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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Diagnostics for Undersampling and Clustering in Monte Carlo Criticality Calculations

For the past 40 years, it has been known from the theoretical work of Gelbard [1] and Brissenden [2] that the results from Monte Carlo (MC) criticality calculations are biased if the number of neutrons per generation is not sufficiently large. The computed k-effective eigenvalue will be lower than the actual eigenvalue, and the computed eigenfunction will be too low in high-importance regions and too high in low-importance regions. This difficulty is commonly called the undersampling problem for criticality calculations. The biases for undersampling were confirmed for practical, realistic problems with modern MC codes by Brown [3]. The solution to undersampling is simple - use a larger number of neutrons per generation to reduce the biases to levels that are negligible. Over the past few years, the OECD-NEA-WPNCS Expert Group on Advanced Monte Carlo Techniques (EGAMCT) [4,5,6] investigated an extreme form of undersampling called clustering. When the number of neutrons per generation is small, neutrons in successive generations tend to group together (cluster) due to correlations, and the clusters tend to migrate through the problem space. While the problems of undersampling and clustering are well known and well understood theoretically, there were no existing diagnostics for MC codes to determine whether a given calculation is using sufficient neutrons per generation to eliminate these problems. That is, no tools were available to diagnose biases due to undersampling or clustering. The tools described herein resolve this longstanding problem by providing 2 robust methods for detecting undersampling and clustering in MC criticality calculations. The diagnosis of undersampling and clustering is part of a larger effort to thoroughly overhaul the calculational methods for criticality problems, providing for automated sampling of the initial fission distribution, acceleration of the iteration convergence process, automated detection of convergence in the iterations and starting of the active tally cycles, and the diagnosis of undersampling. All of these new methods have been prototyped in a local modified version of mcnp6.2 [7] and tested on a variety of critical systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

The major goals of the project were to develop and analyze new ensemble simulation techniques, including trajectory stratification and preconditioned MCMC techniques, as well as develop fast numerical linear algebra techniques closely related to ensemble simulation ideas. The trajectory stratification techniques involve simulating in parallel short trajectory fragments of a Markov process confined to a specific region of space‐time and then patching together the statistics gathered to assemble estimates of very general dynamical properties. We have also developed this approach for rare event simulation and extended the techniques to applications requiring a more general framework (such as electronic structure calculations). The preconditioned MCMC techniques involve simulating multiple Markov chains in parallel and then using information from the ensemble to speed the mixing of each individual chain. The fast randomized linear algebra methods are motivated by the diffusion Monte Carlo technique, but are applicable to finding the dominant eigenvalue of (almost) general matrices. For most non‐negative matrices, the schemes result in an error (compared to the power method) that is constant in the dimension of the problem. For more general matrices, we see a very clear sublinear cost trend in computational tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

An inexact regularized Newton framework with a worst-case iteration complexity of $ {\mathscr O}(\varepsilon^{-3/2}) $ for nonconvex optimization

Abstract An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes ${\mathscr O}(\varepsilon ^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive real number $\varepsilon $ and can take ${\mathscr O}(\varepsilon ^{-3})$ iterations to drive the leftmost eigenvalue of the Hessian of the objective above $-\varepsilon $. The proposed algorithm is a general framework that covers a wide range of techniques including quadratically and cubically regularized Newton methods, such as the Adaptive Regularization using Cubics (arc) method and the recently proposed Trust-Region Algorithm with Contractions and Expansions (trace). The generality of our method is achieved through the introduction of generic conditions that each trial step is required to satisfy, which in particular allows for inexact regularized Newton steps to be used. These conditions center around a new subproblem that can be approximately solved to obtain trial steps that satisfy the conditions. A new instance of the framework, distinct from arc and trace, is described that may be viewed as a hybrid between quadratically and cubically regularized Newton methods. Numerical results demonstrate that our hybrid algorithm outperforms a cubically regularized Newton method.

Mathematics↗
DOE OSTI2024

Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics

We revisit the theory of first-order quasilinear systems with diagonalizable principal part and only real eigenvalues, what is commonly referred to as strongly hyperbolic systems. We provide a self-contained and simple proof of local well-posedness, in the Hadamard sense, of the Cauchy problem. Our regularity assumptions are very minimal. As an application, we apply our results to systems of ideal and viscous relativistic fluids, where the theory of strongly hyperbolic equations has been systematically used to study several systems of physical interest.

Mathematics↗
DOE OSTI2019

Quantum computation of nanosheets in a background magnetic field for external control of nanosystems

We ran quantum simulations on lattices of interacting fermions in a background magnetic field [1]. We created discretized Hamiltonian matrices for each system and pre-processed them so that they could be read by the quantum simulator implemented in IBM's Qiskit package [2]. The simulator uses the variational quantum eigensolver (VQE) algorithm [3] to approximate the ground state energy of the input Hamiltonian, which is then compared to the classically-calculated exact value. This classical evaluation is possible because the systems studied are still within the grasp of classical computers. We also investigated ways to simplify the system before the pre-processing step. We found that in almost all cases these simplifications made our quantum calculations converge to better answers using simpler starting conditions. We are exploring other ways to interface with IBM's quantum computing software so that we no longer need to explicitly define the Hamiltonian matrices for our systems, a problem which will itself soon become intractable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Sodium-Cooled Fast Reactor Reference Plant Model

This report details the progress of Idaho National Laboratory (INL) in creating a reference plant multiphysics model for the Advanced Burner Test Reactor (ABTR). This model was developed under Task 13 of the U.S. Nuclear Regulatory Commission project “Development and Modeling Support for Advanced Non-Light Water Reactors,” and is an extension of the reference plant model developed in Task 4b, which was improved upon in the following ways. (1) The discrete ordinates method was used in lieu of the super-homogenization (SPH)-corrected diffusion approximation in order to better capture the anisotropic scattering contribution and the neutron leakage change due to thermal expansion. (2) The novel neutronic spatial discretization approach, termed the ring-heterogeneous (RH) approximation, was conceptualized and introduced to capture the differential expansion of the materials in the core. This new technique proved capable of preserving fission rates and maintaining the eigenvalue within 2.5% and 266 pcm with 9 neutron energy groups, respectively. Separating the different materials in the core enables the differential expansion of materials to be explicitly accounted for, eliminating the need for problem-specific cross-section functionalization techniques. (3) The SAM model for the core and system thermal-hydraulics analysis was updated to include 61 channels instead of just four representative ones. This enables users to obtain improved spatial resolution for sodium temperature and density scalar fields. (4) All the mesh files were created via the Multiphysics Object-Oriented Simulation Environment (MOOSE) Reactor module, eliminating all reliance on external tools for mesh creation. (5) Finally, the fuel axial expansion now leverages the HT9 and UPuZr material properties that have been validated against experimental data. The reference plant model was used to perform a full-core unprotected loss of flow (ULOF) transient calculation, including neutronics, thermal and mechanical feedback mechanisms. Future work will be devoted to further enhancements of the model. Potential improvements to the model include the addition of the control rod driveline expansion feedback and the upgrading of the support plate model so as to explicitly include 3D effects. Additionally, a Nuclear Energy Advanced Modeling and Simulation funded parallel effort has completely automated the creation of the ring-heterogeneous (RH) mesh from the fully heterogeneous (FH) geometry, thus maximizing user friendliness for the sodium fast reactor sodium-cooled fast reactor (SFR) workflow and will be incorporated in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗
DOE OSTI2021

Extended Applications of Subgrid Representation in the 2D/1D Method

Recent efforts in MPACT have focused on improving the performance of the 2D/1D subplane implementation to help target computational performance goals. Here, we build on previous efforts that targeted the use of subgrid treatments to improve the accuracy of control rod representation, presenting three additional applications of subgrid treatments with the goal of reducing the computational burden of simulations. These subgrid applications include treatment of spacer grids, thermal feedback, and axial reflector material representation. With these approaches, a single method of characteristics (MOC) plane can contain several different materials axially that are represented explicitly via subgrids on the coarse mesh finite difference (CMFD) mesh but are axially homogenized on the MOC mesh. This allows for a substantial reduction in the number of MOC planes needed in the calculation through the introduction of an approximate treatment, particularly with regard to the self-shielded cross sections and MOC-informed radial current coupling coefficients in CMFD. Several test problems ranging from single rod to quarter core are used to assess the solution accuracy and performance of these various subgrid representations. Overall, the accuracy of the approximations seems very reasonable, with extremely small differences in eigenvalue observed and maximum pin power errors in the 0.5% to 1.0% range. Several cases show substantial value in the compromise between accuracy and computational performance. Others highlight the new computational hurdles that future research will aim to resolve.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗
DOE OSTI2022

Rotational symmetry relation for efficient response function generation in the coarse mesh transport method COMET

The coarse mesh transport code COMET is a continuous energy hybrid stochastic-deterministic neutronics solver with high fidelity and formidable computation speed in solving reactor core problems. Its method is based on the incident flux expansion theory. In this work, we take advantage of the local geometric symmetry in many reactor cores lattices (e.g., fuel lattices and reflector blocks) to develop relations among the flux response expansion coefficients for symmetric surfaces to further improve the computational efficiency of the COMET response function generation tool (method). This is done by a rigorous derivation of the transformation matrices for the angular and spatial expansion moments resulting from a rotation of a coarse mesh by an arbitrary angle. The relations for the response coefficients for the symmetric surfaces can be then written as the Kronecker product of those transformation matrices. The method is implemented into COMET and tested on two advanced high temperature reactor (AHTR) full-length single assembly benchmark problems. The COMET results using the response function library based on the symmetry relations were compared to those using the library directly generated by continuous energy Monte Carlo for all surfaces. It was found that the eigenvalues and stripe-wise fission densities using the two libraries are in statistical agreement as expected. This indicates that the new method maintains the high fidelity of the original COMET method while improving the computational efficiency in the response function generation by 270% to 400%, depending on the local geometric symmetry. This method also reduces the size of the response function library by the same magnitude (270% to 400%). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

Development of a Library for Conducting Monte Carlo Tallies on Heterogeneous Systems

A library is introduced that enables users to conduct Monte Carlo tallies on heterogeneous computing systems. The library can be built with or linked to a Monte Carlo transport code to provide tally capabilities for the project. The library provides a set of tools and an interface for constructing tallies that can be computed on CPUs or GPUs regardless of where the sample data was generated. The library can be incorporated into existing Monte Carlo transport codes at both the research and production level with minimal intrusion into the transport code. The tally library is capable of computing a variety of tallies including track-length histogram (mesh) tallies, collisionbased kernel density estimators, functional expansion tallies, eigenvalue sensitivity coefficients via iterated fission probability, and sensitivities of reaction rates or adjoint-weighted quantities via differential operator sampling. The parallelization methods are discussed and speedups are shown for 2-D and 3-D problems with comparisons to both the tally library CPU implementations as well as the tally capabilities in the host transport code. Performance results and examples are shown for MCNP, MCATK, and OpenMC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
DOE OSTI2022

PyAlbany: A Python interface to the C++ multiphysics solver Albany

Albany is a parallel C++ finite element library for solving forward and inverse problems involving partial differential equations (PDEs). In this paper we introduce PyAlbany, a newly developed Python interface to the Albany library. PyAlbany can be used to effectively drive Albany enabling fast and easy analysis and post-processing of applications based on PDEs that are pre-implemented in Albany. PyAlbany relies on the library PyBind11 to bind Python with C++ Albany code. Here we detail the implementation of PyAlbany and showcase its capabilities through a number of examples targeting a heat-diffusion problem. In particular we consider the following: (1) the generation of samples for a Monte Carlo application, (2) a scalability study, (3) a study of parameters on the performance of a linear solver, and finally (4) a tool for performing eigenvalue decompositions of matrix-free operators for a Bayesian inference application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems

In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

MPACT Subgroup Self-Shielding Efficiency Improvements

Recent developments to improve the efficiency of the MOC solvers in MPACT have yielded effective kernels that loop over several energy groups at once, rather that looping over one group at a time. These kernels have produced roughly a 2x speedup on the MOC sweeping time during eigenvalue calculation. However, the self-shielding subgroup calculation had not been reevaluated to take advantage of these new kernels, which typically requires substantial solve time. The improvements covered in this report start by integrating the multigroup kernel concepts into the subgroup calculation, which are then used as the basis for further extensions. The next improvement that is covered is what is currently being termed as “Lumped Parameter MOC”. Because the subgroup calculation is a purely fixed source problem and multiple sweeps are performed only to update the boundary angular fluxes, the sweep procedure can be condensed to allow for the instantaneous propagation of the flux across a spatial domain, without the need to sweep along all segments in a ray. Once the boundary angular fluxes are considered to be converged, an additional sweep that will tally the scalar flux is completed. The last improvement that is investigated is the possible reduction of the number of azimuthal angles per octant in the shielding sweep. Typically 16 azimuthal angles per octant are used for self-shielding and eigenvalue calculations, but it is possible that the self-shielding sweeps are less sensitive to the number of angles than the full eigenvalue calculation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗