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At least 1,297 records · Page 72
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Shocks in the outer helisphere: Voyager 2 observations from 18.9 AU to 30.2 AU (1986-1989)

A search for shocks observed by Voyager 2 from 1986.0 to day 233, 1989, in the region between 18.9 AU and 30.2 AU revealed only five candidate fast forward shocks and no reverse shocks. No shock was observed during 1987 (near solar minimum). Only one candidate shock was observed during 1986, when the heliospheric current sheet (HCS) was still close to the equator. This, the weakest of the shocks, was associated with a weak corotating merged interaction region (CMIR). Only two shocks were observed during 1988, when solar activity and the inclination of the HCS were increasing. One of these shocks was associated with a CMIR, the other with a local merged interaction region (MIR) (a transient MIR localized in space). The shocks observed between 18.9 AU and 28.2 AU from 1986 through 1988 were relatively weak, the estimated magnetoacoustic Mach number being less than or equal to 1.5 for each of the three shocks. Since the shocks observed between 20 AU and 29 AU during the 3-year period centered around solar minimum were weak and few in number, shocks were not important in determining the structure, dynamics, and thermodynamics of the equatorial solar wind. The strongest shock in this study was observed during 1989 at the front of a global merged interaction region (GMIR) (a MIR that extends around the Sun and is presumably formed by the coalescence of several transient ejecta and other interaction regions). A weak shock was also observed inside this GMIR.

Burlaga, L. F.↗
NASA NTRS1995

Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics

The role of cosmic-ray-modified contact discontinuities and pressure balance structures in two-fluid cosmic-ray hydrodynamics in one Cartesian space dimension are investigated by means of analytic and numerical solution examples, as well as by weakly nonlinear asymptotics. The fundamental wave modes of the two-fluid cosmic-ray hydrodynamic equations in the long-wavelength limit consist of the backward and forward propagating cosmic-ray-modified sound waves, with sound speed dependent on both the cosmic-ray and thermal gas pressures; the contact discontinuity; and a pressure balance mode in which the sum ofthe cosmic ray and thermal gas pressure perturbations is zero. The pressure balance mode, like the contact discontinuity is advected with the background flow. The interaction of the pressure balance mode with the contact discontinuity is investigated by means of the method of multiple scales. The thermal gas and cosmic-ray pressure perturbations satisfy a linear diffusion equation, and entropy perturbations arising from nonisentropic initial conditions for the thermal gas are frozen into the fluid. The contact discontinuity and pressure balance eigenmodes both admit nonzero perturbations in the thermal gas, whereas the cosmic-ray-modified sound waves are isentropic. The total entropy perturbation is shared between the contact discontinuity and pressure balance eigenmodes, and examples are given in which there is a transfer of entropy between the two modes. In particular, N-wave type density disturbances are obtained which arise as a result of the entropy transfer between the two modes. A weakly nonlinear geometric optics perturbation expansion is used to study the long timescale evolution of the short-wavelength entropy wave and the thermal gas sound waves in a slowly varying, large-scale background flow. The weakly nonlinear geometric optics expansion is also used to generalize previous studies of squeezing instability for short-wavelength sound waves in the two fluid model, by including a weakly nonlinear wave steepening term that leads to shock formation, as well as the effect of long time and space dependence of the background flow. Implications of cosmic-ray-modified pressure balance structures and contact discontinuities in models of the interaction of traveling interplanetary shocks and compression and rarefraction waves with the solar wind termination shock are briefly discussed.

Webb, G. M.↗
NASA NTRS1997

On the Asymptotic Regimes and the Strongly Stratified Limit of Rotating Boussinesq Equations

Asymptotic regimes of geophysical dynamics are described for different Burger number limits. Rotating Boussinesq equations are analyzed in the asymptotic limit, of strong stratification in the Burger number of order one situation as well as in the asymptotic regime of strong stratification and weak rotation. It is shown that in both regimes horizontally averaged buoyancy variable is an adiabatic invariant for the full Boussinesq system. Spectral phase shift corrections to the buoyancy time scale associated with vertical shearing of this invariant are deduced. Statistical dephasing effects induced by turbulent processes on inertial-gravity waves are evidenced. The 'split' of the energy transfer of the vortical and the wave components is established in the Craya-Herring cyclic basis. As the Burger number increases from zero to infinity, we demonstrate gradual unfreezing of energy cascades for ageostrophic dynamics. The energy spectrum and the anisotropic spectral eddy viscosity are deduced with an explicit dependence on the anisotropic rotation/stratification time scale which depends on the vertical aspect ratio parameter. Intermediate asymptotic regime corresponding to strong stratification and weak rotation is analyzed where the effects of weak rotation are accounted for by an asymptotic expansion with full control (saturation) of vertical shearing. The regularizing effect of weak rotation differs from regularizations based on vertical viscosity. Two scalar prognostic equations for ageostrophic components (divergent velocity potential and geostrophic departure ) are obtained.

Babin, A.↗
NASA NTRS1997

Collaborative, Sequential and Isolated Decisions in Design

The Massachusetts Institute of Technology (MIT) Commission on Industrial Productivity, in their report Made in America, found that six recurring weaknesses were hampering American manufacturing industries. The two weaknesses most relevant to product development were 1) technological weakness in development and production, and 2) failures in cooperation. The remedies to these weaknesses are considered the essential twin pillars of CE: 1) improved development process, and 2) closer cooperation. In the MIT report, it is recognized that total cooperation among teams in a CE environment is rare in American industry, while the majority of the design research in mathematically modeling CE has assumed total cooperation. In this paper, we present mathematical constructs, based on game theoretic principles, to model degrees of collaboration characterized by approximate cooperation, sequential decision making and isolation. The design of a pressure vessel and a passenger aircraft are included as illustrative examples.

Lewis, Kemper↗
NASA NTRS2001

Uncertainties of the Intensity of the 1130 nm Band of Water Vapor

Belmiloud, et al have recently suggested that the HITRAN line intensities in the 1130 nm water vapor band are much too weak. Giver, et at corrected unit conversion errors to make the HITRAN intensities compatible with the original measurements of Mandin, et al, but Belmiloud, et al believe that many of those line intensity measurements were too weak, and they propose the total intensity of the 1130 nm water vapor band is 38% stronger than the sum of the HITRAN line intensities in this region. We have made independent assessments of this proposal using 2 spectra obtained with the Ames 25 meter base path White cell. The first was made using the moderate resolution (8 nm) solar spectral flux radiometer (SSFR) flight instrument with a White cell absorbing path of 506 meters and 10 torr water vapor pressure. Modeling this spectrum using the HITRAN linelist gives a reasonable match, and the model is not compatible when the HITRAN line intensities are increased by 38%. The second spectrum was obtained with a White cell path of 1106 meters and 12 torr water vapor pressure, using a Bomem FTIR with near Doppler width resolution. This spectrum is useful for measuring intensities of isolated weak lines to compare with the measurements of Mandin, et al. Unfortunately, as Belmiloud et al point out, at these conditions the strong lines are much too saturated for good intensity measurements. Our measurements of the weak lines are in reasonable agreement with those of Mandin, et al. Neither of our spectra supports the proposal of Belmiloud et al for a general 38% increase of the absorption intensity in the 1130 nm water vapor band.

Giver, L. P.↗
NASA NTRS2001

Far Ultraviolet Spectroscopy of the Intergalactic and Interstellar Absorption Toward 3C 273

We present Far Ultraviolet Spectroscopic Explorer observations of the molecular, neutral atomic, weakly ionized, and highly ionized components of the interstellar and intergalactic material toward the quasar 3C273. We identify Ly-beta absorption in eight of the known intergalactic Ly-alpha absorbers along the sight line with the rest-frame equivalent widths W(sub r)(Ly-alpha) > 50 micro-angstroms. Refined estimates of the H(I) column densities and Doppler parameters (b) of the clouds are presented. We find a range of b = 16-46 km/s. We detect multiple H(I) lines (Ly-beta - Ly-theta) in the 1590 km/s Virgo absorber and estimate logN(H(I)) = 15.85 +/- 0.10, ten times more H(I) than all of the other absorbers along the sight line combined. The Doppler width of this absorber, b = 16 km/s, implies T < 15,000 K. We detect O(VI) absorption at 1015 km/s at the 2-3(sigma) level that may be associated with hot, X-ray emitting gas in the Virgo Cluster. We detect weak C(III) and O(VI) absorption in the IGM at z=0.12007; this absorber is predominantly ionized and has N(H+)/N(H(I)) > 4000/Z, where Z is the metallicity. Strong Galactic interstellar O(VI) is present between -100 and +100 km/s with an additional high-velocity wing containing about 13% of the total O(VI) between +100 and +240 km/s. The Galactic O(VI), N(V), and C(IV) lines have similar shapes, with roughly constant ratios across the -100 to +100 km/s velocity range. The high velocity O(VI) wing is not detected in other species. Much of the interstellar high ion absorption probably occurs within a highly fragmented medium within the Loop IV remnant or in the outer cavity walls of the remnant. Multiple hot gas production mechanisms are required. The broad O(VI) absorption wing likely traces the expulsion of hot gas out of the Galactic disk into the halo. A flux limit of 5.4 x 10(epx -16) erg/sq cm/s on the amount of diffuse O(VI) emission present = 3.5' off the 3C273 sight line combined with the observed O(VI) column density toward 3C273, logN O(VI) = 14.73 +/- 0.04, implies n(sub e) < 0.02/cubic cm and P/k < 11,500/cubic cm for an assumed temperature of 3 x 10(exp 5) K. The elemental abundances in the neutral and weakly-ionized interstellar clouds are similar to those found for other halo clouds. The warm neutral and warm ionized clouds along the sight line have similar dust-phase abundances, implying that the properties of the dust grains in the two types of clouds are similar. Interstellar H2 absorption is present at positive velocities at a level of logN(H2) = 15.71, but is very weak at the velocities of the main column density concentration along the sight line observed in H(I) 21 cm emission.

Sembach, Kenneth R.↗
NASA NTRS2002

Forecasting Coronal Mass Ejections from Vector Magnetograms

Identification of active regions from which Earthward halo Coronal Mass Ejections (CMEs) are likely to originate is important both for understanding how CMEs are produced and for prediction of hazardous space weather. In previous work, from a set of 17 MSFC (Marshall Space Flight Center) vector magnetograms of 12 bipolar active regions situated within +/- 2 days of rotation from central meridian, we have evaluated four different measures of the global nonpotentiality of the magnetic field of each active region, and have found that the nonpotentiality of these active regions is strongly correlated with their CME productivity during the time interval of +/- 2 days centered on the day of the magnetogram: strongly nonpotential bipolar active regions are much more likely to produce a CME during this interval that are weakly nonpotential bipolar active regions. To further establish the use of active-region nonpotentiality for forecasting CMEs, we have expanded the sample to 19 additional bipolar active regions, with vector magnetograms taken with the upgraded MSFC vector magnetograph from September 2000 through June 2001 with support from our LWS grant (M. J. Hagyard, PI). The four global measures of nonpotentiality are the length of strong-shear, strong-field main neutral line, the net current, and two other measures of the overall twist in the magnetic field of the active-region bipole. We find: 1) The statistical significance of the correlation of the nonpotentiality of active regions with their CME productivity within +/- 2 days of the day of the magnetogram is greater than 99%. 2) 67% of the strongly nonpotential active regions produced CMEs within the +/- 2 day window, while only 17% of the weakly nonpotential ones did. 3) The statistical significance of the correlation of the nonpotentiality of active regions with their CME productivity during 0-2 days after the day of the magnetogram is about 97%. 4) 42% of the strongly nonpotential active regions produced CMEs within the 0-2 day window, while only 10% of the weakly nonpotential ones did. 5) The four different measures of an active region's nonpotentiality agree most of the time in their classification of the nonpotentiality as strong or weak (75%-90% depending on the pair of measurements). Additional information is included in the original extended abstract.

Moore, R. L.↗
NASA NTRS2003

Thermally-Driven Josephson Effect

Break-throughs in the study of superfluid He-3 weak links and recent demonstration of Josephson effect in He-4 are a result of significant advances in ultra-sensitive transducer and nanofabrication technology. However, further progress in the performance of superfluid weak links and quantum rotation interferometry devices depends, in part, on reducing the mechanical noise and increasing the effective duty cycle of such devices. In existing devices, the DC Josephson effect is driven by chemical potential difference produced by a pressure applied across the weak link. We propose a novel drive technique, where the chemical potential is due to a controlled temperature difference. This technique promises to eliminate mechanical shock associated with the switch of the direction of applied pressure and to achieve 100% duty cycle. The thermally driven Josephson effect may also answer outstanding questions about dissipation in superfluid weak links.

Penanen, Konstantin↗
NASA NTRS2015

Role of Longwave Cloud-Radiation Feedback in the Simulation of the Madden-Julian Oscillation

The role of the cloud-radiation interaction in the simulation of the Madden-Julian oscillation (MJO) is investigated. A special focus is on the enhancement of column-integrated diabatic heating due to the greenhouse effects of clouds and moisture in the region of anomalous convection. The degree of this enhancement, the greenhouse enhancement factor (GEF), is measured at different precipitation anomaly regimes as the negative ratio of anomalous outgoing longwave radiation to anomalous precipitation. Observations show that the GEF varies significantly with precipitation anomaly and with the MJO cycle. The greenhouse enhancement is greater in weak precipitation anomaly regimes and its effectiveness decreases monotonically with increasing precipitation anomaly. The GEF also amplifies locally when convection is strengthened in association with the MJO, especially in the weak precipitation anomaly regime (less than 5 mm day(exp -1)). A robust statistical relationship is found among CMIP5 climate model simulations between the GEF and the MJO simulation fidelity. Models that simulate a stronger MJO also simulate a greater GEF, especially in the weak precipitation anomaly regime (less than 5 mm day(exp -1)). Models with a greater GEF in the strong precipitation anomaly regime (greater than 30 mm day(-1)) represent a slightly slower MJO propagation speed. Many models that lack the MJO underestimate the GEF in general and in particular in the weak precipitation anomaly regime. The results herein highlight that the cloud-radiation interaction is a crucial process for climate models to correctly represent the MJO.

Clouds↗
NASA NTRS2016

Fermi GBM Observations of LIGO Gravitational-Wave Event Gw150914

With an instantaneous view of 70% of the sky, the Fermi Gamma-ray Burst Monitor (GBM) is an excellent partner in the search for electromagnetic counterparts to gravitational-wave (GW) events. GBM observations at the time of the Laser Interferometer Gravitational-wave Observatory (LIGO) event GW150914 reveal the presence of a weak transient above 50 keV, 0.4 s after the GW event, with a false-alarm probability of 0.0022 (2.9(sigma)). This weak transient lasting 1 s was not detected by any other instrument and does not appear to be connected with other previously known astrophysical, solar, terrestrial, or magnetospheric activity. Its localization is ill-constrained but consistent with the direction of GW150914. The duration and spectrum of the transient event are consistent with a weak short gamma-ray burst (GRB) arriving at a large angle to the direction in which Fermi was pointing where the GBM detector response is not optimal. If the GBM transient is associated with GW150914, then this electromagnetic signal from a stellar mass black hole binary merger is unexpected. We calculate a luminosity in hard X-ray emission between 1 keV and 10 MeV of 1.8(sup +1.5, sub -1.0) x 10(exp 49) erg/s. Future joint observations of GW events by LIGO/Virgo and Fermi GBM could reveal whether the weak transient reported here is a plausible counterpart to GW150914 or a chance coincidence, and will further probe the connection between compact binary mergers and short GRBs.

gamma-ray burst: general – gravitational waves↗
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↗