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DOE OSTI2025

Improvement and Verification of Online Cross Section Generation Capability of Griffin for TRISO-fueled Reactors

Griffin, a MOOSE-based reactor multiphysics code jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE Office of Nuclear Energy’s NEAMS program, has pursued the development of an online multigroup cross section generation capability for a few years to enable high-fidelity, problem-dependent neutronics analyses of advanced thermal reactors. Recent advancements in Griffin’s online multigroup cross section generation capability have significantly improved the accuracy, robustness, and efficiency of self-shielding calculations for both prismatic and pebble-bed TRISO-fueled reactor applications. Key developments include a unified fuel self-shielding method applicable to both TRISO and annular compact/spherical shell fuel zone geometries; an advanced Dancoff Category-based Equivalence Theory using a bell function for non-fuel resonance treatment, achieving more than an order-of-magnitude speedup compared to the Tone method; an on-the-fly multigroup equivalence approach to mitigate group condensation errors; and a streaming correction method for pebble-bed homogenization. A proof-of-concept demonstration of on-the-fly group condensation with consistent P0 transport correction was also achieved. The method reproduced direct fine-group solutions with excellent accuracy (eigenvalue errors within 10 pcm and pin-power differences within 0.5%), but due to performance limitations of the current fixed-source solver, improvements to solver efficiency will be addressed in future work. Verification tests were performed on graphite-moderated TRISO-fueled two-dimensional core benchmark problems representing gas-cooled microreactors, heat pipe-cooled microreactors, gas-cooled pebble-bed reactors, and fluoride salt-cooled high-temperature reactors. Across all cases, Griffin showed excellent agreement with Serpent2 continuous energy Monte Carlo solutions: eigenvalue errors within 200 pcm, pin-power root-mean-square errors within 2%, and control rod and drum worth errors less than 2%. It should be noted that, for the benchmark problem, cross section generation contributed less than 3% of the total simulation times. These results demonstrate that Griffin’s online cross section generation capability delivers accurate and efficient reactor physics solutions across a wide spectrum of TRISO-fueled advanced reactor designs. With further improvements to the fine-group fixed-source solver and planned extensions to depletion, transients, and coupled neutron–gamma transport, Griffin will be well-positioned to become a powerful and comprehensive tool for advanced reactor analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Pulsed-Neutron Die-Away Response of H 2 O Targets to a D-T Generator Pulse

Pulsed-neutron die-away (PNDA) experiments were completed at Lawrence Livermore National Laboratory (LLNL). The goal of these experiments was to provide a benchmark to validate thermal neutron scattering laws of H 2 O. The experiment was conducted with a deuterium-tritium (D-T) neutron generator producing pulses of 14.1 MeV neutrons that impinged on a moderating target. The neutrons scattered and thermalized within the target and were counted as a function of time using Helium-3 ( 3 He) detectors that surrounded the target. These data provide a time-decay profile of the neutron population from which the time eigenvalue of the experiment is calculated. The time eigenvalue quantity α represents the integral parameter of interest. This report describes the measurements for H 2 O targets. The measurements were conducted over several days beginning on October 23rd, 2023. All measurements were completed at the low-scatter facility at LLNL. The evaluation identifier is FUND-LLNL-DT-H2O-PNDA-001.

3He Detectors↗

DOE OSTI2024

Bilocal Field Theory for Composite Scalar Bosons

We give a bilocal field theory description of a composite scalar with an extended binding potential that reduces to the Nambu–Jona-Lasinio (NJL) model in the pointlike limit. This provides a description of the internal dynamics of the bound state and features a static internal wave function, $\phi(\vec{r})$, in the center-of-mass frame that satisfies a Schrödinger–Klein–Gordon equation with eigenvalues m 2 . We analyze the “coloron” model (single perturbative massive gluon exchange) which yields a UV completion of the NJL model. This has a BCS-like enhancement of its interaction, ∝N c the number of colors, and is classically critical with g critical remarkably close to the NJL quantum critical coupling. Negative eigenvalues for m 2 lead to spontaneous symmetry breaking, and the Yukawa coupling of the bound state to constituent fermions is emergent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Pulsed-Neutron Experiments at the Inherently Safe Subcritical Assembly

The pulsed neutron technique is a powerful, dynamic method to assay the reactivity of a multiplying system. This work presents the novel application of the pulsed neutron technique to the Inherently Safe Subcritical Assembly, an experimental configuration accepted by the International Criticality Safety Benchmark Evaluation Project Handbook. The experiments were replicated with COG11.3, a continuous-energy Monte Carlo code. The pulsed neutron data were analyzed using the Sjöstrand and Gozani area-ratio methods and by extracting the prompt neutron decay constant. Subsequent static k-eigenvalue and 𝛼-eigenvalue simulations were also performed for the same configurations. Neutron detector dead-time effects from the experiments were corrected using the Backwards Extrapolation Method and shown to have a negligible impact on the estimated reactivities. The results highlight that capturing time-dependent effects like delayed neutron precursor buildup are essential to accurately reproduce experimental results. They also highlight the importance of shielding the detectors from generator source neutrons in deeply subcritical configurations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2019

TARDIS. I. A Constrained Reconstruction Approach to Modeling the z ~ 2.5 Cosmic Web Probed by Lyα Forest Tomography

Recent Lyα forest tomography measurements of the intergalactic medium (IGM) have revealed a wealth of cosmic structures at high redshift (z ~ 2.5). In this work, we present the Tomographic Absorption Reconstruction and Density Inference Scheme (TARDIS), a new chronocosmographic analysis tool for understanding the formation and evolution of these observed structures. Here, we use maximum likelihood techniques with a fast nonlinear gravitational model to reconstruct the initial density field of the observed regions. We find that TARDIS allows accurate reconstruction of smaller-scale structures than standard Wiener-filtering techniques. Applying this technique to mock Lyα forest data sets that simulate ongoing and future surveys such as CLAMATO, Subaru PFS, or the ELTs, we are able to infer the underlying matter density field at observed redshift and classify the cosmic web structures. We find good agreement with the underlying truth in both the characteristic eigenvalues and eigenvectors of the pseudo-deformation tensor, with the eigenvalues inferred from 30 m class telescopes correlated at r = 0.95 relative to the truth. As an output of this method, we are able to further evolve the inferred structures to late time (z = 0) and also track the trajectories of coeval z = 2.5 galaxies to their z = 0 cosmic web environments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

FOS: Physical sciences↗

NASA NTRS1966

Matrix methods and automation in structural engineering

The partial differential equations of motion of shell structures subject to arbitrary loads may be extremely difficult or even impossible to solve. Since the digital computer is now an available tool for the structural engineer, current research has been directed toward methods which involve matrix formulation of large systems of algebraic equations and matrix solutions for discrete elements rather than the solution of the partial differential equations. These methods require rapid and accurate computer solutions. Recognizing the accuracy problems inherent in working with large matrices, a comprehensive survey of available computer programs was performed for large matrix inversion and for eigenvalue and eigenvector solutions under a Research Grant from the National Aeronautics and Space Administration and the techniques are developed in this paper for using these programs most efficiently for structural applications. The contents of the paper include: automation of matrix compilation, methods of very large matrix inversion and solution of simultaneous equation, and techniques for finding eigenvalues and vectors. In addition, a finite element stiffness matrix approach developed at the Denver Research Institute for both plates and shells subject to arbitrary dynamic loads is described as it was instrumented with complete automation on the digital computer.

Anita S West↗

NASA NTRS1968

Internal low Reynolds number turbulent heat transfer

The results of a semi-analytical and experimental study of adiabatic tube flow and an analytical and experimental investigation of the thermal entrance region for gas flowing through electrically heated circular tubes are presented. Emphasis is placed on the low Reynolds number turbulent flow regime--defined as fully turbulent flow at bulk Reynolds numbers from 3,000 to about 15,000. Adiabatic air velocity and friction data and localized heat transfer measurements for air and helium, at low heating rates, are presented for this range. The adiabatic data were obtained in a 1.61 inch 1D tube for flow at bulk Reynolds numbers from 3,000 to 15,000. A continuous, Reynolds number-dependent, profile is developed from the data by using a modification of Reichardts' wall and middle law eddy diffusivity expressions. The velocity profile satisfies continuity. It is valid for all Reynolds numbers in excess of 3,000 for which the flow is fully turbulent and the Blasius friction factor expression is valid. The thermal entrance problem for a fully developed velocity profile is solved analytically by the method of Sparrow, Hallman, and Siegel. The solution is based on the profile developed from the velocity study. Tabular values of the eigenvalues and normalized Nusselt numbers for gases are presented for it range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by [Nu/Nu_(∞)] = 1 + 0.8 (1+ 70,000 Re^(-3/2)) ((x/D)^(-1)) to within ± 5 per cent for x/D ≥2. The fully developed value agrees with the Dittus - Boelter correlation, Nu_(∞) = 0.021 Re^(0.8) Pr^(0.4) For the eigenvalues, λ^(2)_(n), and the associated constants, A_(n), correlations of the form λ^(2)_(n) =A_(1,n) Re^(-b_(1,n) + C_(1,n) Re^(-d_(1,n)) A_(n) = -A_(2,n) Re^(-b_(2,n) + C_(2,n) Re^(-d_(2,n)) are obtained. The coefficients and powers are presented in tabular form. Heat transfer data are presented, primarily for helium, for the low Reynolds number turbulent range. A one-quarter inch, resistively heated, vertical, circular tube was used for the study. The data cover an axial range from 1.2 to 96 diameters; wall-to-bulk temperature ratios vary from 1 to 1.4. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution rather than the prediction obtained by applying the eddy diffusivity distribution used by Sparrow, Hallman, and Siegel.

Harold C. Reynolds, Jr.↗

NASA NTRS1971

A contracting-interval program for the Danilewski method

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Harris, J. D.↗

NASA NTRS1972

Synthesis of shuttle vehicle damping using substructure test results

An empirical method is developed for predicting the modal damping of a combined parallel-stage shuttle model by means of damping measurements performed on the individual substructures. Correlations are first determined for each component in terms of damping energy as a function of peak kinetic energy and modal amplitude. The results are then used to predict component damping energies corresponding to the respective kinetic energies and amplitudes that occur for the new modes of the combined system. Modal characteristics for the system, other than damping, are obtained by a real eigenvalue solution of dynamic equations developed by Hurty's procedure of substructures. System equations, which include component modal damping, are also solved by a complex eigenvalue approach for comparison with results of the empirical method.

Kana, D. D.↗

NASA NTRS1972

On the calculation of panel flutter boundaries.

Methods are described for the complete automation of flutter boundary calculations when the aerodynamic forces are derived from linear three-dimensional unsteady potential flow theory. The usual process of visual curve fairing in the mass ratio versus structural damping plane is replaced by numerical procedures for ordering the eigenvalues in such a way that the n-th eigenvalue is always associated with the same flutter boundary. The mass ratio versus structural damping curves are interpolated via parametric cubic spline functions to produce the desired plots in the stiffness-parameter/mass-ratio plane. The entire process is accomplished in a single computer run.

Gaspers, P. A., Jr.↗

NASA NTRS1972

An improved general algorithm for arbitrary pole assignment.

A new pole-placement algorithm for multi-input controllable systems is presented. The algorithm can be used to obtain real-valued feedback gains for arbitrarily specified real and complex, distinct or multiple eigenvalues. The multi-input controllable time-invariant system is converted to a single-input system. Pole assignment is achieved by making use of certain properties of the equation TF - AT = D, where A is the open-loop system matrix and F represents a matrix having the desired closed-loop eigenvalues.

Willner, L.↗

NASA NTRS1973

Multidimensional analysis of fast-spectrum material replacement measurements for systematic estimation of cross section uncertainties

A series of central core and core-reflector interface sample replacement experiments for 16 materials performed in the NASA heavy-metal-reflected, fast spectrum critical assembly (NCA) were analyzed in four and 13 groups using the GAM 2 cross-section set. The individual worths obtained by TDSN and DOT multidimensional transport theory calculations showed significant differences from the experimental results. These were attributed to cross-section uncertainties in the GAM 2 cross sections. Simultaneous analysis of the measured and calculated sample worths permitted separation of the worths into capture and scattering components which systematically provided fast spectrum averaged correction factors to the magnitudes of the GAM 2 absorption and scattering cross sections. Several Los Alamos clean critical assemblies containing Oy, Ta, and Mo as well as one of the NCA compositions were reanalyzed using the corrected cross sections. In all cases the eigenvalues were significantly improved and were recomputed to within 1 percent of the experimental eigenvalue. A comparable procedure may be used for ENDF cross sections when these are available.

Klann, P. G.↗

NASA NTRS1972

SYMAT, COVAR: Test Procedures for Matrix Calculations

The FORTRAN subroutine SYMAT and related subroutines are described. In essence SYMAT is an iterative algorithm in which the problem of finding eigenvalues and eigenvectors of a real symmetric matrix is transformed into an equivalent problem of finding eigenvalues and eigenvectors of an infinite sequence of matrices of order two. A DEMO PROGRAM contains a subroutine COVAR which is used to compute the covariance matrix (denoted by A) of a data matrix (denoted by X). Since a covariance matrix is symmetric it can be analyzed by using subroutine SYMAT.

Morris, W. L.↗

NASA NTRS1972

Diffraction of a plane pulse by a three-dimensional corner.

The conical solutions for the incidence of a plane pulse on a three-dimensional corner are presented. The corner is represented by a trihedron with one edge perpendicular to the other two. Both the boundary condition of the first kind and that of the second kind are considered. Outside the characteristic sphere of the vertex of the corner, the solution is represented by the well-known conical solutions in two variables. Inside the characteristic sphere, the problem involves three conical variables. By the separation of variables, the problem is reduced to that of an eigenvalue problem with an irregular boundary which is in turn reduced to a system of homogeneous algebraic equations. The eigenvalues are then determined numerically. By the superposition of the conical solutions for plane pulses, the solution for the incidence of a plane wave is obtained. Numerical examples simulating the incidence of a sonic boom on the corner of a structure are presented.

Ting, L.↗

NASA NTRS1973

Transient analysis using conical shell elements

The use of the NASTRAN conical shell element in static, eigenvalue, and direct transient analyses is demonstrated. The results of a NASTRAN static solution of an externally pressurized ring-stiffened cylinder agree well with a theoretical discontinuity analysis. Good agreement is also obtained between the NASTRAN direct transient response of a uniform cylinder to a dynamic end load and one-dimensional solutions obtained using a method of characteristics stress wave code and a standing wave solution. Finally, a NASTRAN eigenvalue analysis is performed on a hydroballistic model idealized with conical shell elements.

Yang, J. C. S.↗

NASA NTRS1973

Fast modal extraction in NASTRAN via the FEER computer program

A new eigensolution routine, FEER (Fast Eigensolution Extraction Routine), used in conjunction with NASTRAN at Israel Aircraft Industries is described. The FEER program is based on an automatic matrix reduction scheme whereby the lower modes of structures with many degrees of freedom can be accurately extracted from a tridiagonal eigenvalue problem whose size is of the same order of magnitude as the number of required modes. The process is effected without arbitrary lumping of masses at selected node points or selection of nodes to be retained in the analysis set. The results of computational efficiency studies are presented, showing major arithmetic operation counts and actual computer run times of FEER as compared to other methods of eigenvalue extraction, including those available in the NASTRAN READ module. It is concluded that the tridiagonal reduction method used in FEER would serve as a valuable addition to NASTRAN for highly increased efficiency in obtaining structural vibration modes.

Newman, M. B.↗