidation state and general sulphur bonding environment but also the aromaticity of the bonding radical group with 87% accuracy as well as identifying even finer details in electronic structure within aromatic or aliphatic sub-classes. We find that the chemical information in XANES and VtC-XES is very similar in character and content, although they unexpectedly have different sensitivity within a given molecular class. We also discuss likely benefits from further effort with unsupervised machine learning and from the interplay between supervised and unsupervised machine learning for X-ray spectroscopies. Our overall results, i.e., the ability to reliably classify without user bias and to discover unexpected chemical signatures for XANES and VtC-XES, likely generalize to other systems as well as to other one-dimensional chemical spectroscopies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A protein scaffold enables hydrogen evolution for a Ni-bisdiphosphine complex

We find that an artificial metalloenzyme acting as a functional biomimic of hydrogenase enzymes was activated by assembly via covalent attachment of the molecular complex, [Ni(PN glycine P) 2 ] 2- , within a structured protein scaffold. Electrocatalytic H2 production was observed from pH 3.0 to 10.0 for the artificial enzyme, while no electrocatalytic activity was observed for similar [Ni(PNP) 2 ] 2+ systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Systematic characterization of selenium speciation in coal fly ash

Millions of tons of coal fly ashes (CFAs) are produced annually during coal combustion in the U.S., which are commonly beneficially used in the concrete industry or disposed of in ash ponds. CFAs contain trace amounts of a range of toxic heavy metals including selenium (Se). Because the toxicity of Se is dependent on its speciation, investigating Se speciation in CFAs as affected by coal source and combustion conditions can help understand the related environmental and human health impacts during disposal or beneficial reuse. In this study, a set of representative CFA samples were characterized for Se speciation using synchrotron X-ray absorption spectroscopy (XAS) and micro-X-ray fluorescence spectromicroscopy (μ-XRF/XAS). Se-containing particles were highly heterogeneous, and individual particles might contain multiple oxidation states including Se(0), Se(IV), and Se(VI). Principal component analysis was performed for sample characteristics including Al 2 O 3 , SiO 2 , CaO, FeO, loss on ignition, average particle size, Se concentration, and Se oxidation state. Selective catalytic reduction (SCR), which is used to limit nitrogen oxide (NO x ) emissions during coal combustion, was found to be associated with the presence of reduced Se oxidation states, with up to 90% Se(0) observed in samples with SCR. Alongside SCR, FeO content may also influence Se speciation.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

Machine learning inversion from small-angle scattering for charged polymers

We develop Monte Carlo simulations for uniformly charged polymers and a machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments. The polymer is modeled as a chain of fixed-length bonds, where the connected bonds are subject to bending energy, and there is also a screened Coulomb potential for charge interaction between all joints. The bending energy is determined by the intrinsic bending stiffness, and the charge interaction depends on the interaction strength and screening length. All three contribute to the stiffness of the polymer chain and lead to longer and larger polymer conformations. The screening length also introduces a second length scale for the polymer besides the bending persistence length. To obtain the inverse mapping from the structure factor to these polymer conformation and energy-related parameters, we generate a large data set of structure factors by running simulations for a wide range of polymer energy parameters. We use principal component analysis to investigate the intra-polymer structure factors and determine the feasibility of the inversion using the nearest neighbor distance. We employ Gaussian process regression to achieve the inverse mapping and extract the characteristic parameters of polymers from the structure factor with low relative error.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Remote sensing of Pu in uranyl nitrate crystals using reflectance spectroscopy and chemometrics

Remote quantification of Pu(VI) (0–5 mol%) co-crystallized with U in uranyl nitrate hexahydrate (UNH) crystals was achieved in a glove box using reflectance spectroscopy coupled with chemometric modeling. Reflectance spectra were also acquired for Pu(IV) and Np(VI) (0–5 mol%) crystallized with UNH; revealing spectral features consistent with their solution-phase analogs. Principal component analysis revealed Pu(IV/VI) and Np(VI) concentrations as the primary source of variation in the data, informing the development of a supervised partial least squares regression model for Pu(VI). The resulting calibration demonstrated robust performance, with replicate root mean square errors near 10% and quantifiable limits near 0.2 mol% Pu(VI) relative to U. The Pu(VI) remained stable in the crystalline UNH matrix for at least one week with minimal reduction to Pu(IV). Notably, Pu(VI) and Np(VI) incorporation in UNH quenched U(VI) fluorescence while Pu(IV) did not. This study presents a noninvasive, spectroscopic approach for solid-state Pu quantification, with direct implications for material accountability and nuclear nonproliferation monitoring.

Sadergaski, Luke R. [Oak Ridge National Laboratory↗
DOE OSTI2025

Effects of chemical composition and physicochemical properties of poplar biomass on the performance of 3D printed poplar-reinforced PLA materials

Lignocellulosic biomass has been well-acknowledged as a filler for making 3D printed composites. The technical performances of composites were influenced by the characteristics of the components. The correlations between poplar biomass properties and the mechanical and thermal performances of the 3D printed poplar-plastic composites were investigated. The characteristics of poplar were modified by different pretreatment methods, including using hot water, dilute acid, and organic solvent (organosolv), and each treated poplar biomass was applied as a filler in a polylactic acid (PLA) polymer matrix to produce eco-friendly materials. These solvent pretreatments increased the hydrophobicity and surface area of poplar. Organosolv treated poplar showed the highest cellulose content and significantly increased Young's modulus of its biocomposites. Principal component analysis revealed that the specific surface area and water contact angle of biomass contributed to the thermal stability of biocomposites. Additionally, the degree of polymerization of cellulose and xylan content within the biomass correlated with the biocomposites' break stress. Notably, the crystallinity of biocomposites impacted the modulus of these materials. The reported relationships between biomass characteristics and 3D printed composite behaviors provide guidance for optimizing biomass processing in biocomposite applications.

Ji, Anqi [State Univ. of New York (SUNY), Syracuse↗
DOE OSTI2021

Erratum: Planck 2018 results: VI. Cosmological parameters

In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, (15,30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are: τ(15,30) < 0:018 (lowE, flat τ(15, 30), FlexKnot), (1) τ(15, 30) < 0:023 (lowE, flat knot, FlexKnot): (2) These bounds are a factor of 3 larger than the originally reported results. Consequently, the new bounds do not significantly improve upon previous results from Planck data presented in Millea & Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich & Hu (2021), who used the same Planck 2018 data to derive a 95% upper bound of 0.020 using the principal component analysis (PCA) model and uniform priors on the PCA mode amplitudes.

79 ASTRONOMY AND ASTROPHYSICS↗