Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

OpenAIRE

García Planas, María Isabel; Tarragona Romero, Sonia

2014-01-01

The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family

Covariance expressions for eigenvalue and eigenvector problems

Science.gov (United States)

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.

Hessian eigenvalue distribution in a random Gaussian landscape

Science.gov (United States)

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.

Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2005-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

On the decision threshold of eigenvalue ratio detector based on moments of joint and marginal distributions of extreme eigenvalues

KAUST Repository

Shakir, Muhammad Zeeshan

2013-03-01

Eigenvalue Ratio (ER) detector based on the two extreme eigenvalues of the received signal covariance matrix is currently one of the most effective solution for spectrum sensing. However, the analytical results of such scheme often depend on asymptotic assumptions since the distribution of the ratio of two extreme eigenvalues is exceptionally complex to compute. In this paper, a non-asymptotic spectrum sensing approach for ER detector is introduced to approximate the marginal and joint distributions of the two extreme eigenvalues. The two extreme eigenvalues are considered as dependent Gaussian random variables such that their joint probability density function (PDF) is approximated by a bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. The PDF approximation approach is based on the moment matching method where we calculate the exact analytical moments of joint and marginal distributions of the two extreme eigenvalues. The decision threshold is calculated by exploiting the statistical mean and the variance of each of the two extreme eigenvalues and the correlation coefficient between them. The performance analysis of our newly proposed approximation approach is compared with the already published asymptotic Tracy-Widom approximation approach. It has been shown that our results are in perfect agreement with the simulation results for any number of secondary users and received samples. © 2002-2012 IEEE.

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

Science.gov (United States)

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 study of a chaotic resonator

Energy Technology Data Exchange (ETDEWEB)

Banova, Todorka [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany); Technische Universitaet Darmstadt, Graduate School of Computational Engineering, Dolivostrasse 15, D-64293 Darmstadt (Germany); Ackermann, Wolfgang; Weiland, Thomas [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)

2013-07-01

The field of quantum chaos comprises the study of the manifestations of classical chaos in the properties of the corresponding quantum systems. Within this work, we compute the eigenfrequencies that are needed for the level spacing analysis of a microwave resonator with chaotic characteristics. The major challenges posed by our work are: first, the ability of the approaches to tackle the large scale eigenvalue problem and second, the capability to extract many, i.e. order of thousands, eigenfrequencies for the considered cavity. The first proposed approach for an accurate eigenfrequency extraction takes into consideration the evaluated electric field computations in time domain of a superconducting cavity and by means of signal-processing techniques extracts the eigenfrequencies. The second approach is based on the finite element method with curvilinear elements, which transforms the continuous eigenvalue problem to a discrete generalized eigenvalue problem. Afterwards, the Lanczos algorithm is used for the solution of the generalized eigenvalue problem. In the poster, a summary of the applied algorithms, as well as, critical implementation details together with the simulation results are provided.

Cessna Citation X Business Aircraft Eigenvalue Stability – Part2: Flight Envelope Analysis

Directory of Open Access Journals (Sweden)

Yamina BOUGHARI

2017-12-01

Full Text Available Civil aircraft flight control clearance is a time consuming, thus an expensive process in the aerospace industry. This process has to be investigated and proved to be safe for thousands of combinations in terms of speeds, altitudes, gross weights, Xcg / weight configurations and angles of attack. Even in this case, a worst-case condition that could lead to a critical situation might be missed. To address this problem, models that are able to describe an aircraft’s dynamics by taking into account all uncertainties over a region within a flight envelope have been developed using Linear Fractional Representation. In order to investigate the Cessna Citation X aircraft Eigenvalue Stability envelope, the Linear Fractional Representation models are implemented using the speeds and the altitudes as varying parameters. In this paper Part 2, the aircraft longitudinal eigenvalue stability is analyzed in a continuous range of flight envelope with varying parameter of True airspeed and altitude, instead of a single point, like classical methods. This is known as the aeroelastic stability envelope, required for civil aircraft certification as given by the Circular Advisory “Aeroelastic Stability Substantiation of Transport Category Airplanes AC No: 25.629-18”. In this new methodology the analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms by using the linear matrix inequalities to evaluate the eigenvalue stability, which is reduced to search for the negative eigenvalues in a region of flight envelope. It can also be used to study the stability of a system during an arbitrary motion from one point to another in the flight envelope. A whole aircraft analysis results’ for its entire envelope are presented in the form of graphs, thus offering good readability, and making them easily exploitable.

Analysis of eigenvalue correction applied to biometrics

NARCIS (Netherlands)

Hendrikse, A.J.; Veldhuis, Raymond N.J.; Spreeuwers, Lieuwe Jan; Bazen, A.M.

Eigenvalue estimation plays an important role in biometrics. However, if the number of samples is limited, estimates are significantly biased. In this article we analyse the influence of this bias on the error rates of PCA/LDA based verification systems, using both synthetic data with realistic

A method of the sensitivity analysis of build-up and decay of actinides

International Nuclear Information System (INIS)

Mitani, Hiroshi; Koyama, Kinji; Kuroi, Hideo

1977-07-01

To make sensitivity analysis of build-up and decay of actinides, mathematical methods related to this problem have been investigated in detail. Application of time-dependent perturbation technique and Bateman method to sensitivity analysis is mainly studied. For the purpose, a basic equation and its adjoint equation for build-up and decay of actinides are systematically solved by introducing Laplace and modified Laplace transforms and their convolution theorems. Then, the mathematical method of sensitivity analyses is formulated by the above technique; its physical significance is also discussed. Finally, application of eigenvalue-method is investigated. Sensitivity coefficients can be directly calculated by this method. (auth.)

Sensitivity Analysis of Criticality for Different Nuclear Fuel Shapes

Energy Technology Data Exchange (ETDEWEB)

Kang, Hyun Sik; Jang, Misuk; Kim, Seoung Rae [NESS, Daejeon (Korea, Republic of)

2016-10-15

Rod-type nuclear fuel was mainly developed in the past, but recent study has been extended to plate-type nuclear fuel. Therefore, this paper reviews the sensitivity of criticality according to different shapes of nuclear fuel types. Criticality analysis was performed using MCNP5. MCNP5 is well-known Monte Carlo codes for criticality analysis and a general-purpose Monte Carlo N-Particle code that can be used for neutron, photon, electron or coupled neutron / photon / electron transport, including the capability to calculate eigenvalues for critical systems. We performed the sensitivity analysis of criticality for different fuel shapes. In sensitivity analysis for simple fuel shapes, the criticality is proportional to the surface area. But for fuel Assembly types, it is not proportional to the surface area. In sensitivity analysis for intervals between plates, the criticality is greater as the interval increases, but if the interval is greater than 8mm, it showed an opposite trend that the criticality decrease by a larger interval. As a result, it has failed to obtain the logical content to be described in common for all cases. The sensitivity analysis of Criticality would be always required whenever subject to be analyzed is changed.

Sensitivity Analysis of Criticality for Different Nuclear Fuel Shapes

International Nuclear Information System (INIS)

Kang, Hyun Sik; Jang, Misuk; Kim, Seoung Rae

2016-01-01

Rod-type nuclear fuel was mainly developed in the past, but recent study has been extended to plate-type nuclear fuel. Therefore, this paper reviews the sensitivity of criticality according to different shapes of nuclear fuel types. Criticality analysis was performed using MCNP5. MCNP5 is well-known Monte Carlo codes for criticality analysis and a general-purpose Monte Carlo N-Particle code that can be used for neutron, photon, electron or coupled neutron / photon / electron transport, including the capability to calculate eigenvalues for critical systems. We performed the sensitivity analysis of criticality for different fuel shapes. In sensitivity analysis for simple fuel shapes, the criticality is proportional to the surface area. But for fuel Assembly types, it is not proportional to the surface area. In sensitivity analysis for intervals between plates, the criticality is greater as the interval increases, but if the interval is greater than 8mm, it showed an opposite trend that the criticality decrease by a larger interval. As a result, it has failed to obtain the logical content to be described in common for all cases. The sensitivity analysis of Criticality would be always required whenever subject to be analyzed is changed

Highly indefinite multigrid for eigenvalue problems

Energy Technology Data Exchange (ETDEWEB)

Borges, L.; Oliveira, S.

1996-12-31

Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

Sensitivity analysis for reactivity and power density investigations in nuclear reactors

International Nuclear Information System (INIS)

Naguib, K.; Morcos, H.N.; Sallam, O.H.; Abdelsamei, SH.

1993-01-01

Sensitivity analysis theory based on the variational functional approaches was applied to evaluate sensitivities of eigenvalues and power densities due to variation of the absorber concentration in the reactor core. The practical usefulness of this method is illustrated by considering test cases. The result indicates that this method is as accurate as those obtained from direct calculations, yet it provides an economical means in saving computational time since it requires fewer calculations. The SARC-1/2 code have been written in Fortran-77 to solve this problem.3 tab. 1 fig

Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues

KAUST Repository

Shakir, Muhammad

2011-12-01

In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. The largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results. © 2011 IEEE.

The Application of Vector Fitting to Eigenvalue-based Harmonic Stability Analysis

DEFF Research Database (Denmark)

Dowlatabadi, Mohammadkazem Bakhshizadeh; Yoon, Changwoo; Hjerrild, Jesper

2017-01-01

Participation factor analysis is an interesting feature of the eigenvalue-based stability analysis in a power system, which enables the developers to identify the problematic elements in a multi-vendor project like in an offshore wind power plant. However, this method needs a full state space model...... of the elements that is not always possible to have in a competitive world due to confidentiality. In this paper, by using an identification method, the state space models for power converters are extracted from the provided data by the suppliers. Some uncertainties in the identification process are also...

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Science.gov (United States)

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.

Colpitts, Eigenvalues and Chaos

DEFF Research Database (Denmark)

Lindberg, Erik

1997-01-01

It is possible to obtain insight in the chaotic nature of a nonlinear oscillator by means of a study of the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator. The movements of the eigenvalues as functions of time are found. The instantaneous power in t...

Preconditioned Krylov subspace methods for eigenvalue problems

Energy Technology Data Exchange (ETDEWEB)

Wu, Kesheng; Saad, Y.; Stathopoulos, A. [Univ. of Minnesota, Minneapolis, MN (United States)

1996-12-31

Lanczos algorithm is a commonly used method for finding a few extreme eigenvalues of symmetric matrices. It is effective if the wanted eigenvalues have large relative separations. If separations are small, several alternatives are often used, including the shift-invert Lanczos method, the preconditioned Lanczos method, and Davidson method. The shift-invert Lanczos method requires direct factorization of the matrix, which is often impractical if the matrix is large. In these cases preconditioned schemes are preferred. Many applications require solution of hundreds or thousands of eigenvalues of large sparse matrices, which pose serious challenges for both iterative eigenvalue solver and preconditioner. In this paper we will explore several preconditioned eigenvalue solvers and identify the ones suited for finding large number of eigenvalues. Methods discussed in this paper make up the core of a preconditioned eigenvalue toolkit under construction.

Sensitivity analysis of reactive ecological dynamics.

Science.gov (United States)

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.

Sturm--Liouville eigenvalue problem

International Nuclear Information System (INIS)

Bailey, P.B.

1977-01-01

The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular

Joint density of eigenvalues in spiked multivariate models.

Science.gov (United States)

Dharmawansa, Prathapasinghe; Johnstone, Iain M

2014-01-01

The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative hypotheses which are a low rank departure from the null hypothesis. For rank one alternatives, this note provides a representation for the joint eigenvalue density in terms of a single contour integral. This will be of use for deriving approximate distributions for likelihood ratios and 'linear' statistics used in testing.

Interior transmission eigenvalues of a rectangle

International Nuclear Information System (INIS)

Sleeman, B D; Stocks, D C

2016-01-01

The problem of scattering of acoustic waves by an inhomogeneous medium is intimately connected with so called inside–outside duality, in which the interior transmission eigenvalue problem plays a fundamental role. Here a study of the interior transmission eigenvalues for rectangular domains of constant refractive index is made. By making a nonstandard use of the classical separation of variables technique both real and complex eigenvalues are determined. (paper)

Preconditioned iterations to calculate extreme eigenvalues

Energy Technology Data Exchange (ETDEWEB)

Brand, C.W.; Petrova, S. [Institut fuer Angewandte Mathematik, Leoben (Austria)

1994-12-31

Common iterative algorithms to calculate a few extreme eigenvalues of a large, sparse matrix are Lanczos methods or power iterations. They converge at a rate proportional to the separation of the extreme eigenvalues from the rest of the spectrum. Appropriate preconditioning improves the separation of the eigenvalues. Davidson`s method and its generalizations exploit this fact. The authors examine a preconditioned iteration that resembles a truncated version of Davidson`s method with a different preconditioning strategy.

Evaluation of Eigenvalue Routines for Large Scale Applications

Directory of Open Access Journals (Sweden)

V.A. Tischler

1994-01-01

Full Text Available 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 article is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the block Lanczos aLgorithm. This eigenvalue routine is now availabLe in several mathematics libraries as well as in severaL commerciaL versions of NASTRAN. In addition, the eRA Y library 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, particularly for very large problems.

A numerical method to compute interior transmission eigenvalues

International Nuclear Information System (INIS)

Kleefeld, Andreas

2013-01-01

In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)

Eigenvalue distributions of Wilson loops

International Nuclear Information System (INIS)

Lohmayer, Robert

2010-01-01

In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the modulus square of the characteristic polynomial. Furthermore

The eigenvalue problem for a singular quasilinear elliptic equation

Directory of Open Access Journals (Sweden)

Benjin Xuan

2004-02-01

Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.

Perturbation Theory of Embedded Eigenvalues

DEFF Research Database (Denmark)

Engelmann, Matthias

project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...

SCALE Sensitivity Calculations Using Contributon Theory

International Nuclear Information System (INIS)

Rearden, Bradley T.; Perfetti, Chris; Williams, Mark L.; Petrie, Lester M. Jr.

2010-01-01

The SCALE TSUNAMI-3D sensitivity and uncertainty analysis sequence computes the sensitivity of k-eff to each constituent multigroup cross section using adjoint techniques with the KENO Monte Carlo codes. A new technique to simultaneously obtain the product of the forward and adjoint angular flux moments within a single Monte Carlo calculation has been developed and implemented in the SCALE TSUNAMI-3D analysis sequence. A new concept in Monte Carlo theory has been developed for this work, an eigenvalue contributon estimator, which is an extension of previously developed fixed-source contributon estimators. A contributon is a particle for which the forward solution is accumulated, and its importance to the response, which is equivalent to the adjoint solution, is simultaneously accumulated. Thus, the contributon is a particle coupled with its contribution to the response, in this case k-eff. As implemented in SCALE, the contributon provides the importance of a particle exiting at any energy or direction for each location, energy and direction at which the forward flux solution is sampled. Although currently implemented for eigenvalue calculations in multigroup mode in KENO, this technique is directly applicable to continuous-energy calculations for many other responses such as fixed-source sensitivity analysis and quantification of reactor kinetics parameters. This paper provides the physical bases of eigenvalue contributon theory, provides details of implementation into TSUNAMI-3D, and provides results of sample calculations.

Computation of standard deviations in eigenvalue calculations

International Nuclear Information System (INIS)

Gelbard, E.M.; Prael, R.

1990-01-01

In Brissenden and Garlick (1985), the authors propose a modified Monte Carlo method for eigenvalue calculations, designed to decrease particle transport biases in the flux and eigenvalue estimates, and in corresponding estimates of standard deviations. Apparently a very similar method has been used by Soviet Monte Carlo specialists. The proposed method is based on the generation of ''superhistories'', chains of histories run in sequence without intervening renormalization of the fission source. This method appears to have some disadvantages, discussed elsewhere. Earlier numerical experiments suggest that biases in fluxes and eigenvalues are negligibly small, even for very small numbers of histories per generation. Now more recent experiments, run on the CRAY-XMP, tend to confirm these earlier conclusions. The new experiments, discussed in this paper, involve the solution of one-group 1D diffusion theory eigenvalue problems, in difference form, via Monte Carlo. Experiments covered a range of dominance ratios from ∼0.75 to ∼0.985. In all cases flux and eigenvalue biases were substantially smaller than one standard deviation. The conclusion that, in practice, the eigenvalue bias is negligible has strong theoretical support. (author)

An algebraic substructuring using multiple shifts for eigenvalue computations

International Nuclear Information System (INIS)

Ko, Jin Hwan; Jung, Sung Nam; Byun, Do Young; Bai, Zhaojun

2008-01-01

Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large-sized problems, but originally it was designed to calculate only the smallest eigenvalues. Recently, an updated version of AS has been introduced to calculate the interior eigenvalues over a specified range by using a shift concept that is referred to as the shifted AS. In this work, we propose a combined method of both AS and the shifted AS by using multiple shifts for solving a considerable number of eigensolutions in a large-sized problem, which is an emerging computational issue of noise or vibration analysis in vehicle design. In addition, we investigated the accuracy of the shifted AS by presenting an error criterion. The proposed method has been applied to the FE model of an automobile body. The combined method yielded a higher efficiency without loss of accuracy in comparison to the original AS

The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

The method of fundamental solutions for computing acoustic interior transmission eigenvalues

Science.gov (United States)

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.

Eigenvalue distributions of Wilson loops

Energy Technology Data Exchange (ETDEWEB)

Lohmayer, Robert

2010-07-01

In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the

Generalized eigenvalue based spectrum sensing

KAUST Repository

Shakir, Muhammad

2012-01-01

Spectrum sensing is one of the fundamental components in cognitive radio networks. In this chapter, a generalized spectrum sensing framework which is referred to as Generalized Mean Detector (GMD) has been introduced. In this context, we generalize the detectors based on the eigenvalues of the received signal covariance matrix and transform the eigenvalue based spectrum sensing detectors namely: (i) the Eigenvalue Ratio Detector (ERD) and two newly proposed detectors which are referred to as (ii) the GEometric Mean Detector (GEMD) and (iii) the ARithmetic Mean Detector (ARMD) into an unified framework of generalize spectrum sensing. The foundation of the proposed framework is based on the calculation of exact analytical moments of the random variables of the decision threshold of the respective detectors. The decision threshold has been calculated in a closed form which is based on the approximation of Cumulative Distribution Functions (CDFs) of the respective test statistics. In this context, we exchange the analytical moments of the two random variables of the respective test statistics with the moments of the Gaussian (or Gamma) distribution function. The performance of the eigenvalue based detectors is compared with the several traditional detectors including the energy detector (ED) to validate the importance of the eigenvalue based detectors and the performance of the GEMD and the ARMD particularly in realistic wireless cognitive radio network. Analytical and simulation results show that the newly proposed detectors yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, the presented results based on proposed approximation approaches are in perfect agreement with the empirical results. © 2012 Springer Science+Business Media Dordrecht.

Parallel Symmetric Eigenvalue Problem Solvers

Science.gov (United States)

2015-05-01

Research” and the use of copyright material. Approved by Major Professor(s): Approved by: Head of the Departmental Graduate Program Date Alicia Marie... matrix . . . . . . . . . . . . . . . . . 106 8.15 Sparsity patterns for the Nastran benchmark of order 1.5 million . . . . 108 8.16 Sparsity patterns...magnitude eigenvalues of a given matrix pencil (A,B) along with their associated eigenvectors. Computing the smallest eigenvalues is more difficult

Solving eigenvalue response matrix equations with nonlinear techniques

International Nuclear Information System (INIS)

Roberts, Jeremy A.; Forget, Benoit

2014-01-01

Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness

Modified Bateman solution for identical eigenvalues

International Nuclear Information System (INIS)

Dreher, Raymond

2013-01-01

Highlights: ► Solving indeterminacies due to identical eigenvalues in Bateman’s solution. ► Exact analytical solution of Bateman’s equations for identical eigenvalues. ► Algorithm calculating higher order derivatives appearing in this solution. ► Alternative evaluation of the derivatives through the Taylor polynomial. ► Implementation of an example program demonstrating the developed solution. - Abstract: In this paper we develop a general solution to the Bateman equations taking into account the special case of identical eigenvalues. A characteristic of this new solution is the presence of higher order derivatives. It is shown that the derivatives can be obtained analytically and also computed in an efficient manner

Eigenvalue Decomposition-Based Modified Newton Algorithm

Directory of Open Access Journals (Sweden)

Wen-jun Wang

2013-01-01

Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.

Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions

Directory of Open Access Journals (Sweden)

Manfred Möller

2013-01-01

Full Text Available Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.

The BR eigenvalue algorithm

Energy Technology Data Exchange (ETDEWEB)

Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics

1997-11-01

The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

Energy Technology Data Exchange (ETDEWEB)

Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

1994-12-31

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

Application of collocation meshless method to eigenvalue problem

International Nuclear Information System (INIS)

Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

2012-01-01

The numerical method for solving the nonlinear eigenvalue problem has been developed by using the collocation Element-Free Galerkin Method (EFGM) and its performance has been numerically investigated. The results of computations show that the approximate solution of the nonlinear eigenvalue problem can be obtained stably by using the developed method. Therefore, it can be concluded that the developed method is useful for solving the nonlinear eigenvalue problem. (author)

Inequalities among eigenvalues of Sturm–Liouville problems

Directory of Open Access Journals (Sweden)

Kong Q

1999-01-01

Full Text Available There are well-known inequalities among the eigenvalues of Sturm–Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm–Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm–Liouville problems without using operator theory.

A method for the solution of the RPA eigenvalue

International Nuclear Information System (INIS)

Hoffman, M.J.H.; De Kock, P.R.

1986-01-01

The RPA eigenvalue problem requires the diagonalization of a 2nx2n matrix. In practical calculations, n (the number of particle-hole basis states) can be a few hundred and the diagonalization of such a large non-symmetric matrix may take quite a long time. In this report we firstly discuss sufficient conditions for real and non-zero RPA eigenvalues. The presence of zero or imaginary eigenvalues is related to the relative importance of the groundstate correlations to the total interaction energy. We then rewrite the RPA eigenvalue problem for the cases where these conditions are fulfilled in a form which only requires the diagonalization of two symmetric nxn matrices. The extend to which this method can be applied when zero eigenvalues occur, is also discussed

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Wu, Sheng-Jhih; Chu, Moody T

2017-01-01

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. (paper)

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

Science.gov (United States)

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.

The eigenvalue problem in phase space.

Science.gov (United States)

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.

Extreme eigenvalues of sample covariance and correlation matrices

DEFF Research Database (Denmark)

Heiny, Johannes

This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the sample size n. We generalize the growth rates of p existing in the literature. Assuming a regular variation condition with tail index ... eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high dimension...

An adjoint-based scheme for eigenvalue error improvement

International Nuclear Information System (INIS)

Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.

2011-01-01

A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)

Efficient solutions to the NDA-NCA low-order eigenvalue problem

International Nuclear Information System (INIS)

Willert, J. A.; Kelley, C. T.

2013-01-01

Recent algorithmic advances combine moment-based acceleration and Jacobian-Free Newton-Krylov (JFNK) methods to accelerate the computation of the dominant eigenvalue in a k-eigenvalue calculation. In particular, NDA-NCA [1], builds a sequence of low-order (LO) diffusion-based eigenvalue problems in which the solution converges to the true eigenvalue solution. Within NDA-NCA, the solution to the LO k-eigenvalue problem is computed by solving a system of nonlinear equation using some variant of Newton's method. We show that we can speed up the solution to the LO problem dramatically by abandoning the JFNK method and exploiting the structure of the Jacobian matrix. (authors)

A robust multilevel simultaneous eigenvalue solver

Science.gov (United States)

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.

Computing the eigenvalues and eigenvectors of a fuzzy matrix

Directory of Open Access Journals (Sweden)

A. Kumar

2012-08-01

Full Text Available Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.$

Frequency response as a surrogate eigenvalue problem in topology optimization

DEFF Research Database (Denmark)

Andreassen, Erik; Ferrari, Federico; Sigmund, Ole

2018-01-01

This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...

Multivariate analysis of eigenvalues and eigenvectors in tensor based morphometry

Science.gov (United States)

Rajagopalan, Vidya; Schwartzman, Armin; Hua, Xue; Leow, Alex; Thompson, Paul; Lepore, Natasha

2015-01-01

We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.7 However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer's patients and healthy elderly controls from the Alzheimer's Disease Neuro Imaging Database.

Generalization of Samuelson's inequality and location of eigenvalues

Indian Academy of Sciences (India)

We prove a generalization of Samuelson's inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex × matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.

OECD/NEA expert group on uncertainty analysis for criticality safety assessment: Results of benchmark on sensitivity calculation (phase III)

Energy Technology Data Exchange (ETDEWEB)

Ivanova, T.; Laville, C. [Institut de Radioprotection et de Surete Nucleaire IRSN, BP 17, 92262 Fontenay aux Roses (France); Dyrda, J. [Atomic Weapons Establishment AWE, Aldermaston, Reading, RG7 4PR (United Kingdom); Mennerdahl, D. [E Mennerdahl Systems EMS, Starvaegen 12, 18357 Taeby (Sweden); Golovko, Y.; Raskach, K.; Tsiboulia, A. [Inst. for Physics and Power Engineering IPPE, 1, Bondarenko sq., 249033 Obninsk (Russian Federation); Lee, G. S.; Woo, S. W. [Korea Inst. of Nuclear Safety KINS, 62 Gwahak-ro, Yuseong-gu, Daejeon 305-338 (Korea, Republic of); Bidaud, A.; Sabouri, P. [Laboratoire de Physique Subatomique et de Cosmologie LPSC, CNRS-IN2P3/UJF/INPG, Grenoble (France); Patel, A. [U.S. Nuclear Regulatory Commission (NRC), Washington, DC 20555-0001 (United States); Bledsoe, K.; Rearden, B. [Oak Ridge National Laboratory ORNL, M.S. 6170, P.O. Box 2008, Oak Ridge, TN 37831 (United States); Gulliford, J.; Michel-Sendis, F. [OECD/NEA, 12, Bd des Iles, 92130 Issy-les-Moulineaux (France)

2012-07-01

The sensitivities of the k{sub eff} eigenvalue to neutron cross sections have become commonly used in similarity studies and as part of the validation algorithm for criticality safety assessments. To test calculations of the sensitivity coefficients, a benchmark study (Phase III) has been established by the OECD-NEA/WPNCS/EG UACSA (Expert Group on Uncertainty Analysis for Criticality Safety Assessment). This paper presents some sensitivity results generated by the benchmark participants using various computational tools based upon different computational methods: SCALE/TSUNAMI-3D and -1D, MONK, APOLLO2-MORET 5, DRAGON-SUSD3D and MMKKENO. The study demonstrates the performance of the tools. It also illustrates how model simplifications impact the sensitivity results and demonstrates the importance of 'implicit' (self-shielding) sensitivities. This work has been a useful step towards verification of the existing and developed sensitivity analysis methods. (authors)

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

Science.gov (United States)

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.

Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

Energy Technology Data Exchange (ETDEWEB)

Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

2000-03-15

We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

Eigenvalues of the simplified ideal MHD ballooning equation

International Nuclear Information System (INIS)

Paris, R.B.; Auby, N.; Dagazian, R.Y.

1986-01-01

The investigation of the spectrum of the simplified differential equation describing the variation of the amplitude of the ideal MHD ballooning instability along magnetic field lines constitutes a multiparameter Schroedinger eigenvalue problem. An exact eigenvalue relation for the discrete part of the spectrum is obtained in terms of the oblate spheroidal functions. The dependence of the eigenvalues lambda on the two free parameters γ 2 and μ 2 of the equation is discussed, together with certain analytical approximations in the limits of small and large γ 2 . A brief review of the principal properties of the spheroidal functions is given in an appendix

Fast EEG spike detection via eigenvalue analysis and clustering of spatial amplitude distribution

Science.gov (United States)

Fukami, Tadanori; Shimada, Takamasa; Ishikawa, Bunnoshin

2018-06-01

Objective. In the current study, we tested a proposed method for fast spike detection in electroencephalography (EEG). Approach. We performed eigenvalue analysis in two-dimensional space spanned by gradients calculated from two neighboring samples to detect high-amplitude negative peaks. We extracted the spike candidates by imposing restrictions on parameters regarding spike shape and eigenvalues reflecting detection characteristics of individual medical doctors. We subsequently performed clustering, classifying detected peaks by considering the amplitude distribution at 19 scalp electrodes. Clusters with a small number of candidates were excluded. We then defined a score for eliminating spike candidates for which the pattern of detected electrodes differed from the overall pattern in a cluster. Spikes were detected by setting the score threshold. Main results. Based on visual inspection by a psychiatrist experienced in EEG, we evaluated the proposed method using two statistical measures of precision and recall with respect to detection performance. We found that precision and recall exhibited a trade-off relationship. The average recall value was 0.708 in eight subjects with the score threshold that maximized the F-measure, with 58.6  ±  36.2 spikes per subject. Under this condition, the average precision was 0.390, corresponding to a false positive rate 2.09 times higher than the true positive rate. Analysis of the required processing time revealed that, using a general-purpose computer, our method could be used to perform spike detection in 12.1% of the recording time. The process of narrowing down spike candidates based on shape occupied most of the processing time. Significance. Although the average recall value was comparable with that of other studies, the proposed method significantly shortened the processing time.

Deflation of Eigenvalues for GMRES in Lattice QCD

International Nuclear Information System (INIS)

Morgan, Ronald B.; Wilcox, Walter

2002-01-01

Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors improve convergence for the linear equations, and they help solve other right-hand sides

Jacobi-Davidson methods for generalized MHD-eigenvalue problems

NARCIS (Netherlands)

J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)

1995-01-01

textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The

On the distribution of eigenvalues of certain matrix ensembles

International Nuclear Information System (INIS)

Bogomolny, E.; Bohigas, O.; Pato, M.P.

1995-01-01

Invariant random matrix ensembles with weak confinement potentials of the eigenvalues, corresponding to indeterminate moment problems, are investigated. These ensembles are characterized by the fact that the mean density of eigenvalues tends to a continuous function with increasing matrix dimension contrary to the usual cases where it grows indefinitely. It is demonstrated that the standard asymptotic formulae are not applicable in these cases and that the asymptotic distribution of eigenvalues can deviate from the classical ones. (author)

The universal eigenvalue bounds of Payne–Pólya–Weinberger, Hile ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

following universal inequalities for the λi's in the case when n = 2: λk+1 − λk ≤. 2 .... with V ≥ 0 on and eigenvalue problems with a weight (e.g., the fixed ...... [29] Protter M H, Universal inequalities for eigenvalues, Maximum Principles and Eigenvalue. Problems in ... minimal submanifolds, Ann. Scuola Norm. Sup. Pisa Cl.

Dynamic Eigenvalue Problem of Concrete Slab Road Surface

Science.gov (United States)

Pawlak, Urszula; Szczecina, Michał

2017-10-01

The paper presents an analysis of the dynamic eigenvalue problem of concrete slab road surface. A sample concrete slab was modelled using Autodesk Robot Structural Analysis software and calculated with Finite Element Method. The slab was set on a one-parameter elastic subsoil, for which the modulus of elasticity was separately calculated. The eigen frequencies and eigenvectors (as maximal vertical nodal displacements) were presented. On the basis of the results of calculations, some basic recommendations for designers of concrete road surfaces were offered.

Higher-order relationship between eigen-value separation and static flux tilts

International Nuclear Information System (INIS)

Beckner, W.D.

1975-01-01

Spatial kinetics phenomena in nuclear reactors, such as xenon-induced spatial flux oscillations, are currently being analyzed using the higher harmonic solutions to the static reactor balance equation. An important parameter in such an analysis is a global quantity called eigenvalue separation. It is desirable to be able to experimentally measure this parameter in power reactors in order to confirm design calculations. Since spatial distortions in the flux shape depend on the eigenvalue separation of the reactor, an attempt has been made previously to use this fact as a means of measuring the parameter. It was postulated that an induced flux distortion or ''static flux tilt'' could be measured and theoretically related to eigenvalue separation. Unfortunately, the behavior of experimental data did not exactly agree with theoretical predictions, and values of the parameter found using the original static flux tilt technique were consistently low. The theory has been re-evaluated here and the previously observed discrepancy eliminated. Techniques have been also developed to allow for more accurate interpretation of experimental data. In order to make the method applicable to real systems, the theory has been extended to two spatial dimensions; extension to three dimensions follows directly. Possible trouble areas have been investigated, and experimental procedures for use of the technique to measure the eigenvalue separation in power reactors are presented

Efficient methods for time-absorption (α) eigenvalue calculations

International Nuclear Information System (INIS)

Hill, T.R.

1983-01-01

The time-absorption eigenvalue (α) calculation is one of the options found in most discrete-ordinates transport codes. Several methods have been developed at Los Alamos to improve the efficiency of this calculation. Two procedures, based on coarse-mesh rebalance, to accelerate the α eigenvalue search are derived. A hybrid scheme to automatically choose the more-effective rebalance method is described. The α rebalance scheme permits some simple modifications to the iteration strategy that eliminates many unnecessary calculations required in the standard search procedure. For several fast supercritical test problems, these methods resulted in convergence with one-fifth the number of iterations required for the conventional eigenvalue search procedure

An eigenvalue localization set for tensors and its applications.

Science.gov (United States)

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.

Singular perturbation of simple eigenvalues

International Nuclear Information System (INIS)

Greenlee, W.M.

1976-01-01

Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

Bound-state Dirac eigenvalues for scalar potentials

International Nuclear Information System (INIS)

Ram, B.; Arafah, M.

1981-01-01

The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)

An eigenvalue localization set for tensors and its applications

Directory of Open Access Journals (Sweden)

Jianxing Zhao

2017-03-01

Full Text Available Abstract 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 M $\\mathcal{M}$ -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 N = { 1 , 2 , … , n } $N=\\{1,2,\\ldots,n\\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.

Eigenvalues of PT-symmetric oscillators with polynomial potentials

International Nuclear Information System (INIS)

Shin, Kwang C

2005-01-01

We study the eigenvalue problem -u''(z) - [(iz) m + P m-1 (iz)]u(z) λu(z) with the boundary condition that u(z) decays to zero as z tends to infinity along the rays arg z = -π/2 ± 2π/(m+2) in the complex plane, where P m-1 (z) = a 1 z m-1 + a 2 z m-2 + . . . + a m-1 z is a polynomial and integers m ≥ 3. We provide an asymptotic expansion of the eigenvalues λ n as n → +∞, and prove that for each real polynomial P m-1 , the eigenvalues are all real and positive, with only finitely many exceptions

Oscillators and Eigenvalues

DEFF Research Database (Denmark)

Lindberg, Erik

1997-01-01

In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....

Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

Energy Technology Data Exchange (ETDEWEB)

Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

2006-09-28

A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

Cluster structure in the correlation coefficient matrix can be characterized by abnormal eigenvalues

Science.gov (United States)

Nie, Chun-Xiao

2018-02-01

In a large number of previous studies, the researchers found that some of the eigenvalues of the financial correlation matrix were greater than the predicted values of the random matrix theory (RMT). Here, we call these eigenvalues as abnormal eigenvalues. In order to reveal the hidden meaning of these abnormal eigenvalues, we study the toy model with cluster structure and find that these eigenvalues are related to the cluster structure of the correlation coefficient matrix. In this paper, model-based experiments show that in most cases, the number of abnormal eigenvalues of the correlation matrix is equal to the number of clusters. In addition, empirical studies show that the sum of the abnormal eigenvalues is related to the clarity of the cluster structure and is negatively correlated with the correlation dimension.

On the eigenvalues of S.Π for arbitrary spin in a constant magnetic field

International Nuclear Information System (INIS)

Jayaraman, J.; Oliveira, M.A.B. de.

1985-01-01

Utilizing the intimate connection of a charged particle in a nomogeneous magnetic field to that of a harmonic oscillator, it was established in a recent communication that the eigenvalue spectrum of the matrix operator S.Π for spin 1 is purely real for any intensity of the external magnetic field thereby removing a false impression to the contrary in the recent literature. Here these results are extended to arbitrary spin the reality of the eigenvalue spectrum. The case of spin 3/2 is discussed in some details and it is demonstrated that the complex eigenvalues implied the spectrum by a recent analysis of Weaver, for sufficiently intense magnetic field, when the particle number n assumes values 0 and 1 do not in fact appear at all. (Author) [pt

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

Science.gov (United States)

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.

INDEFINITE COPOSITIVE MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE OR EXACTLY ONE NEGATIVE EIGENVALUE

NARCIS (Netherlands)

Jargalsaikhan, Bolor

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out

The nonconforming virtual element method for eigenvalue problems

Energy Technology Data Exchange (ETDEWEB)

Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications

2018-02-05

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 L²-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 numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

Solving the RPA eigenvalue equation in real-space

CERN Document Server

Muta, A; Hashimoto, Y; Yabana, K

2002-01-01

We present a computational method to solve the RPA eigenvalue equation employing a uniform grid representation in three-dimensional Cartesian coordinates. The conjugate gradient method is used for this purpose as an interactive method for a generalized eigenvalue problem. No construction of unoccupied orbitals is required in the procedure. We expect this method to be useful for systems lacking spatial symmetry to calculate accurate eigenvalues and transition matrix elements of a few low-lying excitations. Some applications are presented to demonstrate the feasibility of the method, considering the simplified mean-field model as an example of a nuclear physics system and the electronic excitations in molecules with time-dependent density functional theory as an example of an electronic system. (author)

MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems

International Nuclear Information System (INIS)

Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.

1986-01-01

1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble

International Nuclear Information System (INIS)

Chen Yang; Liu Dangzheng; Zhou Dasheng

2010-01-01

In this paper we study the entanglement of the reduced density matrix of a bipartite quantum system in a random pure state. It transpires that this involves the computation of the smallest eigenvalue distribution of the fixed-trace Laguerre ensemble of N x N random matrices. We showed that for finite N the smallest eigenvalue distribution may be expressed in terms of Jack polynomials. Furthermore, based on the exact results, we found a limiting distribution when the smallest eigenvalue is suitably scaled with N followed by a large N limit. Our results turn out to be the same as the smallest eigenvalue distribution of the classical Laguerre ensembles without the fixed-trace constraint. This suggests in a broad sense, the global constraint does not influence local correlations, at least, in the large N limit. Consequently, we have solved an open problem: the determination of the smallest eigenvalue distribution of the reduced density matrix-obtained by tracing out the environmental degrees of freedom-for a bipartite quantum system of unequal dimensions.

Modern algorithms for large sparse eigenvalue problems

International Nuclear Information System (INIS)

Meyer, A.

1987-01-01

The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)

The Schrodinger Eigenvalue March

Science.gov (United States)

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…

Topological derivatives of eigenvalues and neural networks in identification of imperfections

International Nuclear Information System (INIS)

Grzanek, M; Nowakowski, A; Sokolowski, J

2008-01-01

Numerical method for identification of imperfections is devised for elliptic spectral problems. The neural networks are employed for numerical solution. The topological derivatives of eigenvalues are used in the learning procedure of the neural networks. The topological derivatives of eigenvalues are determined by the methods of asymptotic analysis in singularly perturbed geometrical domains. The convergence of the numerical method in a probabilistic setting is analysed. The method is presented for the identification of small singular perturbations of the boundary of geometrical domain, however the framework is general and can be used for numerical solutions of inverse problems in the presence of small imperfections in the interior of the domain. Some numerical results are given for elliptic spectral problem in two spatial dimensions.

Periodic Solutions, Eigenvalue Curves, and Degeneracy of the Fractional Mathieu Equation

International Nuclear Information System (INIS)

Parra-Hinojosa, A; Gutiérrez-Vega, J C

2016-01-01

We investigate the eigenvalue curves, the behavior of the periodic solutions, and the orthogonality properties of the Mathieu equation with an additional fractional derivative term using the method of harmonic balance. The addition of the fractional derivative term breaks the hermiticity of the equation in such a way that its eigenvalues need not be real nor its eigenfunctions orthogonal. We show that for a certain choice of parameters the eigenvalue curves reveal the appearance of degenerate eigenvalues. We offer a detailed discussion of the matrix representation of the differential operator corresponding to the fractional Mathieu equation, as well as some numerical examples of its periodic solutions. (paper)

Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

Directory of Open Access Journals (Sweden)

Khalil Ben Haddouch

2016-04-01

Full Text Available In this work we will study the eigenvalues for a fourth order elliptic equation with $p(x$-growth conditions $\\Delta^2_{p(x} u=\\lambda |u|^{p(x-2} u$, under Neumann boundary conditions, where $p(x$ is a continuous function defined on the bounded domain with $p(x>1$. Through the Ljusternik-Schnireleman theory on $C^1$-manifold, we prove the existence of infinitely many eigenvalue sequences and $\\sup \\Lambda =+\\infty$, where $\\Lambda$ is the set of all eigenvalues.

Gravitational lensing by eigenvalue distributions of random matrix models

Science.gov (United States)

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.

TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.

Estimates for lower order eigenvalues of a clamped plate problem

OpenAIRE

Cheng, Qing-Ming; Huang, Guangyue; Wei, Guoxin

2009-01-01

For a bounded domain $\\Omega$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

Eigenvalue treatment of cosmological models

International Nuclear Information System (INIS)

Novello, M.; Soares, D.

1976-08-01

From the decomposition of Weyl tensor into its electric and magnetic parts, it is formulated the eigenvalue problem for cosmological models, and is used quasi-maxwellian form of Einstein's equation to propagate it along a time-like congruence. Three related theorems are presented

Eigenvalues of Words in Two Positive Definite Letters

OpenAIRE

Hillar, Christopher J; Johnson, Charles R

2005-01-01

The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection with a long-standing problem in theoretical physics. A large class of words that do guarantee positive eigenvalues is identified, and considerable evidence is given for the conjecture that no other words do. In the process, a fundamental question about solvability of symmetric word equations is encoun...

Eigenvalues of the Transferences of Gaussian Optical Systems

Directory of Open Access Journals (Sweden)

W.F. Harris

2005-12-01

Full Text Available The  problem  of  how  to  define  an  average eye leads to the question of what eigenvalues are  possible  for  ray  transferences.  This  paper examines the set of possible eigenvalues in the simplest possible case, that of optical systems consisting  of  elements  that  are  stigmatic  and centred on a common axis.

A scheme for the evaluation of dominant time-eigenvalues of a nuclear reactor

International Nuclear Information System (INIS)

Modak, R.S.; Gupta, Anurag

2007-01-01

This paper presents a scheme to obtain the fundamental and few dominant solutions of the prompt time eigenvalue problem (referred to as α-eigenvalue problem) for a nuclear reactor using multi-group neutron diffusion theory. The scheme is based on the use of an algorithm called Orthomin(1). This algorithm was originally proposed by Suetomi and Sekimoto [Suetomi, E., Sekimoto, H., 1991. Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations. Ann. Nucl. Energy 18 (4), 205-227] to obtain the fundamental K-eigenvalue (K-effective) of nuclear reactors. Recently, it has been shown that the algorithm can be used to obtain the further dominant K-modes also. Since α-eigenvalue problem is usually more difficult to solve than the K-eigenvalue problem, an attempt has been made here to use Orthomin(1) for its solution. Numerical results are given for realistic 3-D test case

Eigenvalue sensitivity analysis and uncertainty quantification in SCALE6.2.1 using continuous-energy Monte Carlo Method

Energy Technology Data Exchange (ETDEWEB)

Labarile, A.; Barrachina, T.; Miró, R.; Verdú, G., E-mail: alabarile@iqn.upv.es, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Institute for Industrial, Radiophysical and Environmental Safety - ISIRYM, Valencia (Spain); Pereira, C., E-mail: claubia@nuclear.ufmg.br [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Departamento de Engenharia Nuclear

2017-07-01

The use of Best-Estimate computer codes is one of the greatest concerns in the nuclear industry especially for licensing analysis. Of paramount importance is the estimation of the uncertainties of the whole system to establish the safety margins based on highly reliable results. The estimation of these uncertainties should be performed by applying a methodology to propagate the uncertainties from the input parameters and the models implemented in the code to the output parameters. This study employs two different approaches for the Sensitivity Analysis (SA) and Uncertainty Quantification (UQ), the adjoint-based perturbation theory of TSUNAMI-3D, and the stochastic sampling technique of SAMPLER/KENO. The cases studied are two models of Light Water Reactors in the framework of the OECD/NEA UAM-LWR benchmark, a Boiling Water Reactor (BWR) and a Pressurized Water Reactor (PWR). Both of them at Hot Full Power (HFP) and Hot Zero Power (HZP) conditions, with and without control rod. This work presents the results of k{sub eff} from different simulation, and discuss the comparison of the two methods employed. In particular, a list of the major contributors to the uncertainty of k{sub eff} in terms of microscopic cross sections; their sensitivity coefficients; a comparison between the results of the two modules and with reference values; statistical information from the stochastic approach, and the probability and statistical confidence reached in the simulations. The reader will find all these information discussed in this paper. (author)

Energy eigenvalues of helium-like atoms in dense plasmas

International Nuclear Information System (INIS)

Hashino, Tasuke; Nakazaki, Shinobu; Kato, Takako; Kashiwabara, Hiromichi.

1987-04-01

Calculations based on a variational method with wave functions including the correlation of electrons are carried out to obtain energy eigenvalues of Schroedinger's equation for helium-like atoms embedded in dense plasmas, taking the Debye-Hueckel approximation. Energy eigenvalues for the 1 1 S, 2 1 S, and 2 3 S states are obtained as a function of Debye screening length. (author)

Eigenvalues of the volume operator in loop quantum gravity

International Nuclear Information System (INIS)

Meissner, Krzysztof A

2006-01-01

We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins, which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity

Derivation of the reduced reaction mechanisms of ozone depletion events in the Arctic spring by using concentration sensitivity analysis and principal component analysis

Directory of Open Access Journals (Sweden)

L. Cao

2016-12-01

Full Text Available The ozone depletion events (ODEs in the springtime Arctic have been investigated since the 1980s. It is found that the depletion of ozone is highly associated with an auto-catalytic reaction cycle, which involves mostly the bromine-containing compounds. Moreover, bromide stored in various substrates in the Arctic such as the underlying surface covered by ice and snow can be also activated by the absorbed HOBr. Subsequently, this leads to an explosive increase of the bromine amount in the troposphere, which is called the “bromine explosion mechanism”. In the present study, a reaction scheme representing the chemistry of ozone depletion and halogen release is processed with two different mechanism reduction approaches, namely, the concentration sensitivity analysis and the principal component analysis. In the concentration sensitivity analysis, the interdependence of the mixing ratios of ozone and principal bromine species on the rate of each reaction in the ODE mechanism is identified. Furthermore, the most influential reactions in different time periods of ODEs are also revealed. By removing 11 reactions with the maximum absolute values of sensitivities lower than 10 %, a reduced reaction mechanism of ODEs is derived. The onsets of each time period of ODEs in simulations using the original reaction mechanism and the reduced reaction mechanism are identical while the maximum deviation of the mixing ratio of principal bromine species between different mechanisms is found to be less than 1 %. By performing the principal component analysis on an array of the sensitivity matrices, the dependence of a particular species concentration on a combination of the reaction rates in the mechanism is revealed. Redundant reactions are indicated by principal components corresponding to small eigenvalues and insignificant elements in principal components with large eigenvalues. Through this investigation, aside from the 11 reactions identified as

Absence of positive eigenvalues for hard-core N-body systems

DEFF Research Database (Denmark)

Ito, K.; Skibsted, Erik

We show absence of positive eigenvalues for generalized 2-body hard-core Schrödinger operators under the condition of bounded strictly convex obstacles. A scheme for showing absence of positive eigenvalues for generalized N-body hard-core Schrödinger operators, N≥ 2, is presented. This scheme inv...

Solving complex band structure problems with the FEAST eigenvalue algorithm

Science.gov (United States)

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.

Reflectance variability of surface coatings reveals characteristic eigenvalue spectra

Science.gov (United States)

Medina, José M.; Díaz, José A.; Barros, Rui

2012-10-01

We have examined the trial-to-trial variability of the reflectance spectra of surface coatings containing effect pigments. Principal component analysis of reflectances was done at each detection angle separately. A method for classification of principal components is applied based on the eigenvalue spectra. It was found that the eigenvalue spectra follow characteristic power laws and depend on the detection angle. Three different subsets of principal components were examined to separate the relevant spectral features related to the pigments from other noise sources. Reconstruction of the reflectance spectra by taking only the first subset indicated that reflectance variability was higher at near-specular reflection, suggesting a correlation with the trial-to-trial deposition of effect pigments. Reconstruction by using the second subset indicates that variability was higher at short wavelengths. Finally, reconstruction by using only the third subset indicates that reflectance variability was not totally random as a function of the wavelength. The methods employed can be useful in the evaluation of color variability in industrial paint application processes.

Simplified procedures for fast reactor fuel cycle and sensitivity analysis

International Nuclear Information System (INIS)

Badruzzaman, A.

1979-01-01

The Continuous Slowing Down-Integral Transport Theory has been extended to perform criticality calculations in a Fast Reactor Core-blanket system achieving excellent prediction of the spectrum and the eigenvalue. The integral transport parameters did not need recalculation with source iteration and were found to be relatively constant with exposure. Fuel cycle parameters were accurately predicted when these were not varied, thus reducing a principal potential penalty of the Intergal Transport approach where considerable effort may be required to calculate transport parameters in more complicated geometries. The small variation of the spectrum in the central core region, and its weak dependence on exposure for both this region, the core blanket interface and blanket region led to the extension and development of inexpensive simplified procedures to complement exact methods. These procedures gave accurate predictions of the key fuel cycle parameters such as cost and their sensitivity to variation in spectrum-averaged and multigroup cross sections. They also predicted the implications of design variation on these parameters very well. The accuracy of these procedures and their use in analyzing a wide variety of sensitivities demonstrate the potential utility of survey calculations in Fast Reactor analysis and fuel management

An algorithm of α-and γ-mode eigenvalue calculations by Monte Carlo method

International Nuclear Information System (INIS)

Yamamoto, Toshihiro; Miyoshi, Yoshinori

2003-01-01

A new algorithm for Monte Carlo calculation was developed to obtain α- and γ-mode eigenvalues. The α is a prompt neutron time decay constant measured in subcritical experiments, and the γ is a spatial decay constant measured in an exponential method for determining the subcriticality. This algorithm can be implemented into existing Monte Carlo eigenvalue calculation codes with minimum modifications. The algorithm was implemented into MCNP code and the performance of calculating the both mode eigenvalues were verified through comparison of the calculated eigenvalues with the ones obtained by fixed source calculations. (author)

Complex energy eigenvalues of a linear potential with a parabolical barrier

International Nuclear Information System (INIS)

Malherbe, J.B.

1978-01-01

The physical meaning and restrictions of complex energy eigenvalues are briefly discussed. It is indicated that a quasi-stationary phase describes an idealised disintegration system. Approximate resonance-eigenvalues of the one dimensional Schrodinger equation with a linear potential and parabolic barrier are calculated by means of Connor's semiclassical method. This method is based on the generalized WKB-method of Miller and Good. The results obtained confirm the correctness of a model representation which explains the unusual distribution of eigenvalues by certain other linear potentials in a complex energy level [af

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

Science.gov (United States)

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.

2nd International Workshop on Eigenvalue Problems : Algorithms, Software and Applications in Petascale Computing

CERN Document Server

Zhang, Shao-Liang; Imamura, Toshiyuki; Yamamoto, Yusaku; Kuramashi, Yoshinobu; Hoshi, Takeo

2017-01-01

This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices

International Nuclear Information System (INIS)

Kabashima, Yoshiyuki; Takahashi, Hisanao; Watanabe, Osamu

2010-01-01

A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.

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

Science.gov (United States)

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.

Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems

International Nuclear Information System (INIS)

Vanden Berghe, G.; Van Daele, M.; De Meyer, H.

1994-01-01

A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))

Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

Science.gov (United States)

Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene

2016-03-01

Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

Bounds and estimates for the linearly perturbed eigenvalue problem

International Nuclear Information System (INIS)

Raddatz, W.D.

1983-01-01

This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

Science.gov (United States)

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.

Eigenvalue-dependent neutron energy spectra: Definitions, analyses, and applications

International Nuclear Information System (INIS)

Cacuci, D.G.; Ronen, Y.; Shayer, Z.; Wagschal, J.J.; Yeivin, Y.

1982-01-01

A general qualitative analysis of spectral effects that arise from solving the kappa-, α-, γ-, and sigma-eigenvalue formulations of the neutron transport equation for nuclear systems that deviate (to first order) from criticality is presented. Hierarchies of neutron spectra softness are established and expressed concisely in terms of the newly introduced spatialdependent local spectral indices for the core and for the reflector. It is shown that each hierarchy is preserved, regardless of the nature of the specific physical mechanism that cause the system to deviate from criticality. Qualitative conclusions regarding the general behavior of the spectrum-dependent integral spectral indices and ICRs corresponding to the kappa-, α-, γ-, and sigma-eigenvalue formalisms are also presented. By defining spectral indices separately for the core and for the reflector, it is possible to account for the characteristics of neutron spectra in both the core and the reflector. The distinctions between the spectra in the core and in the reflector could not have been accounted for by using a single type of spectral index (e.g., a spectral index for the entire system or a spectral index solely for the core)

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

Science.gov (United States)

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.

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

Directory of Open Access Journals (Sweden)

Heinrich Voss

2016-06-01

Full Text Available Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.

Estimates of the first Dirichlet eigenvalue from exit time moment spectra

DEFF Research Database (Denmark)

Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente

2013-01-01

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball...

An Optimal Lower Eigenvalue System

Directory of Open Access Journals (Sweden)

Yingfan Liu

2011-01-01

Full Text Available An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1981-01-01

Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

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

Science.gov (United States)

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.

A subspace preconditioning algorithm for eigenvector/eigenvalue computation

Energy Technology Data Exchange (ETDEWEB)

Bramble, J.H.; Knyazev, A.V.; Pasciak, J.E.

1996-12-31

We consider the problem of computing a modest number of the smallest eigenvalues along with orthogonal bases for the corresponding eigen-spaces of a symmetric positive definite matrix. In our applications, the dimension of a matrix is large and the cost of its inverting is prohibitive. In this paper, we shall develop an effective parallelizable technique for computing these eigenvalues and eigenvectors utilizing subspace iteration and preconditioning. Estimates will be provided which show that the preconditioned method converges linearly and uniformly in the matrix dimension when used with a uniform preconditioner under the assumption that the approximating subspace is close enough to the span of desired eigenvectors.

On a quadratic inverse eigenvalue problem

International Nuclear Information System (INIS)

Cai, Yunfeng; Xu, Shufang

2009-01-01

This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

Science.gov (United States)

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.

Eigenvalues and expansion of bipartite graphs

DEFF Research Database (Denmark)

Høholdt, Tom; Janwa, Heeralal

2012-01-01

We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

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.

Science.gov (United States)

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.

A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

Directory of Open Access Journals (Sweden)

Wang Xiaoxiao

2018-04-01

Full Text Available A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014 74-87 and Li et al. (Linear and Multilinear Algebra 63(11 (2015 2159-2170 for estimating the moduli of subdominant eigenvalues.

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

Science.gov (United States)

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

EISPACK-J: subprogram package for solving eigenvalue problems

International Nuclear Information System (INIS)

Fujimura, Toichiro; Tsutsui, Tsuneo

1979-05-01

EISPACK-J, a subprogram package for solving eigenvalue problems, has been developed and subprograms with a variety of functions have been prepared. These subprograms can solve standard problems of complex matrices, general problems of real matrices and special problems in which only the required eigenvalues and eigenvectors are calculated. They are compared to existing subprograms, showing their features through benchmark tests. Many test problems, including realistic scale problems, are provided for the benchmark tests. Discussions are made on computer core storage and computing time required for each subprogram, and accuracy of the solution. The results show that the subprograms of EISPACK-J, based on Householder, QR and inverse iteration methods, are the best in computing time and accuracy. (author)

Critical eigenvalue in LMFBRs: a physics assessment

International Nuclear Information System (INIS)

McKnight, R.D.; Collins, P.J.; Olsen, D.N.

1984-01-01

This paper summarizes recent work to put the analysis of past critical eigenvalue measurements from the US critical experiments program on a consistent basis. The integral data base includes 53 configurations built in 11 ZPPR assemblies which simulate mixed oxide LMFBRs. Both conventional and heterogeneous designs representing 350, 700, and 900 MWe sizes and with and without simulated control rods and/or control rod positions have been studied. The review of the integral data base includes quantitative assessment of experimental uncertainties in the measured excess reactivity. Analyses have been done with design level and higher-order methods using ENDF/B-IV data. Comparisons of these analyses with the experiments are used to generate recommended bias factors for criticality predictions. Recommended methods for analysis of LMFBR fast critical assemblies and LMFBR design calculations are presented. Unresolved issues and areas which require additional experimental or analytical study are identified

Generalized Eigenvalues for pairs on heritian matrices

Science.gov (United States)

Rublein, George

1988-01-01

A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem

KAUST Repository

Haidar, Azzam

2012-01-01

Classical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel\\'s Math Kernel Library.

The total Hartree-Fock energy-eigenvalue sum relationship in atoms

International Nuclear Information System (INIS)

Sen, K.D.

1979-01-01

Using the well known relationships for the isoelectronic changes in the total Hartree-Fock energy, nucleus-electron attraction energy and electron-electron repulsion energy in atoms a simple polynomial expansion in Z is obtained for the sum of the eigenvalues which can be used to calculate the total Hartree-Fock energy. Numerical results are presented for 2-10 electron series to show that the present relationship is a better approximation than the other available energy-eigenvalue relationships. (author)

Photonic band structure calculations using nonlinear eigenvalue techniques

International Nuclear Information System (INIS)

Spence, Alastair; Poulton, Chris

2005-01-01

This paper considers the numerical computation of the photonic band structure of periodic materials such as photonic crystals. This calculation involves the solution of a Hermitian nonlinear eigenvalue problem. Numerical methods for nonlinear eigenvalue problems are usually based on Newton's method or are extensions of techniques for the standard eigenvalue problem. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. This new approach has several advantages over the current methods. First, in our numerical calculations the new variation is more robust than existing techniques, having a larger domain of convergence. Second, the linear systems remain Hermitian and are nonsingular as the method converges. Third, the approach provides an elegant and efficient way of both thinking about the problem and organising the computer solution so that only one linear system needs to be factorised at each stage in the solution process. Finally, first- and higher-order derivatives are calculated as a natural extension of the basic method, and this has advantages in the electromagnetic problem discussed here, where the band structure is plotted as a set of paths in the (ω,k) plane

Extending the subspace hybrid method for eigenvalue problems in reactor physics calculation

International Nuclear Information System (INIS)

Zhang, Q.; Abdel-Khalik, H. S.

2013-01-01

This paper presents an innovative hybrid Monte-Carlo-Deterministic method denoted by the SUBSPACE method designed for improving the efficiency of hybrid methods for reactor analysis applications. The SUBSPACE method achieves its high computational efficiency by taking advantage of the existing correlations between desired responses. Recently, significant gains in computational efficiency have been demonstrated using this method for source driven problems. Within this work the mathematical theory behind the SUBSPACE method is introduced and extended to address core wide level k-eigenvalue problems. The method's efficiency is demonstrated based on a three-dimensional quarter-core problem, where responses are sought on the pin cell level. The SUBSPACE method is compared to the FW-CADIS method and is found to be more efficient for the utilized test problem because of the reason that the FW-CADIS method solves a forward eigenvalue problem and an adjoint fixed-source problem while the SUBSPACE method only solves an adjoint fixed-source problem. Based on the favorable results obtained here, we are confident that the applicability of Monte Carlo for large scale reactor analysis could be realized in the near future. (authors)

Sensitivity analysis

Science.gov (United States)

... page: //medlineplus.gov/ency/article/003741.htm Sensitivity analysis To use the sharing features on this page, please enable JavaScript. Sensitivity analysis determines the effectiveness of antibiotics against microorganisms (germs) ...

Selected Problems of Sensitivity and Reliability of a Jack-Up Platform

Directory of Open Access Journals (Sweden)

Rozmarynowski Bogdan

2018-03-01

Full Text Available The paper deals with sensitivity and reliability applications to numerical studies of an off-shore platform model. Structural parameters and sea conditions are referred to the Baltic jack-up drilling platform. The sudy aims at the influence of particular basic variables on static and dynamic response as well as the probability of failure due to water waves and wind loads. The paper presents the sensitivity approach to a generalized eigenvalue problem and evaluation of the performace functions. The first order time-invariant problems of structural reliability analysis are under concern.

A new localization set for generalized eigenvalues

Directory of Open Access Journals (Sweden)

Jing Gao

2017-05-01

Full Text Available Abstract 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.

High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

Science.gov (United States)

Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

2017-08-21

In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

On a minimization of the eigenvalues of Schroedinger operator relatively domains

International Nuclear Information System (INIS)

Gasymov, Yu.S.; Niftiev, A.A.

2001-01-01

Minimization of the eigenvalues plays an important role in the operators spectral theory. The problem on the minimization of the eigenvalues of the Schroedinger operator by areas is considered in this work. The algorithm, analogous to the conditional gradient method, is proposed for the numerical solution of this problem in the common case. The result is generalized for the case of the positively determined completely continuous operator [ru

A note on eigenfrequency sensitivities and structural eigenfrequency optimization based on local sub-domain frequencies

DEFF Research Database (Denmark)

Pedersen, Pauli; Pedersen, Niels Leergaard

2014-01-01

foundation. A numerical heuristic redesign procedure is proposed and illustrated with examples. For the ideal case, an optimality criterion is fulfilled if the design have the same sub-domain frequency (local Rayleigh quotient). Sensitivity analysis shows an important relation between squared system...... eigenfrequency and squared local sub-domain frequency for a given eigenmode. Higher order eigenfrequenciesmay also be controlled in this manner. The presented examples are based on 2D finite element models with the use of subspace iteration for analysis and a heuristic recursive design procedure based...... on the derived optimality condition. The design that maximize a frequency depend on the total amount of available material and on a necessary interpolation as illustrated by different design cases.In this note we have assumed a linear and conservative eigenvalue problem without multiple eigenvalues. The presence...

The numerical analysis of eigenvalue problem solutions in the multigroup diffusion theory

International Nuclear Information System (INIS)

Woznick, Z.I.

1994-01-01

In this paper a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations is described. Usually the solution method is based on the system of inner and outer iterations. The presented matrix formalism allows us to visualize clearly, how the used matrix splitting influences the structure of the matrix in an eigenvalue problem to be solved as well as the independence between inner and outer iterations within global iterations. To keep the page limit, the present version of the paper consists only with first three of five sections given in the original paper under the same title (which will be published soon). (author). 13 refs

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

Science.gov (United States)

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

Recent developments in semiclassical mechanics: eigenvalues and reaction rate constants

International Nuclear Information System (INIS)

Miller, W.H.

1976-04-01

A semiclassical treatment of eigenvalues for a multidimensional non-separable potential function and of the rate constant for a chemical reaction with an activation barrier is presented. Both phenomena are seen to be described by essentially the same semiclassical formalism, which is based on a construction of the total Hamiltonian in terms of the complete set of ''good'' action variables (or adiabatic invariants) associated with the minimum in the potential energy surface for the eigenvalue case, or the saddle point in the potential energy surface for the case of chemical reaction

Eigenvalue pinching on spinc manifolds

Science.gov (United States)

Roos, Saskia

2017-02-01

We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

Eigenvalues of the -Laplacian and disconjugacy criteria

Directory of Open Access Journals (Sweden)

Pinasco Juan P

2006-01-01

Full Text Available We derive oscillation and nonoscillation criteria for the one-dimensional -Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.

First-order optical systems with unimodular eigenvalues

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2006-01-01

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues, is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the

Uncertainty Estimates in Cold Critical Eigenvalue Predictions

International Nuclear Information System (INIS)

Karve, Atul A.; Moore, Brian R.; Mills, Vernon W.; Marrotte, Gary N.

2005-01-01

A recent cycle of a General Electric boiling water reactor performed two beginning-of-cycle local cold criticals. The eigenvalues estimated by the core simulator were 0.99826 and 1.00610. The large spread in them (= 0.00784) is a source of concern, and it is studied here. An analysis process is developed using statistical techniques, where first a transfer function relating the core observable Y (eigenvalue) to various factors (X's) is established. Engineering judgment is used to recognize the best candidates for X's. They are identified as power-weighted assembly k ∞ 's of selected assemblies around the withdrawn rods. These are a small subset of many X's that could potentially influence Y. However, the intention here is not to do a comprehensive study by accounting for all the X's. Rather, the scope is to demonstrate that the process developed is reasonable and to show its applicability to performing detailed studies. Variability in X's is obtained by perturbing nodal k ∞ 's since they directly influence the buckling term in the quasi-two-group diffusion equation model of the core simulator. Any perturbations introduced in them are bounded by standard well-established uncertainties. The resulting perturbations in the X's may not necessarily be directly correlated to physical attributes, but they encompass numerous biases and uncertainties credited to input and modeling uncertainties. The 'vital few' from the 'unimportant many' X's are determined, and then they are subgrouped according to assembly type, location, exposure, and control rod insertion. The goal is to study how the subgroups influence Y in order to have a better understanding of the variability observed in it

Super-quantum curves from super-eigenvalue models

Energy Technology Data Exchange (ETDEWEB)

Ciosmak, Paweł [Faculty of Mathematics, Informatics and Mechanics, University of Warsaw,ul. Banacha 2, 02-097 Warsaw (Poland); Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, 30-348 Kraków (Poland); Manabe, Masahide [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Sułkowski, Piotr [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E. California Blvd, Pasadena, CA 91125 (United States)

2016-10-10

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

International Nuclear Information System (INIS)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-01-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Super-quantum curves from super-eigenvalue models

Science.gov (United States)

Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

2016-10-01

In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/ β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

Sensitivity and uncertainty analysis of reactivities for UO2 and MOX fueled PWR cells

Energy Technology Data Exchange (ETDEWEB)

Foad, Basma [Research Institute of Nuclear Engineering, University of Fukui, Kanawa-cho 1-2-4, Tsuruga-shi, Fukui-ken, 914-0055 (Japan); Egypt Nuclear and Radiological Regulatory Authority, 3 Ahmad El Zomar St., Nasr City, Cairo, 11787 (Egypt); Takeda, Toshikazu [Research Institute of Nuclear Engineering, University of Fukui, Kanawa-cho 1-2-4, Tsuruga-shi, Fukui-ken, 914-0055 (Japan)

2015-12-31

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO{sub 2} and MOX fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections, where the self-shielding effect is taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity, for each type of reactivity, the sensitivities are calculated for small and large perturbations. The results have demonstrated that the reactivity responses have larger relative uncertainty than eigenvalue responses. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large perturbations. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found.

A numerical study of the eigenvalues in the neutron diffusion theory

International Nuclear Information System (INIS)

Lima Bezerra, J. de.

1982-12-01

A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt

Ab initio nuclear structure - the large sparse matrix eigenvalue problem

Energy Technology Data Exchange (ETDEWEB)

Vary, James P; Maris, Pieter [Department of Physics, Iowa State University, Ames, IA, 50011 (United States); Ng, Esmond; Yang, Chao [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sosonkina, Masha, E-mail: jvary@iastate.ed [Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Ames, IA, 50011 (United States)

2009-07-01

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10{sup 10} and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

Ab initio nuclear structure - the large sparse matrix eigenvalue problem

International Nuclear Information System (INIS)

Vary, James P; Maris, Pieter; Ng, Esmond; Yang, Chao; Sosonkina, Masha

2009-01-01

The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10 10 and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

Large deviations of the maximum eigenvalue in Wishart random matrices

International Nuclear Information System (INIS)

Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol

2007-01-01

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions

Large deviations of the maximum eigenvalue in Wishart random matrices

Energy Technology Data Exchange (ETDEWEB)

Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)

2007-04-20

We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.

A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential

Directory of Open Access Journals (Sweden)

Craig Haile

2000-01-01

Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.

A note on quasilinear elliptic eigenvalue problems

Directory of Open Access Journals (Sweden)

Gianni Arioli

1999-11-01

Full Text Available We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

A teaching proposal for the study of Eigenvectors and Eigenvalues

Directory of Open Access Journals (Sweden)

María José Beltrán Meneu

2017-03-01

Full Text Available 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 eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

Dependence of the fundamental time eigenvalue of linear transport operator on the system size and other parameters - An application of the Perron-Frobenius theorem

International Nuclear Information System (INIS)

Sahni, D.C.

1991-01-01

Many papers have been devoted to the study of the spectral properties of the linear (neutron) transport equation. Most of the theoretical investigations have concentrated on the existence (or otherwise) of a continuous spectrum, point spectrum, a leading/dominant eigenvalue, and a corresponding positive eigenvector. It is shown that the fundamental time eigenvalue of the linear transport operator increases with the size of the system. This follows from the increase in the largest eigenvalue of a non-negative irreducible matrix whenever any matrix element his increased. This result of matrix analysis is generalized to more general Krein-Rutman operators that leave a cone of vectors invariant

Numerical computations of interior transmission eigenvalues for scattering objects with cavities

International Nuclear Information System (INIS)

Peters, Stefan; Kleefeld, Andreas

2016-01-01

In this article we extend the inside-outside duality for acoustic transmission eigenvalue problems by allowing scattering objects that may contain cavities. In this context we provide the functional analytical framework necessary to transfer the techniques that have been used in Kirsch and Lechleiter (2013 Inverse Problems, 29 104011) to derive the inside-outside duality. Additionally, extensive numerical results are presented to show that we are able to successfully detect interior transmission eigenvalues with the inside-outside duality approach for a variety of obstacles with and without cavities in three dimensions. In this context, we also discuss the advantages and disadvantages of the inside-outside duality approach from a numerical point of view. Furthermore we derive the integral equations necessary to extend the algorithm in Kleefeld (2013 Inverse Problems, 29 104012) to compute highly accurate interior transmission eigenvalues for scattering objects with cavities, which we will then use as reference values to examine the accuracy of the inside-outside duality algorithm. (paper)

A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

Directory of Open Access Journals (Sweden)

Muhammed I. Syam

2017-11-01

Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

Eigenvalue translation method for mode calculations

International Nuclear Information System (INIS)

Gerck, E.; Cruz, C.H.B.

1978-11-01

A new method is described for the first few modes calculations in a interferometer that has several advantages over the ALLMAT subroutine, the Prony Method and the Fox and Li Method. In the illustrative results shown for the same cases it can be seen that the eigenvalue translation method is typically 100 fold times faster than the usual Fox and Li Method and 10 times faster than ALLMAT [pt

A non-self-adjoint quadratic eigenvalue problem describing a fluid-solid interaction Part II : analysis of convergence

NARCIS (Netherlands)

Bourne, D.P.; Elman, H.; Osborn, J.E.

2009-01-01

This paper is the second part of a two-part paper treating a non-self-adjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated

New exact approaches to the nuclear eigenvalue problem

International Nuclear Information System (INIS)

Andreozzi, F.; Lo Iudice, N.; Porrino, A.; Knapp, F.; Kvasil, J.

2005-01-01

In a recent past some of us have developed a new algorithm for diagonalizing the shell model Hamiltonian which consists of an iterative sequence of diagonalization of sub-matrices of small dimensions. The method, apart from being easy to implement, is robust, yielding always stable numerical solutions, and free of ghost eigenvalues. Subsequently, we have endowed the algorithm with an importance sampling, which leads to a drastic truncation of the shell model space, while keeping the accuracy of the solutions under control. Applications to typical nuclei show that the sampling yields also an extrapolation law to the exact eigenvalues. Complementary to the shell model algorithm is a method we are developing for studying collective and non collective excitations. To this purpose we solve the nuclear eigenvalue problem in a space which is the direct sum of Tamm-Dancoff n-phonon subspaces (n=0,1, ...N). The multiphonon basis is constructed by an iterative equation of motion method, which generates an over complete set of n-phonon states from the (n-1)-phonon basis. The redundancy is removed completely and exactly by a method based on the Choleski decomposition. The full Hamiltonian matrix comes out to have a simple structure and, therefore, can be drastically truncated before diagonalization by the mentioned importance sampling method. The phonon composition of the basis states allows removing naturally and maximally the spurious admixtures induced by the centre of mass motion. An application of the method to 16 O will be given for illustrative purposes. (authors)

Eigenvalue solutions in finite element thermal transient problems

International Nuclear Information System (INIS)

Stoker, J.R.

1975-01-01

The eigenvalue economiser concept can be useful in solving large finite element transient heat flow problems in which the boundary heat transfer coefficients are constant. The usual economiser theory is equivalent to applying a unit thermal 'force' to each of a small sub-set of nodes on the finite element mesh, and then calculating sets of resulting steady state temperatures. Subsequently it is assumed that the required transient temperature distributions can be approximated by a linear combination of this comparatively small set of master temperatures. The accuracy of a reduced eigenvalue calculation depends upon a good choice of master nodes, which presupposes at least a little knowledge about what sort of shape is expected in the unknown temperature distributions. There are some instances, however, where a reasonably good idea exists of the required shapes, permitting a modification to the economiser process which leads to greater economy in the number of master temperatures. The suggested new approach is to use manually prescribed temperature distributions as the master distributions, rather than using temperatures resulting from unit thermal forces. Thus, with a little pre-knowledge one may write down a set of master distributions which, as a linear combination, can represent the required solution over the range of interest to a reasonable engineering accuracy, and using the minimum number of variables. The proposed modified eigenvalue economiser technique then uses the master distributions in an automatic way to arrive at the required solution. The technique is illustrated by some simple finite element examples

Two-group k-eigenvalue benchmark calculations for planar geometry transport in a binary stochastic medium

International Nuclear Information System (INIS)

Davis, I.M.; Palmer, T.S.

2005-01-01

Benchmark calculations are performed for neutron transport in a two material (binary) stochastic multiplying medium. Spatial, angular, and energy dependence are included. The problem considered is based on a fuel assembly of a common pressurized water reactor. The mean chord length through the assembly is determined and used as the planar geometry system length. According to assumed or calculated material distributions, this system length is populated with alternating fuel and moderator segments of random size. Neutron flux distributions are numerically computed using a discretized form of the Boltzmann transport equation employing diffusion synthetic acceleration. Average quantities (group fluxes and k-eigenvalue) and variances are calculated from an ensemble of realizations of the mixing statistics. The effects of varying two parameters in the fuel, two different boundary conditions, and three different sets of mixing statistics are assessed. A probability distribution function (PDF) of the k-eigenvalue is generated and compared with previous research. Atomic mix solutions are compared with these benchmark ensemble average flux and k-eigenvalue solutions. Mixing statistics with large standard deviations give the most widely varying ensemble solutions of the flux and k-eigenvalue. The shape of the k-eigenvalue PDF qualitatively agrees with previous work. Its overall shape is independent of variations in fuel cross-sections for the problems considered, but its width is impacted by these variations. Statistical distributions with smaller standard deviations alter the shape of this PDF toward a normal distribution. The atomic mix approximation yields large over-predictions of the ensemble average k-eigenvalue and under-predictions of the flux. Qualitatively correct flux shapes are obtained in some cases. These benchmark calculations indicate that a model which includes higher statistical moments of the mixing statistics is needed for accurate predictions of binary

Lagrangian Differentiation, Integration and Eigenvalues Problems

International Nuclear Information System (INIS)

Durand, L.

1983-01-01

Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented. It is then shown that one can 'invert' his differentiation technique to obtain a flexible, factorially convergent Lagrangian integration scheme which should be useful in a variety of problems, e.g. solution of integral equations

An asymptotic expression for the eigenvalues of the normalization kernel of the resonating group method

International Nuclear Information System (INIS)

Lomnitz-Adler, J.; Brink, D.M.

1976-01-01

A generating function for the eigenvalues of the RGM Normalization Kernel is expressed in terms of the diagonal matrix elements of thw GCM Overlap Kernel. An asymptotic expression for the eigenvalues is obtained by using the Method of Steepest Descent. (Auth.)

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

Science.gov (United States)

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.

Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

International Nuclear Information System (INIS)

Yavuz, Musa

1998-01-01

We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods

Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

International Nuclear Information System (INIS)

Yavuz, M.

1997-01-01

We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods. (author)

Hybrid subgroup decomposition method for solving fine-group eigenvalue transport problems

International Nuclear Information System (INIS)

Yasseri, Saam; Rahnema, Farzad

2014-01-01

Highlights: • An acceleration technique for solving fine-group eigenvalue transport problems. • Coarse-group quasi transport theory to solve coarse-group eigenvalue transport problems. • Consistent and inconsistent formulations for coarse-group quasi transport theory. • Computational efficiency amplified by a factor of 2 using hybrid SGD for 1D BWR problem. - Abstract: In this paper, a new hybrid method for solving fine-group eigenvalue transport problems is developed. This method extends the subgroup decomposition method to efficiently couple a new coarse-group quasi transport theory with a set of fixed-source transport decomposition sweeps to obtain the fine-group transport solution. The advantages of the quasi transport theory are its high accuracy, straight-forward implementation and numerical stability. The hybrid method is analyzed for a 1D benchmark problem characteristic of boiling water reactors (BWR). It is shown that the method reproduces the fine-group transport solution with high accuracy while increasing the computational efficiency up to 12 times compared to direct fine-group transport calculations

A parallel additive Schwarz preconditioned Jacobi-Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation

International Nuclear Information System (INIS)

Hwang, F-N; Wei, Z-H; Huang, T-M; Wang Weichung

2010-01-01

We develop a parallel Jacobi-Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi-Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc's efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schroedinger's equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi-Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0 GHz processors.

A multilevel in space and energy solver for multigroup diffusion eigenvalue problems

Directory of Open Access Journals (Sweden)

Ben C. Yee

2017-09-01

Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

Sensitivity and uncertainty analysis

CERN Document Server

Cacuci, Dan G; Navon, Ionel Michael

2005-01-01

As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable scientific tools. Sensitivity and Uncertainty Analysis. Volume I: Theory focused on the mathematical underpinnings of two important methods for such analyses: the Adjoint Sensitivity Analysis Procedure and the Global Adjoint Sensitivity Analysis Procedure. This volume concentrates on the practical aspects of performing these analyses for large-scale systems. The applications addressed include two-phase flow problems, a radiative c

Parallelization of mathematical library for generalized eigenvalue problem for real band matrices

International Nuclear Information System (INIS)

Tanaka, Yasuhisa.

1997-05-01

This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)

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

Science.gov (United States)

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.

Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Pengzhan Huang

2011-01-01

Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

AMDLIBF, IBM 360 Subroutine Library, Eigenvalues, Eigenvectors, Matrix Inversion

International Nuclear Information System (INIS)

Wang, Jesse Y.

1980-01-01

Description of problem or function: AMDLIBF is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne. This subset includes library category F: Identification/Description: F152S F SYMINV: Invert sym. matrices, solve lin. systems; F154S A DOTP: Double plus precision accum. inner prod.; F156S F RAYCOR: Rayleigh corrections for eigenvalues; F161S F XTRADP: A fast extended precision inner product; F162S A XTRADP: Inner product of two DP real vectors; F202S F1 EIGEN: Eigen-system for real symmetric matrix; F203S F: Driver for F202S; F248S F RITZIT: Largest eigenvalue and vec. real sym. matrix; F261S F EIGINV: Inverse eigenvalue problem; F313S F CQZHES: Reduce cmplx matrices to upper Hess and tri; F314S F CQZVAL: Reduce complex matrix to upper Hess. form; F315S F CQZVEC: Eigenvectors of cmplx upper triang. syst.; F316S F CGG: Driver for complex general Eigen-problem; F402S F MATINV: Matrix inversion and sol. of linear eqns.; F403S F: Driver for F402S; F452S F CHOLLU,CHOLEQ: Sym. decomp. of pos. def. band matrices; F453S F MATINC: Inversion of complex matrices; F454S F CROUT: Solution of simultaneous linear equations; F455S F CROUTC: Sol. of simultaneous complex linear eqns.; F456S F1 DIAG: Integer preserving Gaussian elimination

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

International Nuclear Information System (INIS)

Levashov, V. A.

2016-01-01

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ 1 ≥ λ 2 ≥ λ 3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ 2 /λ 1 ) and (λ 3 /λ 2 ) are essentially identical to each other in the liquids state. We also found that λ 2 tends to be equal to the geometric average of λ 1 and λ 3 . In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.

Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors

Energy Technology Data Exchange (ETDEWEB)

Levashov, V. A. [Technological Design Institute of Scientific Instrument Engineering, Novosibirsk 630058 (Russian Federation)

2016-03-07

It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids’ structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic stress tensors. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant stress correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor are positive and they can be ordered: λ{sub 1} ≥ λ{sub 2} ≥ λ{sub 3} ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ{sub 2}/λ{sub 1}) and (λ{sub 3}/λ{sub 2}) are essentially identical to each other in the liquids state. We also found that λ{sub 2} tends to be equal to the geometric average of λ{sub 1} and λ{sub 3}. In our view, correlations between the eigenvalues may represent “the Poisson ratio effect” at the atomic scale.

New algorithms for the symmetric tridiagonal eigenvalue computation

Energy Technology Data Exchange (ETDEWEB)

Pan, V. [City Univ. of New York, Bronx, NY (United States)]|[International Computer Sciences Institute, Berkeley, CA (United States)

1994-12-31

The author presents new algorithms that accelerate the bisection method for the symmetric eigenvalue problem. The algorithms rely on some new techniques, which include acceleration of Newton`s iteration and can also be further applied to acceleration of some other iterative processes, in particular, of iterative algorithms for approximating polynomial zeros.

Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2

Energy Technology Data Exchange (ETDEWEB)

Khalil, Sh M [Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, Atomic Energy Authority, Cairo, (Egypt)

1996-03-01

Relaxed (force-free) toroidal plasmas described by the equations cur 1 B={mu}B, and grad {mu}=O (B is the magnetic field) induces interest in nuclear fusion. Its solution is perceived to describe the gross of the reversed field pinch (RFP), spheromak configuration, current limitation in toroidal plasmas, and others. The parameter {mu} plays an important roll in relaxed states. It cannot exceed the smallest eigenvalue {mu} (min), and that for a toroidal discharge there is a maximum toroidal current which is connected to this value. The values of{mu} were calculated numerically, using the methods of collocation points, for toroids of arbitrary aspect ratio {alpha} ({alpha} = R/a, ratio of major/minor radii of tokamak) and arbitrary curved cross-sections (circle, ellipse, cassini, and D-shaped). The aim of present work is to prove the applicability of the numerical methods for calculating the eigenvalues for toroidal plasmas having sharp edged cross sections and arbitrary aspect ratio. The lowest eigenvalue {mu} (min), satisfy the boundary condition {beta} .n = O (or RB. = O) for which the toroidal flux are calculated. These are the zero field eigenvalues of the equation cur 1 b={mu}B. The poloidal magnetic field lines corresponding to different cross sections are shown by plotting the boundary condition B.n=O. The plots showed good fulfillment of the boundary condition along the whole boundaries of different cross sections. Dependence of eigenvalues {mu}a on aspect ratio {alpha} is also obtained. Several runs of the programme with various wave numbers K showed that {mu}a is very insensitive to the choice of K. 8 figs.

A new formulation for the eigenvalue and the eigenfunction in the perturbation theory

International Nuclear Information System (INIS)

Korek, Mahmoud

1999-01-01

Full text.In infrared transitions, the problem of the ro vibrational eigenvalue and eigenfunction of a diatomic molecule is considered. It is shown that, for the transitions vJ↔v'J' the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E vm =Σ i=o e v (i) m i , Ψ vm =Σ i=0 φ v (i) m i and E v'm =Σ i=0 e v' (i) m i , Ψ v'm =Σ i=0 φ v' (i) m i , where m=[J'(J'+1)-J(J+1)]/2, and the coefficients e v (i) , φ v (i) , e v (i) , and φ v (i) , are given by analytical expressions. This m-representation of the eigenvalues and the eigenfunctions is more advantageous for the calculation of many factors in spectroscopy that are given in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients,...etc. The numerical application to the ground state of the molecule CO shows that the present formulation provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states

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

Science.gov (United States)

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.

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Institute of Scientific and Technical Information of China (English)

Tang Wen-Lin; Tian Gui-Hua

2011-01-01

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.

Algorithm 589. SICEDR: a FORTRAN subroutine for improving the accuracy of computed matrix eigenvalues

International Nuclear Information System (INIS)

Dongarra, J.J.

1982-01-01

SICEDR is a FORTRAN subroutine for improving the accuracy of a computed real eigenvalue and improving or computing the associated eigenvector. It is first used to generate information during the determination of the eigenvalues by the Schur decomposition technique. In particular, the Schur decomposition technique results in an orthogonal matrix Q and an upper quasi-triangular matrix T, such that A = QTQ/sup T/. Matrices A, Q, and T and the approximate eigenvalue, say lambda, are then used in the improvement phase. SICEDR uses an iterative method similar to iterative improvement for linear systems to improve the accuracy of lambda and improve or compute the eigenvector x in O(n 2 ) work, where n is the order of the matrix A

Two new eigenvalue localization sets for tensors and theirs applications

Directory of Open Access Journals (Sweden)

Zhao Jianxing

2017-10-01

Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

Science.gov (United States)

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.

WHAT IF (Sensitivity Analysis

Directory of Open Access Journals (Sweden)

Iulian N. BUJOREANU

2011-01-01

Full Text Available Sensitivity analysis represents such a well known and deeply analyzed subject that anyone to enter the field feels like not being able to add anything new. Still, there are so many facets to be taken into consideration.The paper introduces the reader to the various ways sensitivity analysis is implemented and the reasons for which it has to be implemented in most analyses in the decision making processes. Risk analysis is of outmost importance in dealing with resource allocation and is presented at the beginning of the paper as the initial cause to implement sensitivity analysis. Different views and approaches are added during the discussion about sensitivity analysis so that the reader develops an as thoroughly as possible opinion on the use and UTILITY of the sensitivity analysis. Finally, a round-up conclusion brings us to the question of the possibility of generating the future and analyzing it before it unfolds so that, when it happens it brings less uncertainty.

The solution of a chiral random matrix model with complex eigenvalues

International Nuclear Information System (INIS)

Akemann, G

2003-01-01

We describe in detail the solution of the extension of the chiral Gaussian unitary ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. We briefly discuss applications to the Dirac operator eigenvalue spectrum in quantum chromodynamics with non-vanishing chemical potential. This is an extended version of hep-th/0204068

The cosmological constant as an eigenvalue of the Hamiltonian constraint in a varying speed of light theory

Energy Technology Data Exchange (ETDEWEB)

Garattini, Remo [Univ. degli Studi di Bergamo, Dalmine (Italy). Dept. of Engineering and Applied Sciences; I.N.F.N., Sezione di Milano, Milan (Italy); De Laurentis, Mariafelicia [Tomsk State Pedagogical Univ. (Russian Federation). Dept. of Theoretical Physics; INFN, Sezione di Napoli (Italy); Complutense Univ. di Monte S. Angelo, Napoli (Italy)

2017-01-15

In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler-DeWitt equation for the Friedmann-Lemaitre-Robertson-Walker metric is completely equivalent to a Sturm-Liouville problem provided that the related eigenvalue and the cosmological constant be identified. The explicit calculation is performed with the help of a variational procedure with trial wave functionals related to the Bessel function of the second kind K{sub ν}(x). After having verified that in ordinary General Relativity no eigenvalue appears, we find that in a Varying Speed of Light theory this is not the case. Nevertheless, instead of a single eigenvalue, we discover the existence of a family of eigenvalues associated to a negative power of the scale. A brief comment on what happens at the inflationary scale is also included. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

A Universal Quantum Circuit Scheme For Finding Complex Eigenvalues

OpenAIRE

Daskin, Anmer; Grama, Ananth; Kais, Sabre

2013-01-01

We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of resonance states for quantum systems.

Sensitivity and uncertainty analysis for UO2 and MOX fueled PWR cells

International Nuclear Information System (INIS)

Foad, Basma; Takeda, Toshikazu

2015-01-01

Highlights: • A method for calculating sensitivity coefficients has been improved. • The IR approximation was used in order to get accurate results. • Sensitivities and uncertainties are calculated using the improved method. • The method is applied for UO 2 and MOX fueled PWR cells. • The verification was performed by comparing our results with MCNP6 and TSUNAMI-1D. - Abstract: This paper discusses the improvement of a method for calculating sensitivity coefficients of neutronics parameters relative to infinite dilution cross-sections because the conventional method neglects resonance self-shielding effect. In this study, the self-shielding effect is taken into account by using the intermediate resonance approximation in order to get accurate results in both high and low energy groups. The improved method is applied to calculate sensitivity coefficients and uncertainties of eigenvalue responses for UO 2 and MOX (ThO 2 –UO 2 and PuO 2 –UO 2 ) fueled pressurized water reactor cells. The verification of the improved method was performed by comparing the sensitivities with MCNP6 and TSUNAMI-1D. For uncertainty, calculation comparisons were done with TSUNAMI-1D, and we demonstrate that the differences are caused by the use of different covariance matrices

Eigenvalue estimates of positive integral operators with analytic ...

Indian Academy of Sciences (India)

Eigenvalue estimates of positive integral operators. 337 will be used to denote, respectively, the complex line integral of f along γ and the integral of f with respect to arc-length measure. In the first case we assume γ has an orientation. The notation Lp(γ ) will denote the Lp space of normalized arc length measure on γ with.

Escape rate from strange sets as an eigenvalue

International Nuclear Information System (INIS)

Tel, T.

1986-06-01

A new method is applied for calculating the escape rate from chaotic repellers or semi-attractors, based on the eigenvalue problem of the master equation of discrete dynamical systems. The corresponding eigenfunction is found to be smooth along unstable directions and to be, in general, a fractal measure. Examples of one and two dimensional maps are investigated. (author)

Random matrices, Frobenius eigenvalues, and monodromy

CERN Document Server

Katz, Nicholas M

1998-01-01

The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit

Maximal imaginery eigenvalues in optimal systems

Directory of Open Access Journals (Sweden)

David Di Ruscio

1991-07-01

Full Text Available In this note we present equations that uniquely determine the maximum possible imaginary value of the closed loop eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen, provided a real symmetric solution of the algebraic Riccati equation exists. In addition, the corresponding state weight matrix and the solution to the algebraic Riccati equation are derived for a class of linear systems. A fundamental lemma for the existence of a real symmetric solution to the algebraic Riccati equation is derived for this class of linear systems.

New approach to calculate bound state eigenvalues

International Nuclear Information System (INIS)

Gerck, E.; Gallas, J.A.C.

1983-01-01

A method of solving the radial Schrodinger equation for bound states is discussed. The method is based on a new piecewise representation of the second derivative operator on a set of functions that obey the boundary conditions. This representation is trivially diagonalised and leads to closed form expressions of the type E sub(n)=E(ab+b+c/n+...) for the eigenvalues. Examples are given for the power-law and logarithmic potentials. (Author) [pt

Eigenvalue estimates for submanifolds with bounded f-mean curvature

Indian Academy of Sciences (India)

GUANGYUE HUANG

1College of Mathematics and Information Science, Henan Normal University,. Xinxiang 453007 ... submanifolds in a hyperbolic space with the norm of their mean curvature vector bounded above by a constant. ..... [2] Batista M, Cavalcante M P and Pyo J, Some isoperimetric inequalities and eigenvalue estimates in ...

Genetic Algorithm Applied to the Eigenvalue Equalization Filtered-x LMS Algorithm (EE-FXLMS

Directory of Open Access Journals (Sweden)

Stephan P. Lovstedt

2008-01-01

Full Text Available The FXLMS algorithm, used extensively in active noise control (ANC, exhibits frequency-dependent convergence behavior. This leads to degraded performance for time-varying tonal noise and noise with multiple stationary tones. Previous work by the authors proposed the eigenvalue equalization filtered-x least mean squares (EE-FXLMS algorithm. For that algorithm, magnitude coefficients of the secondary path transfer function are modified to decrease variation in the eigenvalues of the filtered-x autocorrelation matrix, while preserving the phase, giving faster convergence and increasing overall attenuation. This paper revisits the EE-FXLMS algorithm, using a genetic algorithm to find magnitude coefficients that give the least variation in eigenvalues. This method overcomes some of the problems with implementing the EE-FXLMS algorithm arising from finite resolution of sampled systems. Experimental control results using the original secondary path model, and a modified secondary path model for both the previous implementation of EE-FXLMS and the genetic algorithm implementation are compared.

On the calculation of the eigenvalues of the Faddeev equation kernel on the nonphysical sheet of energy

International Nuclear Information System (INIS)

Moeller, K.

1978-01-01

A system of three particles is considered which interacts by rank-1 separable potential. For the Faddeev equation kernel of this system a method is proposed for calculating the eigenvalues on the nonphysical sheet of the three-particle cms-energy. From the consideration of the analytical structure of the eigenvalues in the energy plane it follows that the analytical continuations of the eigenvalues from the physical to the nonphysical region are different above and below the three-particle threshold. In this paper the continuation below the threshold is discussed. (author)

Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

Directory of Open Access Journals (Sweden)

Winfried Auzinger

2006-01-01

Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

A method for eigenvalues of sparse lambda-matrices

International Nuclear Information System (INIS)

Yang, W.H.

1982-01-01

The matrix N(lambda) whose elements are functions of a parameter lambda is called the lambda-matrix. Those values of lambda that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a lambda-matrix is presented. A simple explicit convergence criterion is given as well as the algorithm and two numerical examples

Fundaments of transport equation splitting and the eigenvalue problem

International Nuclear Information System (INIS)

Stancic, V.

2000-01-01

In order to remove some singularities concerning the boundary conditions of one dimensional transport equation, a split form of transport equation describing the forward i.e. μ≥0, and a backward μ<0 directed neutrons is being proposed here. The eigenvalue problem has also been considered here (author)

Elementary Baecklund transformations for a discrete Ablowitz-Ladik eigenvalue problem

International Nuclear Information System (INIS)

Rourke, David E

2004-01-01

Elementary Baecklund transformations (BTs) are described for a discretization of the Zakharov-Shabat eigenvalue problem (a special case of the Ablowitz-Ladik eigenvalue problem). Elementary BTs allow the process of adding bound states to a system (i.e., the add-one-soliton BT) to be 'factorized' to solving two simpler sub-problems. They are used to determine the effect on the scattering data when bound states are added. They are shown to provide a method of calculating discrete solitons-this is achieved by constructing a lattice of intermediate potentials, with the parameters used in the calculation of the lattice simply related to the soliton scattering data. When the potentials, S n , T n , in the system are related by S n = -T n , they enable simple derivations to be obtained of the add-one-soliton BT and the nonlinear superposition formula

Sensitivity functions for uncertainty analysis: Sensitivity and uncertainty analysis of reactor performance parameters

International Nuclear Information System (INIS)

Greenspan, E.

1982-01-01

This chapter presents the mathematical basis for sensitivity functions, discusses their physical meaning and information they contain, and clarifies a number of issues concerning their application, including the definition of group sensitivities, the selection of sensitivity functions to be included in the analysis, and limitations of sensitivity theory. Examines the theoretical foundation; criticality reset sensitivities; group sensitivities and uncertainties; selection of sensitivities included in the analysis; and other uses and limitations of sensitivity functions. Gives the theoretical formulation of sensitivity functions pertaining to ''as-built'' designs for performance parameters of the form of ratios of linear flux functionals (such as reaction-rate ratios), linear adjoint functionals, bilinear functions (such as reactivity worth ratios), and for reactor reactivity. Offers a consistent procedure for reducing energy-dependent or fine-group sensitivities and uncertainties to broad group sensitivities and uncertainties. Provides illustrations of sensitivity functions as well as references to available compilations of such functions and of total sensitivities. Indicates limitations of sensitivity theory originating from the fact that this theory is based on a first-order perturbation theory

Monotonicity of energy eigenvalues for Coulomb systems

International Nuclear Information System (INIS)

Englisch, R.

1983-01-01

Generalising results by earlier workers for a large class of Hamiltonians (among others, Hamiltonians of Coulomb systems) which can be written in the form H(α) = H 0 + αH' the present works shows that their eigenvalues decrease with increasing α. This result is applied to Coulomb systems in which the distances between the infinitely heavy particles are varying and also is used to obtain a completion and simplification of proof for the stability of the biexciton. (author)

Intergenerational Correlation in Monte Carlo k-Eigenvalue Calculation

International Nuclear Information System (INIS)

Ueki, Taro

2002-01-01

This paper investigates intergenerational correlation in the Monte Carlo k-eigenvalue calculation of a neutron effective multiplicative factor. To this end, the exponential transform for path stretching has been applied to large fissionable media with localized highly multiplying regions because in such media an exponentially decaying shape is a rough representation of the importance of source particles. The numerical results show that the difference between real and apparent variances virtually vanishes for an appropriate value of the exponential transform parameter. This indicates that the intergenerational correlation of k-eigenvalue samples could be eliminated by the adjoint biasing of particle transport. The relation between the biasing of particle transport and the intergenerational correlation is therefore investigated in the framework of collision estimators, and the following conclusion has been obtained: Within the leading order approximation with respect to the number of histories per generation, the intergenerational correlation vanishes when immediate importance is constant, and the immediate importance under simulation can be made constant by the biasing of particle transport with a function adjoint to the source neutron's distribution, i.e., the importance over all future generations

Solving eigenvalue problems on curved surfaces using the Closest Point Method

KAUST Repository

Macdonald, Colin B.

2011-06-01

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.

On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems

Directory of Open Access Journals (Sweden)

El-Sayed M. E. Mostafa

2017-01-01

Full Text Available The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples.

Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

International Nuclear Information System (INIS)

Gene Golub; Kwok Ko

2009-01-01

The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.

p-Norm SDD tensors and eigenvalue localization

Directory of Open Access Journals (Sweden)

Qilong Liu

2016-07-01

Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.

Hardy inequality, compact embeddings and properties of certain eigenvalue problems

Czech Academy of Sciences Publication Activity Database

Drábek, P.; Kufner, Alois

2017-01-01

Roč. 49, č. 1 (2017), s. 5-17 ISSN 0049-4704 Institutional support: RVO:67985840 Keywords : BD-property * compact embeddings * degenerate and singular eigenvalue problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://www.openstarts.units.it/handle/10077/16201

CoMFA, CoMSIA and Eigenvalue Analysis on Dibenzodioxepinone and Dibenzodioxocinone Derivatives as Cholesteryl Ester Transfer Protein Inhibitors

Directory of Open Access Journals (Sweden)

Mao-sheng Cheng

2008-08-01

Full Text Available Abstract: CoMFA, CoMSIA and eigenvalue analysis (EVA were performed to study the structural features of 61 diverse dibenzodioxepinone and dibenzodioxocinone analogues to probe cholesteryl ester transfer protein (CETP inhibitory activity. Three methods yielded statistically significant models upon assessment of cross-validation, bootstrapping, and progressive scrambling. This was further validated by an external set of 13 derivatives. Our results demonstrate that three models have a good interpolation as well as extrapolation. The hydrophobic features were confirmed to contribute significantly to inhibitor potencies, while a pre-oriented hydrogen bond provided by the hydroxyl group at the 3-position indicated a good correlation with previous SAR, and a hydrogen bond acceptor may play a crucial role in CETP inhibition. These derived models may help us to gain a deeper understanding of the binding interaction of these lactone-based compounds and aid in the design of new potent compounds against CETP.

Sensitivity Analysis of Multidisciplinary Rotorcraft Simulations

Science.gov (United States)

Wang, Li; Diskin, Boris; Biedron, Robert T.; Nielsen, Eric J.; Bauchau, Olivier A.

2017-01-01

A multidisciplinary sensitivity analysis of rotorcraft simulations involving tightly coupled high-fidelity computational fluid dynamics and comprehensive analysis solvers is presented and evaluated. An unstructured sensitivity-enabled Navier-Stokes solver, FUN3D, and a nonlinear flexible multibody dynamics solver, DYMORE, are coupled to predict the aerodynamic loads and structural responses of helicopter rotor blades. A discretely-consistent adjoint-based sensitivity analysis available in FUN3D provides sensitivities arising from unsteady turbulent flows and unstructured dynamic overset meshes, while a complex-variable approach is used to compute DYMORE structural sensitivities with respect to aerodynamic loads. The multidisciplinary sensitivity analysis is conducted through integrating the sensitivity components from each discipline of the coupled system. Numerical results verify accuracy of the FUN3D/DYMORE system by conducting simulations for a benchmark rotorcraft test model and comparing solutions with established analyses and experimental data. Complex-variable implementation of sensitivity analysis of DYMORE and the coupled FUN3D/DYMORE system is verified by comparing with real-valued analysis and sensitivities. Correctness of adjoint formulations for FUN3D/DYMORE interfaces is verified by comparing adjoint-based and complex-variable sensitivities. Finally, sensitivities of the lift and drag functions obtained by complex-variable FUN3D/DYMORE simulations are compared with sensitivities computed by the multidisciplinary sensitivity analysis, which couples adjoint-based flow and grid sensitivities of FUN3D and FUN3D/DYMORE interfaces with complex-variable sensitivities of DYMORE structural responses.

Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

Directory of Open Access Journals (Sweden)

Niufa Fang

2017-08-01

Full Text Available Abstract By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman’s results and the upper bound is stronger than Osserman’s results (Osserman in Proceedings of the International Congress of Mathematicians, Helsinki, 1978.

Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

Energy Technology Data Exchange (ETDEWEB)

Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

2014-12-15

In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

Solving the generalized symmetric eigenvalue problem using tile algorithms on multicore architectures

KAUST Repository

Ltaief, Hatem

2012-01-01

This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric eigenvalue problem by computing the Cholesky factorization of the right hand side symmetric definite positive matrix (first stage), and applying the inverse of the freshly computed triangular Cholesky factors to the original dense symmetric matrix of the problem (second stage). Calculating the eigenpairs of the resulting problem is then equivalent to the eigenpairs of the original problem. The computation proceeds by reducing the updated dense symmetric matrix to symmetric band form (third stage). The band structure is further reduced by applying a bulge chasing procedure, which annihilates the extra off-diagonal entries using orthogonal transformations (fourth stage). More details on the third and fourth stage can be found in Haidar et al. [Accepted at SC\\'11, November 2011]. The eigenvalues are then calculated from the tridiagonal form using the standard LAPACK QR algorithm (i.e., DTSEQR routine), while the complex and challenging eigenvector computations will be addressed in a companion paper. The tasks from the various stages can concurrently run in an out-of-order fashion. The data dependencies are cautiously tracked by the dynamic runtime system environment QUARK, which ensures the dependencies are not violated for numerical correctness purposes. The obtained tile four-stage generalized symmetric eigenvalue solver significantly outperforms the state-of-the-art numerical libraries (up to 21-fold speed up against multithreaded LAPACK with optimized multithreaded MKL BLAS and up to 4-fold speed up against the corresponding routine from the commercial numerical software Intel MKL) on four sockets twelve cores AMD system with a 24000×24000 matrix size. © 2012 The authors and IOS Press. All rights reserved.

Advanced Variance Reduction for Global k-Eigenvalue Simulations in MCNP

Energy Technology Data Exchange (ETDEWEB)

Edward W. Larsen

2008-06-01

The "criticality" or k-eigenvalue of a nuclear system determines whether the system is critical (k=1), or the extent to which it is subcritical (k<1) or supercritical (k>1). Calculations of k are frequently performed at nuclear facilities to determine the criticality of nuclear reactor cores, spent nuclear fuel storage casks, and other fissile systems. These calculations can be expensive, and current Monte Carlo methods have certain well-known deficiencies. In this project, we have developed and tested a new "functional Monte Carlo" (FMC) method that overcomes several of these deficiencies. The current state-of-the-art Monte Carlo k-eigenvalue method estimates the fission source for a sequence of fission generations (cycles), during each of which M particles per cycle are processed. After a series of "inactive" cycles during which the fission source "converges," a series of "active" cycles are performed. For each active cycle, the eigenvalue and eigenfunction are estimated; after N >> 1 active cycles are performed, the results are averaged to obtain estimates of the eigenvalue and eigenfunction and their standard deviations. This method has several disadvantages: (i) the estimate of k depends on the number M of particles per cycle, (iii) for optically thick systems, the eigenfunction estimate may not converge due to undersampling of the fission source, and (iii) since the fission source in any cycle depends on the estimated fission source from the previous cycle (the fission sources in different cycles are correlated), the estimated variance in k is smaller than the real variance. For an acceptably large number M of particles per cycle, the estimate of k is nearly independent of M; this essentially takes care of item (i). Item (ii) can be addressed by taking M sufficiently large, but for optically thick systems a sufficiently large M can easily be unrealistic. Item (iii) cannot be accounted for by taking M or N sufficiently large; it is an inherent deficiency due

Ordering non-bipartite unicyclic graphs with pendant vertices by the least Q-eigenvalue

Directory of Open Access Journals (Sweden)

Shu-Guang Guo

2016-05-01

Full Text Available Abstract A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Fan et al. (Discrete Math. 313:903-909, 2013 and Liu et al. (Electron. J. Linear Algebra 26:333-344, 2013 determined, independently, the unique unicyclic graph whose least Q-eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with k pendant vertices. In this paper, we extend their results and determine the first three non-bipartite unicyclic graphs of order n with k pendant vertices ordering by least Q-eigenvalue.

Distribution of the Largest Eigenvalues of the Levi-Smirnov Ensemble

International Nuclear Information System (INIS)

Wieczorek, W.

2004-01-01

We calculate the distribution of the k-th largest eigenvalue in the random matrix Levi - Smirnov Ensemble (LSE), using the spectral dualism between LSE and chiral Gaussian Unitary Ensemble (GUE). Then we reconstruct universal spectral oscillations and we investigate an asymptotic behavior of the spectral distribution. (author)

Hopf bifurcation and eigenvalue sensitivity analysis of doubly fed induction generator wind turbine system

DEFF Research Database (Denmark)

Yang, Li Hui; Xu, Zhao; Østergaard, Jacob

2010-01-01

This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variabl...

Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry

International Nuclear Information System (INIS)

Anistratov, D. Y.; Gol'din, V. Y.

2009-01-01

A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

Science.gov (United States)

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.

Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

International Nuclear Information System (INIS)

Pato, Mauricio P; Oshanin, Gleb

2013-01-01

We study the probability distribution function P (β) n (w) of the Schmidt-like random variable w = x 2 1 /(∑ j=1 n x 2 j /n), where x j , (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 (β) (w)∼√((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. (paper)

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

International Nuclear Information System (INIS)

Beer, M.

1980-01-01

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 the 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

MIMO Channel Model with Propagation Mechanism and the Properties of Correlation and Eigenvalue in Mobile Environments

Directory of Open Access Journals (Sweden)

Yuuki Kanemiyo

2012-01-01

Full Text Available This paper described a spatial correlation and eigenvalue in a multiple-input multiple-output (MIMO channel. A MIMO channel model with a multipath propagation mechanism was proposed and showed the channel matrix. The spatial correlation coefficient formula −,′−′( between MIMO channel matrix elements was derived for the model and was expressed as a directive wave term added to the product of mobile site correlation −′( and base site correlation −′( without LOS path, which are calculated independently of each other. By using −,′−′(, it is possible to create the channel matrix element with a fixed correlation value estimated by −,′−′( for a given multipath condition and a given antenna configuration. Furthermore, the correlation and the channel matrix eigenvalue were simulated, and the simulated and theoretical correlation values agreed well. The simulated eigenvalue showed that the average of the first eigenvalue λ1 hardly depends on the correlation −,′−′(, but the others do depend on −,′−′( and approach 1 as −,′−′( decreases. Moreover, as the path moves into LOS, the 1 state with mobile movement becomes more stable than the 1 of NLOS path.

Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

OpenAIRE

Guliyev, Namig J.

2008-01-01

International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

Solving the generalized symmetric eigenvalue problem using tile algorithms on multicore architectures

KAUST Repository

Ltaief, Hatem; Luszczek, Piotr R.; Haidar, Azzam; Dongarra, Jack

2012-01-01

This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric

MOVES regional level sensitivity analysis

Science.gov (United States)

2012-01-01

The MOVES Regional Level Sensitivity Analysis was conducted to increase understanding of the operations of the MOVES Model in regional emissions analysis and to highlight the following: : the relative sensitivity of selected MOVES Model input paramet...

A new S-type eigenvalue inclusion set for tensors and its applications.

Science.gov (United States)

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).

Improved simple graphical solution for the eigenvalues of the finite square well potential

International Nuclear Information System (INIS)

Burge, E.J.

1985-01-01

The three principal graphical methods for obtaining the energy eigenvalues of the finite square well potential are presented. The forms of the wavefunctions within the well, and the corresponding linear probability densities, are derived directly from the method. A simple extension of the method allows the energy level spectrum to be obtained directly on a linear energy scale. The variations of the energy eigenvalues with well depth and width are separately and jointly displayed, and explicit corresponding functional relationships are derived. Two universal graphs are deduced which allow the rapid appreciation and calculation of the dependence of the energy levels on the depth and width of the well and on the mass of the particle. (author)

A Monte Carlo neutron transport code for eigenvalue calculations on a dual-GPU system and CUDA environment

Energy Technology Data Exchange (ETDEWEB)

Liu, T.; Ding, A.; Ji, W.; Xu, X. G. [Nuclear Engineering and Engineering Physics, Rensselaer Polytechnic Inst., Troy, NY 12180 (United States); Carothers, C. D. [Dept. of Computer Science, Rensselaer Polytechnic Inst. RPI (United States); Brown, F. B. [Los Alamos National Laboratory (LANL) (United States)

2012-07-01

Monte Carlo (MC) method is able to accurately calculate eigenvalues in reactor analysis. Its lengthy computation time can be reduced by general-purpose computing on Graphics Processing Units (GPU), one of the latest parallel computing techniques under development. The method of porting a regular transport code to GPU is usually very straightforward due to the 'embarrassingly parallel' nature of MC code. However, the situation becomes different for eigenvalue calculation in that it will be performed on a generation-by-generation basis and the thread coordination should be explicitly taken care of. This paper presents our effort to develop such a GPU-based MC code in Compute Unified Device Architecture (CUDA) environment. The code is able to perform eigenvalue calculation under simple geometries on a multi-GPU system. The specifics of algorithm design, including thread organization and memory management were described in detail. The original CPU version of the code was tested on an Intel Xeon X5660 2.8 GHz CPU, and the adapted GPU version was tested on NVIDIA Tesla M2090 GPUs. Double-precision floating point format was used throughout the calculation. The result showed that a speedup of 7.0 and 33.3 were obtained for a bare spherical core and a binary slab system respectively. The speedup factor was further increased by a factor of {approx}2 on a dual GPU system. The upper limit of device-level parallelism was analyzed, and a possible method to enhance the thread-level parallelism was proposed. (authors)

A Monte Carlo neutron transport code for eigenvalue calculations on a dual-GPU system and CUDA environment

International Nuclear Information System (INIS)

Liu, T.; Ding, A.; Ji, W.; Xu, X. G.; Carothers, C. D.; Brown, F. B.

2012-01-01

Monte Carlo (MC) method is able to accurately calculate eigenvalues in reactor analysis. Its lengthy computation time can be reduced by general-purpose computing on Graphics Processing Units (GPU), one of the latest parallel computing techniques under development. The method of porting a regular transport code to GPU is usually very straightforward due to the 'embarrassingly parallel' nature of MC code. However, the situation becomes different for eigenvalue calculation in that it will be performed on a generation-by-generation basis and the thread coordination should be explicitly taken care of. This paper presents our effort to develop such a GPU-based MC code in Compute Unified Device Architecture (CUDA) environment. The code is able to perform eigenvalue calculation under simple geometries on a multi-GPU system. The specifics of algorithm design, including thread organization and memory management were described in detail. The original CPU version of the code was tested on an Intel Xeon X5660 2.8 GHz CPU, and the adapted GPU version was tested on NVIDIA Tesla M2090 GPUs. Double-precision floating point format was used throughout the calculation. The result showed that a speedup of 7.0 and 33.3 were obtained for a bare spherical core and a binary slab system respectively. The speedup factor was further increased by a factor of ∼2 on a dual GPU system. The upper limit of device-level parallelism was analyzed, and a possible method to enhance the thread-level parallelism was proposed. (authors)

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

Science.gov (United States)

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.

Asymptotic eigenvalue estimates for a Robin problem with a large parameter

Czech Academy of Sciences Publication Activity Database

Exner, Pavel; Minakov, A.; Parnovski, L.

2014-01-01

Roč. 71, č. 2 (2014), s. 141-156 ISSN 0032-5155 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplacian * Robin problem * eigenvalue asymptotics Subject RIV: BE - Theoretical Physics Impact factor: 0.250, year: 2014

On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar N=4 SYM

Energy Technology Data Exchange (ETDEWEB)

Bondarenko, Sergey; Prygarin, Alex [Physics Department, Ariel University,Ariel 40700, territories administered by (Israel)

2016-07-15

We discuss a residual freedom of the next-to-leading BFKL eigenvalue that originates from ambiguity in redistributing the next-to-leading (NLO) corrections between the adjoint BFKL eigenvalue and eigenfunctions in planar N=4 super-Yang-Mills (SYM) Theory. In terms of the remainder function of the Bern-Dixon-Smirnov (BDS) amplitude this freedom is translated to reshuffling correction between the eigenvalue and the impact factors in the multi-Regge kinematics (MRK) in the next-to-leading logarithm approximation (NLA). We show that the modified NLO BFKL eigenvalue suggested by the authors in ref. http://arxiv.org/abs/1510.00589 can be introduced in the MRK expression for the remainder function by shifting the anomalous dimension in the impact factor in such a way that the two and three loop remainder function is left unchanged to the NLA accuracy.

Sensitivity analysis approaches applied to systems biology models.

Science.gov (United States)

Zi, Z

2011-11-01

With the rising application of systems biology, sensitivity analysis methods have been widely applied to study the biological systems, including metabolic networks, signalling pathways and genetic circuits. Sensitivity analysis can provide valuable insights about how robust the biological responses are with respect to the changes of biological parameters and which model inputs are the key factors that affect the model outputs. In addition, sensitivity analysis is valuable for guiding experimental analysis, model reduction and parameter estimation. Local and global sensitivity analysis approaches are the two types of sensitivity analysis that are commonly applied in systems biology. Local sensitivity analysis is a classic method that studies the impact of small perturbations on the model outputs. On the other hand, global sensitivity analysis approaches have been applied to understand how the model outputs are affected by large variations of the model input parameters. In this review, the author introduces the basic concepts of sensitivity analysis approaches applied to systems biology models. Moreover, the author discusses the advantages and disadvantages of different sensitivity analysis methods, how to choose a proper sensitivity analysis approach, the available sensitivity analysis tools for systems biology models and the caveats in the interpretation of sensitivity analysis results.

Sensitivity Analysis Without Assumptions.

Science.gov (United States)

Ding, Peng; VanderWeele, Tyler J

2016-05-01

Unmeasured confounding may undermine the validity of causal inference with observational studies. Sensitivity analysis provides an attractive way to partially circumvent this issue by assessing the potential influence of unmeasured confounding on causal conclusions. However, previous sensitivity analysis approaches often make strong and untestable assumptions such as having an unmeasured confounder that is binary, or having no interaction between the effects of the exposure and the confounder on the outcome, or having only one unmeasured confounder. Without imposing any assumptions on the unmeasured confounder or confounders, we derive a bounding factor and a sharp inequality such that the sensitivity analysis parameters must satisfy the inequality if an unmeasured confounder is to explain away the observed effect estimate or reduce it to a particular level. Our approach is easy to implement and involves only two sensitivity parameters. Surprisingly, our bounding factor, which makes no simplifying assumptions, is no more conservative than a number of previous sensitivity analysis techniques that do make assumptions. Our new bounding factor implies not only the traditional Cornfield conditions that both the relative risk of the exposure on the confounder and that of the confounder on the outcome must satisfy but also a high threshold that the maximum of these relative risks must satisfy. Furthermore, this new bounding factor can be viewed as a measure of the strength of confounding between the exposure and the outcome induced by a confounder.

Sensitivity analysis of critical experiment with direct perturbation compared to TSUNAMI-3D sensitivity analysis

International Nuclear Information System (INIS)

Barber, A. D.; Busch, R.

2009-01-01

The goal of this work is to obtain sensitivities from direct uncertainty analysis calculation and correlate those calculated values with the sensitivities produced from TSUNAMI-3D (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation in Three Dimensions). A full sensitivity analysis is performed on a critical experiment to determine the overall uncertainty of the experiment. Small perturbation calculations are performed for all known uncertainties to obtain the total uncertainty of the experiment. The results from a critical experiment are only known as well as the geometric and material properties. The goal of this relationship is to simplify the uncertainty quantification process in assessing a critical experiment, while still considering all of the important parameters. (authors)

Sensitivity analysis in multi-parameter probabilistic systems

International Nuclear Information System (INIS)

Walker, J.R.

1987-01-01

Probabilistic methods involving the use of multi-parameter Monte Carlo analysis can be applied to a wide range of engineering systems. The output from the Monte Carlo analysis is a probabilistic estimate of the system consequence, which can vary spatially and temporally. Sensitivity analysis aims to examine how the output consequence is influenced by the input parameter values. Sensitivity analysis provides the necessary information so that the engineering properties of the system can be optimized. This report details a package of sensitivity analysis techniques that together form an integrated methodology for the sensitivity analysis of probabilistic systems. The techniques have known confidence limits and can be applied to a wide range of engineering problems. The sensitivity analysis methodology is illustrated by performing the sensitivity analysis of the MCROC rock microcracking model

Global optimization and sensitivity analysis

International Nuclear Information System (INIS)

Cacuci, D.G.

1990-01-01

A new direction for the analysis of nonlinear models of nuclear systems is suggested to overcome fundamental limitations of sensitivity analysis and optimization methods currently prevalent in nuclear engineering usage. This direction is toward a global analysis of the behavior of the respective system as its design parameters are allowed to vary over their respective design ranges. Presented is a methodology for global analysis that unifies and extends the current scopes of sensitivity analysis and optimization by identifying all the critical points (maxima, minima) and solution bifurcation points together with corresponding sensitivities at any design point of interest. The potential applicability of this methodology is illustrated with test problems involving multiple critical points and bifurcations and comprising both equality and inequality constraints

The eigenvalue problem. Alpha, lambda and gamma modes and its applications

International Nuclear Information System (INIS)

Carreno, A.; Vidal-Ferrandiz, A.; Verdu, G.; Ginestar, D.

2017-01-01

Modal analysis has been efficiently used to study different problems in reactor physics. In this sense, several eigenvalue problems can be defined for neutron transport equation: the λ-modes, the γ-modes and the α-modes. However, for simplicity, the neutron diffusion equation is used as approximation of each one of these equations that they have been discretized by a high order finite elements. The obtained algebraic eigenproblems are large problems and have to be solved using iterative methods. In this work, we analyze two methods. The first one is the Krylov-Schur method and the second one is the modified block Newton method. The comparison of modes and the performance of these methods have been studied in two benchmark problems, a homogeneous 3D reactor and the 3D Langenbuch reactor. (author)

Numerical method for the eigenvalue problem and the singular equation by using the multi-grid method and application to ordinary differential equation

International Nuclear Information System (INIS)

Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.

1995-07-01

In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)

Schiffer's Conjecture, Interior Transmission Eigenvalues and Invisibility Cloaking: Singular Problem vs. Nonsingular Problem

OpenAIRE

Liu, Hongyu

2012-01-01

In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Institute of Scientific and Technical Information of China (English)

Tang Wen-Lin; Tian Gui-Hua

2011-01-01

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Imaginary eigenvalue solution in RPA and phase transition

International Nuclear Information System (INIS)

Yao Yujie; Jing Xiaogong; Zhao Guoquan; Wu Shishu

1993-01-01

The phase transition (PT) of a many-particle system with a close-shell configuration, the stability of the Hartree-Fock (HF) solution and the random phase approximation (RPA) are studied by means of a generalized three-level solvable model. The question whether the occurrence of an imaginary eigenvalue solution in RPA (OISA) may be considered as a signature of PT is explored in some detail. It is found that there is no close relation between OISA and PT. Generally, OISA shows that RPA becomes poor

Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

NARCIS (Netherlands)

Janssen, A.J.E.M.

1989-01-01

Asymptotic results for the Perron-Frobenius eigenvalue of a nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix tends to 8 are given. The results are used and interpreted in terms of source entropies in the case where the Hessenberg-Toeplitz matrix arises as the transition matrix

Chemical kinetic functional sensitivity analysis: Elementary sensitivities

International Nuclear Information System (INIS)

Demiralp, M.; Rabitz, H.

1981-01-01

Sensitivity analysis is considered for kinetics problems defined in the space--time domain. This extends an earlier temporal Green's function method to handle calculations of elementary functional sensitivities deltau/sub i//deltaα/sub j/ where u/sub i/ is the ith species concentration and α/sub j/ is the jth system parameter. The system parameters include rate constants, diffusion coefficients, initial conditions, boundary conditions, or any other well-defined variables in the kinetic equations. These parameters are generally considered to be functions of position and/or time. Derivation of the governing equations for the sensitivities and the Green's funciton are presented. The physical interpretation of the Green's function and sensitivities is given along with a discussion of the relation of this work to earlier research

Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix

CSIR Research Space (South Africa)

Vlok, JD

2012-08-14

Full Text Available offers largely simplified computation and provides statistics such as the mean value and region of support of the largest eigenvalue distribution. Numeric results from the literature are compared with the approximation and Monte Carlo simulation results...

Probabilistic sensitivity analysis of biochemical reaction systems.

Science.gov (United States)

Zhang, Hong-Xuan; Dempsey, William P; Goutsias, John

2009-09-07

Sensitivity analysis is an indispensable tool for studying the robustness and fragility properties of biochemical reaction systems as well as for designing optimal approaches for selective perturbation and intervention. Deterministic sensitivity analysis techniques, using derivatives of the system response, have been extensively used in the literature. However, these techniques suffer from several drawbacks, which must be carefully considered before using them in problems of systems biology. We develop here a probabilistic approach to sensitivity analysis of biochemical reaction systems. The proposed technique employs a biophysically derived model for parameter fluctuations and, by using a recently suggested variance-based approach to sensitivity analysis [Saltelli et al., Chem. Rev. (Washington, D.C.) 105, 2811 (2005)], it leads to a powerful sensitivity analysis methodology for biochemical reaction systems. The approach presented in this paper addresses many problems associated with derivative-based sensitivity analysis techniques. Most importantly, it produces thermodynamically consistent sensitivity analysis results, can easily accommodate appreciable parameter variations, and allows for systematic investigation of high-order interaction effects. By employing a computational model of the mitogen-activated protein kinase signaling cascade, we demonstrate that our approach is well suited for sensitivity analysis of biochemical reaction systems and can produce a wealth of information about the sensitivity properties of such systems. The price to be paid, however, is a substantial increase in computational complexity over derivative-based techniques, which must be effectively addressed in order to make the proposed approach to sensitivity analysis more practical.

Dependence of accuracy of ESPRIT estimates on signal eigenvalues: the case of a noisy sum of two real exponentials.

Science.gov (United States)

Alexandrov, Theodore; Golyandina, Nina; Timofeyev, Alexey

2009-02-26

This paper is devoted to estimation of parameters for a noisy sum of two real exponential functions. Singular Spectrum Analysis is used to extract the signal subspace and then the ESPRIT method exploiting signal subspace features is applied to obtain estimates of the desired exponential rates. Dependence of estimation quality on signal eigenvalues is investigated. The special design to test this relation is elaborated.

Sensitivity and Uncertainty Analysis of IAEA CRP HTGR Benchmark Using McCARD

International Nuclear Information System (INIS)

Jang, Sang Hoon; Shim, Hyung Jin

2016-01-01

The benchmark consists of 4 phases starting from the local standalone modeling (Phase I) to the safety calculation of coupled system with transient situation (Phase IV). As a preliminary study of UAM on HTGR, this paper covers the exercise 1 and 2 of Phase I which defines the unit cell and lattice geometry of MHTGR-350 (General Atomics). The objective of these exercises is to quantify the uncertainty of the multiplication factor induced by perturbing nuclear data as well as to analyze the specific features of HTGR such as double heterogeneity and self-shielding treatment. The uncertainty quantification of IAEA CRP HTGR UAM benchmarks were conducted using first-order AWP method in McCARD. Uncertainty of the multiplication factor was estimated only for the microscopic cross section perturbation. To reduce the computation time and memory shortage, recently implemented uncertainty analysis module in MC wielandt calculation was adjusted. The covariance data of cross section was generated by NJOY/ERRORR module with ENDF/B-VII.1. The numerical result was compared with evaluation result of DeCART/MUSAD code system developed by KAERI. IAEA CRP HTGR UAM benchmark problems were analyzed using McCARD. The numerical results were compared with Serpent for eigenvalue calculation and DeCART/MUSAD for S/U analysis. In eigenvalue calculation, inconsistencies were found in the result with ENDF/B-VII.1 cross section library and it was found to be the effect of thermal scattering data of graphite. As to S/U analysis, McCARD results matched well with DeCART/MUSAD, but showed some discrepancy in 238U capture regarding implicit uncertainty.

Eigenvalue inequalities for the Laplacian with mixed boundary conditions

Czech Academy of Sciences Publication Activity Database

Lotoreichik, Vladimir; Rohleder, J.

2017-01-01

Roč. 263, č. 1 (2017), s. 491-508 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

A hybrid approach for global sensitivity analysis

International Nuclear Information System (INIS)

Chakraborty, Souvik; Chowdhury, Rajib

2017-01-01

Distribution based sensitivity analysis (DSA) computes sensitivity of the input random variables with respect to the change in distribution of output response. Although DSA is widely appreciated as the best tool for sensitivity analysis, the computational issue associated with this method prohibits its use for complex structures involving costly finite element analysis. For addressing this issue, this paper presents a method that couples polynomial correlated function expansion (PCFE) with DSA. PCFE is a fully equivalent operational model which integrates the concepts of analysis of variance decomposition, extended bases and homotopy algorithm. By integrating PCFE into DSA, it is possible to considerably alleviate the computational burden. Three examples are presented to demonstrate the performance of the proposed approach for sensitivity analysis. For all the problems, proposed approach yields excellent results with significantly reduced computational effort. The results obtained, to some extent, indicate that proposed approach can be utilized for sensitivity analysis of large scale structures. - Highlights: • A hybrid approach for global sensitivity analysis is proposed. • Proposed approach integrates PCFE within distribution based sensitivity analysis. • Proposed approach is highly efficient.

Maternal sensitivity: a concept analysis.

Science.gov (United States)

Shin, Hyunjeong; Park, Young-Joo; Ryu, Hosihn; Seomun, Gyeong-Ae

2008-11-01

The aim of this paper is to report a concept analysis of maternal sensitivity. Maternal sensitivity is a broad concept encompassing a variety of interrelated affective and behavioural caregiving attributes. It is used interchangeably with the terms maternal responsiveness or maternal competency, with no consistency of use. There is a need to clarify the concept of maternal sensitivity for research and practice. A search was performed on the CINAHL and Ovid MEDLINE databases using 'maternal sensitivity', 'maternal responsiveness' and 'sensitive mothering' as key words. The searches yielded 54 records for the years 1981-2007. Rodgers' method of evolutionary concept analysis was used to analyse the material. Four critical attributes of maternal sensitivity were identified: (a) dynamic process involving maternal abilities; (b) reciprocal give-and-take with the infant; (c) contingency on the infant's behaviour and (d) quality of maternal behaviours. Maternal identity and infant's needs and cues are antecedents for these attributes. The consequences are infant's comfort, mother-infant attachment and infant development. In addition, three positive affecting factors (social support, maternal-foetal attachment and high self-esteem) and three negative affecting factors (maternal depression, maternal stress and maternal anxiety) were identified. A clear understanding of the concept of maternal sensitivity could be useful for developing ways to enhance maternal sensitivity and to maximize the developmental potential of infants. Knowledge of the attributes of maternal sensitivity identified in this concept analysis may be helpful for constructing measuring items or dimensions.

Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem

Energy Technology Data Exchange (ETDEWEB)

Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)

1996-12-31

The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.

Solution of the multigroup neutron diffusion Eigenvalue problem in slab geometry by modified power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática

2017-07-01

We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)

Fourier transform methods for calculating action variables and semiclassical eigenvalues for coupled oscillator systems

International Nuclear Information System (INIS)

Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.

1984-01-01

Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method

Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

Czech Academy of Sciences Publication Activity Database

Antunes, P. R. S.; Freitas, P.; Krejčiřík, David

2017-01-01

Roč. 10, č. 4 (2017), s. 357-379 ISSN 1864-8258 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Eigenvalue optimisation * Robin Laplacian * negative boundary parameter * Bareket's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.182, year: 2016

Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian

Science.gov (United States)

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.

Inversion for Eigenvalues and Modes Using Sierra-SD and ROL.

Energy Technology Data Exchange (ETDEWEB)

Walsh, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Aquino, Wilkins [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kouri, Drew Philip [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-12-01

In this report we formulate eigenvalue-based methods for model calibration using a PDE-constrained optimization framework. We derive the abstract optimization operators from first principles and implement these methods using Sierra-SD and the Rapid Optimization Library (ROL). To demon- strate this approach, we use experimental measurements and an inverse solution to compute the joint and elastic foam properties of a low-fidelity unit (LFU) model.

Overview of the ArbiTER edge plasma eigenvalue code

Science.gov (United States)

Baver, Derek; Myra, James; Umansky, Maxim

2011-10-01

The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

Spectral/spatial optical CDMA code based on Diagonal Eigenvalue Unity

Science.gov (United States)

Najjar, Monia; Jellali, Nabiha; Ferchichi, Moez; Rezig, Houria

2017-11-01

A new two dimensional Diagonal Eigenvalue Unity (2D-DEU) code is developed for the spectral⧹spatial optical code division multiple access (OCDMA) system. It has a lower cross correlation value compared to two dimensional diluted perfect difference (2D-DPD), two dimensional Extended Enhanced Double Weight (2D-Extended-EDW) codes. Also, for the same code length, the number of users can be generated by the 2D-DEU code is higher than that provided by the others codes. The Bit Error Rate (BER) numerical analysis is developed by considering the effects of shot noise, phase induced intensity noise (PIIN), and thermal noise. The main result shows that BER is strongly affected by PIIN for the higher source power. The 2D-DEU code performance is compared with 2D-DPD, 2D-Extended-EDW and two dimensional multi-diagonals (2D-MD) codes. This comparison proves that the proposed 2D-DEU system outperforms the related codes.

A Schur Method for Designing LQ-optimal Systems with Prescribed Eigenvalues

Directory of Open Access Journals (Sweden)

David Di Ruscio

1990-01-01

Full Text Available In this paper a new algorithm for solving the LQ-optimal pole placement problem is presented. The method studied is a variant of the classical eigenvector approach and instead uses a set of Schur vectors, thereby gaining substantial numerical advantages. An important task in this method is the LQ-optimal pole placement problem for a second order (sub system. The paper presents a detailed analytical solution to this problem. This part is not only important for solving the general n-dimensional problem but also provides an understanding of the behaviour of an optimal system: The paper shows that in some cases it is an infinite number; in others a finite number, and in still others, non state weighting matrices Q that give the system a set of prescribed eigenvalues. Equations are presented that uniquely determine these state weight matrices as a function of the new prescribed eigcnvalues. From this result we have been able to derive the maximum possible imaginary part of the eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen.

On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries

Czech Academy of Sciences Publication Activity Database

Dittrich, Jaroslav; Exner, Pavel; Kuhn, C.; Pankrashkin, K.

2016-01-01

Roč. 97, 1-2 (2016), s. 1-25 ISSN 0921-7134 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : singular Schrodinger operator * delta-interaction * strong coupling * eigenvalue Subject RIV: BE - Theoretical Physics Impact factor: 0.933, year: 2016

Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem

Science.gov (United States)

Lakshtanov, E.; Vainberg, B.

2013-10-01

The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).

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

Science.gov (United States)

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.

NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

International Nuclear Information System (INIS)

Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.

1994-06-01

NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation

Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

International Nuclear Information System (INIS)

Kramer, D.; Neugebauer, G.

1981-01-01

The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

Inequalities among partial traces of hermitian operators and partial sums of their eigenvalues

International Nuclear Information System (INIS)

Daboul, J.

1990-01-01

Two different proofs of the following inequality are given: Tr sup(k)(H):= sup(k)Σ sub(i=1) h sub(i) :sup(k)Σ sub(i=1)(X sub(i), Hx sub(i))≥ sup(k)Σ sub(i=1)E sub(i), for k = 1,-,N, where H is a Hermitian matrix, the {X sub(i), i = 1,2-,k } are any k orthonormal vectors and the e sub(i) are the eigenvalues of H, ordered according to increasing values. This result is a generalization of the well-known fact, that ground state of a Hamiltonian is given by its lowest eigenvalue, E sub(i). It can also be regarded as a generalization, for Hermitian operators, of the invariance of the trace under unitary transformation. A few consequences of the above result are also derived. (author)

Interference and Sensitivity Analysis.

Science.gov (United States)

VanderWeele, Tyler J; Tchetgen Tchetgen, Eric J; Halloran, M Elizabeth

2014-11-01

Causal inference with interference is a rapidly growing area. The literature has begun to relax the "no-interference" assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper we briefly review the literature on causal inference in the presence of interference when treatments have been randomized. We then consider settings in which causal effects in the presence of interference are not identified, either because randomization alone does not suffice for identification, or because treatment is not randomized and there may be unmeasured confounders of the treatment-outcome relationship. We develop sensitivity analysis techniques for these settings. We describe several sensitivity analysis techniques for the infectiousness effect which, in a vaccine trial, captures the effect of the vaccine of one person on protecting a second person from infection even if the first is infected. We also develop two sensitivity analysis techniques for causal effects in the presence of unmeasured confounding which generalize analogous techniques when interference is absent. These two techniques for unmeasured confounding are compared and contrasted.

Asymptotic Representation for the Eigenvalues of a Non-selfadjoint Operator Governing the Dynamics of an Energy Harvesting Model

Energy Technology Data Exchange (ETDEWEB)

Shubov, Marianna A., E-mail: marianna.shubov@gmail.com [University of New Hampshire, Department of Mathematics and Statistics (United States)

2016-06-15

We consider a well known model of a piezoelectric energy harvester. The harvester is designed as a beam with a piezoceramic layer attached to its top face (unimorph configuration). A pair of thin perfectly conductive electrodes is covering the top and the bottom faces of the piezoceramic layer. These electrodes are connected to a resistive load. The model is governed by a system consisting of two equations. The first of them is the equation of the Euler–Bernoulli model for the transverse vibrations of the beam and the second one represents the Kirchhoff’s law for the electric circuit. Both equations are coupled due to the direct and converse piezoelectric effects. The boundary conditions for the beam equations are of clamped-free type. We represent the system as a single operator evolution equation in a Hilbert space. The dynamics generator of this system is a non-selfadjoint operator with compact resolvent. Our main result is an explicit asymptotic formula for the eigenvalues of this generator, i.e., we perform the modal analysis for electrically loaded (not short-circuit) system. We show that the spectrum splits into an infinite sequence of stable eigenvalues that approaches a vertical line in the left half plane and possibly of a finite number of unstable eigenvalues. This paper is the first in a series of three works. In the second one we will prove that the generalized eigenvectors of the dynamics generator form a Riesz basis (and, moreover, a Bari basis) in the energy space. In the third paper we will apply the results of the first two to control problems for this model.

Asymptotic Representation for the Eigenvalues of a Non-selfadjoint Operator Governing the Dynamics of an Energy Harvesting Model

International Nuclear Information System (INIS)

Shubov, Marianna A.

2016-01-01

We consider a well known model of a piezoelectric energy harvester. The harvester is designed as a beam with a piezoceramic layer attached to its top face (unimorph configuration). A pair of thin perfectly conductive electrodes is covering the top and the bottom faces of the piezoceramic layer. These electrodes are connected to a resistive load. The model is governed by a system consisting of two equations. The first of them is the equation of the Euler–Bernoulli model for the transverse vibrations of the beam and the second one represents the Kirchhoff’s law for the electric circuit. Both equations are coupled due to the direct and converse piezoelectric effects. The boundary conditions for the beam equations are of clamped-free type. We represent the system as a single operator evolution equation in a Hilbert space. The dynamics generator of this system is a non-selfadjoint operator with compact resolvent. Our main result is an explicit asymptotic formula for the eigenvalues of this generator, i.e., we perform the modal analysis for electrically loaded (not short-circuit) system. We show that the spectrum splits into an infinite sequence of stable eigenvalues that approaches a vertical line in the left half plane and possibly of a finite number of unstable eigenvalues. This paper is the first in a series of three works. In the second one we will prove that the generalized eigenvectors of the dynamics generator form a Riesz basis (and, moreover, a Bari basis) in the energy space. In the third paper we will apply the results of the first two to control problems for this model.

On the numerical solution of coupled eigenvalue differential equations arising in molecular spectroscopy

International Nuclear Information System (INIS)

Friedman, R.S.; Jamieson, M.J.; Preston, S.C.

1990-01-01

A method for solving coupled eigenvalue differential equations is given and its relation to an existing technique is shown. Use of the Gram-Schmidt process to overcome the severe instabilities arising in molecular problems is described in detail. (orig.)

Some remarks on the optimization of eigenvalue problems involving the p-Laplacian

Directory of Open Access Journals (Sweden)

Wacław Pielichowski

2008-01-01

Full Text Available Given a bounded domain \\(\\Omega \\subset \\mathbb{R}^n\\, numbers \\(p \\gt 1\\, \\(\\alpha \\geq 0\\ and \\(A \\in [0,|\\Omega |]\\, consider the optimization problem: find a subset \\(D \\subset \\Omega \\, of measure \\(A\\, for which the first eigenvalue of the operator \\(u\\mapsto -\\text{div} (|\

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

On the number of negative eigenvalues of the Laplacian on a metric graph

International Nuclear Information System (INIS)

Behrndt, Jussi; Luger, Annemarie

2010-01-01

The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).

On the number of negative eigenvalues of the Laplacian on a metric graph

Energy Technology Data Exchange (ETDEWEB)

Behrndt, Jussi [Institut fuer Mathematik, MA 6-4, Technische Universitaet Berlin, Strasse des 17. Juni 136, 10623 Berlin (Germany); Luger, Annemarie, E-mail: behrndt@math.tu-berlin.d, E-mail: luger@maths.lth.s [Center for Mathematical Sciences, Lund Institute of Technology/Lund University, Box 118, SE-221 00 Lund (Sweden)

2010-11-26

The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).

An algebraic sub-structuring method for large-scale eigenvalue calculation

International Nuclear Information System (INIS)

Yang, C.; Gao, W.; Bai, Z.; Li, X.; Lee, L.; Husbands, P.; Ng, E.

2004-01-01

We examine sub-structuring methods for solving large-scale generalized eigenvalue problems from a purely algebraic point of view. We use the term 'algebraic sub-structuring' to refer to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to provide approximate solutions to the original problem. We are interested in the question of which spectral components one should extract from each sub-structure in order to produce an approximate solution to the original problem with a desired level of accuracy. Error estimate for the approximation to the smallest eigenpair is developed. The estimate leads to a simple heuristic for choosing spectral components (modes) from each sub-structure. The effectiveness of such a heuristic is demonstrated with numerical examples. We show that algebraic sub-structuring can be effectively used to solve a generalized eigenvalue problem arising from the simulation of an accelerator structure. One interesting characteristic of this application is that the stiffness matrix produced by a hierarchical vector finite elements scheme contains a null space of large dimension. We present an efficient scheme to deflate this null space in the algebraic sub-structuring process

Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

International Nuclear Information System (INIS)

Wei, J.; Yang, S.

2013-01-01

In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues

Directory of Open Access Journals (Sweden)

Vladimir Kozlov

2006-01-01

Full Text Available We consider eigenvalues of elliptic boundary value problems, written in variational form, when the leading coefficients are perturbed by terms which are small in some integral sense. We obtain asymptotic formulae. The main specific of these formulae is that the leading term is different from that in the corresponding formulae when the perturbation is small in L∞-norm.

Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications

Directory of Open Access Journals (Sweden)

Ruyun Ma

2018-01-01

Full Text Available Let T>2 be an integer and T={1,2,…,T}. We show the existence of the principal eigenvalues of linear periodic eigenvalue problem -Δ2u(j-1+q(ju(j=λg(ju(j,  j∈T, u(0=u(T,  u(1=u(T+1, and we determine the sign of the corresponding eigenfunctions, where λ is a parameter, q(j≥0 and q(j≢0 in T, and the weight function g changes its sign in T. As an application of our spectrum results, we use the global bifurcation theory to study the existence of positive solutions for the corresponding nonlinear problem.

On Polya's inequality for torsional rigidity and first Dirichlet eigenvalue

OpenAIRE

Berg, M. van den; Ferone, V.; Nitsch, C.; Trombetti, C.

2016-01-01

Let $\\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\\Omega|$. We obtain some properties of the set function $F:\\Omega\\mapsto \\R^+$ defined by $$ F(\\Omega)=\\frac{T(\\Omega)\\lambda_1(\\Omega)}{|\\Omega|} ,$$ where $T(\\Omega)$ and $\\lambda_1(\\Omega)$ are the torsional rigidity and the first eigenvalue of the Dirichlet Laplacian respectively. We improve the classical P\\'olya bound $F(\\Omega)\\le 1,$ and show that $$F(\\Omega)\\le 1- \

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

Directory of Open Access Journals (Sweden)

Fatemeh Mohammad

2014-05-01

Full Text Available In this paper‎, ‎we represent an inexact inverse‎ ‎subspace iteration method for computing a few eigenpairs of the‎ ‎generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang‎, ‎Inexact inverse subspace iteration for generalized eigenvalue‎ ‎problems‎, ‎Linear Algebra and its Application‎, ‎434 (2011 1697-1715‎‎]‎. ‎In particular‎, ‎the linear convergence property of the inverse‎ ‎subspace iteration is preserved‎.

Contributions to sensitivity analysis and generalized discriminant analysis

International Nuclear Information System (INIS)

Jacques, J.

2005-12-01

Two topics are studied in this thesis: sensitivity analysis and generalized discriminant analysis. Global sensitivity analysis of a mathematical model studies how the output variables of this last react to variations of its inputs. The methods based on the study of the variance quantify the part of variance of the response of the model due to each input variable and each subset of input variables. The first subject of this thesis is the impact of a model uncertainty on results of a sensitivity analysis. Two particular forms of uncertainty are studied: that due to a change of the model of reference, and that due to the use of a simplified model with the place of the model of reference. A second problem was studied during this thesis, that of models with correlated inputs. Indeed, classical sensitivity indices not having significance (from an interpretation point of view) in the presence of correlation of the inputs, we propose a multidimensional approach consisting in expressing the sensitivity of the output of the model to groups of correlated variables. Applications in the field of nuclear engineering illustrate this work. Generalized discriminant analysis consists in classifying the individuals of a test sample in groups, by using information contained in a training sample, when these two samples do not come from the same population. This work extends existing methods in a Gaussian context to the case of binary data. An application in public health illustrates the utility of generalized discrimination models thus defined. (author)

Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

OpenAIRE

Akemann, G; Bittner, E; Lombardo, M; Markum, H; Pullirsch, R

2004-01-01

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis.

Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

International Nuclear Information System (INIS)

Akemann, Gernot; Bittner, Elmar; Lombardo, Maria-Paola; Markum, Harald; Pullirsch, Rainer

2005-01-01

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis

Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

DEFF Research Database (Denmark)

Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno

2001-01-01

The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...

Coarse-mesh rebalancing acceleration for eigenvalue problems

International Nuclear Information System (INIS)

Asaoka, T.; Nakahara, Y.; Miyasaka, S.

1974-01-01

The coarse-mesh rebalance method is adopted for Monte Carlo schemes for aiming at accelerating the convergence of a source iteration process. At every completion of the Monte Carlo game for one batch of neutron histories, the scaling factor for the neutron flux is calculated to achieve the neutron balance in each coarse-mesh zone into which the total system is divided. This rebalance factor is multiplied to the weight of each fission source neutron in the coarse-mesh zone for playing the next Monte Carlo game. The numerical examples have shown that the coarse-mesh rebalance Monte Carlo calculation gives a good estimate of the eigenvalue already after several batches with a negligible extra computer time compared to the standard Monte Carlo. 5 references. (U.S.)

Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type

Directory of Open Access Journals (Sweden)

Serguei I. Iakovlev

2013-01-01

Full Text Available It is shown that any \\(\\mu \\in \\mathbb{C}\\ is an infinite multiplicity eigenvalue of the Steklov smoothing operator \\(S_h\\ acting on the space \\(L^1_{loc}(\\mathbb{R}\\. For \\(\\mu \

Eigenvalues calculation algorithms for {lambda}-modes determination. Parallelization approach

Energy Technology Data Exchange (ETDEWEB)

Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Ginestart, D. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada

1997-03-01

In this paper, we review two methods to obtain the {lambda}-modes of a nuclear reactor, Subspace Iteration method and Arnoldi`s method, which are popular methods to solve the partial eigenvalue problem for a given matrix. In the developed application for the neutron diffusion equation we include improved acceleration techniques for both methods. Also, we propose two parallelization approaches for these methods, a coarse grain parallelization and a fine grain one. We have tested the developed algorithms with two realistic problems, focusing on the efficiency of the methods according to the CPU times. (author).

A comparison of the eigenvalue equations in kappa, α, lambda and γ in reactor theory. Application to fast and thermal systems in unreflected and reflected configurations

International Nuclear Information System (INIS)

Velarde, G.; Ahnert, C.; Aragones, J.M.

1977-01-01

A comparative study of the eigenvalue transport in kappa, lambda, γ and α is made. The neutronic fluxes obtained by solving the transport equation in the four eigenvalue types are compared numerically for fast and thermal systems in unreflected and reflected configurations. Important conclusions will be obtained about the appropiate use of each eigenvalue depending on the calculation type to be performed. (author)

Dimensionality of social networks using motifs and eigenvalues.

Directory of Open Access Journals (Sweden)

Anthony Bonato

Full Text Available We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.

Effect of continuous eigenvalue spectrum on plasma transport in toroidal systems

International Nuclear Information System (INIS)

Yamagishi, Tomejiro

1993-03-01

The effect of the continuous eigenvalue of the Vlasov equation on the cross field ion thermal flux is investigated. The continuum contribution due to the toroidal drift resonance is found to play an important role in ion transport particularly near the edge, which may apply to the interpretation of the sharp increase of ion heat conductivity near the periphery observed in large tokamaks. (author)

MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation

Energy Technology Data Exchange (ETDEWEB)

Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko

1997-10-01

A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)

Evaluation of upper and lower bounds to energy eigenvalues in Shoenberg's perturbation-theory ground state by means of partitioning technique

International Nuclear Information System (INIS)

Logrado, P.G.; Vianna, J.D.M.

Upper and lower bounds for the energy eigenvalues is Schoenberg's perturbation-theory ground state are studied. After a review of the characteristic features of the partitioning techniques the perturbative expansion proposed by Schoenberg is generated from an exact operator equation. The upper and lower bounds for the ground state eigenvalue are derived by using reaction and wave operators concepts, the bracketing function and operator inequalities. (Author) [pt

Fourth-order Perturbed Eigenvalue Equation for Stepwise Damage Detection of Aeroplane Wing

Directory of Open Access Journals (Sweden)

Wong Chun Nam

2016-01-01

Full Text Available Perturbed eigenvalue equations up to fourth-order are established to detect structural damage in aeroplane wing. Complete set of perturbation terms including orthogonal and non-orthogonal coefficients are computed using perturbed eigenvalue and orthonormal equations. Then the perturbed eigenparameters are optimized using BFGS approach. Finite element model with small to large stepwise damage is used to represent actual aeroplane wing. In small damaged level, termination number is the same for both approaches, while rms errors and termination d-norms are very close. For medium damaged level, termination number is larger for third-order perturbation with lower d-norm and smaller rms error. In large damaged level, termination number is much larger for third-order perturbation with same d-norm and larger rms error. These trends are more significant as the damaged level increases. As the stepwise damage effect increases with damage level, the increase in stepwise effect leads to the increase in model order. Hence, fourth-order perturbation is more accurate to estimate the model solution.

Object-sensitive Type Analysis of PHP

NARCIS (Netherlands)

Van der Hoek, Henk Erik; Hage, J

2015-01-01

In this paper we develop an object-sensitive type analysis for PHP, based on an extension of the notion of monotone frameworks to deal with the dynamic aspects of PHP, and following the framework of Smaragdakis et al. for object-sensitive analysis. We consider a number of instantiations of the

Heuristic geometric ''eigenvalue universality'' in a one-dimensional neutron transport problem with anisotropic scattering

International Nuclear Information System (INIS)

Goncalves, G.A.; Vilhena, M.T. de; Bodmann, B.E.J.

2010-01-01

In the present work we propose a heuristic construction of a transport equation for neutrons with anisotropic scattering considering only the radial cylinder dimension. The eigenvalues of the solutions of the equation correspond to the positive values for the one dimensional case. The central idea of the procedure is the application of the S N method for the discretisation of the angular variable followed by the application of the zero order Hankel transformation. The basis the construction of the scattering terms in form of an integro-differential equation for stationary transport resides in the hypothesis that the eigenvalues that compose the elementary solutions are independent of geometry for a homogeneous medium. We compare the solutions for the cartesian one dimensional problem for an infinite cylinder with azimuthal symmetry and linear anisotropic scattering for two cases. (orig.)

Three-dimensional multiple reciprocity boundary element method for one-group neutron diffusion eigenvalue computations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1996-01-01

The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)

Sensitivity analysis of the Galerkin finite element method neutron diffusion solver to the shape of the elements

Energy Technology Data Exchange (ETDEWEB)

Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

2017-02-15

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

The Second Eigenvalue of the p-Laplacian as p Goes to 1

Directory of Open Access Journals (Sweden)

Enea Parini

2010-01-01

Full Text Available The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1.

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

KAUST Repository

Raman, Aaswath

2010-02-26

We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

KAUST Repository

Raman, Aaswath; Fan, Shanhui

2010-01-01

We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

Ethical sensitivity in professional practice: concept analysis.

Science.gov (United States)

Weaver, Kathryn; Morse, Janice; Mitcham, Carl

2008-06-01

This paper is a report of a concept analysis of ethical sensitivity. Ethical sensitivity enables nurses and other professionals to respond morally to the suffering and vulnerability of those receiving professional care and services. Because of its significance to nursing and other professional practices, ethical sensitivity deserves more focused analysis. A criteria-based method oriented toward pragmatic utility guided the analysis of 200 papers and books from the fields of nursing, medicine, psychology, dentistry, clinical ethics, theology, education, law, accounting or business, journalism, philosophy, political and social sciences and women's studies. This literature spanned 1970 to 2006 and was sorted by discipline and concept dimensions and examined for concept structure and use across various contexts. The analysis was completed in September 2007. Ethical sensitivity in professional practice develops in contexts of uncertainty, client suffering and vulnerability, and through relationships characterized by receptivity, responsiveness and courage on the part of professionals. Essential attributes of ethical sensitivity are identified as moral perception, affectivity and dividing loyalties. Outcomes include integrity preserving decision-making, comfort and well-being, learning and professional transcendence. Our findings promote ethical sensitivity as a type of practical wisdom that pursues client comfort and professional satisfaction with care delivery. The analysis and resulting model offers an inclusive view of ethical sensitivity that addresses some of the limitations with prior conceptualizations.

A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

International Nuclear Information System (INIS)

Liu, T.; Du, X.; Ji, W.; Xu, G.; Brown, F.B.

2013-01-01

For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed. (authors)

A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

Science.gov (United States)

Liu, Tianyu; Du, Xining; Ji, Wei; Xu, X. George; Brown, Forrest B.

2014-06-01

For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed.

Multitarget global sensitivity analysis of n-butanol combustion.

Science.gov (United States)

Zhou, Dingyu D Y; Davis, Michael J; Skodje, Rex T

2013-05-02

A model for the combustion of butanol is studied using a recently developed theoretical method for the systematic improvement of the kinetic mechanism. The butanol mechanism includes 1446 reactions, and we demonstrate that it is straightforward and computationally feasible to implement a full global sensitivity analysis incorporating all the reactions. In addition, we extend our previous analysis of ignition-delay targets to include species targets. The combination of species and ignition targets leads to multitarget global sensitivity analysis, which allows for a more complete mechanism validation procedure than we previously implemented. The inclusion of species sensitivity analysis allows for a direct comparison between reaction pathway analysis and global sensitivity analysis.

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

Science.gov (United States)

2015-03-01

biometrics for physiological characteristics, hyperspectral remote sensing for detecting signals buried in noise and clutter, and medical genetics for...s); %approximate bounds on the eigenvalues used in Eq. (8) that are derived %from the Marcenko- Pastur law k=p./n; %band

Techniques for sensitivity analysis of SYVAC results

International Nuclear Information System (INIS)

Prust, J.O.

1985-05-01

Sensitivity analysis techniques may be required to examine the sensitivity of SYVAC model predictions to the input parameter values, the subjective probability distributions assigned to the input parameters and to the relationship between dose and the probability of fatal cancers plus serious hereditary disease in the first two generations of offspring of a member of the critical group. This report mainly considers techniques for determining the sensitivity of dose and risk to the variable input parameters. The performance of a sensitivity analysis technique may be improved by decomposing the model and data into subsets for analysis, making use of existing information on sensitivity and concentrating sampling in regions the parameter space that generates high doses or risks. A number of sensitivity analysis techniques are reviewed for their application to the SYVAC model including four techniques tested in an earlier study by CAP Scientific for the SYVAC project. This report recommends the development now of a method for evaluating the derivative of dose and parameter value and extending the Kruskal-Wallis technique to test for interactions between parameters. It is also recommended that the sensitivity of the output of each sub-model of SYVAC to input parameter values should be examined. (author)

Sensitivity analysis of a PWR pressurizer

International Nuclear Information System (INIS)

Bruel, Renata Nunes

1997-01-01

A sensitivity analysis relative to the parameters and modelling of the physical process in a PWR pressurizer has been performed. The sensitivity analysis was developed by implementing the key parameters and theoretical model lings which generated a comprehensive matrix of influences of each changes analysed. The major influences that have been observed were the flashing phenomenon and the steam condensation on the spray drops. The present analysis is also applicable to the several theoretical and experimental areas. (author)

An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group

International Nuclear Information System (INIS)

Wang, S.J.

1993-04-01

An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)

Perturbative stability of the approximate Killing field eigenvalue problem

International Nuclear Information System (INIS)

Beetle, Christopher; Wilder, Shawn

2014-01-01

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity. (paper)

A parallel algorithm for the non-symmetric eigenvalue problem

International Nuclear Information System (INIS)

Sidani, M.M.

1991-01-01

An algorithm is presented for the solution of the non-symmetric eigenvalue problem. The algorithm is based on a divide-and-conquer procedure that provides initial approximations to the eigenpairs, which are then refined using Newton iterations. Since the smaller subproblems can be solved independently, and since Newton iterations with different initial guesses can be started simultaneously, the algorithm - unlike the standard QR method - is ideal for parallel computers. The author also reports on his investigation of deflation methods designed to obtain further eigenpairs if needed. Numerical results from implementations on a host of parallel machines (distributed and shared-memory) are presented

Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

International Nuclear Information System (INIS)

Barucq, Helene; Bekkey, Chokri; Djellouli, Rabia

2004-01-01

We present a general procedure based on the pseudo-differential calculus for deriving artificial boundary conditions for an eigenvalue problem that characterizes the propagation of guided modes in optical waveguides. This new approach allows the construction of local conditions that (a) are independent of the frequency regime, (b) preserve the sparsity pattern of the finite element discretization, and (c) are applicable to arbitrarily shaped convex artificial boundaries. The last feature has the potential for reducing the size of the computational domain. Numerical results are presented to highlight the potential of conditions of order 1/2 and 1, for improving significantly the computational efficiency of finite element methods for the solution of optical waveguide problems

Correlation between eigenvalues and sorted diagonal matrix elements of a large dimensional matrix

International Nuclear Information System (INIS)

Arima, A.

2008-01-01

Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states. (author)

Sensitivity Analysis of a Physiochemical Interaction Model ...

African Journals Online (AJOL)

In this analysis, we will study the sensitivity analysis due to a variation of the initial condition and experimental time. These results which we have not seen elsewhere are analysed and discussed quantitatively. Keywords: Passivation Rate, Sensitivity Analysis, ODE23, ODE45 J. Appl. Sci. Environ. Manage. June, 2012, Vol.

Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer

International Nuclear Information System (INIS)

Molchanov, I.N.; Khimich, A.N.

1984-01-01

This article shows how a reflection method can be used to find the eigenvalues of a matrix by transforming the matrix to tridiagonal form. The method of conjugate gradients is used to find the smallest eigenvalue and the corresponding eigenvector of symmetric positive-definite band matrices. Topics considered include the computational scheme of the reflection method, the organization of parallel calculations by the reflection method, the computational scheme of the conjugate gradient method, the organization of parallel calculations by the conjugate gradient method, and the effectiveness of parallel algorithms. It is concluded that it is possible to increase the overall effectiveness of the multiprocessor electronic computers by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information

Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

International Nuclear Information System (INIS)

Macfarlane, A J; Pfeiffer, Hendryk

2003-01-01

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is now well known for powers up to four. The paper describes an extension of this uniformity for the totally antisymmetrized nth powers up to n = 9, identifying families of representations with integer eigenvalues 5, ..., 9 for the quadratic Casimir operator, in each case providing a formula for the dimensions of the representations in the family as a function of D = dim g. This generalizes previous results for powers j and Casimir eigenvalues j, j ≤ 4. Many intriguing, perhaps puzzling, features of the dimension formulae are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered

The discontinuous finite element method for solving Eigenvalue problems of transport equations

International Nuclear Information System (INIS)

Yang, Shulin; Wang, Ruihong

2011-01-01

In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

Eigenvalue condition for the Weinberg angle and possible new leptons and quarks

International Nuclear Information System (INIS)

Ma, E.

1977-01-01

In a given SU(2) x U(1) gauge model of the weak and electro-magnetic interactions, if one assumes that an eigenvalue condition exists for the mixing (Weinberg) angle, then its value can be computed in lower-order perturbation theory. This idea is illustrated with several examples, including two which are in agreement with all the present available data. (auth.)

Korea-NEA Research Project for the Construction of Worldwide Reactor Physics Experiments Database and the Foundation of Sustainable Collaboration Environment

Energy Technology Data Exchange (ETDEWEB)

Kim, Sang Ji; Jang, Jin Wook

2004-07-15

740 documents on PWR, LMR and VHTR related critical experiments are procured by participating in the IRPhE Project under the auspices of the OECD/NEA Data Bank. These documents were reviewed in detail for classification, measurement technique study. Among the database, the SNEAK-7 critical benchmarks were selected for further analysis by modern analysis tool, which requires minimum amount of correction for the raw calculated value. The SNEAK-7A and 7B were selected due to their spectrum similarity with KALIMER-600. Core eigenvalue, spectral indices, central material worths were evaluated and compared with the measurement. JEF-2.2 predict core eigenvalues pretty well, while the conversion ratio was underestimated by about 3%. ENDF/B-VI overestimates core eigenvalue by about 500 pcm while the conversion ratio was underestimated by about 4%. Through the sensitivity analysis of core eigenvalue to the partial cross section, a problem in {sup 238}U capture cross section was identified and a necessity arose to reduce the measurement uncertainty of {sup 239}Pu due to the high high sensitivity of core eigenvalue to {sup 239}Pu fission cross section.

Eigenvector/eigenvalue analysis of a 3D current referential fault detection and diagnosis of an induction motor

International Nuclear Information System (INIS)

Pires, V. Fernao; Martins, J.F.; Pires, A.J.

2010-01-01

In this paper an integrated approach for on-line induction motor fault detection and diagnosis is presented. The need to insure a continuous and safety operation for induction motors involves preventive maintenance procedures combined with fault diagnosis techniques. The proposed approach uses an automatic three step algorithm. Firstly, the induction motor stator currents are measured which will give typical patterns that can be used to identify the fault. Secondly, the eigenvectors/eigenvalues of the 3D current referential are computed. Finally the proposed algorithm will discern if the motor is healthy or not and report the extent of the fault. Furthermore this algorithm is able to identify distinct faults (stator winding faults or broken bars). The proposed approach was experimentally implemented and its performance verified on various types of working conditions.

A note on the gap between the first two eigenvalues for the Schroedinger operator

International Nuclear Information System (INIS)

Benguria, R.

1986-01-01

By means of a commutation formula, the author gives a simple proof of the upper bound of Wong et al on the gap between the first two eigenvalues in the Schrodinger operator. Unfortunately this proof does not seem to generalise into higher dimensions. (author)

Sensitivity Analysis of Viscoelastic Structures

Directory of Open Access Journals (Sweden)

A.M.G. de Lima

2006-01-01

Full Text Available In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations.

Energy eigenvalues and squeezing properties of general systems of coupled quantum anharmonic oscillators

International Nuclear Information System (INIS)

Chung, N. N.; Chew, L. Y.

2007-01-01

We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems

Extended forward sensitivity analysis of one-dimensional isothermal flow

International Nuclear Information System (INIS)

Johnson, M.; Zhao, H.

2013-01-01

Sensitivity analysis and uncertainty quantification is an important part of nuclear safety analysis. In this work, forward sensitivity analysis is used to compute solution sensitivities on 1-D fluid flow equations typical of those found in system level codes. Time step sensitivity analysis is included as a method for determining the accumulated error from time discretization. The ability to quantify numerical error arising from the time discretization is a unique and important feature of this method. By knowing the relative sensitivity of time step with other physical parameters, the simulation is allowed to run at optimized time steps without affecting the confidence of the physical parameter sensitivity results. The time step forward sensitivity analysis method can also replace the traditional time step convergence studies that are a key part of code verification with much less computational cost. One well-defined benchmark problem with manufactured solutions is utilized to verify the method; another test isothermal flow problem is used to demonstrate the extended forward sensitivity analysis process. Through these sample problems, the paper shows the feasibility and potential of using the forward sensitivity analysis method to quantify uncertainty in input parameters and time step size for a 1-D system-level thermal-hydraulic safety code. (authors)

Efficient eigenvalue determination for arbitrary Pauli products based on generalized spin-spin interactions

Science.gov (United States)

Leibfried, D.; Wineland, D. J.

2018-03-01

Effective spin-spin interactions between ? qubits enable the determination of the eigenvalue of an arbitrary Pauli product of dimension N with a constant, small number of multi-qubit gates that is independent of N and encodes the eigenvalue in the measurement basis states of an extra ancilla qubit. Such interactions are available whenever qubits can be coupled to a shared harmonic oscillator, a situation that can be realized in many physical qubit implementations. For example, suitable interactions have already been realized for up to 14 qubits in ion traps. It should be possible to implement stabilizer codes for quantum error correction with a constant number of multi-qubit gates, in contrast to typical constructions with a number of two-qubit gates that increases as a function of N. The special case of finding the parity of N qubits only requires a small number of operations that is independent of N. This compares favorably to algorithms for computing the parity on conventional machines, which implies a genuine quantum advantage.

Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study

International Nuclear Information System (INIS)

Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.

1985-01-01

The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures

Sensitivity analysis of EQ3

International Nuclear Information System (INIS)

Horwedel, J.E.; Wright, R.Q.; Maerker, R.E.

1990-01-01

A sensitivity analysis of EQ3, a computer code which has been proposed to be used as one link in the overall performance assessment of a national high-level waste repository, has been performed. EQ3 is a geochemical modeling code used to calculate the speciation of a water and its saturation state with respect to mineral phases. The model chosen for the sensitivity analysis is one which is used as a test problem in the documentation of the EQ3 code. Sensitivities are calculated using both the CHAIN and ADGEN options of the GRESS code compiled under G-float FORTRAN on the VAX/VMS and verified by perturbation runs. The analyses were performed with a preliminary Version 1.0 of GRESS which contains several new algorithms that significantly improve the application of ADGEN. Use of ADGEN automates the implementation of the well-known adjoint technique for the efficient calculation of sensitivities of a given response to all the input data. Application of ADGEN to EQ3 results in the calculation of sensitivities of a particular response to 31,000 input parameters in a run time of only 27 times that of the original model. Moreover, calculation of the sensitivities for each additional response increases this factor by only 2.5 percent. This compares very favorably with a running-time factor of 31,000 if direct perturbation runs were used instead. 6 refs., 8 tabs

Numerical method for multigroup one-dimensional SN eigenvalue problems with no spatial truncation error

International Nuclear Information System (INIS)

Abreu, M.P.; Filho, H.A.; Barros, R.C.

1993-01-01

The authors describe a new nodal method for multigroup slab-geometry discrete ordinates S N eigenvalue problems that is completely free from all spatial truncation errors. The unknowns in the method are the node-edge angular fluxes, the node-average angular fluxes, and the effective multiplication factor k eff . The numerical values obtained for these quantities are exactly those of the dominant analytic solution of the S N eigenvalue problem apart from finite arithmetic considerations. This method is based on the use of the standard balance equation and two nonstandard auxiliary equations. In the nonmultiplying regions, e.g., the reflector, we use the multigroup spectral Green's function (SGF) auxiliary equations. In the fuel regions, we use the multigroup spectral diamond (SD) auxiliary equations. The SD auxiliary equation is an extension of the conventional auxiliary equation used in the diamond difference (DD) method. This hybrid characteristic of the SD-SGF method improves both the numerical stability and the convergence rate

Wielandt acceleration for MCNP5 Monte Carlo eigenvalue calculations

International Nuclear Information System (INIS)

Brown, F.

2007-01-01

Monte Carlo criticality calculations use the power iteration method to determine the eigenvalue (k eff ) and eigenfunction (fission source distribution) of the fundamental mode. A recently proposed method for accelerating convergence of the Monte Carlo power iteration using Wielandt's method has been implemented in a test version of MCNP5. The method is shown to provide dramatic improvements in convergence rates and to greatly reduce the possibility of false convergence assessment. The method is effective and efficient, improving the Monte Carlo figure-of-merit for many problems. In addition, the method should eliminate most of the underprediction bias in confidence intervals for Monte Carlo criticality calculations. (authors)

SENSIT: a cross-section and design sensitivity and uncertainty analysis code

International Nuclear Information System (INIS)

Gerstl, S.A.W.

1980-01-01

SENSIT computes the sensitivity and uncertainty of a calculated integral response (such as a dose rate) due to input cross sections and their uncertainties. Sensitivity profiles are computed for neutron and gamma-ray reaction cross sections of standard multigroup cross section sets and for secondary energy distributions (SEDs) of multigroup scattering matrices. In the design sensitivity mode, SENSIT computes changes in an integral response due to design changes and gives the appropriate sensitivity coefficients. Cross section uncertainty analyses are performed for three types of input data uncertainties: cross-section covariance matrices for pairs of multigroup reaction cross sections, spectral shape uncertainty parameters for secondary energy distributions (integral SED uncertainties), and covariance matrices for energy-dependent response functions. For all three types of data uncertainties SENSIT computes the resulting variance and estimated standard deviation in an integral response of interest, on the basis of generalized perturbation theory. SENSIT attempts to be more comprehensive than earlier sensitivity analysis codes, such as SWANLAKE

A Proposal on the Advanced Sampling Based Sensitivity and Uncertainty Analysis Method for the Eigenvalue Uncertainty Analysis

International Nuclear Information System (INIS)

Kim, Song Hyun; Song, Myung Sub; Shin, Chang Ho; Noh, Jae Man

2014-01-01

In using the perturbation theory, the uncertainty of the response can be estimated by a single transport simulation, and therefore it requires small computational load. However, it has a disadvantage that the computation methodology must be modified whenever estimating different response type such as multiplication factor, flux, or power distribution. Hence, it is suitable for analyzing few responses with lots of perturbed parameters. Statistical approach is a sampling based method which uses randomly sampled cross sections from covariance data for analyzing the uncertainty of the response. XSUSA is a code based on the statistical approach. The cross sections are only modified with the sampling based method; thus, general transport codes can be directly utilized for the S/U analysis without any code modifications. However, to calculate the uncertainty distribution from the result, code simulation should be enough repeated with randomly sampled cross sections. Therefore, this inefficiency is known as a disadvantage of the stochastic method. In this study, an advanced sampling method of the cross sections is proposed and verified to increase the estimation efficiency of the sampling based method. In this study, to increase the estimation efficiency of the sampling based S/U method, an advanced sampling and estimation method was proposed. The main feature of the proposed method is that the cross section averaged from each single sampled cross section is used. For the use of the proposed method, the validation was performed using the perturbation theory

Variational methods for eigenvalue problems an introduction to the weinstein method of intermediate problems

CERN Document Server

Gould, S H

1966-01-01

The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. This second edition presents new developments in the framework of the material contained in the first edition, which is retained in somewhat modified form.

A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Lerche, I. [Institut für Geowissenschaften, Naturwissenschaftliche Fakultät III, Martin-Luther Universität, D-06099 Halle (Germany); Low, B. C. [High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado 80307 (United States)

2014-10-15

An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4

Multiple predictor smoothing methods for sensitivity analysis.

Energy Technology Data Exchange (ETDEWEB)

Helton, Jon Craig; Storlie, Curtis B.

2006-08-01

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described: (1) locally weighted regression (LOESS), (2) additive models, (3) projection pursuit regression, and (4) recursive partitioning regression. The indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.

Multiple predictor smoothing methods for sensitivity analysis

International Nuclear Information System (INIS)

Helton, Jon Craig; Storlie, Curtis B.

2006-01-01

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described: (1) locally weighted regression (LOESS), (2) additive models, (3) projection pursuit regression, and (4) recursive partitioning regression. The indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present

Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

OpenAIRE

Hillar, Christopher; Johnson, Charles R.

2005-01-01

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eig...

Estimates of the eigenvalues of operator arising in swelling pressure model

International Nuclear Information System (INIS)

Kanguzhin, Baltabek; Zhapsarbayeva, Lyailya

2016-01-01

Swelling pressures from materials confined by structures can cause structural deformations and instability. Due to the complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic spectral problem based on the Euler-elastic beam theory and some simplistic swelling pressure model. In this work estimates of the eigenvalues of some initial/boundary value problem for nonlinear Euler-elastic beam equation are obtained.

Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations

NARCIS (Netherlands)

Jarlebring, E.; Hochstenbach, M.E.

2009-01-01

Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called

Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Feng Qi

2014-10-01

Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.

Ground-state energies and highest occupied eigenvalues of atoms in exchange-only density-functional theory

Science.gov (United States)

Li, Yan; Harbola, Manoj K.; Krieger, J. B.; Sahni, Viraht

1989-11-01

The exchange-correlation potential of the Kohn-Sham density-functional theory has recently been interpreted as the work required to move an electron against the electric field of its Fermi-Coulomb hole charge distribution. In this paper we present self-consistent results for ground-state total energies and highest occupied eigenvalues of closed subshell atoms as obtained by this formalism in the exchange-only approximation. The total energies, which are an upper bound, lie within 50 ppm of Hartree-Fock theory for atoms heavier than Be. The highest occupied eigenvalues, as a consequence of this interpretation, approximate well the experimental ionization potentials. In addition, the self-consistently calculated exchange potentials are very close to those of Talman and co-workers [J. D. Talman and W. F. Shadwick, Phys. Rev. A 14, 36 (1976); K. Aashamar, T. M. Luke, and J. D. Talman, At. Data Nucl. Data Tables 22, 443 (1978)].

LBLOCA sensitivity analysis using meta models

International Nuclear Information System (INIS)

Villamizar, M.; Sanchez-Saez, F.; Villanueva, J.F.; Carlos, S.; Sanchez, A.I.; Martorell, S.

2014-01-01

This paper presents an approach to perform the sensitivity analysis of the results of simulation of thermal hydraulic codes within a BEPU approach. Sensitivity analysis is based on the computation of Sobol' indices that makes use of a meta model, It presents also an application to a Large-Break Loss of Coolant Accident, LBLOCA, in the cold leg of a pressurized water reactor, PWR, addressing the results of the BEMUSE program and using the thermal-hydraulic code TRACE. (authors)

Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

Directory of Open Access Journals (Sweden)

Vicenţiu RăDulescu

2005-06-01

Full Text Available We study nonlinear eigenvalue problems of the type −div(a(x∇u=g(λ,x,u in ℝN, where a(x is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.

Sensitivity analysis in life cycle assessment

NARCIS (Netherlands)

Groen, E.A.; Heijungs, R.; Bokkers, E.A.M.; Boer, de I.J.M.

2014-01-01

Life cycle assessments require many input parameters and many of these parameters are uncertain; therefore, a sensitivity analysis is an essential part of the final interpretation. The aim of this study is to compare seven sensitivity methods applied to three types of case stud-ies. Two

Sensitivity analysis for matched pair analysis of binary data: From worst case to average case analysis.

Science.gov (United States)

Hasegawa, Raiden; Small, Dylan

2017-12-01

In matched observational studies where treatment assignment is not randomized, sensitivity analysis helps investigators determine how sensitive their estimated treatment effect is to some unmeasured confounder. The standard approach calibrates the sensitivity analysis according to the worst case bias in a pair. This approach will result in a conservative sensitivity analysis if the worst case bias does not hold in every pair. In this paper, we show that for binary data, the standard approach can be calibrated in terms of the average bias in a pair rather than worst case bias. When the worst case bias and average bias differ, the average bias interpretation results in a less conservative sensitivity analysis and more power. In many studies, the average case calibration may also carry a more natural interpretation than the worst case calibration and may also allow researchers to incorporate additional data to establish an empirical basis with which to calibrate a sensitivity analysis. We illustrate this with a study of the effects of cellphone use on the incidence of automobile accidents. Finally, we extend the average case calibration to the sensitivity analysis of confidence intervals for attributable effects. © 2017, The International Biometric Society.

Convergence diagnostics for Eigenvalue problems with linear regression model

International Nuclear Information System (INIS)

Shi, Bo; Petrovic, Bojan

2011-01-01

Although the Monte Carlo method has been extensively used for criticality/Eigenvalue problems, a reliable, robust, and efficient convergence diagnostics method is still desired. Most methods are based on integral parameters (multiplication factor, entropy) and either condense the local distribution information into a single value (e.g., entropy) or even disregard it. We propose to employ the detailed cycle-by-cycle local flux evolution obtained by using mesh tally mechanism to assess the source and flux convergence. By applying a linear regression model to each individual mesh in a mesh tally for convergence diagnostics, a global convergence criterion can be obtained. We exemplify this method on two problems and obtain promising diagnostics results. (author)

High order depletion sensitivity analysis

International Nuclear Information System (INIS)

Naguib, K.; Adib, M.; Morcos, H.N.

2002-01-01

A high order depletion sensitivity method was applied to calculate the sensitivities of build-up of actinides in the irradiated fuel due to cross-section uncertainties. An iteration method based on Taylor series expansion was applied to construct stationary principle, from which all orders of perturbations were calculated. The irradiated EK-10 and MTR-20 fuels at their maximum burn-up of 25% and 65% respectively were considered for sensitivity analysis. The results of calculation show that, in case of EK-10 fuel (low burn-up), the first order sensitivity was found to be enough to perform an accuracy of 1%. While in case of MTR-20 (high burn-up) the fifth order was found to provide 3% accuracy. A computer code SENS was developed to provide the required calculations

Computation of dominant eigenvalues and eigenvectors: A comparative study of algorithms

International Nuclear Information System (INIS)

Nightingale, M.P.; Viswanath, V.S.; Mueller, G.

1993-01-01

We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods

An eigenvalue approach to quantum plasmonics based on a self-consistent hydrodynamics method.

Science.gov (United States)

Ding, Kun; Chan, C T

2018-02-28

Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or empirical Feibelman d-parameters have been used to explore the quantum correction of plasmonic resonances. However, most of these methods are formulated within the quasi-static framework. The self-consistent hydrodynamics model offers a reliable approach to study quantum plasmonics because it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent manner. Instead of the standard scattering method, we formulate the self-consistent hydrodynamics method as an eigenvalue problem to study quantum plasmonics with electrons and photons treated on the same footing. We find that the eigenvalue approach must involve a global operator, which originates from the energy functional of the electron gas. This manifests the intrinsic nonlocality of the response of quantum plasmonic resonances. Our model gives the analytical forms of quantum corrections to plasmonic modes, incorporating quantum electron spill-out effects and electrodynamical retardation. We apply our method to study the quantum surface plasmon polariton for a single flat interface.

Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

Directory of Open Access Journals (Sweden)

Boubakari Ibrahimou

2013-01-01

maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.

Automating sensitivity analysis of computer models using computer calculus

International Nuclear Information System (INIS)

Oblow, E.M.; Pin, F.G.

1986-01-01

An automated procedure for performing sensitivity analysis has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with direct and adjoint sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies

Evaluation of Parallel Analysis Methods for Determining the Number of Factors

Science.gov (United States)

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…

Frontier Assignment for Sensitivity Analysis of Data Envelopment Analysis

Science.gov (United States)

Naito, Akio; Aoki, Shingo; Tsuji, Hiroshi

To extend the sensitivity analysis capability for DEA (Data Envelopment Analysis), this paper proposes frontier assignment based DEA (FA-DEA). The basic idea of FA-DEA is to allow a decision maker to decide frontier intentionally while the traditional DEA and Super-DEA decide frontier computationally. The features of FA-DEA are as follows: (1) provides chances to exclude extra-influential DMU (Decision Making Unit) and finds extra-ordinal DMU, and (2) includes the function of the traditional DEA and Super-DEA so that it is able to deal with sensitivity analysis more flexibly. Simple numerical study has shown the effectiveness of the proposed FA-DEA and the difference from the traditional DEA.

Sensitivity analysis in optimization and reliability problems

International Nuclear Information System (INIS)

Castillo, Enrique; Minguez, Roberto; Castillo, Carmen

2008-01-01

The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods

Sensitivity analysis in optimization and reliability problems

Energy Technology Data Exchange (ETDEWEB)

Castillo, Enrique [Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. Castros s/n., 39005 Santander (Spain)], E-mail: castie@unican.es; Minguez, Roberto [Department of Applied Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: roberto.minguez@uclm.es; Castillo, Carmen [Department of Civil Engineering, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: mariacarmen.castillo@uclm.es

2008-12-15

The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods.

Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods

International Nuclear Information System (INIS)

Roberts, Jeremy A.; Forget, Benoit

2011-01-01

The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)

Third-order WKBJ eigenvalues for Lennard-Jones and Varshni V potentials

International Nuclear Information System (INIS)

Kesarwani, R.N.; Varshni, Y.P.

1978-01-01

The WKBJ method is applied to the third order for obtaining the eigenvalues for the fifth potential of Varshni, and the relevant integrals are analytically evaluated. Numerical results are obtained for the Lennard-Jones Potential, which is a special case of the Varshni V potential, and are compared to the results of Harrison and Bernstein obtained by a numerical integration of the wave equation. Error estimates are made. It is shown that for diatomic potentials, the Langer correction is not needed if the WKBJ approximation is carried to second and higher orders. (author)

Computation of Double Eigenvalues for Infinite Matrices of a Certain Class

OpenAIRE

宮崎, 佳典; Yoshinori, MIYAZAKI; 静岡産業大学 国際情報学部; Faculty of Communications and Informatics, Shizuoka Sangyo University

2001-01-01

It has been shown that a series of three-term recurrence relations of a certain class is a powerful tool for solving zeros of some special functions and eigenvalue problems (EVPs) of certain differential equations. Such cases include: the zeros of J_v(z); the zeros of zJ′_v(z)+HJ_v(z); the EVP of the Mathieu differential equation; and the EVP of the spheroidal wave equation. Previously by the author, it was demonstrated that the three-term recurrence relations of the class may be reformulated...

Asymptotics for the number of negative eigenvalues of a model operator related to a system of three-particles on lattices

International Nuclear Information System (INIS)

Rasulov, T.H.

2009-04-01

A model operator H μ , μ > 0 associated to a system of three particles on the three-dimensional lattice Z 3 . We study the case where the parameter function w has a special form with the nondegenerate minimum at the n, n > 1 points. If the associated Friedrichs model has a zero energy resonance, then we prove that the operator H μ has infinitely many negative eigenvalues accumulating at zero. Moreover, we obtain an asymptotic value for the number of negative eigenvalues of H μ lying below z < 0 with respect to the spectral parameter z → -0. (author)

The role of sensitivity analysis in assessing uncertainty

International Nuclear Information System (INIS)

Crick, M.J.; Hill, M.D.

1987-01-01

Outside the specialist world of those carrying out performance assessments considerable confusion has arisen about the meanings of sensitivity analysis and uncertainty analysis. In this paper we attempt to reduce this confusion. We then go on to review approaches to sensitivity analysis within the context of assessing uncertainty, and to outline the types of test available to identify sensitive parameters, together with their advantages and disadvantages. The views expressed in this paper are those of the authors; they have not been formally endorsed by the National Radiological Protection Board and should not be interpreted as Board advice

Sorting waves and associated eigenvalues

Science.gov (United States)

Carbonari, Costanza; Colombini, Marco; Solari, Luca

2017-04-01

The presence of mixed sediment always characterizes gravel bed rivers. Sorting processes take place during bed load transport of heterogeneous sediment mixtures. The two main elements necessary to the occurrence of sorting are the heterogeneous character of sediments and the presence of an active sediment transport. When these two key ingredients are simultaneously present, the segregation of bed material is consistently detected both in the field [7] and in laboratory [3] observations. In heterogeneous sediment transport, bed altimetric variations and sorting always coexist and both mechanisms are independently capable of driving the formation of morphological patterns. Indeed, consistent patterns of longitudinal and transverse sorting are identified almost ubiquitously. In some cases, such as bar formation [2] and channel bends [5], sorting acts as a stabilizing effect and therefore the dominant mechanism driving pattern formation is associated with bed altimetric variations. In other cases, such as longitudinal streaks, sorting enhances system instability and can therefore be considered the prevailing mechanism. Bedload sheets, first observed by Khunle and Southard [1], represent another classic example of a morphological pattern essentially triggered by sorting, as theoretical [4] and experimental [3] results suggested. These sorting waves cause strong spatial and temporal fluctuations of bedload transport rate typical observed in gravel bed rivers. The problem of bed load transport of a sediment mixture is formulated in the framework of a 1D linear stability analysis. The base state consists of a uniform flow in an infinitely wide channel with active bed load transport. The behaviour of the eigenvalues associated with fluid motion, bed evolution and sorting processes in the space of the significant flow and sediment parameters is analysed. A comparison is attempted with the results of the theoretical analysis of Seminara Colombini and Parker [4] and Stecca

Sensitivity Analysis of a Simplified Fire Dynamic Model

DEFF Research Database (Denmark)

Sørensen, Lars Schiøtt; Nielsen, Anker

2015-01-01

This paper discusses a method for performing a sensitivity analysis of parameters used in a simplified fire model for temperature estimates in the upper smoke layer during a fire. The results from the sensitivity analysis can be used when individual parameters affecting fire safety are assessed...

A Note on the Asymptotic and Threshold Behaviour of Discrete Eigenvalues inside the Spectral Gaps of the Difference Operator with a Periodic Potential

Directory of Open Access Journals (Sweden)

Gift Muchatibaya

2018-01-01

Full Text Available The asymptotic and threshold behaviour of the eigenvalues of a perturbed difference operator inside a spectral gap is investigated. In particular, applications of the Titchmarsh-Weyl m-function theory as well as the Birman-Schwinger principle is performed to investigate the existence and behaviour of the eigenvalues of the operator H0+λWn inside the spectral gap of H0 in the limits λ↑∞ and λ↓0.

Probabilistic sensitivity analysis in health economics.

Science.gov (United States)

Baio, Gianluca; Dawid, A Philip

2015-12-01

Health economic evaluations have recently become an important part of the clinical and medical research process and have built upon more advanced statistical decision-theoretic foundations. In some contexts, it is officially required that uncertainty about both parameters and observable variables be properly taken into account, increasingly often by means of Bayesian methods. Among these, probabilistic sensitivity analysis has assumed a predominant role. The objective of this article is to review the problem of health economic assessment from the standpoint of Bayesian statistical decision theory with particular attention to the philosophy underlying the procedures for sensitivity analysis. © The Author(s) 2011.

TOLERANCE SENSITIVITY ANALYSIS: THIRTY YEARS LATER

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Richard E. Wendell

2010-12-01

Full Text Available Tolerance sensitivity analysis was conceived in 1980 as a pragmatic approach to effectively characterize a parametric region over which objective function coefficients and right-hand-side terms in linear programming could vary simultaneously and independently while maintaining the same optimal basis. As originally proposed, the tolerance region corresponds to the maximum percentage by which coefficients or terms could vary from their estimated values. Over the last thirty years the original results have been extended in a number of ways and applied in a variety of applications. This paper is a critical review of tolerance sensitivity analysis, including extensions and applications.

Sensitivity analysis for missing data in regulatory submissions.

Science.gov (United States)

Permutt, Thomas

2016-07-30

The National Research Council Panel on Handling Missing Data in Clinical Trials recommended that sensitivity analyses have to be part of the primary reporting of findings from clinical trials. Their specific recommendations, however, seem not to have been taken up rapidly by sponsors of regulatory submissions. The NRC report's detailed suggestions are along rather different lines than what has been called sensitivity analysis in the regulatory setting up to now. Furthermore, the role of sensitivity analysis in regulatory decision-making, although discussed briefly in the NRC report, remains unclear. This paper will examine previous ideas of sensitivity analysis with a view to explaining how the NRC panel's recommendations are different and possibly better suited to coping with present problems of missing data in the regulatory setting. It will also discuss, in more detail than the NRC report, the relevance of sensitivity analysis to decision-making, both for applicants and for regulators. Published 2015. This article is a U.S. Government work and is in the public domain in the USA. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.

Risk and sensitivity analysis in relation to external events

International Nuclear Information System (INIS)

Alzbutas, R.; Urbonas, R.; Augutis, J.

2001-01-01

This paper presents risk and sensitivity analysis of external events impacts on the safe operation in general and in particular the Ignalina Nuclear Power Plant safety systems. Analysis is based on the deterministic and probabilistic assumptions and assessment of the external hazards. The real statistic data are used as well as initial external event simulation. The preliminary screening criteria are applied. The analysis of external event impact on the NPP safe operation, assessment of the event occurrence, sensitivity analysis, and recommendations for safety improvements are performed for investigated external hazards. Such events as aircraft crash, extreme rains and winds, forest fire and flying parts of the turbine are analysed. The models are developed and probabilities are calculated. As an example for sensitivity analysis the model of aircraft impact is presented. The sensitivity analysis takes into account the uncertainty features raised by external event and its model. Even in case when the external events analysis show rather limited danger, the sensitivity analysis can determine the highest influence causes. These possible variations in future can be significant for safety level and risk based decisions. Calculations show that external events cannot significantly influence the safety level of the Ignalina NPP operation, however the events occurrence and propagation can be sufficiently uncertain.(author)

Automating sensitivity analysis of computer models using computer calculus

International Nuclear Information System (INIS)

Oblow, E.M.; Pin, F.G.

1985-01-01

An automated procedure for performing sensitivity analyses has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with ''direct'' and ''adjoint'' sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies. 24 refs., 2 figs

Sensitivity analysis and related analysis : A survey of statistical techniques

NARCIS (Netherlands)

Kleijnen, J.P.C.

1995-01-01

This paper reviews the state of the art in five related types of analysis, namely (i) sensitivity or what-if analysis, (ii) uncertainty or risk analysis, (iii) screening, (iv) validation, and (v) optimization. The main question is: when should which type of analysis be applied; which statistical

Method for the determination of the dominant eigenvalue of the neutron transport equation in a slab using fractional derivative

International Nuclear Information System (INIS)

Sperotto, Fabiola Aiub; Segatto, Cynthia Feijo; Zabadal, Jorge

2002-01-01

In this work, we determine the dominant eigenvalue of the one-dimensional neutron transport equation in a slab constructing an integral form for the neutron transport equation which is the expressed in terms of fractional derivative of the angular flux. Equating the fractional derivative of the angular flux to the integrate equation, we determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of Riemann-Liouville definition of fractional derivative. Once known the angular flux the dominant eigenvalue is calculated solving a transcendental equation resulting from the application of the boundary conditions. We report the methodology applied, for comparison with available results in literature. (author)

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks.

Science.gov (United States)

Arampatzis, Georgios; Katsoulakis, Markos A; Pantazis, Yannis

2015-01-01

Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over the

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks.

Directory of Open Access Journals (Sweden)

Georgios Arampatzis

Full Text Available Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in "sloppy" systems. In particular, the computational acceleration is quantified by the ratio between the total number of

The role of sensitivity analysis in probabilistic safety assessment

International Nuclear Information System (INIS)

Hirschberg, S.; Knochenhauer, M.

1987-01-01

The paper describes several items suitable for close examination by means of application of sensitivity analysis, when performing a level 1 PSA. Sensitivity analyses are performed with respect to; (1) boundary conditions, (2) operator actions, and (3) treatment of common cause failures (CCFs). The items of main interest are identified continuously in the course of performing a PSA, as well as by scrutinising the final results. The practical aspects of sensitivity analysis are illustrated by several applications from a recent PSA study (ASEA-ATOM BWR 75). It is concluded that sensitivity analysis leads to insights important for analysts, reviewers and decision makers. (orig./HP)

Global Sensitivity Analysis of Environmental Models: Convergence, Robustness and Validation

Science.gov (United States)

Sarrazin, Fanny; Pianosi, Francesca; Khorashadi Zadeh, Farkhondeh; Van Griensven, Ann; Wagener, Thorsten

2015-04-01

Global Sensitivity Analysis aims to characterize the impact that variations in model input factors (e.g. the parameters) have on the model output (e.g. simulated streamflow). In sampling-based Global Sensitivity Analysis, the sample size has to be chosen carefully in order to obtain reliable sensitivity estimates while spending computational resources efficiently. Furthermore, insensitive parameters are typically identified through the definition of a screening threshold: the theoretical value of their sensitivity index is zero but in a sampling-base framework they regularly take non-zero values. There is little guidance available for these two steps in environmental modelling though. The objective of the present study is to support modellers in making appropriate choices, regarding both sample size and screening threshold, so that a robust sensitivity analysis can be implemented. We performed sensitivity analysis for the parameters of three hydrological models with increasing level of complexity (Hymod, HBV and SWAT), and tested three widely used sensitivity analysis methods (Elementary Effect Test or method of Morris, Regional Sensitivity Analysis, and Variance-Based Sensitivity Analysis). We defined criteria based on a bootstrap approach to assess three different types of convergence: the convergence of the value of the sensitivity indices, of the ranking (the ordering among the parameters) and of the screening (the identification of the insensitive parameters). We investigated the screening threshold through the definition of a validation procedure. The results showed that full convergence of the value of the sensitivity indices is not necessarily needed to rank or to screen the model input factors. Furthermore, typical values of the sample sizes that are reported in the literature can be well below the sample sizes that actually ensure convergence of ranking and screening.

Sensitivity analysis of Takagi-Sugeno-Kang rainfall-runoff fuzzy models

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A. P. Jacquin

2009-01-01

Full Text Available This paper is concerned with the sensitivity analysis of the model parameters of the Takagi-Sugeno-Kang fuzzy rainfall-runoff models previously developed by the authors. These models are classified in two types of fuzzy models, where the first type is intended to account for the effect of changes in catchment wetness and the second type incorporates seasonality as a source of non-linearity. The sensitivity analysis is performed using two global sensitivity analysis methods, namely Regional Sensitivity Analysis and Sobol's variance decomposition. The data of six catchments from different geographical locations and sizes are used in the sensitivity analysis. The sensitivity of the model parameters is analysed in terms of several measures of goodness of fit, assessing the model performance from different points of view. These measures include the Nash-Sutcliffe criteria, volumetric errors and peak errors. The results show that the sensitivity of the model parameters depends on both the catchment type and the measure used to assess the model performance.

Sensitivity Analysis in Two-Stage DEA

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Athena Forghani

2015-07-01

Full Text Available Data envelopment analysis (DEA is a method for measuring the efficiency of peer decision making units (DMUs which uses a set of inputs to produce a set of outputs. In some cases, DMUs have a two-stage structure, in which the first stage utilizes inputs to produce outputs used as the inputs of the second stage to produce final outputs. One important issue in two-stage DEA is the sensitivity of the results of an analysis to perturbations in the data. The current paper looks into combined model for two-stage DEA and applies the sensitivity analysis to DMUs on the entire frontier. In fact, necessary and sufficient conditions for preserving a DMU's efficiency classiffication are developed when various data changes are applied to all DMUs.

Sensitivity Analysis in Two-Stage DEA

Directory of Open Access Journals (Sweden)

Athena Forghani

2015-12-01

Full Text Available Data envelopment analysis (DEA is a method for measuring the efficiency of peer decision making units (DMUs which uses a set of inputs to produce a set of outputs. In some cases, DMUs have a two-stage structure, in which the first stage utilizes inputs to produce outputs used as the inputs of the second stage to produce final outputs. One important issue in two-stage DEA is the sensitivity of the results of an analysis to perturbations in the data. The current paper looks into combined model for two-stage DEA and applies the sensitivity analysis to DMUs on the entire frontier. In fact, necessary and sufficient conditions for preserving a DMU's efficiency classiffication are developed when various data changes are applied to all DMUs.

Leak detection of complex pipelines based on the filter diagonalization method: robust technique for eigenvalue assessment

International Nuclear Information System (INIS)

Lay-Ekuakille, Aimé; Pariset, Carlo; Trotta, Amerigo

2010-01-01

The FDM (filter diagonalization method), an interesting technique used in nuclear magnetic resonance data processing for tackling FFT (fast Fourier transform) limitations, can be used by considering pipelines, especially complex configurations, as a vascular apparatus with arteries, veins, capillaries, etc. Thrombosis, which might occur in humans, can be considered as a leakage for the complex pipeline, the human vascular apparatus. The choice of eigenvalues in FDM or in spectra-based techniques is a key issue in recovering the solution of the main equation (for FDM) or frequency domain transformation (for FFT) in order to determine the accuracy in detecting leaks in pipelines. This paper deals with the possibility of improving the leak detection accuracy of the FDM technique thanks to a robust algorithm by assessing the problem of eigenvalues, making it less experimental and more analytical using Tikhonov-based regularization techniques. The paper starts from the results of previous experimental procedures carried out by the authors

Sensitivity Analysis of Simulation Models

NARCIS (Netherlands)

Kleijnen, J.P.C.

2009-01-01

This contribution presents an overview of sensitivity analysis of simulation models, including the estimation of gradients. It covers classic designs and their corresponding (meta)models; namely, resolution-III designs including fractional-factorial two-level designs for first-order polynomial

Sobol' sensitivity analysis for stressor impacts on honeybee ...

Science.gov (United States)

We employ Monte Carlo simulation and nonlinear sensitivity analysis techniques to describe the dynamics of a bee exposure model, VarroaPop. Daily simulations are performed of hive population trajectories, taking into account queen strength, foraging success, mite impacts, weather, colony resources, population structure, and other important variables. This allows us to test the effects of defined pesticide exposure scenarios versus controlled simulations that lack pesticide exposure. The daily resolution of the model also allows us to conditionally identify sensitivity metrics. We use the variancebased global decomposition sensitivity analysis method, Sobol’, to assess firstand secondorder parameter sensitivities within VarroaPop, allowing us to determine how variance in the output is attributed to each of the input variables across different exposure scenarios. Simulations with VarroaPop indicate queen strength, forager life span and pesticide toxicity parameters are consistent, critical inputs for colony dynamics. Further analysis also reveals that the relative importance of these parameters fluctuates throughout the simulation period according to the status of other inputs. Our preliminary results show that model variability is conditional and can be attributed to different parameters depending on different timescales. By using sensitivity analysis to assess model output and variability, calibrations of simulation models can be better informed to yield more

Sensitivity analysis of the RESRAD, a dose assessment code

International Nuclear Information System (INIS)

Yu, C.; Cheng, J.J.; Zielen, A.J.

1991-01-01

The RESRAD code is a pathway analysis code that is designed to calculate radiation doses and derive soil cleanup criteria for the US Department of Energy's environmental restoration and waste management program. the RESRAD code uses various pathway and consumption-rate parameters such as soil properties and food ingestion rates in performing such calculations and derivations. As with any predictive model, the accuracy of the predictions depends on the accuracy of the input parameters. This paper summarizes the results of a sensitivity analysis of RESRAD input parameters. Three methods were used to perform the sensitivity analysis: (1) Gradient Enhanced Software System (GRESS) sensitivity analysis software package developed at oak Ridge National Laboratory; (2) direct perturbation of input parameters; and (3) built-in graphic package that shows parameter sensitivities while the RESRAD code is operational

Sensitivity analysis in a structural reliability context

International Nuclear Information System (INIS)

Lemaitre, Paul

2014-01-01

This thesis' subject is sensitivity analysis in a structural reliability context. The general framework is the study of a deterministic numerical model that allows to reproduce a complex physical phenomenon. The aim of a reliability study is to estimate the failure probability of the system from the numerical model and the uncertainties of the inputs. In this context, the quantification of the impact of the uncertainty of each input parameter on the output might be of interest. This step is called sensitivity analysis. Many scientific works deal with this topic but not in the reliability scope. This thesis' aim is to test existing sensitivity analysis methods, and to propose more efficient original methods. A bibliographical step on sensitivity analysis on one hand and on the estimation of small failure probabilities on the other hand is first proposed. This step raises the need to develop appropriate techniques. Two variables ranking methods are then explored. The first one proposes to make use of binary classifiers (random forests). The second one measures the departure, at each step of a subset method, between each input original density and the density given the subset reached. A more general and original methodology reflecting the impact of the input density modification on the failure probability is then explored. The proposed methods are then applied on the CWNR case, which motivates this thesis. (author)

Instability of the cored barotropic disc: the linear eigenvalue formulation

Science.gov (United States)

Polyachenko, E. V.

2018-05-01

Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

Sensitivity analysis using probability bounding

International Nuclear Information System (INIS)

Ferson, Scott; Troy Tucker, W.

2006-01-01

Probability bounds analysis (PBA) provides analysts a convenient means to characterize the neighborhood of possible results that would be obtained from plausible alternative inputs in probabilistic calculations. We show the relationship between PBA and the methods of interval analysis and probabilistic uncertainty analysis from which it is jointly derived, and indicate how the method can be used to assess the quality of probabilistic models such as those developed in Monte Carlo simulations for risk analyses. We also illustrate how a sensitivity analysis can be conducted within a PBA by pinching inputs to precise distributions or real values

Global sensitivity analysis of computer models with functional inputs

International Nuclear Information System (INIS)

Iooss, Bertrand; Ribatet, Mathieu

2009-01-01

Global sensitivity analysis is used to quantify the influence of uncertain model inputs on the response variability of a numerical model. The common quantitative methods are appropriate with computer codes having scalar model inputs. This paper aims at illustrating different variance-based sensitivity analysis techniques, based on the so-called Sobol's indices, when some model inputs are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary metamodeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked generalized linear models (GLMs) or generalized additive models (GAMs). The 'mean model' allows to estimate the sensitivity indices of each scalar model inputs, while the 'dispersion model' allows to derive the total sensitivity index of the functional model inputs. The proposed approach is compared to some classical sensitivity analysis methodologies on an analytical function. Lastly, the new methodology is applied to an industrial computer code that simulates the nuclear fuel irradiation.

Sensitivity analysis of ranked data: from order statistics to quantiles

NARCIS (Netherlands)

Heidergott, B.F.; Volk-Makarewicz, W.

2015-01-01

In this paper we provide the mathematical theory for sensitivity analysis of order statistics of continuous random variables, where the sensitivity is with respect to a distributional parameter. Sensitivity analysis of order statistics over a finite number of observations is discussed before

Sensitivity analysis in remote sensing

CERN Document Server

Ustinov, Eugene A

2015-01-01

This book contains a detailed presentation of general principles of sensitivity analysis as well as their applications to sample cases of remote sensing experiments. An emphasis is made on applications of adjoint problems, because they are more efficient in many practical cases, although their formulation may seem counterintuitive to a beginner. Special attention is paid to forward problems based on higher-order partial differential equations, where a novel matrix operator approach to formulation of corresponding adjoint problems is presented. Sensitivity analysis (SA) serves for quantitative models of physical objects the same purpose, as differential calculus does for functions. SA provides derivatives of model output parameters (observables) with respect to input parameters. In remote sensing SA provides computer-efficient means to compute the jacobians, matrices of partial derivatives of observables with respect to the geophysical parameters of interest. The jacobians are used to solve corresponding inver...

Sensitivity Analysis for Urban Drainage Modeling Using Mutual Information

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Chuanqi Li

2014-11-01

Full Text Available The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different methods of sensitivity analysis are applied in this study. The first one is the partial rank correlation coefficient (PRCC which measures nonlinear but monotonic relationships between model inputs and outputs. The second one is based on the mutual information which provides a general measure of the strength of the non-monotonic association between two variables. Both methods are based on the Latin Hypercube Sampling (LHS of the parameter space, and thus the same datasets can be used to obtain both measures of sensitivity. The utility of the PRCC and the mutual information analysis methods are illustrated by analyzing a complex SWMM model. The sensitivity analysis revealed that only a few key input variables are contributing significantly to the model outputs; PRCCs and mutual information are calculated and used to determine and rank the importance of these key parameters. This study shows that the partial rank correlation coefficient and mutual information analysis can be considered effective methods for assessing the sensitivity of the SWMM model to the uncertainty in its input parameters.

Rigorous Asymptotics for the Lamé and Mathieu Functions and their Respective Eigenvalues with a Large Parameter

Science.gov (United States)

Ogilvie, Karen; Olde Daalhuis, Adri B.

2015-11-01

By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in the first part of this paper for the Lamé and Mathieu functions with a large real parameter. These approximations are expressed in terms of parabolic cylinder functions, and are uniformly valid in their respective real open intervals. In all cases explicit bounds are supplied for the error terms associated with the approximations. Approximations are also obtained for the large order behaviour for the respective eigenvalues. We restrict ourselves to a two term uniform approximation. Theoretically more terms in these approximations could be computed, but the coefficients would be very complicated. In the second part of this paper we use a simplified method to obtain uniform asymptotic expansions for these functions. The coefficients are just polynomials and satisfy simple recurrence relations. The price to pay is that these asymptotic expansions hold only in a shrinking interval as their respective parameters become large; this interval however encapsulates all the interesting oscillatory behaviour of the functions. This simplified method also gives many terms in asymptotic expansions for these eigenvalues, derived simultaneously with the coefficients in the function expansions. We provide rigorous realistic error bounds for the function expansions when truncated and order estimates for the error when the eigenvalue expansions are truncated. With this paper we confirm that many of the formal results in the literature are correct.

Computing the full spectrum of large sparse palindromic quadratic eigenvalue problems arising from surface Green's function calculations

Science.gov (United States)

Huang, Tsung-Ming; Lin, Wen-Wei; Tian, Heng; Chen, Guan-Hua

2018-03-01

Full spectrum of a large sparse ⊤-palindromic quadratic eigenvalue problem (⊤-PQEP) is considered arguably for the first time in this article. Such a problem is posed by calculation of surface Green's functions (SGFs) of mesoscopic transistors with a tremendous non-periodic cross-section. For this problem, general purpose eigensolvers are not efficient, nor is advisable to resort to the decimation method etc. to obtain the Wiener-Hopf factorization. After reviewing some rigorous understanding of SGF calculation from the perspective of ⊤-PQEP and nonlinear matrix equation, we present our new approach to this problem. In a nutshell, the unit disk where the spectrum of interest lies is broken down adaptively into pieces small enough that they each can be locally tackled by the generalized ⊤-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi (G⊤SHIRA) algorithm with suitable shifts and other parameters, and the eigenvalues missed by this divide-and-conquer strategy can be recovered thanks to the accurate estimation provided by our newly developed scheme. Notably the novel non-equivalence deflation is proposed to avoid as much as possible duplication of nearby known eigenvalues when a new shift of G⊤SHIRA is determined. We demonstrate our new approach by calculating the SGF of a realistic nanowire whose unit cell is described by a matrix of size 4000 × 4000 at the density functional tight binding level, corresponding to a 8 × 8nm2 cross-section. We believe that quantum transport simulation of realistic nano-devices in the mesoscopic regime will greatly benefit from this work.

A general first-order global sensitivity analysis method

International Nuclear Information System (INIS)

Xu Chonggang; Gertner, George Zdzislaw

2008-01-01

Fourier amplitude sensitivity test (FAST) is one of the most popular global sensitivity analysis techniques. The main mechanism of FAST is to assign each parameter with a characteristic frequency through a search function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency. Although FAST has been widely applied, there are two limitations: (1) the aliasing effect among parameters by using integer characteristic frequencies and (2) the suitability for only models with independent parameters. In this paper, we synthesize the improvement to overcome the aliasing effect limitation [Tarantola S, Gatelli D, Mara TA. Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Safety 2006; 91(6):717-27] and the improvement to overcome the independence limitation [Xu C, Gertner G. Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 2007, accepted for publication]. In this way, FAST can be a general first-order global sensitivity analysis method for linear/nonlinear models with as many correlated/uncorrelated parameters as the user specifies. We apply the general FAST to four test cases with correlated parameters. The results show that the sensitivity indices derived by the general FAST are in good agreement with the sensitivity indices derived by the correlation ratio method, which is a non-parametric method for models with correlated parameters

Time-dependent reliability sensitivity analysis of motion mechanisms

International Nuclear Information System (INIS)

Wei, Pengfei; Song, Jingwen; Lu, Zhenzhou; Yue, Zhufeng

2016-01-01

Reliability sensitivity analysis aims at identifying the source of structure/mechanism failure, and quantifying the effects of each random source or their distribution parameters on failure probability or reliability. In this paper, the time-dependent parametric reliability sensitivity (PRS) analysis as well as the global reliability sensitivity (GRS) analysis is introduced for the motion mechanisms. The PRS indices are defined as the partial derivatives of the time-dependent reliability w.r.t. the distribution parameters of each random input variable, and they quantify the effect of the small change of each distribution parameter on the time-dependent reliability. The GRS indices are defined for quantifying the individual, interaction and total contributions of the uncertainty in each random input variable to the time-dependent reliability. The envelope function method combined with the first order approximation of the motion error function is introduced for efficiently estimating the time-dependent PRS and GRS indices. Both the time-dependent PRS and GRS analysis techniques can be especially useful for reliability-based design. This significance of the proposed methods as well as the effectiveness of the envelope function method for estimating the time-dependent PRS and GRS indices are demonstrated with a four-bar mechanism and a car rack-and-pinion steering linkage. - Highlights: • Time-dependent parametric reliability sensitivity analysis is presented. • Time-dependent global reliability sensitivity analysis is presented for mechanisms. • The proposed method is especially useful for enhancing the kinematic reliability. • An envelope method is introduced for efficiently implementing the proposed methods. • The proposed method is demonstrated by two real planar mechanisms.

Eigenvalues and bifurcation for problems with positively homogeneous operators and reaction-diffusion systems with unilateral terms

Czech Academy of Sciences Publication Activity Database

Kučera, Milan; Navrátil, J.

2018-01-01

Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17302559?via%3Dihub

Perturbation of embedded eigenvalue by a near-lying resonance

Energy Technology Data Exchange (ETDEWEB)

Belyaev, V B; Motovilov, A K

1997-12-31

The case of quantum-mechanical system (including electronic molecules) is considered where Hamiltonian allows a separation, in particular by the Faddeev method, of a weakly coupled channel. Width (i.e. the imaginary part) of the resonance generated by a discrete spectrum eigenvalue of the separated channel is studied in the case where main part of the Hamiltonian gives itself another resonance. It is shown that if real parts of these resonances coincide and, at the same time, a coupling between the separated and main channels is sufficiently small then the width of the resonance generated by the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon being a kind of universal law, may play an important role increasing the `cold fusion` probability in electronic molecules whose nuclear constituents have narrow pre-threshold resonances. 21 refs.

Sensitivity analysis methods and a biosphere test case implemented in EIKOS

Energy Technology Data Exchange (ETDEWEB)

Ekstroem, P.A.; Broed, R. [Facilia AB, Stockholm, (Sweden)

2006-05-15

Computer-based models can be used to approximate real life processes. These models are usually based on mathematical equations, which are dependent on several variables. The predictive capability of models is therefore limited by the uncertainty in the value of these. Sensitivity analysis is used to apportion the relative importance each uncertain input parameter has on the output variation. Sensitivity analysis is therefore an essential tool in simulation modelling and for performing risk assessments. Simple sensitivity analysis techniques based on fitting the output to a linear equation are often used, for example correlation or linear regression coefficients. These methods work well for linear models, but for non-linear models their sensitivity estimations are not accurate. Usually models of complex natural systems are non-linear. Within the scope of this work, various sensitivity analysis methods, which can cope with linear, non-linear, as well as non-monotone problems, have been implemented, in a software package, EIKOS, written in Matlab language. The following sensitivity analysis methods are supported by EIKOS: Pearson product moment correlation coefficient (CC), Spearman Rank Correlation Coefficient (RCC), Partial (Rank) Correlation Coefficients (PCC), Standardized (Rank) Regression Coefficients (SRC), Sobol' method, Jansen's alternative, Extended Fourier Amplitude Sensitivity Test (EFAST) as well as the classical FAST method and the Smirnov and the Cramer-von Mises tests. A graphical user interface has also been developed, from which the user easily can load or call the model and perform a sensitivity analysis as well as uncertainty analysis. The implemented sensitivity analysis methods has been benchmarked with well-known test functions and compared with other sensitivity analysis software, with successful results. An illustration of the applicability of EIKOS is added to the report. The test case used is a landscape model consisting of several

Sensitivity analysis methods and a biosphere test case implemented in EIKOS

International Nuclear Information System (INIS)

Ekstroem, P.A.; Broed, R.

2006-05-01

Computer-based models can be used to approximate real life processes. These models are usually based on mathematical equations, which are dependent on several variables. The predictive capability of models is therefore limited by the uncertainty in the value of these. Sensitivity analysis is used to apportion the relative importance each uncertain input parameter has on the output variation. Sensitivity analysis is therefore an essential tool in simulation modelling and for performing risk assessments. Simple sensitivity analysis techniques based on fitting the output to a linear equation are often used, for example correlation or linear regression coefficients. These methods work well for linear models, but for non-linear models their sensitivity estimations are not accurate. Usually models of complex natural systems are non-linear. Within the scope of this work, various sensitivity analysis methods, which can cope with linear, non-linear, as well as non-monotone problems, have been implemented, in a software package, EIKOS, written in Matlab language. The following sensitivity analysis methods are supported by EIKOS: Pearson product moment correlation coefficient (CC), Spearman Rank Correlation Coefficient (RCC), Partial (Rank) Correlation Coefficients (PCC), Standardized (Rank) Regression Coefficients (SRC), Sobol' method, Jansen's alternative, Extended Fourier Amplitude Sensitivity Test (EFAST) as well as the classical FAST method and the Smirnov and the Cramer-von Mises tests. A graphical user interface has also been developed, from which the user easily can load or call the model and perform a sensitivity analysis as well as uncertainty analysis. The implemented sensitivity analysis methods has been benchmarked with well-known test functions and compared with other sensitivity analysis software, with successful results. An illustration of the applicability of EIKOS is added to the report. The test case used is a landscape model consisting of several linked

Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Xuqing Zhang

2013-01-01

Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

Survey of sampling-based methods for uncertainty and sensitivity analysis

International Nuclear Information System (INIS)

Helton, J.C.; Johnson, J.D.; Sallaberry, C.J.; Storlie, C.B.

2006-01-01

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs (ii) generation of samples from uncertain analysis inputs (iii) propagation of sampled inputs through an analysis (iv) presentation of uncertainty analysis results, and (v) determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two-dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition

Survey of sampling-based methods for uncertainty and sensitivity analysis.

Energy Technology Data Exchange (ETDEWEB)

Johnson, Jay Dean; Helton, Jon Craig; Sallaberry, Cedric J. PhD. (.; .); Storlie, Curt B. (Colorado State University, Fort Collins, CO)

2006-06-01

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (1) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (2) Generation of samples from uncertain analysis inputs, (3) Propagation of sampled inputs through an analysis, (4) Presentation of uncertainty analysis results, and (5) Determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition.

Systemization of burnup sensitivity analysis code

International Nuclear Information System (INIS)

Tatsumi, Masahiro; Hyoudou, Hideaki

2004-02-01

To practical use of fact reactors, it is a very important subject to improve prediction accuracy for neutronic properties in LMFBR cores from the viewpoints of improvements on plant efficiency with rationally high performance cores and that on reliability and safety margins. A distinct improvement on accuracy in nuclear core design has been accomplished by development of adjusted nuclear library using the cross-section adjustment method, in which the results of critical experiments of JUPITER and so on are reflected. In the design of large LMFBR cores, however, it is important to accurately estimate not only neutronic characteristics, for example, reaction rate distribution and control rod worth but also burnup characteristics, for example, burnup reactivity loss, breeding ratio and so on. For this purpose, it is desired to improve prediction accuracy of burnup characteristics using the data widely obtained in actual core such as the experimental fast reactor core 'JOYO'. The analysis of burnup characteristics is needed to effectively use burnup characteristics data in the actual cores based on the cross-section adjustment method. So far, development of a analysis code for burnup sensitivity, SAGEP-BURN, has been done and confirmed its effectiveness. However, there is a problem that analysis sequence become inefficient because of a big burden to user due to complexity of the theory of burnup sensitivity and limitation of the system. It is also desired to rearrange the system for future revision since it is becoming difficult to implement new functionalities in the existing large system. It is not sufficient to unify each computational component for some reasons; computational sequence may be changed for each item being analyzed or for purpose such as interpretation of physical meaning. Therefore it is needed to systemize the current code for burnup sensitivity analysis with component blocks of functionality that can be divided or constructed on occasion. For this

Asymmetric modes and complex time eigenvalues of the one-speed neutron transport equation in a homogeneous sphere

International Nuclear Information System (INIS)

Paranjape, S.D.; Kumar, V.; Sahni, D.C.

1993-01-01

The one-speed, time-dependent, isotropically scattering, integral transport equation in a homogeneous sphere has been converted into a criticality-like problem by considering exponential time behaviour of the scalar flux. This criticality problem has been converted into a matrix eigenvalue problem using the Fourier transform technique. The time eigenvalues λ, which are complex in general, have been determined for spherically symmetric as well as asymmetric modes. For the former case, the real decay constants and the real parts of complex decay constants decrease monotonically with increasing system size and form two distinct families of single-valued functions. For the spherically asymmetric modes, certain new features emerge. The real decay constants are found to be multi-valued functions of system size and they do not always decrease monotonically with increasing system size. As the system size increases from zero onwards, the decay constants alternate between complex and real values and the real and complex decay constant curves interlace. (Author)

Equi-frequency contour of photonic crystals with the extended Dirichlet-to-Neumann wave vector eigenvalue equation method

International Nuclear Information System (INIS)

Jiang Bin; Zhang Yejing; Wang Yufei; Liu Anjin; Zheng Wanhua

2012-01-01

We present the extended Dirichlet-to-Neumann wave vector eigenvalue equation (DtN-WVEE) method to calculate the equi-frequency contour (EFC) of square lattice photonic crystals (PhCs). With the extended DtN-WVEE method and Snell's law, the effective refractive index of the mode with a circular EFC can be obtained, which is further validated with the refractive index weighted by the electric field or magnetic field. To further verify the EFC calculated by the DtN-WVEE method, the finite-difference time-domain method is also used. Compared with other wave vector eigenvalue equation methods that calculate EFC directly, the size of the eigenmatrix used in the DtN-WVEE method is much smaller, and the computation time is significantly reduced. Since the DtN-WVEE method solves wave vectors for given arbitrary frequencies, it can also find applications in studying the optical properties of a PhC with dispersive, lossy and magnetic materials. (paper)

The eigenvalues of the SN transport matrix

International Nuclear Information System (INIS)

Ourique, L.E.; Vilhena, M.T. de

2005-01-01

In a recent paper, we analyze the dependence of the eigenvalues of the S N matrix transport, associated with the system of linear differential equations that corresponds to the S N approximations of the transport equation [1]. By considering a control parameter, we have shown that there exist some bifurcation points. This means that the solutions of S N approximations change from oscillatory to non-oscillatory behavior, a different approach of the study by [2]. Nowadays, the one-dimensional transport equation and related problems have been a source of new techniques for solving particular cases as well the development of analytical methods that search aspects of existence and uniqueness of the solutions [3], [4]. In this work, we generalize the results shown in [1], searching for a model of the distribution of the bifurcation points of the S N matrix transport, studying the one-dimensional case in a slab, with anisotropic differential cross section of order 3. The result indicates that the bifurcation points obey a certain rule of distribution. Beside that, the condition number of the matrix transport increases too much in the neighborhood of these points, as we have seen in [1]. (author)

Global sensitivity analysis by polynomial dimensional decomposition

Energy Technology Data Exchange (ETDEWEB)

Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)

2011-07-15

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.

Eigenvalues and bifurcation for problems with positively homogeneous operators and reaction-diffusion systems with unilateral terms

Czech Academy of Sciences Publication Activity Database

Kučera, Milan; Navrátil, J.

2018-01-01

Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www. science direct.com/ science /article/pii/S0362546X17302559?via%3Dihub

Discrete non-parametric kernel estimation for global sensitivity analysis

International Nuclear Information System (INIS)

Senga Kiessé, Tristan; Ventura, Anne

2016-01-01

This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.

Beyond sensitivity analysis

DEFF Research Database (Denmark)

Lund, Henrik; Sorknæs, Peter; Mathiesen, Brian Vad

2018-01-01

of electricity, which have been introduced in recent decades. These uncertainties pose a challenge to the design and assessment of future energy strategies and investments, especially in the economic assessment of renewable energy versus business-as-usual scenarios based on fossil fuels. From a methodological...... point of view, the typical way of handling this challenge has been to predict future prices as accurately as possible and then conduct a sensitivity analysis. This paper includes a historical analysis of such predictions, leading to the conclusion that they are almost always wrong. Not only...... are they wrong in their prediction of price levels, but also in the sense that they always seem to predict a smooth growth or decrease. This paper introduces a new method and reports the results of applying it on the case of energy scenarios for Denmark. The method implies the expectation of fluctuating fuel...

Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

International Nuclear Information System (INIS)

Torrini, M.

1983-01-01

The exponential nature of the translation matrix G of spherical free waves has been set forth in a previous paper.The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectros and the eigenvalues of G have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centered at a different point is solved

Risk Characterization uncertainties associated description, sensitivity analysis

International Nuclear Information System (INIS)

Carrillo, M.; Tovar, M.; Alvarez, J.; Arraez, M.; Hordziejewicz, I.; Loreto, I.

2013-01-01

The power point presentation is about risks to the estimated levels of exposure, uncertainty and variability in the analysis, sensitivity analysis, risks from exposure to multiple substances, formulation of guidelines for carcinogenic and genotoxic compounds and risk subpopulations

Overview of methods for uncertainty analysis and sensitivity analysis in probabilistic risk assessment

International Nuclear Information System (INIS)

Iman, R.L.; Helton, J.C.

1985-01-01

Probabilistic Risk Assessment (PRA) is playing an increasingly important role in the nuclear reactor regulatory process. The assessment of uncertainties associated with PRA results is widely recognized as an important part of the analysis process. One of the major criticisms of the Reactor Safety Study was that its representation of uncertainty was inadequate. The desire for the capability to treat uncertainties with the MELCOR risk code being developed at Sandia National Laboratories is indicative of the current interest in this topic. However, as yet, uncertainty analysis and sensitivity analysis in the context of PRA is a relatively immature field. In this paper, available methods for uncertainty analysis and sensitivity analysis in a PRA are reviewed. This review first treats methods for use with individual components of a PRA and then considers how these methods could be combined in the performance of a complete PRA. In the context of this paper, the goal of uncertainty analysis is to measure the imprecision in PRA outcomes of interest, and the goal of sensitivity analysis is to identify the major contributors to this imprecision. There are a number of areas that must be considered in uncertainty analysis and sensitivity analysis for a PRA: (1) information, (2) systems analysis, (3) thermal-hydraulic phenomena/fission product behavior, (4) health and economic consequences, and (5) display of results. Each of these areas and the synthesis of them into a complete PRA are discussed

Sensitivity Analysis for Design Optimization Integrated Software Tools, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The objective of this proposed project is to provide a new set of sensitivity analysis theory and codes, the Sensitivity Analysis for Design Optimization Integrated...

Seismic analysis of a helical coil type heat exchanger

International Nuclear Information System (INIS)

Nishiguchi, I.; Baba, O.; Yatabe, H.

1984-01-01

The intermediate heat exchanger (IHX) which forms the reactor coolant pressure boundary is one of the most important components of the Multi-purpose Experimental Very High Temperature Gas-cooled Reactor (ex. VHTR) under development at Japan Atomic Energy Research Institute. This paper presents the results of the finite element modeling, eigenvalue analysis and dynamic response analysis of the IHX. For the modeling, the structure of the IHX was separated into a helical tube bundle, inner and outer vessels, and a center pipe. The eigenvalue analysis was made for each structure with a detailed three-dimensional finite element model. Then the simplified model of the whole structure of the IHX was constructed using the result of the eigenvalue analysis. A dynamic response analysis was made for the simplified model with and without stoppers of the helical tube bundle supports and the center pipe. The effect of stoppers on the behavior of the center pipe, the helical tube, and the connecting tube is discussed. (author)

Application of Stochastic Sensitivity Analysis to Integrated Force Method

Directory of Open Access Journals (Sweden)

X. F. Wei

2012-01-01

Full Text Available As a new formulation in structural analysis, Integrated Force Method has been successfully applied to many structures for civil, mechanical, and aerospace engineering due to the accurate estimate of forces in computation. Right now, it is being further extended to the probabilistic domain. For the assessment of uncertainty effect in system optimization and identification, the probabilistic sensitivity analysis of IFM was further investigated in this study. A set of stochastic sensitivity analysis formulation of Integrated Force Method was developed using the perturbation method. Numerical examples are presented to illustrate its application. Its efficiency and accuracy were also substantiated with direct Monte Carlo simulations and the reliability-based sensitivity method. The numerical algorithm was shown to be readily adaptable to the existing program since the models of stochastic finite element and stochastic design sensitivity are almost identical.

Carbon dioxide capture processes: Simulation, design and sensitivity analysis

DEFF Research Database (Denmark)

Zaman, Muhammad; Lee, Jay Hyung; Gani, Rafiqul

2012-01-01

equilibrium and associated property models are used. Simulations are performed to investigate the sensitivity of the process variables to change in the design variables including process inputs and disturbances in the property model parameters. Results of the sensitivity analysis on the steady state...... performance of the process to the L/G ratio to the absorber, CO2 lean solvent loadings, and striper pressure are presented in this paper. Based on the sensitivity analysis process optimization problems have been defined and solved and, a preliminary control structure selection has been made.......Carbon dioxide is the main greenhouse gas and its major source is combustion of fossil fuels for power generation. The objective of this study is to carry out the steady-state sensitivity analysis for chemical absorption of carbon dioxide capture from flue gas using monoethanolamine solvent. First...

Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

The generators of the algebras under consideration can be written in a canonical two-index form and hence the associated standard seuqence of Casimir elements can be constructed. Following the classical approach by Perelomov and Popov, we obtain the eigenvalues of these Casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions. (orig.)

A Global Sensitivity Analysis Methodology for Multi-physics Applications

Energy Technology Data Exchange (ETDEWEB)

Tong, C H; Graziani, F R

2007-02-02

Experiments are conducted to draw inferences about an entire ensemble based on a selected number of observations. This applies to both physical experiments as well as computer experiments, the latter of which are performed by running the simulation models at different input configurations and analyzing the output responses. Computer experiments are instrumental in enabling model analyses such as uncertainty quantification and sensitivity analysis. This report focuses on a global sensitivity analysis methodology that relies on a divide-and-conquer strategy and uses intelligent computer experiments. The objective is to assess qualitatively and/or quantitatively how the variabilities of simulation output responses can be accounted for by input variabilities. We address global sensitivity analysis in three aspects: methodology, sampling/analysis strategies, and an implementation framework. The methodology consists of three major steps: (1) construct credible input ranges; (2) perform a parameter screening study; and (3) perform a quantitative sensitivity analysis on a reduced set of parameters. Once identified, research effort should be directed to the most sensitive parameters to reduce their uncertainty bounds. This process is repeated with tightened uncertainty bounds for the sensitive parameters until the output uncertainties become acceptable. To accommodate the needs of multi-physics application, this methodology should be recursively applied to individual physics modules. The methodology is also distinguished by an efficient technique for computing parameter interactions. Details for each step will be given using simple examples. Numerical results on large scale multi-physics applications will be available in another report. Computational techniques targeted for this methodology have been implemented in a software package called PSUADE.

Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear system A X = λ X when λ ≠ 0 . But λ = 0 implies that det A = 0 for X ≠ 0 and then the rank of matrix A is reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.

Sensitivity analysis techniques applied to a system of hyperbolic conservation laws

International Nuclear Information System (INIS)

Weirs, V. Gregory; Kamm, James R.; Swiler, Laura P.; Tarantola, Stefano; Ratto, Marco; Adams, Brian M.; Rider, William J.; Eldred, Michael S.

2012-01-01

Sensitivity analysis is comprised of techniques to quantify the effects of the input variables on a set of outputs. In particular, sensitivity indices can be used to infer which input parameters most significantly affect the results of a computational model. With continually increasing computing power, sensitivity analysis has become an important technique by which to understand the behavior of large-scale computer simulations. Many sensitivity analysis methods rely on sampling from distributions of the inputs. Such sampling-based methods can be computationally expensive, requiring many evaluations of the simulation; in this case, the Sobol' method provides an easy and accurate way to compute variance-based measures, provided a sufficient number of model evaluations are available. As an alternative, meta-modeling approaches have been devised to approximate the response surface and estimate various measures of sensitivity. In this work, we consider a variety of sensitivity analysis methods, including different sampling strategies, different meta-models, and different ways of evaluating variance-based sensitivity indices. The problem we consider is the 1-D Riemann problem. By a careful choice of inputs, discontinuous solutions are obtained, leading to discontinuous response surfaces; such surfaces can be particularly problematic for meta-modeling approaches. The goal of this study is to compare the estimated sensitivity indices with exact values and to evaluate the convergence of these estimates with increasing samples sizes and under an increasing number of meta-model evaluations. - Highlights: ► Sensitivity analysis techniques for a model shock physics problem are compared. ► The model problem and the sensitivity analysis problem have exact solutions. ► Subtle details of the method for computing sensitivity indices can affect the results.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks.

Science.gov (United States)

Navarro Jimenez, M; Le Maître, O P; Knio, O M

2016-12-28

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol's decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

Global sensitivity analysis in stochastic simulators of uncertain reaction networks

KAUST Repository

Navarro, María

2016-12-26

Stochastic models of chemical systems are often subjected to uncertainties in kinetic parameters in addition to the inherent random nature of their dynamics. Uncertainty quantification in such systems is generally achieved by means of sensitivity analyses in which one characterizes the variability with the uncertain kinetic parameters of the first statistical moments of model predictions. In this work, we propose an original global sensitivity analysis method where the parametric and inherent variability sources are both treated through Sobol’s decomposition of the variance into contributions from arbitrary subset of uncertain parameters and stochastic reaction channels. The conceptual development only assumes that the inherent and parametric sources are independent, and considers the Poisson processes in the random-time-change representation of the state dynamics as the fundamental objects governing the inherent stochasticity. A sampling algorithm is proposed to perform the global sensitivity analysis, and to estimate the partial variances and sensitivity indices characterizing the importance of the various sources of variability and their interactions. The birth-death and Schlögl models are used to illustrate both the implementation of the algorithm and the richness of the proposed analysis method. The output of the proposed sensitivity analysis is also contrasted with a local derivative-based sensitivity analysis method classically used for this type of systems.

A pragmatic approach to voltage stability analysis of large power systems

Energy Technology Data Exchange (ETDEWEB)

Sarmiento, H.G.; Pampin, G. [Inst. de Investigaciones Electricas, Morelos (Mexico); Diaz de Leon, J.A. [American Superconductor, Middleton, WI (United States)

2008-07-01

A methodology for performing voltage stability analyses for large power systems was presented. Modal and time-domain analyses were used for selection and siting solutions for potential voltage instability and collapse. Steady state systems were used to compute the smallest eigenvalues and associated eigenvalues of a reduced Jacobean matrix. The eigenvalues were used to provide a relative measure of proximity to voltage instability. The analysis was applied to provide an indication of a network's proximity to voltage collapse. Negative eigenvalues were representative of voltage instability conditions, while small positive values indicated proximity to voltage instability. The analysis technique was used to identify buses, lines, and generators prone to voltage instabilities for a 10-node network. A comparative analysis of results obtained from modal and time domain analyses were used to identify areas vulnerable to voltage instability conditions. Pre-fault, fault, and post-fault conditions were analyzed statically and dynamically. Results of the study showed that the combined method can be used to identify and place reactive power compensation solutions for voltage collapses in electric networks. 20 refs., 5 tabs., 7 figs.

Allergen Sensitization Pattern by Sex: A Cluster Analysis in Korea.

Science.gov (United States)

Ohn, Jungyoon; Paik, Seung Hwan; Doh, Eun Jin; Park, Hyun-Sun; Yoon, Hyun-Sun; Cho, Soyun

2017-12-01

Allergens tend to sensitize simultaneously. Etiology of this phenomenon has been suggested to be allergen cross-reactivity or concurrent exposure. However, little is known about specific allergen sensitization patterns. To investigate the allergen sensitization characteristics according to gender. Multiple allergen simultaneous test (MAST) is widely used as a screening tool for detecting allergen sensitization in dermatologic clinics. We retrospectively reviewed the medical records of patients with MAST results between 2008 and 2014 in our Department of Dermatology. A cluster analysis was performed to elucidate the allergen-specific immunoglobulin (Ig)E cluster pattern. The results of MAST (39 allergen-specific IgEs) from 4,360 cases were analyzed. By cluster analysis, 39items were grouped into 8 clusters. Each cluster had characteristic features. When compared with female, the male group tended to be sensitized more frequently to all tested allergens, except for fungus allergens cluster. The cluster and comparative analysis results demonstrate that the allergen sensitization is clustered, manifesting allergen similarity or co-exposure. Only the fungus cluster allergens tend to sensitize female group more frequently than male group.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data.

Science.gov (United States)

Zhu, Hongtu; Ibrahim, Joseph G; Tang, Niansheng

2014-04-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.

Beyond the GUM: variance-based sensitivity analysis in metrology

International Nuclear Information System (INIS)

Lira, I

2016-01-01

Variance-based sensitivity analysis is a well established tool for evaluating the contribution of the uncertainties in the inputs to the uncertainty in the output of a general mathematical model. While the literature on this subject is quite extensive, it has not found widespread use in metrological applications. In this article we present a succinct review of the fundamentals of sensitivity analysis, in a form that should be useful to most people familiarized with the Guide to the Expression of Uncertainty in Measurement (GUM). Through two examples, it is shown that in linear measurement models, no new knowledge is gained by using sensitivity analysis that is not already available after the terms in the so-called ‘law of propagation of uncertainties’ have been computed. However, if the model behaves non-linearly in the neighbourhood of the best estimates of the input quantities—and if these quantities are assumed to be statistically independent—sensitivity analysis is definitely advantageous for gaining insight into how they can be ranked according to their importance in establishing the uncertainty of the measurand. (paper)

Benchmark Analysis of Subcritical Noise Measurements on a Nickel-Reflected Plutonium Metal Sphere

Energy Technology Data Exchange (ETDEWEB)

John D. Bess; Jesson Hutchinson

2009-09-01

Subcritical experiments using californium source-driven noise analysis (CSDNA) and Feynman variance-to-mean methods were performed with an alpha-phase plutonium sphere reflected by nickel shells, up to a maximum thickness of 7.62 cm. Both methods provide means of determining the subcritical multiplication of a system containing nuclear material. A benchmark analysis of the experiments was performed for inclusion in the 2010 edition of the International Handbook of Evaluated Criticality Safety Benchmark Experiments. Benchmark models have been developed that represent these subcritical experiments. An analysis of the computed eigenvalues and the uncertainty in the experiment and methods was performed. The eigenvalues computed using the CSDNA method were very close to those calculated using MCNP5; however, computed eigenvalues are used in the analysis of the CSDNA method. Independent calculations using KENO-VI provided similar eigenvalues to those determined using the CSDNA method and MCNP5. A slight trend with increasing nickel-reflector thickness was seen when comparing MCNP5 and KENO-VI results. For the 1.27-cm-thick configuration the MCNP eigenvalue was approximately 300 pcm greater. The calculated KENO eigenvalue was about 300 pcm greater for the 7.62-cm-thick configuration. The calculated results were approximately the same for a 5-cm-thick shell. The eigenvalues determined using the Feynman method are up to approximately 2.5% lower than those determined using either the CSDNA method or the Monte Carlo codes. The uncertainty in the results from either method was not large enough to account for the bias between the two experimental methods. An ongoing investigation is being performed to assess what potential uncertainties and/or biases exist that have yet to be properly accounted for. The dominant uncertainty in the CSDNA analysis was the uncertainty in selecting a neutron cross-section library for performing the analysis of the data. The uncertainty in the

Rethinking Sensitivity Analysis of Nuclear Simulations with Topology

Energy Technology Data Exchange (ETDEWEB)

Dan Maljovec; Bei Wang; Paul Rosen; Andrea Alfonsi; Giovanni Pastore; Cristian Rabiti; Valerio Pascucci

2016-01-01

In nuclear engineering, understanding the safety margins of the nuclear reactor via simulations is arguably of paramount importance in predicting and preventing nuclear accidents. It is therefore crucial to perform sensitivity analysis to understand how changes in the model inputs affect the outputs. Modern nuclear simulation tools rely on numerical representations of the sensitivity information -- inherently lacking in visual encodings -- offering limited effectiveness in communicating and exploring the generated data. In this paper, we design a framework for sensitivity analysis and visualization of multidimensional nuclear simulation data using partition-based, topology-inspired regression models and report on its efficacy. We rely on the established Morse-Smale regression technique, which allows us to partition the domain into monotonic regions where easily interpretable linear models can be used to assess the influence of inputs on the output variability. The underlying computation is augmented with an intuitive and interactive visual design to effectively communicate sensitivity information to the nuclear scientists. Our framework is being deployed into the multi-purpose probabilistic risk assessment and uncertainty quantification framework RAVEN (Reactor Analysis and Virtual Control Environment). We evaluate our framework using an simulation dataset studying nuclear fuel performance.

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

International Nuclear Information System (INIS)

Assawaroongruengchot, M.; Marleau, G.

2008-01-01

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study 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 using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k eff -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-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of -2 mk and k eff -EOC of 0.900 for the first two cases, and a CBCVR-BOC of -2 mk and k eff -EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M. [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, stn. Centre-ville, Montreal, H3C3A7 (Canada)], E-mail: monchaia@gmail.com; Marleau, G. [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, stn. Centre-ville, Montreal, H3C3A7 (Canada)], E-mail: guy.marleau@polymtl.ca

2008-03-15

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k{sub eff} at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k{sub eff}-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-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of -2 mk and k{sub eff}-EOC of 0.900 for the first two cases, and a CBCVR-BOC of -2 mk and k{sub eff}-EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study.

Systemization of burnup sensitivity analysis code. 2

International Nuclear Information System (INIS)

Tatsumi, Masahiro; Hyoudou, Hideaki

2005-02-01

Towards the practical use of fast reactors, it is a very important subject to improve prediction accuracy for neutronic properties in LMFBR cores from the viewpoint of improvements on plant efficiency with rationally high performance cores and that on reliability and safety margins. A distinct improvement on accuracy in nuclear core design has been accomplished by the development of adjusted nuclear library using the cross-section adjustment method, in which the results of criticality experiments of JUPITER and so on are reflected. In the design of large LMFBR cores, however, it is important to accurately estimate not only neutronic characteristics, for example, reaction rate distribution and control rod worth but also burnup characteristics, for example, burnup reactivity loss, breeding ratio and so on. For this purpose, it is desired to improve prediction accuracy of burnup characteristics using the data widely obtained in actual core such as the experimental fast reactor 'JOYO'. The analysis of burnup characteristics is needed to effectively use burnup characteristics data in the actual cores based on the cross-section adjustment method. So far, a burnup sensitivity analysis code, SAGEP-BURN, has been developed and confirmed its effectiveness. However, there is a problem that analysis sequence become inefficient because of a big burden to users due to complexity of the theory of burnup sensitivity and limitation of the system. It is also desired to rearrange the system for future revision since it is becoming difficult to implement new functions in the existing large system. It is not sufficient to unify each computational component for the following reasons; the computational sequence may be changed for each item being analyzed or for purpose such as interpretation of physical meaning. Therefore, it is needed to systemize the current code for burnup sensitivity analysis with component blocks of functionality that can be divided or constructed on occasion. For

POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

Directory of Open Access Journals (Sweden)

FAOUZI HADDOUCHI

2015-11-01

Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

KAUST Repository

Bonito, Andrea; Guermond, Jean-Luc

2011-01-01

We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

The strategy of spectral shifts and the sets of correct methods for calculating eigenvalues of general tridiagonal matrices

International Nuclear Information System (INIS)

Emel'yanenko, G.A.; Sek, I.E.

1988-01-01

Many correctable unknown methods for eigenvalue calculation of general tridiagonal matrices with real elements; criteria of singular tridiagonal matrices; necessary and sufficient conditions of tridiagonal matrix degeneracy; process with boundary conditions according to calculation processes of general upper and lower tridiagonal matrix minors are obtained. 6 refs

The EVEREST project: sensitivity analysis of geological disposal systems

International Nuclear Information System (INIS)

Marivoet, Jan; Wemaere, Isabelle; Escalier des Orres, Pierre; Baudoin, Patrick; Certes, Catherine; Levassor, Andre; Prij, Jan; Martens, Karl-Heinz; Roehlig, Klaus

1997-01-01

The main objective of the EVEREST project is the evaluation of the sensitivity of the radiological consequences associated with the geological disposal of radioactive waste to the different elements in the performance assessment. Three types of geological host formations are considered: clay, granite and salt. The sensitivity studies that have been carried out can be partitioned into three categories according to the type of uncertainty taken into account: uncertainty in the model parameters, uncertainty in the conceptual models and uncertainty in the considered scenarios. Deterministic as well as stochastic calculational approaches have been applied for the sensitivity analyses. For the analysis of the sensitivity to parameter values, the reference technique, which has been applied in many evaluations, is stochastic and consists of a Monte Carlo simulation followed by a linear regression. For the analysis of conceptual model uncertainty, deterministic and stochastic approaches have been used. For the analysis of uncertainty in the considered scenarios, mainly deterministic approaches have been applied

Multiple predictor smoothing methods for sensitivity analysis: Example results

International Nuclear Information System (INIS)

Storlie, Curtis B.; Helton, Jon C.

2008-01-01

The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described in the first part of this presentation: (i) locally weighted regression (LOESS), (ii) additive models, (iii) projection pursuit regression, and (iv) recursive partitioning regression. In this, the second and concluding part of the presentation, the indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present

Sensitivity analysis technique for application to deterministic models

International Nuclear Information System (INIS)

Ishigami, T.; Cazzoli, E.; Khatib-Rahbar, M.; Unwin, S.D.

1987-01-01

The characterization of sever accident source terms for light water reactors should include consideration of uncertainties. An important element of any uncertainty analysis is an evaluation of the sensitivity of the output probability distributions reflecting source term uncertainties to assumptions regarding the input probability distributions. Historically, response surface methods (RSMs) were developed to replace physical models using, for example, regression techniques, with simplified models for example, regression techniques, with simplified models for extensive calculations. The purpose of this paper is to present a new method for sensitivity analysis that does not utilize RSM, but instead relies directly on the results obtained from the original computer code calculations. The merits of this approach are demonstrated by application of the proposed method to the suppression pool aerosol removal code (SPARC), and the results are compared with those obtained by sensitivity analysis with (a) the code itself, (b) a regression model, and (c) Iman's method

Probability density adjoint for sensitivity analysis of the Mean of Chaos

Energy Technology Data Exchange (ETDEWEB)

Blonigan, Patrick J., E-mail: blonigan@mit.edu; Wang, Qiqi, E-mail: qiqi@mit.edu

2014-08-01

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.

WKB analysis of PT-symmetric Sturm–Liouville problems

International Nuclear Information System (INIS)

Bender, Carl M; Jones, Hugh F

2012-01-01

Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schrödinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the case with regular Hermitian Sturm–Liouville problems, the eigenvalues of the PT-symmetric Sturm–Liouville problem grow like n 2 for large n. However, the novelty is that a PT eigenvalue problem on a finite domain typically exhibits a sequence of critical points at which pairs of eigenvalues cease to be real and become complex conjugates of one another. For the potentials considered here this sequence of critical points is associated with a turning point on the imaginary axis in the complex plane. WKB analysis is used to calculate the asymptotic behaviours of the real eigenvalues and the locations of the critical points. The method turns out to be surprisingly accurate even at low energies. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

Computations of zeros of special functions and eigenvalues of differential equations by matrix method

OpenAIRE

Miyazaki, Yoshinori

2000-01-01

This paper is strongly based on two powerful general theorems proved by Ikebe, et. al in 1993[15] and 1996[13], which will be referred to as Theorem A and Theorem B in this paper. They were recently published and justify the approximate computations of simple eigenvalues of infinite matrices of certain types by truncation, giving an extremely accurate error estimates. So far, they have applied to some important problems in engineering, such as computing the zeros of some special functions, an...

Effective Perron-Frobenius eigenvalue for a correlated random map

Science.gov (United States)

Pool, Roman R.; Cáceres, Manuel O.

2010-09-01

We investigate the evolution of random positive linear maps with various type of disorder by analytic perturbation and direct simulation. Our theoretical result indicates that the statistics of a random linear map can be successfully described for long time by the mean-value vector state. The growth rate can be characterized by an effective Perron-Frobenius eigenvalue that strongly depends on the type of correlation between the elements of the projection matrix. We apply this approach to an age-structured population dynamics model. We show that the asymptotic mean-value vector state characterizes the population growth rate when the age-structured model has random vital parameters. In this case our approach reveals the nontrivial dependence of the effective growth rate with cross correlations. The problem was reduced to the calculation of the smallest positive root of a secular polynomial, which can be obtained by perturbations in terms of Green’s function diagrammatic technique built with noncommutative cumulants for arbitrary n -point correlations.

SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool.

Science.gov (United States)

Zi, Zhike; Zheng, Yanan; Rundell, Ann E; Klipp, Edda

2008-08-15

It has long been recognized that sensitivity analysis plays a key role in modeling and analyzing cellular and biochemical processes. Systems biology markup language (SBML) has become a well-known platform for coding and sharing mathematical models of such processes. However, current SBML compatible software tools are limited in their ability to perform global sensitivity analyses of these models. This work introduces a freely downloadable, software package, SBML-SAT, which implements algorithms for simulation, steady state analysis, robustness analysis and local and global sensitivity analysis for SBML models. This software tool extends current capabilities through its execution of global sensitivity analyses using multi-parametric sensitivity analysis, partial rank correlation coefficient, SOBOL's method, and weighted average of local sensitivity analyses in addition to its ability to handle systems with discontinuous events and intuitive graphical user interface. SBML-SAT provides the community of systems biologists a new tool for the analysis of their SBML models of biochemical and cellular processes.

Sensitivity analysis and power for instrumental variable studies.

Science.gov (United States)

Wang, Xuran; Jiang, Yang; Zhang, Nancy R; Small, Dylan S

2018-03-31

In observational studies to estimate treatment effects, unmeasured confounding is often a concern. The instrumental variable (IV) method can control for unmeasured confounding when there is a valid IV. To be a valid IV, a variable needs to be independent of unmeasured confounders and only affect the outcome through affecting the treatment. When applying the IV method, there is often concern that a putative IV is invalid to some degree. We present an approach to sensitivity analysis for the IV method which examines the sensitivity of inferences to violations of IV validity. Specifically, we consider sensitivity when the magnitude of association between the putative IV and the unmeasured confounders and the direct effect of the IV on the outcome are limited in magnitude by a sensitivity parameter. Our approach is based on extending the Anderson-Rubin test and is valid regardless of the strength of the instrument. A power formula for this sensitivity analysis is presented. We illustrate its usage via examples about Mendelian randomization studies and its implications via a comparison of using rare versus common genetic variants as instruments. © 2018, The International Biometric Society.

Nonlinear analysis

CERN Document Server

Gasinski, Leszek

2005-01-01

Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

A multilevel, level-set method for optimizing eigenvalues in shape design problems

International Nuclear Information System (INIS)

Haber, E.

2004-01-01

In this paper, we consider optimal design problems that involve shape optimization. The goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible. To achieve this goal we combine two new ideas for an efficient solution of the problem. First, we replace the eigenvalue problem with an approximation by using inverse iteration. Second, we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques. Combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem

Sensitivity Analysis in Sequential Decision Models.

Science.gov (United States)

Chen, Qiushi; Ayer, Turgay; Chhatwal, Jagpreet

2017-02-01

Sequential decision problems are frequently encountered in medical decision making, which are commonly solved using Markov decision processes (MDPs). Modeling guidelines recommend conducting sensitivity analyses in decision-analytic models to assess the robustness of the model results against the uncertainty in model parameters. However, standard methods of conducting sensitivity analyses cannot be directly applied to sequential decision problems because this would require evaluating all possible decision sequences, typically in the order of trillions, which is not practically feasible. As a result, most MDP-based modeling studies do not examine confidence in their recommended policies. In this study, we provide an approach to estimate uncertainty and confidence in the results of sequential decision models. First, we provide a probabilistic univariate method to identify the most sensitive parameters in MDPs. Second, we present a probabilistic multivariate approach to estimate the overall confidence in the recommended optimal policy considering joint uncertainty in the model parameters. We provide a graphical representation, which we call a policy acceptability curve, to summarize the confidence in the optimal policy by incorporating stakeholders' willingness to accept the base case policy. For a cost-effectiveness analysis, we provide an approach to construct a cost-effectiveness acceptability frontier, which shows the most cost-effective policy as well as the confidence in that for a given willingness to pay threshold. We demonstrate our approach using a simple MDP case study. We developed a method to conduct sensitivity analysis in sequential decision models, which could increase the credibility of these models among stakeholders.

Sensitivity analysis of the reactor safety study. Final report

International Nuclear Information System (INIS)

Parkinson, W.J.; Rasmussen, N.C.; Hinkle, W.D.

1979-01-01

The Reactor Safety Study (RSS) or Wash 1400 developed a methodology estimating the public risk from light water nuclear reactors. In order to give further insights into this study, a sensitivity analysis has been performed to determine the significant contributors to risk for both the PWR and BWR. The sensitivity to variation of the point values of the failure probabilities reported in the RSS was determined for the safety systems identified therein, as well as for many of the generic classes from which individual failures contributed to system failures. Increasing as well as decreasing point values were considered. An analysis of the sensitivity to increasing uncertainty in system failure probabilities was also performed. The sensitivity parameters chosen were release category probabilities, core melt probability, and the risk parameters of early fatalities, latent cancers and total property damage. The latter three are adequate for describing all public risks identified in the RSS. The results indicate reductions of public risk by less than a factor of two for factor reductions in system or generic failure probabilities as high as one hundred. There also appears to be more benefit in monitoring the most sensitive systems to verify adherence to RSS failure rates than to backfitting present reactors. The sensitivity analysis results do indicate, however, possible benefits in reducing human error rates

Sensitivity analysis for contagion effects in social networks

Science.gov (United States)

VanderWeele, Tyler J.

2014-01-01

Analyses of social network data have suggested that obesity, smoking, happiness and loneliness all travel through social networks. Individuals exert “contagion effects” on one another through social ties and association. These analyses have come under critique because of the possibility that homophily from unmeasured factors may explain these statistical associations and because similar findings can be obtained when the same methodology is applied to height, acne and head-aches, for which the conclusion of contagion effects seems somewhat less plausible. We use sensitivity analysis techniques to assess the extent to which supposed contagion effects for obesity, smoking, happiness and loneliness might be explained away by homophily or confounding and the extent to which the critique using analysis of data on height, acne and head-aches is relevant. Sensitivity analyses suggest that contagion effects for obesity and smoking cessation are reasonably robust to possible latent homophily or environmental confounding; those for happiness and loneliness are somewhat less so. Supposed effects for height, acne and head-aches are all easily explained away by latent homophily and confounding. The methodology that has been employed in past studies for contagion effects in social networks, when used in conjunction with sensitivity analysis, may prove useful in establishing social influence for various behaviors and states. The sensitivity analysis approach can be used to address the critique of latent homophily as a possible explanation of associations interpreted as contagion effects. PMID:25580037

Sensitivity analysis of an Advanced Gas-cooled Reactor control rod model

International Nuclear Information System (INIS)

Scott, M.; Green, P.L.; O’Driscoll, D.; Worden, K.; Sims, N.D.

2016-01-01

Highlights: • A model was made of the AGR control rod mechanism. • The aim was to better understand the performance when shutting down the reactor. • The model showed good agreement with test data. • Sensitivity analysis was carried out. • The results demonstrated the robustness of the system. - Abstract: A model has been made of the primary shutdown system of an Advanced Gas-cooled Reactor nuclear power station. The aim of this paper is to explore the use of sensitivity analysis techniques on this model. The two motivations for performing sensitivity analysis are to quantify how much individual uncertain parameters are responsible for the model output uncertainty, and to make predictions about what could happen if one or several parameters were to change. Global sensitivity analysis techniques were used based on Gaussian process emulation; the software package GEM-SA was used to calculate the main effects, the main effect index and the total sensitivity index for each parameter and these were compared to local sensitivity analysis results. The results suggest that the system performance is resistant to adverse changes in several parameters at once.

On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values

International Nuclear Information System (INIS)

Wei Yi; Fyodorov, Yan V

2008-01-01

Given any fixed N x N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A=U√G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure. (fast track communication)

A numerical method for eigenvalue problems in modeling liquid crystals

Energy Technology Data Exchange (ETDEWEB)

Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A. [Kent State Univ., OH (United States); Calvetti, D. [Stevens Inst. of Technology, Hoboken, NJ (United States)

1996-12-31

Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.

A global sensitivity analysis approach for morphogenesis models

KAUST Repository

Boas, Sonja E. M.

2015-11-21

Background Morphogenesis is a developmental process in which cells organize into shapes and patterns. Complex, non-linear and multi-factorial models with images as output are commonly used to study morphogenesis. It is difficult to understand the relation between the uncertainty in the input and the output of such ‘black-box’ models, giving rise to the need for sensitivity analysis tools. In this paper, we introduce a workflow for a global sensitivity analysis approach to study the impact of single parameters and the interactions between them on the output of morphogenesis models. Results To demonstrate the workflow, we used a published, well-studied model of vascular morphogenesis. The parameters of this cellular Potts model (CPM) represent cell properties and behaviors that drive the mechanisms of angiogenic sprouting. The global sensitivity analysis correctly identified the dominant parameters in the model, consistent with previous studies. Additionally, the analysis provided information on the relative impact of single parameters and of interactions between them. This is very relevant because interactions of parameters impede the experimental verification of the predicted effect of single parameters. The parameter interactions, although of low impact, provided also new insights in the mechanisms of in silico sprouting. Finally, the analysis indicated that the model could be reduced by one parameter. Conclusions We propose global sensitivity analysis as an alternative approach to study the mechanisms of morphogenesis. Comparison of the ranking of the impact of the model parameters to knowledge derived from experimental data and from manipulation experiments can help to falsify models and to find the operand mechanisms in morphogenesis. The workflow is applicable to all ‘black-box’ models, including high-throughput in vitro models in which output measures are affected by a set of experimental perturbations.

A global sensitivity analysis approach for morphogenesis models.

Science.gov (United States)