Statistical properties of cross-correlation in the Korean stock market

NASA Astrophysics Data System (ADS)

Oh, G.; Eom, C.; Wang, F.; Jung, W.-S.; Stanley, H. E.; Kim, S.

2011-01-01

We investigate the statistical properties of the cross-correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the cross-correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original cross-correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The β_{473} coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function E(σ) with the portfolio risk σ for the original and filtered cross-correlation matrices are consistent with a power-law function, E( σ) σ^{-γ}, with the exponent γ 2.92 and those for Asian currency crisis decreases significantly.

A discourse on sensitivity analysis for discretely-modeled structures

NASA Technical Reports Server (NTRS)

Adelman, Howard M.; Haftka, Raphael T.

1991-01-01

A descriptive review is presented of the most recent methods for performing sensitivity analysis of the structural behavior of discretely-modeled systems. The methods are generally but not exclusively aimed at finite element modeled structures. Topics included are: selections of finite difference step sizes; special consideration for finite difference sensitivity of iteratively-solved response problems; first and second derivatives of static structural response; sensitivity of stresses; nonlinear static response sensitivity; eigenvalue and eigenvector sensitivities for both distinct and repeated eigenvalues; and sensitivity of transient response for both linear and nonlinear structural response.

Sensitivity analysis and approximation methods for general eigenvalue problems

NASA Technical Reports Server (NTRS)

Murthy, D. V.; Haftka, R. T.

1986-01-01

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Substructure Versus Property-Level Dispersed Modes Calculation

NASA Technical Reports Server (NTRS)

Stewart, Eric C.; Peck, Jeff A.; Bush, T. Jason; Fulcher, Clay W.

2016-01-01

This paper calculates the effect of perturbed finite element mass and stiffness values on the eigenvectors and eigenvalues of the finite element model. The structure is perturbed in two ways: at the "subelement" level and at the material property level. In the subelement eigenvalue uncertainty analysis the mass and stiffness of each subelement is perturbed by a factor before being assembled into the global matrices. In the property-level eigenvalue uncertainty analysis all material density and stiffness parameters of the structure are perturbed modified prior to the eigenvalue analysis. The eigenvalue and eigenvector dispersions of each analysis (subelement and property-level) are also calculated using an analytical sensitivity approximation. Two structural models are used to compare these methods: a cantilevered beam model, and a model of the Space Launch System. For each structural model it is shown how well the analytical sensitivity modes approximate the exact modes when the uncertainties are applied at the subelement level and at the property level.

Sensitivity analysis of hydrodynamic stability operators

NASA Technical Reports Server (NTRS)

Schmid, Peter J.; Henningson, Dan S.; Khorrami, Mehdi R.; Malik, Mujeeb R.

1992-01-01

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

On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

A comparison of maximum likelihood and other estimators of eigenvalues from several correlated Monte Carlo samples

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beer, M.

1980-12-01

The maximum likelihood method for the multivariate normal distribution is applied to the case of several individual eigenvalues. Correlated Monte Carlo estimates of the eigenvalue are assumed to follow this prescription and aspects of the assumption are examined. Monte Carlo cell calculations using the SAM-CE and VIM codes for the TRX-1 and TRX-2 benchmark reactors, and SAM-CE full core results are analyzed with this method. Variance reductions of a few percent to a factor of 2 are obtained from maximum likelihood estimation as compared with the simple average and the minimum variance individual eigenvalue. The numerical results verify that themore » use of sample variances and correlation coefficients in place of the corresponding population statistics still leads to nearly minimum variance estimation for a sufficient number of histories and aggregates.« less

A spectral approach for the stability analysis of turbulent open-channel flows over granular beds

NASA Astrophysics Data System (ADS)

Camporeale, C.; Canuto, C.; Ridolfi, L.

2012-01-01

A novel Orr-Sommerfeld-like equation for gravity-driven turbulent open-channel flows over a granular erodible bed is here derived, and the linear stability analysis is developed. The whole spectrum of eigenvalues and eigenvectors of the complete generalized eigenvalue problem is computed and analyzed. The fourth-order eigenvalue problem presents singular non-polynomial coefficients with non-homogenous Robin-type boundary conditions that involve first and second derivatives. Furthermore, the Exner condition is imposed at an internal point. We propose a numerical discretization of spectral type based on a single-domain Galerkin scheme. In order to manage the presence of singular coefficients, some properties of Jacobi polynomials have been carefully blended with numerical integration of Gauss-Legendre type. The results show a positive agreement with the classical experimental data and allow one to relate the different types of instability to such parameters as the Froude number, wavenumber, and the roughness scale. The eigenfunctions allow two types of boundary layers to be distinguished, scaling, respectively, with the roughness height and the saltation layer for the bedload sediment transport.

Cascade flutter analysis with transient response aerodynamics

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Mahajan, Aparajit J.; Keith, Theo G., Jr.; Stefko, George L.

1991-01-01

Two methods for calculating linear frequency domain aerodynamic coefficients from a time marching Full Potential cascade solver are developed and verified. In the first method, the Influence Coefficient, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier Transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers.

ORACLE INEQUALITIES FOR THE LASSO IN THE COX MODEL

PubMed Central

Huang, Jian; Sun, Tingni; Ying, Zhiliang; Yu, Yi; Zhang, Cun-Hui

2013-01-01

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. However, the presented oracle inequalities are sharper since the compatibility and cone invertibility factors are always greater than the corresponding restricted eigenvalue. In the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, so that the compatibility and cone invertibility factors, and the restricted eigenvalue as well, are random variables even when they are evaluated for the Hessian at the true regression coefficients. Under mild conditions, we prove that these quantities are bounded from below by positive constants for time-dependent covariates, including cases where the number of covariates is of greater order than the sample size. Consequently, the compatibility and cone invertibility factors can be treated as positive constants in our oracle inequalities. PMID:24086091

ORACLE INEQUALITIES FOR THE LASSO IN THE COX MODEL.

PubMed

Huang, Jian; Sun, Tingni; Ying, Zhiliang; Yu, Yi; Zhang, Cun-Hui

2013-06-01

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. However, the presented oracle inequalities are sharper since the compatibility and cone invertibility factors are always greater than the corresponding restricted eigenvalue. In the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, so that the compatibility and cone invertibility factors, and the restricted eigenvalue as well, are random variables even when they are evaluated for the Hessian at the true regression coefficients. Under mild conditions, we prove that these quantities are bounded from below by positive constants for time-dependent covariates, including cases where the number of covariates is of greater order than the sample size. Consequently, the compatibility and cone invertibility factors can be treated as positive constants in our oracle inequalities.

Spectral analysis of Chinese language: Co-occurrence networks from four literary genres

NASA Astrophysics Data System (ADS)

Liang, Wei; Chen, Guanrong

2016-05-01

The eigenvalues and eigenvectors of the adjacency matrix of a network contain essential information about its topology. For each of the Chinese language co-occurrence networks constructed from four literary genres, i.e., essay, popular science article, news report, and novel, it is found that the largest eigenvalue depends on the network size N, the number of edges, the average shortest path length, and the clustering coefficient. Moreover, it is found that their node-degree distributions all follow a power-law. The number of different eigenvalues, Nλ, is found numerically to increase in the manner of Nλ ∝ log N for novel and Nλ ∝ N for the other three literary genres. An ;M; shape or a triangle-like distribution appears in their spectral densities. The eigenvector corresponding to the largest eigenvalue is mostly localized to a node with the largest degree. For the above observed phenomena, mathematical analysis is provided with interpretation from a linguistic perspective.

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

NASA Astrophysics Data System (ADS)

Wang, Gang-Jin; Xie, Chi; Chen, Shou; Yang, Jiao-Jiao; Yang, Ming-Yan

2013-09-01

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko-Pastur distribution.

Eigenvalue Contributon Estimator for Sensitivity Calculations with TSUNAMI-3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rearden, Bradley T; Williams, Mark L

2007-01-01

Since the release of the Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) codes in SCALE [1], the use of sensitivity and uncertainty analysis techniques for criticality safety applications has greatly increased within the user community. In general, sensitivity and uncertainty analysis is transitioning from a technique used only by specialists to a practical tool in routine use. With the desire to use the tool more routinely comes the need to improve the solution methodology to reduce the input and computational burden on the user. This paper reviews the current solution methodology of the Monte Carlo eigenvalue sensitivity analysismore » sequence TSUNAMI-3D, describes an alternative approach, and presents results from both methodologies.« less

Inverse resonance scattering for Jacobi operators

NASA Astrophysics Data System (ADS)

Korotyaev, E. L.

2011-12-01

The Jacobi operator ( Jf) n = a n-1 f n-1 + a n f n+1 + b n f n on ℤ with real finitely supported sequences ( a n - 1) n∈ℤ and ( b n ) n∈ℤ is considered. The inverse problem for two mappings (including their characterization): ( a n , b n , n ∈ ℤ) → {the zeros of the reflection coefficient} and ( a n , b n , n ∈ ℤ) → {the eigenvalues and the resonances} is solved. All Jacobi operators with the same eigenvalues and resonances are also described.

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system

NASA Astrophysics Data System (ADS)

Chen, G. X.; Zhou, Z. R.; Ouyang, H.; Jin, X. S.; Zhu, M. H.; Liu, Q. Y.

2010-10-01

The present work proposes friction coupling at the wheel-rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset-track system is studied using the finite element complex eigenvalue method. Two models for a wheelset-track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset-track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60-1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.

Changes in diffusion tensor imaging (DTI) eigenvalues of skeletal muscle due to hybrid exercise training.

PubMed

Okamoto, Yoshikazu; Kemp, Graham J; Isobe, Tomonori; Sato, Eisuke; Hirano, Yuji; Shoda, Junichi; Minami, Manabu

2014-12-01

Several studies have proposed the cell membrane as the main water diffusion restricting factor in the skeletal muscle cell. We sought to establish whether a particular form of exercise training (which is likely to affect only intracellular components) could affect water diffusion. The purpose of this study is to characterise prospectively the changes in diffusion tensor imaging (DTI) eigenvalues of thigh muscle resulting from hybrid training (HYBT) in patients with non-alcoholic fatty liver disease (NAFLD). Twenty-one NAFLD patients underwent HYBT for 30 minutes per day, twice a week for 6 months. Patients were scanned using DTI of the thigh pre- and post-HYBT. Fractional anisotropy (FA), apparent diffusion coefficient (ADC), the three eigenvalues lambda 1 (λ1), λ2, λ3, and the maximal cross sectional area (CSA) were measured in bilateral thigh muscles: knee flexors (biceps femoris (BF), semitendinosus (ST), semimembranous (SM)) and knee extensors (medial vastus (MV), intermediate vastus (IV), lateral vastus (LV), and rectus femoris (RF)), and compared pre- and post-HYBT by paired t-test. Muscle strength of extensors (P<0.01), but not flexors, increased significantly post-HYBT. For FA, ADC and eigenvalues, the overall picture was of increase. Some (P<0.05 in λ2 and P<0.01 in λ1) eigenvalues of flexors and all (λ1-λ3) eigenvalues of extensors increased significantly (P<0.01) post-HYBT. HYBT increased all 3 eigenvalues. We suggest this might be caused by enlargement of muscle intracellular space. Copyright © 2014 Elsevier Inc. All rights reserved.

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

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.

On the identification of continuous vibrating systems modelled by hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Udwadia, F. E.; Garba, J. A.

1983-01-01

This paper deals with the identification of spatially varying parameters in systems of finite spatial extent which can be described by second order hyperbolic differential equations. Two questions have been addressed. The first deals with 'partial identification' and inquires into the possibility of retrieving all the eigenvalues of the system from response data obtained at one location x-asterisk epsilon (0, 1). The second deals with the identification of the distributed coefficients rho(x), a(x) and b(x). Sufficient conditions for unique identification of all the eigenvalues of the system are obtained, and conditions under which the coefficients can be uniquely identified using suitable response data obtained at one point in the spatial domain are determined. Application of the results and their usefulness is demonstrated in the identification of the properties of tall building structural systems subjected to dynamic load environments.

Sensitivity of coronal loop sausage mode frequencies and decay rates to radial and longitudinal density inhomogeneities: a spectral approach

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Xiong, Ming

2018-01-01

Fast sausage modes in solar magnetic coronal loops are only fully contained in unrealistically short dense loops. Otherwise they are leaky, losing energy to their surrounds as outgoing waves. This causes any oscillation to decay exponentially in time. Simultaneous observations of both period and decay rate therefore reveal the eigenfrequency of the observed mode, and potentially insight into the tubes’ nonuniform internal structure. In this article, a global spectral description of the oscillations is presented that results in an implicit matrix eigenvalue equation where the eigenvalues are associated predominantly with the diagonal terms of the matrix. The off-diagonal terms vanish identically if the tube is uniform. A linearized perturbation approach, applied with respect to a uniform reference model, is developed that makes the eigenvalues explicit. The implicit eigenvalue problem is easily solved numerically though, and it is shown that knowledge of the real and imaginary parts of the eigenfrequency is sufficient to determine the width and density contrast of a boundary layer over which the tubes’ enhanced internal densities drop to ambient values. Linearized density kernels are developed that show sensitivity only to the extreme outside of the loops for radial fundamental modes, especially for small density enhancements, with no sensitivity to the core. Higher radial harmonics do show some internal sensitivity, but these will be more difficult to observe. Only kink modes are sensitive to the tube centres. Variation in internal and external Alfvén speed along the loop is shown to have little effect on the fundamental dimensionless eigenfrequency, though the associated eigenfunction becomes more compact at the loop apex as stratification increases, or may even displace from the apex.

Hessian eigenvalue distribution in a random Gaussian landscape

NASA Astrophysics Data System (ADS)

Yamada, Masaki; Vilenkin, Alexander

2018-03-01

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.

Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-01-01

In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

Cubic Polynomials, Their Roots and the Perron-Frobenius Theorem

ERIC Educational Resources Information Center

Dealba, Luz Maria

2002-01-01

In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

Survey of methods for calculating sensitivity of general eigenproblems

NASA Technical Reports Server (NTRS)

Murthy, Durbha V.; Haftka, Raphael T.

1987-01-01

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Diffusion with Varying Drag; the Runaway Problem.

NASA Astrophysics Data System (ADS)

Rollins, David Kenneth

We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a Fokker-Planck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon. We treat the electric field as a small perturbation. We consider various diffusion coefficients for the one dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity are then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analysed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the three dimensional problem.

Determining entire mean first-passage time for Cayley networks

NASA Astrophysics Data System (ADS)

Wang, Xiaoqian; Dai, Meifeng; Chen, Yufei; Zong, Yue; Sun, Yu; Su, Weiyi

In this paper, we consider the entire mean first-passage time (EMFPT) with random walks for Cayley networks. We use Laplacian spectra to calculate the EMFPT. Firstly, we calculate the constant term and monomial coefficient of characteristic polynomial. By using the Vieta theorem, we then obtain the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix. Finally, we obtain the scaling of the EMFPT for Cayley networks by using the relationship between the sum of reciprocals of all nonzero eigenvalues of Laplacian matrix and the EMFPT. We expect that our method can be adapted to other types of self-similar networks, such as vicsek networks, polymer networks.

Wave Propagation and Localization via Quasi-Normal Modes and Transmission Eigenchannels

NASA Astrophysics Data System (ADS)

Wang, Jing; Shi, Zhou; Davy, Matthieu; Genack, Azriel Z.

2013-10-01

Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ1 is near unity for diffusive waves even in turbid samples. For localized waves, τ1 is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στn. The spacings between the ensemble averages of successive values of lnτn are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues Neff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.

Wave Propagation and Localization via Quasi-Normal Modes and Transmission Eigenchannels

NASA Astrophysics Data System (ADS)

Wang, Jing; Shi, Zhou; Davy, Matthieu; Genack, Azriel Z.

Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ1 is near unity for diffusive waves even in turbid samples. For localized waves, τ1 is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στn. The spacings between the ensemble averages of successive values of lnτn are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues Neff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guba, O.; Taylor, M. A.; Ullrich, P. A.

2014-11-27

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

The spectral element method on variable resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE PAGES

Guba, O.; Taylor, M. A.; Ullrich, P. A.; ...

2014-06-25

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

Generalized uncertainty principle and quantum gravity phenomenology

NASA Astrophysics Data System (ADS)

Bosso, Pasquale

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canonical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Random matrix approach to cross correlations in financial data

NASA Astrophysics Data System (ADS)

Plerou, Vasiliki; Gopikrishnan, Parameswaran; Rosenow, Bernd; Amaral, Luís A.; Guhr, Thomas; Stanley, H. Eugene

2002-06-01

We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices C of returns constructed from (i) 30-min returns of 1000 US stocks for the 2-yr period 1994-1995, (ii) 30-min returns of 881 US stocks for the 2-yr period 1996-1997, and (iii) 1-day returns of 422 US stocks for the 35-yr period 1962-1996. We test the statistics of the eigenvalues λi of C against a ``null hypothesis'' - a random correlation matrix constructed from mutually uncorrelated time series. We find that a majority of the eigenvalues of C fall within the RMT bounds [λ-,λ+] for the eigenvalues of random correlation matrices. We test the eigenvalues of C within the RMT bound for universal properties of random matrices and find good agreement with the results for the Gaussian orthogonal ensemble of random matrices-implying a large degree of randomness in the measured cross-correlation coefficients. Further, we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the RMT bound display systematic deviations from the RMT prediction. In addition, we find that these ``deviating eigenvectors'' are stable in time. We analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks. Our analysis of the remaining deviating eigenvectors shows distinct groups, whose identities correspond to conventionally identified business sectors. Finally, we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return.

Sensitivity analysis for large-scale problems

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Whitworth, Sandra L.

1987-01-01

The development of efficient techniques for calculating sensitivity derivatives is studied. The objective is to present a computational procedure for calculating sensitivity derivatives as part of performing structural reanalysis for large-scale problems. The scope is limited to framed type structures. Both linear static analysis and free-vibration eigenvalue problems are considered.

Spectral properties of the temporal evolution of brain network structure.

PubMed

Wang, Rong; Zhang, Zhen-Zhen; Ma, Jun; Yang, Yong; Lin, Pan; Wu, Ying

2015-12-01

The temporal evolution properties of the brain network are crucial for complex brain processes. In this paper, we investigate the differences in the dynamic brain network during resting and visual stimulation states in a task-positive subnetwork, task-negative subnetwork, and whole-brain network. The dynamic brain network is first constructed from human functional magnetic resonance imaging data based on the sliding window method, and then the eigenvalues corresponding to the network are calculated. We use eigenvalue analysis to analyze the global properties of eigenvalues and the random matrix theory (RMT) method to measure the local properties. For global properties, the shifting of the eigenvalue distribution and the decrease in the largest eigenvalue are linked to visual stimulation in all networks. For local properties, the short-range correlation in eigenvalues as measured by the nearest neighbor spacing distribution is not always sensitive to visual stimulation. However, the long-range correlation in eigenvalues as evaluated by spectral rigidity and number variance not only predicts the universal behavior of the dynamic brain network but also suggests non-consistent changes in different networks. These results demonstrate that the dynamic brain network is more random for the task-positive subnetwork and whole-brain network under visual stimulation but is more regular for the task-negative subnetwork. Our findings provide deeper insight into the importance of spectral properties in the functional brain network, especially the incomparable role of RMT in revealing the intrinsic properties of complex systems.

Spectral properties of the temporal evolution of brain network structure

NASA Astrophysics Data System (ADS)

Wang, Rong; Zhang, Zhen-Zhen; Ma, Jun; Yang, Yong; Lin, Pan; Wu, Ying

2015-12-01

The temporal evolution properties of the brain network are crucial for complex brain processes. In this paper, we investigate the differences in the dynamic brain network during resting and visual stimulation states in a task-positive subnetwork, task-negative subnetwork, and whole-brain network. The dynamic brain network is first constructed from human functional magnetic resonance imaging data based on the sliding window method, and then the eigenvalues corresponding to the network are calculated. We use eigenvalue analysis to analyze the global properties of eigenvalues and the random matrix theory (RMT) method to measure the local properties. For global properties, the shifting of the eigenvalue distribution and the decrease in the largest eigenvalue are linked to visual stimulation in all networks. For local properties, the short-range correlation in eigenvalues as measured by the nearest neighbor spacing distribution is not always sensitive to visual stimulation. However, the long-range correlation in eigenvalues as evaluated by spectral rigidity and number variance not only predicts the universal behavior of the dynamic brain network but also suggests non-consistent changes in different networks. These results demonstrate that the dynamic brain network is more random for the task-positive subnetwork and whole-brain network under visual stimulation but is more regular for the task-negative subnetwork. Our findings provide deeper insight into the importance of spectral properties in the functional brain network, especially the incomparable role of RMT in revealing the intrinsic properties of complex systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smed, T.

Traditional eigenvalue sensitivity for power systems requires the formulation of the system matrix, which lacks sparsity. In this paper, a new sensitivity analysis, derived for a sparse formulation, is presented. Variables that are computed as intermediate results in established eigen value programs for power systems, but not used further, are given a new interpretation. The effect of virtually any control action can be assessed based on a single eigenvalue-eigenvector calculation. In particular, the effect of active and reactive power modulation can be found as a multiplication of two or three complex numbers. The method is illustrated in an example formore » a large power system when applied to the control design for an HVDC-link.« less

Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

PubMed Central

SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

2016-01-01

In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

A Taxometric Study of the Latent Structure of Disgust Sensitivity: Converging Evidence for Dimensionality

ERIC Educational Resources Information Center

Olatunji, Bunmi O.; Broman-Fulks, Joshua J.

2007-01-01

Disgust sensitivity has recently been implicated as a specific vulnerability factor for several anxiety-related disorders. However, it is not clear whether disgust sensitivity is a dimensional or categorical phenomenon. The present study examined the latent structure of disgust by applying three taxometric procedures (maximum eigenvalue, mean…

Coupling coefficients for tensor product representations of quantum SU(2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Groenevelt, Wolter, E-mail: w.g.m.groenevelt@tudelft.nl

2014-10-15

We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometricmore » orthogonal polynomials and q-Bessel-type functions.« less

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

2017-09-01

We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

Possibility of modifying the growth trajectory in Raeini Cashmere goat.

PubMed

Ghiasi, Heydar; Mokhtari, M S

2018-03-27

The objective of this study was to investigate the possibility of modifying the growth trajectory in Raeini Cashmere goat breed. In total, 13,193 records on live body weight collected from 4788 Raeini Cashmere goats were used. According to Akanke's information criterion (AIC), the sing-trait random regression model included fourth-order Legendre polynomial for direct and maternal genetic effect; maternal and individual permanent environmental effect was the best model for estimating (co)variance components. The matrices of eigenvectors for (co)variances between random regression coefficients of direct additive genetic were used to calculate eigenfunctions, and different eigenvector indices were also constructed. The obtained results showed that the first eigenvalue explained 79.90% of total genetic variance. Therefore, changing the body weights applying the first eigenfunction will be obtained rapidly. Selection based on the first eigenvector will cause favorable positive genetic gains for all body weight considered from birth to 12 months of age. For modifying the growth trajectory in Raeini Cashmere goat, the selection should be based on the second eigenfunction. The second eigenvalue accounted for 14.41% of total genetic variance for body weights that is low in comparison with genetic variance explained by the first eigenvalue. The complex patterns of genetic change in growth trajectory observed under the third and fourth eigenfunction and low amount of genetic variance explained by the third and fourth eigenvalues.

Energy levels of one-dimensional systems satisfying the minimal length uncertainty relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardo, Reginald Christian S., E-mail: rcbernardo@nip.upd.edu.ph; Esguerra, Jose Perico H., E-mail: jesguerra@nip.upd.edu.ph

2016-10-15

The standard approach to calculating the energy levels for quantum systems satisfying the minimal length uncertainty relation is to solve an eigenvalue problem involving a fourth- or higher-order differential equation in quasiposition space. It is shown that the problem can be reformulated so that the energy levels of these systems can be obtained by solving only a second-order quasiposition eigenvalue equation. Through this formulation the energy levels are calculated for the following potentials: particle in a box, harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well. For the particle in a box, the second-order quasiposition eigenvalue equation is a second-ordermore » differential equation with constant coefficients. For the harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well, a method that involves using Wronskians has been used to solve the second-order quasiposition eigenvalue equation. It is observed for all of these quantum systems that the introduction of a nonzero minimal length uncertainty induces a positive shift in the energy levels. It is shown that the calculation of energy levels in systems satisfying the minimal length uncertainty relation is not limited to a small number of problems like particle in a box and the harmonic oscillator but can be extended to a wider class of problems involving potentials such as the Pöschl–Teller and Gaussian wells.« less

Bose-Einstein condensation on a manifold with non-negative Ricci curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akant, Levent, E-mail: levent.akant@boun.edu.tr; Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr; Tapramaz, Ferzan, E-mail: waskhez@gmail.com

The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with non-negative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite sizemore » effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.« less

Stability of streamwise vortices

NASA Technical Reports Server (NTRS)

Khorrami, M. K.; Grosch, C. E.; Ash, R. L.

1987-01-01

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Neural network approach for the calculation of potential coefficients in quantum mechanics

NASA Astrophysics Data System (ADS)

Ossandón, Sebastián; Reyes, Camilo; Cumsille, Patricio; Reyes, Carlos M.

2017-05-01

A numerical method based on artificial neural networks is used to solve the inverse Schrödinger equation for a multi-parameter class of potentials. First, the finite element method was used to solve repeatedly the direct problem for different parametrizations of the chosen potential function. Then, using the attainable eigenvalues as a training set of the direct radial basis neural network a map of new eigenvalues was obtained. This relationship was later inverted and refined by training an inverse radial basis neural network, allowing the calculation of the unknown parameters and therefore estimating the potential function. Three numerical examples are presented in order to prove the effectiveness of the method. The results show that the method proposed has the advantage to use less computational resources without a significant accuracy loss.

Preliminary demonstration of a robust controller design method

NASA Technical Reports Server (NTRS)

Anderson, L. R.

1980-01-01

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Vibrational shape tracking of atomic force microscopy cantilevers for improved sensitivity and accuracy of nanomechanical measurements

NASA Astrophysics Data System (ADS)

Wagner, Ryan; Killgore, Jason P.; Tung, Ryan C.; Raman, Arvind; Hurley, Donna C.

2015-01-01

Contact resonance atomic force microscopy (CR-AFM) methods currently utilize the eigenvalues, or resonant frequencies, of an AFM cantilever in contact with a surface to quantify local mechanical properties. However, the cantilever eigenmodes, or vibrational shapes, also depend strongly on tip-sample contact stiffness. In this paper, we evaluate the potential of eigenmode measurements for improved accuracy and sensitivity of CR-AFM. We apply a recently developed, in situ laser scanning method to experimentally measure changes in cantilever eigenmodes as a function of tip-sample stiffness. Regions of maximum sensitivity for eigenvalues and eigenmodes are compared and found to occur at different values of contact stiffness. The results allow the development of practical guidelines for CR-AFM experiments, such as optimum laser spot positioning for different experimental conditions. These experiments provide insight into the complex system dynamics that can affect CR-AFM and lay a foundation for enhanced nanomechanical measurements with CR-AFM.

Statistics of transmission eigenvalues in two-dimensional quantum cavities: Ballistic versus stochastic scattering

NASA Astrophysics Data System (ADS)

Rotter, Stefan; Aigner, Florian; Burgdörfer, Joachim

2007-03-01

We investigate the statistical distribution of transmission eigenvalues in phase-coherent transport through quantum dots. In two-dimensional ab initio simulations for both clean and disordered two-dimensional cavities, we find markedly different quantum-to-classical crossover scenarios for these two cases. In particular, we observe the emergence of “noiseless scattering states” in clean cavities, irrespective of sharp-edged entrance and exit lead mouths. We find the onset of these “classical” states to be largely independent of the cavity’s classical chaoticity, but very sensitive with respect to bulk disorder. Our results suggest that for weakly disordered cavities, the transmission eigenvalue distribution is determined both by scattering at the disorder potential and the cavity walls. To properly account for this intermediate parameter regime, we introduce a hybrid crossover scheme, which combines previous models that are valid in the ballistic and the stochastic limit, respectively.

Analytical bound-state solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-01-01

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any l≠0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

The behaviour of resonances in Hecke triangular billiards under deformation

NASA Astrophysics Data System (ADS)

Howard, P. J.; O'Mahony, P. F.

2007-08-01

The right-hand boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of chaotic billiards which includes fundamental domains of the Hecke groups Γ(2, n) at certain values of the deformation parameter. The quantum scattering problem in these open chaotic billiards is described and the distributions of both real and imaginary parts of the resonant eigenvalues are investigated. The transitions to arithmetic chaos in the cases n ∈ {4, 6} are closely examined and the explicit analytic form for the scattering matrix is given together with the Fourier coefficients for the scattered wavefunction. The n = 4 and 6 cases have an additional set of regular equally spaced resonances compared to Artin's billiard (n = 3). For a general deformation, a numerical procedure is presented which generates the resonance eigenvalues and the evolution of the eigenvalues is followed as the boundary is varied continuously which leads to dramatic changes in their distribution. For deformations away from the non-generic arithmetic cases, including that of the tiling Hecke triangular billiard n = 5, the distributions of the positions and widths of the resonances are consistent with the predictions of a random matrix theory.

Pad-mode-induced instantaneous mode instability for simple models of brake systems

NASA Astrophysics Data System (ADS)

Oberst, S.; Lai, J. C. S.

2015-10-01

Automotive disc brake squeal is fugitive, transient and remains difficult to predict. In particular, instantaneous mode squeal observed experimentally does not seem to be associated with mode coupling and its mechanism is not clear. The effects of contact pressures, friction coefficients as well as material properties (pressure and temperature dependency and anisotropy) for brake squeal propensity have not been systematically explored. By analysing a finite element model of an isotropic pad sliding on a plate similar to that of a previously reported experimental study, pad modes have been identified and found to be stable using conventional complex eigenvalue analysis. However, by subjecting the model to contact pressure harmonic excitation for a range of pressures and friction coefficients, a forced response analysis reveals that the dissipated energy for pad modes is negative and becomes more negative with increasing contact pressures and friction coefficients, indicating the potential for instabilities. The frequency of the pad mode in the sliding direction is within the range of squeal frequencies observed experimentally. Nonlinear time series analysis of the vibration velocity also confirms the evolution of instabilities induced by pad modes as the friction coefficient increases. By extending this analysis to a more realistic but simple brake model in the form of a pad-on-disc system, in-plane pad-modes, which a complex eigenvalue analysis predicts to be stable, have also been identified by negative dissipated energy for both isotropic and anisotropic pad material properties. The influence of contact pressures on potential instabilities has been found to be more dominant than changes in material properties owing to changes in pressure or temperature. Results here suggest that instantaneous mode squeal is likely caused by in-plane pad-mode instabilities.

Recurrence quantity analysis based on matrix eigenvalues

NASA Astrophysics Data System (ADS)

Yang, Pengbo; Shang, Pengjian

2018-06-01

Recurrence plots is a powerful tool for visualization and analysis of dynamical systems. Recurrence quantification analysis (RQA), based on point density and diagonal and vertical line structures in the recurrence plots, is considered to be alternative measures to quantify the complexity of dynamical systems. In this paper, we present a new measure based on recurrence matrix to quantify the dynamical properties of a given system. Matrix eigenvalues can reflect the basic characteristics of the complex systems, so we show the properties of the system by exploring the eigenvalues of the recurrence matrix. Considering that Shannon entropy has been defined as a complexity measure, we propose the definition of entropy of matrix eigenvalues (EOME) as a new RQA measure. We confirm that EOME can be used as a metric to quantify the behavior changes of the system. As a given dynamical system changes from a non-chaotic to a chaotic regime, the EOME will increase as well. The bigger EOME values imply higher complexity and lower predictability. We also study the effect of some factors on EOME,including data length, recurrence threshold, the embedding dimension, and additional noise. Finally, we demonstrate an application in physiology. The advantage of this measure lies in a high sensitivity and simple computation.

Impedance computed tomography using an adaptive smoothing coefficient algorithm.

PubMed

Suzuki, A; Uchiyama, A

2001-01-01

In impedance computed tomography, a fixed coefficient regularization algorithm has been frequently used to improve the ill-conditioning problem of the Newton-Raphson algorithm. However, a lot of experimental data and a long period of computation time are needed to determine a good smoothing coefficient because a good smoothing coefficient has to be manually chosen from a number of coefficients and is a constant for each iteration calculation. Thus, sometimes the fixed coefficient regularization algorithm distorts the information or fails to obtain any effect. In this paper, a new adaptive smoothing coefficient algorithm is proposed. This algorithm automatically calculates the smoothing coefficient from the eigenvalue of the ill-conditioned matrix. Therefore, the effective images can be obtained within a short computation time. Also the smoothing coefficient is automatically adjusted by the information related to the real resistivity distribution and the data collection method. In our impedance system, we have reconstructed the resistivity distributions of two phantoms using this algorithm. As a result, this algorithm only needs one-fifth the computation time compared to the fixed coefficient regularization algorithm. When compared to the fixed coefficient regularization algorithm, it shows that the image is obtained more rapidly and applicable in real-time monitoring of the blood vessel.

Expendable launch vehicle studies

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reiss, Robert

1995-01-01

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Optimization of cascade blade mistuning. I - Equations of motion and basic inherent properties

NASA Technical Reports Server (NTRS)

Nissim, E.

1985-01-01

Attention is given to the derivation of the equations of motion of mistuned compressor blades, interpolating aerodynamic coefficients by means of quadratic expressions in the reduced frequency. If the coefficients of the quadratic expressions are permitted to assume complex values, excellent accuracy is obtained and Pade rational expressions are obviated. On the basis of the resulting equations, it is shown analytically that the sum of all the real parts of the eigenvalues is independent of the mistuning introduced into the system. Blade mistuning is further treated through the aerodynamic energy approach, and the limiting vibration modes associated with alternative mistunings are identified.

Perturbation solutions for the influence of forward flight on helicopter rotor flapping stability

NASA Technical Reports Server (NTRS)

Johnson, W.

1974-01-01

The stability of the flapping motion of a helicopter rotor blade in forward flight is investigated, using a perturbation technique which gives analytic expressions for the eigenvalues, including the influence of the periodic aerodynamic forces in forward flight. The perturbation solutions are based on small advance ratio (the ratio of the helicopter forward speed to the rotor tip speed). The rotor configurations considered are a single, independent blade; a teetering rotor; a gimballed rotor with three, four, and five or more blades; and a rotor with N independent blades. The constant coefficient approximation with the equations and degrees of freedom in the nonrotating frame represents the flap dynamic reasonably well for the lower frequency modes, although it cannot, of course, be completely correct. The transfer function of the rotor flap response to sinusoidal pitch input is examined, as an alternative to the eigenvalues as a representation of the dynamic characteristics of the flap motion.

The ZH ratio Analysis of Global Seismic Data

NASA Astrophysics Data System (ADS)

Yano, T.; Shikato, S.; Rivera, L.; Tanimoto, T.

2007-12-01

The ZH ratio, the ratio of vertical to horizontal component of the fundamental Rayleigh wave as a function of frequency, is an alternative approach to phase/group velocity analysis for constructing the S-wave velocity structure. In this study, teleseismic Rayleigh wave data for the frequency range between 0.004Hz to 0.04Hz is used to investigate the interior structure. We have analyzed most of the GEOSCOPE network data and some IRIS GSN stations using a technique developed by Tanimoto and Rivera (2007). Stable estimates of the ZH ratios were obtained for the frequency range for most stations. We have performed the inversion of the measured ZH ratios for the structure in the crust and mantle by using nonlinear iterative scheme. The depth sensitivity kernels for inversion are numerically calculated. Depth sensitivity of the lowest frequency extends to depths beyond 500 km but the sensitivity of the overall data for the frequency band extends down to about 300km. We found that an appropriate selection of an initial model, particularly the depth of Mohorovicic discontinuity, is important for this inversion. The inversion result depends on the initial model and turned out to be non-unique. We have constructed the initial model from the CRUST 2.0. Inversion with equal weighting to each data point tends to reduce variance of certain frequency range only. Therefore, we have developed a scheme to increase weighting to data points that do not fit well after the fifth iteration. This occurs more often for low frequency range, 0.004-0.007Hz. After fitting the lower frequency region, the low velocity zone around a depth of 100km is observed under some stations such as KIP (Kipapa, Hawaii) and ATD (Arta Cave, Djibouti). We have also carried out an analysis on the resolving power of data by examining the eigenvalues-eigenvectors of the least-squares problem. Unfortunately, the normal matrix usually has 1-2 very large eigenvalues, followed by much smaller eigenvalues. The third one is often an order of magnitude smaller. The largest eigenvalue is always dominated by an eigenfunction that has the peak at the surface. It indicates that the ZH ratio is sensitive to shallow structure but it has limited form in resolving power for underlying structure. We will report on the details on the resolving capabilities of the ZH ratios.

Eigenvalue sensitivity of sampled time systems operating in closed loop

NASA Astrophysics Data System (ADS)

Bernal, Dionisio

2018-05-01

The use of feedback to create closed-loop eigenstructures with high sensitivity has received some attention in the Structural Health Monitoring field. Although practical implementation is necessarily digital, and thus in sampled time, work thus far has center on the continuous time framework, both in design and in checking performance. It is shown in this paper that the performance in discrete time, at typical sampling rates, can differ notably from that anticipated in the continuous time formulation and that discrepancies can be particularly large on the real part of the eigenvalue sensitivities; a consequence being important error on the (linear estimate) of the level of damage at which closed-loop stability is lost. As one anticipates, explicit consideration of the sampling rate poses no special difficulties in the closed-loop eigenstructure design and the relevant expressions are developed in the paper, including a formula for the efficient evaluation of the derivative of the matrix exponential based on the theory of complex perturbations. The paper presents an easily reproduced numerical example showing the level of error that can result when the discrete time implementation of the controller is not considered.

Computation of steady and unsteady quasi-one-dimensional viscous/inviscid interacting internal flows at subsonic, transonic, and supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Swafford, Timothy W.; Huddleston, David H.; Busby, Judy A.; Chesser, B. Lawrence

1992-01-01

Computations of viscous-inviscid interacting internal flowfields are presented for steady and unsteady quasi-one-dimensional (Q1D) test cases. The unsteady Q1D Euler equations are coupled with integral boundary-layer equations for unsteady, two-dimensional (planar or axisymmetric), turbulent flow over impermeable, adiabatic walls. The coupling methodology differs from that used in most techniques reported previously in that the above mentioned equation sets are written as a complete system and solved simultaneously; that is, the coupling is carried out directly through the equations as opposed to coupling the solutions of the different equation sets. Solutions to the coupled system of equations are obtained using both explicit and implicit numerical schemes for steady subsonic, steady transonic, and both steady and unsteady supersonic internal flowfields. Computed solutions are compared with measurements as well as Navier-Stokes and inverse boundary-layer methods. An analysis of the eigenvalues of the coefficient matrix associated with the quasi-linear form of the coupled system of equations indicates the presence of complex eigenvalues for certain flow conditions. It is concluded that although reasonable solutions can be obtained numerically, these complex eigenvalues contribute to the overall difficulty in obtaining numerical solutions to the coupled system of equations.

Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ahmadov, A. I.; Naeem, Maria; Qocayeva, M. V.; Tarverdiyeva, V. A.

2018-02-01

In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Aircraft model prototypes which have specified handling-quality time histories

NASA Technical Reports Server (NTRS)

Johnson, S. H.

1976-01-01

Several techniques for obtaining linear constant-coefficient airplane models from specified handling-quality time histories are discussed. One technique, the pseudodata method, solves the basic problem, yields specified eigenvalues, and accommodates state-variable transfer-function zero suppression. The method is fully illustrated for a fourth-order stability-axis small-motion model with three lateral handling-quality time histories specified. The FORTRAN program which obtains and verifies the model is included and fully documented.

Revealing how network structure affects accuracy of link prediction

NASA Astrophysics Data System (ADS)

Yang, Jin-Xuan; Zhang, Xiao-Dong

2017-08-01

Link prediction plays an important role in network reconstruction and network evolution. The network structure affects the accuracy of link prediction, which is an interesting problem. In this paper we use common neighbors and the Gini coefficient to reveal the relation between them, which can provide a good reference for the choice of a suitable link prediction algorithm according to the network structure. Moreover, the statistical analysis reveals correlation between the common neighbors index, Gini coefficient index and other indices to describe the network structure, such as Laplacian eigenvalues, clustering coefficient, degree heterogeneity, and assortativity of network. Furthermore, a new method to predict missing links is proposed. The experimental results show that the proposed algorithm yields better prediction accuracy and robustness to the network structure than existing currently used methods for a variety of real-world networks.

FastSKAT: Sequence kernel association tests for very large sets of markers.

PubMed

Lumley, Thomas; Brody, Jennifer; Peloso, Gina; Morrison, Alanna; Rice, Kenneth

2018-06-22

The sequence kernel association test (SKAT) is widely used to test for associations between a phenotype and a set of genetic variants that are usually rare. Evaluating tail probabilities or quantiles of the null distribution for SKAT requires computing the eigenvalues of a matrix related to the genotype covariance between markers. Extracting the full set of eigenvalues of this matrix (an n×n matrix, for n subjects) has computational complexity proportional to n 3 . As SKAT is often used when n>104, this step becomes a major bottleneck in its use in practice. We therefore propose fastSKAT, a new computationally inexpensive but accurate approximations to the tail probabilities, in which the k largest eigenvalues of a weighted genotype covariance matrix or the largest singular values of a weighted genotype matrix are extracted, and a single term based on the Satterthwaite approximation is used for the remaining eigenvalues. While the method is not particularly sensitive to the choice of k, we also describe how to choose its value, and show how fastSKAT can automatically alert users to the rare cases where the choice may affect results. As well as providing faster implementation of SKAT, the new method also enables entirely new applications of SKAT that were not possible before; we give examples grouping variants by topologically associating domains, and comparing chromosome-wide association by class of histone marker. © 2018 WILEY PERIODICALS, INC.

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

NASA Astrophysics Data System (ADS)

Ahmed, S. Jbara; Zulkafli, Othaman; M, A. Saeed

2016-05-01

Based on the Schrödinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients. Project supported by the Ministry of Higher Education and Scientific Research in Iraq, Ibnu Sina Institute and Physics Department of Universiti Teknologi Malaysia (UTM RUG Vote No. 06-H14).

Assessment of diffusion tensor imaging indices in calf muscles following postural change from standing to supine position.

PubMed

Elzibak, Alyaa H; Noseworthy, Michael D

2014-10-01

To investigate whether postural change from erect to recumbent position affects calf muscle water diffusivity. Ten healthy adults (27.2 ± 4.9 years, 3 females) were imaged at baseline (following assumption of recumbent position), and after 34 min (session 2) and 64 min (session 3) of laying supine within a 3T MRI scanner. Diffusion tensor imaging (DTI) eigenvalues, fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were evaluated in five calf muscles (anterior and posterior tibialis and triceps surae) during each of the three imaging sessions. Significant decreases were observed in all of the eigenvalues and ADC in each of the muscles with postural change. These reductions ranged from 3.2 to 6.7% and 3.4 to 7.5% for the various DTI metrics, following 34 and 64 min of supine rest, respectively (P < 0.05). No significant differences were noted in ADC or eigenvalues between the second and third imaging sessions for any muscle. FA did not change significantly with postural manipulation in any muscle compartment. Diffusion tensor imaging indices were altered with postural change. As differences were not apparent between the latter two imaging sessions, we suggest that a short supine resting period (~34 min) is sufficient for muscle diffusivity to stabilize prior to quantitative MR imaging in healthy young adults.

Stellarator Saddle Coils

NASA Astrophysics Data System (ADS)

Boozer, Allen H.

1999-11-01

Modern stellarators are designed using J. Nuehrenberg’s method of varying Fourier coefficients in the shape of the plasma boundary to maximize a target function. The matrix of second derivatives of the target function at the optimum determines a quality matrix. This matrix gives the degradation in the quality of the configuration as the normal magnetic field is varied on a control surface, which lies on or outside the plasma surface. The task is finding saddle coils that produce the desired configuration in the presence of a given toroidal field. An eigenvector of the quality matrix can be important for two reasons: (1) the normal field that must be produced by the saddles is large or (2) the eigenvalue is large (an island-causing resonant perturbation). The rank of the important part of the quality matrix is the number of important eigenvectors. The current in each saddle coil produces a normal field on the control surface, which can be described by an inductance matrix. The relevant part of the inductance matrix has large eigenvalues. The coils can produce the configuration if the rank of the important part of the quality matrix and its product with the relevant part of the inductance matrix are the same. Existing coil design codes, pioneered by P. Merkel, approximate the quality matrix by the unit matrix. Stellarator flexibility could be enhanced by using a more realistic quality matrix and by using trim coils to balance large eigenvalues.

Contrasting eigenvalue and singular-value spectra for lasing and antilasing in a PT -symmetric periodic structure

NASA Astrophysics Data System (ADS)

Ge, Li; Feng, Liang

2017-01-01

It has been proposed and demonstrated that lasing and coherent perfect absorption (CPA or "antilasing") coexist in parity-time (PT ) symmetric photonic systems. In this work we show that the spectral signature of such a CPA laser displayed by the singular value spectrum of the scattering matrix (S ) can be orders of magnitude wider than that displayed by the eigenvalue spectrum of S . Since the former reflects how strongly light can be absorbed or amplified and the latter announces the spontaneous symmetry breaking of S , these contrasting spectral signatures indicate that near perfect absorption and extremely strong amplification can be achieved even in the PT -symmetric phase of S , which is known for and defined by its flux-conserving eigenstates. We also show that these contrasting spectral signatures are accompanied by strikingly different sensitivities to disorder and imperfection, suggesting that the eigenvalue spectrum is potentially suitable for sensing and the singular value spectrum for robust switching. A differential light amplifier may also be devised based on these two spectra.

Development of a Microsoft Excel tool for applying a factor retention criterion of a dimension coefficient to a survey on patient safety culture.

PubMed

Chien, Tsair-Wei; Shao, Yang; Jen, Dong-Hui

2017-10-27

Many quality-of-life studies have been conducted in healthcare settings, but few have used Microsoft Excel to incorporate Cronbach's α with dimension coefficient (DC) for describing a scale's characteristics. To present a computer module that can report a scale's validity, we manipulated datasets to verify a DC that can be used as a factor retention criterion for demonstrating its usefulness in a patient safety culture survey (PSC). Microsoft Excel Visual Basic for Applications was used to design a computer module for simulating 2000 datasets fitting the Rasch rating scale model. The datasets consisted of (i) five dual correlation coefficients (correl. = 0.3, 0.5, 0.7, 0.9, and 1.0) on two latent traits (i.e., true scores) following a normal distribution and responses to their respective 1/3 and 2/3 items in length; (ii) 20 scenarios of item lengths from 5 to 100; and (iii) 20 sample sizes from 50 to 1000. Each item containing 5-point polytomous responses was uniformly distributed in difficulty across a ± 2 logit range. Three methods (i.e., dimension interrelation ≥0.7, Horn's parallel analysis (PA) 95% confidence interval, and individual random eigenvalues) were used for determining one factor to retain. DC refers to the binary classification (1 as one factor and 0 as many factors) used for examining accuracy with the indicators sensitivity, specificity, and area under receiver operating characteristic curve (AUC). The scale's reliability and DC were simultaneously calculated for each simulative dataset. PSC real data were demonstrated with DC to interpret reports of the unit-based construct validity using the author-made MS Excel module. The DC method presented accurate sensitivity (=0.96), specificity (=0.92) with a DC criterion (≥0.70), and AUC (=0.98) that were higher than those of the two PA methods. PA combined with DC yielded good sensitivity (=0.96), specificity (=1.0) with a DC criterion (≥0.70), and AUC (=0.99). Advances in computer technology may enable healthcare users familiar with MS Excel to apply DC as a factor retention criterion for determining a scale's unidimensionality and evaluating a scale's quality.

Analysis techniques for multivariate root loci. [a tool in linear control systems

NASA Technical Reports Server (NTRS)

Thompson, P. M.; Stein, G.; Laub, A. J.

1980-01-01

Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.

Detection of Wind Turbine Power Performance Abnormalities Using Eigenvalue Analysis

DTIC Science & Technology

2014-12-23

area, Cp is the power coefficient, β is the blade-pitch angle, λ is the tip-speed ra- tio and u is the wind speed (Lydia, Selvakumar , Kumar, & Kumar...2013). Furthermore, the air density ρ is equal to: ρ = p RT (2) where p is the absolute air pressure and R is the specific gas constant; these two...CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2014 2013 conference on. Cios, K. J., Pedrycz, W., Swiniarski, R . W., & Kurgan, L. A

Detection of Wind Turbine Power Performance Abnormalities Using Eigenvalue Analysis

DTIC Science & Technology

2014-10-02

area, Cp is the power coefficient, β is the blade-pitch angle, λ is the tip-speed ra- tio and u is the wind speed (Lydia, Selvakumar , Kumar, & Kumar...2013). Furthermore, the air density ρ is equal to: ρ = p RT (2) where p is the absolute air pressure and R is the specific gas constant; these two...CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2014 2013 conference on. Cios, K. J., Pedrycz, W., Swiniarski, R . W., & Kurgan, L. A

Analytic Regularity and Polynomial Approximation of Parametric and Stochastic Elliptic PDEs

DTIC Science & Technology

2010-05-31

Todor : Finite elements for elliptic problems with stochastic coefficients Comp. Meth. Appl. Mech. Engg. 194 (2005) 205-228. [14] R. Ghanem and P. Spanos...for elliptic partial differential equations with random input data SIAM J. Num. Anal. 46(2008), 2411–2442. [20] R. Todor , Robust eigenvalue computation...for smoothing operators, SIAM J. Num. Anal. 44(2006), 865– 878. [21] Ch. Schwab and R.A. Todor , Karhúnen-Loève Approximation of Random Fields by

Analytical approach to peel stresses in bonded composite stiffened panels

NASA Technical Reports Server (NTRS)

Barkey, Derek A.; Madan, Ram C.; Sutton, Jason O.

1987-01-01

A closed-form solution was obtained for the stresses and displacements of two bonded beams. A system of two fourth-order and two second-order differential equations with the associated boundary equations was determined using a variational work approach. A FORTRAN computer program was devised to solve for the eigenvalues and eigenvectors of this system and to calculate the coefficients from the boundary conditions. The results were then compared with NASTRAN finite-element solutions and shown to agree closely.

The Shock and Vibration Bulletin. Part 2. Vibration Analysis.

DTIC Science & Technology

1977-09-01

Spring, MD and J.C.S. Yang, University of Maryland, College Park, MD APPLICATION O LIGHT-INITIATED EXPLOSIVE FOR SIMULATING X -RAY BLOWOFF IMPULSE...0.785t to the free end. effectiveness being produced from the For a spring located at the free end poorest ( X /1=1) to the optimal location ( X /L=1...the eigenvalue coefficient ( X /L=0.785). Although accurate support varies from 1.875 for a null spring placement is imperative, the second mode rate to

Influence of parameter changes to stability behavior of rotors

NASA Technical Reports Server (NTRS)

Fritzen, C. P.; Nordmann, R.

1982-01-01

The occurrence of unstable vibrations in rotating machinery requires corrective measures for improvement of the stability behavior. A simple approximate method is represented to find out the influence of parameter changes to the stability behavior. The method is based on an expansion of the eigenvalues in terms of system parameters. Influence coefficients show the effect of structural modifications. The method first of all was applied to simple nonconservative rotor models. It was approved for an unsymmetric rotor of a test rig.

Non-linear vibrations of sandwich viscoelastic shells

NASA Astrophysics Data System (ADS)

Benchouaf, Lahcen; Boutyour, El Hassan; Daya, El Mostafa; Potier-Ferry, Michel

2018-04-01

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

2015-12-15

We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

Periodic solutions for one dimensional wave equation with bounded nonlinearity

NASA Astrophysics Data System (ADS)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

On the solution of two-point linear differential eigenvalue problems. [numerical technique with application to Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Antar, B. N.

1976-01-01

A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.

Krein signature for instability of PT-symmetric states

NASA Astrophysics Data System (ADS)

Chernyavsky, Alexander; Pelinovsky, Dmitry E.

2018-05-01

Krein quantity is introduced for isolated neutrally stable eigenvalues associated with the stationary states in the PT-symmetric nonlinear Schrödinger equation. Krein quantity is real and nonzero for simple eigenvalues but it vanishes if two simple eigenvalues coalesce into a defective eigenvalue. A necessary condition for bifurcation of unstable eigenvalues from the defective eigenvalue is proved. This condition requires the two simple eigenvalues before the coalescence point to have opposite Krein signatures. The theory is illustrated with several numerical examples motivated by recent publications in physics literature.

Sloppy-model universality class and the Vandermonde matrix.

PubMed

Waterfall, Joshua J; Casey, Fergal P; Gutenkunst, Ryan N; Brown, Kevin S; Myers, Christopher R; Brouwer, Piet W; Elser, Veit; Sethna, James P

2006-10-13

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Development of an efficient multigrid method for the NEM form of the multigroup neutron diffusion equation

NASA Astrophysics Data System (ADS)

Al-Chalabi, Rifat M. Khalil

1997-09-01

Development of an improvement to the computational efficiency of the existing nested iterative solution strategy of the Nodal Exapansion Method (NEM) nodal based neutron diffusion code NESTLE is presented. The improvement in the solution strategy is the result of developing a multilevel acceleration scheme that does not suffer from the numerical stalling associated with a number of iterative solution methods. The acceleration scheme is based on the multigrid method, which is specifically adapted for incorporation into the NEM nonlinear iterative strategy. This scheme optimizes the computational interplay between the spatial discretization and the NEM nonlinear iterative solution process through the use of the multigrid method. The combination of the NEM nodal method, calculation of the homogenized, neutron nodal balance coefficients (i.e. restriction operator), efficient underlying smoothing algorithm (power method of NESTLE), and the finer mesh reconstruction algorithm (i.e. prolongation operator), all operating on a sequence of coarser spatial nodes, constitutes the multilevel acceleration scheme employed in this research. Two implementations of the multigrid method into the NESTLE code were examined; the Imbedded NEM Strategy and the Imbedded CMFD Strategy. The main difference in implementation between the two methods is that in the Imbedded NEM Strategy, the NEM solution is required at every MG level. Numerical tests have shown that the Imbedded NEM Strategy suffers from divergence at coarse- grid levels, hence all the results for the different benchmarks presented here were obtained using the Imbedded CMFD Strategy. The novelties in the developed MG method are as follows: the formulation of the restriction and prolongation operators, and the selection of the relaxation method. The restriction operator utilizes a variation of the reactor physics, consistent homogenization technique. The prolongation operator is based upon a variant of the pin power reconstruction methodology. The relaxation method, which is the power method, utilizes a constant coefficient matrix within the NEM non-linear iterative strategy. The choice of the MG nesting within the nested iterative strategy enables the incorporation of other non-linear effects with no additional coding effort. In addition, if an eigenvalue problem is being solved, it remains an eigenvalue problem at all grid levels, simplifying coding implementation. The merit of the developed MG method was tested by incorporating it into the NESTLE iterative solver, and employing it to solve four different benchmark problems. In addition to the base cases, three different sensitivity studies are performed, examining the effects of number of MG levels, homogenized coupling coefficients correction (i.e. restriction operator), and fine-mesh reconstruction algorithm (i.e. prolongation operator). The multilevel acceleration scheme developed in this research provides the foundation for developing adaptive multilevel acceleration methods for steady-state and transient NEM nodal neutron diffusion equations. (Abstract shortened by UMI.)

Brain vascular image segmentation based on fuzzy local information C-means clustering

NASA Astrophysics Data System (ADS)

Hu, Chaoen; Liu, Xia; Liang, Xiao; Hui, Hui; Yang, Xin; Tian, Jie

2017-02-01

Light sheet fluorescence microscopy (LSFM) is a powerful optical resolution fluorescence microscopy technique which enables to observe the mouse brain vascular network in cellular resolution. However, micro-vessel structures are intensity inhomogeneity in LSFM images, which make an inconvenience for extracting line structures. In this work, we developed a vascular image segmentation method by enhancing vessel details which should be useful for estimating statistics like micro-vessel density. Since the eigenvalues of hessian matrix and its sign describes different geometric structure in images, which enable to construct vascular similarity function and enhance line signals, the main idea of our method is to cluster the pixel values of the enhanced image. Our method contained three steps: 1) calculate the multiscale gradients and the differences between eigenvalues of Hessian matrix. 2) In order to generate the enhanced microvessels structures, a feed forward neural network was trained by 2.26 million pixels for dealing with the correlations between multi-scale gradients and the differences between eigenvalues. 3) The fuzzy local information c-means clustering (FLICM) was used to cluster the pixel values in enhance line signals. To verify the feasibility and effectiveness of this method, mouse brain vascular images have been acquired by a commercial light-sheet microscope in our lab. The experiment of the segmentation method showed that dice similarity coefficient can reach up to 85%. The results illustrated that our approach extracting line structures of blood vessels dramatically improves the vascular image and enable to accurately extract blood vessels in LSFM images.

Reformulation and solution of the master equation for multiple-well chemical reactions.

PubMed

Georgievskii, Yuri; Miller, James A; Burke, Michael P; Klippenstein, Stephen J

2013-11-21

We consider an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products. Within this formulation the dynamical phase space consists of only the microscopic populations of the various isomers making up the reactive complex, while the bimolecular reactants and products are treated equally as sources and sinks. This reformulation yields compact expressions for the phenomenological rate coefficients describing all chemical processes, i.e., internal isomerization reactions, bimolecular-to-bimolecular reactions, isomer-to-bimolecular reactions, and bimolecular-to-isomer reactions. The applicability of the detailed balance condition is discussed and confirmed. We also consider the situation where some of the chemical eigenvalues approach the energy relaxation time scale and show how to modify the phenomenological rate coefficients so that they retain their validity.

On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps

NASA Astrophysics Data System (ADS)

Gonchenko, M.; Gonchenko, S. V.; Ovsyannikov, I.; Vieiro, A.

2018-04-01

We study the 1:4 resonance for the conservative cubic Hénon maps C± with positive and negative cubic terms. These maps show up different bifurcation structures both for fixed points with eigenvalues ±i and for 4-periodic orbits. While for C-, the 1:4 resonance unfolding has the so-called Arnold degeneracy [the first Birkhoff twist coefficient equals (in absolute value) to the first resonant term coefficient], the map C+ has a different type of degeneracy because the resonant term can vanish. In the last case, non-symmetric points are created and destroyed at pitchfork bifurcations and, as a result of global bifurcations, the 1:4 resonant chain of islands rotates by π/4. For both maps, several bifurcations are detected and illustrated.

Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

PubMed

Sztepanacz, Jacqueline L; Blows, Mark W

2017-07-01

The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

A simple method for finding the scattering coefficients of quantum graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cottrell, Seth S.

2015-09-15

Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial ofmore » the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected.« less

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

NASA Astrophysics Data System (ADS)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition.

DFT study on oxidation of HS(CH2) m SH ( m = 1-8) in oxidative desulfurization

NASA Astrophysics Data System (ADS)

Song, Y. Z.; Song, J. J.; Zhao, T. T.; Chen, C. Y.; He, M.; Du, J.

2016-06-01

Density functional theory was employed for calculation of HS(CH2) m SH ( m = 1-8) and its derivatives at B3LYP method at 6-31++g ( d, p) level. Using eigenvalues of LUMO and HOMO for HS(CH2) m SH, the standard electrode potentials were estimated by a stepwise multiple regression techniques (MLR), and obtained as E° = 1.500 + 7.167 × 10-3 HOMO-0.229 LUMO with high correlation coefficients of 0.973 and F values of 43.973.

Study of electron-related intersubband optical properties in three coupled quantum wells wires with triangular transversal section

NASA Astrophysics Data System (ADS)

Tiutiunnyk, A.; Tulupenko, V.; Akimov, V.; Demediuk, R.; Morales, A. L.; Mora-Ramos, M. E.; Radu, A.; Duque, C. A.

2015-11-01

This work concerns theoretical study of confined electrons in a low-dimensional structure consisting of three coupled triangular GaAs/AlxGa1-xAs quantum wires. Calculations have been made in the effective mass and parabolic band approximations. In the calculations a diagonalization method to find the eigenfunctions and eigenvalues of the Hamiltonian was used. A comparative analysis of linear and nonlinear optical absorption coefficients and the relative change in the refractive index was made, which is tied to the intersubband electron transitions.

Scattering of Dirac waves off Kerr black holes

NASA Astrophysics Data System (ADS)

Chakrabarti, Sandip K.; Mukhopadhyay, Banibrata

2000-10-01

Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry into radial and angular parts. Here we solve the complete wave equation and find out how the Dirac wave scatters off Kerr black holes. The eigenfunctions, eigenvalues and reflection and transmission co-efficients are computed. We compare the solutions with several parameters to show how a spinning black hole recognizes the mass and energy of incoming waves. Very close to the horizon the solutions become independent of the particle parameters, indicating the universality of the behaviour.

On the modular structure of the genus-one Type II superstring low energy expansion

NASA Astrophysics Data System (ADS)

D'Hoker, Eric; Green, Michael B.; Vanhove, Pierre

2015-08-01

The analytic contribution to the low energy expansion of Type II string amplitudes at genus-one is a power series in space-time derivatives with coefficients that are determined by integrals of modular functions over the complex structure modulus of the world-sheet torus. These modular functions are associated with world-sheet vacuum Feynman diagrams and given by multiple sums over the discrete momenta on the torus. In this paper we exhibit exact differential and algebraic relations for a certain infinite class of such modular functions by showing that they satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series. Furthermore, we argue that the set of modular functions that contribute to the coefficients of interactions up to order are linear sums of functions in this class and quadratic polynomials in Eisenstein series and odd Riemann zeta values. Integration over the complex structure results in coefficients of the low energy expansion that are rational numbers multiplying monomials in odd Riemann zeta values.

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Lucero, John M.

1996-01-01

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

The problem of complex eigensystems in the semianalytical solution for advancement of time in solute transport simulations: a new method using real arithmetic

USGS Publications Warehouse

Umari, Amjad M.J.; Gorelick, Steven M.

1986-01-01

In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

Dynamic of consumer groups and response of commodity markets by principal component analysis

NASA Astrophysics Data System (ADS)

Nobi, Ashadun; Alam, Shafiqul; Lee, Jae Woo

2017-09-01

This study investigates financial states and group dynamics by applying principal component analysis to the cross-correlation coefficients of the daily returns of commodity futures. The eigenvalues of the cross-correlation matrix in the 6-month timeframe displays similar values during 2010-2011, but decline following 2012. A sharp drop in eigenvalue implies the significant change of the market state. Three commodity sectors, energy, metals and agriculture, are projected into two dimensional spaces consisting of two principal components (PC). We observe that they form three distinct clusters in relation to various sectors. However, commodities with distinct features have intermingled with one another and scattered during severe crises, such as the European sovereign debt crises. We observe the notable change of the position of two dimensional spaces of groups during financial crises. By considering the first principal component (PC1) within the 6-month moving timeframe, we observe that commodities of the same group change states in a similar pattern, and the change of states of one group can be used as a warning for other group.

Analysis of cross-correlations between financial markets after the 2008 crisis

NASA Astrophysics Data System (ADS)

Sensoy, A.; Yuksel, S.; Erturk, M.

2013-10-01

We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.

A new method for multi-bit and qudit transfer based on commensurate waveguide arrays

NASA Astrophysics Data System (ADS)

Petrovic, J.; Veerman, J. J. P.

2018-05-01

The faithful state transfer is an important requirement in the construction of classical and quantum computers. While the high-speed transfer is realized by optical-fibre interconnects, its implementation in integrated optical circuits is affected by cross-talk. The cross-talk between densely packed optical waveguides limits the transfer fidelity and distorts the signal in each channel, thus severely impeding the parallel transfer of states such as classical registers, multiple qubits and qudits. Here, we leverage on the suitably engineered cross-talk between waveguides to achieve the parallel transfer on optical chip. Waveguide coupling coefficients are designed to yield commensurate eigenvalues of the array and hence, periodic revivals of the input state. While, in general, polynomially complex, the inverse eigenvalue problem permits analytic solutions for small number of waveguides. We present exact solutions for arrays of up to nine waveguides and use them to design realistic buses for multi-(qu)bit and qudit transfer. Advantages and limitations of the proposed solution are discussed in the context of available fabrication techniques.

A low dimensional dynamical system for the wall layer

NASA Technical Reports Server (NTRS)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections.

PubMed

Foldnes, Njål; Olsson, Ulf Henning

2015-01-01

This simulation study investigates the performance of three test statistics, T1, T2, and T3, used to evaluate structural equation model fit under non normal data conditions. T1 is the well-known mean-adjusted statistic of Satorra and Bentler. T2 is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T3 is a recently proposed version of T2 that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T1 and under-rejected by T2 and T3, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T2 and T3. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.

Diffusion Properties and 3D Architecture of Human Lower Leg Muscles Assessed with Ultra-High-Field-Strength Diffusion-Tensor MR Imaging and Tractography: Reproducibility and Sensitivity to Sex Difference and Intramuscular Variability.

PubMed

Fouré, Alexandre; Ogier, Augustin C; Le Troter, Arnaud; Vilmen, Christophe; Feiweier, Thorsten; Guye, Maxime; Gondin, Julien; Besson, Pierre; Bendahan, David

2018-05-01

Purpose To demonstrate the reproducibility of the diffusion properties and three-dimensional structural organization measurements of the lower leg muscles by using diffusion-tensor imaging (DTI) assessed with ultra-high-field-strength (7.0-T) magnetic resonance (MR) imaging and tractography of skeletal muscle fibers. On the basis of robust statistical mapping analyses, this study also aimed at determining the sensitivity of the measurements to sex difference and intramuscular variability. Materials and Methods All examinations were performed with ethical review board approval; written informed consent was obtained from all volunteers. Reproducibility of diffusion tensor indexes assessment including eigenvalues, mean diffusivity, and fractional anisotropy (FA) as well as muscle volume and architecture (ie, fiber length and pennation angle) were characterized in lower leg muscles (n = 8). Intramuscular variability and sex differences were characterized in young healthy men and women (n = 10 in each group). Student t test, statistical parametric mapping, correlation coefficients (Spearman rho and Pearson product-moment) and coefficient of variation (CV) were used for statistical data analysis. Results High reproducibility of measurements (mean CV ± standard deviation, 4.6% ± 3.8) was determined in diffusion properties and architectural parameters. Significant sex differences were detected in FA (4.2% in women for the entire lower leg; P = .001) and muscle volume (21.7% in men for the entire lower leg; P = .008), whereas architecture parameters were almost identical across sex. Additional differences were found independently of sex in diffusion properties and architecture along several muscles of the lower leg. Conclusion The high-spatial-resolution DTI assessed with 7.0-T MR imaging allows a reproducible assessment of structural organization of superficial and deep muscles, giving indirect information on muscle function. © RSNA, 2018 Online supplemental material is available for this article.

Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem

DOE PAGES

Shao, Meiyue; da Jornada, Felipe H.; Yang, Chao; ...

2015-10-02

The Bethe–Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe–Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice. In this paper, we establish the equivalence between Bethe–Salpeter eigenvalue problems and real Hamiltonian eigenvalue problems. Based on theoretical analysis, structure preserving algorithms for a class of Bethe–Salpeter eigenvalue problems are proposed. We also show that for this class of problems all eigenvalues obtained from the Tamm–Dancoff approximation are overestimated. In order to solve large scale problemsmore » of practical interest, we discuss parallel implementations of our algorithms targeting distributed memory systems. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms.« less

Observer-Pattern Modeling and Slow-Scale Bifurcation Analysis of Two-Stage Boost Inverters

NASA Astrophysics Data System (ADS)

Zhang, Hao; Wan, Xiaojin; Li, Weijie; Ding, Honghui; Yi, Chuanzhi

2017-06-01

This paper deals with modeling and bifurcation analysis of two-stage Boost inverters. Since the effect of the nonlinear interactions between source-stage converter and load-stage inverter causes the “hidden” second-harmonic current at the input of the downstream H-bridge inverter, an observer-pattern modeling method is proposed by removing time variance originating from both fundamental frequency and hidden second harmonics in the derived averaged equations. Based on the proposed observer-pattern model, the underlying mechanism of slow-scale instability behavior is uncovered with the help of eigenvalue analysis method. Then eigenvalue sensitivity analysis is used to select some key system parameters of two-stage Boost inverter, and some behavior boundaries are given to provide some design-oriented information for optimizing the circuit. Finally, these theoretical results are verified by numerical simulations and circuit experiment.

Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research.

PubMed

Waller, Niels G

2016-01-01

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

Quantum Hurwitz numbers and Macdonald polynomials

NASA Astrophysics Data System (ADS)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Comparison of scalar measures used in magnetic resonance diffusion tensor imaging.

PubMed

Bahn, M M

1999-07-01

The tensors derived from diffusion tensor imaging describe complex diffusion in tissues. However, it is difficult to compare tensors directly or to produce images that contain all of the information of the tensor. Therefore, it is convenient to produce scalar measures that extract desired aspects of the tensor. These measures map the three-dimensional eigenvalues of the diffusion tensor into scalar values. The measures impose an order on eigenvalue space. Many invariant scalar measures have been introduced in the literature. In the present manuscript, a general approach for producing invariant scalar measures is introduced. Because it is often difficult to determine in clinical practice which of the many measures is best to apply to a given situation, two formalisms are introduced for the presentation, definition, and comparison of measures applied to eigenvalues: (1) normalized eigenvalue space, and (2) parametric eigenvalue transformation plots. All of the anisotropy information contained in the three eigenvalues can be retained and displayed in a two-dimensional plot, the normalized eigenvalue plot. An example is given of how to determine the best measure to use for a given situation by superimposing isometric contour lines from various anisotropy measures on plots of actual measured eigenvalue data points. Parametric eigenvalue transformation plots allow comparison of how different measures impose order on normalized eigenvalue space to determine whether the measures are equivalent and how the measures differ. These formalisms facilitate the comparison of scalar invariant measures for diffusion tensor imaging. Normalized eigenvalue space allows presentation of eigenvalue anisotropy information. Copyright 1999 Academic Press.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages.

PubMed

Bienvenu, François; Akçay, Erol; Legendre, Stéphane; McCandlish, David M

2017-06-01

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units. Copyright © 2017 Elsevier Inc. All rights reserved.

Large computer simulations on elastic networks: Small eigenvalues and eigenvalue spectra of the Kirchhoff matrix

NASA Astrophysics Data System (ADS)

Shy, L. Y.; Eichinger, B. E.

1989-05-01

Computer simulations of the formation of trifunctional and tetrafunctional polydimethyl-siloxane networks that are crosslinked by condensation of telechelic chains with multifunctional crosslinking agents have been carried out on systems containing up to 1.05×106 chains. Eigenvalue spectra of Kirchhoff matrices for these networks have been evaluated at two levels of approximation: (1) inclusion of all midchain modes, and (2) suppression of midchain modes. By use of the recursion method of Haydock and Nex, we have been able to effectively diagonalize matrices with 730 498 rows and columns without actually constructing matrices of this size. The small eigenvalues have been computed by use of the Lanczos algorithm. We demonstrate the following results: (1) The smallest eigenvalues (with chain modes suppressed) vary as μ-2/3 for sufficiently large μ, where μ is the number of junctions in the network; (2) the eigenvalue spectra of the Kirchhoff matrices are well described by McKay's theory for random regular graphs in the range of the larger eigenvalues, but there are significant departures in the region of small eigenvalues where computed spectra have many more small eigenvalues than random regular graphs; (3) the smallest eigenvalues vary as n-1.78 where n is the number of Rouse beads in the chains that comprise the network. Computations are done for both monodisperse and polydisperse chain length distributions. Large eigenvalues associated with localized motion of the junctions are found as predicted by theory. The relationship between the small eigenvalues and the equilibrium modulus of elasticity is discussed, as is the relationship between viscoelasticity and the band edge of the spectrum.

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

NASA Technical Reports Server (NTRS)

Jara-Almonte, J.; Mitchell, L. D.

1988-01-01

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Aeroelastic modal characteristics of mistuned blade assemblies: Mode localization and loss of eigenstructure

NASA Technical Reports Server (NTRS)

Pierre, Christophe; Murthy, Durbha V.

1991-01-01

An investigation of the effects of small mistuning on the aeroelastic modes of bladed disk assemblies with aerodynamic coupling between blades is presented. The cornerstone of the approach is the use and development of perturbation methods that exhibit the crucial role of the interblade coupling and yield general findings regarding mistuning effects. It is shown that blade assemblies with weak aerodynamic interblade coupling are highly sensitive to small blade mistuning, and that their dynamics is quantitatively altered in the following ways: the regular pattern that characterizes the root locus of the tuned aeroelastic eigenvalues in the complex plane is totally lost; the aeroelastic mode shapes becomes severely localized to only a few blades of the assembly and lose their constant interblade phase angle feature; and curve veering phenomena take place when the eigenvalues are plotted versus a mistuning parameter.

Modal interaction in linear dynamic systems near degenerate modes

NASA Technical Reports Server (NTRS)

Afolabi, D.

1991-01-01

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Aircraft model prototypes which have specified handling-quality time histories

NASA Technical Reports Server (NTRS)

Johnson, S. H.

1978-01-01

Several techniques for obtaining linear constant-coefficient airplane models from specified handling-quality time histories are discussed. The pseudodata method solves the basic problem, yields specified eigenvalues, and accommodates state-variable transfer-function zero suppression. The algebraic equations to be solved are bilinear, at worst. The disadvantages are reduced generality and no assurance that the resulting model will be airplane like in detail. The method is fully illustrated for a fourth-order stability-axis small motion model with three lateral handling quality time histories specified. The FORTRAN program which obtains and verifies the model is included and fully documented.

On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

Transmission eigenvalues

NASA Astrophysics Data System (ADS)

Cakoni, Fioralba; Haddar, Houssem

2013-10-01

In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission eigenvalue problem. The need to answer these questions became important after a series of papers by Cakoni et al [5], and Cakoni et al [6] suggesting that these transmission eigenvalues could be used to obtain qualitative information about the material properties of the scattering object from far-field data. The first answer to the existence of transmission eigenvalues in the general case was given in 2008 when Päivärinta and Sylvester showed the existence of transmission eigenvalues for the index of refraction sufficiently large [7] followed in 2010 by the paper of Cakoni et al who removed the size restriction on the index of refraction [8]. More importantly, in the latter it was shown that transmission eigenvalues yielded qualitative information on the material properties of the scattering object and Cakoni et al established in [9] that transmission eigenvalues could be determined from the Tikhonov regularized solution of the far-field equation. Since the appearance of these papers there has been an explosion of interest in the transmission eigenvalue problem (we refer the reader to our recent survey paper [10] for a detailed account of the developments in this field up to 2012) and the papers in this special issue are representative of the myriad directions that this research has taken. Indeed, we are happy to see that many open theoretical and numerical questions raised in [10] have been answered (totally or partially) in the contributions of this special issue: the existence of transmission eigenvalues with minimal assumptions on the contrast, the numerical evaluation of transmission eigenvalues, the inverse spectral problem, applications to non-destructive testing, etc. In addition to these topics, many other new investigations and research directions have been proposed as we shall see in the brief content summary below. A number of papers in this special issue are concerned with the question of existence of transmission eigenvalues and the structure of the associated transmission eigenfunctions. The three papers by respectively Robbiano [11], Blasten and Päivärinta [12], and Lakshtanov and Vainberg [13] provide new complementary results on the existence of transmission eigenvalues for the scalar problem under weak assumptions on the (possibly complex valued) refractive index that mainly stipulates that the contrast does not change sign on the boundary. It is interesting here to see three different new methods to obtain these results. On the other hand, the paper by Bonnet-Ben Dhia and Chesnel [14] addresses the Fredholm properties of the interior transmission problem when the contrast changes sign on the boundary, exhibiting cases where this property fails. Using more standard approaches, the existence and structure of transmission eigenvalues are analyzed in the paper by Delbary [15] for the case of frequency dependent materials in the context of Maxwell's equations, whereas the paper by Vesalainen [16] initiates the study of the transmission eigenvalue problem in unbounded domains by considering the transmission eigenvalues for Schrödinger equation with non-compactly supported potential. The paper by Monk and Selgas [17] addresses the case where the dielectric is mounted on a perfect conductor and provides some numerical examples of the localization of associated eigenvalues using the linear sampling method. A series of papers then addresses the question of localization of transmission eigenvalues and the associated inverse spectral problem for spherically stratified media. More specifically, the paper by Colton and Leung [18] provides new results on complex transmission eigenvalues and a new proof for uniqueness of a solution to the inverse spectral problem, whereas the paper by Sylvester [19] provides sharp results on how to locate all the transmission eigenvalues associated with angular independent eigenfunctions when the index of refraction is constant. The paper by Gintides and Pallikarakis [20] investigates an iterative least square method to identify the spherically stratified index of refraction from transmission eigenvalues. On the characterization of transmission eigenvalues in terms of far-field measurements, a promising new result is obtained by Kirsch and Lechleiter [21] showing how one can identify the transmission eigenvalues using the eigenvalues of the scattering operator which are available in terms of measured scattering data. In the paper by Kleefeld [22], an accurate method for computing transmission eigenvalues based on a surface integral formulation of the interior transmission problem and numerical methods for nonlinear eigenvalue problems is proposed and numerically validated for the scalar problem in three dimensions. On the other hand, the paper by Sun and Xu [23] investigates the computation of transmission eigenvalues for Maxwell's equations using a standard iterative method associated with a variational formulation of the interior transmission problem with an emphasis on the effect of anisotropy on transmission eigenvalues. From the perspective of using transmission eigenvalues in non-destructive testing, the paper by Cakoni and Moskow [24] investigates the asymptotic behavior of transmission eigenvalues with respect to small inhomogeneities. The paper by Nakamura and Wang [25] investigates the linear sampling method for the time dependent heat equation and analyses the interior transmission problem associated with this equation. Finally, in the paper by Finch and Hickmann [26], the spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. We hope that this collection of papers will stimulate further research in the rapidly growing area of transmission eigenvalues and inverse scattering theory.

New sets of eigenvalues in inverse scattering for inhomogeneous media and their determination from scattering data

NASA Astrophysics Data System (ADS)

Audibert, Lorenzo; Cakoni, Fioralba; Haddar, Houssem

2017-12-01

In this paper we develop a general mathematical framework to determine interior eigenvalues from a knowledge of the modified far field operator associated with an unknown (anisotropic) inhomogeneity. The modified far field operator is obtained by subtracting from the measured far field operator the computed far field operator corresponding to a well-posed scattering problem depending on one (possibly complex) parameter. Injectivity of this modified far field operator is related to an appropriate eigenvalue problem whose eigenvalues can be determined from the scattering data, and thus can be used to obtain information about material properties of the unknown inhomogeneity. We discuss here two examples of such modification leading to a Steklov eigenvalue problem, and a new type of the transmission eigenvalue problem. We present some numerical examples demonstrating the viability of our method for determining the interior eigenvalues form far field data.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

Galerkin analysis of kinematic dynamos in the von Kármán geometry

NASA Astrophysics Data System (ADS)

Marié, L.; Normand, C.; Daviaud, F.

2006-01-01

We investigate dynamo action by solving the kinematic dynamo problem for velocity fields of the von Kármán type between two coaxial counter-rotating propellers in a cylinder. A Galerkin method is implemented that takes advantage of the symmetries of the flow and their subsequent influence on the nature of the magnetic field at the dynamo threshold. Distinct modes of instability have been identified that differ by their spatial and temporal behaviors. Our calculations give the result that a stationary and antisymmetric mode prevails at the dynamo threshold. We then present a quantitative analysis of the results based on the parametric study of four interaction coefficients obtained by reduction of our initially large eigenvalue problem. We propose these coefficients to measure the relative importance of the different mechanisms at play in the von Kármán kinematic dynamo.

Two-electron bond-orbital model, 1

NASA Technical Reports Server (NTRS)

Huang, C.; Moriarty, J. A.; Sher, A.; Breckenridge, R. A.

1975-01-01

Harrison's one-electron bond-orbital model of tetrahedrally coordinated solids was generalized to a two-electron model, using an extension of the method of Falicov and Harris for treating the hydrogen molecule. The six eigenvalues and eigenstates of the two-electron anion-cation Hamiltonian entering this theory can be found exactly general. The two-electron formalism is shown to provide a useful basis for calculating both non-magnetic and magnetic properties of semiconductors in perturbation theory. As an example of the former, expressions for the electric susceptibility and the dielectric constant were calculated. As an example of the latter, new expressions for the nuclear exchanges and pseudo-dipolar coefficients were calculated. A simple theoretical relationship between the dielectric constant and the exchange coefficient was also found in the limit of no correlation. These expressions were quantitatively evaluated in the limit of no correlation for twenty semiconductors.

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Experimental observation of the topological structure of exceptional points in an ultrathin hybridized metamaterial

NASA Astrophysics Data System (ADS)

Kang, Ming; Zhu, Weiren; Rukhlenko, Ivan D.

2017-12-01

The exceptional point (EP), which is one of the most important branch-type singularities exclusive to non-Hermitian systems, has been observed recently in various synthetic materials, giving rise to counterintuitive phenomena due to the nontrivial topology of the EP. Here, we present a direct experimental observation of the topological structure of the EPs via the angle-resolved transmission measurement of a hybridized metamaterial. Both eigenvalues and eigenvectors show branch-point singularities in the investigated biparametric space of frequency and incident angle. Importantly, the angle-resolved transmission coefficients provide all the information about the eigenvalues as well as the corresponding eigenvectors in the biparametric space, revealing the nontrivial topological structure of the EP, such as mode switching and the topological phase for a parameter loop encircling the EP. It is shown that the appearance of the EP in the scattering matrix is related directly to the perfect unidirectional transmission and the chirality of the EP corresponds to the maximum or minimum value of the asymmetric factor. Our investigation uncovers the capabilities of metamaterials for exploring the physics of EPs and their potential for having extreme optical properties, which provide potential applications in the spectral band ranging from microwaves to visible frequencies.

Eigenvalues of the Wentzell-Laplace operator and of the fourth order Steklov problems

NASA Astrophysics Data System (ADS)

Xia, Changyu; Wang, Qiaoling

2018-05-01

We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Steklov problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Steklov problems on a Euclidean ball.

Finite-difference solution of the compressible stability eigenvalue problem

NASA Technical Reports Server (NTRS)

Malik, M. R.

1982-01-01

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Diffusion tensor imaging and 1H-MRS study on radiation-induced brain injury after nasopharyngeal carcinoma radiotherapy.

PubMed

Wang, H-Z; Qiu, S-J; Lv, X-F; Wang, Y-Y; Liang, Y; Xiong, W-F; Ouyang, Z-B

2012-04-01

To investigate the metabolic characteristics of the temporal lobes following radiation therapy for nasopharyngeal carcinoma using diffusion tensor imaging (DTI) and proton magnetic resonance spectroscopy ((1)H-MRS). DTI and (1)H-MRS were performed in 48 patients after radiotherapy for nasopharyngeal carcinoma and in 24 healthy, age-matched controls. All patients and controls had normal findings on conventional MRI. Apparent diffusion coefficient (ADC), fractional anisotropy (FA), three eigenvalues λ1, λ2, λ3, N-acetylaspartic acid (NAA)/choline (Cho), NAA/creatinine (Cr), and Cho/Cr were measured in both temporal lobes. Patients were divided into three groups according to time after completion of radiotherapy: group 1, less than 6 months; group 2, 6-12 months; group 3, more than 12 months. Mean values for each parameter were compared using one-way analysis of variance (ANOVA). Mean FA in group 1 was significantly lower compared to group 3 and the control group (p < 0.05). Group-wise comparisons of apparent diffusion coefficient (ADC) values among all the groups were not significantly different. Eigenvalue λ1 was significantly lower in groups 1 and 3 compared to the control group (p < 0.05). NAA/Cho and NAA/Cr were significantly lower in each group compared to the control group (p < 0.01 for both). The decrease in NAA/Cho was greatest in group 1. There were no significant between-group differences regarding Cho/Cr. A combination of DTI and (1)H-MRS can be used to detect radiation-induced brain injury, in patients treated for nasopharyngeal carcinoma. Copyright © 2011 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.

Select-divide-and-conquer method for large-scale configuration interaction

NASA Astrophysics Data System (ADS)

Bunge, Carlos F.; Carbó-Dorca, Ramon

2006-07-01

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,…,SR. S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds T0≡{T0egy,T0etc.}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above T1⩽T0. An eigenproblem of dimension d0+d1 for S0+S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j ⩾2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {Tj;j=0,1,2,…,R} regulate accuracy; for large-dimensional S, high accuracy requires S0+S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One μhartree accuracy is achieved for an eigenproblem of order 24×106, involving 1.2×1012 nonzero matrix elements, and 8.4×109 Slater determinants.

Statistical dynamo theory: Mode excitation.

PubMed

Hoyng, P

2009-04-01

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Type I and Type II Error Rates and Overall Accuracy of the Revised Parallel Analysis Method for Determining the Number of Factors

ERIC Educational Resources Information Center

Green, Samuel B.; Thompson, Marilyn S.; Levy, Roy; Lo, Wen-Juo

2015-01-01

Traditional parallel analysis (T-PA) estimates the number of factors by sequentially comparing sample eigenvalues with eigenvalues for randomly generated data. Revised parallel analysis (R-PA) sequentially compares the "k"th eigenvalue for sample data to the "k"th eigenvalue for generated data sets, conditioned on"k"-…

EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.

PubMed

Tal-Ezer, Hillel

2016-05-19

Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.

Eigenvalue density of cross-correlations in Sri Lankan financial market

NASA Astrophysics Data System (ADS)

Nilantha, K. G. D. R.; Ranasinghe; Malmini, P. K. C.

2007-05-01

We apply the universal properties with Gaussian orthogonal ensemble (GOE) of random matrices namely spectral properties, distribution of eigenvalues, eigenvalue spacing predicted by random matrix theory (RMT) to compare cross-correlation matrix estimators from emerging market data. The daily stock prices of the Sri Lankan All share price index and Milanka price index from August 2004 to March 2005 were analyzed. Most eigenvalues in the spectrum of the cross-correlation matrix of stock price changes agree with the universal predictions of RMT. We find that the cross-correlation matrix satisfies the universal properties of the GOE of real symmetric random matrices. The eigen distribution follows the RMT predictions in the bulk but there are some deviations at the large eigenvalues. The nearest-neighbor spacing and the next nearest-neighbor spacing of the eigenvalues were examined and found that they follow the universality of GOE. RMT with deterministic correlations found that each eigenvalue from deterministic correlations is observed at values, which are repelled from the bulk distribution.

Vibration properties of a rotating piezoelectric energy harvesting device that experiences gyroscopic effects

NASA Astrophysics Data System (ADS)

Lu, Haohui; Chai, Tan; Cooley, Christopher G.

2018-03-01

This study investigates the vibration of a rotating piezoelectric device that consists of a proof mass that is supported by elastic structures with piezoelectric layers. Vibration of the proof mass causes deformation in the piezoelectric structures and voltages to power the electrical loads. The coupled electromechanical equations of motion are derived using Newtonian mechanics and Kirchhoff's circuit laws. The free vibration behavior is investigated for devices with identical (tuned) and nonidentical (mistuned) piezoelectric support structures and electrical loads. These devices have complex-valued, speed-dependent eigenvalues and eigenvectors as a result of gyroscopic effects caused by their constant rotation. The characteristics of the complex-valued eigensolutions are related to physical behavior of the device's vibration. The free vibration behaviors differ significantly for tuned and mistuned devices. Due to gyroscopic effects, the proof mass in the tuned device vibrates in either forward or backward decaying circular orbits in single-mode free response. This is proven analytically for all tuned devices, regardless of the device's specific parameters or operating speed. For mistuned devices, the proof mass has decaying elliptical forward and backward orbits. The eigenvalues are shown to be sensitive to changes in the electrical load resistances. Closed-form solutions for the eigenvalues are derived for open and close circuits. At high rotation speeds these devices experience critical speeds and instability.

Calculation of transmission probability by solving an eigenvalue problem

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Varga, Kálmán

2010-11-01

The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

Computationally robust and noise resistant numerical detector for the detection of atmospheric infrasound.

PubMed

Lee, Dong-Chang; Olson, John V; Szuberla, Curt A L

2013-07-01

This work reports on a performance study of two numerical detectors that are particularly useful for infrasound arrays operating under windy conditions. The sum of squares of variance ratios (SSVR1)-proposed for detecting signals with frequency ranging from 1 to 10 Hz-is computed by taking the ratio of the squared sum of eigenvalues to the square of largest eigenvalue of the covariance matrix of the power spectrum. For signals with lower frequency between 0.015 and 0.1 Hz, SSVR2 is developed to reduce the detector's sensitivity to noise. The detectors' performances are graphically compared against the current method, the mean of cross correlation maxima (MCCM), using the receiver operating characteristics curves and three types of atmospheric infrasound, corrupted by Gaussian and Pink noise. The MCCM and SSVR2 detectors were also used to detect microbaroms from the 24 h-long infrasound data. It was found that the two detectors outperform the MCCM detector in both sensitivity and computational efficiency. For mine blasts corrupted by Pink noise (signal-to-noise ratio = -7 dB), the MCCM and SSVR1 detectors yield 62 and 88 % true positives when accepting 20% false positives. For an eight-sensor array, the speed gain is approximately eleven-fold for a 50 s long signal.

A numerical projection technique for large-scale eigenvalue problems

NASA Astrophysics Data System (ADS)

Gamillscheg, Ralf; Haase, Gundolf; von der Linden, Wolfgang

2011-10-01

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large-scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.

Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Electron transport near the Mott transition in n-GaAs and n-GaN

NASA Astrophysics Data System (ADS)

Romanets, P. N.; Sachenko, A. V.

2016-01-01

In this paper, we study the temperature dependence of the conductivity and the Hall coefficient near the metal-insulator phase transition. A theoretical investigation is performed within the effective mass approximation. The variational method is used to calculate the eigenvalues and eigenfunctions of the impurity states. Unlike previous studies, we have included nonlinear corrections to the screened impurity potential, because the Thomas-Fermi approximation is incorrect for the insulator phase. It is also shown that near the phase transition the exchange interaction is essential. The obtained temperature dependencies explain several experimental measurements in gallium arsenide (GaAs) and gallium nitride (GaN).

Evidence of tampering in watermark identification

NASA Astrophysics Data System (ADS)

McLauchlan, Lifford; Mehrübeoglu, Mehrübe

2009-08-01

In this work, watermarks are embedded in digital images in the discrete wavelet transform (DWT) domain. Principal component analysis (PCA) is performed on the DWT coefficients. Next higher order statistics based on the principal components and the eigenvalues are determined for different sets of images. Feature sets are analyzed for different types of attacks in m dimensional space. The results demonstrate the separability of the features for the tampered digital copies. Different feature sets are studied to determine more effective tamper evident feature sets. The digital forensics, the probable manipulation(s) or modification(s) performed on the digital information can be identified using the described technique.

Cg/Stability Map for the Reference H Cycle 3 Supersonic Transport Concept Along the High Speed Research Baseline Mission Profile

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Christhilf, David M.

1999-01-01

A comparison is made between the results of trimming a High Speed Civil Transport (HSCT) concept along a reference mission profile using two trim modes. One mode uses the stabilator. The other mode uses fore and aft placement of the center of gravity. A comparison is make of the throttle settings (cruise segments) or the total acceleration (ascent and descent segments) and of the drag coefficient. The comparative stability of trimming using the two modes is also assessed by comparing the stability margins and the placement of the lateral and longitudinal eigenvalues.

Ab initio calculation of one-nucleon halo states

NASA Astrophysics Data System (ADS)

Rodkin, D. M.; Tchuvil'sky, Yu M.

2018-02-01

We develop an approach to microscopic and ab initio description of clustered systems, states with halo nucleon and one-nucleon resonances. For these purposes a basis combining ordinary shell-model components and cluster-channel terms is built up. The transformation of clustered wave functions to the uniform Slater-determinant type is performed using the concept of cluster coefficients. The resulting basis of orthonormalized wave functions is used for calculating the eigenvalues and the eigenvectors of Hamiltonians built in the framework of ab initio approaches. Calculations of resonance and halo states of 5He, 9Be and 9B nuclei demonstrate that the approach is workable and labor-saving.

Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications

NASA Astrophysics Data System (ADS)

Julaiti, Alafate; Wu, Bin; Zhang, Zhongzhi

2013-05-01

The eigenvalues of the normalized Laplacian matrix of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian matrices of a family of fractal trees and dendrimers modeled by Cayley trees, both of which are built in an iterative way. For the fractal trees, we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities, with the eigenvalues provided by a recursive relation governing the eigenvalues of networks at two successive generations. For Cayley trees, we show that all their eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. By using the relation between normalized Laplacian spectra and eigentime identity, we derive the explicit solution to the eigentime identity for random walks on the two treelike networks, the leading scalings of which follow quite different behaviors. In addition, we corroborate the obtained eigenvalues and their degeneracies through the link between them and the number of spanning trees.

Calibration test of the temperature and strain sensitivity coefficient in regional reference grating method

NASA Astrophysics Data System (ADS)

Wu, Jing; Huang, Junbing; Wu, Hanping; Gu, Hongcan; Tang, Bo

2014-12-01

In order to verify the validity of the regional reference grating method in solve the strain/temperature cross sensitive problem in the actual ship structural health monitoring system, and to meet the requirements of engineering, for the sensitivity coefficients of regional reference grating method, national standard measurement equipment is used to calibrate the temperature sensitivity coefficient of selected FBG temperature sensor and strain sensitivity coefficient of FBG strain sensor in this modal. And the thermal expansion sensitivity coefficient of the steel for ships is calibrated with water bath method. The calibration results show that the temperature sensitivity coefficient of FBG temperature sensor is 28.16pm/°C within -10~30°C, and its linearity is greater than 0.999, the strain sensitivity coefficient of FBG strain sensor is 1.32pm/μɛ within -2900~2900μɛ whose linearity is almost to 1, the thermal expansion sensitivity coefficient of the steel for ships is 23.438pm/°C within 30~90°C, and its linearity is greater than 0.998. Finally, the calibration parameters are used in the actual ship structure health monitoring system for temperature compensation. The results show that the effect of temperature compensation is good, and the calibration parameters meet the engineering requirements, which provide an important reference for fiber Bragg grating sensor is widely used in engineering.

Gain selection method and model for coupled propulsion and airframe systems

NASA Technical Reports Server (NTRS)

Murphy, P. C.

1982-01-01

A longitudinal model is formulated for an advanced fighter from three subsystem models: the inlet, the engine, and the airframe. Notable interaction is found in the coupled system. A procedure, based on eigenvalue sensitivities, is presented which indicates the importance of the feedback gains to the optimal solution. This allows ineffectual gains to be eliminated; thus, hardware and expense may be saved in the realization of the physical controller.

A novel method to quantify the activity of alcohol acetyltransferase Using a SnO2-based sensor of electronic nose.

PubMed

Hu, Zhongqiu; Li, Xiaojing; Wang, Huxuan; Niu, Chen; Yuan, Yahong; Yue, Tianli

2016-07-15

Alcohol acetyltransferase (AATFase) extensively catalyzes the reactions of alcohols to acetic esters in microorganisms and plants. In this work, a novel method has been proposed to quantify the activity of AATFase using a SnO2-based sensor of electronic nose, which was determined on the basis of its higher sensitivity to the reducing alcohol than the oxidizing ester. The maximum value of the first-derivative of the signals from the SnO2-based sensor was therein found to be an eigenvalue of isoamyl alcohol concentration. Quadratic polynomial regression perfectly fitted the correlation between the eigenvalue and the isoamyl alcohol concentration. The method was used to determine the AATFase activity in this type of reaction by calculating the conversion rate of isoamyl alcohol. The proposed method has been successfully applied to determine the AATFase activity of a cider yeast strain. Compared with GC-MS, the method shows promises with ideal recovery and low cost. Copyright © 2016 Elsevier Ltd. All rights reserved.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1979-01-01

Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

Sensitivity analysis of discrete structural systems: A survey

NASA Technical Reports Server (NTRS)

Adelman, H. M.; Haftka, R. T.

1984-01-01

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications addressed to structural analysis, but also includes a number of methods developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Multicomponent diffusion in basaltic melts at 1350 °C

NASA Astrophysics Data System (ADS)

Guo, Chenghuan; Zhang, Youxue

2018-05-01

Nine successful diffusion couple experiments were conducted in an 8-component SiO2-TiO2-Al2O3-FeO-MgO-CaO-Na2O-K2O system at ∼1350 °C and at 1 GPa, to study multicomponent diffusion in basaltic melts. At least 3 traverses were measured to obtain diffusion profiles for each experiment. Multicomponent diffusion matrix at 1350 °C was obtained by simultaneously fitting diffusion profiles of diffusion couple experiments. Furthermore, in order to better constrain the diffusion matrix and reconcile mineral dissolution data, mineral dissolution experiments in the literature and diffusion couple experiments from this study, were fit together. All features of diffusion profiles in both diffusion couple and mineral dissolution experiments were well reproduced by the diffusion matrix. Diffusion mechanism is inferred from eigenvectors of the diffusion matrix, and it shows that the diffusive exchange between network-formers SiO2 and Al2O3 is the slowest, the exchange of SiO2 with other oxide components is the second slowest with an eigenvalue that is only ∼10% larger, then the exchange between divalent oxide components and all the other oxide components is the third slowest with an eigenvalue that is twice the smallest eigenvalue, then the exchange of FeO + K2O with all the other oxide components is the fourth slowest with an eigenvalue that is 5 times the smallest eigenvalue, then the exchange of MgO with FeO + CaO is the third fastest with an eigenvalue that is 6.3 times the smallest eigenvalue, then the exchange of CaO + K2O with all the other oxide components is the second fastest with an eigenvalue that is 7.5 times the smallest eigenvalue, and the exchange of Na2O with all other oxide components is the fastest with an eigenvalue that is 31 times the smallest eigenvalue. The slowest and fastest eigenvectors are consistent with those for simpler systems in most literature. The obtained diffusion matrix was successfully applied to predict diffusion profiles during mineral dissolution in basaltic melts.

A comparison of linear approaches to filter out environmental effects in structural health monitoring

NASA Astrophysics Data System (ADS)

Deraemaeker, A.; Worden, K.

2018-05-01

This paper discusses the possibility of using the Mahalanobis squared-distance to perform robust novelty detection in the presence of important environmental variability in a multivariate feature vector. By performing an eigenvalue decomposition of the covariance matrix used to compute that distance, it is shown that the Mahalanobis squared-distance can be written as the sum of independent terms which result from a transformation from the feature vector space to a space of independent variables. In general, especially when the size of the features vector is large, there are dominant eigenvalues and eigenvectors associated with the covariance matrix, so that a set of principal components can be defined. Because the associated eigenvalues are high, their contribution to the Mahalanobis squared-distance is low, while the contribution of the other components is high due to the low value of the associated eigenvalues. This analysis shows that the Mahalanobis distance naturally filters out the variability in the training data. This property can be used to remove the effect of the environment in damage detection, in much the same way as two other established techniques, principal component analysis and factor analysis. The three techniques are compared here using real experimental data from a wooden bridge for which the feature vector consists in eigenfrequencies and modeshapes collected under changing environmental conditions, as well as damaged conditions simulated with an added mass. The results confirm the similarity between the three techniques and the ability to filter out environmental effects, while keeping a high sensitivity to structural changes. The results also show that even after filtering out the environmental effects, the normality assumption cannot be made for the residual feature vector. An alternative is demonstrated here based on extreme value statistics which results in a much better threshold which avoids false positives in the training data, while allowing detection of all damaged cases.

S4 solution of the transport equation for eigenvalues using Legendre polynomials

NASA Astrophysics Data System (ADS)

Öztürk, Hakan; Bülbül, Ahmet

2017-09-01

Numerical solution of the transport equation for monoenergetic neutrons scattered isotropically through the medium of a finite homogeneous slab is studied for the determination of the eigenvalues. After obtaining the discrete ordinates form of the transport equation, separated homogeneous and particular solutions are formed and then the eigenvalues are calculated using the Gauss-Legendre quadrature set. Then, the calculated eigenvalues for various values of the c0, the mean number of secondary neutrons per collision, are given in the tables.

Bethe-Salpeter Eigenvalue Solver Package (BSEPACK) v0.1

DOE Office of Scientific and Technical Information (OSTI.GOV)

SHAO, MEIYEU; YANG, CHAO

2017-04-25

The BSEPACK contains a set of subroutines for solving the Bethe-Salpeter Eigenvalue (BSE) problem. This type of problem arises in this study of optical excitation of nanoscale materials. The BSE problem is a structured non-Hermitian eigenvalue problem. The BSEPACK software can be used to compute all or subset of eigenpairs of a BSE Hamiltonian. It can also be used to compute the optical absorption spectrum without computing BSE eigenvalues and eigenvectors explicitly. The package makes use of the ScaLAPACK, LAPACK and BLAS.

Generalized Friedberg-Lee model for CP violation in neutrino physics

NASA Astrophysics Data System (ADS)

Razzaghi, N.; Gousheh, S. S.

2012-09-01

We propose a phenomenological model of Dirac neutrino mass operator based on the Friedberg-Lee neutrino mass model to include CP violation. By considering the most general set of complex coefficients, and imposing the condition that the mass eigenvalues are real, we find a neutrino mass matrix which is non-Hermitian, symmetric, and magic. In particular, we find that the requirement of obtaining real mass eigenvalues by transferring the residual phases to the mass eigenstates self-consistently dictates the following relationship between the imaginary part of the mass matrix elements B and the parameters of the Friedberg-Lee model: B=±(3)/(4)(a-br)2sin⁡22θ13cos⁡2θ12. We obtain inverted neutrino mass hierarchy m3=0. Making a correspondence between our model and the experimental data produces stringent conditions on the parameters as follows: 35.06°≲θ12≲36.27°, θ23=45°, 7.27°≲θ13≲11.09°, and 82.03°≲δ≲85.37°. We get mildly broken μ-τ symmetry, which reduces the resultant neutrino mixing pattern from tri-bimaximal to trimaximal. The CP violation as measured by the Jarlskog parameter is restricted by 0.027≲J≲0.044.

Multifractal analysis and topological properties of a new family of weighted Koch networks

NASA Astrophysics Data System (ADS)

Huang, Da-Wen; Yu, Zu-Guo; Anh, Vo

2017-03-01

Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c) in the limit of large generation t; the second smallest eigenvalue μ2 and the maximum eigenvalue μn are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ2 is approximately a quartic polynomial of c and μn= 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c. We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Sturm-Liouville eigenproblems with an interior pole

NASA Technical Reports Server (NTRS)

Boyd, J. P.

1981-01-01

The eigenvalues and eigenfunctions of self-adjoint Sturm-Liouville problems with a simple pole on the interior of an interval are investigated. Three general theorems are proved, and it is shown that as n approaches infinity, the eigenfunctions more and more closely resemble those of an ordinary Sturm-Liouville problem. The low-order modes differ significantly from those of a nonsingular eigenproblem in that both eigenvalues and eigenfunctions are complex, and the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. In addition, the WKB is shown to be accurate for all n, and all eigenvalues of a normal one-dimensional Sturm-Liouville equation with nonperiodic boundary conditions are well separated.

Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf.

PubMed

Galbán, Craig J; Maderwald, Stefan; Uffmann, Kai; de Greiff, Armin; Ladd, Mark E

2004-12-01

The aim of this study was to examine the diffusive properties of adjacent muscles at rest, and to determine the relationship between diffusive and architectural properties, which are task-specific to muscles. The principle, second, and third eigenvalues, trace of the diffusion tensor, and two anisotropic parameters, ellipsoid eccentricity (e) and fractional anisotropy (FA), of various muscles in the human calf were calculated by diffusion tensor imaging (DTI). Linear correlations of the calculated parameters to the muscle physiological cross-sectional area (PCSA), which is proportional to maximum muscle force, were performed to ascertain any linear relation between muscle architecture and diffusivity. Images of the left calf were acquired from six healthy male volunteers. Seven muscles were investigated in this study. These comprised the soleus, lateral gastrocnemius, medial gastrocnemius, posterior tibialis, anterior tibialis, extensor digitorum longus, and peroneus longus. All data were presented as the mean and standard error of the mean (SEM). In general, differences in diffusive parameter values occurred primarily between functionally different muscles. A strong correlation was also found between PCSA and the third eigenvalue, e, and FA. A mathematical derivation revealed a linear relationship between PCSA and the third eigenvalue as a result of their dependence on the average radius of all fibers within a single muscle. These findings demonstrated the ability of DTI to differentiate between functionally different muscles in the same region of the body on the basis of their diffusive properties.

MPACT Subgroup Self-Shielding Efficiency Improvements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stimpson, Shane; Liu, Yuxuan; Collins, Benjamin S.

Recent developments to improve the efficiency of the MOC solvers in MPACT have yielded effective kernels that loop over several energy groups at once, rather that looping over one group at a time. These kernels have produced roughly a 2x speedup on the MOC sweeping time during eigenvalue calculation. However, the self-shielding subgroup calculation had not been reevaluated to take advantage of these new kernels, which typically requires substantial solve time. The improvements covered in this report start by integrating the multigroup kernel concepts into the subgroup calculation, which are then used as the basis for further extensions. The nextmore » improvement that is covered is what is currently being termed as “Lumped Parameter MOC”. Because the subgroup calculation is a purely fixed source problem and multiple sweeps are performed only to update the boundary angular fluxes, the sweep procedure can be condensed to allow for the instantaneous propagation of the flux across a spatial domain, without the need to sweep along all segments in a ray. Once the boundary angular fluxes are considered to be converged, an additional sweep that will tally the scalar flux is completed. The last improvement that is investigated is the possible reduction of the number of azimuthal angles per octant in the shielding sweep. Typically 16 azimuthal angles per octant are used for self-shielding and eigenvalue calculations, but it is possible that the self-shielding sweeps are less sensitive to the number of angles than the full eigenvalue calculation.« less

Evaluation of the eigenvalue method in the solution of transient heat conduction problems

NASA Astrophysics Data System (ADS)

Landry, D. W.

1985-01-01

The eigenvalue method is evaluated to determine the advantages and disadvantages of the method as compared to fully explicit, fully implicit, and Crank-Nicolson methods. Time comparisons and accuracy comparisons are made in an effort to rank the eigenvalue method in relation to the comparison schemes. The eigenvalue method is used to solve the parabolic heat equation in multidimensions with transient temperatures. Extensions into three dimensions are made to determine the method's feasibility in handling large geometry problems requiring great numbers of internal mesh points. The eigenvalue method proves to be slightly better in accuracy than the comparison routines because of an exact treatment, as opposed to a numerical approximation, of the time derivative in the heat equation. It has the potential of being a very powerful routine in solving long transient type problems. The method is not well suited to finely meshed grid arrays or large regions because of the time and memory requirements necessary for calculating large sets of eigenvalues and eigenvectors.

A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts

NASA Technical Reports Server (NTRS)

Watson, W.; Lansing, D. L.

1976-01-01

Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Optimal Frequency-Domain System Realization with Weighting

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Maghami, Peiman G.

1999-01-01

Several approaches are presented to identify an experimental system model directly from frequency response data. The formulation uses a matrix-fraction description as the model structure. Frequency weighting such as exponential weighting is introduced to solve a weighted least-squares problem to obtain the coefficient matrices for the matrix-fraction description. A multi-variable state-space model can then be formed using the coefficient matrices of the matrix-fraction description. Three different approaches are introduced to fine-tune the model using nonlinear programming methods to minimize the desired cost function. The first method uses an eigenvalue assignment technique to reassign a subset of system poles to improve the identified model. The second method deals with the model in the real Schur or modal form, reassigns a subset of system poles, and adjusts the columns (rows) of the input (output) influence matrix using a nonlinear optimizer. The third method also optimizes a subset of poles, but the input and output influence matrices are refined at every optimization step through least-squares procedures.

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

NASA Astrophysics Data System (ADS)

Hulko, Artem

2018-03-01

In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1989-01-01

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

An eigenvalue localization set for tensors and its applications.

PubMed

Zhao, Jianxing; Sang, Caili

2017-01-01

A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al . (Linear Algebra Appl. 481:36-53, 2015) and Huang et al . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al ., the advantage of our results is that, without considering the selection of nonempty proper subsets S of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.

Design of a New Concentration Series for the Orthogonal Sample Design Approach and Estimation of the Number of Reactions in Chemical Systems.

PubMed

Shi, Jiajia; Liu, Yuhai; Guo, Ran; Li, Xiaopei; He, Anqi; Gao, Yunlong; Wei, Yongju; Liu, Cuige; Zhao, Ying; Xu, Yizhuang; Noda, Isao; Wu, Jinguang

2015-11-01

A new concentration series is proposed for the construction of a two-dimensional (2D) synchronous spectrum for orthogonal sample design analysis to probe intermolecular interaction between solutes dissolved in the same solutions. The obtained 2D synchronous spectrum possesses the following two properties: (1) cross peaks in the 2D synchronous spectra can be used to reflect intermolecular interaction reliably, since interference portions that have nothing to do with intermolecular interaction are completely removed, and (2) the two-dimensional synchronous spectrum produced can effectively avoid accidental collinearity. Hence, the correct number of nonzero eigenvalues can be obtained so that the number of chemical reactions can be estimated. In a real chemical system, noise present in one-dimensional spectra may also produce nonzero eigenvalues. To get the correct number of chemical reactions, we classified nonzero eigenvalues into significant nonzero eigenvalues and insignificant nonzero eigenvalues. Significant nonzero eigenvalues can be identified by inspecting the pattern of the corresponding eigenvector with help of the Durbin-Watson statistic. As a result, the correct number of chemical reactions can be obtained from significant nonzero eigenvalues. This approach provides a solid basis to obtain insight into subtle spectral variations caused by intermolecular interaction.

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Constrained multibody system dynamics: An automated approach

NASA Technical Reports Server (NTRS)

Kamman, J. W.; Huston, R. L.

1982-01-01

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. The closed loop problem of multibody chain systems is addressed. The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. The modifications is based upon a solution of the constraint equations obtained through a zero eigenvalues theorem, is a contraction of the dynamical equations. For a system with n-generalized coordinates and m-constraint equations, the coefficients in the constraint equations may be viewed as constraint vectors in n-dimensional space. In this setting the system itself is free to move in the n-m directions which are orthogonal to the constraint vectors.

A new mathematical adjoint for the modified SAAF -SN equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Martineau, Richard

2015-01-01

We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF -SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF -SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF -SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both formore » fixed source and eigenvalue problems.« less

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Replication Study of the Milwaukee Inventory for Subtypes of Trichotillomania–Adult Version in a Clinically Characterized Sample

PubMed Central

Keuthen, Nancy J.; Tung, Esther S.; Woods, Douglas W.; Franklin, Martin E.; Altenburger, Erin M.; Pauls, David L.; Flessner, Christopher A.

2015-01-01

In the present study, we evaluated the Milwaukee Inventory for Subtypes of Trichotillomania–Adult Version (MIST-A) in a replication sample of clinically characterized hair pullers using exploratory factor analysis (EFA; N = 193). EFA eigenvalues and visual inspection of our scree plot revealed a two-factor solution. Factor structure coefficients and internal consistencies suggested a 13-item scale with an 8-item “Intention” scale and a 5-item “Emotion” scale. Both scales displayed good construct and discriminant validity. These findings indicate the need for a revised scale that provides a more refined assessment of pulling phenomenology that can facilitate future treatment advances. PMID:25868534

Sensitivity Analysis of Nuclide Importance to One-Group Neutron Cross Sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sekimoto, Hiroshi; Nemoto, Atsushi; Yoshimura, Yoshikane

The importance of nuclides is useful when investigating nuclide characteristics in a given neutron spectrum. However, it is derived using one-group microscopic cross sections, which may contain large errors or uncertainties. The sensitivity coefficient shows the effect of these errors or uncertainties on the importance.The equations for calculating sensitivity coefficients of importance to one-group nuclear constants are derived using the perturbation method. Numerical values are also evaluated for some important cases for fast and thermal reactor systems.Many characteristics of the sensitivity coefficients are derived from the derived equations and numerical results. The matrix of sensitivity coefficients seems diagonally dominant. However,more » it is not always satisfied in a detailed structure. The detailed structure of the matrix and the characteristics of coefficients are given.By using the obtained sensitivity coefficients, some demonstration calculations have been performed. The effects of error and uncertainty of nuclear data and of the change of one-group cross-section input caused by fuel design changes through the neutron spectrum are investigated. These calculations show that the sensitivity coefficient is useful when evaluating error or uncertainty of nuclide importance caused by the cross-section data error or uncertainty and when checking effectiveness of fuel cell or core design change for improving neutron economy.« less

Accurate Valence Ionization Energies from Kohn-Sham Eigenvalues with the Help of Potential Adjustors.

PubMed

Thierbach, Adrian; Neiss, Christian; Gallandi, Lukas; Marom, Noa; Körzdörfer, Thomas; Görling, Andreas

2017-10-10

An accurate yet computationally very efficient and formally well justified approach to calculate molecular ionization potentials is presented and tested. The first as well as higher ionization potentials are obtained as the negatives of the Kohn-Sham eigenvalues of the neutral molecule after adjusting the eigenvalues by a recently [ Görling Phys. Rev. B 2015 , 91 , 245120 ] introduced potential adjustor for exchange-correlation potentials. Technically the method is very simple. Besides a Kohn-Sham calculation of the neutral molecule, only a second Kohn-Sham calculation of the cation is required. The eigenvalue spectrum of the neutral molecule is shifted such that the negative of the eigenvalue of the highest occupied molecular orbital equals the energy difference of the total electronic energies of the cation minus the neutral molecule. For the first ionization potential this simply amounts to a ΔSCF calculation. Then, the higher ionization potentials are obtained as the negatives of the correspondingly shifted Kohn-Sham eigenvalues. Importantly, this shift of the Kohn-Sham eigenvalue spectrum is not just ad hoc. In fact, it is formally necessary for the physically correct energetic adjustment of the eigenvalue spectrum as it results from ensemble density-functional theory. An analogous approach for electron affinities is equally well obtained and justified. To illustrate the practical benefits of the approach, we calculate the valence ionization energies of test sets of small- and medium-sized molecules and photoelectron spectra of medium-sized electron acceptor molecules using a typical semilocal (PBE) and two typical global hybrid functionals (B3LYP and PBE0). The potential adjusted B3LYP and PBE0 eigenvalues yield valence ionization potentials that are in very good agreement with experimental values, reaching an accuracy that is as good as the best G 0 W 0 methods, however, at much lower computational costs. The potential adjusted PBE eigenvalues result in somewhat less accurate ionization energies, which, however, are almost as accurate as those obtained from the most commonly used G 0 W 0 variants.

Cucheb: A GPU implementation of the filtered Lanczos procedure

NASA Astrophysics Data System (ADS)

Aurentz, Jared L.; Kalantzis, Vassilis; Saad, Yousef

2017-11-01

This paper describes the software package Cucheb, a GPU implementation of the filtered Lanczos procedure for the solution of large sparse symmetric eigenvalue problems. The filtered Lanczos procedure uses a carefully chosen polynomial spectral transformation to accelerate convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective for eigenvalue problems that arise in electronic structure calculations and density functional theory. We compare our implementation against an equivalent CPU implementation and show that using the GPU can reduce the computation time by more than a factor of 10. Program Summary Program title: Cucheb Program Files doi:http://dx.doi.org/10.17632/rjr9tzchmh.1 Licensing provisions: MIT Programming language: CUDA C/C++ Nature of problem: Electronic structure calculations require the computation of all eigenvalue-eigenvector pairs of a symmetric matrix that lie inside a user-defined real interval. Solution method: To compute all the eigenvalues within a given interval a polynomial spectral transformation is constructed that maps the desired eigenvalues of the original matrix to the exterior of the spectrum of the transformed matrix. The Lanczos method is then used to compute the desired eigenvectors of the transformed matrix, which are then used to recover the desired eigenvalues of the original matrix. The bulk of the operations are executed in parallel using a graphics processing unit (GPU). Runtime: Variable, depending on the number of eigenvalues sought and the size and sparsity of the matrix. Additional comments: Cucheb is compatible with CUDA Toolkit v7.0 or greater.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, Zhaojun; Yang, Chao

What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcasemore » some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.« less

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

Two-faced property of a market factor in asset pricing and diversification effect

NASA Astrophysics Data System (ADS)

Eom, Cheoljun

2017-04-01

This study empirically investigates the test hypothesis that a market factor acting as a representative common factor in the pricing models has a negative influence on constructing a well-diversified portfolio from the Markowitz mean-variance optimization function (MVOF). We use the comparative correlation matrix (C-CM) method to control a single eigenvalue among all eigenvalues included in the sample correlation matrix (S-CM), through the random matrix theory (RMT). In particular, this study observes the effect of the largest eigenvalue that has the property of the market factor. According to the results, the largest eigenvalue has the highest explanatory power on the stock return changes. The C-CM without the largest eigenvalue in the S-CM constructs a more diversified portfolio capable of improving the practical applicability of the MVOF. Moreover, the more diversified portfolio constructed from this C-CM has better out-of-sample performance in the future period. These results support the test hypothesis for the two-faced property of the market factor, defined by the largest eigenvalue.

Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Yunfeng, E-mail: yfcai@math.pku.edu.cn; Department of Computer Science, University of California, Davis 95616; Bai, Zhaojun, E-mail: bai@cs.ucdavis.edu

2013-12-15

The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for ab initio electronic structure calculations. We propose a hybrid preconditioning scheme to effectively combine global and locally accelerated preconditioners for rapid iterative diagonalization of such eigenvalue problems. In partition-of-unity finite-element (PUFE) pseudopotential density-functional calculations, employing a nonorthogonal basis, we show that the hybrid preconditioned block steepest descent method is a cost-effective eigensolver, outperforming current state-of-the-art global preconditioning schemes, and comparably efficient for the ill-conditioned generalized eigenvalue problems produced by PUFE as the locally optimal blockmore » preconditioned conjugate-gradient method for the well-conditioned standard eigenvalue problems produced by planewave methods.« less

An inverse method using toroidal mode data

USGS Publications Warehouse

Willis, C.

1986-01-01

The author presents a numerical method for calculating the density and S-wave velocity in the upper mantle of a spherically symmetric, non-rotating Earth which consists of a perfect elastic, isotropic material. The data comes from the periods of the toroidal oscillations. She tests the method on a smoothed version of model A. The error in the reconstruction is less than 1%. The effects of perturbations in the eigenvalues are studied and she finds that the final model is sensitive to errors in the data.

The Cr dependence problem of eigenvalues of the Laplace operator on domains in the plane

NASA Astrophysics Data System (ADS)

Haddad, Julian; Montenegro, Marcos

2018-03-01

The Cr dependence problem of multiple Dirichlet eigenvalues on domains is discussed for elliptic operators by regarding C r + 1-smooth one-parameter families of C1 perturbations of domains in Rn. As applications of our main theorem (Theorem 1), we provide a fairly complete description for all eigenvalues of the Laplace operator on disks and squares in R2 and also for its second eigenvalue on balls in Rn for any n ≥ 3. The central tool used in our proof is a degenerate implicit function theorem on Banach spaces (Theorem 2) of independent interest.

Computing interior eigenvalues of nonsymmetric matrices: application to three-dimensional metamaterial composites.

PubMed

Terao, Takamichi

2010-08-01

We propose a numerical method to calculate interior eigenvalues and corresponding eigenvectors for nonsymmetric matrices. Based on the subspace projection technique onto expanded Ritz subspace, it becomes possible to obtain eigenvalues and eigenvectors with sufficiently high precision. This method overcomes the difficulties of the traditional nonsymmetric Lanczos algorithm, and improves the accuracy of the obtained interior eigenvalues and eigenvectors. Using this algorithm, we investigate three-dimensional metamaterial composites consisting of positive and negative refractive index materials, and it is demonstrated that the finite-difference frequency-domain algorithm is applicable to analyze these metamaterial composites.

The first eigenvalue of the p-Laplacian on quantum graphs

NASA Astrophysics Data System (ADS)

Del Pezzo, Leandro M.; Rossi, Julio D.

2016-12-01

We study the first eigenvalue of the p-Laplacian (with 1

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.

PubMed

Mazandarani, Mehran; Pariz, Naser

2018-05-01

This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

NASA Astrophysics Data System (ADS)

Assawaroongruengchot, Monchai

Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and keff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and keff-EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these techniques to the CVR-BOC, CVR-EOC and keff-EOC adjustment of a CANDU lattice of which the burnup period is extended from 300 to 450 FPDs. The cases with the central pin containing either Dysprosium or Gadolinium in the natural Uranium are considered in our study. (Abstract shortened by UMI.)

A new approach to the method of source-sink potentials for molecular conduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pickup, Barry T., E-mail: B.T.Pickup@sheffield.ac.uk, E-mail: P.W.Fowler@sheffield.ac.uk; Fowler, Patrick W., E-mail: B.T.Pickup@sheffield.ac.uk, E-mail: P.W.Fowler@sheffield.ac.uk; Borg, Martha

2015-11-21

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue ofmore » the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy.« less

The Use of Sphere Indentation Experiments to Characterize Ceramic Damage Models

DTIC Science & Technology

2011-09-01

state having two equal eigenvalues. For TXC, the axial stress (single eigenvalue) is more compressive than the lateral stresses (dual eigenvalues). For...parameters. These dynamic experiments supplement traditional characterization experiments such as tension, triaxial compression , Brazilian, and...These dynamic experiments supplement traditional characterization experiments such as tension, triaxial compression , Brazilian, and plate impact, which

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

Principle component analysis (PCA) for investigation of relationship between population dynamics of microbial pathogenesis, chemical and sensory characteristics in beef slices containing Tarragon essential oil.

PubMed

Alizadeh Behbahani, Behrooz; Tabatabaei Yazdi, Farideh; Shahidi, Fakhri; Mortazavi, Seyed Ali; Mohebbi, Mohebbat

2017-04-01

Principle component analysis (PCA) was employed to examine the effect of the exerted treatments on the beef shelf life as well as discovering the correlations between the studied responses. Considering the variability of the dimensions of the responses, correlation coefficients were applied to form the matrix and extract the eigenvalue. Antimicrobial effect was evaluated on 10 pathogenic microorganisms through the methods of hole-plate diffusion method, disk diffusion method, pour plate method, minimum inhibitory concentration and minimum bactericidal/fungicidal concentration. Antioxidant potential and total phenolic content were examined through the method of 2,2-diphenyl-1-picrylhydrazyl (DPPH) and Folin-Ciocalteu method, respectively. The components were identified through gas chromatography and gas chromatography/mass spectrometry. Barhang seed mucilage (BSM) based edible coating containing 0, 0.5, 1 and 1.5% (w/w) Tarragon (T) essential oil mix were applied on beef slices to control the growth of pathogenic microorganisms. Microbiological (total viable count, psychrotrophic count, Escherichia coli, Staphylococcus aureus and fungi), chemical (thiobarbituric acid, peroxide value and pH) and sensory characteristics (odor, color and overall acceptability) analysis measurements were made during the storage periodically. PCA was employed to examine the effect of the exerted treatments on the beef shelf life as well as discovering the correlations between the studied responses. Considering the variability of the dimensions of the responses, correlation coefficients were applied to form the matrix and extract the eigenvalue. The PCA showed that the properties of the uncoated meat samples on the 9th, 12th, 15th and 18th days of storage are continuously changing independent of the exerted treatments on the other samples. This reveals the effect of the exerted treatments on the samples. Copyright © 2017 Elsevier Ltd. All rights reserved.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

Asymptotics of empirical eigenstructure for high dimensional spiked covariance.

PubMed

Wang, Weichen; Fan, Jianqing

2017-06-01

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies.

Asymptotics of empirical eigenstructure for high dimensional spiked covariance

PubMed Central

Wang, Weichen

2017-01-01

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. (2013). They also reveal the biases of estimating leading eigenvalues and eigenvectors by using principal component analysis, and lead to a new covariance estimator for the approximate factor model, called shrinkage principal orthogonal complement thresholding (S-POET), that corrects the biases. Our results are successfully applied to outstanding problems in estimation of risks of large portfolios and false discovery proportions for dependent test statistics and are illustrated by simulation studies. PMID:28835726

The construction of partner potential from the general potential anharmonic in D-dimensional Schrodinger system

NASA Astrophysics Data System (ADS)

Suparmi; Cari, C.; Wea, K. N.; Wahyulianti

2018-03-01

The Schrodinger equation is the fundamental equation in quantum physics. The characteristic of the particle in physics potential field can be explained by using the Schrodinger equation. In this study, the solution of 4 dimensional Schrodinger equation for the anharmonic potential and the anharmonic partner potential have done. The method that used to solve the Schrodinger equation was the ansatz wave method, while to construction the partner potential was the supersymmetric method. The construction of partner potential used to explain the experiment result that cannot be explained by the original potential. The eigenvalue for anharmonic potential and the anharmonic partner potential have the same characteristic. Every increase of quantum orbital number the eigenvalue getting smaller. This result corresponds to Bohrn’s atomic theory that the eigenvalue is inversely proportional to the atomic shell. But the eigenvalue for the anharmonic partner potential higher than the eigenvalue for the anharmonic original potential.

Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Thompson, P. M.

1980-01-01

Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalue and the directional derivatives of closed loop eigenvectors. An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties. An algorithm is presented that can be used to select a feedback gain matrix for the linear state feedback problem which produces a specified asymptotic eigenstructure. Another algorithm is given to compute the asymptotic eigenstructure properties inherent in a given set of quadratic weights. Finally, it is shown that optimal root loci for nongeneric problems can be approximated by generic ones in the nonasymptotic region.

Iterative Methods for Elliptic Problems and the Discovery of ’q’.

DTIC Science & Technology

1984-07-01

K = M’IlN LN 12 is a nonnegative irreducible matrix. Hence the Perron - Frobenius theory [19] tells us that there is exactly one eigenvalue A with W = p...earlier, the Perron - Frobenius theory implies that p is itself an eigenvalue. However, as we have said, in this instance the eigenvalue problem (l.12a

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Brody, Dorje C.

2018-04-01

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads to a challenging open problem concerning the formulation of the eigenvalue problem in the momentum space. The WKB analysis gives the exact asymptotic behavior of the eigenfunction.

Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

DOE PAGES

Willert, Jeffrey; Park, H.; Taitano, William

2015-11-01

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

Solving complex band structure problems with the FEAST eigenvalue algorithm

NASA Astrophysics Data System (ADS)

Laux, S. E.

2012-08-01

With straightforward extension, the FEAST eigenvalue algorithm [Polizzi, Phys. Rev. B 79, 115112 (2009)] is capable of solving the generalized eigenvalue problems representing traveling-wave problems—as exemplified by the complex band-structure problem—even though the matrices involved are complex, non-Hermitian, and singular, and hence outside the originally stated range of applicability of the algorithm. The obtained eigenvalues/eigenvectors, however, contain spurious solutions which must be detected and removed. The efficiency and parallel structure of the original algorithm are unaltered. The complex band structures of Si layers of varying thicknesses and InAs nanowires of varying radii are computed as test problems.

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

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1977-01-01

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.

Comment on ‘Numerical estimates of the spectrum for anharmonic PT symmetric potentials’

NASA Astrophysics Data System (ADS)

Amore, Paolo; Fernández, Francisco M.

2013-04-01

We show that the authors of the commented paper (Bowen et al 2012 Phys. Scr. 85 065005) draw their conclusions from the eigenvalues of truncated Hamiltonian matrices that do not converge as the matrix dimension increases. In some of the studied examples, the authors missed the real positive eigenvalues that already converge towards the exact eigenvalues of the non-Hermitian operators and focused their attention on the complex ones that do not. We also show that the authors misread Bender's argument about the eigenvalues of the harmonic oscillator with boundary conditions in the complex-x plane (Bender 2007 Rep. Prog. Phys. 70 947).

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Ultrarelativistic bound states in the spherical well

DOE Office of Scientific and Technical Information (OSTI.GOV)

Żaba, Mariusz; Garbaczewski, Piotr

2016-07-15

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ){sup 1/2}, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E{sub (k,l)} series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth seriesmore » eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E{sub (k,0)} are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E{sub (k,0)}(d = 3) = E{sub 2k}(d = 1). Likewise, the eigenfunctions ψ{sub (k,0)}(d = 3) and ψ{sub 2k}(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).« less

A Generalized Framework for Reduced-Order Modeling of a Wind Turbine Wake

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamilton, Nicholas; Viggiano, Bianca; Calaf, Marc

A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode. Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a seriesmore » of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. A high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM.« less

A divide and conquer approach to the nonsymmetric eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jessup, E.R.

1991-01-01

Serial computation combined with high communication costs on distributed-memory multiprocessors make parallel implementations of the QR method for the nonsymmetric eigenvalue problem inefficient. This paper introduces an alternative algorithm for the nonsymmetric tridiagonal eigenvalue problem based on rank two tearing and updating of the matrix. The parallelism of this divide and conquer approach stems from independent solution of the updating problems. 11 refs.

The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

PubMed

Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H

2014-05-28

Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem sizes arising in the field of electronic structure theory is demonstrated for current high-performance computer architectures such as Cray or Intel/Infiniband. For a matrix of dimension 260,000, scalability up to 295,000 CPU cores has been shown on BlueGene/P.

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Bin; Chen, Luoping; Hu, Xiaozhe

2016-03-05

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigatemore » the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.« less

Development of an unsteady wake theory appropriate for aeroelastic analyses of rotors in hover and forward flight

NASA Technical Reports Server (NTRS)

Peters, David A.

1988-01-01

The purpose of this research is the development of an unsteady aerodynamic model for rotors such that it can be used in conventional aeroelastic analysis (e.g., eigenvalue determination and control system design). For this to happen, the model must be in a state-space formulation such that the states of the flow can be defined, calculated and identified as part of the analysis. The fluid mechanics of the problem is given by a closed-form inversion of an acceleration potential. The result is a set of first-order differential equations in time for the unknown flow coefficients. These equations are hierarchical in the sense that they may be truncated at any number of radial or azimuthal terms.

Simple, Effective Computation of Principal Eigen-Vectors and Their Eigenvalues and Application to High-Resolution Estimation of Frequencies

DTIC Science & Technology

1985-10-01

written 3 as follows: m 4 cg ° + C + + - c =0n-1u-1 n C + c 2 g 1 +. . c 0 clg o Cngn-1 cn+ 1 (10a) cng° + Cn+11 + + C 2n-lgn_1 + C 2 n 0 or in...matrix form, C " I = 0 (10b) A non-zero solution is possible if the determinant of C is zero. From the theory of Prony’s method [133 g (k1 = % n + kn... g , ki + go = 0 II) hence the polynomial coefficient vector g is also orthogonal to the vector (1 X i ki 2 .Xik)T where %i’s are the

Emerging spectra of singular correlation matrices under small power-map deformations

NASA Astrophysics Data System (ADS)

Vinayak; Schäfer, Rudi; Seligman, Thomas H.

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Computational procedures for evaluating the sensitivity derivatives of vibration frequencies and Eigenmodes of framed structures

NASA Technical Reports Server (NTRS)

Fetterman, Timothy L.; Noor, Ahmed K.

1987-01-01

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

Emerging spectra of singular correlation matrices under small power-map deformations.

PubMed

Vinayak; Schäfer, Rudi; Seligman, Thomas H

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

NASA Astrophysics Data System (ADS)

Aguilar, José G.; Magri, Luca; Juniper, Matthew P.

2017-07-01

Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.

The method of fundamental solutions for computing acoustic interior transmission eigenvalues

NASA Astrophysics Data System (ADS)

Kleefeld, Andreas; Pieronek, Lukas

2018-03-01

We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.

Aeroelastic Stability of Idling Wind Turbines

NASA Astrophysics Data System (ADS)

Wang, Kai; Riziotis, Vasilis A.; Voutsinas, Spyros G.

2016-09-01

Wind turbine rotors in idling operation mode can experience high angles of attack, within the post stall region that are capable of triggering stall-induced vibrations. In the present paper rotor stability in slow idling operation is assessed on the basis of non-linear time domain and linear eigenvalue analysis. Analysis is performed for a 10 MW conceptual wind turbine designed by DTU. First the flow conditions that are likely to favour stall induced instabilities are identified through non-linear time domain aeroelastic analysis. Next, for the above specified conditions, eigenvalue stability simulations are performed aiming at identifying the low damped modes of the turbine. Finally the results of the eigenvalue analysis are evaluated through computations of the work of the aerodynamic forces by imposing harmonic vibrations following the shape and frequency of the various modes. Eigenvalue analysis indicates that the asymmetric and symmetric out-of-plane modes have the lowest damping. The results of the eigenvalue analysis agree well with those of the time domain analysis.

Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics

NASA Astrophysics Data System (ADS)

Li, Keqiang; Gao, Feng; Li, Shengbo Eben; Zheng, Yang; Gao, Hongbo

2017-12-01

This study presents a distributed H-infinity control method for uncertain platoons with dimensionally and structurally unknown interaction topologies provided that the associated topological eigenvalues are bounded by a predesigned range.With an inverse model to compensate for nonlinear powertrain dynamics, vehicles in a platoon are modeled by third-order uncertain systems with bounded disturbances. On the basis of the eigenvalue decomposition of topological matrices, we convert the platoon system to a norm-bounded uncertain part and a diagonally structured certain part by applying linear transformation. We then use a common Lyapunov method to design a distributed H-infinity controller. Numerically, two linear matrix inequalities corresponding to the minimum and maximum eigenvalues should be solved. The resulting controller can tolerate interaction topologies with eigenvalues located in a certain range. The proposed method can also ensure robustness performance and disturbance attenuation ability for the closed-loop platoon system. Hardware-in-the-loop tests are performed to validate the effectiveness of our method.

Spectrum of walk matrix for Koch network and its application

NASA Astrophysics Data System (ADS)

Xie, Pinchen; Lin, Yuan; Zhang, Zhongzhi

2015-06-01

Various structural and dynamical properties of a network are encoded in the eigenvalues of walk matrix describing random walks on the network. In this paper, we study the spectra of walk matrix of the Koch network, which displays the prominent scale-free and small-world features. Utilizing the particular architecture of the network, we obtain all the eigenvalues and their corresponding multiplicities. Based on the link between the eigenvalues of walk matrix and random target access time defined as the expected time for a walker going from an arbitrary node to another one selected randomly according to the steady-state distribution, we then derive an explicit solution to the random target access time for random walks on the Koch network. Finally, we corroborate our computation for the eigenvalues by enumerating spanning trees in the Koch network, using the connection governing eigenvalues and spanning trees, where a spanning tree of a network is a subgraph of the network, that is, a tree containing all the nodes.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

A hybrid-perturbation-Galerkin technique which combines multiple expansions

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials

NASA Astrophysics Data System (ADS)

Volkmer, Hans

2008-04-01

Sequences of polynomials, orthogonal with respect to signed measures, are associated with a class of differential equations including the Mathieu, Lame and Whittaker-Hill equation. It is shown that the zeros of pn form sequences which converge to the eigenvalues of the corresponding differential equations. Moreover, interlacing properties of the zeros of pn are found. Applications to the numerical treatment of eigenvalue problems are given.

Eigenvectors determination of the ribosome dynamics model during mRNA translation using the Kleene Star algorithm

NASA Astrophysics Data System (ADS)

Ernawati; Carnia, E.; Supriatna, A. K.

2018-03-01

Eigenvalues and eigenvectors in max-plus algebra have the same important role as eigenvalues and eigenvectors in conventional algebra. In max-plus algebra, eigenvalues and eigenvectors are useful for knowing dynamics of the system such as in train system scheduling, scheduling production systems and scheduling learning activities in moving classes. In the translation of proteins in which the ribosome move uni-directionally along the mRNA strand to recruit the amino acids that make up the protein, eigenvalues and eigenvectors are used to calculate protein production rates and density of ribosomes on the mRNA. Based on this, it is important to examine the eigenvalues and eigenvectors in the process of protein translation. In this paper an eigenvector formula is given for a ribosome dynamics during mRNA translation by using the Kleene star algorithm in which the resulting eigenvector formula is simpler and easier to apply to the system than that introduced elsewhere. This paper also discusses the properties of the matrix {B}λ \\otimes n of model. Among the important properties, it always has the same elements in the first column for n = 1, 2,… if the eigenvalue is the time of initiation, λ = τin , and the column is the eigenvector of the model corresponding to λ.

Eigenvalue Attraction

NASA Astrophysics Data System (ADS)

Movassagh, Ramis

2016-02-01

We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix M. If M is Normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and when M is circulant the strength of interaction can be related to the power spectrum of white noise. We extend this by calculating the expected force (Eq. 41) for real stochastic processes with zero-mean and independent intervals. To quantify the dominance of the c.c. attraction, we calculate the variance of other forces. We apply the results to the Hatano-Nelson model and provide other numerical illustrations. It is our hope that the simple dynamical perspective herein might help better understanding of the aggregation and low density of the eigenvalues of real random matrices on and near the real line respectively. In the appendix we provide a Matlab code for plotting the trajectories of the eigenvalues.

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; Govind, Niranjan; Yang, Chao

2017-12-01

We present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.

Market Correlation Structure Changes Around the Great Crash: A Random Matrix Theory Analysis of the Chinese Stock Market

NASA Astrophysics Data System (ADS)

Han, Rui-Qi; Xie, Wen-Jie; Xiong, Xiong; Zhang, Wei; Zhou, Wei-Xing

The correlation structure of a stock market contains important financial contents, which may change remarkably due to the occurrence of financial crisis. We perform a comparative analysis of the Chinese stock market around the occurrence of the 2008 crisis based on the random matrix analysis of high-frequency stock returns of 1228 Chinese stocks. Both raw correlation matrix and partial correlation matrix with respect to the market index in two time periods of one year are investigated. We find that the Chinese stocks have stronger average correlation and partial correlation in 2008 than in 2007 and the average partial correlation is significantly weaker than the average correlation in each period. Accordingly, the largest eigenvalue of the correlation matrix is remarkably greater than that of the partial correlation matrix in each period. Moreover, each largest eigenvalue and its eigenvector reflect an evident market effect, while other deviating eigenvalues do not. We find no evidence that deviating eigenvalues contain industrial sectorial information. Surprisingly, the eigenvectors of the second largest eigenvalues in 2007 and of the third largest eigenvalues in 2008 are able to distinguish the stocks from the two exchanges. We also find that the component magnitudes of the some largest eigenvectors are proportional to the stocks’ capitalizations.

A comparison of acceleration methods for solving the neutron transport k-eigenvalue problem

NASA Astrophysics Data System (ADS)

Willert, Jeffrey; Park, H.; Knoll, D. A.

2014-10-01

Over the past several years a number of papers have been written describing modern techniques for numerically computing the dominant eigenvalue of the neutron transport criticality problem. These methods fall into two distinct categories. The first category of methods rewrite the multi-group k-eigenvalue problem as a nonlinear system of equations and solve the resulting system using either a Jacobian-Free Newton-Krylov (JFNK) method or Nonlinear Krylov Acceleration (NKA), a variant of Anderson Acceleration. These methods are generally successful in significantly reducing the number of transport sweeps required to compute the dominant eigenvalue. The second category of methods utilize Moment-Based Acceleration (or High-Order/Low-Order (HOLO) Acceleration). These methods solve a sequence of modified diffusion eigenvalue problems whose solutions converge to the solution of the original transport eigenvalue problem. This second class of methods is, in our experience, always superior to the first, as most of the computational work is eliminated by the acceleration from the LO diffusion system. In this paper, we review each of these methods. Our computational results support our claim that the choice of which nonlinear solver to use, JFNK or NKA, should be secondary. The primary computational savings result from the implementation of a HOLO algorithm. We display computational results for a series of challenging multi-dimensional test problems.

Design of bearings for rotor systems based on stability

NASA Technical Reports Server (NTRS)

Dhar, D.; Barrett, L. E.; Knospe, C. R.

1992-01-01

Design of rotor systems incorporating stable behavior is of great importance to manufacturers of high speed centrifugal machinery since destabilizing mechanisms (from bearings, seals, aerodynamic cross coupling, noncolocation effects from magnetic bearings, etc.) increase with machine efficiency and power density. A new method of designing bearing parameters (stiffness and damping coefficients or coefficients of the controller transfer function) is proposed, based on a numerical search in the parameter space. The feedback control law is based on a decentralized low order controller structure, and the various design requirements are specified as constraints in the specification and parameter spaces. An algorithm is proposed for solving the problem as a sequence of constrained 'minimax' problems, with more and more eigenvalues into an acceptable region in the complex plane. The algorithm uses the method of feasible directions to solve the nonlinear constrained minimization problem at each stage. This methodology emphasizes the designer's interaction with the algorithm to generate acceptable designs by relaxing various constraints and changing initial guesses interactively. A design oriented user interface is proposed to facilitate the interaction.

Prediction of Film Cooling on Gas Turbine Airfoils

NASA Technical Reports Server (NTRS)

Garg, Vijay K.; Gaugler, Raymond E.

1994-01-01

A three-dimensional Navier-Stokes analysis tool has been developed in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine airfoils. An existing code (Arnone et al., 1991) has been modified for the purpose. The code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. Eigenvalue scaled artificial dissipation and variable-coefficient implicit residual smoothing are used with a full-multigrid technique. Moreover, Mayle's transition criterion (Mayle, 1991) is used. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the airfoil surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison is fair with near mid-span experimental data for four and nine rows of cooling holes, five on the shower head, and two rows each on the pressure and suction surfaces. The computations, however, show a strong spanwise variation of the heat transfer coefficient on the airfoil surface, specially with shower-head cooling.

Determination of Rotordynamic Coefficients for Labyrinth Seals and Application to Rotordynamic Design Calculations

NASA Technical Reports Server (NTRS)

Weiser, P.; Nordmann, R.

1991-01-01

In today's rotordynamic calculations, the input parameters for a finite element analysis (FEA) determine very much the reliability of eigenvalue and eigenmode predictions. While modeling of an elastic structure by means of beam elements etc. is relatively straightforward to perform and the input data for journal bearings are usually known exactly enough, the determination of stiffness and damping for labyrinth seals is still the subject of many investigations. Therefore, the rotordynamic influence of labyrinths is often not included in FEA for rotating machinery because of a lack of computer programs to calculate these parameters. This circumstance can give rise to severe vibration problems especially for high performance turbines or compressors, resulting in remarkable economic losses. The forces generated in labyrinths can be described for small motions around the seal center with a linearized force-motion relationship. Several years ago, we started with the development of computer codes for the determination of rotordynamic seal coefficients. Our different approaches to evaluate the dynamic fluid forces generated by turbulent, compressible seal flow are introduced.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments.

PubMed

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Eigenvalues of Random Matrices with Isotropic Gaussian Noise and the Design of Diffusion Tensor Imaging Experiments*

PubMed Central

Gasbarra, Dario; Pajevic, Sinisa; Basser, Peter J.

2017-01-01

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D, observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄. When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model. PMID:28989561

Hessian matrix approach for determining error field sensitivity to coil deviations

NASA Astrophysics Data System (ADS)

Zhu, Caoxiang; Hudson, Stuart R.; Lazerson, Samuel A.; Song, Yuntao; Wan, Yuanxi

2018-05-01

The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code (Zhu et al 2018 Nucl. Fusion 58 016008) is utilized to provide fast and accurate calculations of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1992-01-01

Research conducted during the period from July 1991 through December 1992 is covered. A method based upon the quasi-analytical approach was developed for computing the aerodynamic sensitivity coefficients of three dimensional wings in transonic and subsonic flow. In addition, the method computes for comparison purposes the aerodynamic sensitivity coefficients using the finite difference approach. The accuracy and validity of the methods are currently under investigation.

Sensitivity analysis of reactive ecological dynamics.

PubMed

Verdy, Ariane; Caswell, Hal

2008-08-01

Ecological systems with asymptotically stable equilibria may exhibit significant transient dynamics following perturbations. In some cases, these transient dynamics include the possibility of excursions away from the equilibrium before the eventual return; systems that exhibit such amplification of perturbations are called reactive. Reactivity is a common property of ecological systems, and the amplification can be large and long-lasting. The transient response of a reactive ecosystem depends on the parameters of the underlying model. To investigate this dependence, we develop sensitivity analyses for indices of transient dynamics (reactivity, the amplification envelope, and the optimal perturbation) in both continuous- and discrete-time models written in matrix form. The sensitivity calculations require expressions, some of them new, for the derivatives of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix calculus. Sensitivity analysis provides a quantitative framework for investigating the mechanisms leading to transient growth. We apply the methodology to a predator-prey model and a size-structured food web model. The results suggest predator-driven and prey-driven mechanisms for transient amplification resulting from multispecies interactions.

Active Flow Control and Global Stability Analysis of Separated Flow Over a NACA 0012 Airfoil

NASA Astrophysics Data System (ADS)

Munday, Phillip M.

The objective of this computational study is to examine and quantify the influence of fundamental flow control inputs in suppressing flow separation over a canonical airfoil. Most flow control studies to this date have relied on the development of actuator technology, and described the control input based on specific actuators. Taking advantage of a computational framework, we generalize the inputs to fundamental perturbations without restricting inputs to a particular actuator. Utilizing this viewpoint, generalized control inputs aim to aid in the quantification and support the design of separation control techniques. This study in particular independently introduces wall-normal momentum and angular momentum to the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. By closely studying different variables, the influence of the wall-normal and angular momentum injections on separated flow is identified. As an example, open-loop control of fully separated, incompressible flow over a NACA 0012 airfoil at alpha = 6° and 9° with Re = 23,000 is examined with large-eddy simulations. For the shallow angle of attack alpha = 6°, the small recirculation region is primarily affected by wall-normal momentum injection. For a larger separation region at alpha = 9°, it is observed that the addition of angular momentum input to wall-normal momentum injection enhances the suppression of flow separation. Reducing the size of the separated flow region significantly impacts the forces, and in particular reduces drag and increases lift on the airfoil. It was found that the influence of flow control on the small recirculation region (alpha = 6°) can be sufficiently quantified with the traditional coefficient of momentum. At alpha = 9°, the effects of wall-normal and angular momentum inputs are captured by modifying the standard definition of the coefficient of momentum, which successfully characterizes suppression of separation and lift enhancement. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With the modified coefficient of momentum, this single value is able to categorize controlled flows into separated, transitional, and attached flows. With inadequate control input (separated flow regime), lift decreased compared to the baseline flow. Increasing the modified coefficient of momentum, flow transitions from separated to attached and accordingly results in improved aerodynamic forces. Modifying the spanwise spacing, it is shown that the minimum modified coefficient of momentum input required to begin transitioning the flow is dependent on actuator spacing. The growth (or decay) of perturbations can facilitate or inhibit the influence of flow control inputs. Biglobal stability analysis is considered to further analyze the behavior of control inputs on separated flow over a symmetric airfoil. Assuming a spanwise periodic waveform for the perturbations, the eigenvalues and eigenvectors about a base flow are solved to understand the influence of spanwise variation on the development of the flow. Two algorithms are developed and validated to solve for the eigenvalues of the flow: an algebraic eigenvalue solver (matrix based) and a time-stepping algorithm. The matrix based approach is formulated without ever storing the matrices, creating a computationally memory efficient algorithm. Increasing the Reynolds number to Re = 23,000 over a NACA 0012 airfoil, the time-stepper method is implemented due to rising computational cost of the matrix-based method. Stability analysis about the time-averaged flow is performed for spanwise wavenumbers of beta = 1/c, 10pi/ c and 20pi/c, which the latter two wavenumbers are representative of the spanwise spacing between the actuators. The largest spanwise wavelength (beta = 1/c) contained unstable modes that ranged from low to high frequency, and a particular unstable low-frequency mode corresponding to a frequency observed in the lift forces of the baseline large-eddy simulation. For the larger spanwise wavenumbers, beta = 10pi/ c (Lz/c = 0.2) and 20pi/c (Lz/c = 0.1), low-frequency modes were damped and only modes with f > 5were unstable. These results help us gain further insight into the influence of the flow control inputs. In conclusion, it was shown that the influence of wall-normal and angular momentum inputs on fully separated flow can adequately be described by the modified coefficient of momentum. Through further analysis and the development of a biglobal stability solver, spanwise spacing effects observed in the flow control study can be explained. The findings from this study should aid in the development of more intelligently designed flow control strategies and provide guidance in the selection of flow control actuators.

Algorithm-Eigenvalue Estimation of Hyperspectral Wishart Covariance Matrices from a Limited Number of Samples

DTIC Science & Technology

2015-03-01

ALGORITHM—EIGENVALUE ESTIMATION OF HYPERSPECTRAL WISHART COVARIANCE MATRICES FROM A LIMITED NUMBER OF SAMPLES ECBC-TN-067 Avishai Ben- David ...NUMBER 6. AUTHOR(S) Ben- David , Avishai (ECBC) and Davidson, Charles E. (STC) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7...and published by Avishai Ben- David and Charles E. Davidson (Eigenvalue Estimation of Hyperspectral WishartCovariance Matrices from Limited Number of

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

The nonconforming virtual element method for eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

NASA Astrophysics Data System (ADS)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

The Impact of the Network Topology on the Viral Prevalence: A Node-Based Approach

PubMed Central

Yang, Lu-Xing; Draief, Moez; Yang, Xiaofan

2015-01-01

This paper addresses the impact of the structure of the viral propagation network on the viral prevalence. For that purpose, a new epidemic model of computer virus, known as the node-based SLBS model, is proposed. Our analysis shows that the maximum eigenvalue of the underlying network is a key factor determining the viral prevalence. Specifically, the value range of the maximum eigenvalue is partitioned into three subintervals: viruses tend to extinction very quickly or approach extinction or persist depending on into which subinterval the maximum eigenvalue of the propagation network falls. Consequently, computer virus can be contained by adjusting the propagation network so that its maximum eigenvalue falls into the desired subinterval. PMID:26222539

Thermal sensitivity of elastic coefficients of langasite and langatate.

PubMed

Bourquin, Roger; Dulmet, Bernard

2009-10-01

Thermal coefficients of elastic constants of langasite and langatate crystals have been determined from frequency-temperature curves of contoured resonators operating in thickness modes. The effect of the trapping of the vibration has been taken into account to improve the accuracy. In a first step, the thermal sensitivities of stiffness coefficients in Lagrangian description are obtained. Thermal sensitivities of the usual elastic constants are further deduced. Predictions of thermally compensated cuts are given.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Nicholas; Burns, Joseph R.

The aftermath of the Tōhoku earthquake and the Fukushima accident has led to a global push to improve the safety of existing light water reactors. A key component of this initiative is the development of nuclear fuel and cladding materials with potentially enhanced accident tolerance, also known as accident-tolerant fuels (ATF). These materials are intended to improve core fuel and cladding integrity under beyond design basis accident conditions while maintaining or enhancing reactor performance and safety characteristics during normal operation. To complement research that has already been carried out to characterize ATF neutronics, the present study provides an initial investigationmore » of the sensitivity and uncertainty of ATF systems responses to nuclear cross section data. ATF concepts incorporate novel materials, including SiC and FeCrAl cladding and high density uranium silicide composite fuels, in turn introducing new cross section sensitivities and uncertainties which may behave differently from traditional fuel and cladding materials. In this paper, we conducted sensitivity and uncertainty analysis using the TSUNAMI-2D sequence of SCALE with infinite lattice models of ATF assemblies. Of all the ATF materials considered, it is found that radiative capture in 56Fe in FeCrAl cladding is the most significant contributor to eigenvalue uncertainty. 56Fe yields significant potential eigenvalue uncertainty associated with its radiative capture cross section; this is by far the largest ATF-specific uncertainty found in these cases, exceeding even those of uranium. We found that while significant new sensitivities indeed arise, the general sensitivity behavior of ATF assemblies does not markedly differ from traditional UO2/zirconium-based fuel/cladding systems, especially with regard to uncertainties associated with uranium. We assessed the similarity of the IPEN/MB-01 reactor benchmark model to application models with FeCrAl cladding. We used TSUNAMI-IP to calculate similarity indices of the application model and IPEN/MB-01 reactor benchmark model. This benchmark was selected for its use of SS304 as a cladding and structural material, with significant 56Fe content. The similarity indices suggest that while many differences in reactor physics arise from differences in design, sensitivity to and behavior of 56Fe absorption is comparable between systems, thus indicating the potential for this benchmark to reduce uncertainties in 56Fe radiative capture cross sections.« less

Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

NASA Astrophysics Data System (ADS)

Costiner, Sorin; Ta'asan, Shlomo

1995-07-01

Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

Eigentime identities for on weighted polymer networks

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Tang, Hualong; Zou, Jiahui; He, Di; Sun, Yu; Su, Weiyi

2018-01-01

In this paper, we first analytically calculate the eigenvalues of the transition matrix of a structure with very complex architecture and their multiplicities. We call this structure polymer network. Based on the eigenvalues obtained in the iterative manner, we then calculate the eigentime identity. We highlight two scaling behaviors (logarithmic and linear) for this quantity, strongly depending on the value of the weight factor. Finally, by making use of the obtained eigenvalues, we determine the weighted counting of spanning trees.

A New Measure of Wireless Network Connectivity

DTIC Science & Technology

2014-10-31

matrix QG. From Lemma 1, QG is a non-zero nonnegative matrix. Thus from the Perron - Frobenius Theorem, [24], its largest magni- tude eigenvalue, known as...the Perron - Frobenius eigenvalue is real and positive. Further as QG is symmetric, all its eigenval- ues are real, and its largest magnitude...eigenvalue λmax(QG) is also its largest singular value. Also from the Perron - Frobenius Theorem, should the network be connected, i.e. QG is positive as opposed

Asymptotic theory of a slender rotating beam with end masses.

NASA Technical Reports Server (NTRS)

Whitman, A. M.; Abel, J. M.

1972-01-01

The method of matched asymptotic expansions is employed to solve the singular perturbation problem of the vibrations of a rotating beam of small flexural rigidity with concentrated end masses. The problem is complicated by the appearance of the eigenvalue in the boundary conditions. Eigenfunctions and eigenvalues are developed as power series in the perturbation parameter beta to the 1/2 power, and results are given for mode shapes and eigenvalues through terms of the order of beta.

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

In this article, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE PAGES

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; ...

2017-12-01

In this article, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE PAGES

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue; ...

2017-08-24

Within this paper, we present two efficient iterative algorithms for solving the linear response eigenvalue problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into an eigenvalue problem that involves the product of two matrices M and K. We show that, because MK is self-adjoint with respect to the inner product induced by the matrix K, this product eigenvalue problem can be solved efficiently by amore » modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. Additionally, the solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. We show that the other component of the eigenvector can be easily recovered in an inexpensive postprocessing procedure. As a result, the algorithms we present here become more efficient than existing methods that try to approximate both components of the eigenvectors simultaneously. In particular, our numerical experiments demonstrate that the new algorithms presented here consistently outperform the existing state-of-the-art Davidson type solvers by a factor of two in both solution time and storage.« less

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vecharynski, Eugene; Brabec, Jiri; Shao, Meiyue

We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-innermore » product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.« less

The wasteland of random supergravities

NASA Astrophysics Data System (ADS)

Marsh, David; McAllister, Liam; Wrase, Timm

2012-03-01

We show that in a general {N} = {1} supergravity with N ≫ 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kähler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P ∝ exp(- c N p ), with c, p being constants. For generic critical points we find p ≈ 1 .5, while for approximately-supersymmetric critical points, p ≈ 1 .3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.

3-D phononic crystals with ultra-wide band gaps

PubMed Central

Lu, Yan; Yang, Yang; Guest, James K.; Srivastava, Ankit

2017-01-01

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions. PMID:28233812

3-D phononic crystals with ultra-wide band gaps.

PubMed

Lu, Yan; Yang, Yang; Guest, James K; Srivastava, Ankit

2017-02-24

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.

The eigenvalue problem in phase space.

PubMed

Cohen, Leon

2018-06-30

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1991-01-01

The three dimensional quasi-analytical sensitivity analysis and the ancillary driver programs are developed needed to carry out the studies and perform comparisons. The code is essentially contained in one unified package which includes the following: (1) a three dimensional transonic wing analysis program (ZEBRA); (2) a quasi-analytical portion which determines the matrix elements in the quasi-analytical equations; (3) a method for computing the sensitivity coefficients from the resulting quasi-analytical equations; (4) a package to determine for comparison purposes sensitivity coefficients via the finite difference approach; and (5) a graphics package.

Efficient sensitivity analysis method for chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Liao, Haitao

2016-05-01

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results in an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.

Low temperature nano-spin filtering using a diluted magnetic semiconductor core-shell quantum dot

NASA Astrophysics Data System (ADS)

Chattopadhyay, Saikat; Sen, Pratima; Andrews, Joshep Thomas; Sen, Pranay Kumar

2014-07-01

The spin polarized electron transport properties and spin polarized tunneling current have been investigated analytically in a diluted magnetic semiconductor core-shell quantum dot in the presence of applied electric and magnetic fields. Assuming the electron wave function to satisfy WKB approximation, the electron energy eigenvalues have been calculated. The spin polarized tunneling current and the spin dependent tunneling coefficient are obtained by taking into account the exchange interaction and Zeeman splitting. Numerical estimates made for a specific diluted magnetic semiconductor, viz., Zn1-xMnxSe/ZnS core-shell quantum dot establishes the possibility of a nano-spin filter for a particular biasing voltage and applied magnetic field. Influence of applied voltage on spin polarized electron transport has been investigated in a CSQD.

Scaling and correlations in foreign exchange market

NASA Astrophysics Data System (ADS)

Jiang, J.; Ma, K.; Cai, X.

2007-02-01

We observe that the distribution of the relative return, describing the variation of a certain currency, of 74 global currencies obeys a power-law. By using the random matrix theory we find that the distribution of eigenvalues of correlation matrix of relative return also follows a power-law. Using a scaled factorial moment we investigate the distribution of correlation coefficients of the relative return and observe intermittence phenomenon. Furthermore, we define the influence strength for a certain currency, which reflects the influence of its price change to the community interested. By doing that, we find that the distribution of influence strength is again a power-law. Beyond that, we compare the influence strength of Chinese Yuan (RMB) to those of other seven important currencies, which may have some interesting indications.

Dynamic modeling of vegetation change in arid lands

NASA Technical Reports Server (NTRS)

Robinson, V. B.; Coiner, J. C.; Barringer, T. H.

1982-01-01

A general framework for a digital desertification monitoring system (DDMS) for assessing the worldwide desertification growth rate is presented. The system relies on the development of Landsat derived indicators to identify local processes signalling the growth of arid regions. A study area consisting of the eastern edge of the Niger River delta in Mali was used to characterize three indicators in terms of the covariance of the multispectral scanner (MSS) bands 2 and 4, the correlation of the two bands, and the percent variance expressed by the first eigenvalue. The scenes are imaged multitemporallly in a 400 x 400 pixel array to detect vegetation cover changes. Criteria were defined which characterized the decrease or increase of vegetation. It was determined that the correlation coefficients are the best indicators, and are easily computed.

Method for computing self-consistent solution in a gun code

DOEpatents

Nelson, Eric M

2014-09-23

Complex gun code computations can be made to converge more quickly based on a selection of one or more relaxation parameters. An eigenvalue analysis is applied to error residuals to identify two error eigenvalues that are associated with respective error residuals. Relaxation values can be selected based on these eigenvalues so that error residuals associated with each can be alternately reduced in successive iterations. In some examples, relaxation values that would be unstable if used alone can be used.

PT-symmetric eigenvalues for homogeneous potentials

NASA Astrophysics Data System (ADS)

Eremenko, Alexandre; Gabrielov, Andrei

2018-05-01

We consider one-dimensional Schrödinger equations with potential x2M(ix)ɛ, where M ≥ 1 is an integer and ɛ is real, under appropriate parity and time (PT)-symmetric boundary conditions. We prove the phenomenon which was discovered by Bender and Boettcher by numerical computation: as ɛ changes, the real spectrum suddenly becomes non-real in the sense that all but finitely many eigenvalues become non-real. We find the limit arguments of these non-real eigenvalues E as E → ∞.

Spectral properties of Google matrix of Wikipedia and other networks

NASA Astrophysics Data System (ADS)

Ermann, Leonardo; Frahm, Klaus M.; Shepelyansky, Dima L.

2013-05-01

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.

An accurate method for solving a class of fractional Sturm-Liouville eigenvalue problems

NASA Astrophysics Data System (ADS)

Kashkari, Bothayna S. H.; Syam, Muhammed I.

2018-06-01

This article is devoted to both theoretical and numerical study of the eigenvalues of nonsingular fractional second-order Sturm-Liouville problem. In this paper, we implement a fractional-order Legendre Tau method to approximate the eigenvalues. This method transforms the Sturm-Liouville problem to a sparse nonsingular linear system which is solved using the continuation method. Theoretical results for the considered problem are provided and proved. Numerical results are presented to show the efficiency of the proposed method.

Dynamic evolution of cross-correlations in the Chinese stock market.

PubMed

Ren, Fei; Zhou, Wei-Xing

2014-01-01

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management.

Dynamic Evolution of Cross-Correlations in the Chinese Stock Market

PubMed Central

Ren, Fei; Zhou, Wei-Xing

2014-01-01

The analysis of cross-correlations is extensively applied for the understanding of interconnections in stock markets and the portfolio risk estimation. Current studies of correlations in Chinese market mainly focus on the static correlations between return series, and this calls for an urgent need to investigate their dynamic correlations. Our study aims to reveal the dynamic evolution of cross-correlations in the Chinese stock market, and offer an exact interpretation for the evolution behavior. The correlation matrices constructed from the return series of 367 A-share stocks traded on the Shanghai Stock Exchange from January 4, 1999 to December 30, 2011 are calculated over a moving window with a size of 400 days. The evolutions of the statistical properties of the correlation coefficients, eigenvalues, and eigenvectors of the correlation matrices are carefully analyzed. We find that the stock correlations are significantly increased in the periods of two market crashes in 2001 and 2008, during which only five eigenvalues significantly deviate from the random correlation matrix, and the systemic risk is higher in these volatile periods than calm periods. By investigating the significant contributors of the deviating eigenvectors in different time periods, we observe a dynamic evolution behavior in business sectors such as IT, electronics, and real estate, which lead the rise (drop) before (after) the crashes. Our results provide new perspectives for the understanding of the dynamic evolution of cross-correlations in the Chines stock markets, and the result of risk estimation is valuable for the application of risk management. PMID:24867071

Mean Flow Augmented Acoustics in Rocket Systems

NASA Technical Reports Server (NTRS)

Fischbach, Sean R.

2014-01-01

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) - (lambda/c)(exp 2)(psi) - M(dot)[M(dot)(del)(del(psi))] - 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)-2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Reliability and validity of the Incontinence Quiz-Turkish version.

PubMed

Kara, Kerime C; Çıtak Karakaya, İlkim; Tunalı, Nur; Karakaya, Mehmet G

2018-01-01

The aim of this study was to investigate the reliability and validity of the Turkish version of the Incontinence Quiz, which was developed by Branch et al. (1994), to assess women's knowledge of and attitudes toward urinary incontinence. Comprehensibility of the Turkish version of the 14-item Incontinence Quiz, which was prepared following translation-back translation procedures, was tested on a pilot group of eight women, and its internal reliability, test-retest reliability and construct validity were assessed in 150 women who attended the gynecology clinics of three hospitals in İçel, Turkey. Physical and sociodemographic characteristics and presence of incontinence complaints were also recorded. Data were analyzed at the 0.05 alpha level, using SPSS version 22. The scale had good reliability and validity. The internal reliability coefficient (Cronbach α) was 0.80, test-retest correlation coefficients were 0.83-0.94; and with regard to construct validity, Kaiser-Meyer-Olkin coefficient was 0.76 and Barlett sphericity test was 562.777 (P = 0.000). Turkish version of the Incontinence Quiz had a four-factor structure, with Eigenvalues ranging from 1.17 to 4.08. The Incontinence Quiz-Turkish version is a highly comprehensible, reliable and valid scale, which may be used to assess Turkish-speaking women's knowledge of and attitudes toward urinary incontinence. © 2017 Japan Society of Obstetrics and Gynecology.

Effect of noise in principal component analysis with an application to ozone pollution

NASA Astrophysics Data System (ADS)

Tsakiri, Katerina G.

This thesis analyzes the effect of independent noise in principal components of k normally distributed random variables defined by a covariance matrix. We prove that the principal components as well as the canonical variate pairs determined from joint distribution of original sample affected by noise can be essentially different in comparison with those determined from the original sample. However when the differences between the eigenvalues of the original covariance matrix are sufficiently large compared to the level of the noise, the effect of noise in principal components and canonical variate pairs proved to be negligible. The theoretical results are supported by simulation study and examples. Moreover, we compare our results about the eigenvalues and eigenvectors in the two dimensional case with other models examined before. This theory can be applied in any field for the decomposition of the components in multivariate analysis. One application is the detection and prediction of the main atmospheric factor of ozone concentrations on the example of Albany, New York. Using daily ozone, solar radiation, temperature, wind speed and precipitation data, we determine the main atmospheric factor for the explanation and prediction of ozone concentrations. A methodology is described for the decomposition of the time series of ozone and other atmospheric variables into the global term component which describes the long term trend and the seasonal variations, and the synoptic scale component which describes the short term variations. By using the Canonical Correlation Analysis, we show that solar radiation is the only main factor between the atmospheric variables considered here for the explanation and prediction of the global and synoptic scale component of ozone. The global term components are modeled by a linear regression model, while the synoptic scale components by a vector autoregressive model and the Kalman filter. The coefficient of determination, R2, for the prediction of the synoptic scale ozone component was found to be the highest when we consider the synoptic scale component of the time series for solar radiation and temperature. KEY WORDS: multivariate analysis; principal component; canonical variate pairs; eigenvalue; eigenvector; ozone; solar radiation; spectral decomposition; Kalman filter; time series prediction

Lyapunov exponents, covariant vectors and shadowing sensitivity analysis of 3D wakes: from laminar to chaotic regimes

NASA Astrophysics Data System (ADS)

Wang, Qiqi; Rigas, Georgios; Esclapez, Lucas; Magri, Luca; Blonigan, Patrick

2016-11-01

Bluff body flows are of fundamental importance to many engineering applications involving massive flow separation and in particular the transport industry. Coherent flow structures emanating in the wake of three-dimensional bluff bodies, such as cars, trucks and lorries, are directly linked to increased aerodynamic drag, noise and structural fatigue. For low Reynolds laminar and transitional regimes, hydrodynamic stability theory has aided the understanding and prediction of the unstable dynamics. In the same framework, sensitivity analysis provides the means for efficient and optimal control, provided the unstable modes can be accurately predicted. However, these methodologies are limited to laminar regimes where only a few unstable modes manifest. Here we extend the stability analysis to low-dimensional chaotic regimes by computing the Lyapunov covariant vectors and their associated Lyapunov exponents. We compare them to eigenvectors and eigenvalues computed in traditional hydrodynamic stability analysis. Computing Lyapunov covariant vectors and Lyapunov exponents also enables the extension of sensitivity analysis to chaotic flows via the shadowing method. We compare the computed shadowing sensitivities to traditional sensitivity analysis. These Lyapunov based methodologies do not rely on mean flow assumptions, and are mathematically rigorous for calculating sensitivities of fully unsteady flow simulations.

A control system design approach for flexible spacecraft

NASA Technical Reports Server (NTRS)

Silverberg, L. M.

1985-01-01

A control system design approach for flexible spacecraft is presented. The control system design is carried out in two steps. The first step consists of determining the ideal control system in terms of a desirable dynamic performance. The second step consists of designing a control system using a limited number of actuators that possess a dynamic performance that is close to the ideal dynamic performance. The effects of using a limited number of actuators is that the actual closed-loop eigenvalues differ from the ideal closed-loop eigenvalues. A method is presented to approximate the actual closed-loop eigenvalues so that the calculation of the actual closed-loop eigenvalues can be avoided. Depending on the application, it also may be desirable to apply the control forces as impulses. The effect of digitizing the control to produce the appropriate impulses is also examined.

Fine structure of spectral properties for random correlation matrices: An application to financial markets

NASA Astrophysics Data System (ADS)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

The Theory of Quantized Fields. III

DOE R&D Accomplishments Database

Schwinger, J.

1953-05-01

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

Multigrid method for stability problems

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo

1988-01-01

The problem of calculating the stability of steady state solutions of differential equations is addressed. Leading eigenvalues of large matrices that arise from discretization are calculated, and an efficient multigrid method for solving these problems is presented. The resulting grid functions are used as initial approximations for appropriate eigenvalue problems. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a nonstandard way in which the right-hand side of the coarse grid equations involves unknown parameters to be solved on the coarse grid. This leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem are presented which demonstrate the effectiveness of the method.

Sensitivity study on durability variables of marine concrete structures

NASA Astrophysics Data System (ADS)

Zhou, Xin'gang; Li, Kefei

2013-06-01

In order to study the influence of parameters on durability of marine concrete structures, the parameter's sensitivity analysis was studied in this paper. With the Fick's 2nd law of diffusion and the deterministic sensitivity analysis method (DSA), the sensitivity factors of apparent surface chloride content, apparent chloride diffusion coefficient and its time dependent attenuation factor were analyzed. The results of the analysis show that the impact of design variables on concrete durability was different. The values of sensitivity factor of chloride diffusion coefficient and its time dependent attenuation factor were higher than others. Relative less error in chloride diffusion coefficient and its time dependent attenuation coefficient induces a bigger error in concrete durability design and life prediction. According to probability sensitivity analysis (PSA), the influence of mean value and variance of concrete durability design variables on the durability failure probability was studied. The results of the study provide quantitative measures of the importance of concrete durability design and life prediction variables. It was concluded that the chloride diffusion coefficient and its time dependent attenuation factor have more influence on the reliability of marine concrete structural durability. In durability design and life prediction of marine concrete structures, it was very important to reduce the measure and statistic error of durability design variables.

CONTINUOUS-ENERGY MONTE CARLO METHODS FOR CALCULATING GENERALIZED RESPONSE SENSITIVITIES USING TSUNAMI-3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M; Rearden, Bradley T

2014-01-01

This work introduces a new approach for calculating sensitivity coefficients for generalized neutronic responses to nuclear data uncertainties using continuous-energy Monte Carlo methods. The approach presented in this paper, known as the GEAR-MC method, allows for the calculation of generalized sensitivity coefficients for multiple responses in a single Monte Carlo calculation with no nuclear data perturbations or knowledge of nuclear covariance data. The theory behind the GEAR-MC method is presented here, and proof of principle is demonstrated by using the GEAR-MC method to calculate sensitivity coefficients for responses in several 3D, continuous-energy Monte Carlo applications.

Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

1992-01-01

An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

Determination of aerodynamic sensitivity coefficients for wings in transonic flow

NASA Technical Reports Server (NTRS)

Carlson, Leland A.; El-Banna, Hesham M.

1992-01-01

The quasianalytical approach is applied to the 3-D full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. The quasianalytical approach is believed to be reasonably accurate and computationally efficient for 3-D problems.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Edge connectivity and the spectral gap of combinatorial and quantum graphs

NASA Astrophysics Data System (ADS)

Berkolaiko, Gregory; Kennedy, James B.; Kurasov, Pavel; Mugnolo, Delio

2017-09-01

We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are ‘asymptotically correct’, i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liao, Haitao, E-mail: liaoht@cae.ac.cn

The direct differentiation and improved least squares shadowing methods are both developed for accurately and efficiently calculating the sensitivity coefficients of time averaged quantities for chaotic dynamical systems. The key idea is to recast the time averaged integration term in the form of differential equation before applying the sensitivity analysis method. An additional constraint-based equation which forms the augmented equations of motion is proposed to calculate the time averaged integration variable and the sensitivity coefficients are obtained as a result of solving the augmented differential equations. The application of the least squares shadowing formulation to the augmented equations results inmore » an explicit expression for the sensitivity coefficient which is dependent on the final state of the Lagrange multipliers. The LU factorization technique to calculate the Lagrange multipliers leads to a better performance for the convergence problem and the computational expense. Numerical experiments on a set of problems selected from the literature are presented to illustrate the developed methods. The numerical results demonstrate the correctness and effectiveness of the present approaches and some short impulsive sensitivity coefficients are observed by using the direct differentiation sensitivity analysis method.« less

Eigenvalue Detonation of Combined Effects Aluminized Explosives

NASA Astrophysics Data System (ADS)

Capellos, C.; Baker, E. L.; Nicolich, S.; Balas, W.; Pincay, J.; Stiel, L. I.

2007-12-01

Theory and performance for recently developed combined—effects aluminized explosives are presented. Our recently developed combined-effects aluminized explosives (PAX-29C, PAX-30, PAX-42) are capable of achieving excellent metal pushing, as well as high blast energies. Metal pushing capability refers to the early volume expansion work produced during the first few volume expansions associated with cylinder and wall velocities and Gurney energies. Eigenvalue detonation explains the observed detonation states achieved by these combined effects explosives. Cylinder expansion data and thermochemical calculations (JAGUAR and CHEETAH) verify the eigenvalue detonation behavior.

NASA Astrophysics Data System (ADS)

2018-05-01

Eigenvalues and eigenvectors, together, constitute the eigenstructure of the system. The design of vibrating systems aimed at satisfying specifications on eigenvalues and eigenvectors, which is commonly known as eigenstructure assignment, has drawn increasing interest over the recent years. The most natural mathematical framework for such problems is constituted by the inverse eigenproblems, which consist in the determination of the system model that features a desired set of eigenvalues and eigenvectors. Although such a problem is intrinsically challenging, several solutions have been proposed in the literature. The approaches to eigenstructure assignment can be basically divided into passive control and active control.

Dimension from covariance matrices.

PubMed

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1978-01-01

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular.

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

A new localization set for generalized eigenvalues.

PubMed

Gao, Jing; Li, Chaoqian

2017-01-01

A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16:883-898, 2009). Numerical examples are given to verify the corresponding results.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar

2016-06-15

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators aremore » useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.« less

Rich structure in the correlation matrix spectra in non-equilibrium steady states

NASA Astrophysics Data System (ADS)

Biswas, Soham; Leyvraz, Francois; Monroy Castillero, Paulino; Seligman, Thomas H.

2017-01-01

It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this paper is to show that the converse is generally incorrect: a power-law tail in the high-lying eigenvalues of the correlation matrix may exist even in the absence of equal-time power law correlations in the initial model. We may therefore view the study of the eigenvalue distribution of the correlation matrix as a more powerful tool than the study of spatial Correlations, one which may in fact uncover structure, that would otherwise not be apparent. Specifically, we show that in the Totally Asymmetric Simple Exclusion Process, whereas there are no clearly visible correlations in the steady state, the eigenvalues of its correlation matrix exhibit a rich structure which we describe in detail.

A Decentralized Eigenvalue Computation Method for Spectrum Sensing Based on Average Consensus

NASA Astrophysics Data System (ADS)

Mohammadi, Jafar; Limmer, Steffen; Stańczak, Sławomir

2016-07-01

This paper considers eigenvalue estimation for the decentralized inference problem for spectrum sensing. We propose a decentralized eigenvalue computation algorithm based on the power method, which is referred to as generalized power method GPM; it is capable of estimating the eigenvalues of a given covariance matrix under certain conditions. Furthermore, we have developed a decentralized implementation of GPM by splitting the iterative operations into local and global computation tasks. The global tasks require data exchange to be performed among the nodes. For this task, we apply an average consensus algorithm to efficiently perform the global computations. As a special case, we consider a structured graph that is a tree with clusters of nodes at its leaves. For an accelerated distributed implementation, we propose to use computation over multiple access channel (CoMAC) as a building block of the algorithm. Numerical simulations are provided to illustrate the performance of the two algorithms.

Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects

NASA Astrophysics Data System (ADS)

Castellano, Claudio; Pastor-Satorras, Romualdo

2017-10-01

The largest eigenvalue of a network's adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expression relating the value of the largest eigenvalue of a given network to the largest eigenvalue of two network subgraphs, considered as isolated: the hub with its immediate neighbors and the densely connected set of nodes with maximum K -core index. We validate this formula by showing that it predicts, with good accuracy, the largest eigenvalue of a large set of synthetic and real-world topologies. We also present evidence of the consequences of these findings for broad classes of dynamics taking place on the networks. As a by-product, we reveal that the spectral properties of heterogeneous networks built according to the linear preferential attachment model are qualitatively different from those of their static counterparts.

Intrinsic character of Stokes matrices

NASA Astrophysics Data System (ADS)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.

Eigenvalue routines in NASTRAN: A comparison with the Block Lanczos method

NASA Technical Reports Server (NTRS)

Tischler, V. A.; Venkayya, Vipperla B.

1993-01-01

The NASA STRuctural ANalysis (NASTRAN) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this paper is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the Block Lanczos algorithm by Boeing Computer Services (BCS). This eigenvalue routine is now available in the BCS mathematics library as well as in several commercial versions of NASTRAN. In addition, CRAY maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The Block Lanczos algorithm was found to be extremely efficient, in particular, for very large size problems.

Eigenvalue statistics for the sum of two complex Wishart matrices

NASA Astrophysics Data System (ADS)

Kumar, Santosh

2014-09-01

The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However, analytical results concerning the corresponding eigenvalue statistics have remained unavailable, even for the sum of two Wishart matrices. This can be attributed to the complicated and rotationally noninvariant nature of the matrix distribution that makes extracting the information about eigenvalues a nontrivial task. Using a generalization of the Harish-Chandra-Itzykson-Zuber integral, we find exact solution to this problem for the complex Wishart case when one of the covariance matrices is proportional to the identity matrix, while the other is arbitrary. We derive exact and compact expressions for the joint probability density and marginal density of eigenvalues. The analytical results are compared with numerical simulations and we find perfect agreement.

Rich structure in the correlation matrix spectra in non-equilibrium steady states.

PubMed

Biswas, Soham; Leyvraz, Francois; Monroy Castillero, Paulino; Seligman, Thomas H

2017-01-17

It has been shown that, if a model displays long-range (power-law) spatial correlations, its equal-time correlation matrix will also have a power law tail in the distribution of its high-lying eigenvalues. The purpose of this paper is to show that the converse is generally incorrect: a power-law tail in the high-lying eigenvalues of the correlation matrix may exist even in the absence of equal-time power law correlations in the initial model. We may therefore view the study of the eigenvalue distribution of the correlation matrix as a more powerful tool than the study of spatial Correlations, one which may in fact uncover structure, that would otherwise not be apparent. Specifically, we show that in the Totally Asymmetric Simple Exclusion Process, whereas there are no clearly visible correlations in the steady state, the eigenvalues of its correlation matrix exhibit a rich structure which we describe in detail.

Clinical and microperimetric predictors of reading speed in low vision patients: a structural equation modeling approach.

PubMed

Giacomelli, Giovanni; Virgili, Gianni; Giansanti, Fabrizio; Sato, Giovanni; Cappello, Ezio; Cruciani, Filippo; Varano, Monica; Menchini, Ugo

2013-06-27

To investigate the simultaneous association of several psychophysical measures with reading ability in patients with mild and moderate low vision attending rehabilitation services. Standard measurements of reading ability (Minnesota Reading [MNREAD] charts), visual acuity (Early Treatment of Diabetic Retinopathy Study [ETDRS] charts), contrast sensitivity (Pelli-Robson charts), reading contrast threshold (Reading Explorer [REX] charts), retinal sensitivity, and fixation stability and localization (Micro Perimeter 1 [MP1] fundus perimetry) were obtained in 160 low vision patients with better eye visual acuity ranging from 0.3 to 1.0 logarithm of the minimum angle of resolution and affected by either age-related macular degeneration or diabetic retinopathy. All variables were moderately associated with reading performance measures (MNREAD reading speed and reading acuity and REX reading contrast threshold), as well as among each other. In a structural equation model, REX reading contrast threshold was highly associated with MNREAD reading speed (standardized coefficient, 0.63) and moderately associated with reading acuity (standardized coefficient, -0.30). REX test also mediated the effects of Pelli-Robson contrast sensitivity (standardized coefficient, 0.44), MP1 fixation eccentricity (standardized coefficient, -0.19), and the mean retinal sensitivity (standardized coefficient, 0.23) on reading performance. The MP1 fixation stability was associated with both MNREAD reading acuity (standardized coefficient, -0.24) and MNREAD reading speed (standardized coefficient, 0.23), while ETDRS visual acuity only affected reading acuity (standardized coefficient, 0.44). Fixation instability and contrast sensitivity loss are key factors limiting reading performance of patients with mild or moderate low vision. REX charts directly assess the impact of text contrast on letter recognition and text navigation and may be a useful aid in reading rehabilitation.

A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.

PubMed

Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui

2018-06-01

The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.

More insights into early brain development through statistical analyses of eigen-structural elements of diffusion tensor imaging using multivariate adaptive regression splines

PubMed Central

Chen, Yasheng; Zhu, Hongtu; An, Hongyu; Armao, Diane; Shen, Dinggang; Gilmore, John H.; Lin, Weili

2013-01-01

The aim of this study was to characterize the maturational changes of the three eigenvalues (λ1 ≥ λ2 ≥ λ3) of diffusion tensor imaging (DTI) during early postnatal life for more insights into early brain development. In order to overcome the limitations of using presumed growth trajectories for regression analysis, we employed Multivariate Adaptive Regression Splines (MARS) to derive data-driven growth trajectories for the three eigenvalues. We further employed Generalized Estimating Equations (GEE) to carry out statistical inferences on the growth trajectories obtained with MARS. With a total of 71 longitudinal datasets acquired from 29 healthy, full-term pediatric subjects, we found that the growth velocities of the three eigenvalues were highly correlated, but significantly different from each other. This paradox suggested the existence of mechanisms coordinating the maturations of the three eigenvalues even though different physiological origins may be responsible for their temporal evolutions. Furthermore, our results revealed the limitations of using the average of λ2 and λ3 as the radial diffusivity in interpreting DTI findings during early brain development because these two eigenvalues had significantly different growth velocities even in central white matter. In addition, based upon the three eigenvalues, we have documented the growth trajectory differences between central and peripheral white matter, between anterior and posterior limbs of internal capsule, and between inferior and superior longitudinal fasciculus. Taken together, we have demonstrated that more insights into early brain maturation can be gained through analyzing eigen-structural elements of DTI. PMID:23455648

Hessian matrix approach for determining error field sensitivity to coil deviations.

DOE PAGES

Zhu, Caoxiang; Hudson, Stuart R.; Lazerson, Samuel A.; ...

2018-03-15

The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculationsmore » of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.« less

Hessian matrix approach for determining error field sensitivity to coil deviations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Caoxiang; Hudson, Stuart R.; Lazerson, Samuel A.

The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculationsmore » of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.« less

Dimensionality of genomic information and performance of the Algorithm for Proven and Young for different livestock species.

PubMed

Pocrnic, Ivan; Lourenco, Daniela A L; Masuda, Yutaka; Misztal, Ignacy

2016-10-31

A genomic relationship matrix (GRM) can be inverted efficiently with the Algorithm for Proven and Young (APY) through recursion on a small number of core animals. The number of core animals is theoretically linked to effective population size (N e ). In a simulation study, the optimal number of core animals was equal to the number of largest eigenvalues of GRM that explained 98% of its variation. The purpose of this study was to find the optimal number of core animals and estimate N e for different species. Datasets included phenotypes, pedigrees, and genotypes for populations of Holstein, Jersey, and Angus cattle, pigs, and broiler chickens. The number of genotyped animals varied from 15,000 for broiler chickens to 77,000 for Holsteins, and the number of single-nucleotide polymorphisms used for genomic prediction varied from 37,000 to 61,000. Eigenvalue decomposition of the GRM for each population determined numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of variation. The number of eigenvalues corresponding to 90% (98%) of variation was 4527 (14,026) for Holstein, 3325 (11,500) for Jersey, 3654 (10,605) for Angus, 1239 (4103) for pig, and 1655 (4171) for broiler chicken. Each trait in each species was analyzed using the APY inverse of the GRM with randomly selected core animals, and their number was equal to the number of largest eigenvalues. Realized accuracies peaked with the number of core animals corresponding to 98% of variation for Holstein and Jersey and closer to 99% for other breed/species. N e was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, N e was equal to 149 for Holsteins, 101 for Jerseys, 113 for Angus, 32 for pigs, and 44 for broilers. Eigenvalue profiles of GRM for common species are similar to those in simulation studies although they are affected by number of genotyped animals and genotyping quality. For all investigated species, the APY required less than 15,000 core animals. Realized accuracies were equal or greater with the APY inverse than with regular inversion. Eigenvalue analysis of GRM can provide a realistic estimate of N e .

Dynamical eigenfunction decomposition of turbulent channel flow

NASA Technical Reports Server (NTRS)

Ball, K. S.; Sirovich, L.; Keefe, L. R.

1991-01-01

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re(tau) = 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 percent of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions.

Plunges in the Bombay stock exchange: Characteristics and indicators

NASA Astrophysics Data System (ADS)

Banerjee, Kinjal; Sharma, Chandradew; Bittu, N.

2017-09-01

We study the various sectors of the Bombay Stock Exchange (BSE) for a period of eight years from January 2006-March 2014. Using the data of the daily returns of a period of eight years we investigate the financial cross-correlation co-efficients among the sectors of BSE and Price by Earning (PE) ratio of BSE Sensex. We show that the behavior of these quantities during normal periods and during crisis is very different. We show that the PE ratio shows a particular distinctive trend in the approach to a crash of the financial market and can therefore be used as an indicator of an impending catastrophe. We propose that a model of analysis of crashes in a financial market can be built using two parameters: (i) the PE ratio and (ii) the largest eigenvalue of the cross-correlation matrix.

Control of mechanical systems by the mixed "time and expenditure" criterion

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

The optimal controlled motion of a mechanical system, that is determined by the linear system ODE with constant coefficients and piecewise constant control components, is considered. The number of control switching points and the heights of control steps are considered as preset. The optimized functional is combination of classical time criteria and "Expenditure criteria", that is equal to the total area of all steps of all control components. In the absence of control, the solution of the system is equal to the sum of components (frequency components) corresponding to different eigenvalues of the matrix of the ODE system. Admissible controls are those that turn to zero (at a non predetermined time moment) the previously chosen frequency components of the solution. An algorithm for the finding of control switching points, based on the necessary minimum conditions for mixed criteria, is proposed.

Sensitivity of mRNA Translation

PubMed Central

Poker, Gilad; Margaliot, Michael; Tuller, Tamir

2015-01-01

Using the dynamic mean-field approximation of the totally asymmetric simple exclusion process (TASEP), we investigate the effect of small changes in the initiation, elongation, and termination rates along the mRNA strand on the steady-state protein translation rate. We show that the sensitivity of mRNA translation is equal to the sensitivity of the maximal eigenvalue of a symmetric, nonnegative, tridiagonal, and irreducible matrix. This leads to new analytical results as well as efficient numerical schemes that are applicable for large-scale models. Our results show that in the usual endogenous case, when initiation is more rate-limiting than elongation, the sensitivity of the translation rate to small mutations rapidly increases towards the 5′ end of the ORF. When the initiation rate is high, as may be the case for highly expressed and/or heterologous optimized genes, the maximal sensitivity is with respect to the elongation rates at the middle of the mRNA strand. We also show that the maximal possible effect of a small increase/decrease in any of the rates along the mRNA is an increase/decrease of the same magnitude in the translation rate. These results are in agreement with previous molecular evolutionary and synthetic biology experimental studies. PMID:26238363

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Bains, N. J. C.

1986-01-01

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Eigenvalues of the Laplacian of a graph

NASA Technical Reports Server (NTRS)

Anderson, W. N., Jr.; Morley, T. D.

1971-01-01

Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix of G, Delta(G), is defined by Delta sub ii = degree of vertex i and Delta sub ij = -1 if there is an edge between vertex i and vertex j. The structure of the graph G is related to the eigenvalues of Delta(G); in particular, it is proved that all the eigenvalues of Delta(G) are nonnegative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given.

A differentiable reformulation for E-optimal design of experiments in nonlinear dynamic biosystems.

PubMed

Telen, Dries; Van Riet, Nick; Logist, Flip; Van Impe, Jan

2015-06-01

Informative experiments are highly valuable for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. The E-criterion which can be used as objective function in optimal experiment design requires the maximization of the smallest eigenvalue of the Fisher information matrix. However, one problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, no closed form expression exists for the computation of eigenvalues of a matrix larger than a 4 by 4 one. As eigenvalues are normally computed with iterative methods, state-of-the-art optimal control solvers are not able to exploit automatic differentiation to compute the derivatives with respect to the decision variables. In the current paper a reformulation strategy from the field of convex optimization is suggested to circumvent these difficulties. This reformulation requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. In this paper, this positive semidefiniteness constraint is imposed via Sylverster's criterion. As a result the maximization of the minimum eigenvalue function can be formulated in standard optimal control solvers through the addition of nonlinear constraints. The presented methodology is successfully illustrated with a case study from the field of predictive microbiology. Copyright © 2015. Published by Elsevier Inc.

A Novel Hyperbolization Procedure for The Two-Phase Six-Equation Flow Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samet Y. Kadioglu; Robert Nourgaliev; Nam Dinh

2011-10-01

We introduce a novel approach for the hyperbolization of the well-known two-phase six equation flow model. The six-equation model has been frequently used in many two-phase flow applications such as bubbly fluid flows in nuclear reactors. One major drawback of this model is that it can be arbitrarily non-hyperbolic resulting in difficulties such as numerical instability issues. Non-hyperbolic behavior can be associated with complex eigenvalues that correspond to characteristic matrix of the system. Complex eigenvalues are often due to certain flow parameter choices such as the definition of inter-facial pressure terms. In our method, we prevent the characteristic matrix receivingmore » complex eigenvalues by fine tuning the inter-facial pressure terms with an iterative procedure. In this way, the characteristic matrix possesses all real eigenvalues meaning that the characteristic wave speeds are all real therefore the overall two-phase flowmodel becomes hyperbolic. The main advantage of this is that one can apply less diffusive highly accurate high resolution numerical schemes that often rely on explicit calculations of real eigenvalues. We note that existing non-hyperbolic models are discretized mainly based on low order highly dissipative numerical techniques in order to avoid stability issues.« less

Emergent spectral properties of river network topology: an optimal channel network approach.

PubMed

Abed-Elmdoust, Armaghan; Singh, Arvind; Yang, Zong-Liang

2017-09-13

Characterization of river drainage networks has been a subject of research for many years. However, most previous studies have been limited to quantities which are loosely connected to the topological properties of these networks. In this work, through a graph-theoretic formulation of drainage river networks, we investigate the eigenvalue spectra of their adjacency matrix. First, we introduce a graph theory model for river networks and explore the properties of the network through its adjacency matrix. Next, we show that the eigenvalue spectra of such complex networks follow distinct patterns and exhibit striking features including a spectral gap in which no eigenvalue exists as well as a finite number of zero eigenvalues. We show that such spectral features are closely related to the branching topology of the associated river networks. In this regard, we find an empirical relation for the spectral gap and nullity in terms of the energy dissipation exponent of the drainage networks. In addition, the eigenvalue distribution is found to follow a finite-width probability density function with certain skewness which is related to the drainage pattern. Our results are based on optimal channel network simulations and validated through examples obtained from physical experiments on landscape evolution. These results suggest the potential of the spectral graph techniques in characterizing and modeling river networks.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

TIMEDELN: A programme for the detection and parametrization of overlapping resonances using the time-delay method

NASA Astrophysics Data System (ADS)

Little, Duncan A.; Tennyson, Jonathan; Plummer, Martin; Noble, Clifford J.; Sunderland, Andrew G.

2017-06-01

TIMEDELN implements the time-delay method of determining resonance parameters from the characteristic Lorentzian form displayed by the largest eigenvalues of the time-delay matrix. TIMEDELN constructs the time-delay matrix from input K-matrices and analyses its eigenvalues. This new version implements multi-resonance fitting and may be run serially or as a high performance parallel code with three levels of parallelism. TIMEDELN takes K-matrices from a scattering calculation, either read from a file or calculated on a dynamically adjusted grid, and calculates the time-delay matrix. This is then diagonalized, with the largest eigenvalue representing the longest time-delay experienced by the scattering particle. A resonance shows up as a characteristic Lorentzian form in the time-delay: the programme searches the time-delay eigenvalues for maxima and traces resonances when they pass through different eigenvalues, separating overlapping resonances. It also performs the fitting of the calculated data to the Lorentzian form and outputs resonance positions and widths. Any remaining overlapping resonances can be fitted jointly. The branching ratios of decay into the open channels can also be found. The programme may be run serially or in parallel with three levels of parallelism. The parallel code modules are abstracted from the main physics code and can be used independently.

Sensitivity analysis of a multilayer, finite-difference model of the Southeastern Coastal Plain regional aquifer system; Mississippi, Alabama, Georgia, and South Carolina

USGS Publications Warehouse

Pernik, Meribeth

1987-01-01

The sensitivity of a multilayer finite-difference regional flow model was tested by changing the calibrated values for five parameters in the steady-state model and one in the transient-state model. The parameters that changed under the steady-state condition were those that had been routinely adjusted during the calibration process as part of the effort to match pre-development potentiometric surfaces, and elements of the water budget. The tested steady-state parameters include: recharge, riverbed conductance, transmissivity, confining unit leakance, and boundary location. In the transient-state model, the storage coefficient was adjusted. The sensitivity of the model to changes in the calibrated values of these parameters was evaluated with respect to the simulated response of net base flow to the rivers, and the mean value of the absolute head residual. To provide a standard measurement of sensitivity from one parameter to another, the standard deviation of the absolute head residual was calculated. The steady-state model was shown to be most sensitive to changes in rates of recharge. When the recharge rate was held constant, the model was more sensitive to variations in transmissivity. Near the rivers, the riverbed conductance becomes the dominant parameter in controlling the heads. Changes in confining unit leakance had little effect on simulated base flow, but greatly affected head residuals. The model was relatively insensitive to changes in the location of no-flow boundaries and to moderate changes in the altitude of constant head boundaries. The storage coefficient was adjusted under transient conditions to illustrate the model 's sensitivity to changes in storativity. The model is less sensitive to an increase in storage coefficient than it is to a decrease in storage coefficient. As the storage coefficient decreased, the aquifer drawdown increases, the base flow decreased. The opposite response occurred when the storage coefficient was increased. (Author 's abstract)

Effect of mesh distortion on the accuracy of transverse shear stresses and their sensitivity coefficients in multilayered composites

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Yong H.

1995-01-01

A study is made of the effect of mesh distortion on the accuracy of transverse shear stresses and their first-order and second-order sensitivity coefficients in multilayered composite panels subjected to mechanical and thermal loads. The panels are discretized by using a two-field degenerate solid element, with the fundamental unknowns consisting of both displacement and strain components, and the displacement components having a linear variation throughout the thickness of the laminate. A two-step computational procedure is used for evaluating the transverse shear stresses. In the first step, the in-plane stresses in the different layers are calculated at the numerical quadrature points for each element. In the second step, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of transverse shear stresses. Numerical results are presented showing no noticeable degradation in the accuracy of the in-plane stresses and their sensitivity coefficients with mesh distortion. However, such degradation is observed for the transverse shear stresses and their sensitivity coefficients. The standard of comparison is taken to be the exact solution of the three-dimensional thermoelasticity equations of the panel.

Psychometric Properties of the Serbian Version of the Maslach Burnout Inventory-Human Services Survey: A Validation Study among Anesthesiologists from Belgrade Teaching Hospitals

PubMed Central

Matejić, Bojana; Milenović, Miodrag; Kisić Tepavčević, Darija; Simić, Dušica; Pekmezović, Tatjana; Worley, Jody A.

2015-01-01

We report findings from a validation study of the translated and culturally adapted Serbian version of Maslach Burnout Inventory-Human Services Survey (MBI-HSS), for a sample of anesthesiologists working in the tertiary healthcare. The results showed the sufficient overall reliability (Cronbach's α = 0.72) of the scores (items 1–22). The results of Bartlett's test of sphericity (χ 2 = 1983.75, df = 231, p < 0.001) and Kaiser-Meyer-Olkin measure of sampling adequacy (0.866) provided solid justification for factor analysis. In order to increase sensitivity of this questionnaire, we performed unfitted factor analysis model (eigenvalue greater than 1) which enabled us to extract the most suitable factor structure for our study instrument. The exploratory factor analysis model revealed five factors with eigenvalues greater than 1.0, explaining 62.0% of cumulative variance. Velicer's MAP test has supported five-factor model with the smallest average squared correlation of 0,184. This study indicated that Serbian version of the MBI-HSS is a reliable and valid instrument to measure burnout among a population of anesthesiologists. Results confirmed strong psychometric characteristics of the study instrument, with recommendations for interpretation of two new factors that may be unique to the Serbian version of the MBI-HSS. PMID:26090517

Psychometric Properties of the Serbian Version of the Maslach Burnout Inventory-Human Services Survey: A Validation Study among Anesthesiologists from Belgrade Teaching Hospitals.

PubMed

Matejić, Bojana; Milenović, Miodrag; Kisić Tepavčević, Darija; Simić, Dušica; Pekmezović, Tatjana; Worley, Jody A

2015-01-01

We report findings from a validation study of the translated and culturally adapted Serbian version of Maslach Burnout Inventory-Human Services Survey (MBI-HSS), for a sample of anesthesiologists working in the tertiary healthcare. The results showed the sufficient overall reliability (Cronbach's α = 0.72) of the scores (items 1-22). The results of Bartlett's test of sphericity (χ(2) = 1983.75, df = 231, p < 0.001) and Kaiser-Meyer-Olkin measure of sampling adequacy (0.866) provided solid justification for factor analysis. In order to increase sensitivity of this questionnaire, we performed unfitted factor analysis model (eigenvalue greater than 1) which enabled us to extract the most suitable factor structure for our study instrument. The exploratory factor analysis model revealed five factors with eigenvalues greater than 1.0, explaining 62.0% of cumulative variance. Velicer's MAP test has supported five-factor model with the smallest average squared correlation of 0,184. This study indicated that Serbian version of the MBI-HSS is a reliable and valid instrument to measure burnout among a population of anesthesiologists. Results confirmed strong psychometric characteristics of the study instrument, with recommendations for interpretation of two new factors that may be unique to the Serbian version of the MBI-HSS.

Detecting Seismic Activity with a Covariance Matrix Analysis of Data Recorded on Seismic Arrays

NASA Astrophysics Data System (ADS)

Seydoux, L.; Shapiro, N.; de Rosny, J.; Brenguier, F.

2014-12-01

Modern seismic networks are recording the ground motion continuously all around the word, with very broadband and high-sensitivity sensors. The aim of our study is to apply statistical array-based approaches to processing of these records. We use the methods mainly brought from the random matrix theory in order to give a statistical description of seismic wavefields recorded at the Earth's surface. We estimate the array covariance matrix and explore the distribution of its eigenvalues that contains information about the coherency of the sources that generated the studied wavefields. With this approach, we can make distinctions between the signals generated by isolated deterministic sources and the "random" ambient noise. We design an algorithm that uses the distribution of the array covariance matrix eigenvalues to detect signals corresponding to coherent seismic events. We investigate the detection capacity of our methods at different scales and in different frequency ranges by applying it to the records of two networks: (1) the seismic monitoring network operating on the Piton de la Fournaise volcano at La Réunion island composed of 21 receivers and with an aperture of ~15 km, and (2) the transportable component of the USArray composed of ~400 receivers with ~70 km inter-station spacing.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

The Spaeth/Richman contrast sensitivity test (SPARCS): design, reproducibility and ability to identify patients with glaucoma.

PubMed

Richman, Jesse; Zangalli, Camila; Lu, Lan; Wizov, Sheryl S; Spaeth, Eric; Spaeth, George L

2015-01-01

(1) To determine the ability of a novel, internet-based contrast sensitivity test titled the Spaeth/Richman Contrast Sensitivity Test (SPARCS) to identify patients with glaucoma. (2) To determine the test-retest reliability of SPARCS. A prospective, cross-sectional study of patients with glaucoma and controls was performed. Subjects were assessed by SPARCS and the Pelli-Robson chart. Reliability of each test was assessed by the intraclass correlation coefficient and the coefficient of repeatability. Sensitivity and specificity for identifying glaucoma was also evaluated. The intraclass correlation coefficient for SPARCS was 0.97 and 0.98 for Pelli-Robson. The coefficient of repeatability for SPARCS was ±6.7% and ±6.4% for Pelli-Robson. SPARCS identified patients with glaucoma with 79% sensitivity and 93% specificity. SPARCS has high test-retest reliability. It is easily accessible via the internet and identifies patients with glaucoma well. NCT01300949. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Development and psychometric properties rating scale of “clinical competency evaluation in mental health nurses”: Exploratory factor analysis

PubMed Central

Moskoei, Sara; Mohtashami, Jamileh; Ghalenoeei, Mahdie; Nasiri, Maliheh; Tafreshi, Mansoreh Zaghari

2017-01-01

Introduction Evaluation of clinical competency in nurses has a distinct importance in healthcare due to its significant impact on improving the quality of patient care and creation of opportunities for professional promotion. This is a psychometric study for development of the “Clinical Competency of Mental Health Nursing”(CCMHN) rating scale. Methods In this methodological research that was conducted in 2015, in Tehran, Iran, the main items were developed after literature review and the validity and reliability of the tool were identified. The face, content (content validity ratio and content validity index) and construct validities were calculated. For face and content validity, experts’ comments were used. Exploratory factor analysis was used to determine the construct validity. The reliability of scale was determined by the internal consistency and inter-rater correlation. The collected data were analyzed by SPSS version 16, using descriptive statistical analysis. Results A scale with 45 items in two parts including Emotional/Moral and Specific Care competencies was developed. Content validity ratio and content validity index were 0.88, 0.97 respectively. Exploratory factor analysis indicated two factors: The first factor with 23.93 eigenvalue and second factor with eigenvalue 2.58. Cronbach’s alpha coefficient for determination of internal consistency was 0.98 and the ICC for confirmation inter-rater correlation was 0.98. Conclusion A scale with 45 items and two areas was developed with appropriate validity and reliability. This scale can be used to assess the clinical competency in nursing students and mental health nurses. PMID:28607650

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

NASA Astrophysics Data System (ADS)

Chekroun, Mickaël D.; Kondrashov, Dmitri

2017-09-01

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey, furthermore, a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled—provided the decay of temporal correlations is sufficiently well-resolved—within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.

Network-Based Detection and Classification of Seismovolcanic Tremors: Example From the Klyuchevskoy Volcanic Group in Kamchatka

NASA Astrophysics Data System (ADS)

Soubestre, Jean; Shapiro, Nikolai M.; Seydoux, Léonard; de Rosny, Julien; Droznin, Dmitry V.; Droznina, Svetlana Ya.; Senyukov, Sergey L.; Gordeev, Evgeniy I.

2018-01-01

We develop a network-based method for detecting and classifying seismovolcanic tremors. The proposed approach exploits the coherence of tremor signals across the network that is estimated from the array covariance matrix. The method is applied to four and a half years of continuous seismic data recorded by 19 permanent seismic stations in the vicinity of the Klyuchevskoy volcanic group in Kamchatka (Russia), where five volcanoes were erupting during the considered time period. We compute and analyze daily covariance matrices together with their eigenvalues and eigenvectors. As a first step, most coherent signals corresponding to dominating tremor sources are detected based on the width of the covariance matrix eigenvalues distribution. Thus, volcanic tremors of the two volcanoes known as most active during the considered period, Klyuchevskoy and Tolbachik, are efficiently detected. As a next step, we consider the daily array covariance matrix's first eigenvector. Our main hypothesis is that these eigenvectors represent the principal components of the daily seismic wavefield and, for days with tremor activity, characterize dominant tremor sources. Those daily first eigenvectors, which can be used as network-based fingerprints of tremor sources, are then grouped into clusters using correlation coefficient as a measure of the vector similarity. As a result, we identify seven clusters associated with different periods of activity of four volcanoes: Tolbachik, Klyuchevskoy, Shiveluch, and Kizimen. The developed method does not require a priori knowledge and is fully automatic; and the database of the network-based tremor fingerprints can be continuously enriched with newly available data.

On the Aharonov-Bohm Operators with Varying Poles: The Boundary Behavior of Eigenvalues

NASA Astrophysics Data System (ADS)

Noris, Benedetta; Nys, Manon; Terracini, Susanna

2015-11-01

We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (the Aharonov-Bohm effect, Phys Rev (2) 115:485-491, 1959). Moreover, the numerical computations performed in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010) show a rather complex behavior of the eigenvalues as the pole varies in a planar domain. In this paper, in continuation of the analysis started in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010), we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions. We deal with planar domains with Dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain: then, the operator loses its singular character and the k-th magnetic eigenvalue converges to that of the standard Laplacian. We can predict both the rate of convergence and whether the convergence happens from above or from below, in relation with the number of nodal lines of the k-th eigenfunction of the Laplacian. The proof relies on the variational characterization of eigenvalues, together with a detailed asymptotic analysis of the eigenfunctions, based on an Almgren-type frequency formula for magnetic eigenfunctions and on the blow-up technique.

A robust multilevel simultaneous eigenvalue solver

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1993-01-01

Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.

Validation of the Maslach Burnout Inventory-Human Services Survey for Estimating Burnout in Dental Students.

PubMed

Montiel-Company, José María; Subirats-Roig, Cristian; Flores-Martí, Pau; Bellot-Arcís, Carlos; Almerich-Silla, José Manuel

2016-11-01

The aim of this study was to examine the validity and reliability of the Maslach Burnout Inventory-Human Services Survey (MBI-HSS) as a tool for assessing the prevalence and level of burnout in dental students in Spanish universities. The survey was adapted from English to Spanish. A sample of 533 dental students from 15 Spanish universities and a control group of 188 medical students self-administered the survey online, using the Google Drive service. The test-retest reliability or reproducibility showed an Intraclass Correlation Coefficient of 0.95. The internal consistency of the survey was 0.922. Testing the construct validity showed two components with an eigenvalue greater than 1.5, which explained 51.2% of the total variance. Factor I (36.6% of the variance) comprised the items that estimated emotional exhaustion and depersonalization. Factor II (14.6% of the variance) contained the items that estimated personal accomplishment. The cut-off point for the existence of burnout achieved a sensitivity of 92.2%, a specificity of 92.1%, and an area under the curve of 0.96. Comparison of the total dental students sample and the control group of medical students showed significantly higher burnout levels for the dental students (50.3% vs. 40.4%). In this study, the MBI-HSS was found to be viable, valid, and reliable for measuring burnout in dental students. Since the study also found that the dental students suffered from high levels of this syndrome, these results suggest the need for preventive burnout control programs.

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2008-01-01

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

What can be learned from optical two-color diffusion and thermodiffusion experiments on ternary fluid mixtures?

NASA Astrophysics Data System (ADS)

Gebhardt, M.; Köhler, W.

2015-02-01

A number of optical techniques have been developed during the recent years for the investigation of diffusion and thermodiffusion in ternary fluid mixtures, both on ground and on-board the International Space Station. All these methods are based on the simultaneous measurement of refractive index changes at two different wavelengths. Here, we discuss and compare different techniques with the emphasis on optical beam deflection (OBD), optical digital interferometry, and thermal diffusion forced Rayleigh scattering (TDFRS). We suggest to formally split the data evaluation into a phenomenological parameterization of the measured transients and a subsequent transformation from the refractive index into the concentration space. In all experiments, the transients measured at two different detection wavelengths can be described by four amplitudes and two eigenvalues of the diffusion coefficient matrix. It turns out that these six parameters are subjected to large errors and cannot be determined reliably. Five good quantities, which can be determined with a high accuracy, are the stationary amplitudes, the initial slopes as defined in TDFRS experiments and by application of a heuristic criterion for similar curves, a certain mean diffusion coefficient. These amplitudes and slopes are directly linked to the Soret and thermodiffusion coefficients after transformation with the inverse contrast factor matrix, which is frequently ill-conditioned. Since only five out of six free parameters are reliably determined, including the single mean diffusion coefficient, the determination of the four entries of the diffusion matrix is not possible. We apply our results to new OBD measurements of the symmetric (mass fractions 0.33/0.33/0.33) ternary benchmark mixture n-dodecane/isobutylbenzene/1,2,3,4-tetrahydronaphthalene and existing literature data for the same system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gebhardt, M.; Köhler, W., E-mail: werner.koehler@uni-bayreuth.de

A number of optical techniques have been developed during the recent years for the investigation of diffusion and thermodiffusion in ternary fluid mixtures, both on ground and on-board the International Space Station. All these methods are based on the simultaneous measurement of refractive index changes at two different wavelengths. Here, we discuss and compare different techniques with the emphasis on optical beam deflection (OBD), optical digital interferometry, and thermal diffusion forced Rayleigh scattering (TDFRS). We suggest to formally split the data evaluation into a phenomenological parameterization of the measured transients and a subsequent transformation from the refractive index into themore » concentration space. In all experiments, the transients measured at two different detection wavelengths can be described by four amplitudes and two eigenvalues of the diffusion coefficient matrix. It turns out that these six parameters are subjected to large errors and cannot be determined reliably. Five good quantities, which can be determined with a high accuracy, are the stationary amplitudes, the initial slopes as defined in TDFRS experiments and by application of a heuristic criterion for similar curves, a certain mean diffusion coefficient. These amplitudes and slopes are directly linked to the Soret and thermodiffusion coefficients after transformation with the inverse contrast factor matrix, which is frequently ill-conditioned. Since only five out of six free parameters are reliably determined, including the single mean diffusion coefficient, the determination of the four entries of the diffusion matrix is not possible. We apply our results to new OBD measurements of the symmetric (mass fractions 0.33/0.33/0.33) ternary benchmark mixture n-dodecane/isobutylbenzene/1,2,3,4-tetrahydronaphthalene and existing literature data for the same system.« less

A method to stabilize linear systems using eigenvalue gradient information

NASA Technical Reports Server (NTRS)

Wieseman, C. D.

1985-01-01

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Deterministically estimated fission source distributions for Monte Carlo k-eigenvalue problems

DOE PAGES

Biondo, Elliott D.; Davidson, Gregory G.; Pandya, Tara M.; ...

2018-04-30

The standard Monte Carlo (MC) k-eigenvalue algorithm involves iteratively converging the fission source distribution using a series of potentially time-consuming inactive cycles before quantities of interest can be tallied. One strategy for reducing the computational time requirements of these inactive cycles is the Sourcerer method, in which a deterministic eigenvalue calculation is performed to obtain an improved initial guess for the fission source distribution. This method has been implemented in the Exnihilo software suite within SCALE using the SPNSPN or SNSN solvers in Denovo and the Shift MC code. The efficacy of this method is assessed with different Denovo solutionmore » parameters for a series of typical k-eigenvalue problems including small criticality benchmarks, full-core reactors, and a fuel cask. Here it is found that, in most cases, when a large number of histories per cycle are required to obtain a detailed flux distribution, the Sourcerer method can be used to reduce the computational time requirements of the inactive cycles.« less

Quadratic Zeeman effect in hydrogen Rydberg states: Rigorous error estimates for energy eigenvalues, energy eigenfunctions, and oscillator strengths

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falsaperla, P.; Fonte, G.

1994-10-01

A variational method, based on some results due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], and previously discussed is here applied to the hydrogen atom in uniform magnetic fields of tesla in order to calculate, with a rigorous error estimate, energy eigenvalues, energy eigenfunctions, and oscillator strengths relative to Rydberg states up to just below the field-free ionization threshold. Making use of a basis (parabolic Sturmian basis) with a size varying from 990 up to 5050, we obtain, over the energy range of [minus]190 to [minus]24 cm[sup [minus]1], all of the eigenvalues and a good part ofmore » the oscillator strengths with a remarkable accuracy. This, however, decreases with increasing excitation energy and, thus, above [similar to][minus]24 cm[sup [minus]1], we obtain results of good accuracy only for eigenvalues ranging up to [similar to][minus]12 cm[sup [minus]1].« less

Solution of an eigenvalue problem for the Laplace operator on a spherical surface. M.S. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Walden, H.

1974-01-01

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

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

NASA Technical Reports Server (NTRS)

Mielke, R. R.; Tung, L. J.; Carraway, P. I., III

1984-01-01

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.

Multitasking the Davidson algorithm for the large, sparse eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umar, V.M.; Fischer, C.F.

1989-01-01

The authors report how the Davidson algorithm, developed for handling the eigenvalue problem for large and sparse matrices arising in quantum chemistry, was modified for use in atomic structure calculations. To date these calculations have used traditional eigenvalue methods, which limit the range of feasible calculations because of their excessive memory requirements and unsatisfactory performance attributed to time-consuming and costly processing of zero valued elements. The replacement of a traditional matrix eigenvalue method by the Davidson algorithm reduced these limitations. Significant speedup was found, which varied with the size of the underlying problem and its sparsity. Furthermore, the range ofmore » matrix sizes that can be manipulated efficiently was expended by more than one order or magnitude. On the CRAY X-MP the code was vectorized and the importance of gather/scatter analyzed. A parallelized version of the algorithm obtained an additional 35% reduction in execution time. Speedup due to vectorization and concurrency was also measured on the Alliant FX/8.« less

Deterministically estimated fission source distributions for Monte Carlo k-eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biondo, Elliott D.; Davidson, Gregory G.; Pandya, Tara M.

The standard Monte Carlo (MC) k-eigenvalue algorithm involves iteratively converging the fission source distribution using a series of potentially time-consuming inactive cycles before quantities of interest can be tallied. One strategy for reducing the computational time requirements of these inactive cycles is the Sourcerer method, in which a deterministic eigenvalue calculation is performed to obtain an improved initial guess for the fission source distribution. This method has been implemented in the Exnihilo software suite within SCALE using the SPNSPN or SNSN solvers in Denovo and the Shift MC code. The efficacy of this method is assessed with different Denovo solutionmore » parameters for a series of typical k-eigenvalue problems including small criticality benchmarks, full-core reactors, and a fuel cask. Here it is found that, in most cases, when a large number of histories per cycle are required to obtain a detailed flux distribution, the Sourcerer method can be used to reduce the computational time requirements of the inactive cycles.« less

Effective dimensional reduction algorithm for eigenvalue problems for thin elastic structures: A paradigm in three dimensions

PubMed Central

Ovtchinnikov, Evgueni E.; Xanthis, Leonidas S.

2000-01-01

We present a methodology for the efficient numerical solution of eigenvalue problems of full three-dimensional elasticity for thin elastic structures, such as shells, plates and rods of arbitrary geometry, discretized by the finite element method. Such problems are solved by iterative methods, which, however, are known to suffer from slow convergence or even convergence failure, when the thickness is small. In this paper we show an effective way of resolving this difficulty by invoking a special preconditioning technique associated with the effective dimensional reduction algorithm (EDRA). As an example, we present an algorithm for computing the minimal eigenvalue of a thin elastic plate and we show both theoretically and numerically that it is robust with respect to both the thickness and discretization parameters, i.e. the convergence does not deteriorate with diminishing thickness or mesh refinement. This robustness is sine qua non for the efficient computation of large-scale eigenvalue problems for thin elastic structures. PMID:10655469

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

NASA Technical Reports Server (NTRS)

Mielke, R. R.; Tung, L. J.; Carraway, P. I., III

1985-01-01

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.

On Fluctuations of Eigenvalues of Random Band Matrices

NASA Astrophysics Data System (ADS)

Shcherbina, M.

2015-10-01

We consider the fluctuations of linear eigenvalue statistics of random band matrices whose entries have the form with i.i.d. possessing the th moment, where the function u has a finite support , so that M has only nonzero diagonals. The parameter b (called the bandwidth) is assumed to grow with n in a way such that . Without any additional assumptions on the growth of b we prove CLT for linear eigenvalue statistics for a rather wide class of test functions. Thus we improve and generalize the results of the previous papers (Jana et al., arXiv:1412.2445; Li et al. Random Matrices 2:04, 2013), where CLT was proven under the assumption . Moreover, we develop a method which allows to prove automatically the CLT for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory: deformed Wigner and sample covariance matrices, sparse matrices, diluted random matrices, matrices with heavy tales etc.

A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

2014-01-01

We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

On the Time-Dependent Analysis of Gamow Decay

ERIC Educational Resources Information Center

Durr, Detlef; Grummt, Robert; Kolb, Martin

2011-01-01

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wavefunctions. Observing that the time evolution of any…

nu-TRLan User Guide Version 1.0: A High-Performance Software Package for Large-Scale Harmitian Eigenvalue Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamazaki, Ichitaro; Wu, Kesheng; Simon, Horst

2008-10-27

The original software package TRLan, [TRLan User Guide], page 24, implements the thick restart Lanczos method, [Wu and Simon 2001], page 24, for computing eigenvalues {lambda} and their corresponding eigenvectors v of a symmetric matrix A: Av = {lambda}v. Its effectiveness in computing the exterior eigenvalues of a large matrix has been demonstrated, [LBNL-42982], page 24. However, its performance strongly depends on the user-specified dimension of a projection subspace. If the dimension is too small, TRLan suffers from slow convergence. If it is too large, the computational and memory costs become expensive. Therefore, to balance the solution convergence and costs,more » users must select an appropriate subspace dimension for each eigenvalue problem at hand. To free users from this difficult task, nu-TRLan, [LNBL-1059E], page 23, adjusts the subspace dimension at every restart such that optimal performance in solving the eigenvalue problem is automatically obtained. This document provides a user guide to the nu-TRLan software package. The original TRLan software package was implemented in Fortran 90 to solve symmetric eigenvalue problems using static projection subspace dimensions. nu-TRLan was developed in C and extended to solve Hermitian eigenvalue problems. It can be invoked using either a static or an adaptive subspace dimension. In order to simplify its use for TRLan users, nu-TRLan has interfaces and features similar to those of TRLan: (1) Solver parameters are stored in a single data structure called trl-info, Chapter 4 [trl-info structure], page 7. (2) Most of the numerical computations are performed by BLAS, [BLAS], page 23, and LAPACK, [LAPACK], page 23, subroutines, which allow nu-TRLan to achieve optimized performance across a wide range of platforms. (3) To solve eigenvalue problems on distributed memory systems, the message passing interface (MPI), [MPI forum], page 23, is used. The rest of this document is organized as follows. In Chapter 2 [Installation], page 2, we provide an installation guide of the nu-TRLan software package. In Chapter 3 [Example], page 3, we present a simple nu-TRLan example program. In Chapter 4 [trl-info structure], page 7, and Chapter 5 [trlan subroutine], page 14, we describe the solver parameters and interfaces in detail. In Chapter 6 [Solver parameters], page 21, we discuss the selection of the user-specified parameters. In Chapter 7 [Contact information], page 22, we give the acknowledgements and contact information of the authors. In Chapter 8 [References], page 23, we list reference to related works.« less

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

PubMed Central

Eshraghi, Iman; Jalali, Seyed K.; Pugno, Nicola Maria

2016-01-01

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs. PMID:28773911

Method of confidence domains in the analysis of noise-induced extinction for tritrophic population system

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2017-09-01

A problem of the analysis of the noise-induced extinction in multidimensional population systems is considered. For the investigation of conditions of the extinction caused by random disturbances, a new approach based on the stochastic sensitivity function technique and confidence domains is suggested, and applied to tritrophic population model of interacting prey, predator and top predator. This approach allows us to analyze constructively the probabilistic mechanisms of the transition to the noise-induced extinction from both equilibrium and oscillatory regimes of coexistence. In this analysis, a method of principal directions for the reducing of the dimension of confidence domains is suggested. In the dispersion of random states, the principal subspace is defined by the ratio of eigenvalues of the stochastic sensitivity matrix. A detailed analysis of two scenarios of the noise-induced extinction in dependence on parameters of considered tritrophic system is carried out.

Surrogate models for efficient stability analysis of brake systems

NASA Astrophysics Data System (ADS)

Nechak, Lyes; Gillot, Frédéric; Besset, Sébastien; Sinou, Jean-Jacques

2015-07-01

This study assesses capacities of the global sensitivity analysis combined together with the kriging formalism to be useful in the robust stability analysis of brake systems, which is too costly when performed with the classical complex eigenvalues analysis (CEA) based on finite element models (FEMs). By considering a simplified brake system, the global sensitivity analysis is first shown very helpful for understanding the effects of design parameters on the brake system's stability. This is allowed by the so-called Sobol indices which discriminate design parameters with respect to their influence on the stability. Consequently, only uncertainty of influent parameters is taken into account in the following step, namely, the surrogate modelling based on kriging. The latter is then demonstrated to be an interesting alternative to FEMs since it allowed, with a lower cost, an accurate estimation of the system's proportions of instability corresponding to the influent parameters.

Three-dimensional geometry of coronal loops inferred by the Principal Component Analysis

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe; Nakariakov, Valery

We propose a new method for the determination of the three dimensional (3D) shape of coronal loops from stereoscopy. The common approach requires to find a 1D geometric curve, as circumference or ellipse, that best-fits the 3D tie-points which sample the loop shape in a given coordinate system. This can be easily achieved by the Principal Component (PC) analysis. It mainly consists in calculating the eigenvalues and eigenvectors of the covariance matrix of the 3D tie-points: the eigenvalues give a measure of the variability of the distribution of the tie-points, and the corresponding eigenvectors define a new cartesian reference frame directly related to the loop. The eigenvector associated with the smallest eigenvalues defines the normal to the loop plane, while the other two determine the directions of the loop axes: the major axis is related to the largest eigenvalue, and the minor axis with the second one. The magnitude of the axes is directly proportional to the square roots of these eigenvalues. The technique is fast and easily implemented in some examples, returning best-fitting estimations of the loop parameters and 3D reconstruction with a reasonable small number of tie-points. The method is suitable for serial reconstruction of coronal loops in active regions, providing a useful tool for comparison between observations and theoretical magnetic field extrapolations from potential or force-free fields.

Fast Eigensolver for Computing 3D Earth's Normal Modes

NASA Astrophysics Data System (ADS)

Shi, J.; De Hoop, M. V.; Li, R.; Xi, Y.; Saad, Y.

2017-12-01

We present a novel parallel computational approach to compute Earth's normal modes. We discretize Earth via an unstructured tetrahedral mesh and apply the continuous Galerkin finite element method to the elasto-gravitational system. To resolve the eigenvalue pollution issue, following the analysis separating the seismic point spectrum, we utilize explicitly a representation of the displacement for describing the oscillations of the non-seismic modes in the fluid outer core. Effectively, we separate out the essential spectrum which is naturally related to the Brunt-Väisälä frequency. We introduce two Lanczos approaches with polynomial and rational filtering for solving this generalized eigenvalue problem in prescribed intervals. The polynomial filtering technique only accesses the matrix pair through matrix-vector products and is an ideal candidate for solving three-dimensional large-scale eigenvalue problems. The matrix-free scheme allows us to deal with fluid separation and self-gravitation in an efficient way, while the standard shift-and-invert method typically needs an explicit shifted matrix and its factorization. The rational filtering method converges much faster than the standard shift-and-invert procedure when computing all the eigenvalues inside an interval. Both two Lanczos approaches solve for the internal eigenvalues extremely accurately, comparing with the standard eigensolver. In our computational experiments, we compare our results with the radial earth model benchmark, and visualize the normal modes using vector plots to illustrate the properties of the displacements in different modes.

Random matrix theory and cross-correlations in global financial indices and local stock market indices

NASA Astrophysics Data System (ADS)

Nobi, Ashadun; Maeng, Seong Eun; Ha, Gyeong Gyun; Lee, Jae Woo

2013-02-01

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [ λ -, λ +], where λ - and λ + are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.

Tracking a Heavy Pollution Process in Beijing in Winter 2016 Using GRAPES-CUACE Adjoint Model

NASA Astrophysics Data System (ADS)

Wang, C.; An, X.; Zhai, S.; Zhaobin, S.

2017-12-01

By using the GRAPES-CUACE (Global-Regional Assimilation and Prediction System coupled with the CMA Unified Atmospheric Chemistry Environmental Forecasting System) adjoint model, the adjoint sensitivity of the heavy pollution process in the winter of 2016 in Beijing is traced, and the key emission sources and periods that impacted this heavy pollution process most seriously are analyzed. The research findings suggest that the peak concentration of PM2.5 has a rapid response to the local emission, and the local hourly sensitivity coefficient, which is 9.31 μg m-3, reaches the peak at the moment 1h before the objective time. From the cumulative sensitivity coefficient, the local emission plays the main theme within 20h before the objective time. The contribution of the surrounding emission is the accumulation of the neighboring sources of Beijing, Tianjin, Hebei and Shanxi, whose cumulative contribution ratios are 34.2%, 3.0%, 49.4% and 13.4% respectively within 72h before the objective time. From the hourly sensitivity coefficient, the major contribution period of Tianjin source is 1-26h before the objective time and its hourly contribution peak value is 0.59 μg m-3, appearing at the moment 4h before the objective time. The main contribution periods of Hebei and Shanxi emission sources are respectively 1-54h and 14-53h before the objective time and their hourly sensitivity coefficients both show periodic fluctuations. The Hebei source shows three peaks of sensitivity coefficients, which are 3.45 μg m-3, 4.27 μg m-3 and 0.71 μg m-3, respectively appearing at the time of 4h, 16h and 38h before the objective time. For the Shanxi source, sensitivity coefficient peaks twice with the values of 1.41 μg m-3 and 0.64 μg m-3, which are seen at the time 24h and 45h before the objective time, respectively.

The relationship between coefficient of restitution and state of charge of zinc alkaline primary LR6 batteries [Bouncing alkaline batteries: A basic solution

DOE PAGES

Bhadra, S.; Hertzberg, B. J.; Croft, M.; ...

2015-03-13

The coefficient of restitution of alkaline batteries had been shown to increase as a function of depth of discharge. In this work, using non-destructive mechanical testing, the change in coefficient of restitution is compared to in situ energy-dispersive x-ray diffraction data to determine the cause of the macroscopic change in coefficient of restitution. The increase in coefficient of restitution correlates to the formation of a percolation pathway of ZnO within the anode of the cell, and that the coefficient of restitution saturates at a value of 0.63 ± .05 at 50% state if charge when the anode has densified intomore » porous ZnO solid. Of note is the sensitivity of coefficient of restitution to the amount of ZnO formation that rivals the sensitivity on in situ energy-dispersive x-ray diffraction spectroscopy.« less

Unreliable Retrial Queues in a Random Environment

DTIC Science & Technology

2007-09-01

equivalent to the stochasticity of the matrix Ĝ. It is generally known from Perron - Frobenius theory that a given square ma- trix M is stochastic if and...only if its maximum positive eigenvalue (i.e., its Perron eigenvalue) sp(M) is equal to unity. A simple analytical condition that guarantees the

Weyl's type estimates on the eigenvalues of critical Schrödinger operators using improved Hardy-Sobolev inequalities

NASA Astrophysics Data System (ADS)

Zographopoulos, N. B.

2009-11-01

Motivated by the work (Karachalios N I 2008 Lett. Math. Phys. 83 189-99), we present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator, involving inverse-square potential, based on improved Hardy-Sobolev-type inequalities.

Matrix with Prescribed Eigenvectors

ERIC Educational Resources Information Center

Ahmad, Faiz

2011-01-01

It is a routine matter for undergraduates to find eigenvalues and eigenvectors of a given matrix. But the converse problem of finding a matrix with prescribed eigenvalues and eigenvectors is rarely discussed in elementary texts on linear algebra. This problem is related to the "spectral" decomposition of a matrix and has important technical…

The Schrodinger Eigenvalue March

ERIC Educational Resources Information Center

Tannous, C.; Langlois, J.

2011-01-01

A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

Obtaining eigensolutions for multiple frequency ranges in a single NASTRAN execution

NASA Technical Reports Server (NTRS)

Pamidi, P. R.; Brown, W. K.

1990-01-01

A novel and general procedure for obtaining eigenvalues and eigenvectors for multiple frequency ranges in a single NASTRAN execution is presented. The scheme is applicable to normal modes analyzes employing the FEER and Inverse Power methods of eigenvalue extraction. The procedure is illustrated by examples.

Psychometric Evaluation of a Persian Version of the Cardiac Depression Scale in Iranian Patients With Acute Myocardial Infarction.

PubMed

Nia, Hamid Sharif; Sharif, Saeed Pahlevan; Froelicher, Erika Sivarajan; Boyle, Christopher; Goudarzian, Amir Hossein; Yaghoobzadeh, Ameneh; Oskouie, Fatemeh

2018-04-01

The aim of this study was to validate a Persian version of the Cardiac Depression Scale (CDS) in Iranian patients with acute myocardial infarction (AMI). The CDS was forward translated from English into Persian and back-translated to English. Validity was assessed using face, content, and construct validity. Also Cronbach's alpha (α), theta (), and McDonald's omega coefficient were used to evaluate the reliability. Construct validity of the scale showed two factors with eigenvalues greater than one. The Cronbach's α, , McDonald's omega, and construct reliability were greater than .70. The Persian version of the CDS has a two-factor structure (i.e., death anxiety and life satisfaction) and has acceptable reliability and validity. Therefore, the validated instrument can be used in future studies to assess depression in patients with AMI in Iranians.

Complex network approach to fractional time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manshour, Pouya

In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacencymore » matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.« less

Automorphic properties of low energy string amplitudes in various dimensions

NASA Astrophysics Data System (ADS)

Green, Michael B.; Russo, Jorge G.; Vanhove, Pierre

2010-04-01

This paper explores the moduli-dependent coefficients of higher-derivative interactions that appear in the low-energy expansion of the four-supergraviton amplitude of maximally supersymmetric string theory compactified on a d torus. These automorphic functions are determined for terms up to order ∂6R4 and various values of d by imposing a variety of consistency conditions. They satisfy Laplace eigenvalue equations with or without source terms, whose solutions are given in terms of Eisenstein series, or more general automorphic functions, for certain parabolic subgroups of the relevant U-duality groups. The ultraviolet divergences of the corresponding supergravity field theory limits are encoded in various logarithms, although the string theory expressions are finite. This analysis includes intriguing representations of SL(d) and SO(d,d) Eisenstein series in terms of toroidally compactified one and two-loop string and supergravity amplitudes.

Factor analysis of an instrument to measure the impact of disease on daily life.

PubMed

Pedrosa, Rafaela Batista Dos Santos; Rodrigues, Roberta Cunha Matheus; Padilha, Kátia Melissa; Gallani, Maria Cecília Bueno Jayme; Alexandre, Neusa Maria Costa

2016-01-01

to verify the structure of factors of an instrument to measure the Heart Valve Disease Impact on Daily Life (IDCV) when applied to coronary artery disease patients. the study included 153 coronary artery disease patients undergoing outpatient follow-up care. The IDCV structure of factors was initially assessed by means of confirmatory factor analysis and, subsequently, by exploratory factor analysis. The Varimax rotation method was used to estimate the main components of analysis, eigenvalues greater than one for extraction of factors, and factor loading greater than 0.40 for selection of items. Internal consistency was estimated using Cronbach's alpha coefficient. confirmatory factor analysis did not confirm the original structure of factors of the IDCV. Exploratory factor analysis showed three dimensions, which together explained 78% of the measurement variance. future studies with expansion of case selection are necessary to confirm the IDCV new structure of factors.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

PubMed

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Extraordinary-mode refractive-index change produced by the linear electro-optic effect in LiNbO3 and reverse-poled LiNbO3

NASA Astrophysics Data System (ADS)

Boyd, Joseph T.; Servizzi, Anthony J.; Sriram, S.; Kingsley, Stuart A.

1995-07-01

To examine aspects of an integrated photonic electric-field sensor, we calculate electro-optically induced refractive-index change in regular and reverse-poled LiNbO3. Specifically, for y-propagating extraordinary modes, we determine how index change depends on electric-field magnitude and direction. To accomplish this, changes in index-ellipsoid shape and orientation are found by the use of a numerical eigenvalue procedure to diagonalize the impermeability tensor; then, refractive index is calculated by the use of a vector reference-frame transformation and a small perturbation approximation. A general formula is inferred from calculations for specific field directions. Electro-optic coefficients for reverse-poled LiNbO3 are obtained by application of a tensor reference-frame transformation to those of LiNbO3. The index-calculation procedure has utility beyond the problem that is considered.

Using the phase shift to asymptotically characterize the dipolar mixed modes in post-main-sequence stars

NASA Astrophysics Data System (ADS)

Jiang, C.; Christensen-Dalsgaard, J.; Cunha, M.

2018-03-01

Mixed modes have been extensively observed in post-main-sequence stars by the Kepler and CoRoT space missions. The mixture of the p and g modes can be measured by the dimensionless coefficient q, the so-called coupling strength factor. In this paper, we discuss the utility of the phase shifts θ from the eigenvalue condition for mixed modes as a tool to characterize dipolar mixed modes from the theoretical as well as the practical point of view. Unlike the coupling strength, whose variation in a given star is very small over the relevant frequency range, the phase shifts vary significantly for different modes. The analysis in terms of θ can also provide a better understanding of the pressure and gravity radial order for a given mixed mode. Observed frequencies of the Kepler red-giant star KIC 3744043 are used to test the method. The results are very promising.

Optical properties in GaAs/AlGaAs semiparabolic quantum wells by the finite difference method: Combined effects of electric field and magnetic field

NASA Astrophysics Data System (ADS)

Yan, Ru-Yu; Tang, Jian; Zhang, Zhi-Hai; Yuan, Jian-Hui

2018-05-01

In the present work, the optical properties of GaAs/AlGaAs semiparabolic quantum wells (QWs) are studied under the effect of applied electric field and magnetic field by using the compact-density-matrix method. The energy eigenvalues and their corresponding eigenfunctions of the system are calculated by using the differential method. Simultaneously, the nonlinear optical rectification (OR) and optical absorption coefficients (OACs) are investigated, which are modulated by the applied electric field and magnetic field. It is found that the position and the magnitude of the resonant peaks of the nonlinear OR and OACs can depend strongly on the applied electric field, magnetic field and confined potential frequencies. This gives a new way to control the device applications based on the intersubband transitions of electrons in this system.

Robust consensus control with guaranteed rate of convergence using second-order Hurwitz polynomials

NASA Astrophysics Data System (ADS)

Fruhnert, Michael; Corless, Martin

2017-10-01

This paper considers homogeneous networks of general, linear time-invariant, second-order systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilisable. We show that consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. To achieve this, we provide a new and simple derivation of the conditions for a second-order polynomial with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback.

XCOM intrinsic dimensionality for low-Z elements at diagnostic energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bornefalk, Hans

2012-02-15

Purpose: To determine the intrinsic dimensionality of linear attenuation coefficients (LACs) from XCOM for elements with low atomic number (Z = 1-20) at diagnostic x-ray energies (25-120 keV). H{sub 0}{sup q}, the hypothesis that the space of LACs is spanned by q bases, is tested for various q-values. Methods: Principal component analysis is first applied and the LACs are projected onto the first q principal component bases. The residuals of the model values vs XCOM data are determined for all energies and atomic numbers. Heteroscedasticity invalidates the prerequisite of i.i.d. errors necessary for bootstrapping residuals. Instead wild bootstrap is applied,more » which, by not mixing residuals, allows the effect of the non-i.i.d residuals to be reflected in the result. Credible regions for the eigenvalues of the correlation matrix for the bootstrapped LAC data are determined. If subsequent credible regions for the eigenvalues overlap, the corresponding principal component is not considered to represent true data structure but noise. If this happens for eigenvalues l and l + 1, for any l{<=}q, H{sub 0}{sup q} is rejected. Results: The largest value of q for which H{sub 0}{sup q} is nonrejectable at the 5%-level is q = 4. This indicates that the statistically significant intrinsic dimensionality of low-Z XCOM data at diagnostic energies is four. Conclusions: The method presented allows determination of the statistically significant dimensionality of any noisy linear subspace. Knowledge of such significant dimensionality is of interest for any method making assumptions on intrinsic dimensionality and evaluating results on noisy reference data. For LACs, knowledge of the low-Z dimensionality might be relevant when parametrization schemes are tuned to XCOM data. For x-ray imaging techniques based on the basis decomposition method (Alvarez and Macovski, Phys. Med. Biol. 21, 733-744, 1976), an underlying dimensionality of two is commonly assigned to the LAC of human tissue at diagnostic energies. The finding of a higher statistically significant dimensionality thus raises the question whether a higher assumed model dimensionality (now feasible with the advent of multibin x-ray systems) might also be practically relevant, i.e., if better tissue characterization results can be obtained.« less

Structural robustness with suboptimal responses for linear state space model

NASA Technical Reports Server (NTRS)

Keel, L. H.; Lim, Kyong B.; Juang, Jer-Nan

1989-01-01

A relationship between the closed-loop eigenvalues and the amount of perturbations in the open-loop matrix is addressed in the context of performance robustness. If the allowable perturbation ranges of elements of the open-loop matrix A and the desired tolerance of the closed-loop eigenvalues are given such that max(j) of the absolute value of Delta-lambda(j) (A+BF) should be less than some prescribed value, what is a state feedback controller F which satisfies the closed-loop eigenvalue perturbation-tolerance requirement for a class of given perturbation in A? The paper gives an algorithm to design such a controller. Numerical examples are included for illustration.

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

DOE PAGES

Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; ...

2016-08-16

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from onemore » another.« less

Initial values for the integration scheme to compute the eigenvalues for propagation in ducts

NASA Technical Reports Server (NTRS)

Eversman, W.

1977-01-01

A scheme for the calculation of eigenvalues in the problem of acoustic propagation in a two-dimensional duct is described. The computation method involves changing the coupled transcendental nonlinear algebraic equations into an initial value problem involving a nonlinear ordinary differential equation. The simplest approach is to use as initial values the hardwall eigenvalues and to integrate away from these values as the admittance varies from zero to its actual value with a linear variation. The approach leads to a powerful root finding routine capable of computing the transverse and axial wave numbers for two-dimensional ducts for any frequency, lining, admittance and Mach number without requiring initial guesses or starting points.

Stability of a laminar premixed supersonic free shear layer with chemical reactions

NASA Technical Reports Server (NTRS)

Menon, S.; Anderson, J. D., Jr.; Pai, S. I.

1984-01-01

The stability of a two-dimensional compressible supersonic flow in the wake of a flat plate is discussed. The fluid is a multi-species mixture which is undergoing finite rate chemical reactions. The spatial stability of an infinitesimal disturbance in the fluid is considered. Numerical solutions of the eigenvalue stability equations for both reactive and nonreactive supersonic flows are presented and discussed. The chemical reactions have significant influence on the stability behavior. For instance, a neutral eigenvalue is observed near the freestream Mach number of 2.375 for the nonreactive case, but disappears when the reaction is turned on. For reactive flows, the eigenvalues are not very dependent on the free stream Mach number.

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

DOE PAGES

Burke, Timothy P.; Kiedrowski, Brian C.

2017-12-11

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivitiesmore » of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.« less

Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

NASA Technical Reports Server (NTRS)

Elbanna, Hesham M.; Carlson, Leland A.

1992-01-01

The quasi-analytical approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. Results are compared to those obtained by the direct finite difference approach and both methods are evaluated to determine their computational accuracy and efficiency. The quasi-analytical approach is shown to be accurate and efficient for large aerodynamic systems.

Eigenvalues of Rectangular Waveguide Using FEM With Hybrid Elements

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Hall, John M.

2002-01-01

A finite element analysis using hybrid triangular-rectangular elements is developed to estimate eigenvalues of a rectangular waveguide. Use of rectangular vector-edge finite elements in the vicinity of the PEC boundary and triangular elements in the interior region more accurately models the physical nature of the electromagnetic field, and consequently quicken the convergence.

Nonunitary and unitary approach to Eigenvalue problem of Boson operators and squeezed coherent states

NASA Technical Reports Server (NTRS)

Wunsche, A.

1993-01-01

The eigenvalue problem of the operator a + zeta(boson creation operator) is solved for arbitrarily complex zeta by applying a nonunitary operator to the vacuum state. This nonunitary approach is compared with the unitary approach leading for the absolute value of zeta less than 1 to squeezed coherent states.

Noncanonical harmonic and anharmonic oscillator in high-energy physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jannussis, A.; Vavougios, D.

1986-09-01

We study the eigenvalues of the noncanonical harmonic and anharmonic oscillator, by using different values of the elementary length l corresponding to typical cross sections for the strong interactions. There is evidence for a correlation between the energies of elementary particles (mesons, baryons, resonances) and the energy eigenvalues of the noncanonical theory.

Evaluation of Parallel Analysis Methods for Determining the Number of Factors

ERIC Educational Resources Information Center

Crawford, Aaron V.; Green, Samuel B.; Levy, Roy; Lo, Wen-Juo; Scott, Lietta; Svetina, Dubravka; Thompson, Marilyn S.

2010-01-01

Population and sample simulation approaches were used to compare the performance of parallel analysis using principal component analysis (PA-PCA) and parallel analysis using principal axis factoring (PA-PAF) to identify the number of underlying factors. Additionally, the accuracies of the mean eigenvalue and the 95th percentile eigenvalue criteria…

Twisting singular solutions of Betheʼs equations

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Wang, Chunguang

2014-12-01

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

An Isoperimetric Inequality for Fundamental Tones of Free Plates

ERIC Educational Resources Information Center

Chasman, Laura

2009-01-01

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given tau greater than 0, the free plate eigenvalues omega and eigenfunctions upsilon are determined by the equation Delta Delta upsilon - tau Delta upsilon = omega upsilon together with…

A Teaching Proposal for the Study of Eigenvectors and Eigenvalues

ERIC Educational Resources Information Center

Meneu, María José Beltrán; Murillo Arcila, Marina; Jordá Mora, Enrique

2017-01-01

In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students' difficulties when treating…

Emphasizing Visualization and Physical Applications in the Study of Eigenvectors and Eigenvalues

ERIC Educational Resources Information Center

BeltrÁn-Meneu, María José; Murillo-Arcila, Marina; Albarracín, Lluís

2017-01-01

This article presents a teaching proposal that emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, these concepts were introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was designed after observing architecture students…

An Application of the Vandermonde Determinant

ERIC Educational Resources Information Center

Xu, Junqin; Zhao, Likuan

2006-01-01

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

Approximating natural connectivity of scale-free networks based on largest eigenvalue

NASA Astrophysics Data System (ADS)

Tan, S.-Y.; Wu, J.; Li, M.-J.; Lu, X.

2016-06-01

It has been recently proposed that natural connectivity can be used to efficiently characterize the robustness of complex networks. The natural connectivity has an intuitive physical meaning and a simple mathematical formulation, which corresponds to an average eigenvalue calculated from the graph spectrum. However, as a network model close to the real-world system that widely exists, the scale-free network is found difficult to obtain its spectrum analytically. In this article, we investigate the approximation of natural connectivity based on the largest eigenvalue in both random and correlated scale-free networks. It is demonstrated that the natural connectivity of scale-free networks can be dominated by the largest eigenvalue, which can be expressed asymptotically and analytically to approximate natural connectivity with small errors. Then we show that the natural connectivity of random scale-free networks increases linearly with the average degree given the scaling exponent and decreases monotonically with the scaling exponent given the average degree. Moreover, it is found that, given the degree distribution, the more assortative a scale-free network is, the more robust it is. Experiments in real networks validate our methods and results.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Free Fermions and the Classical Compact Groups

NASA Astrophysics Data System (ADS)

Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil

2018-06-01

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

Space shuttle SRM plume expansion sensitivity analysis. [flow characteristics of exhaust gases from solid propellant rocket engines

NASA Technical Reports Server (NTRS)

Smith, S. D.; Tevepaugh, J. A.; Penny, M. M.

1975-01-01

The exhaust plumes of the space shuttle solid rocket motors can have a significant effect on the base pressure and base drag of the shuttle vehicle. A parametric analysis was conducted to assess the sensitivity of the initial plume expansion angle of analytical solid rocket motor flow fields to various analytical input parameters and operating conditions. The results of the analysis are presented and conclusions reached regarding the sensitivity of the initial plume expansion angle to each parameter investigated. Operating conditions parametrically varied were chamber pressure, nozzle inlet angle, nozzle throat radius of curvature ratio and propellant particle loading. Empirical particle parameters investigated were mean size, local drag coefficient and local heat transfer coefficient. Sensitivity of the initial plume expansion angle to gas thermochemistry model and local drag coefficient model assumptions were determined.

Repeatability of DTI-based skeletal muscle fiber tracking

PubMed Central

Heemskerk, Anneriet M.; Sinha, Tuhin K.; Wilson, Kevin J.; Ding, Zhaohua; Damon, Bruce M.

2015-01-01

Diffusion tensor imaging (DTI)-based muscle fiber tracking enables the measurement of muscle architectural parameters, such as pennation angle (θ) and fiber tract length (Lft), throughout the entire muscle. Little is known, however, about the repeatability of either the muscle architectural measures or the underlying diffusion measures. Therefore, the goal of this study was to investigate the repeatability of DTI fiber tracking-based measurements and θ and Lft. Four DTI acquisitions were performed on two days that allowed for between acquisition, within day, and between day analyses. The eigenvalues and fractional anisotropy were calculated at the maximum cross-sectional area of, and fiber tracking was performed in, the tibialis anterior muscle of nine healthy subjects. The between acquisitions condition had the highest repeatability for the DTI indices and the architectural parameters. The overall inter class correlation coefficients (ICC’s) were greater than 0.6 for both θ and Lft and the repeatability coefficients were θ <10.2° and Lft < 50 mm. In conclusion, under the experimental and data analysis conditions used, the repeatability of the diffusion measures is very good and repeatability of the architectural measurements is acceptable. Therefore, this study demonstrates the feasibility for longitudinal studies of alterations in muscle architecture using DTI-based fiber tracking, under similar noise conditions and with similar diffusion characteristics. PMID:20099372

Underlying construct of empathy, optimism, and burnout in medical students.

PubMed

Hojat, Mohammadreza; Vergare, Michael; Isenberg, Gerald; Cohen, Mitchell; Spandorfer, John

2015-01-29

This study was designed to explore the underlying construct of measures of empathy, optimism, and burnout in medical students. Three instruments for measuring empathy (Jefferson Scale of Empathy, JSE); Optimism (the Life Orientation Test-Revised, LOT-R); and burnout (the Maslach Burnout Inventory, MBI, which includes three scales of Emotional Exhaustion, Depersonalization, and Personal Accomplishment) were administered to 265 third-year students at Sidney Kimmel (formerly Jefferson) Medical College at Thomas Jefferson University. Data were subjected to factor analysis to examine relationships among measures of empathy, optimism, and burnout in a multivariate statistical model. Factor analysis (principal component with oblique rotation) resulted in two underlying constructs, each with an eigenvalue greater than one. The first factor involved "positive personality attributes" (factor coefficients greater than .58 for measures of empathy, optimism, and personal accomplishment). The second factor involved "negative personality attributes" (factor coefficients greater than .78 for measures of emotional exhaustion, and depersonalization). Results confirmed that an association exists between empathy in the context of patient care and personality characteristics that are conducive to relationship building, and considered to be "positive personality attributes," as opposed to personality characteristics that are considered as "negative personality attributes" that are detrimental to interpersonal relationships. Implications for the professional development of physicians-in-training and in-practice are discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favorite, Jeffrey A.

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff, and α using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every isotope and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations. The tool can be used for one-dimensional spherical (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used formore » fixed-source and eigenvalue problems. The tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists all of the input files whose results are presented in Sec. VI.« less

Multigrid method for stability problems

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1988-01-01

The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization are to be calculated. An efficient multigrid method for solving these problems is presented. The method begins by obtaining an initial approximation for the dominant subspace on a coarse level using a damped Jacobi relaxation. This proceeds until enough accuracy for the dominant subspace has been obtained. The resulting grid functions are then used as an initial approximation for appropriate eigenvalue problems. These problems are being solved first on coarse levels, followed by refinement until a desired accuracy for the eigenvalues has been achieved. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a non-standard way in which the right hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem demonstrate the effectiveness of the method proposed. Using an FMG algorithm a solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relization on the finest level.

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Sensitivity Analysis of Flutter Response of a Wing Incorporating Finite-Span Corrections

NASA Technical Reports Server (NTRS)

Issac, Jason Cherian; Kapania, Rakesh K.; Barthelemy, Jean-Francois M.

1994-01-01

Flutter analysis of a wing is performed in compressible flow using state-space representation of the unsteady aerodynamic behavior. Three different expressions are used to incorporate corrections due to the finite-span effects of the wing in estimating the lift-curve slope. The structural formulation is based on a Rayleigh-Pitz technique with Chebyshev polynomials used for the wing deflections. The aeroelastic equations are solved as an eigen-value problem to determine the flutter speed of the wing. The flutter speeds are found to be higher in these cases, when compared to that obtained without accounting for the finite-span effects. The derivatives of the flutter speed with respect to the shape parameters, namely: aspect ratio, area, taper ratio and sweep angle, are calculated analytically. The shape sensitivity derivatives give a linear approximation to the flutter speed curves over a range of values of the shape parameter which is perturbed. Flutter and sensitivity calculations are performed on a wing using a lifting-surface unsteady aerodynamic theory using modules from a system of programs called FAST.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles

NASA Astrophysics Data System (ADS)

Zhang, Pei; Galindo-Torres, S. A.; Tang, Hongwu; Jin, Guangqiu; Scheuermann, A.; Li, Ling

2016-06-01

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100 . The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

Biophotonic applications of eigenchannels in a scattering medium (Conference Presentation)

NASA Astrophysics Data System (ADS)

Kim, Moonseok; Choi, Wonjun; Choi, Youngwoon; Yoon, Changhyeong; Choi, Wonshik

2016-03-01

When waves travel through disordered media such as ground glass and skin tissues, they are scattered multiple times. Most of the incoming energy bounces back at the superficial layers and only a small fraction can penetrate deep inside. This has been a limiting factor for the working depth of various optical techniques. We present a systematic method to enhance wave penetration to the scattering media. Specifically, we measured the reflection matrix of a disordered medium with wide angular coverage for each orthogonal polarization states. From the reflection matrix, we identified reflection eigenchannels of the medium, and shaped the incident wave into the reflection eigenchannel with smallest eigenvalue, which we call anti-reflection mode. This makes reflectance reduced and wave penetration increased as a result of the energy conservation. We demonstrated transmission enhancement by more than a factor of 3 by the coupling of the incident waves to the anti-reflection modes. Based on the uneven distribution of eigenvalues of reflection eigenchannels, we further developed an iterative feedback control method for finding and coupling light to anti-reflection modes. Since this adaptive control method can keep up with sample perturbation, it promotes the applicability of exploiting reflection eigenchannels. Our approach of delivering light deep into the scattering media will contribute to enhancing the sensitivity of detecting objects hidden under scattering layers, which is universal problem ranging from geology to life science.

Thermal and Mechanical Buckling Analysis of Hypersonic Aircraft Hat-Stiffened Panels With Varying Face Sheet Geometry and Fiber Orientation

NASA Technical Reports Server (NTRS)

Ko, William L.

1996-01-01

Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened panels were investigated. The panels have three types of face-sheet geometry: Flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal buckling analysis required both eigenvalue and material property iterations. Graphical methods of the dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with different face-sheet geometry are compared. It was found that by just microdenting or microbulging of the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metal-matrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated in great detail, and various composite layup combinations offering, high panel buckling strengths are presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of hat fiber orientation.

Nonlinear Analysis of the Space Shuttle Superlightweight LO2 Tank. Part 2; Behavior Under 3g End-of-Flight Loads

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H.,Jr.

1998-01-01

Results of linear bifurcation and nonlinear analyses of the Space Shuttle super lightweight (SLWT) external liquid-oxygen (LO2) tank are presented for an important end-of-flight loading condition. These results illustrate an important type of response mode for thin-walled shells, that are subjected to combined mechanical and thermal loads, that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the aft dome of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of a short-wavelength bending deformation in the aft elliptical dome of the LO2 tank that grows in amplitude in a stable manner with increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the aft dome. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shell generally require a large-scale, high fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 1.9 times the values of the operational loads considered.

Automatic classification of unexploded ordnance applied to Spencer Range live site for 5x5 TEMTADS sensor

NASA Astrophysics Data System (ADS)

Sigman, John B.; Barrowes, Benjamin E.; O'Neill, Kevin; Shubitidze, Fridon

2013-06-01

This paper details methods for automatic classification of Unexploded Ordnance (UXO) as applied to sensor data from the Spencer Range live site. The Spencer Range is a former military weapons range in Spencer, Tennessee. Electromagnetic Induction (EMI) sensing is carried out using the 5x5 Time-domain Electromagnetic Multi-sensor Towed Array Detection System (5x5 TEMTADS), which has 25 receivers and 25 co-located transmitters. Every transmitter is activated sequentially, each followed by measuring the magnetic field in all 25 receivers, from 100 microseconds to 25 milliseconds. From these data target extrinsic and intrinsic parameters are extracted using the Differential Evolution (DE) algorithm and the Ortho-Normalized Volume Magnetic Source (ONVMS) algorithms, respectively. Namely, the inversion provides x, y, and z locations and a time series of the total ONVMS principal eigenvalues, which are intrinsic properties of the objects. The eigenvalues are fit to a power-decay empirical model, the Pasion-Oldenburg model, providing 3 coefficients (k, b, and g) for each object. The objects are grouped geometrically into variably-sized clusters, in the k-b-g space, using clustering algorithms. Clusters matching a priori characteristics are identified as Targets of Interest (TOI), and larger clusters are automatically subclustered. Ground Truths (GT) at the center of each class are requested, and probability density functions are created for clusters that have centroid TOI using a Gaussian Mixture Model (GMM). The probability functions are applied to all remaining anomalies. All objects of UXO probability higher than a chosen threshold are placed in a ranked dig list. This prioritized list is scored and the results are demonstrated and analyzed.

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

PubMed

Negahbani, Ehsan; Steyn-Ross, D Alistair; Steyn-Ross, Moira L; Aguirre, Luis A

2016-01-01

Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems. Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal. By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs. In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the P variance initially shows a decaying trend. Here we resolve this puzzle using observability measures from control theory. By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics. We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition. Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation. We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.

Observability Analysis of a MEMS INS/GPS Integration System with Gyroscope G-Sensitivity Errors

PubMed Central

Fan, Chen; Hu, Xiaoping; He, Xiaofeng; Tang, Kanghua; Luo, Bing

2014-01-01

Gyroscopes based on micro-electromechanical system (MEMS) technology suffer in high-dynamic applications due to obvious g-sensitivity errors. These errors can induce large biases in the gyroscope, which can directly affect the accuracy of attitude estimation in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS). The observability determines the existence of solutions for compensating them. In this paper, we investigate the observability of the INS/GPS system with consideration of the g-sensitivity errors. In terms of two types of g-sensitivity coefficients matrix, we add them as estimated states to the Kalman filter and analyze the observability of three or nine elements of the coefficient matrix respectively. A global observable condition of the system is presented and validated. Experimental results indicate that all the estimated states, which include position, velocity, attitude, gyro and accelerometer bias, and g-sensitivity coefficients, could be made observable by maneuvering based on the conditions. Compared with the integration system without compensation for the g-sensitivity errors, the attitude accuracy is raised obviously. PMID:25171122

Observability analysis of a MEMS INS/GPS integration system with gyroscope G-sensitivity errors.

PubMed

Fan, Chen; Hu, Xiaoping; He, Xiaofeng; Tang, Kanghua; Luo, Bing

2014-08-28

Gyroscopes based on micro-electromechanical system (MEMS) technology suffer in high-dynamic applications due to obvious g-sensitivity errors. These errors can induce large biases in the gyroscope, which can directly affect the accuracy of attitude estimation in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS). The observability determines the existence of solutions for compensating them. In this paper, we investigate the observability of the INS/GPS system with consideration of the g-sensitivity errors. In terms of two types of g-sensitivity coefficients matrix, we add them as estimated states to the Kalman filter and analyze the observability of three or nine elements of the coefficient matrix respectively. A global observable condition of the system is presented and validated. Experimental results indicate that all the estimated states, which include position, velocity, attitude, gyro and accelerometer bias, and g-sensitivity coefficients, could be made observable by maneuvering based on the conditions. Compared with the integration system without compensation for the g-sensitivity errors, the attitude accuracy is raised obviously.

Sensitivity of the reference evapotranspiration to key climatic variables during the growing season in the Ejina oasis northwest China.

PubMed

Hou, Lan-Gong; Zou, Song-Bing; Xiao, Hong-Lang; Yang, Yong-Gang

2013-01-01

The standardized FAO56 Penman-Monteith model, which has been the most reasonable method in both humid and arid climatic conditions, provides reference evapotranspiration (ETo) estimates for planning and efficient use of agricultural water resources. And sensitivity analysis is important in understanding the relative importance of climatic variables to the variation of reference evapotranspiration. In this study, a non-dimensional relative sensitivity coefficient was employed to predict responses of ETo to perturbations of four climatic variables in the Ejina oasis northwest China. A 20-year historical dataset of daily air temperature, wind speed, relative humidity and daily sunshine duration in the Ejina oasis was used in the analysis. Results have shown that daily sensitivity coefficients exhibited large fluctuations during the growing season, and shortwave radiation was the most sensitive variable in general for the Ejina oasis, followed by air temperature, wind speed and relative humidity. According to this study, the response of ETo can be preferably predicted under perturbation of air temperature, wind speed, relative humidity and shortwave radiation by their sensitivity coefficients.

Checking Dimensionality in Item Response Models with Principal Component Analysis on Standardized Residuals

ERIC Educational Resources Information Center

Chou, Yeh-Tai; Wang, Wen-Chung

2010-01-01

Dimensionality is an important assumption in item response theory (IRT). Principal component analysis on standardized residuals has been used to check dimensionality, especially under the family of Rasch models. It has been suggested that an eigenvalue greater than 1.5 for the first eigenvalue signifies a violation of unidimensionality when there…

Some Results on Mean Square Error for Factor Score Prediction

ERIC Educational Resources Information Center

Krijnen, Wim P.

2006-01-01

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript…

Entropy-driven phase transitions of entanglement

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio; Yuasa, Kazuya

2013-05-01

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

Inflationary dynamics for matrix eigenvalue problems

PubMed Central

Heller, Eric J.; Kaplan, Lev; Pollmann, Frank

2008-01-01

Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the acoustic modes of a concert hall, or hundreds of other physical quantities. Often only the few eigenpairs with the lowest or highest frequency (extremal solutions) are needed. Methods that have been developed over the past 60 years to solve such problems include the Lanczos algorithm, Jacobi–Davidson techniques, and the conjugate gradient method. Here, we present a way to solve the extremal eigenvalue/eigenvector problem, turning it into a nonlinear classical mechanical system with a modified Lagrangian constraint. The constraint induces exponential inflationary growth of the desired extremal solutions. PMID:18511564

Validity and reliability of the Turkish version of the European Health Literacy Survey Questionnaire.

PubMed

Abacigil, Filiz; Harlak, Hacer; Okyay, Pinar; Kiraz, Didem Evci; Gursoy Turan, Selen; Saruhan, Gulnur; Karakaya, Kagan; Tuzun, Hakan; Baran Deniz, Emine; Tontus, Omer; Beser, Erdal

2018-04-10

Health literacy is a public health priority which refers to individual's knowledge, motivation and competence to access, understand, appraise and apply health information to prevent disease and promote health in daily life. This study aimed to adapt European Health Literacy Survey Questionnaire (HLS-EU-Q47) into Turkish and to investigate its psychometric properties. The questionnaire was translated into Turkish by using both group translation and expert opinion methods. Forward translation-back translation method was used for language validity and the final Turkish version (HLS-TR) was formed. HLS-EU-Q47 and Health Awareness Scale (HAS) were administered to 505 respondents. The scale reliability was examined using Crohnbach's alpha coefficient and the construct validity was assessed by principal axis factoring procedure. The convergent validity was obtained by Pearson correlation coefficients between HLS-TR and HAS scores and discriminant validity was examined comparing the scores of participants who were stratified according to ages, educational status, gender, general health status and social status. Cronbach's alpha coefficient for the whole scale was 0.95. Principal axis factoring extracted nine factors which eigenvalues were >1 and explained 50.01% of total variance. Factor matrix displayed that all items gave greater load in factor 1, showing that health literacy measured with one factor. Positive and significant correlation was found between HLS-TR and HAS. Significant relations were found between HLS-TR scores and selected determinants of health. This study revealed that the HLS-TR was a valid and reliable measuring instrument with appropriate psychometric characteristics.

Tracking a Severe Pollution Event in Beijing in December 2016 with the GRAPES-CUACE Adjoint Model

NASA Astrophysics Data System (ADS)

Wang, Chao; An, Xingqin; Zhai, Shixian; Sun, Zhaobin

2018-02-01

We traced the adjoint sensitivity of a severe pollution event in December 2016 in Beijing using the adjoint model of the GRAPES-CUACE (Global/Regional Assimilation and Prediction System coupled with the China Meteorological Administration Unified Atmospheric Chemistry Environmental Forecasting System). The key emission sources and periods affecting this severe pollution event are analyzed. For comaprison, we define 2000 Beijing Time 3 December 2016 as the objective time when PM2.5 reached the maximum concentration in Beijing. It is found that the local hourly sensitivity coefficient amounts to a peak of 9.31 μg m-3 just 1 h before the objective time, suggesting that PM2.5 concentration responds rapidly to local emissions. The accumulated sensitivity coefficient in Beijing is large during the 20-h period prior to the objective time, showing that local emissions are the most important in this period. The accumulated contribution rates of emissions from Beijing, Tianjin, Hebei, and Shanxi are 34.2%, 3.0%, 49.4%, and 13.4%, respectively, in the 72-h period before the objective time. The evolution of hourly sensitivity coefficient shows that the main contribution from the Tianjin source occurs 1-26 h before the objective time and its peak hourly contribution is 0.59 μg m-3 at 4 h before the objective time. The main contributions of the Hebei and Shanxi emission sources occur 1-54 and 14-53 h, respectively, before the objective time and their hourly sensitivity coefficients both show periodic fluctuations. The Hebei source shows three sensitivity coefficient peaks of 3.45, 4.27, and 0.71 μg m-3 at 4, 16, and 38 h before the objective time, respectively. The sensitivity coefficient of the Shanxi source peaks twice, with values of 1.41 and 0.64 μg m-3 at 24 and 45 h before the objective time, respectively. Overall, the adjoint model is effective in tracking the crucial sources and key periods of emissions for the severe pollution event.

[Validity of expired carbon monoxide and urine cotinine using dipstick method to assess smoking status].

PubMed

Park, Su San; Lee, Ju Yul; Cho, Sung-Il

2007-07-01

We investigated the validity of the dipstick method (Mossman Associates Inc. USA) and the expired CO method to distinguish between smokers and nonsmokers. We also elucidated the related factors of the two methods. This study included 244 smokers and 50 ex-smokers, recruited from smoking cessation clinics at 4 local public health centers, who had quit for over 4 weeks. We calculated the sensitivity, specificity and Kappa coefficient of each method for validity. We obtained ROC curve, predictive value and agreement to determine the cutoff of expired air CO method. Finally, we elucidated the related factors and compared their effect powers using the standardized regression coefficient. The dipstick method showed a sensitivity of 92.6%, specificity of 96.0% and Kappa coefficient of 0.79. The best cutoff value to distinguish smokers was 5-6 ppm. At 5 ppm, the expired CO method showed a sensitivity of 94.3%, specificity of 82.0% and Kappa coefficient of 0.73. And at 6 ppm, sensitivity, specificity and Kappa coefficient were 88.5%, 86.0% and 0.64, respectively. Therefore, the dipstick method had higher sensitivity and specificity than the expired CO method. The dipstick and expired CO methods were significantly increased with increasing smoking amount. With longer time since the last smoking, expired CO showed a rapid decrease after 4 hours, whereas the dipstick method showed relatively stable levels for more than 4 hours. The dipstick and expired CO methods were both good indicators for assessing smoking status. However, the former showed higher sensitivity and specificity and stable levels over longer hours after smoking, compared to the expired CO method.

Cryogenic fiber optic temperature sensor and method of manufacturing the same

NASA Technical Reports Server (NTRS)

Kochergin, Vladimir (Inventor)

2012-01-01

This invention teaches the fiber optic sensors temperature sensors for cryogenic temperature range with improved sensitivity and resolution, and method of making said sensors. In more detail, the present invention is related to enhancement of temperature sensitivity of fiber optic temperature sensors at cryogenic temperatures by utilizing nanomaterials with a thermal expansion coefficient that is smaller than the thermal expansion coefficient of the optical fiber but larger in absolute value than the thermal expansion coefficient of the optical fiber at least over a range of temperatures.

The Description of Shale Reservoir Pore Structure Based on Method of Moments Estimation

PubMed Central

Li, Wenjie; Wang, Changcheng; Shi, Zejin; Wei, Yi; Zhou, Huailai; Deng, Kun

2016-01-01

Shale has been considered as good gas reservoir due to its abundant interior nanoscale pores. Thus, the study of the pore structure of shale is of great significance for the evaluation and development of shale oil and gas. To date, the most widely used approaches for studying the shale pore structure include image analysis, radiation and fluid invasion methods. The detailed pore structures can be studied intuitively by image analysis and radiation methods, but the results obtained are quite sensitive to sample preparation, equipment performance and experimental operation. In contrast, the fluid invasion method can be used to obtain information on pore size distribution and pore structure, but the relative simple parameters derived cannot be used to evaluate the pore structure of shale comprehensively and quantitatively. To characterize the nanoscale pore structure of shale reservoir more effectively and expand the current research techniques, we proposed a new method based on gas adsorption experimental data and the method of moments to describe the pore structure parameters of shale reservoir. Combined with the geological mixture empirical distribution and the method of moments estimation principle, the new method calculates the characteristic parameters of shale, including the mean pore size (x¯), standard deviation (σ), skewness (Sk) and variation coefficient (c). These values are found by reconstructing the grouping intervals of observation values and optimizing algorithms for eigenvalues. This approach assures a more effective description of the characteristics of nanoscale pore structures. Finally, the new method has been applied to analyze the Yanchang shale in the Ordos Basin (China) and Longmaxi shale from the Sichuan Basin (China). The results obtained well reveal the pore characteristics of shale, indicating the feasibility of this new method in the study of the pore structure of shale reservoir. PMID:26992168

The Description of Shale Reservoir Pore Structure Based on Method of Moments Estimation.

PubMed

Li, Wenjie; Wang, Changcheng; Shi, Zejin; Wei, Yi; Zhou, Huailai; Deng, Kun

2016-01-01

Shale has been considered as good gas reservoir due to its abundant interior nanoscale pores. Thus, the study of the pore structure of shale is of great significance for the evaluation and development of shale oil and gas. To date, the most widely used approaches for studying the shale pore structure include image analysis, radiation and fluid invasion methods. The detailed pore structures can be studied intuitively by image analysis and radiation methods, but the results obtained are quite sensitive to sample preparation, equipment performance and experimental operation. In contrast, the fluid invasion method can be used to obtain information on pore size distribution and pore structure, but the relative simple parameters derived cannot be used to evaluate the pore structure of shale comprehensively and quantitatively. To characterize the nanoscale pore structure of shale reservoir more effectively and expand the current research techniques, we proposed a new method based on gas adsorption experimental data and the method of moments to describe the pore structure parameters of shale reservoir. Combined with the geological mixture empirical distribution and the method of moments estimation principle, the new method calculates the characteristic parameters of shale, including the mean pore size (mean), standard deviation (σ), skewness (Sk) and variation coefficient (c). These values are found by reconstructing the grouping intervals of observation values and optimizing algorithms for eigenvalues. This approach assures a more effective description of the characteristics of nanoscale pore structures. Finally, the new method has been applied to analyze the Yanchang shale in the Ordos Basin (China) and Longmaxi shale from the Sichuan Basin (China). The results obtained well reveal the pore characteristics of shale, indicating the feasibility of this new method in the study of the pore structure of shale reservoir.

Calculation and Analysis of Magnetic Gradient Tensor Components of Global Magnetic Models

NASA Astrophysics Data System (ADS)

Schiffler, M.; Queitsch, M.; Schneider, M.; Goepel, A.; Stolz, R.; Krech, W.; Meyer, H. G.; Kukowski, N.

2014-12-01

Global Earth's magnetic field models like the International Geomagnetic Reference Field (IGRF), the World Magnetic Model (WMM) or the High Definition Geomagnetic Model (HDGM) are harmonic analysis regressions to available magnetic observations stored as spherical harmonic coefficients. Input data combine recordings from magnetic observatories, airborne magnetic surveys and satellite data. The advance of recent magnetic satellite missions like SWARM and its predecessors like CHAMP offer high resolution measurements while providing a full global coverage. This deserves expansion of the theoretical framework of harmonic synthesis to magnetic gradient tensor components. Measurement setups for Full Tensor Magnetic Gradiometry equipped with high sensitive gradiometers like the JeSSY STAR system can directly measure the gradient tensor components, which requires precise knowledge about the background regional gradients which can be calculated with this extension. In this study we develop the theoretical framework for calculation of the magnetic gradient tensor components from the harmonic series expansion and apply our approach to the IGRF and HDGM. The gradient tensor component maps for entire Earth's surface produced for the IGRF show low gradients reflecting the variation from the dipolar character, whereas maps for the HDGM (up to degree N=729) reveal new information about crustal structure, especially across the oceans, and deeply situated ore bodies. From the gradient tensor components, the rotational invariants, the Eigenvalues, and the normalized source strength (NSS) are calculated. The NSS focuses on shallower and stronger anomalies. Euler deconvolution using either the tensor components or the NSS applied to the HDGM reveals an estimate of the average source depth for the entire magnetic crust as well as individual plutons and ore bodies. The NSS reveals the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

A few shape optimization results for a biharmonic Steklov problem

NASA Astrophysics Data System (ADS)

Buoso, Davide; Provenzano, Luigi

2015-09-01

We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

Periodic orbit spectrum in terms of Ruelle-Pollicott resonances

NASA Astrophysics Data System (ADS)

Leboeuf, P.

2004-02-01

Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g., a trajectory “p” returns to its initial conditions after some fixed time τp. Our aim is to investigate the spectrum {τ1,τ2,…} of periods of the periodic orbits. An explicit formula for the density ρ(τ)=∑pδ(τ-τp) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle-Pollicott resonances). For large periods, corrections to the well-known exponential growth of the smooth part of the density are obtained. An alternative formula for ρ(τ) in terms of the zeros and poles of the Ruelle ζ function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random-matrix theory, and discrete maps are also considered. In particular, a random-matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards.

Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration.

PubMed

Cui, Yao; Bulik, Ireneusz W; Jiménez-Hoyos, Carlos A; Henderson, Thomas M; Scuseria, Gustavo E

2013-10-21

We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

NASA Astrophysics Data System (ADS)

Pato, Mauricio P.; Oshanin, Gleb

2013-03-01

We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.

Evaluation of RAPID for a UNF cask benchmark problem

NASA Astrophysics Data System (ADS)

Mascolino, Valerio; Haghighat, Alireza; Roskoff, Nathan J.

2017-09-01

This paper examines the accuracy and performance of the RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system for the simulation of a used nuclear fuel (UNF) cask. RAPID is capable of determining eigenvalue, subcritical multiplication, and pin-wise, axially-dependent fission density throughout a UNF cask. We study the source convergence based on the analysis of the different parameters used in an eigenvalue calculation in the MCNP Monte Carlo code. For this study, we consider a single assembly surrounded by absorbing plates with reflective boundary conditions. Based on the best combination of eigenvalue parameters, a reference MCNP solution for the single assembly is obtained. RAPID results are in excellent agreement with the reference MCNP solutions, while requiring significantly less computation time (i.e., minutes vs. days). A similar set of eigenvalue parameters is used to obtain a reference MCNP solution for the whole UNF cask. Because of time limitation, the MCNP results near the cask boundaries have significant uncertainties. Except for these, the RAPID results are in excellent agreement with the MCNP predictions, and its computation time is significantly lower, 35 second on 1 core versus 9.5 days on 16 cores.

Implicity restarted Arnoldi/Lanczos methods for large scale eigenvalue calculations

NASA Technical Reports Server (NTRS)

Sorensen, Danny C.

1996-01-01

Eigenvalues and eigenfunctions of linear operators are important to many areas of applied mathematics. The ability to approximate these quantities numerically is becoming increasingly important in a wide variety of applications. This increasing demand has fueled interest in the development of new methods and software for the numerical solution of large-scale algebraic eigenvalue problems. In turn, the existence of these new methods and software, along with the dramatically increased computational capabilities now available, has enabled the solution of problems that would not even have been posed five or ten years ago. Until very recently, software for large-scale nonsymmetric problems was virtually non-existent. Fortunately, the situation is improving rapidly. The purpose of this article is to provide an overview of the numerical solution of large-scale algebraic eigenvalue problems. The focus will be on a class of methods called Krylov subspace projection methods. The well-known Lanczos method is the premier member of this class. The Arnoldi method generalizes the Lanczos method to the nonsymmetric case. A recently developed variant of the Arnoldi/Lanczos scheme called the Implicitly Restarted Arnoldi Method is presented here in some depth. This method is highlighted because of its suitability as a basis for software development.

Squared eigenvalue condition numbers and eigenvector correlations from the single ring theorem

NASA Astrophysics Data System (ADS)

Belinschi, Serban; Nowak, Maciej A.; Speicher, Roland; Tarnowski, Wojciech

2017-03-01

We extend the so-called ‘single ring theorem’ (Feinberg and Zee 1997 Nucl. Phys. B 504 579), also known as the Haagerup-Larsen theorem (Haagerup and Larsen 2000 J. Funct. Anal. 176 331). We do this by showing that in the limit when the size of the matrix goes to infinity a particular correlator between left and right eigenvectors of the relevant non-hermitian matrix X, being the spectral density weighted by the squared eigenvalue condition number, is given by a simple formula involving only the radial spectral cumulative distribution function of X. We show that this object allows the calculation of the conditional expectation of the squared eigenvalue condition number. We give examples and provide a cross-check of the analytic prediction by the large scale numerics.

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

NASA Astrophysics Data System (ADS)

Pelinovsky, Dmitry E.; Sulem, Catherine

A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

Numerical method of applying shadow theory to all regions of multilayered dielectric gratings in conical mounting.

PubMed

Wakabayashi, Hideaki; Asai, Masamitsu; Matsumoto, Keiji; Yamakita, Jiro

2016-11-01

Nakayama's shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.

Existence and analyticity of eigenvalues of a two-channel molecular resonance model

NASA Astrophysics Data System (ADS)

Lakaev, S. N.; Latipov, Sh. M.

2011-12-01

We consider a family of operators Hγμ(k), k ∈ mathbb{T}^d := (-π,π]d, associated with the Hamiltonian of a system consisting of at most two particles on a d-dimensional lattice ℤd, interacting via both a pair contact potential (μ > 0) and creation and annihilation operators (γ > 0). We prove the existence of a unique eigenvalue of Hγμ(k), k ∈ mathbb{T}^d , or its absence depending on both the interaction parameters γ,μ ≥ 0 and the system quasimomentum k ∈ mathbb{T}^d . We show that the corresponding eigenvector is analytic. We establish that the eigenvalue and eigenvector are analytic functions of the quasimomentum k ∈ mathbb{T}^d in the existence domain G ⊂ mathbb{T}^d.

Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach

NASA Astrophysics Data System (ADS)

Tarai, Madhumita; Kumar, Keshav; Divya, O.; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

2017-09-01

The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix.

Spin 0 and spin 1/2 quantum relativistic particles in a constant gravitational field

NASA Astrophysics Data System (ADS)

Khorrami, M.; Alimohammadi, M.; Shariati, A.

2003-04-01

The Klein-Gordon and Dirac equations in a semi-infinite lab ( x>0), in the background metric d s2= u2( x)(-d t2+d x2)+d y2+d z2, are investigated. The resulting equations are studied for the special case u( x)=1+ gx. It is shown that in the case of zero transverse-momentum, the square of the energy eigenvalues of the spin-1/2 particles are less than the squares of the corresponding eigenvalues of spin-0 particles with same masses, by an amount of mgℏ c. Finally, for non-zero transverse-momentum, the energy eigenvalues corresponding to large quantum numbers are obtained and the results for spin-0 and spin-1/2 particles are compared to each other.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

A new S-type eigenvalue inclusion set for tensors and its applications.

PubMed

Huang, Zheng-Ge; Wang, Li-Gong; Xu, Zhong; Cui, Jing-Jing

2016-01-01

In this paper, a new S -type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H -eigenvalue of strong M -tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).

Sensitivity Analysis of Biome-Bgc Model for Dry Tropical Forests of Vindhyan Highlands, India

NASA Astrophysics Data System (ADS)

Kumar, M.; Raghubanshi, A. S.

2011-08-01

A process-based model BIOME-BGC was run for sensitivity analysis to see the effect of ecophysiological parameters on net primary production (NPP) of dry tropical forest of India. The sensitivity test reveals that the forest NPP was highly sensitive to the following ecophysiological parameters: Canopy light extinction coefficient (k), Canopy average specific leaf area (SLA), New stem C : New leaf C (SC:LC), Maximum stomatal conductance (gs,max), C:N of fine roots (C:Nfr), All-sided to projected leaf area ratio and Canopy water interception coefficient (Wint). Therefore, these parameters need more precision and attention during estimation and observation in the field studies.

On the design of wave digital filters with low sensitivity properties.

NASA Technical Reports Server (NTRS)

Renner, K.; Gupta, S. C.

1973-01-01

The wave digital filter patterned after doubly terminated maximum available power (MAP) networks by means of the Richard's transformation has been shown to have low-coefficient-sensitivity properties. This paper examines the exact nature of the relationship between the wave-digital-filter structure and the MAP networks and how the sensitivity property arises, which permits implementation of the digital structure with a lower coefficient word length than that possible with the conventional structures. The proper design procedure is specified and the nature of the unique complementary outputs is discussed. Finally, an example is considered which illustrates the design, the conversion techniques, and the low sensitivity properties.

[Research on optimization of mathematical model of flow injection-hydride generation-atomic fluorescence spectrometry].

PubMed

Cui, Jian; Zhao, Xue-Hong; Wang, Yan; Xiao, Ya-Bing; Jiang, Xue-Hui; Dai, Li

2014-01-01

Flow injection-hydride generation-atomic fluorescence spectrometry was a widely used method in the industries of health, environmental, geological and metallurgical fields for the merit of high sensitivity, wide measurement range and fast analytical speed. However, optimization of this method was too difficult as there exist so many parameters affecting the sensitivity and broadening. Generally, the optimal conditions were sought through several experiments. The present paper proposed a mathematical model between the parameters and sensitivity/broadening coefficients using the law of conservation of mass according to the characteristics of hydride chemical reaction and the composition of the system, which was proved to be accurate as comparing the theoretical simulation and experimental results through the test of arsanilic acid standard solution. Finally, this paper has put a relation map between the parameters and sensitivity/broadening coefficients, and summarized that GLS volume, carrier solution flow rate and sample loop volume were the most factors affecting sensitivity and broadening coefficients. Optimizing these three factors with this relation map, the relative sensitivity was advanced by 2.9 times and relative broadening was reduced by 0.76 times. This model can provide a theoretical guidance for the optimization of the experimental conditions.

Using Perturbation Theory to Compute the Morphological Similarity of Diffusion Tensors

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Royal, Jason; Peterson, Bradley S.

2008-01-01

Computing the morphological similarity of Diffusion Tensors (DTs) at neighboring voxels within a DT image, or at corresponding locations across different DT images, is a fundamental and ubiquitous operation in the post-processing of DT images. The morphological similarity of DTs typically has been computed using either the Principal Directions (PDs) of DTs (i.e., the direction along which water molecules diffuse preferentially) or their tensor elements. Although comparing PDs allows the similarity of one morphological feature of DTs to be visualized directly in eigenspace, this method takes into account only a single eigenvector, and it is therefore sensitive to the presence of noise in the images that can introduce error into the estimation of that vector. Although comparing tensor elements, rather than PDs, is comparatively more robust to the effects of noise, the individual elements of a given tensor do not directly reflect the diffusion properties of water molecules. We propose a measure for computing the morphological similarity of DTs that uses both their eigenvalues and eigenvectors, and that also accounts for the noise levels present in DT images. Our measure presupposes that DTs in a homogeneous region within or across DT images are random perturbations of one another in the presence of noise. The similarity values that are computed using our method are smooth (in the sense that small changes in eigenvalues and eigenvectors cause only small changes in similarity), and they are symmetric when differences in eigenvalues and eigenvectors are also symmetric. In addition, our method does not presuppose that the corresponding eigenvectors across two DTs have been identified accurately, an assumption that is problematic in the presence of noise. Because we compute the similarity between DTs using their eigenspace components, our similarity measure relates directly to both the magnitude and the direction of the diffusion of water molecules. The favorable performance characteristics of our measure offer the prospect of substantially improving additional post-processing operations that are commonly performed on DTI datasets, such as image segmentation, fiber tracking, noise filtering, and spatial normalization. PMID:18450533

Gravitational lensing by eigenvalue distributions of random matrix models

NASA Astrophysics Data System (ADS)

Martínez Alonso, Luis; Medina, Elena

2018-05-01

We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.

Sur le spectre du laplacien des fibrés en tores qui s'effondrent

NASA Astrophysics Data System (ADS)

Jammes, Pierre

2005-06-01

We study the small eigenvalues of the Hodge Laplacian on collaping torus bundles with bounded curvature. In the first part of this dissertation, we consider examples of bundles on S^1 and T^2 with homogeneous structure. In the second part, we give a lower bound of the first non-zero eigenvalue of the 1-form Laplacian on principal torus bundles.

Those Do What? Connecting Eigenvectors and Eigenvalues to the Rest of Linear Algebra: Using Visual Enhancements to Help Students Connect Eigenvectors to the Rest of Linear Algebra

ERIC Educational Resources Information Center

Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.

2010-01-01

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Sensitivity of the Lidar ratio to changes in size distribution and index of refraction

NASA Technical Reports Server (NTRS)

Evans, B. T. N.

1986-01-01

In order to invert lidar signals to obtain reliable extinction coefficients, sigma, a relationship between sigma and the backscatter coefficient, beta, must be given. These two coefficients are linearly related if the complex index of refraction, m, particle shape size distribution, N, does not change along the path illuminated by the laser beam. This, however, is generally not the case. An extensive Mie computation of the lidar ratio R = beta/sigma and the sensitivity of R to the changes in a parametric space defined by N and m were examined.

Turbulence model sensitivity and scour gap effect of unsteady flow around pipe: a CFD study.

PubMed

Ali, Abbod; Sharma, R K; Ganesan, P; Akib, Shatirah

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed.

Influential factors on thermoacoustic efficiency of multilayered graphene film loudspeakers for optimal design

NASA Astrophysics Data System (ADS)

Xing, Qianhe; Li, Shuang; Fan, Xueliang; Bian, Anhua; Cao, Shi-Jie; Li, Cheng

2017-09-01

Graphene thermoacoustic loudspeakers, composed of a graphene film on a substrate, generate sound with heat. Improving thermoacoustic efficiency of graphene speakers is a goal for optimal design. In this work, we first modified the existing TA model with respect to small thermal wavelengths, and then built an acoustic platform for model validation. Additionally, sensitivity analyses for influential factors on thermoacoustic efficiency were performed, including the thickness of multilayered graphene films, the thermal effusivity of substrates, and the characteristics of inserted gases. The higher sensitivity coefficients result in the stronger effects on thermoacoustic efficiency. We find that the thickness (5 nm-15 nm) of graphene films plays a trivial role in efficiency, resulting in the sensitivity coefficient less than 0.02. The substrate thermal effusivity, however, has significant effects on efficiency, with the sensitivity coefficient around 1.7. Moreover, substrates with a lower thermal effusivity show better acoustic performances. For influences of ambient gases, the sensitivity coefficients of density ρg, thermal conductivity κg, and specific heat cp,g are 2.7, 0.98, and 0.8, respectively. Furthermore, large magnitudes of both ρg and κg lead to a higher efficiency and the sound pressure level generated by graphene films is approximately proportional to the inverse of cp,g. These findings can refer to the optimal design for graphene thermoacoustic speakers.

Convergence of the Light-Front Coupled-Cluster Method in Scalar Yukawa Theory

NASA Astrophysics Data System (ADS)

Usselman, Austin

We use Fock-state expansions and the Light-Front Coupled-Cluster (LFCC) method to study mass eigenvalue problems in quantum field theory. Specifically, we study convergence of the method in scalar Yukawa theory. In this theory, a single charged particle is surrounded by a cloud of neutral particles. The charged particle can create or annihilate neutral particles, causing the n-particle state to depend on the n + 1 and n - 1-particle state. Fock state expansion leads to an infinite set of coupled equations where truncation is required. The wave functions for the particle states are expanded in a basis of symmetric polynomials and a generalized eigenvalue problem is solved for the mass eigenvalue. The mass eigenvalue problem is solved for multiple values for the coupling strength while the number of particle states and polynomial basis order are increased. Convergence of the mass eigenvalue solutions is then obtained. Three mass ratios between the charged particle and neutral particles were studied. This includes a massive charged particle, equal masses and massive neutral particles. Relative probability between states can also be explored for more detailed understanding of the process of convergence with respect to the number of Fock sectors. The reliance on higher order particle states depended on how large the mass of the charge particle was. The higher the mass of the charged particle, the more the system depended on higher order particle states. The LFCC method solves this same mass eigenvalue problem using an exponential operator. This exponential operator can then be truncated instead to form a finite system of equations that can be solved using a built in system solver provided in most computational environments, such as MatLab and Mathematica. First approximation in the LFCC method allows for only one particle to be created by the new operator and proved to be not powerful enough to match the Fock state expansion. The second order approximation allowed one and two particles to be created by the new operator and converged to the Fock state expansion results. This showed the LFCC method to be a reliable replacement method for solving quantum field theory problems.

Electrical impedance tomography in anisotropic media with known eigenvectors

NASA Astrophysics Data System (ADS)

Abascal, Juan-Felipe P. J.; Lionheart, William R. B.; Arridge, Simon R.; Schweiger, Martin; Atkinson, David; Holder, David S.

2011-06-01

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, most implementations have neglected anisotropy even though human tissues like bone, muscle and brain white matter are markedly anisotropic. The recovery of an anisotropic conductivity tensor is uniquely determined by boundary measurements only up to a diffeomorphism that fixes the boundary. Nevertheless, uniqueness can be restored by providing information about the diffeomorphism. There are uniqueness results for two constraints: one eigenvalue and a multiple scalar of a general tensor. A useable constraint for medical applications is when the eigenvectors of the underlying tissue are known, which can be approximated from MRI or estimated from DT-MRI, although the eigenvalues are unknown. However there is no known theoretical result guaranteeing uniqueness for this constraint. In fact, only a few previous inversion studies have attempted to recover one or more eigenvalues assuming certain symmetries while ignoring nonuniqueness. In this work, the aim was to undertake a numerical study of the feasibility of the recovery of a piecewise linear finite element conductivity tensor in anisotropic media with known eigenvectors from the complete boundary data. The work suggests that uniqueness holds for this constraint, in addition to proposing a methodology for the incorporation of this prior for general conductivity tensors. This was carried out by performing an analysis of the Jacobian rank and by reconstructing four conductivity distributions: two diagonal tensors whose eigenvalues were linear and sinusoidal functions, and two general tensors whose eigenvectors resembled physiological tissue, one with eigenvectors spherically orientated like a spherical layered structure, and a sample of DT-MRI data of brain white matter. The Jacobian with respect to three eigenvalues was full-rank and it was possible to recover three eigenvalues for the four simulated distributions. This encourages further theoretical study of the uniqueness for this constraint and supports the use of this as a relevant usable method for medical applications.

How to Test the SME with Space Missions?

NASA Technical Reports Server (NTRS)

Hees, A.; Lamine, B.; Le Poncin-Lafitte, C.; Wolf, P.

2013-01-01

In this communication, we focus on possibilities to constrain SME coefficients using Cassini and Messenger data. We present simulations of radio science observables within the framework of the SME, identify the linear combinations of SME coefficients the observations depend on and determine the sensitivity of these measurements to the SME coefficients. We show that these datasets are very powerful for constraining SME coefficients.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

NASA Astrophysics Data System (ADS)

Bäcker, A.

Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

NASA Technical Reports Server (NTRS)

Balakumar, P.; Jeyasingham, Samarasingham

1999-01-01

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Uncovering the Internal Structure of the Indian Financial Market: Large Cross-correlation Behavior in the NSE

NASA Astrophysics Data System (ADS)

Sinha, Sitabhra; Pan, Raj Kumar

The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, C, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market, first by generating the minimum spanning tree from the unfiltered correlation matrix, and later, using an improved method of generating the graph after filtering out the market mode and random effects from the data. Both methods show, compared to developed markets, the relative absence of clusters of co-moving stocks that belong to the same business sector. This is consistent with the general belief that emerging markets tend to be more correlated than developed markets.

The Malay Version of the Perceived Stress Scale (PSS)-10 is a Reliable and Valid Measure for Stress among Nurses in Malaysia.

PubMed

Sandhu, Sukhvinder Singh; Ismail, Noor Hassim; Rampal, Krishna Gopal

2015-11-01

The Perceived Stress Scale-10 (PSS-10) is widely used to assess stress perception. The aim of this study was to translate the original PSS-10 into Malay and assess the reliability and validity of the Malay version among nurses. The Malay version of the PSS-10 was distributed among 229 nurses from four government hospitals in Selangor State. Test-retest reliability and concurrent validity was conducted with 25 nurses with the Malay version of the Depression Anxiety Stress Scales (DASS) 21. Cronbach's alpha, confirmatory factor analysis (CFA), intraclass correlation coefficient and Pearson's r correlation coefficient were used to determine the psychometric properties of the Malay PSS-10. Two factor components were yielded through exploratory factor analysis with eigenvalues of 3.37 and 2.10, respectively. Both of the factors accounted for 54.6% of the variance. CFA yielded a two-factor structure with satisfactory goodness-of-fit indices [x 2 /df = 2.43; comparative fit index (CFI) = 0.92, goodness-of-fit Index (GFI) = 0.94; standardised root mean square residual (SRMR) = 0.07 and root mean square error of approximation (RMSEA) = 0.08 (90% CI = 0.07-0.09)]. The Cronbach's alpha coefficient for the total items was 0.63 (0.82 for factor 1 and 0.72 for factor 2). The intraclass correlation coefficient (ICC) was 0.81 (95% CI: 0.62-0.91) for test-retest reliability testing after seven days. The total score and the negative component of the PSS-10 correlated significantly with the stress component of the DASS-21: (r = 0.61, P < 0.001) and (r = 0.56, P < 0.004), respectively. The Malay version of the PSS-10 demonstrated a satisfactory level of validity and reliability to assess stress perception. Therefore, this questionnaire is valid in assessing stress perception among nurses in Malaysia.

Evaluation of the reliability and validity for X16 balance testing scale for the elderly.

PubMed

Ju, Jingjuan; Jiang, Yu; Zhou, Peng; Li, Lin; Ye, Xiaolei; Wu, Hongmei; Shen, Bin; Zhang, Jialei; He, Xiaoding; Niu, Chunjin; Xia, Qinghua

2018-05-10

Balance performance is considered as an indicator of functional status in the elderly, a large scale population screening and evaluation in the community context followed by proper interventions would be of great significance at public health level. However, there has been no suitable balance testing scale available for large scale studies in the unique community context of urban China. A balance scale named X16 balance testing scale was developed, which was composed of 3 domains and 16 items. A total of 1985 functionally independent and active community-dwelling elderly adults' balance abilities were tested using the X16 scale. The internal consistency, split-half reliability, content validity, construct validity, discriminant validity of X16 balance testing scale were evaluated. Factor analysis was performed to identify alternative factor structure. The Eigenvalues of factors 1, 2, and 3 were 8.53, 1.79, and 1.21, respectively, and their cumulative contribution to the total variance reached 72.0%. These 3 factors mainly represented domains static balance, postural stability, and dynamic balance. The Cronbach alpha coefficient for the scale was 0.933. The Spearman correlation coefficients between items and its corresponding domains were ranged from 0.538 to 0.964. The correlation coefficients between each item and its corresponding domain were higher than the coefficients between this item and other domains. With the increase of age, the scores of balance performance, domains static balance, postural stability, and dynamic balance in the elderly declined gradually (P < 0.001). With the increase of age, the proportion of the elderly with intact balance performance decreased gradually (P < 0.001). The reliability and validity of the X16 balance testing scale is both adequate and acceptable. Due to its simple and quick use features, it is practical to be used repeatedly and routinely especially in community setting and on large scale screening.

Sum over Histories Representation for Kinetic Sensitivity Analysis: How Chemical Pathways Change When Reaction Rate Coefficients Are Varied

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, Shirong; Davis, Michael J.; Skodje, Rex T.

2015-11-12

The sensitivity of kinetic observables is analyzed using a newly developed sum over histories representation of chemical kinetics. In the sum over histories representation, the concentrations of the chemical species are decomposed into the sum of probabilities for chemical pathways that follow molecules from reactants to products or intermediates. Unlike static flux methods for reaction path analysis, the sum over histories approach includes the explicit time dependence of the pathway probabilities. Using the sum over histories representation, the sensitivity of an observable with respect to a kinetic parameter such as a rate coefficient is then analyzed in terms of howmore » that parameter affects the chemical pathway probabilities. The method is illustrated for species concentration target functions in H-2 combustion where the rate coefficients are allowed to vary over their associated uncertainty ranges. It is found that large sensitivities are often associated with rate limiting steps along important chemical pathways or by reactions that control the branching of reactive flux« less

Accuracy of analytic energy level formulas applied to hadronic spectroscopy of heavy mesons

NASA Technical Reports Server (NTRS)

Badavi, Forooz F.; Norbury, John W.; Wilson, John W.; Townsend, Lawrence W.

1988-01-01

Linear and harmonic potential models are used in the nonrelativistic Schroedinger equation to obtain article mass spectra for mesons as bound states of quarks. The main emphasis is on the linear potential where exact solutions of the S-state eigenvalues and eigenfunctions and the asymptotic solution for the higher order partial wave are obtained. A study of the accuracy of two analytical energy level formulas as applied to heavy mesons is also included. Cornwall's formula is found to be particularly accurate and useful as a predictor of heavy quarkonium states. Exact solution for all partial waves of eigenvalues and eigenfunctions for a harmonic potential is also obtained and compared with the calculated discrete spectra of the linear potential. Detailed derivations of the eigenvalues and eigenfunctions of the linear and harmonic potentials are presented in appendixes.

Hydrodynamics of the Polyakov line in SU(N c) Yang-Mills

DOE PAGES

Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail

2015-12-08

We discuss a hydrodynamical description of the eigenvalues of the Polyakov line at large but finite N c for Yang-Mills theory in even and odd space-time dimensions. The hydro-static solutions for the eigenvalue densities are shown to interpolate between a uniform distribution in the confined phase and a localized distribution in the de-confined phase. The resulting critical temperatures are in overall agreement with those measured on the lattice over a broad range of N c, and are consistent with the string model results at N c = ∞. The stochastic relaxation of the eigenvalues of the Polyakov line out ofmore » equilibrium is captured by a hydrodynamical instanton. An estimate of the probability of formation of a Z(N c)bubble using a piece-wise sound wave is suggested.« less

Coherence analysis of a class of weighted networks

NASA Astrophysics Data System (ADS)

Dai, Meifeng; He, Jiaojiao; Zong, Yue; Ju, Tingting; Sun, Yu; Su, Weiyi

2018-04-01

This paper investigates consensus dynamics in a dynamical system with additive stochastic disturbances that is characterized as network coherence by using the Laplacian spectrum. We introduce a class of weighted networks based on a complete graph and investigate the first- and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. First, the recursive relationship of its eigenvalues at two successive generations of Laplacian matrix is deduced. Then, we compute the sum and square sum of reciprocal of all nonzero Laplacian eigenvalues. The obtained results show that the scalings of first- and second-order coherence with network size obey four and five laws, respectively, along with the range of the weight factor. Finally, it indicates that the scalings of our studied networks are smaller than other studied networks when 1/√{d }

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach.

PubMed

Tarai, Madhumita; Kumar, Keshav; Divya, O; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

2017-09-05

The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix. Copyright © 2017 Elsevier B.V. All rights reserved.

Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently

NASA Technical Reports Server (NTRS)

Williams, F. W.; Kennedy, D.

1988-01-01

The analytical derivation, numerical implementation, and performance of a multiple-determinant parabolic interpolation method (MDPIM) for use in solving transcendental eigenvalue (critical buckling or undamped free vibration) problems in structural mechanics are presented. The overall bounding, eigenvalue-separation, qualified parabolic interpolation, accuracy-confirmation, and convergence-recovery stages of the MDPIM are described in detail, and the numbers of iterations required to solve sample plane-frame problems using the MDPIM are compared with those for a conventional bisection method and for the Newtonian method of Simpson (1984) in extensive tables. The MDPIM is shown to use 31 percent less computation time than bisection when accuracy of 0.0001 is required, but 62 percent less when accuracy of 10 to the -8th is required; the time savings over the Newtonian method are about 10 percent.

Calibration of gyro G-sensitivity coefficients with FOG monitoring on precision centrifuge

NASA Astrophysics Data System (ADS)

Lu, Jiazhen; Yang, Yanqiang; Li, Baoguo; Liu, Ming

2017-07-01

The advantages of mechanical gyros, such as high precision, endurance and reliability, make them widely used as the core parts of inertial navigation systems (INS) utilized in the fields of aeronautics, astronautics and underground exploration. In a high-g environment, the accuracy of gyros is degraded. Therefore, the calibration and compensation of the gyro G-sensitivity coefficients is essential when the INS operates in a high-g environment. A precision centrifuge with a counter-rotating platform is the typical equipment for calibrating the gyro, as it can generate large centripetal acceleration and keep the angular rate close to zero; however, its performance is seriously restricted by the angular perturbation in the high-speed rotating process. To reduce the dependence on the precision of the centrifuge and counter-rotating platform, an effective calibration method for the gyro g-sensitivity coefficients under fiber-optic gyroscope (FOG) monitoring is proposed herein. The FOG can efficiently compensate spindle error and improve the anti-interference ability. Harmonic analysis is performed for data processing. Simulations show that the gyro G-sensitivity coefficients can be efficiently estimated to up to 99% of the true value and compensated using a lookup table or fitting method. Repeated tests indicate that the G-sensitivity coefficients can be correctly calibrated when the angular rate accuracy of the precision centrifuge is as low as 0.01%. Verification tests are performed to demonstrate that the attitude errors can be decreased from 0.36° to 0.08° in 200 s. The proposed measuring technology is generally applicable in engineering, as it can reduce the accuracy requirements for the centrifuge and the environment.

Cause and cure of sloppiness in ordinary differential equation models.

PubMed

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Investigation of the flight mechanics simulation of a hovering helicopter

NASA Technical Reports Server (NTRS)

Chaimovich, M.; Rosen, A.; Rand, O.; Mansur, M. H.; Tischler, M. B.

1992-01-01

The flight mechanics simulation of a hovering helicopter is investigated by comparing the results of two different numerical models with flight test data for a hovering AH-64 Apache. The two models are the U.S. Army BEMAP and the Technion model. These nonlinear models are linearized by applying a numerical linearization procedure. The results of the linear models are compared with identification results in terms of eigenvalues, stability and control derivatives, and frequency responses. Detailed time histories of the responses of the complete nonlinear models, as a result of various pilots' inputs, are compared with flight test results. In addition the sensitivity of the models to various effects are also investigated. The results are discussed and problematic aspects of the simulation are identified.

Cause and cure of sloppiness in ordinary differential equation models

NASA Astrophysics Data System (ADS)

Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

2014-08-01

Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

Underlying construct of empathy, optimism, and burnout in medical students

PubMed Central

Vergare, Michael; Isenberg, Gerald; Cohen, Mitchell; Spandorfer, John

2015-01-01

Objectives This study was designed to explore the underlying construct of measures of empathy, optimism, and burnout in medical students. Methods Three instruments for measuring empathy (Jefferson Scale of Empathy, JSE); Optimism (the Life Orientation Test-Revised, LOT-R); and burnout (the Maslach Burnout Inventory, MBI, which includes three scales of Emotional Exhaustion, Depersonalization, and Personal Accomplishment) were administered to 265 third-year students at Sidney Kimmel (formerly Jefferson) Medical College at Thomas Jefferson University. Data were subjected to factor analysis to examine relationships among measures of empathy, optimism, and burnout in a multivariate statistical model.  Results Factor analysis (principal component with oblique rotation) resulted in two underlying constructs, each with an eigenvalue greater than one. The first factor involved “positive personality attributes” (factor coefficients greater than .58 for measures of empathy, optimism, and personal accomplishment). The second factor involved “negative personality attributes” (factor coefficients greater than .78 for measures of emotional exhaustion, and depersonalization). Conclusions Results confirmed that an  association exists between empathy in the context of patient care and personality characteristics that are conducive to relationship building, and considered to be  “positive personality attributes,” as opposed to personality characteristics that are considered as “negative personality attributes” that are detrimental to interpersonal relationships. Implications for the professional development of physicians-in-training and in-practice are discussed. PMID:25633650

A Quantitative Structure-Property Relationship (QSPR) Study of Aliphatic Alcohols by the Method of Dividing the Molecular Structure into Substructure

PubMed Central

Liu, Fengping; Cao, Chenzhong; Cheng, Bin

2011-01-01

A quantitative structure–property relationship (QSPR) analysis of aliphatic alcohols is presented. Four physicochemical properties were studied: boiling point (BP), n-octanol–water partition coefficient (lg POW), water solubility (lg W) and the chromatographic retention indices (RI) on different polar stationary phases. In order to investigate the quantitative structure–property relationship of aliphatic alcohols, the molecular structure ROH is divided into two parts, R and OH to generate structural parameter. It was proposed that the property is affected by three main factors for aliphatic alcohols, alkyl group R, substituted group OH, and interaction between R and OH. On the basis of the polarizability effect index (PEI), previously developed by Cao, the novel molecular polarizability effect index (MPEI) combined with odd-even index (OEI), the sum eigenvalues of bond-connecting matrix (SX1CH) previously developed in our team, were used to predict the property of aliphatic alcohols. The sets of molecular descriptors were derived directly from the structure of the compounds based on graph theory. QSPR models were generated using only calculated descriptors and multiple linear regression techniques. These QSPR models showed high values of multiple correlation coefficient (R > 0.99) and Fisher-ratio statistics. The leave-one-out cross-validation demonstrated the final models to be statistically significant and reliable. PMID:21731451

Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder

NASA Astrophysics Data System (ADS)

Wang, Rong; Wang, Li; Yang, Yong; Li, Jiajia; Wu, Ying; Lin, Pan

2016-11-01

Attention deficit hyperactivity disorder (ADHD) is the most common childhood neuropsychiatric disorder and affects approximately 6 -7 % of children worldwide. Here, we investigate the statistical properties of undirected and directed brain functional networks in ADHD patients based on random matrix theory (RMT), in which the undirected functional connectivity is constructed based on correlation coefficient and the directed functional connectivity is measured based on cross-correlation coefficient and mutual information. We first analyze the functional connectivity and the eigenvalues of the brain functional network. We find that ADHD patients have increased undirected functional connectivity, reflecting a higher degree of linear dependence between regions, and increased directed functional connectivity, indicating stronger causality and more transmission of information among brain regions. More importantly, we explore the randomness of the undirected and directed functional networks using RMT. We find that for ADHD patients, the undirected functional network is more orderly than that for normal subjects, which indicates an abnormal increase in undirected functional connectivity. In addition, we find that the directed functional networks are more random, which reveals greater disorder in causality and more chaotic information flow among brain regions in ADHD patients. Our results not only further confirm the efficacy of RMT in characterizing the intrinsic properties of brain functional networks but also provide insights into the possibilities RMT offers for improving clinical diagnoses and treatment evaluations for ADHD patients.

Control of large flexible systems via eigenvalue relocation

NASA Technical Reports Server (NTRS)

Denman, E. D.; Jeon, G. J.

1985-01-01

For the vibration control of large flexible systems, a control scheme by which the eigenvalues of the closed-loop systems are assigned to predetermined locations within the feasible region through velocity-only feedback is presented. Owing to the properties of second-order lambda-matrices and an efficient model decoupling technique, the control scheme makes it possible that selected modes are damped with the rest of the modes unchanged.

Visibility of quantum graph spectrum from the vertices

NASA Astrophysics Data System (ADS)

Kühn, Christian; Rohleder, Jonathan

2018-03-01

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh-Weyl function.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Gauge equivalence of the Gross Pitaevskii equation and the equivalent Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Radha, R.; Kumar, V. Ramesh

2007-11-01

In this paper, we construct an equivalent spin chain for the Gross-Pitaevskii equation with quadratic potential and exponentially varying scattering lengths using gauge equivalence. We have then generated the soliton solutions for the spin components S3 and S-. We find that the spin solitons for S3 and S- can be compressed for exponentially growing eigenvalues while they broaden out for decaying eigenvalues.

On functional determinants of matrix differential operators with multiple zero modes

NASA Astrophysics Data System (ADS)

Falco, G. M.; Fedorenko, Andrei A.; Gruzberg, Ilya A.

2017-12-01

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of r× r matrix second order differential operators O with 0 < n ≤slant 2r linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r-n or 2r-n (depending on the boundary conditions) solutions of the homogeneous equation O h=0 , in the spirit of Gel’fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

PubMed

Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

2015-12-01

Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlou, A. T.; Betzler, B. R.; Burke, T. P.

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3)more » a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)« less

Topics in Bethe Ansatz

NASA Astrophysics Data System (ADS)

Wang, Chunguang

Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains corresponding. to two choices of integrable boundary conditions have the symmetries Uq(Bn) and. Uq(Cn), respectively. The deformation of Cn is novel, with a nonstandard coproduct. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of. each type. With the help of this formula, we verify numerically (for a generic value of. the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

Random matrix approach to the dynamics of stock inventory variations

NASA Astrophysics Data System (ADS)

Zhou, Wei-Xing; Mu, Guo-Hua; Kertész, János

2012-09-01

It is well accepted that investors can be classified into groups owing to distinct trading strategies, which forms the basic assumption of many agent-based models for financial markets when agents are not zero-intelligent. However, empirical tests of these assumptions are still very rare due to the lack of order flow data. Here we adopt the order flow data of Chinese stocks to tackle this problem by investigating the dynamics of inventory variations for individual and institutional investors that contain rich information about the trading behavior of investors and have a crucial influence on price fluctuations. We find that the distributions of cross-correlation coefficient Cij have power-law forms in the bulk that are followed by exponential tails, and there are more positive coefficients than negative ones. In addition, it is more likely that two individuals or two institutions have a stronger inventory variation correlation than one individual and one institution. We find that the largest and the second largest eigenvalues (λ1 and λ2) of the correlation matrix cannot be explained by random matrix theory and the projections of investors' inventory variations on the first eigenvector u(λ1) are linearly correlated with stock returns, where individual investors play a dominating role. The investors are classified into three categories based on the cross-correlation coefficients CV R between inventory variations and stock returns. A strong Granger causality is unveiled from stock returns to inventory variations, which means that a large proportion of individuals hold the reversing trading strategy and a small part of individuals hold the trending strategy. Our empirical findings have scientific significance in the understanding of investors' trading behavior and in the construction of agent-based models for emerging stock markets.

Towards the reanalysis of void coefficients measurements at proteus for high conversion light water reactor lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hursin, M.; Koeberl, O.; Perret, G.

2012-07-01

High Conversion Light Water Reactors (HCLWR) allows a better usage of fuel resources thanks to a higher breeding ratio than standard LWR. Their uses together with the current fleet of LWR constitute a fuel cycle thoroughly studied in Japan and the US today. However, one of the issues related to HCLWR is their void reactivity coefficient (VRC), which can be positive. Accurate predictions of void reactivity coefficient in HCLWR conditions and their comparisons with representative experiments are therefore required. In this paper an inter comparison of modern codes and cross-section libraries is performed for a former Benchmark on Void Reactivitymore » Effect in PWRs conducted by the OECD/NEA. It shows an overview of the k-inf values and their associated VRC obtained for infinite lattice calculations with UO{sub 2} and highly enriched MOX fuel cells. The codes MCNPX2.5, TRIPOLI4.4 and CASMO-5 in conjunction with the libraries ENDF/B-VI.8, -VII.0, JEF-2.2 and JEFF-3.1 are used. A non-negligible spread of results for voided conditions is found for the high content MOX fuel. The spread of eigenvalues for the moderated and voided UO{sub 2} fuel are about 200 pcm and 700 pcm, respectively. The standard deviation for the VRCs for the UO{sub 2} fuel is about 0.7% while the one for the MOX fuel is about 13%. This work shows that an appropriate treatment of the unresolved resonance energy range is an important issue for the accurate determination of the void reactivity effect for HCLWR. A comparison to experimental results is needed to resolve the presented discrepancies. (authors)« less

Application of design sensitivity analysis for greater improvement on machine structural dynamics

NASA Technical Reports Server (NTRS)

Yoshimura, Masataka

1987-01-01

Methodologies are presented for greatly improving machine structural dynamics by using design sensitivity analyses and evaluative parameters. First, design sensitivity coefficients and evaluative parameters of structural dynamics are described. Next, the relations between the design sensitivity coefficients and the evaluative parameters are clarified. Then, design improvement procedures of structural dynamics are proposed for the following three cases: (1) addition of elastic structural members, (2) addition of mass elements, and (3) substantial charges of joint design variables. Cases (1) and (2) correspond to the changes of the initial framework or configuration, and (3) corresponds to the alteration of poor initial design variables. Finally, numerical examples are given for demonstrating the availability of the methods proposed.

Kirchhoff index of linear hexagonal chains

NASA Astrophysics Data System (ADS)

Yang, Yujun; Zhang, Heping

The resistance distance rij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain Ln consists of the Laplacian spectrum of path P2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed-form formula for Kirchhoff index of Ln is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of Ln is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including Ln.0

Semiblind channel estimation for MIMO-OFDM systems

NASA Astrophysics Data System (ADS)

Chen, Yi-Sheng; Song, Jyu-Han

2012-12-01

This article proposes a semiblind channel estimation method for multiple-input multiple-output orthogonal frequency-division multiplexing systems based on circular precoding. Relying on the precoding scheme at the transmitters, the autocorrelation matrix of the received data induces a structure relating the outer product of the channel frequency response matrix and precoding coefficients. This structure makes it possible to extract information about channel product matrices, which can be used to form a Hermitian matrix whose positive eigenvalues and corresponding eigenvectors yield the channel impulse response matrix. This article also tests the resistance of the precoding design to finite-sample estimation errors, and explores the effects of the precoding scheme on channel equalization by performing pairwise error probability analysis. The proposed method is immune to channel zero locations, and is reasonably robust to channel order overestimation. The proposed method is applicable to the scenarios in which the number of transmitters exceeds that of the receivers. Simulation results demonstrate the performance of the proposed method and compare it with some existing methods.

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

PubMed

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Turbulence Model Sensitivity and Scour Gap Effect of Unsteady Flow around Pipe: A CFD Study

PubMed Central

Ali, Abbod; Sharma, R. K.; Ganesan, P.

2014-01-01

A numerical investigation of incompressible and transient flow around circular pipe has been carried out at different five gap phases. Flow equations such as Navier-Stokes and continuity equations have been solved using finite volume method. Unsteady horizontal velocity and kinetic energy square root profiles are plotted using different turbulence models and their sensitivity is checked against published experimental results. Flow parameters such as horizontal velocity under pipe, pressure coefficient, wall shear stress, drag coefficient, and lift coefficient are studied and presented graphically to investigate the flow behavior around an immovable pipe and scoured bed. PMID:25136666

Experimental study on the sensitive depth of backwards detected light in turbid media.

PubMed

Zhang, Yunyao; Huang, Liqing; Zhang, Ning; Tian, Heng; Zhu, Jingping

2018-05-28

In the recent past, optical spectroscopy and imaging methods for biomedical diagnosis and target enhancing have been widely researched. The challenge to improve the performance of these methods is to know the sensitive depth of the backwards detected light well. Former research mainly employed a Monte Carlo method to run simulations to statistically describe the light sensitive depth. An experimental method for investigating the sensitive depth was developed and is presented here. An absorption plate was employed to remove all the light that may have travelled deeper than the plate, leaving only the light which cannot reach the plate. By measuring the received backwards light intensity and the depth between the probe and the plate, the light intensity distribution along the depth dimension can be achieved. The depth with the maximum light intensity was recorded as the sensitive depth. The experimental results showed that the maximum light intensity was nearly the same in a short depth range. It could be deduced that the sensitive depth was a range, rather than a single depth. This sensitive depth range as well as its central depth increased consistently with the increasing source-detection distance. Relationships between sensitive depth and optical properties were also investigated. It also showed that the reduced scattering coefficient affects the central sensitive depth and the range of the sensitive depth more than the absorption coefficient, so they cannot be simply added as reduced distinct coefficients to describe the sensitive depth. This study provides an efficient method for investigation of sensitive depth. It may facilitate the development of spectroscopy and imaging techniques for biomedical diagnosis and underwater imaging.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Sensitivity analysis of water consumption in an office building

NASA Astrophysics Data System (ADS)

Suchacek, Tomas; Tuhovcak, Ladislav; Rucka, Jan

2018-02-01

This article deals with sensitivity analysis of real water consumption in an office building. During a long-term real study, reducing of pressure in its water connection was simulated. A sensitivity analysis of uneven water demand was conducted during working time at various provided pressures and at various time step duration. Correlations between maximal coefficients of water demand variation during working time and provided pressure were suggested. The influence of provided pressure in the water connection on mean coefficients of water demand variation was pointed out, altogether for working hours of all days and separately for days with identical working hours.

On Distributed Strategies in Defense of a High Value Unit (HVU) Against a Swarm Attack

DTIC Science & Technology

2012-09-01

function [ lam ,U] = tqr(a,b,U) % [ lam u] = tqr(a,b) or [ lam U] = tqr(a,b,U... lam u] = tqr(a,b): % % The column lam contains the eigenvalues of the Hermitian tridiagonal % matrix T = mxt(a,b) computed by one version of the...computed. The computed eigenvalues are real and are sorted to be % nonincreasing. % % [ lam U] = tqr(a,b,U): % % This replaces the input U

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

NASA Technical Reports Server (NTRS)

Ito, K.

1984-01-01

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.