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DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗

NASA NTRS2006

Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes

The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.

Herencia-Zapana, Heber↗

NASA NTRS2007

The Prelude to and Aftermath of the Giant Flare of 2004 December 27: Persistent and Pulsed X-ray Properties of SGR 1806-20 from 1993 to 2005

We report on the evolution of key spectral and temporal parameters of SGR 1806-20 prior to and following the highly energetic giant flare of 2004 December 27. Using RXTE, we track the pulse frequency of the SGR and find that the spin-down rate varied erratically in the months before and after the flare. Contrary to the giant flare in SGR 1900+14, we find no evidence for a discrete jump in spin frequency at the time of the December 27th flare (Absolute value of (Delta * upsilon/upsilon) < 5 10 (exp -6)). In the months surrounding the flare, we find a strong correlation between pulsed flux and torque consistent with the model for magnetar magnetosphere electrodynamics proposed. As with the flare in SGR 1900+14, the pulse morphology of SGR 1806-20 changes drastically following the flare. Using Chandra and other publicly available imaging X-ray detector observations, we construct a spectral history of SGR 1806-20 from 1993 to 2005. The usual magnetar persistent emission spectral model of a power law plus a blackbody provides an excellent fit to the data. We confirm the earlier finding of increasing spectral hardness of SGR 1806-20 between 1993 and 2004. However, our results indicate significant differences in the temporal evolution of the spectral hardening. Rather than a direct correlation between torque and spectral hardness, we find evidence for a sudden torque change that preceded a gradual hardening of the energy spectrum on a timescale of years. Interestingly, the spectral hardness, spin-down rate, phase-averaged flux, and pulsed flux of SGR 1806-20 all peak months before the flare epoch.

Woods, Peter M.↗

NASA NTRS2019

GOES-16 ABI Solar Reflective Channel Validation for Earth Science Application

This paper presents the validation results of GOES-16 Satellite's Advanced Baseline Imager (ABI) obtained from a reflectance-based field campaign undertaken at the Salar de Uyuni in Bolivia in June 2017. In situ ground measurements are used to characterize the surface reflectance and the atmosphere in order to constrain the radiative transfer code and predict at-sensor reflectance (also referred to as top-of-atmosphere (TOA) reflectance) to compare with concurrent GOES-16 ABI measurements. The five-day field campaign provided repeated TOA reflectance estimates, allowing assessment not only of the calibration accuracy of the ABI reflective channels 1, 2, 3, 5 and 6, but also of its stability over the duration of the campaign. The results show that the accuracy of the ABI reflective channels calibration is within specification for channels 1, 3, 5, and 6 - average biases within 2%; for channel 2 the bias is 5%. The estimated uncertainty on the derived biases is 2–2.4%. Some calibration stability issues were present in the ABI calibration at the time of the campaign: (i) a jump on the order of 2% in channels 1 and 6, coincident with an ABI solar calibration event, reflects an instability of the ABI gains in these channels, and (ii) short-term variability in channels 1 and 2 is due to striping (ABI detector-todetector calibration differences). Continued validation and subsequent reprocessing of ABI reflectance imagery would allow Earth scientists to fully benefit from the high spatial and spectral fidelity of the GOES-16 ABI diurnal measurements at the continental scale.

Joel McCorkel↗

NASA NTRSDate not supplied

Functional Task Tests in Partial Gravity During Parabolic Flight

BACKGROUND Critical mission tasks that are required by crews immediately after landing on a planetary surface are seat egress, jump, and walk. To be able to define an effective and comprehensive countermeasure strategy for preserving crew performance during exploration-class missions, there is a need to understand how these functional tasks are actually performed in partial gravity such as on the Moon or Mars. We propose to study the performance in the execution of these tasks during the partial gravity and hypergravity phases of parabolic flight. These tasks will be completed using the same equipment and procedures as the Standard Measures Sensorimotor protocol, which is performed by astronauts returning from spaceflight and by ground-based subjects after prolonged axial body unloading during bed rest. HYPOTHESIS We hypothesize that partial gravity during parabolic flight will cause acute changes in vestibular, proprioceptive, and sensorimotor functions, and these changes will impact the performance of mission critical tasks such as standing, walking, and jumping. The largest changes in performance are expected at the lowest gravity level (0.25g) because subjects will no longer be able to use the gravitational reference for the perception of vertical. Ultimately, this information could be used to assess performance risks and inform the design of countermeasures for NASA exploration-class human missions. METHODS Twelve subjects will be tested during three flights of 30 parabolas, including 10 parabolas at 0.25g, 10 parabolas at 0.5g and 10 parabolas at 0.75g. Subject also will perform tests in 1g between parabolas and in hypergravity (1.8g) during the pull-out phases. Subjects will perform the same tasks as those tested on astronauts returning from spaceflight: sit-to-stand and obstacle walk, tandem walk, jump down, and recovery from fall. Measurements will include: (a) the time for the subject to complete the test (sit-to-stand and obstacle walk, recovery from fall); (b) the time elapsed between the start of motion and the stabilization of upright posture (recovery from fall, jump down); (c) the mean sway speed during quiet standing (recovery from fall, jump down); (d) changes in heart rate and blood pressure (recovery from fall); (e) the percentage of correct steps and torso acceleration (tandem walk); and (f) the severity of motion sickness symptoms. RELEVANCE Although gravitational dose-response curves have been obtained for some biochemical systems in animals, these dose-responses are unknown for most human physiologic systems. Our study will compare the outcomes of 5 functional task tests in 0.25g, 0.5g, 0.75g, 1g, and 1.8g with those previously obtained in ground-based subjects after prolonged axial body unloading and in astronauts immediately after spaceflight. This comparison will help understanding the true extent of functional task performance deficits in partial gravity. The dose-response relationship between gravity level and task performance decrement also will help determining the gravity threshold for these functional tasks. ACKNOWLEDGEMENT This work is supported by the NASA’s Human Research Program Human Health Countermeasures Element

Gilles Clement↗

NASA NTRSDate not supplied

Functional Task Tests in Partial Gravity During Parabolic Flight

BACKGROUND Understanding how critical mission tasks are performed in partial gravity such as on the moon or Mars is necessary to define effective and comprehensive countermeasure strategies for preserving crew performance during exploration missions. We studied the performance of tasks such as standing, walking, and jumping during the partial gravity phases of parabolic flight. We hypothesized that the acute effects of partial gravity on vestibular, proprioceptive, and sensorimotor functions would negatively impact performance. METHODS Twelve subjects were tested over three flights of 30 parabolas each, including 10 parabolas at 0.25g, 10 parabolas at 0.5g, and 10 parabolas at 0.75g. Subjects also performed tests in 1g between parabolas. During the sit-to-stand with obstacle walk task, subjects rose from a seated position and walked as quickly as possible straight ahead towards a cone (4 m distance), walked around the cone making a 180° left turn, returned, and sat in the chair. On the way to and from the cone, subjects stepped over a 30 cm high obstacle. For the recovery from fall task, subjects lay prone for the pull-up phase and initial 10 sec of the parabola. Then they were asked to rise as quickly as possible and maintain a quiet stance for 10 sec. The tandem rail balance task involved standing with both feet on a 4.5 cm wide rail. The time ended when subjects either stepped off the rail or grabbed on to support straps. The jump down task started with the subjects standing on a 30 cm high platform, then the subjects were instructed to step off the platform, land with both feet simultaneously, and settle in a quiet stance. The cone of stability task involved subjects leaning about the ankles as far as they could in the anterior, posterior, and lateral directions without unfolding their arms or taking a step. The center of pressure distance between endpoints was calculated. Data were collected using inertial measurement units (Opal V2, APDM, Portland, OR) worn on the head and trunk, heart rate monitors (RS800CX, Polar, Kempele, Finland), and a force plate (Bertec, Columbus, OH). RESULTS Gravity level had a significant effect on performance, with the greatest changes from 1g tending to be at the 0.25g level (Table 1). Lower gravity levels were associated with increased times to complete the sit-to-stand obstacle walk task and the recovery from fall task, decreased change in heart rate during the recovery from fall task, decreased rail balance times, and increased cone of stability distance in the anterior-posterior direction. Table 1. Functional task performance at different gravity levels during parabolic flight. Measure0.25g0.5g0.75g1gp-valueSit-to-stand with obstacle walk time (sec)9.8 ±1.4*7.2 ±0.76.9 ±0.8*7.4 ±0.9<0.001Recovery from fall time to settle (sec)5.3 ± 0.9*4.6 ± 0.84.2 ± 0.64.3 ± 0.70.002Recovery from fall change in heart rate (bpm)6.0 ± 7.3*11.2 ± 6.5*14.9 ± 4.915.9 ± 6.5<0.001Rail balance with eyes open time (sec)2.7 ±0.8*4.8 ±2.16.6 ±4.78.4 ±6.70.031Rail balance with eyes closed time (sec)1.6 ±0.4*2.1 ±0.42.4 ±0.62.6 ±0.8<0.001Jump down time to settle (sec)2.1 ± 0.41.9 ± 0.42.0 ± 0.31.8 ± 0.30.328Cone of stability –anterior-posterior (cm)20.8 ±2.7*18.8 ±2.218.6 ±1.717.9 ±2.00.039Cone of stability –lateral (cm)26.8 ±6.624.4 ±2.123.0 ±2.123.8 ±2.30.215p-value: one-way repeated measures analysis of variance; *Significant pairwise difference from 1g (p<0.05). DISCUSSION These data suggest that there is a dose-response relationship between gravity level and functional task performance. The largest changes in performance were expected at the lowest gravity level (0.25g) because subjects would no longer be able to use the gravitational reference for the perception of upright. Understanding the extent of performance deficits informs the risks and design of countermeasures for exploration spaceflight missions. ACKNOWLEDGEMENT This work is supported by NASA’s Human Research Program Human Health Countermeasures Element.

T R Macaulay↗

NASA NTRS2002

Marangoni Effects of a Drop in an Extensional Flow: The Role of Surfactant Physical Chemistry

While the changes in stresses caused by surfactant adsorption on non-deforming interfaces have been fairly well established, prior to this work, there were few studies addressing how surfactants alter stresses on strongly deforming interfaces. We chose the model problem of a drop in a uniaxial extensional flow to study these stress conditions To model surfactant effects at fluid interfaces, a proper description of the dependence of the surface tension on surface concentration, the surface equation of state, is required. We have adopted a surface equation of state that accounts for the maximum coverage limit; that is, because surfactants have a finite cross sectional area, there is an upper bound to the amount of surfactant that can adsorb in a monolayer. The surface tension reduces strongly only when this maximum coverage is approached. Since the Marangoni stresses go as the derivative of the surface equation of state times the surface concentration gradient, the non-linear equation of state determines both the effect of surfactants in the normal stress jump, (which is balanced by the product of the mean curvature of the interface times the surface tension), and the tangential stress jump, which is balanced by Marangoni stresses. First, the effects of surface coverage and intermolecular interactions among surfactants which drive aggregation of surfactants in the interface were studied. (see Pawar and Stebe, Physics of Fluids).

Stebe, Kathleen J.↗

NASA NTRS2014

A Total Lightning Perspective of the 20 May 2013 Moore, Oklahoma Supercell

In the early afternoon of 20 May 2013, a storm initiated to the west‐southwest of Newcastle, Oklahoma. This storm would rapidly intensify into the parent supercell of the tornado that struck the city of Moore, Oklahoma. This article describes what contributions total lightning observations from the Oklahoma Lightning Mapping Array could provide to operational forecasters had these observations been available in real‐time. This effort includes a focus on the GOES‐R pseudo‐geostationary lightning mapper demonstration product as well as the NASA SPoRT / Meteorological Development Laboratory's total lightning tracking tool. These observations and tools identified several contributions. Two distinct lightning jumps at 1908 and 1928 UTC provided a lead time of 19 minutes ahead of severe hail and 26 minutes ahead of the Moore, Oklahoma tornado's touchdown. These observations provide strong situational awareness to forecasters, as the lightning jumps are related to the rapid strengthening of the storm's updraft and mesocyclone and serve as a precursor to the stretching of the storm vortex ahead severe weather.

Stano, Geoffrey T.↗

NASA NTRS2006

JMR Noise Diode Stability and Recalibration Methodology after Three Years On-Orbit

The Jason Microwave Radiometer (JMR) is included on the Jason-1 ocean altimeter satellite to measure the wet tropospheric path delay (PD) experienced by the radar altimeter signal. JMR is nadir pointing and measures the radiometric brightness temperature (T(sub B)) at 18.7, 23.8 and 34.0 GHz. JMR is a Dicke radiometer and it is the first radiometer to be flown in space that uses noise diodes for calibration. Therefore, monitoring the long term stability of the noise diodes is essential. Each channel has three redundant noise diodes which are individually coupled into the antenna signal to provide an estimate of the gain. Two significant jumps in the JMR path delays, relative to ground truth, were observed around 300 and 700 days into the mission. Slow drifts in the retrieved products were also evident over the entire mission. During a recalibration effort, it was determined that a single set of calibration coefficients was not able to remove the calibration jumps and drifts, suggesting that there was a change in the hardware and time dependent coefficients would be required. To facilitate the derivation of time dependent coefficients, an optimal estimation based calibration system was developed which iteratively determines that set of calibration coefficients which minimize the RMS difference between the JMR TBs and on-Earth hot and cold absolute references. This optimal calibration algorithm was used to fine tune the front end path loss coefficients and derive a time series of the JMR noise diode brightness temperatures for each of the nine diodes. Jumps and drifts, on the order of 1% to 2%, are observed among the noise diodes in the first three years on-orbit.

Jason 1↗

DOE OSTI2025

Evaluating a Transition-jump System for the Fermilab Main Injector Using Xsuite

We describe an Xsuite simulation framework for the Fermilab Main Injector (MI) along with an evaluation of transition-crossing behaviors in the accelerator. In particular, we studied the introduction of quadrupole magnets into the lattice as part of a transition-jump system that will be implemented through the $2^{nd}$ Proton Improvement Plan (PIP-II). Simulated beam losses spurred by transition-induced instabilities were assessed under several systematic effects, including MI quad errors, magnet-to-magnet variability in the jump magnets, power-supply errors, and timing jitter.

Schreckenberger, A. P. [Fermilab] (ORCID:000000016↗

DOE OSTI2025

Evaluating a Transition-Jump System for the Fermilab Main Injector Using Xsuite

Schreckenberger, Adam Paul [Fermilab] (ORCID:00000↗

NASA NTRS1982

Unsteady Transonic Small Disturbance theory with strong shock waves

Transonic Small Disturbance (TSD) theory is modified to yield steady and unsteady solutions in the case of strong shock waves (where the local Mach number ahead of the shock exceeds 1.3). The modification consists of an additional adjustable nonlinear term which allows the exact Rankine-Hugoniot shock jump relation to be satisfied at all times. The modified TSD theory is applied to steady and unsteady oscillatory transonic flows, and yields results which are in good agreement with solutions of the unsteady Euler equations, and which compare favorably with solutions of the full potential equation when shock waves are weak.

Kerlick, G. D.↗

NASA NTRS1990

Electron energetics in the inner coma of Comet Halley

A quasi-two-dimensional model of the spatial and energy distribution of electrons in the inner coma of Comet Halley has been constructed from a spherically symmetric ion density profile based on Giotto measurements, using the two-stream electron transport method and the time-dependent electron energy equation. A sharp jump in the electron temperature was found to be present at a cometocentric distance of about 15,000 km. This thermal boundary separates an inner region where cooling processes are dominant from an outer region where heat transport is more important. Both thermal and suprathermal electron populations exist inside the thermal boundary with comparable kinetic pressures. Outside the thermal boundary, a cloud electron population does not exist, and the electrons are almost isothermal along the magnetic field lines.

Gan, LU↗

NASA NTRS1991

Supercomputer optimizations for stochastic optimal control applications

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

Chung, Siu-Leung↗

NASA NTRS2014

Exploring Lightning Jump Characteristics

This study is concerned with the characteristics of storms exhibiting an abrupt temporal increase in the total lightning flash rate (i.e., lightning jump, LJ). An automated storm tracking method is used to identify storm "clusters" and total lightning activity from three different lightning detection systems over Oklahoma, northern Alabama and Washington, D.C. On average and for different employed thresholds, the clusters that encompass at least one LJ (LJ1) last longer, relate to higher Maximum Expected Size of Hail, Vertical Integrated Liquid and lightning flash rates (area-normalized) than the clusters that did not exhibit any LJ (LJ0). The respective mean values for LJ1 (LJ0) clusters are 80 min (35 min), 14 mm (8 mm), 25 kg per square meter (18 kg per square meter) and 0.05 flash per min per square kilometer (0.01 flash per min per square kilometer). Furthermore, the LJ1 clusters are also characterized by slower decaying autocorrelation functions, a result that implies a less "random" behavior in the temporal flash rate evolution. In addition, the temporal occurrence of the last LJ provides an estimate of the time remaining to the storm's dissipation. Depending of the LJ strength (i.e., varying thresholds), these values typically range between 20-60 min, with stronger jumps indicating more time until storm decay. This study's results support the hypothesis that the LJ is a proxy for the storm's kinematic and microphysical state rather than a coincidental value.

lightning jump↗

NASA NTRS1982

An analysis of shock wave disturbances observed at 1 AU from 1971 through 1978

IMP 6, 7, and 8 data from 104 shock wave disturbances were employed to document the occurrence frequency and properties of the solar wind shock which produce He ion abundance enhancements. The shocks were identified over the 1971-1978 time period and were characterized by a preshock flow with lower than usual average bulk density, a shocked gas layer 12 hr thick, and a postshocked gas layer 1.5 days thick with a high He abundance. A high-temperature peak was found to occur in the first 12 hrs after a He-enriched shock and was not seen when He-enhancement was absent. The total pressure was also three times higher with He-shocks, and speed jumps were greater than 50 km/sec in 56% of the He events. It is concluded that all shock waves in the solar wind at 1 AU originate in coronal mass ejection events, and the presence of He-enrichment is attributable to the geometry of the area that produced the event.

Borrini, G.↗

NASA NTRS1992

A model for the radio brightness of the supernova remnant 1987A

The recently observed rise in radio flux from SN1987A is earlier than predicted in models of the interaction with the observed line-emitting gas. The observed size of the radio source is roughly consistent with the expected position of the SN shock wave and the position of the termination shock of the blue supergiant progenitor wind. The radio increase is attributed to the interaction of the SN shock with this density jump. The required efficiency of electron acceleration and magnetic field amplification is larger than usually occurs in SNe and SNR. Possible reasons for the enhanced radio emission are particle acceleration by the weak reflected shock that travels through the interaction region, and the action of the Richtmyer-Meshkov instability near the initial termination-shock density jump. The action of these mechanisms is time-limited; the prediction of this model is that the radio flux should begin to decline within the next year.

Chevalier, Roger A.↗

NASA NTRS2017

How Long Do Satellites Need to Overlap? Evaluation of Climate Data Stability from Overlapping Satellite Records

Sensors on satellites provide unprecedented understanding of the Earth's climate system by measuring incoming solar radiation, as well as both passive and active observations of the entire Earth with outstanding spatial and temporal coverage. A common challenge with satellite observations is to quantify their ability to provide well-calibrated, long-term, stable records of the parameters they measure. Ground-based intercomparisons offer some insight, while reference observations and internal calibrations give further assistance for understanding long-term stability. A valuable tool for evaluating and developing long-term records from satellites is the examination of data from overlapping satellite missions. This paper addresses how the length of overlap affects the ability to identify an offset or a drift in the overlap of data between two sensors. Ozone and temperature data sets are used as examples showing that overlap data can differ by latitude and can change over time. New results are presented for the general case of sensor overlap by using Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) and Solar Stellar Irradiance Comparison Experiment (SOLSTICE) solar irradiance data as an example. To achieve a 1 % uncertainty in estimating the offset for these two instruments' measurement of the Mg II core (280 nm) requires approximately 5 months of overlap. For relative drift to be identified within 0.1 %/yr uncertainty (0.00008 W/sq m/nm/yr), the overlap for these two satellites would need to be 2.5 years. Additional overlap of satellite measurements is needed if, as is the case for solar monitoring, unexpected jumps occur adding uncertainty to both offsets and drifts; the additional length of time needed to account for a single jump in the overlap data may be as large as 50 % of the original overlap period in order to achieve the same desired confidence in the stability of the merged data set. Results presented here are directly applicable to satellite Earth observations. Approaches for Earth observations offer additional challenges due to the complexity of the observations, but Earth observations may also benefit from ancillary observations taken from ground-based and in situ sources. Difficult choices need to be made when monitoring approaches are considered; we outline some attempts at optimizing networks based on economic principles. The careful evaluation of monitoring overlap is important to the appropriate application of observational resources and to the usefulness of current and future observations.

climate data records↗