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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 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Probing the Crystal Structure and Formation Mechanism of Lanthanide-Doped Upconverting Nanocrystals

Lanthanide (Ln)-doped upconverting nanocrystals (UCNCs), such as NaLnF 4 (with Ln = lanthanide), constitute an important class of nanoscale materials due to their capacity to convert near-infrared photons into near-ultraviolet or visible light. Although under intense investigation for more than a decade, UCNCs have been relatively underexplored especially regarding their crystal structure and mechanisms of formation in organic media. The former is needed to explain the relationship between atomic scale structure and upconversion (UC) properties of UCNCs (i.e., local symmetry for 4f–4f transition probability, Ln 3+ distances for energy migration), while the latter is essential to finely tune the size, morphology, chemical composition, and architecture of well-defined upconverting nanostructures, which constitute the experimental levers to modify the optical properties. In this contribution, we use synchrotron-based diffraction experiments coupled to Rietveld and pair distribution function (PDF) analyses to understand the formation of NaGdF 4 :Yb:Er UCNCs in organic media and to investigate their crystal structure. Our results reveal a complex mechanism of the formation of NaGdF 4 :Yb:Er UCNCs based on chemical reactions involving molecular clusters and in situ-generated, crystalline sodium fluoride at high temperature. Additionally, a detailed crystallographic investigation of NaGdF 4 :Yb:Er UCNCs is presented. Our Rietveld and PDF analyses show that the space group P$\bar{6}$ is the one that best describes the crystal structure of NaGdF 4 :Yb:Er UCNCs contrary to what has been recently proposed. Further, our Rietveld and PDF data reveal the formation of bulk-like crystal structure down to 10 nm with limited distortions. Finally, the results presented in this paper constitute an important step toward the comprehensive understanding of the underlying picture that governs UC properties of lanthanide-doped nanostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Quantum work statistics, Loschmidt echo and information scrambling

A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

SPATIALLY RESOLVING THE HK Tau B EDGE-ON DISK FROM 1.2 TO 4.7 {mu}m: A UNIQUE SCATTERED LIGHT DISK

We present spatially resolved scattered light images of the circumstellar disk around HK Tau B at 3.8 and 4.7 {mu}m taken with the Keck Telescope Laser Guide Star Adaptive Optics (AO) system, and 1.6-2.12 {mu}m images taken with the Very Large Telescope/NACO AO system. Combined with previously published optical Hubble Space Telescope data, we investigate the spatially resolved scattered light properties of this edge-on circumstellar disk and probe for the presence of large grains. The 0.6-3.8 {mu}m scattered light observations reveal strong, and in some cases, unusual, wavelength dependencies in the observed disk morphology. The separation between the two scattered light nebulae, which is directly proportional to the disk-mass-opacity product, decreases by 30% between 0.6 and 3.8 {mu}m. Over the same wavelength range, the FWHM of the disk nebulosity declines by a factor of two, while the flux ratio between the two nebulae increases by a factor of {approx}8. No other disk known to date shows a flux ratio that increases with wavelength. Both the FWHM and nebula flux ratio are affected by the scattering phase function and the observed behavior can most readily be explained by a phase function that becomes more forward throwing with wavelength. The multi-wavelength scattered light observations also confirm the asymmetric nature of the disk and show that the level of asymmetry is a function of wavelength. We use the MCFOST radiative transfer code to model the disk at four wavelengths, corresponding to the I, H, Ks, and L' bandpasses. A single power-law grain size distribution can recreate the observed disk properties simultaneously at all four wavelengths. Bayesian analysis of the dust parameters finds a 99% probability that the maximum grain size is 5.5 {mu}m or larger. We also find that the grain size distribution is steep, with a 99% probability of a power-law index of 4.2 or larger, suggesting that these large grains are a small fraction of the overall dust population. The best-fit dust asymmetry parameter for each individual wavelength shows an unusual behavior, increasing with wavelength from the optical through the near-infrared, peaking at {approx}0.8 between 2.2 and 3.8 {mu}m, then decreasing by a factor of two by {approx}12 {mu}m. Comparing the wavelength dependence of the asymmetry parameter for HK Tau B with those for the interstellar medium (ISM) and dark cloud dust models, we find considerable evolution from an ISM state and argue for the presence of grain growth within the disk. Further, comparing the wavelength dependence of the asymmetry parameter for GG Tau, HV Tau C, and HK Tau B, the three disks that have been spatially resolved in scattered light between 0.8 and 3.8 {mu}m, finds a diverse range of dust properties, indicating differing degrees of grain growth for disks at a similar age.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

EVIDENCE FOR ENVIRONMENTAL DEPENDENCE OF THE UPPER STELLAR INITIAL MASS FUNCTION IN ORION A

We extend our previous study of the stellar population of L1641, the lower-density star-forming region of the Orion A cloud south of the dense Orion Nebula Cluster (ONC), with the goal of testing whether there is a statistically significant deficiency of high-mass stars in low-density regions. Previously, we compared the observed ratio of low-mass stars to high-mass stars with theoretical models of the stellar initial mass function (IMF) to infer a deficiency of the highest-mass stars in L1641. We expand our population study to identify the intermediate-mass (late B to G) L1641 members in an attempt to make a more direct comparison with the mass function of the nearby ONC. The spectral-type distribution and the K-band luminosity function of L1641 are similar to those of the ONC, but problems of incompleteness and contamination prevent us from making a detailed test for differences. We limit our analysis to statistical tests of the ratio of high-mass to low-mass stars, which indicate a probability of only 3% that the ONC and the southern region of L1641 were drawn from the same population, supporting the hypothesis that the upper-mass end of the IMF is dependent on environmental density.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

RECONSTRUCTING THE INITIAL DENSITY FIELD OF THE LOCAL UNIVERSE: METHODS AND TESTS WITH MOCK CATALOGS

Our research objective in this paper is to reconstruct an initial linear density field, which follows the multivariate Gaussian distribution with variances given by the linear power spectrum of the current cold dark matter model and evolves through gravitational instabilities to the present-day density field in the local universe. For this purpose, we develop a Hamiltonian Markov Chain Monte Carlo method to obtain the linear density field from a posterior probability function that consists of two components: a prior of a Gaussian density field with a given linear spectrum and a likelihood term that is given by the current density field. The present-day density field can be reconstructed from galaxy groups using the method developed in Wang et al. Using a realistic mock Sloan Digital Sky Survey DR7, obtained by populating dark matter halos in the Millennium simulation (MS) with galaxies, we show that our method can effectively and accurately recover both the amplitudes and phases of the initial, linear density field. To examine the accuracy of our method, we use N-body simulations to evolve these reconstructed initial conditions to the present day. The resimulated density field thus obtained accurately matches the original density field of the MS in the density range 0.3{approx}<{rho}/ {rho}-bar {approx}<20 without any significant bias. In particular, the Fourier phases of the resimulated density fields are tightly correlated with those of the original simulation down to a scale corresponding to a wavenumber of {approx}1 h Mpc{sup -1}, much smaller than the translinear scale, which corresponds to a wavenumber of {approx}0.15 h Mpc{sup -1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CORRELATIONS OF THE ARRIVAL DIRECTIONS OF ULTRA-HIGH ENERGY COSMIC RAYS WITH EXTRAGALACTIC OBJECTS AS OBSERVED BY THE TELESCOPE ARRAY EXPERIMENT

We search for correlations between the positions of extragalactic objects and the arrival directions of ultra-high energy cosmic rays (UHECRs) with primary energy E ≥ 40 EeV as observed by the surface detector array of the Telescope Array (TA) experiment during the first 40 months of operation. We examine several public astronomical object catalogs, including the Veron-Cetty and Veron catalog of active galactic nuclei. We count the number of TA events correlated with objects in each catalog as a function of three parameters: the maximum angular separation between a TA event and an object, the minimum energy of the events, and the maximum redshift of the objects. We determine the combination of these parameters that maximizes the correlations, and we calculate the probability of having the same levels of correlations from an isotropic distribution of UHECR arrival directions. No statistically significant correlations are found when penalties for scanning over the above parameters and for searching in several catalogs are taken into account.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Real-time fault detection and transient identification using extended Kalman filters - 254

In this paper, real-time fault detection and transient identification are studied with adaptive estimation methods, in particular parallel processing methods by implementing a bank of extended Kalman filters. Adaptive estimation is combined with probabilistic risk assessment to allow for real-time continuous monitoring of initiating events. The approach provides a probability of an initiating event happening. Real-time monitoring of initiating events can reduce labor demand. Each extended Kalman filter is configured to operate at a single configuration, either at normal operation or a faulted state. Fault detection is based on calculating a likelihood function for each extended Kalman filter to determine the posteriori conditional probability that the system configuration is the true configuration. The transient identification is determined by performing a multivariate statistical analysis on each extended Kalman filter to provide a posterior probability assessment that the reactor states and its dynamics are within the allowable limits. The probability distribution being outside the allowable limits indicate a transient has occurred. The combination of parallel processing methods with the multivariate statistical analysis for transient identification allows for the operator to perform transient identification with having a high level of certainty of the current system configuration. We demonstrate the real-time fault detection and transient identification on a simple reactor example to determine the reactor power, reactor temperature, and coolant temperature in the presence of various faults. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Communication-Constrained Robust Control and Learning of Grid-Connected

The electric grid of things (EGoT) promises great potential for innovative grid services by tapping into vast load flexibility. However, the unique characteristics of EGoT, being a part of the cyber-physical electric power system, present both opportunities and challenges, especially concerning supply-demand balancing, stability, and communication constraints. Traditionally, centralized control was employed to ensure balance and stability in power systems. However, with the massive influx of EGoT devices, new strategies are needed to efficiently coordinate and control these distributed devices for optimal grid operations. While some studies have explored efficiency and economic models, there remains a gap in ensuring reliability under everyday operations and resilience during extreme conditions. Addressing this gap, this project develops the technology for an Energy Service Interface (ESI) that includes novel pricing, control, learning, and distributed optimization algorithms, which will enable utilities to recruit EGoT assets for crucial grid services such as load flexibility, voltage regulation, and situation-awareness. The key novelty of the proposed technology is the careful distribution of learning and control functions across utility and EGoT asset owners such that provably efficient and resilient grid operations are attained while respecting communication and information-exchange constraints. Specifically, the project team develops machine-learning enhanced load modeling methods to allow EGoT asset owners to learn their load capability and flexibility, and develops pricing-based and decentralized learning-based control so that asset owners can coordinate to meet system-wide demand-supply balance and reliability goals. For extreme situations involving high-impact, low-probability catastrophic events (termed the “black-sky” events), the team also develops (1) a “Feeder-Operating Center-on-a-Laptop” (FOCAL) software that can assist utility personnel in leveraging EGoT assets to accelerate the service recovery of damaged feeders, and (2) distributed optimization algorithms that can coordinate the operation points of EGoT devices under severe communication constraints. The proposed technology has been extensively tested and evaluated through simulations and on a testbed. In summary, as we transition into a more interconnected and digital power grid era, our project’s findings and developments offer a pivotal step toward guaranteeing both efficiency and resilience in the face of both everyday operations and rare “black-sky” events.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Characterization of a cold-active bacterium isolated from the South Pole “Ice Tunnel”

Abstract Extremely cold microbial habitats on Earth (those below -30 °C) are rare and have not been surveyed for microbes as extensively as environments in the 0 to -20 °C range. Using cryoprotected growth media incubated at -5 °C, we enriched a cold-active Pseudomonas species from -50 °C ice collected from a utility tunnel for wastewater pipes under Amundsen–Scott South Pole Station, Antarctica. The isolate, strain UC-1, is related to other cold-active Pseudomonas species, most notably P. psychrophila, and grew at -5 °C to +34–37 °C; growth of UC-1 at +3 °C was significantly faster than at +34 °C. Strain UC-1 synthesized a surface exopolymer and high levels of unsaturated fatty acids under cold growth conditions. A 16S rRNA gene diversity screen of the ice sample that yielded strain UC-1 revealed over 1200 operational taxonomic units (OTUs) distributed across eight major classes of Bacteria. Many of the OTUs were Clostridia and Bacteriodia and some of these were probably of wastewater origin. However, a significant fraction of the OTUs were Proteobacteria and Actinobacteria of likely environmental origin. Our results shed light on the lower temperature limits to life and the possible existence of functional microbial communities in ultra-cold environments.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Regional variability in the environmental controls of precipitation regimes in the tropics

The environmental factors that control precipitation regimes in Boreal winter rainfall in the tropics and their regional variabilities are examined using a simple statistical analysis and a machine learning model. Radar-derived precipitation from field campaigns at Darwin Australia, Manaus Brazil, and the Equatorial Indian Ocean, along with the corresponding large-scale environmental variables from ERA5 reanalysis, are used. The dependence of marginal distributions of frequencies of these regimes on five environmental variables are calculated. The variables are hourly column integrated precipitable water (PW), convective available potential energy (CAPE), convective inhibition (CIN), and lower and upper tropospheric wind shear. The simple machine learning model that predicts the probability of transition from suppressed to an active regime as a function of the environmental variables is designed and optimized for a potential application as a trigger function for convection parameterizations. To the first order the analysis shows an abrupt increase in the probability of an active regime near PW > 60 mm and CIN of <100 J kg -1 . The key differences in the frequencies of active regimes among the regions are found to be related to the fact that over Darwin there is strong variability in PW while CIN is generally low. Over Amazon, on the other hand, both PW and CIN are quite variable. Over the DYNAMO domain the comparatively frequent low PW is compensated for by consistently low CIN resulting in a moderate frequency of an active regime.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

The RR Lyrae variable population in the Phoenix dwarf galaxy

We present the first detailed study of the RR Lyrae variable population in the Local Group dSph/dIrr transition galaxy, Phoenix, using previously obtained HST/WFPC2 observations of the galaxy. We utilize template light curve fitting routines to obtain best fit light curves for RR Lyrae variables in Phoenix. Our technique has identified 78 highly probable RR Lyrae stars (54 ab-type; 24 c-type) with about 40 additional candidates. We find mean periods for the two populations of (P {sub ab}) = 0.60 ± 0.03 days and (P{sub c} ) = 0.353 ± 0.002 days. We use the properties of these light curves to extract, among other things, a metallicity distribution function for ab-type RR Lyrae. Our analysis yields a mean metallicity of ([Fe/H]) = –1.68 ± 0.06 dex for the RRab stars. From the mean period and metallicity calculated from the ab-type RR Lyrae, we conclude that Phoenix is more likely of intermediate Oosterhoff type; however the morphology of the Bailey diagram for Phoenix RR Lyraes appears similar to that of an Oosterhoff type I system. Using the RRab stars, we also study the chemical enrichment law for Phoenix. We find that our metallicity distribution is reasonably well fitted by a closed-box model. The parameters of this model are compatible with the findings of Hidalgo et al., further supporting the idea that Phoenix appears to have been chemically enriched as a closed-box-like system during the early stage of its formation and evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multimodal fission from self-consistent calculations

When multiple fission modes coexist in a given nucleus, distinct fragment yield distributions appear. Multimodal fission has been observed in a number of fissioning nuclei spanning the nuclear chart, and this phenomenon is expected to affect the nuclear abundances synthesized during the rapid neutron-capture process (𝑟-process). In this study, we generalize the previously proposed hybrid model for fission-fragment yield distributions to predict competing fission modes and estimate the resulting yield distributions. Here, our framework allows for a comprehensive large-scale calculation of fission-fragment yields suited for 𝑟-process nuclear network studies. Nuclear density functional theory is employed to obtain the potential energy and collective inertia tensor on a multidimensional collective space defined by mass multipole moments. Fission pathways and their relative probabilities are determined using the nudged elastic band method. Based on this information, mass and charge fission yields are predicted using the recently developed hybrid model. Fission properties of fermium isotopes are calculated in the axial quadrupole-octupole collective space for three energy density functionals (EDFs). Disagreement between the EDFs appears when multiple fission modes are present. Within our framework, the UNEDF⁢1 HFB EDF agrees best with experimental data. Calculations in the axial quadrupole-octupole-hexadecapole collective space improve the agreement with the experiment for SkM*. We also discuss the sensitivity of fission predictions on the choice of EDF for several superheavy nuclei. Fission-fragment yield predictions for nuclei with multiple fission modes are sensitive to the underlying EDF. For large-scale calculations in which a minimal number of collective coordinates is considered, UNEDF⁢1 HFB provides the best description of experimental data, though the sensitivity motivates robust quantification of the uncertainties of the theoretical model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Technical Note: Improved implementation of doppler broadening in MCNP5

Purpose: Incoherent scattering has a substantial effect on spectroscopic measurements and simulations. Many general-purpose Monte Carlo codes include models that account for the effects of bound electrons on incoherent scattering, including Doppler broadening (DB). This work investigates the DB model used in the Monte Carlo N-particle transport code (MCNP5). Methods: Simulations were run with three versions of MCNP5: v1.51, v1.60, and a modified form of v1.60 (v1.60m). All simulations used the MCPLIB04 photon data library, which presents the electron subshell data for incoherent scattering in the form of a probability density function. In v1.60m, the source code was altered to sample the electron subshell from a cumulative density function instead. Each version of the code was tested using an identical set of simulations that investigated DB in a slab of silicon at scattering angles of 15 Degree-Sign , 30 Degree-Sign , and 45 Degree-Sign . For each angle, simulations were run for multiple energies between 200 keV and 800 keV. The spectrum of singly-scattered photons at the exit of the slab was scored. Spectra were analytically calculated for comparison. Results: In v1.51, DB was modeled for incident photon energies below 760 keV, 384 keV, and 260 keV at scattering angles of 15 Degree-Sign , 30 Degree-Sign , and 45 Degree-Sign , respectively. Above these energy thresholds, v1.51 did not model DB. The spectra calculated using v1.60 and v1.60m exhibited DB for all energy-angle combinations; however, v1.60m, exhibited more energy broadening than did v1.60. The spectra calculated with v1.60m agreed with the analytical calculations. Conclusions: MCNP5 v1.51 and v1.60 model partial broadening when used with the MCPLIB04 data library. MCNP5 v1.60m models DB more accurately due to the form of the electron subshell data. In response to these results, Los Alamos National Laboratory has released a new photon data library, MCPLIB84, that presents the electron subshell data in cumulative distribution form. MCNP5 v1.60 should be used with this library when incoherent scattering has a significant impact on simulation results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

The Electromagnetic Counterpart of the Binary Neutron Star Merger LIGO/Virgo GW170817. VII. Properties of the Host Galaxy and Constraints on the Merger Timescale

We present the properties of NGC 4993, the host galaxy of GW170817, the first gravitational-wave (GW) event from the merger of a binary neutron star (BNS) system and the first with an electromagnetic (EM) counterpart. We use both archival photometry and new optical/near-IR imaging and spectroscopy, together with stellar population synthesis models to infer the global properties of the host galaxy. We infer a star formation history peaked at ≳10 Gyr ago, with subsequent exponential decline leading to a low current star formation rate of 0.01 M{sub ⊙} yr{sup −1}, which we convert into a binary merger timescale probability distribution. We find a median merger timescale of 11.2{sub −1.4}{sup +0.7} Gyr, with a 90% confidence range of 6.8--13.6 Gyr. This in turn indicates an initial binary separation of ≈4.5 R{sub ⊙}, comparable to the inferred values for Galactic BNS systems. We also use new and archival Hubble Space Telescope images to measure a projected offset of the optical counterpart of 2.1 kpc (0.64r {sub e}) from the center of NGC 4993 and to place a limit of M{sub r}≳−7.2 mag on any pre-existing emission, which rules out the brighter half of the globular cluster luminosity function. Finally, the age and offset of the system indicates it experienced a modest natal kick with an upper limit of ∼200 km s{sup −1}. Future GW–EM observations of BNS mergers will enable measurement of their population delay time distribution, which will directly inform their viability as the dominant source of r-process enrichment in the universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗