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Results for “eigenvalue transformation”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1976

Eigenvalue properties of structural mean-axis systems

The authors review some of the properties of the pseudoinverse and oblique pseudoinverse of a linear transformation T from one finite-dimensional inner-product space into another, and then use these properties and a theorem of Milne (1968), which states that the oblique pseudoinverse can be expressed in terms of a weak generalized inverse and two projection operators, in order to compute a mean-axis influence coefficient matrix for the dynamic analysis of an elastic body. Some eigenvalue invariance properties of the mean-axis structural dynamics equations are demonstrated, and on the simple example of a uniform beam, it is shown that the finite frequencies and mode shapes of the mean axis structural system are identical to the nonzero frequencies and mode shapes of the free structure.

Cavin, R. K., III↗
DOE OSTI2021

Delocalization of a non-Hermitian quantum walk on random media in one dimension

Highlights: • We study the localization-delocalization transition of a non-Hermitian quantum walk. • We find that the phase transition is similar to the one in the Hatano-Nelson model. • All eigenvectors get extended and all eigenvalues become complex at the transition. • This implies that the localization lengths of all eigenvectors are the same. We first review the localization–delocalization transition of a non-Hermitian random tight-binding Anderson model, called the Hatano–Nelson model. We then report a new result for a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium; we numerically find a delocalization transition similar to one of the Hatano–Nelson model. As a common feature to both models, at the transition point, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (for the latter quantum-walk model, the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. One of the unique properties of the present non-Hermitian quantum walk is that the localization length of all eigenvectors is the same, and thereby all eigenstates simultaneously undergo the delocalization transition and all energy eigenvalues become complex at the same time when we turn up a non-Hermitian parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

A new method to real-normalize measured complex modes

A time domain subspace iteration technique is presented to compute a set of normal modes from the measured complex modes. By using the proposed method, a large number of physical coordinates are reduced to a smaller number of model or principal coordinates. Subspace free decay time responses are computed using properly scaled complex modal vectors. Companion matrix for the general case of nonproportional damping is then derived in the selected vector subspace. Subspace normal modes are obtained through eigenvalue solution of the (M sub N) sup -1 (K sub N) matrix and transformed back to the physical coordinates to get a set of normal modes. A numerical example is presented to demonstrate the outlined theory.

Wei, Max L.↗
DOE OSTI2021

IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures

Here, we present IrRep – a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the [CheckTopologicalMat: https://www.cryst.ehu.es/cgi-bin/cryst/programs/magnetictopo.pl] routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model

In this work, we propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1974

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix.

Houts, R. C.↗
NASA NTRS1983

Feature selection methodologies using simulated Thematic Mapper data

The present investigation is concerned with the determination of the intrinsic dimensionality of a simulated Thematic Mapper data set. In addition, the effectiveness and sensitivity of 'standard' statistics separability measures (i.e., transformed divergence) is evaluated in comparison to eigenvectors for identifying the optimum subset of the original Thematic Mapper Simulator (TMS) bands for classifying the various cover types. TMS data were collected on May 2, 1979 by NASA's NS001 aircraft multispectral scanner over a bottomland forested area in South Carolina near the city of Camden. It is found that the eigenvectors and eigenvalues of a covariance matrix from a multispectral scanner system (MSS) data set can be obtained without having to actually transform the data.

Dean, M. E.↗
DOE OSTI2025

Application of Lagrangian techniques for calculating the on-axis rotational transform

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis rotational transform. A discrete solution suitable for numerical implementation is introduced, which gives the Floquet exponents as solutions to an eigenvalue problem. This discrete formalism expresses the exponents as the eigenvalues of a $6$ X $6$ matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Fractional occupation numbers and self-interaction correction-scaling methods with the Fermi-Löwdin orbital self-interaction correction approach

In this work, we present a new assessment of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) approach with an emphasis on its performance for predicting energies as a function of fractional occupation numbers (FONs) for various multielectron systems. Our approach is implemented in the massively parallelized NWChem quantum chemistry software package and has been benchmarked on the prediction of total energies, atomization energies, and ionization potentials of small molecules and relatively large aromatic systems. Within our study, we also derive an alternate expression for the FLO-SIC energy gradient expressed in terms of gradients of the Fermi-orbital eigenvalues and revisit how the FLO-SIC methodology can be seen as a constrained unitary transformation of the canonical Kohn–Sham orbitals. Finally, we conclude with calculations of energies as a function of FONs using various SIC-scaling methods to test the limits of the FLO-SIC formalism on a variety of multielectron systems. We find that these relatively simple scaling methods do improve the prediction of total energies of atomic systems as well as enhance the accuracy of energies as a function of FONs for other multielectron chemical species.

fractional occupation number↗
DOE OSTI2022

Quasi-deuteron model at low renormalization group resolution

The quasi-deuteron model introduced by Levinger is used to explain cross sections for knocking out high-momentum protons in photoabsorption on nuclei. This is within a framework we characterize as exhibiting high renormalization group (RG) resolution. Assuming a one-body reaction operator, the nuclear wave function must include two-body short-range correlations (SRCs) with deuteronlike quantum numbers. In Phys. Rev. C 104, 034311 (2021), we showed that SRC physics can be naturally accounted for at low RG resolution. We describe the quasi-deuteron model at low RG resolution and determine the Levinger constant, which is proportional to the ratio of nuclear photoabsorption to that for photodisintegration of a deuteron. We extract the Levinger constant based on the ratio of momentum distributions at high relative momentum. We compute momentum distributions evolved under similarity RG (SRG) transformations where the SRC physics is shifted into the operator as a universal two-body term. The short-range nature of this operator motivates using local-density approximations with uncorrelated wave functions in evaluating nuclear matrix elements, which greatly simplifies the analysis. The operator must be consistently matched to the RG scale and scheme of the interaction for a reliable extraction. We apply SRG transformations to different nucleon-nucleon (NN) interactions and use the deuteron wave functions and Weinberg eigenvalues to determine approximate matching scales. We predict the Levinger constant for several NN interactions and a wide range of nuclei comparing to experimental extractions. The predictions at low RG resolution are in good agreement with experiment when starting with a hard NN interaction and the initial operator. Similar agreement is found using soft NN interactions when the additional two-body operator induced by evolution from hard to soft is included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

In recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices appeared in the literature. We study restricted congruence transformation of Hermitian matrices M which, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain short proofs of most of the known inertia theorems and also derive some new results of this type. For some applications, a special class of almost unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form which, in particular, displays the eigenvalues of A. Finally, applications of this quasi-spectral decomposition to generalize inverses and Hermitian matrix pencils are discussed.

Freund, Roland W.↗
NASA NTRS2013

Mixture-Tuned, Clutter Matched Filter for Remote Detection of Subpixel Spectral Signals

Mapping localized spectral features in large images demands sensitive and robust detection algorithms. Two aspects of large images that can harm matched-filter detection performance are addressed simultaneously. First, multimodal backgrounds may thwart the typical Gaussian model. Second, outlier features can trigger false detections from large projections onto the target vector. Two state-of-the-art approaches are combined that independently address outlier false positives and multimodal backgrounds. The background clustering models multimodal backgrounds, and the mixture tuned matched filter (MT-MF) addresses outliers. Combining the two methods captures significant additional performance benefits. The resulting mixture tuned clutter matched filter (MT-CMF) shows effective performance on simulated and airborne datasets. The classical MNF transform was applied, followed by k-means clustering. Then, each cluster s mean, covariance, and the corresponding eigenvalues were estimated. This yields a cluster-specific matched filter estimate as well as a cluster- specific feasibility score to flag outlier false positives. The technology described is a proof of concept that may be employed in future target detection and mapping applications for remote imaging spectrometers. It is of most direct relevance to JPL proposals for airborne and orbital hyperspectral instruments. Applications include subpixel target detection in hyperspectral scenes for military surveillance. Earth science applications include mineralogical mapping, species discrimination for ecosystem health monitoring, and land use classification.

Thompson, David R.↗
DOE OSTI2024

Explicit Form for the Most General Lorentz Transformation Revisited

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Science & Technology - Other Topics↗
DOE OSTI2020

Twisted bulk-boundary correspondence of fragile topology

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Science & Technology - Other Topics↗
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 NTRS1990

An efficient design sensitivity analysis of eigenvectors

Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.

Ting, T.↗
NASA NTRS1976

Stiffness coupling application to modal synthesis program, users guide

A FORTRAN IV computer program used to perform modal synthesis of structures by stiffness coupling, using the dynamic transformation method is described. The program was named SCAMP (Stiffness Coupling Approach Modal-Synthesis Program). The program begins with the entry of a substructure's physical mode shapes and eigenvalues or a substructure's mass and stiffness matrix. If the mass and stiffness matrices are entered, the eigen problem for the individual substructure is solved. Provisions are included for a maximum of 20 substructures which are coupled by stiffness matrix springs. Each substructure has a number degrees of freedom (DOF), except that for DOF greater than 100; vector sets having maximum row and column size of 100 were generated prior to entering SCAMP. The substructures are then coupled together via coupling springs, and the dynamic transformation is used to reduce the size of the eigen problem.

Kuhar, E. J.↗