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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 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Non-perturbative Approach to Computing Seismic Normal Modes in Rotating Planets

In this work, a continuous Galerkin method based approach is presented to compute the seismic normal modes of rotating planets. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core using a polynomial filtering eigensolver. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method. Our discretization utilizes fully unstructured tetrahedral meshes for both solid and fluid regions. The relevant eigenvalue problem is solved by a combination of several highly parallel and computationally efficient methods. We validate our three-dimensional results in the non-rotating case using analytical results for constant elastic balls, as well as numerical results for an isotropic Earth model from standard “radial” algorithms. We also validate the computations in the rotating case, but only in the slowly-rotating regime where perturbation theory applies, because no other independent algorithms are available in the general case. The algorithm and code are used to compute the point spectra of eigenfrequencies in several Earth and Mars models studying the effects of heterogeneity on a large range of scales.

58 GEOSCIENCES↗
DOE OSTI2023

Non-Boolean quantum amplitude amplification and quantum mean estimation

This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-Boolean oracles. The action of a non-Boolean oracle $U_\varphi $ on an eigenstate $\mathinner {|{x}\rangle }$ is to apply a state-dependent phase-shift $\varphi (x)$. Unlike Boolean oracles, the eigenvalues $\exp (i\varphi (x))$ of a non-Boolean oracle are not restricted to be $\pm 1$. Two new oracular algorithms based on such non-Boolean oracles are introduced. The first is the non-Boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\varphi (x)$. Starting from a given initial superposition state $\mathinner {|{\psi _0}\rangle }$, the basis states with lower values of $\cos (\varphi )$ are amplified at the expense of the basis states with higher values of $\cos (\varphi )$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\mathinner {\langle {\psi _0|U_\varphi |\psi _0}\rangle }$, i.e., the expected value of $\exp (i\varphi (x))$ for a random x sampled by making a measurement on $\mathinner {|{\psi _0}\rangle }$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Enhancing scalability and accuracy of quantum poisson solver

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the problem and thus have no practical usage. In this regard, our previous work showed a proof-of-concept demonstration in advancing quantum Poisson solver algorithm and validated preliminary results for a simple case of 3 x 3 problem. In this work, we delve into comprehensive research details, presenting the results on up to 15 x 15 problems that include step-by-step improvements in Poisson equation solutions, scaling performance, and experimental exploration. In particular, we demonstrate the implementation of eigenvalue amplification by a factor of up to 2 8 , achieving a significant improvement in the accuracy of our quantum Poisson solver and comparing that to the exact solution. Additionally, we present success probability results, highlighting the reliability of our quantum Poisson solver. Moreover, we explore the scaling performance of our algorithm against the circuit depth and width, demonstrating how our approach scales with larger problem sizes and thus further solidifies the practicality of easy adaptation of this algorithm in real-world applications. We also discuss a multilevel strategy for how this algorithm might be further improved to explore much larger problems with greater performance. Finally, through our experiments on the IBM quantum hardware, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as U(1) gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. Here, we briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Effective construction of eigenvectors for a class of singular sparse matrices

Fundamental results and an efficient algorithm for constructing eigenvectors corresponding to non-zero eigenvalues of matrices with zero rows and/or columns are developed. The formulation is built on the relation between eigenvectors of such matrices and the eigenvectors of their submatrices after removing all zero rows and columns. While being easily utilized, the algorithm decreases the computation time needed for numerical eigenanalysis, and resolves potential numerical eigensolver instabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Multigroup Monte Carlo on GPUs: Comparison of history- and event-based algorithms

This article presents an investigation of the performance of different multigroup Monte Carlo transport algorithms on GPUs with a discussion of both history-based and event-based approaches. Several algorithmic improvements are introduced for both approaches. By modifying the history-based algorithm that is traditionally favored in CPU-based MC codes to occasionally filter out dead particles to reduce thread divergence, performance exceeds that of either the pure history-based or event-based approaches. The impacts of several algorithmic choices are discussed, including performance studies on Kepler and Pascal generation NVIDIA GPUs for fixed source and eigenvalue calculations. Single-device performance equivalent to 20–40 CPU cores on the K40 GPU and 60–80 CPU cores on the P100 GPU is achieved. Last, in addition, nearly perfect multi-device parallel weak scaling is demonstrated on more than 16,000 nodes of the Titan supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Sensitivity/uncertainty analyses comparing LR-0 reactor experiments containing FLiBe salt with models for molten-salt-cooled and molten-salt-fueled reactors

Here, critical experiments using an insertion zone with FLiBe salt performed at the LR-0 reactor at Research Centre Rež (RC Rež) have been compared to application models for solid-fueled, fluoride-salt-cooled high-temperature reactor (FHR) and liquid-fueled molten salt reactor (MSR) concepts using sensitivity and uncertainty (S/U) analysis techniques. These experiments support FHR and MSR advanced reactor concepts by informing on neutron spectral effects and nuclear data uncertainties related to fluoride salts. The FLiBe salt in the LR-0 experiments is from the Oak Ridge National Laboratory Molten Salt Reactor Experiment and is enriched to greater than 99.99% 7 Li. This work is part of a broader collaboration between the United States and the Czech Republic on MSR and FHR technology. Results from the S/U analyses for FHR and MSR models indicated the most significant potential source of eigenvalue bias due to nuclear data within the FLiBe salt is radiative capture in 7 Li. Other smaller but potentially significant contributions come from 19 F, 6 Li, and other 7 Li reactions. Similarity comparisons of the RC Rež LR-0 experiments and FHR and MSR application models indicate that the LR-0 FLiBe experiments could be useful as candidate benchmarks for low-enriched uranium–fueled application models. However, sensitivity differences observed included both spectral effects, due to the LR-0 reactor being moderated by water instead of graphite and fluoride salt, and sensitivity magnitude effects driven by the amount of FLiBe inserted and its location. New experiments with refined designs to increase the volume and importance of salt in the system could provide improved data. Results also demonstrate that salt systems using thorium and/or 233 U fuel will require additional experiments with relevant driver fuels. Increased contributions from the graphite moderator and 19 F and covariance between reactions such as 233 U fission and 233 U radiative capture indicate higher uncertainty contributions from the salt and significant differences in contributions from the fuel species due to underlying uncertainties in their nuclear data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion

This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require to scale the fission terms with the reference eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Consistent spatial expansion functions on hexagonal surfaces for use in radiation transport methods

Some of the radiation transport solvers that are based on expansion function methods in hexagonal geometry generally use projection techniques that transform the spatial dependence of the angular flux in hexagonal geometry to Cartesian geometry by mapping and then expanding in terms of expansion functions (e.g., Legendre polynomials). However, this approach usually requires a relatively higherorder expansion in space for accurate representation of the spatial distribution of the flux. To overcome this limitation, a set of consistent spatial expansion functions have been developed in hexagonal geometry in this paper. These functions satisfy the orthogonality condition on hexagonal surfaces and guarantee the conservation of currents after expansion regardless of the truncation order. The latter is an important property for preservation of neutron balance. The new spatial expansion method has been implemented into the coarse mesh radiation transport (COMET) code and tested in both the single assembly and the full core Advanced High Temperature Reactor (AHTR) benchmark problems. The eigenvalues and assembly-averaged and stripe-wise fission density distributions predicted by the new method with 2nd order spatial expansion functions were found to exhibit similar accuracy as those computed by the current mapping method with 4th order spatial expansion functions. This indicates that the angular fluxes in AHTRs can be predominantly represented by a low order expansion if the new spatial expansion functions are used. As a result, to maintain the same accuracy, the computational efficiency of COMET is improved significantly (2–5 times) by using the new spatial expansion method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

SCALE/AMPX multigroup libraries for sodium-cooled fast reactor systems

New multigroup cross section libraries and associated covariance files that are optimized for the analysis of sodium-cooled fast reactors were generated with the AMPX tools distributed with the SCALE code system. These new libraries account for the fast neutron flux spectrum with sufficient resolution of resonances in the higher energy range to reproduce continuous-energy reference results and to provide the basis for sensitivity and uncertainty analyses of fast spectrum systems with the SCALE code system. The performance of the new libraries was investigated in terms of the eigenvalue, the neutron flux and reaction rates in criticality calculations, and the generation of group constants. A library using 302 energy groups and a fast neutron flux spectrum as the weighting function led to very good agreement with reference continuous-energy results. As a result, the performance of the new library was demonstrated in calculations of experiments from the International Criticality Safety Benchmark Evaluation Project handbook.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Lattice Physics Calculations Using the Embedded Self-Shielding Method in Polaris, Part I: Methods and Implementation

Polaris is a 2-dimensional multigroup lattice physics capability in the SCALE code system for the analysis of light water reactor fuel designs. The goal of light water reactor lattice physics codes is to generate few-group homogenized cross sections for downstream full-core nodal diffusion calculations. Additionally, lattice physics calculations contain three primary components: the cross section processing calculation, the 2D transport calculation, and the depletion calculation. This paper summarizes the calculational methods and their implementation into Polaris, with an emphasis on implementation of the embedded self-shielding method. The accuracy of the embedded self-shielding method depends on the procedure used to generate self-shielding factors on the multigroup library. Numerical benchmarks calculations reveal that the accuracy of Polaris eigenvalue predictions is enhanced by (1) using heterogeneous unit cell models to generate the self-shielding factors on the library and (2) using self-shielding factors for within-group scattering cross section.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Extension of SCALE/Sampler’s sensitivity analysis

Nuclear data are a major source of uncertainties in reactor physics calculations. The propagation of nuclear data uncertainties to important system responses is instrumental when determining appropriate safety margins in reactor safety analyses. It is also important to understand the major contributors to the observed uncertainties to make recommendations for further measurements and evaluations and aid in the understanding of the studied system. The SCALE code system allows for nuclear data uncertainty analysis based on the random sampling approach as implemented in SCALE’s Sampler sequence. Sampler was recently extended by a sensitivity analysis in terms of the calculation of two correlation-based sensitivity indices. This analysis allows for the identification of the top contributing nuclear reactions to any analyzed output uncertainty. This paper presents the sensitivity indices, along with their interpretation and limitations. It demonstrates the application in an eigenvalue and decay heat analysis for a boiling water reactor fuel assembly.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A multiphysics model of the versatile test reactor based on the MOOSE framework

The traditional modeling approach for sodium fast reactor cores relies on separate physics models, where the fuel performance, thermal–hydraulics, and neutronics calculations required to predict the core physics characteristics for nominal conditions are decoupled by relying on user-imposed boundary conditions. Here, this paper aims at evaluating the impact of multiphysics simulations for predicting the core characteristics of the Versatile Test Reactor, which is being designed as a 300-MWt sodium-cooled fast reactor. The purpose of the Versatile Test Reactor is to accelerate the testing of advanced nuclear materials in the United States. The proposed multiphysics model relies on the Griffin reactor physics code, the SAM thermal–hydraulic system code, the BISON fuel performance code, as well as generic Multiphysics Object-Oriented Simulation Environment capabilities implemented in the open-source tensor mechanics module. For k eff calculations, the introduction of a tight coupling between the neutronics, thermo-mechanical and thermal–hydraulics models induces a change of around 543 pcm in the eigenvalue, compared to the traditional standalone neutronics calculation where approximate temperature profiles are used. The multiphysics model is then employed for quantifying the impact of the thermal conductivity uncertainties on some of the key figures of merit, such as the fuel centerline temperature, assembly powers, and keff for nominal core conditions. As anticipated, uncertainties on fuel thermal conductivity mostly impact the fuel centerline temperature, and to a lesser extend the k eff .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Layered CAD/CSG geometry for spatially complex radiation transport scenarios

Many spatially complex fission, fusion, and national security Monte Carlo (MC) radiation transport scenarios involve combining computer-aided design (CAD) models with constructive solid geometry (CSG) models. A layered geometry method has been implemented in the Shift MC code to address this need. With layered geometry, multiple CAD and/or CSG models can be clipped, translated, rotated, and placed in overlapping layers to form transport-ready geometries. Here, the utility of this method is demonstrated with two problems: (1) a fixed-source simulation with a layered geometry consisting of a LiDAR-generated CAD model of the Combined Arms Collective Training Facility urban environment overlaid with CSG models of a mock hotel and a detector apparatus, and (2) a k-eigenvalue calculation using a layered geometry model of the Transformational Challenge Reactor consisting of CAD fuel elements placed in a CSG core. Tallied particle flux distributions match expectations, but tracking robustness must be improved prior to general-purpose use.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Deployment of neural-network-based neutron microscopic cross sections in the Griffin reactor physics application

The capability to utilize neural networks to predict macroscopic and microscopic cross section parametric spaces has been developed for the Griffin reactor physics application. The LibTorch interface enables Griffin's MOOSE-based materials to interact with LibTorch-trained models, allowing for the evaluation of complex macroscopic or microscopic cross section spaces, which are then used to evaluate the neutronic properties of the Griffin finite element model. This study benchmarks traditional ISOXML-formatted tabulation libraries against neural network-based models for 279 nuclides on 20,160 grid points for zero-dimensional and two-dimensional reactor models. Benchmark metrics include the fundamental mode eigenvalue, fission and absorption rates, and various temperature coefficients of reactivity (isothermal, fuel, and moderator). From the perspective of storage space, the complete set of LibTorch models uses 11 MB on disk, compared to the 10 GB for the ISOXML multigroup library that covers the same grid space. For the two-dimensional performance case considered in Griffin, the Torch model uses 97% less RAM than the reference ISOXML dataset while runtime increases by a factor of 3 when using the LibTorch model compared to the ISOXML dataset with multi-linear interpolation. The LibTorch model consistently yields errors within 0.01% for most analyzed quantities except for the temperature coefficients of reactivity where the maximum discrepancies are up to 0.3 $\frac{pcm}{K}$. Due to the neural network attempting to best predict quantities with no regard for a positive or negative bias for any given quantity, predictions may experience random fluctuations, resulting in both positive and negative errors. Future work will entail both depletion and coupled transient analysis to determine the predictive capabilities of Griffin with neural network-based cross sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Generalized Uncertainty Principle and angular momentum

Various models of quantum gravity suggest a modification of the Heisenberg’s Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the theory of angular momentum in Quantum Mechanics. In particular, we compute Planck scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern–Gerlach experiment and the Clebsch–Gordan coefficients. We also examine effects of the Generalized Uncertainty Principle on multi-particle systems. - Highlights: • Corrections to the angular momentum spectra due to Generalized Uncertainty Principle. • GUP corrections to the hydrogen atom spectrum. • Experimental signatures of GUP, minimum length and Planck scale effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Distributed finite-time estimation of the bounds on algebraic connectivity for directed graphs

This paper studied distributed estimation of the bounds on algebraic connectivity for a directed graph (i.e., digraph). As is well known, the main challenge of the underlying problem is how to enable local awareness of an entity otherwise prone to global information, in the presence of communication topology. More specifically, we introduce a novel state-dependent approach to estimate the bounds on algebraic connectivity with mild requirement on topology and communication effort. Finally, compared with existing results, the proposed algorithm does not estimate eigenvalues or eigenvectors directly, rather it exploits their implications on the consensus procedure, and achieves a tradeoff between estimation accuracy and topological/communication requirement, and its convergence can be expected in a finite time. Simulation results verified the performance of the proposed strategy.

42 ENGINEERING↗