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Results for “eigenvalue problem”

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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Minimization of the Vibration Energy of Thin-Plate Structures and the Application to the Reduction of Gearbox Vibration

While the vibration analysis of gear systems has been developed, a systematic approach to the reduction of gearbox vibration has been lacking. The technique of reducing vibration by shifting natural frequencies is proposed here for gearboxes and other thin-plate structures using the theories of finite elements, modal analysis, and optimization. A triangular shell element with 18 degrees of freedom is developed for structural and dynamic analysis. To optimize, the overall vibration energy is adopted as the objective function to be minimized at the excitation frequency by varying the design variable (element thickness) under the constraint of overall constant weight. Modal analysis is used to determine the sensitivity of the vibration energy as a function of the eigenvalues and eigenvectors. The optimum design is found by the gradient projection method and a unidimensional search procedure. By applying the computer code to design problems for beams and plates, it was verified that the proposed method is effective in reducing vibration energy. The computer code is also applied to redesign the NASA Lewis gear noise rig test gearbox housing. As one example, only the shape of the top plate is varied, and the vibration energy levels of all the surfaces are reduced, yielding an overall reduction of 1/5 compared to the initial design. As a second example, the shapes of the top and two side plates are varied to yield an overall reduction in vibration energy of 1/30.

Inoue, Katsumi↗
NASA NTRS1996

Classical Trajectories and Quantum Spectra

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

Mielnik, Bogdan↗
DOE OSTI2022

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Symmetry and stability in Taylor-Couette flow

The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.

Golubitsky, M.↗
NASA NTRS1992

Viscous and inviscid instabilities of a trailing vortex

The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Mayer, Ernst W.↗
NASA NTRS1989

Wentzel-Kramers-Brillouin method in the Bargmann representation

It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

Voros, A.↗
NASA NTRS2005

Introduction to Quantum Simulation

This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.

quantum simulation↗
DOE OSTI2022

Fast Reactor Physics Model Verification Studies using ARC and PyARC Workflows

PyARC was recently developed at Argonne National Laboratory to automate many of the tasks required in the ARC (Argonne Reactor Computation) fast reactor simulation workflow, from input file generation, code execution, data transfer between ARC codes, and output postprocessing. PyARC will likely be the path forward to train new users of the ARC codes with the goal of wide adoption by the national laboratories, academia, and industry. In particular, for the ANL-JAEA collaboration under the Civil Nuclear Working Group (CNWG) project agreement NE-01, PyARC will be used to model the Joyo and EBR-II reactors for comparisons with measured data and calculated results from JAEA (Task 3: Fast Reactor Fuel and Core). As an additional avenue for verification and validation, this report investigates the use of PyARC towards a variety of existing ARC-based reactor models, in order to understand its efficacy in replicating the behavior of base ARC codes and better understand any limitations within modeling realistic fast reactor problems. To this end, PyARC was used to model the Joyo MKI, RBEC Benchmark-M, PRISM Mod-B, and EBR-II Run 138B cores, and its results were compared to those from existing ARC-based models. It was found that for hexagonal-based geometries PyARC was able to replicate the behavior of ARC codes to within 10 pcm for small reactor cores, and ~150pcm difference in eigenvalue for larger cores. These discrepancies are attributed primarily to differences in local mesh refinement options between ARC and PyARC, which currently cannot be resolved with PyARC’s latest version (1.6.0). In some of these cases, PyARC was used to model steady-state problems with initial core compositions originating from a prior REBUS depletion calculation. While PyARC was not designed to support such steady-state calculations, workarounds were applied to replicate the behavior of ARC-based calculations as closely as possible. Thus, these results demonstrate the wide extent to which they can be applied to fast reactor problems while still providing immense benefit to the user in terms of automating and standardizing common routines within the fast reactor analysis workflow. This study concluded that PyARC will be suitable for modeling the steady-state conditions of the EBR-II and Joyo fast reactors as part of the CNWG project agreement.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1978

Minimal order observers for linear functions of the state vector

The problem of estimating linear functions of a state vector in a multi-input/output system is considered. A simple lower bound on the observer order with arbitrary eigenvalues is established. Algorithms to construct minimal-order stable (or arbitrary dynamics) observers are also outlined.

Srinathkumar, S.↗
NASA NTRS1983

Direct and implicit optical matrix-vector algorithms

New direct and implicit algorithms for optical matrix-vector and systolic array processors are considered. Direct rather than indirect algorithms to solve linear systems and implicit rather than explicit solutions to solve second-order partial differential equations are discussed. In many cases, such approaches more properly utilize the advantageous features of optical systolic array processors. The matrix-decomposition operation (rather than solution of the simplified matrix-vector equation that results) is recognized as the computationally burdensome aspect of such problems that should be computed on an optical system. The Householder QR matrix-decomposition algorithm is considered as a specific example of a direct solution. Extensions to eigenvalue computation and formation of matrices of special structure are also noted.

Casasent, D.↗
NASA NTRS1992

On the placement of active members in adaptive truss structures for vibration control

The problem of optimal placement of active members which are used for vibration control in adaptive truss structures is investigated. The control scheme is based on the method of eigenvalue assignment as a means of shaping the transient response of the controlled adaptive structures, and the minimization of required control action is considered as the optimization criterion. To this end, a performance index which measures the control strokes of active members is formulated in an efficient way. In order to reduce the computation burden, particularly for the case where the locations of active members have to be selected from a large set of available sites, several heuristic searching schemes are proposed for obtaining the near-optimal locations. The proposed schemes significantly reduce the computational complexity of placing multiple active members to the order of that when a single active member is placed.

Lu, L.-Y.↗
NASA NTRS1993

A study of eigenvalue sensitivity for hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗
DOE OSTI2020

Uncoupling Electrokinetic Flow Solutions

The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.

58 GEOSCIENCES↗
DOE OSTI2025

Ensemble Simulation Techniques and Fast Randomized Algorithms

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

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1984

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The full state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system rmain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗
NASA NTRS1985

Design of multivariable feedback control systems via spectral assignment using reduced-order models and reduced-order observers

The feasibility of using reduced order models and reduced order observers with eigenvalue/eigenvector assignment procedures is investigated. A review of spectral assignment synthesis procedures is presented. Then, a reduced order model which retains essential system characteristics is formulated. A constant state feedback matrix which assigns desired closed loop eigenvalues and approximates specified closed loop eigenvectors is calculated for the reduced order model. It is shown that the eigenvalue and eigenvector assignments made in the reduced order system are retained when the feedback matrix is implemented about the full order system. In addition, those modes and associated eigenvectors which are not included in the reduced order model remain unchanged in the closed loop full order system. The fulll state feedback design is then implemented by using a reduced order observer. It is shown that the eigenvalue and eigenvector assignments of the closed loop full order system remain unchanged when a reduced order observer is used. The design procedure is illustrated by an actual design problem.

Mielke, R. R.↗
NASA NTRS1992

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Fischer, Bernd↗