Search NASA⌕ Search

SEARCH · Search NASA

Results for “Stein equation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

62 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Deviations from LTE in a stellar atmosphere

Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.

Kalkofen, W.↗
DOE OSTI2024

Benchmarking Optimizers for Qumode State Preparation with Variational Quantum Algorithms

Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in qumodes due to advancements in the field and their potential applications. However there is a notable gap in the literature specifically addressing this area. This paper aims to bridge this gap by providing performance benchmarks of various optimizers used in state preparation with Variational Quantum Algorithms. We conducted extensive testing across multiple scenarios, including different target states, both ideal and sampling simulations, and varying numbers of basis gate layers. Our evaluations offer insights into the complexity of learning each type of target state and demonstrate that some optimizers perform better than others in this context. Notably, the Powell optimizer was found to be exceptionally robust against sampling errors, making it a preferred choice in scenarios prone to such inaccuracies. Additionally, the Simultaneous Perturbation Stochastic Approximation optimizer was distinguished for its efficiency and ability to handle increased parameter dimensionality effectively.

Kan, Shuwen [Fordham University]↗
NASA NTRS1992

Non-LTE radiating acoustic shocks and Ca II K2V bright points

We present, for the first time, a self-consistent solution of the time-dependent 1D equations of non-LTE radiation hydrodynamics in solar chromospheric conditions. The vertical propagation of sinusoidal acoustic waves with periods of 30, 180, and 300 s is calculated. We find that departures from LTE and ionization recombination determine the temperature profiles of the shocks that develop. In LTE almost all the thermal energy goes into ionization, so the temperature rise is very small. In non-LTE, the finite transition rates delay the ionization to behind the shock front. The compression thus goes into thermal energy at the shock front leading to a high temperature amplitude. Further behind the shock front, the delayed ionization removes energy from the thermal pool, which reduces the temperature, producing a temperature spike. The 180 s waves reproduce the observed temporal changes in the calcium K line profiles quite well. The observed wing brightening pattern, the violet/red peak asymmetry and the observed line center behavior are all well reproduced. The short-period waves and the 5 minute period waves fail especially in reproducing the observed behavior of the wings.

Carlsson, Mats↗
NASA NTRS1998

On Wave Processes in the Solar Atmosphere

This grant was awarded by NASA/MSFC to The University of Alabama in Huntsville (UAH) to investigate the physical processes responsible for heating and wind acceleration in the solar atmosphere, and to construct theoretical, self-consistent and time-dependent solar wind models based on the momentum deposition by finite amplitude and nonlinear Alfven waves. In summary, there are three main goals of the proposed research: (1) Calculate the wave energy spectra and wave energy fluxes carried by magnetic non- magnetic waves. (2) Find out which mechanism dominates in supplying the wave energy to different parts of the solar atmosphere. (3) Use the results obtained in (1) and (2) to construct theoretical, self-consistent and time- dependent models of the solar wind. We have completed the first goal by calculating the amount of non-radiative energy generated in the solar convection zone as acoustic waves and as magnetic tube waves. To calculate the amount of wave energy carried by acoustic waves, we have used the Lighthill-Stein theory for sound generation modified by Musielak, Rosner, Stein & Ulmschneider (1994). The acoustic wave energy fluxes for stars located in different regions of the Hertzsprung-Russell (H-R) diagram have also been computed. The wave energy fluxes carried by longitudinal and transverse waves along magnetic flux tubes have been calculated by using both analytical and numerical methods. Our analytical approach is based a theory developed by Musielak, Rosner & Ulmschnelder and Musielak, Rosner, Gall & Ulmschneider, which allows computing the wave energy fluxes for linear tube waves. A numerical approach has been developed by Huang, Musielak & Ulmschneider and Ulmschneider & Musielak to compute the energy fluxes for nonlinear tube waves. Both methods have been used to calculate the wave energy fluxes for stars located in different regions of the HR diagram (Musielak, Rosner & Ulmschneider 1998; Ulmschneider, Musielak & Fawzy 1998). Having obtained the wave energy fluxes for acoustic and magnetic tube waves, we have investigated the behavior of these waves in the solar and stellar atmospheres. The results of our extensive studies have been published in many papers and presented at numerous scientific meetings. In these studies we have investigated different aspects of propagation of acoustic and magnetic waves, the efficiency of energy transfer along magnetic structures in the solar atmosphere, and behavior of Alfven waves in stgeady and expanding solar and stellar atmospheres. Recently, we have used some of these results to construct first purely theoretical, two component and time-dependent models of solar and stellar chromospheres. Finally, to address the third goal, we have constructed first fully theoretical, self-consistent and time dependent wind models based on the momentum deposition by non-linear Alfven waves. The full set of single-fluid MHD equations with the background flow has been solved by using a modified version of the ZEUS MHD code. The constructed wind models are radially symmetric with the magnetic field decreasing radially and the initial outflow is described by the standard Parker wind solution. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; the models thus naturally account for the backreaction of the wind on the waves as well as for the nonlinear interaction between different types of MHD waves. The models have been used to explain the origin of fast speed streams in solar coronal holes. The obtained results clearly demonstrate that the momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast stream components of the solar wind. The range of wave amplitudes required to obtain the desired results seems to be in good agreement with recent observations.

Musielak, Z. E.↗
DOE OSTI2020

Optical follow-up of the neutron star–black hole mergers S200105ae and S200115j

LIGO and Virgo’s third observing run revealed the first neutron star–black hole (NSBH) merger candidates in gravitational waves. These events are predicted to synthesize r-process elements creating optical/near-infrared ‘kilonova’ emission. The joint gravitational wave and electromagnetic detection of an NSBH merger could be used to constrain the equation of state of dense nuclear matter, and independently measure the local expansion rate of the Universe. Here, we present the optical follow-up and analysis of two of the only three high-significance NSBH merger candidates detected to date, S200105ae and S200115j, with the Zwicky Transient Facility. The Zwicky Transient Facility observed ~48% of S200105ae and ~22% of S200115j’s localization probabilities, with observations sensitive to kilonovae brighter than –17.5 mag fading at 0.5 mag d –1 in the g- and r-bands; extensive searches and systematic follow-up of candidates did not yield a viable counterpart. We present state-of-the-art kilonova models tailored to NSBH systems that place constraints on the ejecta properties of these NSBH mergers. Here, we show that with observed depths of apparent magnitude ~22 mag, attainable in metre-class, wide-field-of-view survey instruments, strong constraints on ejecta mass are possible, with the potential to rule out low mass ratios, high black hole spins and large neutron star radii.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2020

Optical Follow-Up of the Neutron Star-Black Hole Mergers S200105ae and S200115j

LIGO and Virgo’s third observing run revealed the first neutron star–black hole (NSBH) merger candidates in gravitational waves. These events are predicted to synthesize r-process elements creating optical/near-infrared ‘kilonova’ emission. The joint gravitational wave and electromagnetic detection of an NSBH merger could be used to constrain the equation of state of dense nuclear matter, and independently measure the local expansion rate of the Universe. Here, we present the optical follow-up and analysis of two of the only three high-significance NSBH merger candidates detected to date, S200105ae and S200115j, with the Zwicky Transient Facility. The Zwicky Transient Facility observed ~48% of S200105ae and ~22% of S200115j’s localization probabilities, with observations sensitive to kilonovae brighter than −17.5 mag fading at 0.5 mag d−1 in the g- and r-bands; extensive searches and systematic follow-up of candidates did not yield a viable counterpart. We present state-of-the-art kilonova models tailored to NSBH systems that place constraints on the ejecta properties of these NSBH mergers. We show that with observed depths of apparent magnitude ~22 mag, attainable in metre-class, wide-field-of-view survey instruments, strong constraints on ejecta mass are possible, with the potential to rule out low mass ratios, high black hole spins and large neutron star radii.

Shreya Anand↗
NASA NTRS1992

Trends in column ozone based on TOMS data - Dependence on month, latitude, and longitude

On the basis of the TOMS satellite column ozone data in latitudes 70 deg S-70 deg N from November 1978 to May 1990, a statistical model is used to estimate the trends in ozone as a function of latitude, longitude, and month. The trends in the TOMS ozone data are highly seasonal and dependent on location. Near the equator, the estimated monthly trends are not significantly different from zero. For high latitudes, most of the estimated monthly trends are negative. In January, February, and March, there are some positive trend estimates in the western hemisphere around latitude 60 deg N. The most negative trends for these three months also appear in the high latitudes of the northern hemisphere. Starting in June, more negative trends appear in the latitudes 50 deg S-70 deg S than the trends in the rest of the world considered. A large depletion develops during the spring time (September to November) in the southern high-latitude region, and the area of peak ozone decline is moving eastward during the period. The largest negative trends (about -29 percent per decade) for the area considered in this study appear in October around the latitude 70 deg S and longitudes 20 deg W-100 deg W region. For the northern hemisphere, the year-round trend estimates for latitudes 30 deg N-70 deg N range from -0.96 percent to -7.43 percent per decade. In the latitudes 30 deg N-50 deg N, the winter trend estimates are more negative than those for the summer and the fall. However, this pattern did not hold for latitudes 50 deg N-70 deg N.

Niu, Xufeng↗
DOE OSTI2024

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗