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Results for “weak stage order”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
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↗
NASA NTRS1988

On the interpretation of integrated water vapor patterns in midlatitude cyclones derived from the Nimbus 7 scanning multichannel microwave radiometer

The present exploration of methods for the interpretation of the Nimbus 7 satellite's Scanning Multichannel Microwave Radiometer (SMMR) vapor patterns and the ways in which they relate to the dynamical structure of individual midlatitude storms employs gridded meteorological data from the First GARP Global Experiment special observing period in order to calculate diagnostic quantities. SMMR patterns for a storm at a weak stage determined from the diagnostic quantities are compared with SMMR patterns for the storm at a stronger stage. A more complete interpretation of the SMMR patterns emerges from these considerations.

Mcmurdie, Lynn A.↗
NASA NTRS1990

Optimal guidance law development for an advanced launch system

A regular perturbation analysis is presented. Closed-loop simulations were performed with a first order correction including all of the atmospheric terms. In addition, a method was developed for independently checking the accuracy of the analysis and the rather extensive programming required to implement the complete first order correction with all of the aerodynamic effects included. This amounted to developing an equivalent Hamiltonian computed from the first order analysis. A second order correction was also completed for the neglected spherical Earth and back-pressure effects. Finally, an analysis was begun on a method for dealing with control inequality constraints. The results on including higher order corrections do show some improvement for this application; however, it is not known at this stage if significant improvement will result when the aerodynamic forces are included. The weak formulation for solving optimal problems was extended in order to account for state inequality constraints. The formulation was tested on three example problems and numerical results were compared to the exact solutions. Development of a general purpose computational environment for the solution of a large class of optimal control problems is under way. An example, along with the necessary input and the output, is given.

Calise, Anthony J.↗
DOE OSTI2024

A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data

Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.

Astronomy & Astrophysics↗
DOE OSTI2022

Weak lensing trispectrum and Kurt-spectra

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-Cℓ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model — the hierarchical ansatz — can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Enhanced antineutrino emission from 𝛽 decay in core-collapse supernovae with self-consistent weak decay rates

Nuclear weak-interaction rates are known to exert a prominent effect in the late stages of stellar collapse. Despite their importance, most studies to date on core-collapse supernovae (CCSNe) have focused primarily on the effects of electron captures, neglecting 𝛽 decay contributions. In this work, we present the first CCSNe simulation incorporating global 𝛽 decay rates from a microscopic theory. These are enabled by a large-scale evaluation of both electron capture and 𝛽 decay rates, obtained self-consistently utilizing the relativistic energy density functional theory and finite-temperature quasiparticle random-phase approximation. Including 𝛽 decay leads to a dramatic enhancement of the pre-bounce antineutrino signal as the antineutrino emissivity increases by more than two orders of magnitude and the luminosity by a factor of 50 relative to thermal emission alone, while the average antineutrino energy increases by over 1 MeV. Furthermore, it is expected that these new rates could help us constrain the model uncertainties related to weak-interaction processes, improving the prediction of antineutrino signal during the final stages of stellar death.

Beta decay↗
NASA NTRS1991

The Langley Research Center CSI phase-0 evolutionary model testbed-design and experimental results

A testbed for the development of Controls Structures Interaction (CSI) technology is described. The design philosophy, capabilities, and early experimental results are presented to introduce some of the ongoing CSI research at NASA-Langley. The testbed, referred to as the Phase 0 version of the CSI Evolutionary model (CEM), is the first stage of model complexity designed to show the benefits of CSI technology and to identify weaknesses in current capabilities. Early closed loop test results have shown non-model based controllers can provide an order of magnitude increase in damping in the first few flexible vibration modes. Model based controllers for higher performance will need to be robust to model uncertainty as verified by System ID tests. Data are presented that show finite element model predictions of frequency differ from those obtained from tests. Plans are also presented for evolution of the CEM to study integrated controller and structure design as well as multiple payload dynamics.

Belvin, W. K.↗
DOE OSTI2023

Magnetic order in the two-dimensional metal-organic framework manganese pyrazinecarboxylate with Mn-Mn dimers

The magnetic properties of [Mn(pyrazinecarboxylate) 2 ] n , empirical formula C 10 H 6 MnN 4 O 4 , are investigated through susceptibility, heat capacity, and neutron scattering measurements. The structure consists of Mn-Mn dimers linked on a distorted 2D hexagonal structure. The weak out-of-plane interactions create a quasi-2D magnetic material within the larger three-dimensional metal-organic framework structure. Here, we show that this material undergoes a two-stage magnetic transition, related to the low dimensionality of the Mn lattice. First, at 5 K, which is assigned to the initial development of short-range order in the 2D layers. This is followed by long-range order at 3.3 K. Applied field measurements reveal the potential to induce magnetic transitions in moderately small fields of ~2 T. Neutron powder diffraction enabled the determination of a unique magnetic space group P2 1 '/c (No. 14.77) at 1.5 K. This magnetic structure consists of antiferromagnetically coupled Mn-Mn dimers with spins principally along the out-of-plane $a$ axis.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Unraveling the Early-Stage Ordering of Krypton Solid Bubbles in Molybdenum: A Multimodal Study

Self-organization of defects such as fission gas bubbles in materials can lead to high inventory capacity for fission gas storage and help mitigate swelling caused by fission gases in nuclear fuel materials under radiation in nuclear reactors. Here, we report the physical mechanism of self-organization of krypton (Kr) gas bubbles in molybdenum (Mo) under ion implantation. The ion fluence and temperature-dependent formation of Kr solid bubble superlattice (SBS) in Mo were investigated by using both synchrotron-based small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). Early stage self-organization of gas bubbles is observed at a fluence of 2.5 × 10 16 ions/cm 2 at temperatures of 300–400 °C. The bubble lattice constant increases with increasing implantation temperature from 300 to 400 °C. Both experiments and atomic kinetic Monte Carlo modeling indicate that the Kr solid bubbles are weakly ordered in comparison to previously studied helium (He) gas bubble superlattice (GBS) while the lattice constant are relatively smaller for Kr SBS compared to that of He GBS. The irradiation conditions suggest that spinodal decomposition, which is a form of phase separation, probably precedes gas bubble ordering in Mo. Altogether, our work sheds light on the formation mechanism of noble gas superlattice toward the development of radiation-tolerant materials which are important for the design of advanced nuclear reactors.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

We study the phase ordering dynamics of the classical antiferromagnetic 𝐽 1 −𝐽 2 (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime (𝐽 2 /𝐽 1 > 1/2). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a nonconserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. Here, we also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

Antiferromagnets↗
DOE OSTI2025

A theoretical study of the upper bound of surface elevation variance in the Phillips initial stage during wind-wave generation

The resonance mechanism in the initial of wind-wave generation proposed by Phillips is a foundation of wind-wave generation theory, but a precise theoretical quantification of wave energy growth in this initial stage has not been obtained yet after more than six decades of research. In this study, we aim to address this knowledge gap by developing an analytical approach based on a novel complex analysis method to theoretically investigate the temporal evolution of the wave energy in the Phillips initial stage. We quantitatively derive and analyse the growth behaviour of the surface wave energy and obtain an analytical solution for its upper bound. Our result highlights the crucial effects of surface tension. Because the phase velocity of gravity–capillary waves has a minimal value at a critical wavenumber, gravity–capillary waves and gravity waves (which neglect surface tension) exhibit distinct resonance curve properties and wave energy growth behaviours. For gravity waves, the resonance curve extends indefinitely; for gravity–capillary waves, it either forms a finite-length curve or does not exist, depending on the wind speed. The leading-order term of the upper-bound solution of the energy of gravity waves increases linearly over time, while for gravity–capillary waves, the term increases linearly over time under strong wind conditions but remains finite under weak wind conditions. This theoretical study provides an analytical framework for the generation of wind-waves in the Phillips initial stage, which may inspire further theoretical, numerical and experimental research.

58 GEOSCIENCES↗
NASA NTRS1990

Magnetic reconnection driven by current repulsion

The evolution of an equilibrium consisting of two magnetic islands with oppositely directed currents embedded in a strong magnetic field is investigated, using numerical simulation methods. The rapid development of an ideal magnetohydrodynamic instability is observed, which first rotates and then expels the islands. The growth rate is on the order of the inverse of the Alfven transit time and is much higher than that for magnetic island coalescence. In the nonlinear stage, resistivity becomes important as the reconnection process ensues and dissipates the magnetic energy. The growth rate of the instability is a weak function of the plasma beta and other plasma parameters such as S, the magnetic Reynolds number. An energy principle analysis, based on eigenfunctions obtained from the simulation, confirms the existence of the instability.

Richard, R. L.↗
DOE OSTI2024

Mitigation of the Brighter-fatter Effect in the LSST Camera

Abstract Thick, fully depleted charge-coupled devices are known to exhibit nonlinear behavior at high signal levels due to the dynamic behavior of charges collecting in the potential wells of pixels, called the brighter-fatter effect (BFE). The effect results in distorted images of bright calibration stars, creating a flux-dependent point-spread function that if left unmitigated, could make up a large fraction of the error budget in Stage IV weak-lensing (WL) surveys such as the Legacy Survey of Space and Time (LSST). In this paper, we analyze image measurements of flat fields and artificial stars taken at different illumination levels with the LSST Camera (LSSTCam) at SLAC National Accelerator Laboratory in order to quantify this effect in the LSSTCam before and after a previously introduced correction technique. We observe that the BFE evolves anisotropically as a function of flux due to higher-order BFEs, which violates the fundamental assumption of this correction method. We then introduce a new method based on a physically motivated model to account for these higher-order terms in the correction, and then we test the modified correction on both data sets. We find that the new method corrects the effect in flat fields better than it corrects the effect in artificial stars, which we suggest is the result of sub-pixel physics not included in this correction model. We use these results to define a new metric for the full-well capacity of our sensors and advise image processing strategies to further limit the impact of the effect on LSST WL science pathways.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Mitigation of the Brighter-Fatter Effect in the LSST Camera

Thick, fully depleted charge-coupled devices (CCDs) are known to exhibit non-linear behavior at high signal levels due to the dynamic behavior of charges collecting in the potential wells of pixels, called the brighter-fatter effect (BFE). This particularly impacts bright calibration stars, which appear larger than their intrinsic shape, creating a flux-dependent point-spread function (PSF) that if left unmitigated, could make up a large fraction of the error budget in Stage IV weak-lensing (WL) surveys such as the Legacy Survey of Space and Time (LSST). In this paper, we analyze image measurements of flat fields and artificial stars taken at different illumination levels with the LSST Camera (LSSTCam) at SLAC National Accelerator Laboratory in order to quantify this effect in the LSST Camera before and after a previously introduced correction technique. We observe that the BFE evolves anisotropically as a function of flux due to higher-order BFEs, which violates the fundamental assumption of this correction method. We then introduce a new sampling method based on a physically motivated model to account these higher-order terms in the correction, and then we test the modified correction on both datasets. We find that the new method corrects the effect in flat fields better than it corrects the effect in artificial stars which we conclude is the result of a unmodeled curl component of the deflection field by the correction. We use these results to define a new metric for the full-well capacity of our sensors and advise image processing strategies to further limit the impact of the effect on LSST WL science pathways.

47 OTHER INSTRUMENTATION↗
NASA NTRS1981

The dynamics of superclusters - Initial determination of the mass density of the universe at large scales

The radial velocities of cluster members of two rich, large superclusters have been measured in order to probe the supercluster mass densities, and simple evolutionary models have been computed to place limits upon the mass density within each supercluster. These superclusters represent true physical associations of size of about 100 Mpc seen presently at an early stage of evolution. One supercluster is weakly bound, the other probably barely bound, but possibly marginally unbound. Gravity has noticeably slowed the Hubble expansion of both superclusters. Galaxy surface-density counts and the density enhancement of Abell clusters within each supercluster were used to derive the ratio of mass densities of the superclusters to the mean field mass density. The results strongly exclude a closed universe.

Ford, H. C.↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evidence of underdeveloped torus and broad-line region of weak emission line quasars based on their spectral energy distribution

To unravel the dominant cause of the weak emission line in a subset of optically selected radio-quiet ‘weak emission line quasars’ (WLQs), we have investigated the possibility of an underdeveloped broad line region (BLR). For this, we have modelled spectral energy distributions (SED) of 61 WLQs by using their optical and infrared (IR) photometric observations from Sloan Digital Sky Survey (SDSS) and WISE, respectively. SED fit consists of various emission components, including the luminosity from the dusty torus (L tor ). For comparison with the normal quasar, we have used a control sample of 55 Quasi-Stellar Objects (QSOs) for each WLQ matching in emission redshift and SDSS r-band. Based on our measurement of L tor , we found a decrement of 42 ± 2 per cent in IR luminosity in WLQs with respect to the control sample of normal QSOs. Using L tor /L bol as the measure of torus covering factor (CF tor ), we found a similar decrement in WLQ covering factor, with their CF tor distribution being significantly different with respect to the normal QSOs with a KS test P null of 4.27 × 10 −14 . As dusty torus and BLR covering factors are expected to be of a similar order in active galactic nucleus (AGN), our results suggest that the BLR in the WLQs is underdeveloped and could be a dominant cause of the weakness of their emission line. As a result, our analysis gives support to the models of WLQs based on the evolution scenario being in an early stage of AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Electromagnetic & Weak Probes: Experimental Overview

Electromagnetic and electroweak probes are the most versatile probes in the study of heavy-ion collisions. Produced at every stage in the evolution of QCD matter, its messengers are practically inert to the strongly interacting medium they travel through. In this contribution, I will discuss a selection of new results from experiments at the LHC, RHIC, and SIS facilities, spanning almost four orders of magnitude in beam energy. Finally, I will conclude with a brief overview of the experimental landscape in the near future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗