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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Limited Role of Absolute Humidity in Intraurban Heat Variability

Abstract Monitoring and understanding the variability of heat within cities is important for urban planning and public health, and the number of studies measuring intraurban temperature variability is growing. Recognizing that the physiological effects of heat depend on humidity as well as temperature, measurement campaigns have included measurements of relative humidity alongside temperature. However, the role the spatial structure in humidity, independent from temperature, plays in intraurban heat variability is unknown. Here we use summer temperature and humidity from networks of stationary sensors in multiple cities in the United States to show spatial variations in the absolute humidity within these cities are weak. This variability in absolute humidity plays an insignificant role in the spatial variability of the heat index and humidity index (humidex), and the spatial variability of the heat metrics is dominated by temperature variability. Thus, results from previous studies that considered only intraurban variability in temperature will carry over to intraurban heat variability. Also, this suggests increases in humidity from green infrastructure interventions designed to reduce temperature will be minimal. In addition, a network of sensors that only measures temperature is sufficient to quantify the spatial variability of heat across these cities when combined with humidity measured at a single location, allowing for lower-cost heat monitoring networks. Significance Statement Monitoring the variability of heat within cities is important for urban planning and public health. While the physiological effects of heat depend on temperature and humidity, it is shown that there are only weak spatial variations in the absolute humidity within nine U.S. cities, and the spatial variability of heat metrics is dominated by temperature variability. This suggests increases in humidity will be minimal resulting from green infrastructure interventions designed to reduce temperature. It also means a network of sensors that only measure temperature is sufficient to quantify the spatial variability of heat across these cities when combined with humidity measured at a single location.

Meteorology & Atmospheric Sciences↗
DOE OSTI2023

Vertical nanoscale strain-induced electronic localization in epitaxial La2/3Sr1/3MnO3 films with ZrO2 nanopillar inclusions

Abstract Unusual electrical transport properties associated with weak or strong localization are sometimes found in disordered electronic materials. Here, we report experimental observation of a crossover of electronic behavior from weak localization to enhanced weak localization due to the spatial influence of disorder induced by ZrO 2 nanopillars in (La 2/3 Sr 1/3 MnO 3 ) 1− x :(ZrO 2 ) x ( x = 0, 0.2, and 0.3) nanocomposite films. The spatial strain regions, identified by scanning transmission electron microscopy and high-resolution x-ray diffraction, induce a coexistence of two-dimentional (2D) and three-dimentional (3D) localization and switches to typical 2D localization with increasing density of ZrO 2 pillars due to length scale confinement, which interestingly accords with enhancing vertically interfacial strain. Based on the excellent agreement of our experimental results with one-parameter scaling theory of localization, the enhanced weak localization exists in metal range close to the fixed point. These films provide a tunable experimental model for studying localization in particular the transition regime by appropriate choice of the second epitaxial phase. Graphical Abstract

36 MATERIALS SCIENCE↗
DOE OSTI2021

Refinements to the Graves–Pitarka Kinematic Rupture Generator, Including a Dynamically Consistent Slip-Rate Function, Applied to the 2019 Mw 7.1 Ridgecrest Earthquake

The main objective of this study is to develop physics–based constraints on the spatiotemporal variation of the slip–rate function using a simplified dynamic rupture model. First, we performed dynamic rupture modeling of the 2019 M w 7.1 Ridgecrest, California, earthquake, to analyze the effects of depth–dependent stress and material friction on slip rate. Then, we used our modeling results to guide refinements to the slip–rate function that were implemented in the Graves–Pitarka kinematic rupture generation technique. The dynamic ruptures were computed on a surface–rupturing, planar strike–slip fault that includes a weak (negative to low–stress–drop) zone in the upper 4 km of the crust. Below the weak zone, we placed high–stress–drop patches designed to mirror the large–slip areas seen in various rupture model inversions of the event. The locations of the high–stress–drop patches and the hypocenter were varied in multiple realizations to investigate how changing the dynamic conditions affected the resulting rupture kinematics, in particular, the slip rate. From these simulations, we observed a systematic change in the shape of the slip–rate function from Kostrov type below the weak zone to a predominantly symmetric shape within the weak zone, along with a depth–dependent reduction of peak slip rate. We generalized these shallow rupture features into a depth–dependent parametric variation of the slip–rate function and implemented it in the Graves–Pitarka kinematic rupture model generator. The performance of the updated kinematic approach was then verified in 0–4 Hz simulations of the M w 7.1 Ridgecrest earthquake, which showed that incorporating the depth–dependent variation in the shape of the slip–rate function improves the fit to the observed near–fault ground motions in the 0.5–3 s period range.

58 GEOSCIENCES↗
DOE OSTI2020

Rupture Dynamics Simulations of Shallow Crustal Earthquakes on Reverse Slip Faults

The main goal of this study was to perform dynamic rupture simulations in order constrain the characterization of kinematic rupture models implemented in techniques for simulating strong ground motion for crustal earthquakes. First, we investigated the rupture process of the 2008 Iwate-Miyagi Nairiku earthquake by developing a dynamic rupture model on a reverse fault using a trial-and-error technique that produced a slip distribution and near-fault ground motion that matched the recorded ones. The simulations were performed in the frequency range 0-2 Hz, using a 3D staggered grid finite-difference method and a linear slip weakening friction law. Constrained by the observed slip distribution and consistent with dynamic rupture models, the derived kinematic rupture model of the Iwate-Miyagi Nairiku earthquake contains areas with relatively large slip rate, representing strong motion generation areas, set against lower amplitude heterogeneous background slip, and a relatively low slip rate in the weak zone of the top-most crust (upper 3km). Second, we performed rupture dynamics modeling to constrain shallow slip characterization in rupture models for strike-slip crustal earthquakes. The objective was to establish general rules about the characterization of slip rate function and slip at shallow depths and in the strong motion generation areas (SMGAs). The simulations of spontaneous rupture were performed in the frequency range 0-2.0Hz, using a 3D staggered-grid finite-difference method and a layer over half-space 1D crustal velocity model with a minimum shear-wave velocity of 2.8 km/s. In order to account for changes in material ductility and reduction of stress drop, observed in the shallow crust (upper 3-5 km), and the transition from ductile state to brittle state in the upper seismogenic zone, in our stress models we included a shallow weak zone (<4km). In this zone the stress drop was set to zero at the free surface and gradually increased with depth, while the slip weakening distance was set to 75 cm at the free surface and decreased to 50 cm at the base of the weak zone. As in the case of reverse faulting during the Iwate-Miyagi Nairiku earthquake, from these computations we found a systematic change in the shape of the slip-rate function, from Kostrov-type in the deeper part of the fault to a more symmetric cosine-type in the upper few kilometers, near the free-surface. Moreover, the average slip duration in the weak zone, with respect to slip duration in the deeper parts of the fault, increases by at most a factor of 1.5. We found a systematic and gradual change in the shape of the slip-rate function from Kostrov-type in the asperity areas (SMGAs), to more symmetric cosine-type in the upper few km near the free-surface, on the long period motion generation area (LMGA). The effective rise time in the LMGA, with respect to that in the SMGAs, increases by at most a factor of 2. Effective rise time is the time difference between the time at which the slip rate drops to a level that is equal to 25% of its peak and the onset time of the signal. In addition, the slip in the LMGA located above the SMGAs is almost the same as the one in the SMGAs, and about 1.5 times larger than the average slip.

58 GEOSCIENCES↗
DOE OSTI2023

Quantum Information Science in High Energy Physics at the Large Hadron Collider (Final Report-QuantISED)

We pursue scientific research at the interface of High Energy Physics and Quantum Information Science. This includes studies of thermal radiation and quantum entanglement in high-energy collisions at the Large Hadron Collider (LHC), with special emphasis on entanglement entropy and the Higgs boson. This project has also been extended to include quantum entanglement and charged current weak interactions using Fermilab results. And most recently, we have begun tests of the temporal entanglement using LHC data. Collider experiments such as proton-proton collisions at the LHC yield hadrons that exhibit an exponential behavior at low transverse momenta. This surprising behavior is seen in data from both the ATLAS and CMS collaborations. We attribute this phenomenon to quantum entanglement between the regions in the nucleon wave function. The exponential component to the transverse momentum distribution is a result of thermal radiation that is akin to Hawking or Unruh radiation that should exist at the event horizon of astrophysical black holes and neutron stars. The Principal Investigator, in collaboration with a theoretical physicist at Stony Brook University and Brookhaven National Laboratory, and with Yale University students, has shown evidence for this thermal radiation in several production and decay processes in the ATLAS and CMS data, and its connection to entanglement entropy (O.K. Baker and D.E Kharzeev, Phys. Rev. D 98, 054007 (2018)), including even the Higgs boson sector. Interestingly, this thermal behavior is also seen in momentum distributions of charged current weak interactions according to our studies. These findings suggest a deep connection between quantum entanglement (entanglement entropy) and thermalization in both hadron collisions at the energy frontier and neutrino scattering at the intensity frontier. We have confirmed the proposed relation between the effective temperature and the hard-scattering scale at lower energies using the most recent LHC data for the following systems: Higgs bosons, top quarks, and charged hadrons. Additionally, we have results for hadron production in neutrino scattering from nuclei using Fermilab weak interaction data. This study is carried out using data from the MINERvA collaboration. In those cases where entanglement is expected, there is an exponential component to the momentum distribution, while this component is absent in those processes where no entanglement is expected. This research thus tests the hypothesis about a link between quantum entanglement and thermalization in strong and weak interactions. See Phys Lett B 811, 135948 (2020). We also initiated research applying a quantum search algorithm (Grover's Algorithm) to LHC data. This quantum algorithm was used to show how rare events in LHC data can be searched for in large, unsorted databases, with quadratic speedup compared to classical search algorithms on classical computers. See "Application of a Quantum Search Algorithm to High- Energy Physics Data at the Large Hadron Collider", arXiv:2010.00649 [quant-ph].

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Gradient Amine Sorbents for Low Vacuum Swing CO 2 Capture at Ambient Temperature

The growing concerns over CO 2 emissions have led to the development of various methods for CO 2 capture. CO 2 capture by amine-based sorbents has been achieved by temperature (thermal) swing adsorption (TSA) process, pressure swing adsorption (PSA) process, and temperature pressure or vacuuming swing adsorption (TPSA or TVSA) process for CO 2 capture. Amine sorbents for energy-efficient TSA, PSA, VSA, TPSA or TVSA CO 2 capture should possess a capability which allow adsorbed CO 2 to desorb and amine sorbent to be regenerated at low temperatures or low vacuums. Development of such amine sorbents would significantly decrease energy consumption and sorbent degradation during the regeneration step. The objective of this project is to develop a low vacuum swing adsorption (VSA) process for the capture of CO 2 from air. The focus is on the development of amine sorbent which allows CO 2 to adsorb in the form of weakly adsorbed CO 2 . The weakly adsorbed CO 2 species can be collected from the sorbent by applying a low vacuum at ambient temperature. Specifically, no heating (i.e., thermal energy) is needed for regeneration of amine sorbents. This novel sorbent allows VSA to be operated at ambient temperature without a significant energy demand. This process eliminates the energy-intensive heating and cooling process in temperature swing adsorption (TSA) process. Ambient temperature operation could prolong the lifetime of sorbent and minimize the maintenance cost. Extensive sorbent studies with in-situ infrared spectroscopy have revealed the modifications of conventional amine sorbents with additives can increase the fraction of weakly adsorbed CO 2 . The amine sorbents with loaded CO 2 can be regenerated in part by the following approaches: (i) mild heating to temperatures below 70 °C, (ii) flowing purging gas over modified amine sorbents at temperatures below 40 °C, (iii) vacuuming at pressure below 0.2 atm and temperatures below 40 °C. The performance of these modified amine sorbents has been tested in a 60 grams VSA unit at ambient temperatures. The results show that weakly adsorbed CO 2 which can be desorbed from modified amine sorbents with purging gas at 100 cc/min can also be evacuated at a vacuum of 1 psia at room temperature. A preliminary techno- economic analysis indicates the major cost of the VSA process with modified amine sorbents stems from the operation of vacuum pumps. Thus, developing an excellent sealing with minimum leakage for the VSA unit is the most critical task for further the development of this VSA technology.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Dilute Paramagnetism and Non-Trivial Topology in Quasicrystal Approximant Fe4Al13

A very fundamental property of both weakly and strongly interacting materials is the nature of their magnetic response. In this work, we detail the growth of crystals of the quasicrystal approximant Fe4Al13 with an Al flux solvent method. We characterize our samples using electrical transport and heat capacity, yielding results consistent with a simple non-magnetic metal. However, magnetization measurements portray an extremely unusual response for a dilute paramagnet and do not exhibit the characteristic Curie behavior expected for a weakly interacting material at high temperature. Electronic structure calculations confirm metallic behavior but also indicate that each isolated band near the Fermi energy hosts non-trivial topologies, including strong, weak, and nodal components, with resultant topological surface states distinguishable from bulk states on the (001) surface. With half-filled flat bands apparent in the calculation, but an absence of long-range magnetic order, the unusual quasi-paramagnetic response suggests the dilute paramagnetic behavior in this quasicrystal approximant is surprising and may serve as a test of the fundamental assumptions that are taken for granted for the magnetic response of weakly interacting systems.

Avers, Keenan E. (ORCID:0000000223441939)↗
DOE OSTI2021

An RTDS-Based Testbed for Investigating the Impacts of Transmission-Level Disturbances on Solar PV Operation

The increasing penetration of renewable energy resources such as solar and wind via power electronic inverters is challenging grid dynamics, as well as grid planning, operation, and protection. Recently, the North American Electric Reliability Corporation (NERC) has reported a series of similar events of the unintended loss of solar generation in Southern California over a large geographic area following the transmission-level disturbances. These events highlight the importance of understanding the characteristics of the transmission-side disturbances propagating into the distribution systems and their impacts on the operation of inverter-based resources. In this paper, a real-time electromagnetic simulation testbed is constructed for real-time electromagnetic simulations to generate realistic transmission-level disturbances and investigate their impacts on the solar PV operation under different fault types and locations, solar penetration levels, and loading levels. Through the simulation analysis and grid strength assessment, it is found that the grid strength at points of integration (POIs) of solar PVs significantly affects the transient stability of solar generators. Particularly, undesirable transient stability events are more likely to occur at the weak POIs following the transmission-level disturbances. Moreover, undesirable transient stability events become severer when the transmission-level disturbance is closer to the weak POIs or the disturbances become more serious. Additionally, the impact of the transmission-level disturbances on the solar PVs at the weak POIs exacerbate with the increasing solar penetration levels and loading levels. Thus, it is important to study and develop new technologies for grid planning, operation, and protection in weak grid conditions to address the emerging issues of integrating the high penetration of solar PVs and other IBRs.

14 SOLAR ENERGY↗
DOE OSTI2025

Impact of the Latest 22 Ne+ α Reaction Rates on Nucleosynthesis in Massive Stars and Galactic Chemical Evolution

In massive stars (initial mass of ≳9 M ⊙ ), the weak s- (slow neutron capture) process produces elements between Fe and Zr, enriching the Galaxy with these elements through core-collapse supernova explosions. The weak s-process nucleosynthesis is driven by neutrons produced in the 22 Ne(α, n) 25 Mg reaction during convective He core and C shell burning. The yields of heavy elements thus depend on the 22 Ne(α, n) 25 Mg and the competitive 22 Ne(α, γ) 26 Mg reaction rates, which are dominated by several narrow-resonance reactions. While the accuracy of these rates has been under debate for decades, recent experimental efforts, including ours, drastically reduced these uncertainties. In this work, we use a set of 280 massive star nucleosynthesis models calculated using different 22 Ne(α, n) 25 Mg and 22 Ne(α, γ) 26 Mg rates and a galactic chemical evolution (GCE) study to probe their impact on the weak s-process elemental abundances in the Galaxy. The GCE was computed with the OMEGA+ code, using the new sets of stellar yields with different 22 Ne+α rates. From GCE, we find that these rates are causing up to 0.45 dex of variations in the [Cu/Fe], [Ga/Fe], and [Ge/Fe] ratios predicted at solar metallicity. The greatest impact on the stellar nucleosynthesis and GCE results derives from uncertainties in the (α, n) strength (ωγ (α,n) ) of the E x = 11.32 MeV resonance. We show that variations observed in the GCE calculations for weak s-process elements become negligibly smaller than dispersions found in observations once the ωγ (α,n) is accurately determined within the uncertainty of 10%–20% (typically reported experimental errors for the resonance) in future nuclear physics experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Accurate Dark Energy Constraints via the Precise Characterization of Galaxy Intrinsic Alignment Coupled with Shear and Redshift Interference

One of the most fundamental mysteries we face in physics is understanding what the nature of the dark energy component of our Universe is that causes the accelerated expansion of space. A powerful way to study dark energy is via weak gravitational lensing due to large-scale structure in the Universe, which we observe as tiny distortions in the shapes of very distant galaxies due to the bending of light by foreground mass. The Dark Energy Survey (DES) and Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) were designed to enable unprecedented measurements of these distortions in the shapes of galaxies to study dark energy. The intrinsic shapes of galaxies before they are distorted by weak gravitational lensing can cancel out some of the effects of lensing to obscure or bias what we infer about the nature of dark energy. This research program has led to improved image-level simulations of the Rubin Observatory LSST data. These simulations have made it possible to characterize for the first time the cosmic impact of these intrinsic shapes on biasing weak gravitational lensing calibration. This work will inform crucial improvements in methodology for studying dark energy with weak gravitational lensing at the precision promised by the the Rubin Observatory LSST over the next decade to ensure we are able to infer unbiased information about the nature of dark energy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Benchmarking Cylindrical Blast Wave Theory Against the OSIRIS-REx Sample Return Capsule Reentry

Weak shock theory based on cylindrical blast waves has been used to interpret meteor infrasound, but it has not been systematically benchmarked against a non-ablating hypersonic source with independently known parameters. The objective of this study is not to propose a new theoretical framework, but to evaluate the operational validity of the existing suite of blast radius formulations against a high-fidelity ground truth dataset. The OSIRIS-REx Sample Return Capsule reentry on 24 September 2023 provides such a benchmark because the capsule geometry, trajectory, and infrasound emission points are constrained from mission data and ray tracing, reducing source-side uncertainty associated with ablation. Using observations from 39 infrasound stations, this benchmarking study evaluates six published blast radius (${R}_{0}$ ) formulations and three weak-shock transition coefficients ( C ) within a stratified atmospheric propagation model to predict signal period and peak overpressure. The benchmarking identifies the Sakurai formulation as the best-performing formulation for non-ablating bodies, with the Jones/Plooster formulation performing comparably when a physically appropriate C is adopted. Sakurai and Jones/Plooster yield linear-period median absolute percentage residuals of 9% and 11%, respectively. The period predictions show only weak sensitivity to C at these propagation distances. The Mach-diameter approximation commonly used in meteor studies overestimates ${R}_{0}$ by more than a factor of 3 in the absence of ablation. Finally, these results establish a performance baseline for applying cylindrical blast wave theory to effectively non-ablating hypersonic bodies and demonstrate that the signal period is a robust observable for constraining ${R}_{0}$.

atmospheric entry↗
DOE OSTI2024

Implementation and Exploration of Parameterizations of Large-Scale Dynamics in NCAR's Single Column Atmosphere Model SCAM6

A single column model with parameterized large-scale (LS) dynamics is used to better understand the response of steady-state tropical precipitation to relative sea surface temperature under various representations of radiation, convection, and circulation. The large-scale dynamics are parametrized via the weak temperature gradient (WTG), damped gravity wave (DGW), and spectral weak temperature gradient (Spectral WTG) method in NCAR's Single Column Atmosphere Model (SCAM6). Radiative cooling is either specified or interactive, and the convective parameterization is run using two different values of a parameter that controls the degree of convective inhibition. Results are interpreted in the context of the Global Atmospheric System Studies -Weak Temperature Gradient (GASS-WTG) Intercomparison project. Using the same parameter settings and simulation configuration as in the GASS-WTG Intercomparison project, SCAM6 under the WTG and DGW methods produces erratic results, suggestive of numerical instability. However, when key parameters are changed to weaken the large-scale circulation's damping of tropospheric temperature variations, SCAM6 performs comparably to single column models in the GASS-WTG Intercomparison project. The Spectral WTG method is less sensitive to changes in convection and radiation than are the other two methods, performing qualitatively similarly across all configurations considered. Under all three methods, circulation strength, represented in 1D by grid-scale vertical velocity, is decreased when barriers to convection are reduced. This effect is most extreme under specified radiative cooling, and is shown to come from increased static stability in the column's reference radiative-convective equilibrium profile. This argument can be extended to interactive radiation cases as well, though perhaps less conclusively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies (log M*/M ⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u - g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, L r, 10 , and the light-weighted surface brightness slope, Γ 10 . Results. We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with L r,10 and anti-correlates with Γ 10 . At fixed redshift, L r, 10 and Γ 10 , the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multiscale Flow for robust and optimal cosmological analysis

We propose Multiscale Flow, a generative Normalizing Flow that creates samples and models the field-level likelihood of two-dimensional cosmological data such as weak lensing. Multiscale Flow uses hierarchical decomposition of cosmological fields via a wavelet basis and then models different wavelet components separately as Normalizing Flows. The log-likelihood of the original cosmological field can be recovered by summing over the log-likelihood of each wavelet term. This decomposition allows us to separate the information from different scales and identify distribution shifts in the data such as unknown scale-dependent systematics. The resulting likelihood analysis can not only identify these types of systematics, but can also be made optimal, in the sense that the Multiscale Flow can learn the full likelihood at the field without any dimensionality reduction. We apply Multiscale Flow to weak lensing mock datasets for cosmological inference and show that it significantly outperforms traditional summary statistics such as power spectrum and peak counts, as well as machine learning–based summary statistics such as scattering transform and convolutional neural networks. We further show that Multiscale Flow is able to identify distribution shifts not in the training data such as baryonic effects. Finally, we demonstrate that Multiscale Flow can be used to generate realistic samples of weak lensing data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗
DOE OSTI2021

Inter-IBR Oscillation Modes

This research addresses the following question: For a weak grid with multiple-IBRs, what is the nature of oscillation modes? The analysis of a system consisting of two identical IBRs offers a glimpse of the picture. It shows that the system has a weak-grid mode and an inter-IBR mode. For the weak-grid mode, two IBRs work as an aggregated one to interact with the grid. Furthermore, this mode is sensitive to IBR exporting power level and grid strength. For the inter-IBR mode, two IBRs oscillate against each other. This mode is less sensitive to grid strength and power level.

14 SOLAR ENERGY↗
DOE OSTI2025

Explicit Runge–Kutta Methods that Alleviate Order Reduction

Explicit Runge–Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to an initial boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high order convergence for linear problems; we refer to these conditions as weak stage order conditions. We prove a general relationship between the method’s order, weak stage order, and number of stages. Furthermore, we derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear problems.

explicit Runge–Kutta↗