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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗
DOE OSTI2024

A Second Moment Method for k -Eigenvalue Acceleration with Continuous Diffusion and Discontinuous Transport Discretizations

The second moment method is a linear acceleration technique that couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent of the transport discretization, unlike diffusion synthetic acceleration, and is symmetric positive definite, unlike quasidiffusion. While this method has been shown to be comparable to quasidiffusion in iterative performance for fixed source and time-dependent problems, it is largely unexplored as an eigenvalue problem acceleration scheme due to the belief that the resulting inhomogeneous source makes the problem ill posed. Recently, a preliminary feasibility study was performed on the second moment method for eigenvalue problems. The results suggested comparable performance to quasidiffusion and more robust performance than diffusion synthetic acceleration. This work extends the initial study to more realistic reactor problems using state-of-the-art discretization techniques. Finally, the results in this paper show that the second moment method is more computationally efficient than its alternatives on complex reactor problems with unstructured meshes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Spectrum of Dirac eigenvalues across QCD chiral transition

Here, we show that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are encoded in the microscopic energy levels of the quarks in the background of gluon fields, defined as eigenvalues of the Dirac operator. We introduce a novel relation between the cumulants of the chiral condensate, and the correlations among the energy levels of quarks, i.e., the eigenspectra of the massless QCD Dirac operator. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to a generalization of the Banks-Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations using HISQ action with varying light quark masses around the chiral phase transition temperature, we demonstrate that the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective D -dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class AI † . For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature β . We confirm that such an effective description of random matrices also applies in classes AI † and AII † up to next-to-nearest-neighbor spacings. Published by the American Physical Society 2025

Akemann, Gernot (ORCID:0000000217104258)↗
DOE OSTI2022

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Solving a class of infinite-dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

Here, we examine a method for solving an infinite-dimensional tensor eigenvalue problem Hx = λx, where the infinite-dimensional symmetric matrix H exhibits a translational invariant structure. We provide a formulation of this type of problem from a numerical linear algebra point of view and describe how a power method applied to e -Ht is used to obtain an approximation to the desired eigenvector. This infinite-dimensional eigenvector is represented in a compact way by a translational invariant infinite Tensor Ring (iTR). Low rank approximation is used to keep the cost of subsequent power iterations bounded while preserving the iTR structure of the approximate eigenvector. We show how the averaged Rayleigh quotient of an iTR eigenvector approximation can be efficiently computed and introduce a projected residual to monitor its convergence. In the numerical examples, we illustrate that the norm of this projected iTR residual can also be used to automatically modify the time step to ensure accurate and rapid convergence of the power method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A quantum eigenvalue solver based on tensor networks

Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.

chemistry↗
DOE OSTI2023

On the accuracy of the chemically significant eigenvalue method

We study the accuracy and convergence properties of the chemically significant eigenvalues method as proposed by Georgievskii et al. [J. Phys. Chem. A 117, 12146-12154 (2013)] and its close relative, dominant subspace truncation, for reduction of the energy-grained master equation. We formally derive the connection between both reduction techniques and provide hard error bounds for the accuracy of the latter which confirm the empirically excellent accuracy and convergence properties but also unveil practically relevant cases in which both methods are bound to fall short. We propose the use of balanced truncation as an effective alternative in these cases.

Chemistry↗
DOE OSTI2023

MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (E||), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfv\'en wave (KAW), ion sound wave (ISW), low-n kink, high-n ion temperature gradient mode (ITG) and kinetic ballooning mode (KBM). Moreover, MAS is successfully applied to model the Alfv\'en eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear Alfv\'en eigenmode (RSAE), the tunneling damping of toroidal Alfv\'en eigenmode (TAE), as well as the polarization characteristics of kinetic beta-induced Alfv\'en eigenmode (KBAE) and beta-induced Alfv\'en-acoustic eigenmode (BAAE) being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Controlled gate networks: theory and application to eigenvalue estimation

We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed with the fewest number of gates. We present the general theory of controlled gate networks and show that, under quite general conditions, it can significantly reduce the number of two-qubit gates needed to produce linear combinations of unitary operators. The first example we consider is a variational subspace calculation for a two-qubit system. The second example is estimating the eigenvalues of a two-qubit Hamiltonian via the rodeo algorithm (Choi et al. in Phys Rev Lett 127(4):040505, 2021. https://doi.org/10.1103/PhysRevLett.127.040505) using operators that we call controlled reversal gates. We use the Quantinuum H1-2 and IBM Perth devices to realize the quantum circuits. The third example is the application of controlled gate networks to the controlled time evolution of a free nucleon on a three-dimensional lattice. For all of the examples, we show very substantial reductions in the number of two-qubit gates required. Our work demonstrates that controlled gate networks are a useful tool for reducing gate complexity in quantum algorithms for quantum many-body problems such as those relevant to nuclear physics.

Bee-Lindgren, Max [Georgia Institute of Technology↗
DOE OSTI2024

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr↗
DOE OSTI2023

Beyond Generalized Eigenvalues

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials which we call block Prony method (BPM).

Fleming, George T.↗
DOE OSTI2026

The Eigenvector-Eigenvalue Identity and other pragmatic topics in linear algebra for physicists

Diagonalization of an Hermitian matrix is a common task in physics. All of us have diagonalized 2x2 matrices but few have diagonalized a 3x3 matrix algebraically except in special simplifying cases. In this colloquium, I will discuss the mathematics and methods for diagonalizing small, but larger than 2x2 marices, and discuss the recently rediscovered Eigenvector-Eigenvalue identity. As an explicit, pragmatic example I will use the propagation of neutrino's propagating through matter which is inherently a 3x3 problem.

Parke, Stephen [Fermilab] (ORCID:0000000320286782)↗
DOE OSTI2023

Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Beyond Generalized Eigenvalues in Lattice Quantum Field Theory

Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's (or related) method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials. As these algebraic methods are well known for producing extensive spectral information about statistically-noisy data, the method should be paired with some information criteria, like the recently proposed Bayesean model averaging.

Fleming, George T.↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Deterministic-Monte Carlo Hybrid Methods for Eigenvalue Sensitivity Coefficient Calculations

The TSUNAMI suite within the SCALE code package includes several methods for generating sensitivity data, including multigroup (MG) and continuous-energy (CE) capabilities. For generating sensitivities with CE data, three methods are available in SCALE 6.3.0: (1) the iterated fission probability (IFP) method with the KENO Monte Carlo transport solver, (2) IFP with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance Characterization (CLUTCH) with the KENO Monte Carlo transport solver. Currently, it is difficult to generate accurate sensitivities with large reflectors when using the CLUTCH method, specifically with fissionable and hydrogenous materials. To address this issue, the work presented herein examines a methodology to calculate the adjoint flux externally with the 3D deterministic SN transport code DENOVO in SCALE; the result is then read directly into the CLUTCH-TSUNAMI sequence. This hybridization method replaces the Monte Carlo F*(r) calculation in CLUTCH while still utilizing the forward calculation. The critical benchmark HEU-MET-FAST-028-001 is used to generate sensitivities based on the inability of CLUTCH to generate accurate sensitivities. Results from the hybrid method appear to generate sensitivity values that are in excellent agreement with direct perturbations. Although further testing is needed, the method provides promising results for the development and utility of a hybrid method for use in TSUNAMI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗