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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 271 records · Page 15
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DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Accelerated Monte Carlo Fission Source Convergence with Fission Matrix and Kernel Density Estimators

Accurate solution of the k-eigenvalue form of the Boltzmann radiation transport equation is required in many application areas, including nuclear reactor analysis and criticality safety. Monte Carlo calculations are free of the discretization errors inherent to deterministic methods and therefore offer the most accurate solutions. However, converging the fission source can be difficult for many problems, resulting in either a substantial computational overhead or potential inaccuracies that negate many of the benefits of using Monte Carlo methods. Difficulty in converging the fission source occurs for two distinct reasons. The first is the existence of a high dominance ratio in the problem (i.e. the largest and second largest eigenvalues have approximately the same magnitude). The second difficulty arises due to undersampling of the fission source because an insufficient number of particle histories are simulated. The first difficulty is shared by deterministic solvers when using power iteration, while the second difficulty is unique to Monte Carlo solvers. In practice, both difficulties may be present in the same problem, compounding the difficulty in achieving a converged distribution. In this paper, we consider a new approach to accelerate the convergence of the fission source based on combining the use of fission matrix methods with kernel density estimators (KDEs). It has been observed that deterministic fission matrix methods show the potential to accelerate the convergence of the fission source in Monte Carlo criticality calculations but may introduce significant additional noise for difficult problems. In this paper, we have demonstrated the use of a KDE approach in combination with the fission matrix acceleration. Although the addition of the KDE initially slows the convergence of the fission matrix acceleration, it decreases the magnitude of the noise while still offering significantly improved convergence relative to analog Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

On Some Degenerate Elliptic Equations Arising in Geometric Problems

We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

MC21/CTF and VERA-CS Mutiphysics Solutions to VERA Core Physics Benchmark Problems 6 and 7

The continuous energy Monte Carlo neutron transport code, MC21, was coupled to the CTF subchannel thermal-hydraulics code using a combination of CASL tools and in-house Python scripts. An MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 6 demonstrated excellent agreement with MC21/COBRA-IE and VERA solutions. The MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 7, Watts Bar Unit 1 at beginning of cycle (BOC) hot full power (HFP) equilibrium xenon conditions, is the first published coupled Monte Carlo neutronics / subchannel T-H solution for this problem. MC21/CTF predicted a critical boron concentration of 854.5 ppm, yielding a critical eigenvalue of 0.99994 ± 6.8E-6 (95% CI). Excellent agreement with a VERA solution of Problem 7 was also demonstrated for integral and local power and temperature parameters.

Aviles, Brian↗
DOE OSTI2020

Assessment of the Griffin Reactor Multiphysics Application Using the Empire Micro Reactor Design Concept

In late 2019, INL and ANL agreed to jointly develop the reactor physics code named Griffin based on the integration of the two code suites, MAMMOTH/Rattlesnake (INL) and MC2 - 3/PROTEUS (ANL). Griffin is being developed based on the MOOSE framework and MOOSE quality assurance procedures. This decision was made to be able to allow DOE-NE to efficiently invest funding to this area and to provide effective and timely support for existing and potential users; the latter includes industry and government organizations who are developing various types of advanced reactors in the near and long term. Since MAMMOTH/Rattlesnake has been developed based on the MOOSE framework, the INL/ANL Griffin development team agreed to build Griffin beginning with a merger of MAMMOTH and Rattlesnake into a single code and moving forward by implementing capabilities from the PROTEUS suite into Griffin. Moving forward, both ANL and INL efforts are equally invested in the Griffin project, with management support, to provide an advanced reactor multiphysics tool to assist in reactor design, optimization, and safety analysis. Much work remains in moving Griffin forward to migrate PROTEUS capabilities and to optimize performance to meet user needs. The main objective of this work is to assess the current status of Griffin capabilities in terms of performance and accuracy, to determine priorities for PROTEUS migration, and to identify capabilities and features to improve for supporting the code integration effort. For this assessment, the Empire micro reactor problem that was developed in the ARPA-E MEITNER program was selected as an advance reactor concept of interest to the technical community. The Empire reactor problem was expanded from its original incomplete specification to be a small heat-pipe-cooled micro reactor core with ~113 cm radius and 70 cm in height, composed of 18 fuel assemblies, 12 control drums, and beryllium radial and axial reflectors. In the current model, using 5 cm axial reflectors specified in the original Empire assembly model, more than 10% of neutrons leak axially and through the empty center safety hole, as well as through heat pipe channels in fuel assembly elements that extend through the top reflector region. Several calculation models of the core were defined for systematic assessment, including 2-D and 3-D fuel assemblies and whole cores with cylindrical boundaries. Cross sections were generated using Serpent 2, and meshes were produced using the Argonne mesh tool or the INL neutronics meshing tools combined with CUBIT. Cross sections and meshes were converted to the ISOXML and Exodus formats, respectively, so that Griffin and PROTEUS could use consistent data for solving the reactor problems. With the prepared cross sections and meshes, PROTEUS was run first to ensure that all input data were correctly generated and input options in terms of angle, mesh, and energy group were accurately determined. Comparisons against Serpent 2 solutions were made in terms of eigenvalue and pin power. The same calculations and comparisons were then conducted using Griffin. For the fuel assembly and whole core problems, the PROTEUS eigenvalues agreed well with reference Serpent 2 solutions within 100 and 30 pcm, respectively, and pin power differences relative to Serpent 2 were overall less than 2.2% and RMS 0.8% for the whole core models. This indicated that all input data were properly prepared. Using the same data, Griffin was run selecting the SAAF-CFEM SN solver with Legendre-Gaussian quadrature and NDA and DSA for acceleration. It was found that the SAAF-CFEM solver of Griffin required finer meshes to achieve eigenvalue and pin power solutions in good agreement with Serpent 2, consequently requiring more memory requirement and longer computation time. On the other hand, the SPH-Diffusion 2-D core calculations performed using Griffin were able to recover the exact eigenvalue from the reference Serpent 2 solutions, resulting in a pin-power distribution with an RMS of 0.6% and maximum absolute difference of less than 1.4%. The runtimes for SPH-Diffusion for the 2-D core were less than 3 minutes on 40 cores. During this evolution of this evaluation, many updates were made in Griffin by the Griffin development team of INL (focusing on software updates) and ANL (reviewing and supporting software updates) to complete this assessment. Observations from the code assessment are presented in the conclusion section of this report, followed by a discussion of recommendations for future work.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Survey of Dynamic Mode Decomposition Methods

Dynamic mode decomposition (DMD) is a data-driven reduced order modeling (ROM) technique used for dynamic systems. The widely adopted algorithm was first introduced and demonstrated on fluid flow data by Schmid. In recent years, various other fields, such as nuclear engineering, have begun to adopt this method. For example, DMD has been used for estimating α-eigenvalues, as an ROM for pulsed neutron problems, for predicting isotopic composition in burnup calculations, as acceleration techniques for iterative methods, and in capturing dynamic behaviors in molten salt reactor transients. This report seeks to demonstrate the capabilities and limits of the standard DMD algorithm, and identify problem spaces where variants may be better suited. The primary variant this report considers is Multi-Resolution DMD (mrDMD). Because this serves as a survey, synthetically produced data is used in lieu of simulation results. The remainder of this report will go into detail on the DMD theory, outline the standard DMD and mrDMD algorithms, present test cases highlighting the applicability of each, and finally present a discussion on how to determine the best suited algorithm for a given problem. All calculations performed in this report are carried out using the open source DMD library, PyDMD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

REBUS-PC v1.5 Verification Test Summary

Motivated in part by its usage for analysis of the University of Missouri Research Reactor (MURR), the verification of the REBUS-PC software for θ-R-Z geometries is discussed and displayed in this manuscript. Of particular importance is to show that the eigenvalue, flux, power, and burnup outputs of the software given a user problem is correct. REBUS-PC contains many features and MURR only makes use of some of those aspects. As an example, the use of region specific cross section sets, interpolation of the cross section data with respect to burnup, and automatic movement of control rods during the fuel cycle is discussed and displayed. To demonstrate the accuracy, 22 verification tests based upon 7 physical geometries are discussed. Geometry descriptions are provided in Section 2 and the REBUS-PC results for each verification test are discussed in Section 3. These verification tests consist of both analytic problems with known solutions and a more complicated input consistent with usage of REBUS-PC on the MURR reactor itself called STRZ. In this verification test summary report, the REBUS-PC software is repeatedly demonstrated to reproduce, or closely match, the eigenvalue, flux, and power distributions from analytic test problem solutions, demonstrating that the implemented finite difference approximation in θ-R-Z is working as intended. Several additional REBUS-PC features are tested, such as control rod movement by detailed comparisons of the results against reference solutions obtained using an auxiliary implemented MatLab program. As expected, the REBUS-PC software produces results that are 100% consistent with the stated capabilities and thus the verification exercise is completed. These verification tests should be executed with each re-compilation of the REBUS-PC source and after any source code changes. All output results from any such new work should be rigorously compared against the stored output of the 22 verification tests cited in this report that forms the basis of the verification process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Extension of the DIF3D Code for Molten Salt Reactor Analysis

The molten salt reactor (MSR) with the fuel dissolved into the liquid salt has been selected as one of the six Generation-IV reactors due to its excellent characteristics in the aspects of sustainability, economy, passive safety, and resource utilization. In a MSR, the fuel salt is circulated throughout the whole system and thus some of delayed neutron precursors generated in the core decay in position of low importance or even out of the core. As a result, the multiplication factor (k-eff) of MSR is smaller than that of a reactor of stationary fuel when all the other conditions are same. Therefore, the neutronics code developed for stationary fuel cannot be applied directly to MSR analysis. In this paper, we describe the extension and application of the DIF3D code to MSR neutronics analysis. The DIF3D code system is a multi-group steady-state neutron diffusion and transport theory solver. It provides three flux solution options: finite-difference diffusion theory, nodal diffusion theory, and variational nodal transport theory methods. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. The DIF3D code has recently been modified to model the flowing fuel. To verify the new capability of DIF3D, the MSFR [4] core was analyzed with a wide range of velocity field of fuel salt and time spent outside of the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Exact QFT duals of AdS black holes

We construct large N saddle points of the matrix model for the $\mathcal{N}$ = 4 Yang- Mills index dual to the BPS black holes in AdS 5 × S 5 , in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large N saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Machine Learning Moment Closure Models for the Radiative Transfer Equation III: Enforcing Hyperbolicity and Physical Characteristic Speeds

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation. In our previous work (Huang et al. in J Comput Phys 453:110941, 2022), we proposed an approach to learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, while the ML moment closure has better accuracy, it is not able to guarantee hyperbolicity and has issues with long time stability. In our second paper (Huang et al., in: Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, 2021. arXiv:2105.14410), we identified a symmetrizer which leads to conditions that enforce that the gradient based ML closure is symmetrizable hyperbolic and stable over long time. The limitation of this approach is that in practice the highest moment can only be related to four, or fewer, lower moments. In this paper, we propose a new method to enforce the hyperbolicity of the ML closure model. Motivated by the observation that the coefficient matrix of the closure system is a lower Hessenberg matrix, we relate its eigenvalues to the roots of an associated polynomial. Here, we design two new neural network architectures based on this relation. The ML closure model resulting from the first neural network is weakly hyperbolic and guarantees the physical characteristic speeds, i.e., the eigenvalues are bounded by the speed of light. The second model is strictly hyperbolic and does not guarantee the boundedness of the eigenvalues. Several benchmark tests including the Gaussian source problem and the two-material problem show the good accuracy, stability and generalizability of our hyperbolic ML closure model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Recent Updates in ETOE-2 and MC 2 -3

The MC 2 -3 code is a multigroup cross section generation code for fast reactor applications, developed by Argonne National Laboratory (ANL) under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, first, the cross section libraries for ENDF/B-VII.1 and ENDF/B-VIII.0 data were generated using the updated ETOE-2 code. Preliminary verification and validation tests of the ENDF/B-VII.1 MC 2 -3 library were performed with the selected fast reactor benchmark problems. Processing and verifying the libraries suggested that significant efforts would be required for thoroughly verifying the ENDF/B-VII.1 MC 2 -3 library and successfully processing the ENDF/B-VIII.0 MC 2 -3 library. Secondly, the cross section generation capability of MC 2 -3 was updated with the intermediate group lattice calculation and the equivalent Dancoff-factor cell (EDC) method to significantly improve the performance of a twodimensional assembly calculation using the method of characteristics (MOC). This effort was made useful in implementing and verifying the EDC method in the Griffin cross section API. Finally, we analyzed a SFR problem, for which unusually large deviations in core eigenvalues from Monte Carlo solutions were reported, by generating multigroup cross sections with MC 2 -3, performing core calculations with DIF3D-VARIANT, and analyzing cross section and eigenvalue results against Monte Carlo solutions. The analysis confirmed that the MC 2 -3/DIF3D solutions were in good agreement with Monte Carlo solutions, providing the correct process of accurately generating broad-group cross sections with MC 2 -3

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Evaluation of Rapid for a UNF cask benchmark problem

To ensure criticality safety and maintain a high level of security of Used Nuclear Fuel (UNF), it is necessary to perform detailed Particle Transport simulations. The commonly used technique is the 3-D, continuous energy Monte Carlo method that is time-consuming and, for eigenvalue calculations, may have difficulties with the source convergence. Wenner and Haghighat and Dufek demonstrated that in criticality problems with high dominance ratio and/or under-sampling possibilities, the fission matrix (FM) methodology should be used in order to be able to obtain unbiased solution. The RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system is based on the Multi-stage Response-function Transport (MRT) methodology, and uses the FM formulation to determine eigenvalue, subcritical multiplication and fission density distribution of nuclear systems. This paper uses a benchmark problem similar to the GBC-32 Cask to evaluate the accuracy and performance of RAPID against the results of a reference MCNP solution. We performed a detailed sensitivity analysis on a single-assembly model in order to determine the MCNP eigenvalue parameters necessary to obtain a reliable reference solution. These results provided a guide for the selection of an appropriate set of parameters for the eigenvalue calculation for the whole cask. The paper is organized as follows: initially, the RAPID code system is briefly discussed; then, the benchmark problem is introduced. The methodology used to analyze results is proposed and some of the results of different cases are analyzed to identify the best set of eigenvalue parameters for a reference MCNP calculation. The selected case is then compared with the RAPID calculation for both a single assembly and a full cask model. In the end some conclusions and future work perspectives are drawn.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗
DOE OSTI2018

A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The parameterized preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

A parameterized preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalues and eigenvectors of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is efficient to accelerate the convergence rate of Krylov subspace methods, such as GMRES method.

97 MATHEMATICS AND COMPUTING↗