Search NASA⌕ Search

SEARCH · Search NASA

Results for “eigenvalue method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

As-Loaded Criticality Margin Assessment of Dual-Purpose Canisters Using UNF-ST&DARDS

A novel assessment has been completed in this paper to determine the previously unquantified and uncredited criticality margin available in as-loaded commercial spent nuclear fuel (SNF) canisters. This assessment was performed as part of a broader effort to assess issues and uncertainties with storage, subsequent transportation, and final disposal of SNF canister systems. Detailed analyses crediting the burnup, initial enrichment, and postirradiation cooling time of actual SNF inventory were performed for 554 SNF canisters stored at 23 commercial reactor sites to determine realistic criticality safety margins. These detailed analyses were automated by the Used Nuclear Fuel-Storage, Transportation & Disposal Analysis Resource and Data System (UNF-ST&DARDS), a comprehensive, integrated data and analysis tool. Calculated, uncredited criticality margins (Δk eff ) with respect to the safety analysis results range from 0 to almost 0.30 Δk eff for normal storage and transportation cases. Calculated eigenvalues (k eff ) range from 0.72 to 1.11 assuming a degraded neutron absorber disposal condition, and they range from 0.94 to 1.20 assuming a degraded basket disposal condition. Calculations with NaCl present in the moderator (which is possible for certain disposal geologies) were used to demonstrate the possibility for subcriticality for degraded cases with a k eff above 0.98 with freshwater. The methods used to calculate k eff for the canisters analyzed in this work are discussed in detail. The results demonstrate that, for the majority of canisters analyzed here, significant uncredited safety margin is available that could be used to compensate for uncertainties in the SNF assembly and canister internal components. These uncertainties are associated with long-term storage and subsequent transportation and disposal. Results also suggest that the inherent margins associated with how canisters are loaded could support future changes in licensing SNF storage and transportation systems to directly or indirectly credit the margins associated with actual SNF characteristics. Finally, ongoing research continues to gather additional data to quantify uncredited safety margins for SNF canisters loaded at other nuclear reactor sites and to explore potential methods for applying this uncredited margin.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Assessment of the MAMMOTH and PRONGHORN Pebble Bed Reactor Modeling Capabilities for the HTR-PM Design

This assessment explores the current analysis methodologies of various external and MOOSE-based tools available at the Idaho National Laboratory to model pebble bed reactor multiphysics phenomena. The study involves three MOOSE-based, coupled codes: 1) MAMMOTH for reactor physics, 2) Rattlesnake for neutron transport and 3) Pronghorn for thermal fluids and strongly coupled conjugate heat transfer. These advanced tools are being developed under DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program (NEAMS). They currently contain a collection of advanced modeling capabilities that allow high-fidelity simulations of advanced reactor concepts including gas and fluoride-salt cooled pebble bed reactors. Software development of these tools follows NQA-1 standards ensuring software quality that many of the currently deployed legacy codes lack. In this work, the MAMMOTH Pronghorn tools are compared to the legacy codes PEBBED-THERMIX-KONVEK. The external codes in use are LAMMPS for pebble mechanics and Serpent for cross section preparation. The coupling under MOOSE enables significant flexibility for modern engineering tools since MOOSE applications can be seamlessly coupled with various levels of resolution. This report focuses on low-resolution (r-z) and midresolution (3-D) homogenized geometries. The high-resolution Pebble Tracking Transport solution is not pursued herein and is postponed to future work. The results from this assessment show that the new MOOSE-based tools compare well with the results from legacy tools (r-z) and produce reasonable accuracy limited by the methods in the legacy tools. In the 3-D studies, the PJFNK-SPH methodology available in MAMMOTH allows the reproduction of Monte Carlo results with a transport-corrected diffusion solution. This has implications for the coupled solutions since without the SPH correction the temperature coefficient of reactivity is under-predicted and leads to lower temperature feedback and a significantly higher eigenvalue showing a difference of 2000 pcm.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗

The continuum and leading twist limits of parton distribution functions in lattice QCD

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Projection algorithm for state preparation on quantum computers

We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one additional auxiliary qubit. The total time evolved for an accurate solution is proportional to the ratio of the spectrum range of the trial state to the gap to the lowest excited state, a substantial improvement over other projection algorithms, and the accuracy increases exponentially with the time evolved. Isolating the quantum numbers is efficient because of the known eigenvalues and increases the gap thus shortening the propagation time required. The success rate of the algorithm, or the probability of producing the desired state, is a simple function of measurement times and phases and is dominated by the square overlap of the original state to the desired state. We present examples from the nuclear shell model and the Heisenberg model. In conclusion, we compare this algorithm to previous algorithms for short evolution times and discuss potential further improvements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analysis of core asymmetries in inertial confinement fusion implosions using three-dimensional hot-spot reconstruction

Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ = 1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. Furthermore, this work establishes a platform to analyze 3D low-mode core asymmetries in ICF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transition to metallization in warm dense helium-hydrogen mixtures using stochastic density functional theory within the Kubo-Greenwood formalism

The Kubo-Greenwood (KG) formula is often used in conjunction with Kohn-Sham (KS) density functional theory (DFT) to compute the optical conductivity, particularly for warm dense matter. For applying the KG formula, all KS eigenstates and eigenvalues up to an energy cutoff are required and thus the approach becomes expensive, especially for high temperatures and large systems, scaling cubically with both system size and temperature. Here, we develop an approach to calculate the KS conductivity within the stochastic DFT framework, which requires knowledge only of the KS Hamiltonian but not its eigenstates and values. We show that the computational effort associated with the method scales linearly with system size and reduces in proportion to the temperature, unlike the cubic increase with traditional deterministic approaches. In addition, we find that the method allows an accurate description of the entire spectrum, including the high-frequency range, unlike the deterministic method which is compelled to introduce a high-frequency cutoff due to memory and computational time constraints. Finally, we apply the method to helium-hydrogen mixtures in the warm dense matter regime at temperatures of ~60 kK and find that the system displays two conductivity phases, where a transition from nonmetal to metal occurs when hydrogen atoms constitute ~0.3 of the total atoms in the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew-Zunger and locally scaled self-interaction corrected methods

Here, we studied the effects of self-interaction error (SIE) on the static dipole polarizabilities of water clusters modelled with three increasingly sophisticated, non-empirical density functional approximations (DFAs), viz. the local spin density approximation (LDA), the Perdew-Burke-Ernzherof (PBE) generalized-gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA, using the Perdew-Zunger self-interaction-correction (PZ-SIC) energy functional in the Fermi-Lowdin orbital SIC (FLO-SIC) framework. Our results show that while all three DFAs overestimate the cluster polarizabilities, the description systematically improves from LDA to PBE to SCAN. The self-correlation free SCAN predicts polarizabilities quite accurately with a mean absolute error (MAE) of 0.58 Bohr 3 with respect to coupled cluster singles and doubles (CCSD) values. Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but over-corrects, resulting in underestimated polarizabilities in SIC-LDA, -PBE, and -SCAN. Finally, we applied a recently proposed local-scaling SIC (LSIC) method using a quasi self-consistent scheme and using the kinetic energy density ratio as an iso-orbital indicator. The results show that the LSIC polarizabilities are in excellent agreement with mean absolute error of 0.08 Bohr 3 for LSIC-LDA and 0.06 Bohr 3 for LSIC-PBE with most recent CCSD polarizabilities. Likewise, the ionization energy estimates as an absolute of highest occupied energy eigenvalue predicted by LSIC are also in excellent agreement with CCSD(T) ionization energies with MAE of 0.4 eV for LSIC-LDA and 0.04 eV for LSIC-PBE. The LSIC-LDA predictions of ionization energies are comparable to the reported GW ionization energies while the LSIC-PBE ionization energies are more accurate than reported GW results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The role of breakup and coalescence in fine-scale bubble-induced turbulence. II. Kinematics

This second part of our research explores the kinematic aspect of fine-scale bubble-induced turbulence (BIT) to (i) present the effect of bubble breakup and coalescence and (ii) compare it against the universal kinematic fine-scale turbulence characteristics reported in the literature. To this end, we simulate a dilute bubbly system of 0.5% void fraction using two distinct numerical simulations. In the volume-of-fluid (VoF) simulation, bubbles undergo breakup and coalescence. In the immersed boundary method (IBM) simulation, however, they act as rigid spheres. We also perform a simulation of classical homogeneous isotropic turbulence (HIT). The first important outcome of this study is that BIT is radically different from HIT in terms of its kinematic fine-scale characteristics. In the vorticity-dominating regions, BIT exhibits a weak vortex stretching. This weak vortex stretching is due to (a) the intermediate strain-rate eigenvalues skewed weakly to positive and (b) the extensive strain-rate eigenvector aligning perpendicular to the vorticity vector. The BIT has, on average, not only a weak enstrophy production but also a weak strain production in strain-dominating regions. The weak strain production is due to (a) the presence of vortex stretching in highly strained fluid elements and (b) the absolute magnitude of compressive strain-rate eigenvalue being as close to the extensive strain-rate eigenvalue. Thus, none of the kinematic fine-scale HIT characteristics is noted for BIT. The second important conclusion is that bubble breakup and coalescence play little to no influence on the kinematics of fine-scale BIT as VoF and IBM simulations produce similar results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗

An adjoint-based method for optimising MHD equilibria against the infinite- n , ideal ballooning mode

We demonstrate a fast adjoint-based method to optimise tokamak and stellarator equilibria against a pressure-driven instability known as the infinite-n ideal ballooning mode. We present three finite-β (the ratio of thermal to magnetic pressure) equilibria: one tokamak equilibrium and two stellarator equilibria that are unstable against the ballooning mode. Using the self-adjoint property of ideal magnetohydrodynamics, we construct a technique to rapidly calculate the change in the eigenvalue, a measure of ideal ballooning instability. Using the SIMSOPT optimisation framework, we then implement our fast adjoint gradient-based optimiser to minimise the eigenvalue and find stable equilibria for each of the three originally unstable equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Note on the Probability of Initiation Problem

The purpose of this note is to draw attention to Pál’s derivation of the Pál Bell equation which is used by LLNL and LANL to model Probability of Initiation (POI) problems. Both laboratories credit the equation to Bell and Lee. Although the equation formulated by Bell and Lee and the equation derived by Pál appear to be the same, the derivation by Bell and Lee is flawed. Scattering, which was absent in Bell’s original formulation of a POI problem, was later introduced by Bell and Lee by simply replacing a fission term with a scattering term. Such a replacement, however, leads to an inaccurate average number v̅ of neutrons that is produced by a fission event. By approaching a POI problem from probabilistic point of view, Pál formulates the problem as a branching process that determines v̅ correctly. There are six reasons for writing this report. The first is to clarify the failing in Bell and Lee’s derivation. The second is to establish the origin of the equation used by the laboratories. The third is to elucidate the fixed point technique formulated by Mokhtar-Kharroubi for solving the Pál-Bell equation. The fourth is to derive the α eigenvalue that is associated with a time dependent Pál-Bell equation. The fifth is to show in Appendix A that the non-linear fission operator of the Pál-Bell equation is descended from the operator of the Galton-Watson process of stochastic theory. The sixth is to describe in Appendix B a second order positivity preserving technique that accelerates the convergence of the first order fixed point method developed by Mokhtar-Kharroubi.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

Multi-Objective Optimization of Uranium Target Assembly–3: A Comparison of Genetic and Traditional Methods

Commonly produced as a byproduct of uranium fission, 99 Mo is a key medical isotope that is in high demand in the United States. An international goal is to switch from medical isotope production technologies that require highly enriched uranium to medical isotope production technologies that require only low-enriched uranium. Niowave Inc. is contributing to this goal by developing an accelerator-driven subcritical assembly called the Uranium Target Assembly (UTA). This work compares the performance of Dakota’s Multi-Objective Genetic Algorithm (MOGA) against traditional sensitivity analysis in the neutronic optimization of the UTA-3 system. The design objectives are k-eigenvalue (k eff ) and natural uranium fission power, which are directly correlated with the amount of 99 Mo produced. Dakota:MOGA did not perform as well as human engineering ingenuity in optimization studies with high numbers of input parameters, such as fuel rod type selection and fuel rod placement. However, Dakota:MOGA did outperform traditional sensitivity analysis in optimization studies with fewer than 20 parameters and revealed the degree to which each parameter influences the optimal design space for k eff and natural uranium fission power (to a lesser extent). As the design model became more complex in the final stage of design, the computational resources required to calculate the design objective values in the Monte Carlo N-Particle transport code from selected input parameter combinations limited Dakota:MOGA’s performance, and, unfortunately, human intervention was required to discern the optimal design space. In conclusion, future work will attempt to reduce computational resource constraints by incorporating areduced-order neutronics model into the optimization cycle.

Accelerator-driven systems↗

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

Delocalization↗

Constraints on the finite volume two-nucleon spectrum at 𝑚𝜋 ≈806 MeV

The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of 𝑚𝜋≈806 MeV is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, Phys. Rev. D 107, 094508 (2023).] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electronic structure with direct diagonalization on a D-wave quantum annealer

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

97 MATHEMATICS AND COMPUTING↗