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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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

On the spectrum of some singular equations in magnetohydrodynamics

A class of singular differential equations that often occurs in problems in magnetohydrodynamics, plasma physics, and astrophysics is studied; first by means of the specific and fairly straightforward example of motions in a stratified magnetofluid, and secondly in terms of the nature of the eigenvalue spectrum for the more general class of problems. It is shown that in the absence of discontinuities in the basic profiles, the eigenvalue spectrum is real and continuous, and no discrete spectrum exists. Bounds are obtained on the location of the continuous spectrum.

Adam, J. A.↗
NASA NTRS1976

Gaussian ideal impulsive loading of rigid viscoplastic plates

The response of a thin, rigid, viscoplastic plate subjected to a spatially axisymmetric Gaussian ideal impulse loading was studied analytically. The Gaussian ideal impulse distribution instantaneously imparts a Gaussian initial velocity distribution to the plate, except at the fixed boundary. The plate deforms with monotonically increasing deflections until the initial dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid, viscoplastic materials. For the small deflection bending response of the plate, neglecting the transverse shear stress in the yield condition and rotary inertia in the equations of dynamic equilibrium, the governing system of equations is essentially nonlinear. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and obtain analytical solution in the form of eigenvalue expansions. The linearized governing equations required the knowledge of the collapse load of the corresponding static problem.

Hayduk, R. J.↗
NASA NTRS1972

A fast numerical method for determining the optimum SNR of an array subject to a Q factor constraint.

The problem of finding the optimum current excitations for a point-detector array which extracts a signal from background noise using the criterion of maximizing the SNR subject to a constraint on the supergain ratio (or Q factor) has recently been solved. The formulation reduced the problem to one of solving for the roots of a polynomial whose coefficients are, in general, complex. We demonstrate that by making a certain transformation, it becomes possible to employ a state variable technique which changes the problem into one of finding the eigenvalues of a real matrix which is considerably faster to do.

Winkler, L. P.↗
NASA NTRS1976

Determination of poles and zeros of transfer functions for flexible spacecraft attitude control

The transfer function matrix is obtained for a three-input and three-output model of minimum sensors and actuators for the attitude control system of flexible spacecraft, and a method is described for determining the poles and zeros of this transfer function. Three cases are considered: (1) the actuators and the sensors are all attached to the primary body, (2) the actuators are on the primary body and the sensors are on the sub-body, and (3) the actuators are on the sub-body and the sensors are on the primary body. The zero-determination problem is shown to reduce to eigenvalue calculations of a matrix which is constructed from the inertial and modal matrices in a simple fashion.

Ohkami, Y.↗
NASA NTRS1992

Negative-energy states in the Dirac-Hartree-Fock problem - The effect of omission of two-electron integrals involving the small component

The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.

Dyall, Kenneth G.↗
NASA NTRS1988

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.

Bergen, Fred D.↗
NASA NTRS1989

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other.

Kapania, Rakesh K.↗
NASA NTRS1990

Spurious frequencies as a result of numerical boundary treatments

The stability theory for finite difference Initial Boundary-Value approximations to systems of hyperbolic partial differential equations states that the exclusion of eigenvalues and generalized eigenvalues is a sufficient condition for stability. The theory, however, does not discuss the nature of numerical approximations in the presence of such eigenvalues. In fact, as was shown previously, for the problem of vortex shedding by a 2-D cylinder in subsonic flow, stating boundary conditions in terms of the primitive (non-characteristic) variables may lead to such eigenvalues, causing perturbations that decay slowly in space and remain periodic time. Characteristic formulation of the boundary conditions avoided this problem. A more systematic study of the behavior of the (linearized) one-dimensional gas dynamic equations under various sets of oscillation-inducing legal boundary conditions is reported.

Abarbanel, Saul↗
NASA NTRS1991

Sequential design of linear quadratic state regulators with prescribed eigenvalues and specified relative stability

This paper considers the problem of optimal regulator design of linear multivariable systems with prescribed pole locations and/or poles corresponding to specified relative stability. A sequential method based on the frequency-domain optimality condition is proposed for achieving the desired pole assignment and determination of the corresponding quadratic performance index. This design method enables the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Ganesan, Sekar↗
DOE OSTI2018

On Some Degenerate Elliptic Equations Arising in Geometric Problems

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

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method

Implementation of the tridiagonal reduction method for real eigenvalue extraction in structural vibration and buckling problems is described. The basic concepts underlying the method are summarized and special features, such as the computation of error bounds and default modes of operation are discussed. In addition, the new user information and error messages and optional diagnostic output relating to the tridiagonal reduction method are presented. Some numerical results and initial experiences relating to usage in the NASTRAN environment are provided, including comparisons with other existing NASTRAN eigenvalue methods.

Newman, M.↗
DOE OSTI2020

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

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

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1988

On the eigenvalue and eigenvector derivatives of a non-defective matrix

A novel approach is introduced to address the problem of existence of differentiable eigenvectors for a nondefective matrix which may have repeated eigenvalues. The existence of eigenvector derivatives for a unique set of continuous eigenvectors corresponding to a repeated eigenvalue is rigorously established for nondefective and analytic matrices. A numerically implementable method is then developed to compute the differentiable eigenvectors associated with repeated eigenvalues. The solutions of eigenvalue and eigenvector derivatives for repeated eigenvalues are then derived. An example is given to illustrate the validity of formulations developed in this paper.

Juang, Jer-Nan↗
DOE OSTI2020

Survey of Dynamic Mode Decomposition Methods

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

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

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

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

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO↗