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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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗
DOE OSTI2018

Layer potential approach for fast eigenvalue characterization of the Helmholtz equation with mixed boundary conditions

Our goal is to propose an efficient approach to characterize the eigenvalues and eigenfunctions of the Helmholtz equation with mixed (Dirichlet and Neumann) boundary conditions. Our approach is based on layer potentials. We extend the eigenvalue characterization known for Neumann boundary conditions to the case of mixed boundary conditions. The problem is motivated by the need of such methods for real-time wave-field shaping by electronically tunable surfaces.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Nonlinear Marangoni convection in bounded layers. I - Circular cylindrical containers. II - Rectangular cylindrical containers

Liquid undergoing nonlinear Marangoni instability in a circular cylinder is examined, with attention given to roll-cell development and interaction. Surface deflections are neglected and the side walls are considered as adiabatic and impenetrable, allowing the liquid to freely slip. The nonlinear convective states are calculated and their stability is defined. The behavior and amplitude of cells forming in the liquid, heated from below, are modeled in order to derive all the transport properties. A new small parameter is formulated which is related to the critical Marangoni number of the infinite matrix expressing the eigenvalue expansion of the problem. The observed roll cell amplitudes and transport properties are shown to be available from simple eigenvalues, with double eigenvalues, indicating the existence of two roll-states as predicted by linear theory, nonlinear theory indicates transitions from one steady convective state to another.

Rosenblat, S.↗
NASA NTRS2003

Quantum Adiabatic Optimization and Combinatorial Landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.

Smelyanskiy, V. N.↗
NASA NTRS1988

Stability of semi-discrete approximations for hyperbolic initial-boundary-value problems. II - Asymptotic estimates

The stability of semi-discrete approximations for hyperbolic initial-boundary-value problems is considered. Asymptotic estimates of the eigenvalues of the finite-domain problem are given. These estimates are used to examine questions relating the normal mode analysis of the finite-domain problem and the normal mode quarter-plane analysis of the Gustafsson, Kreiss, and Sundstroem theory.

Warming, Robert F.↗
NASA NTRS1974

Application of antiresonance theory to helicopters

Antiresonance theory is the principle underlying nonresonant nodes in a structure, and covers both nonresonant nodes occurring naturally and those introduced by devices such as dynamic absorbers and antiresonant isolators. The dynamic antiresonant vibration isolator (DAVI) and the nodale module are examples of the applications of transfer antiresonances. It is shown that antiresonances are eigenvalues, and that they can be determined by matrix iteration. Applications of antiresonance theory to helicopter engineering problems, using the antiresonant eigenvalue equation are suggested.

Bartlett, F. D., Jr.↗
NASA NTRS1987

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗
DOE OSTI2018

On nonlinear inexact Uzawa algorithms for stabilized saddle point problems

In this paper, the nonlinear inexact Uzawa (NIU) methods for saddle point problems are studied. A further improved convergence result of the NIU algorithm for stabilized saddle point problems is presented, which results in much smaller convergence factor. This result can also be viewed as a generalization of some previous work for classical saddle point problems. Based on this result, we generalize some adaptive versions of the NIU algorithm with variable iteration parameters for classical saddle point problems to solve stabilized saddle point problems. Convergence analyses of these algorithms are presented. It shows that they converge under similar conditions as those in classical cases, which are more practical and without estimates on the extreme eigenvalues of the involved preconditioned systems. Numerical experiments are given to demonstrate the effectiveness of these algorithms over some original NIU algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition

A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time-dependent transport equation. Using these solutions, we use the dynamic mode decomposition to form an approximate transport operator. This approximate operator has eigenvalues that are mathematically related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that contribute the most to the change in the solution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution at short and intermediate times.

42 ENGINEERING↗
DOE OSTI2020

Comparison of Generation of Higher-Order Neutron Scattering Cross Sections

The generation of high-order neutron scattering cross sections consistent with high-fidelity simulations remains an area of active research. Popular options include generating cross sections from continuous energy Monte Carlo calculations or generating cross sections from a deterministic neutron transport calculation with high-fidelity tabulated cross sections. Both options present challenges. Monte Carlo simulations can naturally process continuous energy cross section data and allow for the general description of anisotropic neutron scattering given a scattering law. However, Monte Carlo simulations are inherently related to particle weighting and it has been suggested that this may be unacceptable for generating high-order neutron scattering cross sections. Deterministic neutron transport calculations can easily calculate high-order moments of the flux to appropriately calculate higher-order neutron scattering cross sections but are generally limited by discretization of space, energy, and angle. In this work, the trade-offs between generation of high-order neutron scattering cross sections via Monte Carlo and deterministic neutron transport methods are investigated. The methods implemented in the Monte Carlo computer program Serpent and the deterministic fast reactor neutron cross section generator MC2-3 are compared. Cross sections resulting from these methods are used in Rattlesnake, a deterministic neutron transport code developed by Idaho National Laboratory (INL), and results are compared to a reference continuous energy Monte Carlo calculation. Whereas previous work investigating the effects of anisotropic neutron scattering has focused on light water reactor (LWR) simulations, this work focuses on high-order neutron scattering cross sections as they relate to fast reactor simulations. To investigate the consequences of the Serpent and MC2-3 methodologies, a test problem is developed. The test problem is a one-dimensional geometry with fast reactor materials designed to demonstrate deep penetration and exacerbate the effects of high-order neutron scattering. Based on the results of the deep penetration test problem, it is concluded that P3 neutron scattering cross sections are sufficient to describe anisotropic scattering in fast reactor materials. Any neutron scattering of order higher than P3 offers negligible change in the eigenvalue of the test problem. Additionally, it is determined that the methodology as implemented in Serpent is applicable for generating high-order neutron scattering cross sections through at least P3 in fast reactor materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems

For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

On the All-Fiber Optical Methods of the Generation and Recognition of Soliton States

The state of a soliton is characterized by the eigenvalues of the Zakharov–Shabat problem. The data transfer rate in the fiber-optic communication lines that use eigenvalues for coding signals can be significantly increased only by developing optical eigenvalue control methods. We propose to use optical fibers with a sinusoidally changing dispersion to generate given sets of complex eigenvalues and to detect soliton states. Under the action of a periodic change in dispersion, multisoliton pulses divide into several solitons moving at different group velocities. This effect can be used to prepare fixed sets of eigenvalues. A soliton signal can be recognized by analyzing pulses and their spectra at the exit from a fiber with a periodically changing dispersion. Using the solitons specified by sets of four eigenvalues, we show that the field at the exit from a fiber corresponds to a unique combination of the spectrum and the number of pulses determined by initial eigenvalues.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

OpenMC

OpenMC is an open source, community-developed framework for performing Monte Carlo particle transport calculations.It is capable of simulating neutron and photon transport below ~50 MeV and also includes a model for bremsstrahlung production of photons by electrons/positrons. Fixed source, k-eigenvalue, and subcritical multiplication problems can be solved. Problem geometries can be modeled either using constructive solid geometry or a CAD representation. A flexible and efficient tally system enables a wide variety of physical quantities to be tallied and analyzed. OpenMC can run in parallel using a hybrid MPI and OpenMP programming model and has been extensively tested on leadership class supercomputers. A built-in Bateman equation solver enables the modeling of material composition changes due to irradiation. One of the unique features of OpenMC is its rich, extensible Python and C/C++ programming interfaces that enable programming pre- and post-processing, multigroup cross section generation, workflow automation, multiphysics coupling, and the visualization of geometry and tally results. In addition to the core Monte Carlo transport solver and associated APIs, OpenMC includes a Python-based nuclear data interface that enables power users to inspect, modify,and perform various types of nuclear data processing on ENDF, ACE, and OpenMC¿s native HDF5 files

ROMANO, PaulK.↗
DOE OSTI2019

(U) LNK3DNT Capability in SENSMG

The SENSMG multigroup neutron sensitivity code has been extended to read materials and geometry from redoin and lnk3dnt files written by the PARTISN multigroup discrete ordinates code or the MCNP6 Monte Carlo code. This report describes the user interface for this capability and the code verification that was done. Not all of the capability of SENSMG is available for redoin/lnk3dnt inputs. The only responses allowed are k eff or α eigenvalues. Fixed-source problems are not allowed, and there is no mechanism to input reaction rates or reaction-rate ratios. The next section of this report describes the user interface. Section III describes the verification of the capability. Section IV is a summary and conclusions. The input files used for verification are listed in the appendix.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Analytical and experimental study of the vibration of bonded beams with a lap joint

A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.

Rao, M. D.↗
NASA NTRS1992

A new direction in hydrodynamic stability: Beyond eigenvalues

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the 'pseudospectra' of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 10(exp 5) by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions.

Trefethen, Lloyd N.↗