Results for “kernel” — Page 2

NASA NTRS2008

Integrating the Gradient of the Thin Wire Kernel

A formulation for integrating the gradient of the thin wire kernel is presented. This approach employs a new expression for the gradient of the thin wire kernel derived from a recent technique for numerically evaluating the exact thin wire kernel. This approach should provide essentially arbitrary accuracy and may be used with higher-order elements and basis functions using the procedure described in [4].When the source and observation points are close, the potential integrals over wire segments involving the wire kernel are split into parts to handle the singular behavior of the integrand [1]. The singularity characteristics of the gradient of the wire kernel are different than those of the wire kernel, and the axial and radial components have different singularities. The characteristics of the gradient of the wire kernel are discussed in [2]. To evaluate the near electric and magnetic fields of a wire, the integration of the gradient of the wire kernel needs to be calculated over the source wire. Since the vector bases for current have constant direction on linear wire segments, these integrals reduce to integrals of the form

Champagne, Nathan J.↗

NASA NTRS2011

Spectral Kernel Approach to Study Radiative Response of Climate Variables and Interannual Variability of Reflected Solar Spectrum

The radiative kernel approach provides a simple way to separate the radiative response to different climate parameters and to decompose the feedback into radiative and climate response components. Using CERES/MODIS/Geostationary data, we calculated and analyzed the solar spectral reflectance kernels for various climate parameters on zonal, regional, and global spatial scales. The kernel linearity is tested. Errors in the kernel due to nonlinearity can vary strongly depending on climate parameter, wavelength, surface, and solar elevation; they are large in some absorption bands for some parameters but are negligible in most conditions. The spectral kernels are used to calculate the radiative responses to different climate parameter changes in different latitudes. The results show that the radiative response in high latitudes is sensitive to the coverage of snow and sea ice. The radiative response in low latitudes is contributed mainly by cloud property changes, especially cloud fraction and optical depth. The large cloud height effect is confined to absorption bands, while the cloud particle size effect is found mainly in the near infrared. The kernel approach, which is based on calculations using CERES retrievals, is then tested by direct comparison with spectral measurements from Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) (a different instrument on a different spacecraft). The monthly mean interannual variability of spectral reflectance based on the kernel technique is consistent with satellite observations over the ocean, but not over land, where both model and data have large uncertainty. RMS errors in kernel ]derived monthly global mean reflectance over the ocean compared to observations are about 0.001, and the sampling error is likely a major component.

Jin, Zhonghai↗

DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

DOE OSTI2021

Modeling Nanosecond-Pulsed Spark Discharge and Flame Kernel Evolution

Dilute combustion, either using exhaust gas recirculation or with excess air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, a comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond-pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. Here, the proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion Schlieren images.

42 ENGINEERING↗

NASA NTRS2021

Evaluation of CloudSat Radiative Kernels Using ARM and CERES Observations and ERA5 Reanalysis

Despite the widespread use of the radiative kernel technique for studying radiative feedbacks and radiative forcings, there has not been any systematic, observation-based validation of the radiative kernel method. Here, we utilize observed and reanalyzed radiative fluxes and atmospheric profiles from the Atmospheric Radiation Measurement (ARM) program and ERA5 reanalysis to assess a set of observation-based radiative kernels from CloudSat for six ARM sites. The CloudSat radiative kernels, convoluted with the ERA5 state variables, can almost perfectly reconstruct the monthly anomalies of shortwave (SW) and longwave (LW) radiative fluxes in ERA5 at the surface (SFC) and top-of atmosphere (TOA) with correlations significantly being greater than 0.95. The biases of kernel-estimated flux anomalies calculated using the ARM-observed state variables can be more than twice as large when compared with the ARM-observed surface flux anomalies and Clouds and Earth’s Radiant Energy System (CERES) observed anomalies at the TOA. Generally, clouds contribute to most (>60%) of the variance of flux anomalies at Southern Great Plain (SGP), Tropical Western Pacific (TWP), and Eastern North Atlantic (ENA), and surface albedo dominates (>69%) the variance of SW flux anomalies at North Slope of Alaska (NSA). The radiative kernels exhibit the lowest correlation (r~[0.55,0.85]) when reconstructing SFC LW flux anomalies at SGP, TWP, and ENA, whose biases are related to the possibility that the kernels may not fully capture the characteristics 47 associated with MJO and ENSO at TWP and the presence of clouds at SGP and ENA.

Radiative kernels↗

DOE OSTI2025

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel Jana Howard1,3, Guang Yang3, Haiyan Zhao1*, Patrick Warren4, Tiankai Yao3, Steven Cavazos4 Elizabeth Sooby Wood4*, Ching-heng Shiau2 1 University of Idaho, Environmental Science, Idaho Falls, Idaho, USA 2 Boise State University, Microscopy and Characterization Suite, Idaho Falls, Idaho, USA 3 Idaho National Laboratory, Idaho Falls, Idaho, USA 4 University of Texas San Antonio, Department of Physics and Astronomy, San Antonio, Texas, USA *Corresponding author: haiyanz@uidaho.edu; elizabeth.soobywood@utsa.edu Tri-structural Isotropic (TRISO) particle fuel is the preferred choice for the newest and next-generation high-temperature nuclear reactors due to its robust construction [1]. The fuel design effectively contains fission products inside the particle at extremely high temperatures [2]. However, the effect of transition metal fission products on fuel performance and structural integrity remains largely unknown, creating uncertainties in predicting fuel performance and potential failure mechanisms [2]. For example, palladium (Pd) has a strong tendency to form intermetallic phases with uranium (U). These new phases tend to be hard and brittle which could lead to fracture of fuel kernel during irradiation [3,4]. Pd is not normally produced in high concentrations in normal fission reactions however, driving the production of Pd into the locality of a Uranium Oxycarbide (UCO) nuclear fuel provides an opportunity to closely observe the diffusion and chemical interactions. This study focuses on detailed transmission electron microscopy characterization of the intermetallic phases formed by the interaction between a UCO kernel and a Pd bar after annealing at 1100 °C for 100 hours. Figure 1 provides an overview of the UCO kernel in contact with the Pd bar. The UCO-Pd sample surface was examined using a Focused Ion Beam (FIB) Quanta 3D FEG FEI in VCD detector mode at 10kV, 83pA to reveal surface features. Several key surface features in the interaction region were observed including: (1) a small area with dendritic microstructure, (2) color contrast near the UCO kernel and Pd boundary, and (3) darker and lighter regions throughout the sample surface. To analyze diffusion behavior, FIB was used to prepare lamellae from five different areas of the UCO-Pd sample, as well as one for the as-received sample. These lamellae were examined using a Scanning Transmission Electron Microscope ThermoFisher Spectra 300 (STEM-Spectra). Energy Dispersive Spectroscopy results confirmed the diffusion between the UCO fuel and Pd bar. Figure 2 shows the identified phases of UC, UO2, and Pd dispersed throughout the interaction region. It was also found that the Pd concentration decreases as the radial distance from the UCO-Pd interface increases. The Pd concentration was 36.93% atomic fraction 11µm from the interaction region then decreased to 7.51% atomic fraction at 257 µm away from the interaction region. Figure 3 shows how concentrations of U and Pd vary across the interaction zone, highlighting the extent of diffusion. This study confirms that Pd interacts with surrounding material to form U-Pd phase and diffusion zones. These diffusion zones vary in composition depending on its radial distance from the point of contact with the Pd bar. These findings contribute to a deeper understanding of the fission product behavior in high temperature nuclear fuels, aiding in the prediction and mitigation of potential fuel degradation mechanisms. A B C Fig. 1. SEM micrographs of UCO fuel kernel in contact with solid Pd bar and the lift out locations. Figure 1A shows UCO fuel kernel in contact with solid Pd bar. Figure 1B shows a higher magnification image of the UCO fuel-Pd interaction zone. Figure 1C shows lift out sites for the lamellae. A B C Fig 2. EDS maps reveal the distribution of U, O, and Pd in location 3. Figure 2A shows the distribution of uranium. Figure 2B shows the distribution of oxygen. Figure 2C shows the distribution of palladium. A B C Fig 3. Palladium and uranium concentration across interaction zone in location 2. Figure 3A shows EDS map of lift out number 2. Figure 3B shows a zoomed in EDS map taken from the interaction zone. Figure 3C shows a line graph of uranium and palladium concentrations across the interaction zone. References: 1. B.E. Wells, N.R. Phillips, K.J. Geelhood. Pacific West Laboratory. (2021). TRISO Fuel: Properties and Failure Modes. https://www.nrc.gov/docs/ML2117/ML21175A152.pdf (Accessed January 16, 2025). 2. American Nuclear Society. TRISO Fuel Development Progresses in INL, ORNL. https://www.gen-4.org/gif/upload/docs/application/pdf/2014-03/nov13nn_fuel_reprint.pdf (Accessed January 16, 2025) 3. Clark R.A., M.A. Con

36 - MATERIALS SCIENCE↗

DOE OSTI2025

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel

Chemical Interaction of Palladium in Uranium Oxycarbide Nuclear Fuel Kernel Jana Howard1,3, Guang Yang3, Haiyan Zhao1*, Patrick Warren4, Tiankai Yao3, Steven Cavazos4 Elizabeth Sooby Wood4*, Ching-heng Shiau2 1 University of Idaho, Environmental Science, Idaho Falls, Idaho, USA 2 Boise State University, Microscopy and Characterization Suite, Idaho Falls, Idaho, USA 3 Idaho National Laboratory, Idaho Falls, Idaho, USA 4 University of Texas San Antonio, Department of Physics and Astronomy, San Antonio, Texas, USA *Corresponding author: haiyanz@uidaho.edu; elizabeth.soobywood@utsa.edu Tri-structural Isotropic (TRISO) particle fuel is the preferred choice for the newest and next-generation high-temperature nuclear reactors due to its robust construction [1]. The fuel design effectively contains fission products inside the particle at extremely high temperatures [2]. However, the effect of transition metal fission products on fuel performance and structural integrity remains largely unknown, creating uncertainties in predicting fuel performance and potential failure mechanisms [2]. For example, palladium (Pd) has a strong tendency to form intermetallic phases with uranium (U). These new phases tend to be hard and brittle which could lead to fracture of fuel kernel during irradiation [3,4]. Pd is not normally produced in high concentrations in normal fission reactions however, driving the production of Pd into the locality of a Uranium Oxycarbide (UCO) nuclear fuel provides an opportunity to closely observe the diffusion and chemical interactions. This study focuses on detailed transmission electron microscopy characterization of the intermetallic phases formed by the interaction between a UCO kernel and a Pd bar after annealing at 1100 °C for 100 hours. Figure 1 provides an overview of the UCO kernel in contact with the Pd bar. The UCO-Pd sample surface was examined using a Focused Ion Beam (FIB) Quanta 3D FEG FEI in VCD detector mode at 10kV, 83pA to reveal surface features. Several key surface features in the interaction region were observed including: (1) a small area with dendritic microstructure, (2) color contrast near the UCO kernel and Pd boundary, and (3) darker and lighter regions throughout the sample surface. To analyze diffusion behavior, FIB was used to prepare lamellae from five different areas of the UCO-Pd sample, as well as one for the as-received sample. These lamellae were examined using a Scanning Transmission Electron Microscope ThermoFisher Spectra 300 (STEM-Spectra). Energy Dispersive Spectroscopy results confirmed the diffusion between the UCO fuel and Pd bar. Figure 2 shows the identified phases of UC, UO2, and Pd dispersed throughout the interaction region. It was also found that the Pd concentration decreases as the radial distance from the UCO-Pd interface increases. The Pd concentration was 36.93% atomic fraction 11µm from the interaction region then decreased to 7.51% atomic fraction at 257 µm away from the interaction region. Figure 3 shows how concentrations of U and Pd vary across the interaction zone, highlighting the extent of diffusion. This study confirms that Pd interacts with surrounding material to form U-Pd phase and diffusion zones. These diffusion zones vary in composition depending on its radial distance from the point of contact with the Pd bar. These findings contribute to a deeper understanding of the fission product behavior in high temperature nuclear fuels, aiding in the prediction and mitigation of potential fuel degradation mechanisms. A B C Fig. 1. SEM micrographs of UCO fuel kernel in contact with solid Pd bar and the lift out locations. Figure 1A shows UCO fuel kernel in contact with solid Pd bar. Figure 1B shows a higher magnification image of the UCO fuel-Pd interaction zone. Figure 1C shows lift out sites for the lamellae. A B C Fig 2. EDS maps reveal the distribution of U, O, and Pd in location 3. Figure 2A shows the distribution of uranium. Figure 2B shows the distribution of oxygen. Figure 2C shows the distribution of palladium. A B C Fig 3. Palladium and uranium concentration across interaction zone in location 2. Figure 3A shows EDS map of lift out number 2. Figure 3B shows a zoomed in EDS map taken from the interaction zone. Figure 3C shows a line graph of uranium and palladium concentrations across the interaction zone. References: 1. B.E. Wells, N.R. Phillips, K.J. Geelhood. Pacific West Laboratory. (2021). TRISO Fuel: Properties and Failure Modes. https://www.nrc.gov/docs/ML2117/ML21175A152.pdf (Accessed January 16, 2025). 2. American Nuclear Society. TRISO Fuel Development Progresses in INL, ORNL. https://www.gen-4.org/gif/upload/docs/application/pdf/2014-03/nov13nn_fuel_reprint.pdf (Accessed January 16, 2025) 3. Clark R.A., M.A. Con

36 - MATERIALS SCIENCE↗

DOE OSTI2021

Evaluation of CloudSat Radiative Kernels Using ARM and CERES Observations and ERA5 Reanalysis

Despite the widespread use of the radiative kernel technique for studying radiative feedbacks and radiative forcings, there has not been any systematic, observation-based validation of the radiative kernel method. Here, we utilize observed and reanalyzed radiative fluxes and atmospheric profiles from the Atmospheric Radiation Measurement (ARM) program and ERA5 reanalysis to assess a set of observation-based radiative kernels from CloudSat for six ARM sites. The CloudSat radiative kernels, convoluted with the ERA5 state variables, can almost perfectly reconstruct the monthly anomalies of shortwave (SW) and longwave (LW) radiative fluxes in ERA5 at the surface (SFC) and top-of-atmosphere (TOA) with correlations significantly being greater than 0.95. The biases of kernel-estimated flux anomalies calculated using the ARM-observed state variables can be more than twice as large when compared with the ARM-observed surface flux anomalies and Clouds and Earth’s Radiant Energy System (CERES) observed anomalies at the TOA. Generally, clouds contribute to most (>60%) of the variance of flux anomalies at Southern Great Plain (SGP), Tropical Western Pacific (TWP), and Eastern North Atlantic (ENA), and surface albedo dominates (>69%) the variance of SW flux anomalies at North Slope of Alaska (NSA). Furthermore, the radiative kernels exhibit the lowest correlation (r ~ [0.55,0.85]) when reconstructing SFC LW flux anomalies at SGP, TWP, and ENA, whose biases are related to the possibility that the kernels may not fully capture the characteristics associated with MJO and ENSO at TWP and the presence of clouds at SGP and ENA.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Importance of kernel bandwidth in quantum machine learning

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial given the central role hyperparameters play in determining the performance of classical machine learning methods. In this work we introduce the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the expressivity of the resulting model. We use extensive numerical experiments with multiple quantum kernels and classical data sets to show consistent change in the model behavior from underfitting (bandwidth too large) to overfitting (bandwidth too small), with optimal generalization in between. We draw a connection between the bandwidth of classical and quantum kernels and show analogous behavior in both cases. Furthermore, we show that optimizing the bandwidth can help mitigate the exponential decay of kernel values with qubit count, which is the cause behind recent observations that the performance of quantum kernel methods decreases with qubit count. Here, we reproduce these negative results and show that if the kernel bandwidth is optimized, the performance instead improves with growing qubit count and becomes competitive with the best classical methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Numerical evidence against advantage with quantum fidelity kernels on classical data

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential “flattening” of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.

Quantum Information, Science & Technology↗

DOE OSTI2022

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

Here we propose a spatially and temporally nonlocal exchange correlation (XC) kernel for the spin-unpolarized fluid phase of ground-state jellium for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact XC kernel to accurately describe the correlation energies of bulk jellium and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel are maintained in the revised MCP07 (rMCP07) kernel, while others are added. The revision $f^{rMCP07}_{XC}$ (q, ω) differs from MCP07 only for nonzero frequencies ω. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wave vector q tends to zero, the kernel has a -4$πα(ω)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $α(ω)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Non-Blind Deblurring for Fluorescence: A Deformable Latent Space Approach with Kernel Parameterization

We report N\non-blind deblurring (NBD) is a modeling method of the image deblurring problem in computer vision, where the blurring kernel is known or can be externally estimated. In this paper, we attempt to solve a parametric NBD problem, inspired by the simultaneous acquisition of ptychography and fluorescent imaging (FI). Ptychography is an imaging method that favors larger probes, i.e. convolutional kernels, while FI relies on a small probe for high resolution. Also, the kernel can be solved during ptychographic reconstruction. With Ptycho-FI using the same larger kernel, we can perform NBD on the blurred fluorescent images to achieve high-resolution FI, and thus speed up the experiments. To this end, we design a deep latent space deformation network that is directly parameterized by the kernel. The network consists of three components: encoder, deformer, and decoder, where the deformer is specifically meant to rectify the latent space representations of blurred images to a standard latent space, regardless of the kernel. The deformation network is trained with a two-stage training scheme. We conduct extensive experiments to confirm that our parametric model can adapt to drastically different blurring kernels and perform robust deblurring.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

We formulate the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that both the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we show that the adjoint wave propagator preserves the dispersion and compensates the amplitude, while the time-reversed adjoint wave propagator behaves identically as the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit Q parameterization, which avoids the implicit Q in the conventional viscoacoustic/viscoelastic full waveform inversion (Q-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. Here, we find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel.

58 GEOSCIENCES↗

DOE OSTI2024

Temperature Distribution Within an Ignition Kernel Initiated by a Laser-Induced Plasma

The sizes of, and temperature distributions within, ignition kernels initiated by a Q-switched neodymium-doped yttrium aluminum garnet laser-induced plasma in an unconfined lean premixed hydrogen-air upward jet flow are investigated. The experiments involved a range of jet velocities and a range of deposited laser energies at a fixed height above the exit along the axis of a burner. The growth of, and the temperature distributions within, the ignition kernels, as affected by the size and the energy distribution of the laser-induced plasma, are monitored with an infrared camera. The initial ignition kernels’ areas are larger with higher laser pulse energies and remain unchanged up to [Formula: see text] and then increase by factors of up to 3 at [Formula: see text]. The change in the kernel area caused by the jet velocities is less than 1.5%. An increase of the bulk velocity by 190% decreases the ignition kernel temperature by 6%. This reduction in the ignition kernel temperatures is because of an increase in energy losses by a factor of 2 and decreases in heat releases by 2% at [Formula: see text] and by 11% at [Formula: see text]. The present contributions are: measurements of and insights into temperature distributions and kernel development rates during the laser-induced plasma ignition process at different deposited energies and flow velocities.

Engineering↗

NASA NTRS1979

The site, size, spatial stability, and energetics of an X-ray flare kernel

The site, size evolution, and energetics of an X-ray kernel that dominated a solar flare during its rise and somewhat during its peak are investigated. The position of the kernel remained stationary to within about 3 arc sec over the 30-min interval of observations, despite pulsations in the kernel X-ray brightness in excess of a factor of 10. This suggests a tightly bound, deeply rooted magnetic structure, more plausibly associated with the near chromosphere or low corona rather than with the high corona. The H-alpha flare onset coincided with the appearance of the kernel, again suggesting a close spatial and temporal coupling between the chromospheric H-alpha event and the X-ray kernel. At the first kernel brightness peak its size was no larger than about 2 arc sec, when it accounted for about 40% of the total flare flux. In the second rise phase of the kernel, a source power input of order 2 times 10 to the 24th ergs/sec is minimally required.

Petrasso, R.↗

NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗

DOE OSTI2022

Atomistic and cluster dynamics modeling of fission gas (Xe) diffusivity in TRISO fuel kernels

TRISO fuel particles are candidates for use in next generation reactors including gas reactors, fluoride salt-cooled high temperature reactors, and micro-reactors. The UCO fuel kernel consists of a uranium dioxide (UO) and uranium carbide mixture. The addition of UC helps suppress the formation of carbon monoxide gas, which led to failures during initial TRISO development. The addition of uranium carbide alters the chemistry of the UO kernel, which is known to influence performance parameters such as fission gas diffusivity, although the impact has not been quantified and no models exist that take the change in chemistry into account. Therefore, better understanding and more accurate models of the impact of chemistry on fuel performance are of high priority. In this paper, a first-principles density functional theory (DFT) and empirical potential based multi-scale study has been carried out to model the diffusivity of fission gas xenon (Xe) in UCO TRISO fuel kernels. The focus is on the UO component in the UCO fuel kernels, as that represents the largest volume fraction of the fuel kernels. The study relies on DFT and empirical potential calculations to determine Xe and point defect properties, which are then used in thermodynamic and kinetic models to predict diffusion for intrinsic conditions. In addition, the information is utilized in cluster dynamics simulations using the Centipede code to estimate the impact of irradiation on defect transport. Additionally, the presence of UC or UC in the UCO fuel kernels is shown to have a substantial impact on the UO non-stoichiometry by inducing oxygen vacancies and driving UO sub-stoichiometric, which causes much slower Xe diffusion in UCO compared to light water reactor UO fuel. The application of this model in fuel performance simulations using the Bison code is also demonstrated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Progress towards understanding ultranonlocality through the wave-vector and frequency dependence of approximate exchange-correlation kernels

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel f xc (n, q, ω) determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel f xc (n, q, ω) of A. Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe f xc of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, lim q→0 f xc (n, q, ω) = -α(ω)e 2 /q 2 , of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wavevector and frequency dependence of the “ultranonlocality” coefficient α(ω) is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes α(ω). Comparisons to kernels derived from correlated-wavefunction calculations are drawn.

36 MATERIALS SCIENCE↗