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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multivariate degradation modeling using generalized cauchy process and application in life prediction of dye-sensitized solar cells

Recently, the Generalized Cauchy (GC) process has been applied to capture a Long Memory (LM) phenomenon in product degradation modeling and life prediction. Compared with the traditional fractional Brownian motion that captures the LM using a single Hurst parameter, the GC process has two free parameters (Hurst and fractal dimension parameters) that flexibly capture both global LM and local irregularity. However, all existing GC-based degradation models are for a single Degradation Characteristic (DC). In this article, motivated by a real degradation problem of dye-sensitized solar cells that jointly exhibits multiple DCs, global LM, local irregularity and DC-wise cross-correlation, we propose a novel GC-based Multivariate Degradation Model (GC-MDM) to simultaneously capture the aforementioned effects. A maximum likelihood estimation approach is developed to estimate parameters of the GC-MDM. Subsequently, product life prediction based on the GC-MDM is developed. The proposed GC-MDM is validated through a simulation study and a physical experiment of dye-sensitized solar cells. Furthermore, results show that the proposed GC-MDM fundamentally improves the life prediction accuracy in comparison with conventional degradation models which significantly misestimate the uncertainty of product life.

14 SOLAR ENERGY↗
DOE OSTI2025

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Magnetic flux distribution, quasiparticle spectroscopy, and quality factors in Nb films for superconducting qubits

Niobium is a practical material platform for superconducting microwave circuits; however, device-level performance can vary significantly depending on film growth and processing conditions. We compare three epitaxial Nb films grown on $c-$plane sapphire substrates under nominally identical conditions, except for the deposition temperature. To correlate internal quality factors, $Q_{\mathrm {i}}$, with material properties, we combine magneto-optical imaging of magnetic flux distribution with quasiparticle spectroscopy via measurements of the London penetration depth, $λ(T)$. In the low-$Q_{\mathrm i}$ film, there is a lesser ability to screen the magnetic field and an irregular temperature variation of $λ(T)$, implying the existence of localized in-gap states. High $Q_{\mathrm i}$ films show the opposite trend. We conclude that our measurements provide an efficient method for characterizing and optimizing superconducting films for quantum informatics applications.

Datta, Amlan [Ames Lab; Iowa State U.]↗
DOE OSTI2024

Thermal relaxation of strain and twist in ferroelectric hexagonal boron nitride moiré interfaces

New properties can arise at van der Waals (vdW) interfaces hosting a moiré pattern generated by interlayer twist and strain. However, achieving precise control of interlayer twist/strain remains an ongoing challenge in vdW heterostructure assembly, and even subtle variation in these structural parameters can create significant changes in the moiré period and emergent properties. Characterizing the rate of interlayer twist/strain relaxation during thermal annealing is critical to establish a thermal budget for vdW heterostructure construction and may provide a route to improve the homogeneity of the interface or to control its final state. Here, we characterize the spatial and temporal dependence of interfacial twist and strain relaxation in marginally-twisted hBN/hBN interfaces heated under conditions relevant to vdW heterostructure assembly and typical sample annealing. We find that the ferroelectric hBN/hBN moiré at very small twist angles (θ ≤ 0.1°) relaxes minimally during annealing in air at typical assembly temperatures of 170°C. However, at 400°C, twist angle relaxes significantly, accompanied by a decrease in spatial uniformity. Uniaxial heterostrain initially increases and then decreases over time, becoming increasingly non-uniform in direction. Structural irregularities such as step edges, contamination bubbles, or contact with the underlying substrate result in local inhomogeneity in the rate of relaxation.

2D materials↗
DOE OSTI2024

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300⁠. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

42 ENGINEERING↗
DOE OSTI2025

10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations↗
DOE OSTI2025

Non-destructive structural characterization of graphite components using mechanical resonance and deep learning

As compared to conventional nuclear reactors, microreactors have the potential to significantly reduce construction timelines and capital costs, decreasing the barriers for advanced nuclear reactor technologies. However, the lower power output of these microreactors (typically < 20 MWe) creates challenging economics if operation and maintenance costs cannot be sufficiently reduced. The compact size of these designs presents an opportunity for comprehensive in-situ structural health monitoring to provide real-time feedback in order to reduce operational costs associated with maintenance and downtime. Many microreactor concepts use graphite for both in-core neutron moderation and as a structural material, which has typically required some form of periodic and laborious inspection. This report provides a description and assessment of recent work with graphite to couple acoustic-based experimental measurements and characterization with machine learning models to mature structural health monitoring capabilities and generate benefits for the nuclear microreactor industry. With resilient embedded sensors in development in other programs funded by the US Department of Energy’s Office of Nuclear Energy and elsewhere, the work described herein builds upon previously funded efforts to mature non-destructive testing technology that relates measured vibrational signatures to structural changes, using a combination of new experimental measurements and machine learning processing. Building on past successful demonstrations of predictive workflows to identify structural changes in a hexagonal stainless steel test article with excellent acoustic propagation, we first performed baseline characterization on graphite samples with canonical geometries to ensure compatibility and confidence in the applied techniques for a material with distinctly different mechanical properties. In contrast to efforts in previous years, we worked exclusively with unidirectional vibration data that is more comparable to those expected from the existing embedded sensor technologies which are suitable for deployment in a reactor setting. Established acoustic and modern machine-learning-based characterization approaches were applied to the resulting datasets from these simple geometries. Both approaches were found to be highly capable of detecting even small geometric irregularities amongst nominally identical samples. As such, we then moved to testing these approaches for detection of artificial local stress perturbations introduced into a more complex geometry: a hexagonal block with drilled holes. A main outcome of this work is that a generalizable ML workflow can be used to detect and predict the characteristics of small artificial anomalies in a graphite component with a relevant geometry. While this work was performed using surficial vibration data, we expect the approach to be flexible and viable for other monitoring scenarios, such as those with different arrangements or types of sensor arrays. As compared to previously funded efforts, an existing ML workflow based on neural networks was enhanced through the addition of recently developed Fourier neural operators. As applied to previously collected and new vibration datasets, prediction accuracies of anomaly characterizations were greatly improved with minimal added computational cost. As trained on small durations of vibration data (tens of seconds) collected over a realistic number of locations, the model was able to reliably determine the presence of a subtle stress anomaly and begin to provide location estimates. Such an approach is likely to be viable for more relevant reactor damage scenarios for graphite components, such as progressive crack growth or creep.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Three-dimensional nucleation and growth of deformation twins in magnesium

At two-thirds the weight of aluminum, magnesium alloys have the potential to reduce the fuel consumption of transportation vehicles. These advancements depend on our ability to optimize the desirable versus undesirable effects of deformation twins, which are three-dimensional (3D) microstructural domains that form under mechanical stresses. Previously only characterized through surface or thin-film measurements, we here present 3D in situ characterization of deformation twinning inside an embedded grain over mesoscopic fields of view using dark-field x-ray microscopy supported by crystal plasticity finite element analysis. The results revealed the role of triple junctions on twin nucleation and the sequence and irregularity of twin growth and showed that twin-grain junctions, twin-twin junctions, and twin boundaries were the sites of localized dislocation accumulation.

Lee, Sangwon [Univ. of Michigan, Ann Arbor, MI (Un↗
DOE OSTI2026

SORCER TEST UTQIAĠVIK DEPLOYMENT FOR IONOGRAMS (STUDI) 2021-2024

The Air Force Research Laboratory (AFRL) has developed a passive broadband radio frequency (RF) receiver, called a Sounder Receiver (SoRcer), as an ionospheric diagnostic instrument. These systems can produce ionospheric specifications to characterize the local ionosphere. The specifications from the SoRcers can then be used to inform data-assimilation models; monitor diurnal, seasonal, or other cyclical changes; and detect irregularities or abnormalities in the ionosphere, such as traveling ionospheric disturbances (TIDs), sporadic E, and spread F.

frequency↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2024

Learning Topological Operations on Meshes with Application to Block Decomposition of Polygons

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Parametric Finite Element Analysis of Naturally Corroded Steel Specimens Using 3D Surface Laser Scans

Corrosion is considered a uniform thickness reduction design guideline of the maritime industry. However, additionally, the corroded and irregular morphology of the surface affects the steel's load-bearing capacity and its impact on the strength and elongation behaviour of the steel is not yet fully understood. These effects on the local behaviour of steel structures under tensile loading were investigated with tensile tests on naturally corroded steel specimens and nonlinear finite element simulations including the corroded surface morphology with a uniform surface idealation. The models also include the deformed specimen shape. The developed approach led to highly accurate parametric finite element models predicting the ultimate tensile strength and longitudinal position of fracture. The results show that all included aspects are essential for accurate simulations, while solely the maximum available surface resolution was not as decisive.

corrosion↗
DOE OSTI2024

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. Here we describe a kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the standard nontwist map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the structure that we call a torus free barrier occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism, and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with nonuniformly distributed points.

classical mechanics↗
DOE OSTI2025

Introducing a multiscale feature integration network for inpainting with applications to enhanced CMB map reconstruction

We introduce a novel neural network, SkyReconNet, which combines the expanded receptive fields of dilated convolutional layers along with standard convolutions, to capture both the global and local features for reconstructing the missing information in an image. We implement our network to inpaint the masked regions in a full-sky cosmic microwave background (CMB) map. Inpainting CMB maps is a particularly formidable challenge when dealing with extensive and irregular masks, such as galactic masks which can obscure substantial fractions of the sky. The hybrid design of SkyReconNet leverages the strengths of standard and dilated convolutions to accurately predict CMB fluctuations in the masked regions by effectively utilizing the information from surrounding unmasked areas. During training, the network optimizes its weights by minimizing a composite loss function that combines the structural similarity index measure (SSIM) and mean squared error (MSE). SSIM preserves the essential structural features of the CMB, ensuring an accurate and coherent reconstruction of the missing CMB fluctuations, while MSE minimizes the pixelwise deviations, thus enhancing the overall accuracy of the predictions. The predicted CMB maps and their corresponding angular power spectra align closely with the targets, achieving the performance limited only by the fundamental uncertainty of cosmic variance. The network’s generic architecture enables application to other physics-based challenges involving data with missing or defective pixels, systematic artifacts, etc. In conclusion, our results demonstrate its effectiveness in addressing the challenges posed by large irregular masks, offering a significant inpainting tool not only for CMB analyses but also for image-based experiments across disciplines where such data imperfections are prevalent.

Cosmic microwave background↗
DOE OSTI2026

Measurement of Local Impedance Characteristics of In-Plane PEM Electrolyzer Component Features via Segmented Cell

Segmented cells are a class of advanced diagnostic devices that enable the measurement of current distribution within the active area of an electrochemical cell, allowing for the evaluation of localized impacts from operating conditions, flow fields and component inhomogeneities. Segmented cell devices have been applied to support R&D efforts for the advancement of polymer electrolyte membrane fuel cell technologies and more recently proton exchange membrane water electrolysis (PEMWE). Beyond current density distributions, segmented cells have been successfully deployed to collect the distribution of other relevant parameters such as high frequency resistance and electrode potentials. Very recently, a promising impedance method has been reported for water electrolysis where a one-dimensional segmented cell is coupled to a multichannel potentiostat, to enable the measurement of local cell impedances, further expanding the diagnostic capabilities of the segmented cell. In this study, we will present recent efforts to accurately measure local impedance characteristics for a PEMWE cell using a two-dimensional segmented cell device coupled with a multichannel potentiostat. The distribution of local resistances, i.e. high frequency, charge transfer, mass transport and catalyst layer, and iR-free overpotentials were successfully measured after eliminating sources of random and systematic error. We will discuss the application of this diagnostic on a cell containing a 1 cm feature simulating an ionomer skin. The results from these tests give insights if such an irregularity needs to be classified as a defect, and highlight the usefulness of coupling impedance spectroscopy with segmented cells for holistic spatial diagnostics of electrochemical devices.

08 HYDROGEN↗
DOE OSTI2024

Nanoscale elemental and morphological imaging of nitrogen-fixing cyanobacteria

Nitrogen-fixing cyanobacteria bind atmospheric nitrogen and carbon dioxide using sunlight. This experimental study focused on a laboratory-based model system, Anabaena sp., in nitrogen-depleted culture. When combined nitrogen is scarce, the filamentous prokaryotes reconcile photosynthesis and nitrogen fixation by cellular differentiation into heterocysts. To better understand the influence of micronutrients on cellular function, 2D and 3D synchrotron X-ray fluorescence mappings were acquired from whole biological cells in their frozen-hydrated state at the Bionanoprobe, Advanced Photon Source. To study elemental homeostasis within these chain-like organisms, biologically relevant elements were mapped using X-ray fluorescence spectroscopy and energy-dispersive X-ray microanalysis. Higher levels of cytosolic K + , Ca 2+ , and Fe 2+ were measured in the heterocyst than in adjacent vegetative cells, supporting the notion of elevated micronutrient demand. P-rich clusters, identified as polyphosphate bodies involved in nutrient storage, metal detoxification, and osmotic regulation, were consistently co-localized with K + and occasionally sequestered Mg 2+ , Ca 2+ , Fe 2+ , and Mn 2+ ions. Machine-learning-based k-mean clustering revealed that P/K clusters were associated with either Fe or Ca, with Fe and Ca clusters also occurring individually. In accordance with XRF nanotomography, distinct P/K-containing clusters close to the cellular envelope were surrounded by larger Ca-rich clusters. The transition metal Fe, which is a part of nitrogenase enzyme, was detected as irregularly shaped clusters. The elemental composition and cellular morphology of diazotrophic Anabaena sp. was visualized by multimodal imaging using atomic force microscopy, scanning electron microscopy, and fluorescence microscopy. This paper discusses the first experimental results obtained with a combined in-line optical and X-ray fluorescence microscope at the Bionanoprobe.

Anabaena sp↗
DOE OSTI2025

HexWeather: Hexagonal Spatial Data Aggregation for Weather-Driven Grid Resilience Analysis

Extreme weather accounts for over 8 0 % of major U.S. power outages since 2000, highlighting the need for spatial tools that align weather data with the irregular boundaries of electric infrastructure. This paper introduces HexWeather, a modular, resolution-aware framework for aggregating historical and forecasted weather data using Uber's H3 hexagonal spatial indexing system. Unlike traditional methods that rely on state or county-level grids, HexWeather enables weather analysis across custom geographies such as utility service areas where public datasets are often unavailable or misaligned. Using Open-Meteo data, we evaluate how H3 resolution affects anomaly detection, spatial variability, and forecast uncertainty across three scales: state, county, and utility. Results show that while coarse resolutions suffice for broad trend tracking, finer resolutions are essential for identifying localized variability and operational risks. By applying metrics like Z-score standard deviation and interquartile range, HexWeather quantifies the spatial spread of both historical anomalies and forecasted conditions, allowing users to assess resolution adequacy for each analysis. This framework supports rapid weather data reuse, reproducible anomaly detection, and predictive modeling for infrastructure resilience. By bridging spatial misalignment in traditional datasets and enabling retrospective and forward-looking analysis within the same pipeline, HexWeather lays the groundwork for better post event analysis, outage prediction, and resilience planning.

Morris, Jacob [ORNL]↗
DOE OSTI2024

Electronic rotons and Wigner crystallites in a two-dimensional dipole liquid

A key concept proposed by Landau to explain superfluid liquid helium is the elementary excitation of quantum particles called rotons1–8. The irregular arrangement of atoms in a liquid leads to the aperiodic dispersion of rotons, which played a pivotal role in understanding fractional quantum Hall liquids (magneto-rotons)9,10 and the supersolidity of Bose–Einstein condensates11–13. Even for a two-dimensional electron or dipole liquid, in the absence of a magnetic field, the repulsive interactions have been predicted to form a roton minimum14–19, which can be used to trace the transition to Wigner crystals20–24 and superconductivity25–27, although this has not yet been observed. Here, we report the observation of such electronic rotons in a two-dimensional dipole liquid of alkali-metal ions donating electrons to surface layers of black phosphorus. Our data reveal the striking aperiodic dispersion of rotons, which is characterized by a local minimum of energy at finite momentum. As the density of dipoles decreases so that interactions dominate over the kinetic energy, the roton gap reduces to 0, as in a crystal, signalling Wigner crystallization. Our model shows the importance of short-range order arising from repulsion between dipoles, which can be viewed as the formation of Wigner crystallites (bubbles or stripes) floating in the sea of a Fermi liquid. Our results reveal that the primary origin of electronic rotons (and the pseudogap) is strong correlations.

Park, Soobin↗