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Sample records for chebyshev spectral methods

  1. Chebyshev and Fourier spectral methods

    CERN Document Server

    Boyd, John P

    2001-01-01

    Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

  2. Chebyshev super spectral viscosity method for water hammer analysis

    Directory of Open Access Journals (Sweden)

    Hongyu Chen

    2013-09-01

    Full Text Available In this paper, a new fast and efficient algorithm, Chebyshev super spectral viscosity (SSV method, is introduced to solve the water hammer equations. Compared with standard spectral method, the method's advantage essentially consists in adding a super spectral viscosity to the equations for the high wave numbers of the numerical solution. It can stabilize the numerical oscillation (Gibbs phenomenon and improve the computational efficiency while discontinuities appear in the solution. Results obtained from the Chebyshev super spectral viscosity method exhibit greater consistency with conventional water hammer calculations. It shows that this new numerical method offers an alternative way to investigate the behavior of the water hammer in propellant pipelines.

  3. Chebyshev super spectral viscosity method for a fluidized bed model

    International Nuclear Information System (INIS)

    Sarra, Scott A.

    2003-01-01

    A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the solution. A modified Gegenbauer postprocessing procedure is used to obtain a solution which is free of oscillations caused by the Gibbs-Wilbraham phenomenon in the spectral viscosity solution. Conservation is maintained by working with unphysical negative particle concentrations

  4. Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation

    Science.gov (United States)

    Im, Dong Kyun; Kim, Hyun Soon; Choi, Seongim

    2018-05-01

    A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev-Gauss-Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass-spring-damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments.

  5. A multidomain chebyshev pseudo-spectral method for fluid flow and heat transfer from square cylinders

    KAUST Repository

    Wang, Zhiheng

    2015-01-01

    A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.

  6. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2014-01-01

    Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  7. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

    Science.gov (United States)

    Motsa, S S; Magagula, V M; Sibanda, P

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  8. A multidomain chebyshev pseudo-spectral method for fluid flow and heat transfer from square cylinders

    KAUST Repository

    Wang, Zhiheng; Huang, Zhu; Zhang, Wei; Xi, Guang

    2015-01-01

    of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated

  9. The application of the Chebyshev-spectral method in transport phenomena

    CERN Document Server

    Guo, Weidong; Narayanan, Ranga

    2012-01-01

    Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character.  When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists  to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer.  To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems.  The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs.  The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interes...

  10. Rational Chebyshev spectral transform for the dynamics of broad-area laser diodes

    International Nuclear Information System (INIS)

    Javaloyes, J.; Balle, S.

    2015-01-01

    This manuscript details the use of the rational Chebyshev transform for describing the transverse dynamics of broad-area laser diodes and amplifiers. This spectral method can be used in combination with the delay algebraic equations approach developed in [1], which substantially reduces the computation time. The theory is presented in such a way that it encompasses the case of the Fourier spectral transform presented in [2] as a particular case. It is also extended to the consideration of index guiding with an arbitrary transverse profile. Because their domain of definition is infinite, the convergence properties of the Chebyshev rational functions allow handling the boundary conditions with higher accuracy than with the previously studied Fourier transform method. As practical examples, we solve the beam propagation problem with and without index guiding: we obtain excellent results and an improvement of the integration time between one and two orders of magnitude as compared with a fully distributed two dimensional model

  11. Modified Chebyshev Collocation Method for Solving Differential Equations

    Directory of Open Access Journals (Sweden)

    M Ziaul Arif

    2015-05-01

    Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

  12. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boundary

    2015-09-01

    Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

  13. Simulation of electrically driven jet using Chebyshev collocation method

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with invariants.Then the implicit differential equations solver "ddaskr" is used to solve the ODEs and ...

  14. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    Science.gov (United States)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  15. Shifted-modified Chebyshev filters

    OpenAIRE

    ŞENGÜL, Metin

    2013-01-01

    This paper introduces a new type of filter approximation method that utilizes shifted-modified Chebyshev filters. Construction of the new filters involves the use of shifted-modified Chebyshev polynomials that are formed using the roots of conventional Chebyshev polynomials. The study also includes 2 tables containing the shifted-modified Chebyshev polynomials and the normalized element values for the low-pass prototype filters up to degree 6. The transducer power gain, group dela...

  16. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    International Nuclear Information System (INIS)

    Lee, Yoon Hee; Cho, Nam Zin

    2016-01-01

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  17. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)

    2016-05-15

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  18. An embedded formula of the Chebyshev collocation method for stiff problems

    Science.gov (United States)

    Piao, Xiangfan; Bu, Sunyoung; Kim, Dojin; Kim, Philsu

    2017-12-01

    In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge-Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.

  19. Spectral element method for wave propagation on irregular domains

    Indian Academy of Sciences (India)

    Yan Hui Geng

    2018-03-14

    Mar 14, 2018 ... Abstract. A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the ...

  20. Spectral element method for wave propagation on irregular domains

    Indian Academy of Sciences (India)

    A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss–Lobatto–Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are ...

  1. A linear stability analysis of thermal convection in spherical shells with variable radial gravity based on the Tau-Chebyshev method

    International Nuclear Information System (INIS)

    Avila, Ruben; Cabello-González, Ares; Ramos, Eduardo

    2013-01-01

    Highlights: • The Tau-Chebyshev method solves the linear fluid flow equations in spherical shells. • The fluid motion is driven by a central force proportional to the radial position. • The full Navier–Stokes equations are solved by the spectral element method. • The linear results are verified with the solution of the Navier–Stokes equations. • The solution of the linear problems is used to initiate non-linear calculations. -- Abstract: The onset of thermal convection in a non-rotating spherical shell is investigated using linear theory. The Tau-Chebyshev spectral method is used to integrate the linearized equations. We investigate the onset of thermal convection by considering two cases of the radial gravitational field (i) a local acceleration, acting radially inward, that is proportional to the distance from the center r, and (ii) a radial gravitational central force that is proportional to r −n . The former case has been widely analyzed in the literature, because it constitutes a simplified model that is usually used, in astrophysics and geophysics, and is studied here to validate the numerical method. The latter case was analyzed since the case n = 5 has been experimentally realized (by means of the dielectrophoretic effect) under microgravity condition, in the experimental container called GeoFlow, inside the International Space Station. Our study is aimed to clarify the role of (i) a radially inward central force (either proportional to r or to r −n ), (ii) a base conductive temperature distribution provided by either a uniform heat source or an imposed temperature difference between outer and inner spheres, and (iii) the aspect ratio η (ratio of the radii of the inner and outer spheres), on the critical Rayleigh number. In all cases the surface of the spheres has been assumed to be rigid. The results obtained with the linear theory based on the Tau-Chebyshev spectral method are compared with those of the integration of the full non

  2. Spectral methods in numerical plasma simulation

    International Nuclear Information System (INIS)

    Coutsias, E.A.; Hansen, F.R.; Huld, T.; Knorr, G.; Lynov, J.P.

    1989-01-01

    An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded in a two-dimensional Fourier series, while a Chebyshev-Fourier expansion is employed in the second case. A new, efficient algorithm for the solution of Poisson's equation on an annulus is introduced. Problems connected to aliasing and to short wavelength noise generated by gradient steepening are discussed. (orig.)

  3. The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval

    Directory of Open Access Journals (Sweden)

    Majid Tavassoli Kajani

    2013-01-01

    Full Text Available We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-kind Chebyshev pseudospectral method that is indeed a combination of Tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.

  4. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

    National Research Council Canada - National Science Library

    Mitchell, Jason

    2002-01-01

    A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...

  5. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

    Science.gov (United States)

    Kaporin, I. E.

    2012-02-01

    In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

  6. Spectral methods for time dependent partial differential equations

    Science.gov (United States)

    Gottlieb, D.; Turkel, E.

    1983-01-01

    The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

  7. Antireflection coatings with Chebyshev or Butterworth response - Design

    Science.gov (United States)

    Baumeister, Philip

    1986-12-01

    The approximation of Kard (1971) is used to find values for the refractive indices of nonabsorbing layers with equal optical thickness to produce an antireflection (AR) coating for a dielectric substrate that has a Chebyshev spectral response, with application to the design of bandpass filters. The method is numerically demonstrated with the example of four-layer Chebyshev AR coatings with narrow, medium and wide bandwidths, and substrates of indices 2, 5, and 10. Approximate indices are also given for the case when the radiant reflectance/transmittance of the coating vs frequency is maximally flat (Butterworth response).

  8. and chebyshev functions

    Directory of Open Access Journals (Sweden)

    Mohsen Razzaghi

    2000-01-01

    Full Text Available A direct method for finding the solution of variational problems using a hybrid function is discussed. The hybrid functions which consist of block-pulse functions plus Chebyshev polynomials are introduced. An operational matrix of integration and the integration of the cross product of two hybrid function vectors are presented and are utilized to reduce a variational problem to the solution of an algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.

  9. Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

    Science.gov (United States)

    Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

    2018-06-12

    We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

  10. Pseudospectral methods on a semi-infinite interval with application to the hydrogen atom: a comparison of the mapped Fourier-sine method with Laguerre series and rational Chebyshev expansions

    International Nuclear Information System (INIS)

    Boyd, John P.; Rangan, C.; Bucksbaum, P.H.

    2003-01-01

    The Fourier-sine-with-mapping pseudospectral algorithm of Fattal et al. [Phys. Rev. E 53 (1996) 1217] has been applied in several quantum physics problems. Here, we compare it with pseudospectral methods using Laguerre functions and rational Chebyshev functions. We show that Laguerre and Chebyshev expansions are better suited for solving problems in the interval r in R set of [0,∞] (for example, the Coulomb-Schroedinger equation), than the Fourier-sine-mapping scheme. All three methods give similar accuracy for the hydrogen atom when the scaling parameter L is optimum, but the Laguerre and Chebyshev methods are less sensitive to variations in L. We introduce a new variant of rational Chebyshev functions which has a more uniform spacing of grid points for large r, and gives somewhat better results than the rational Chebyshev functions of Boyd [J. Comp. Phys. 70 (1987) 63

  11. Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

    Directory of Open Access Journals (Sweden)

    Hassan Saberi Nik

    2014-01-01

    Full Text Available We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

  12. A Chebyshev method for state-to-state reactive scattering using reactant-product decoupling: OH + H2 → H2O + H.

    Science.gov (United States)

    Cvitaš, Marko T; Althorpe, Stuart C

    2013-08-14

    We extend a recently developed wave packet method for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions [M. T. Cvitaš and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)] to include the Chebyshev propagator. The method uses the further partitioned approach to reactant-product decoupling, which uses artificial decoupling potentials to partition the coordinate space of the reaction into separate reactant, product, and transition-state regions. Separate coordinates and basis sets can then be used that are best adapted to each region. We derive improved Chebyshev partitioning formulas which include Mandelshtam-and-Taylor-type decoupling potentials, and which are essential for the non-unitary discrete variable representations that must be used in 4-atom reactive scattering calculations. Numerical tests on the fully dimensional OH + H2 → H2O + H reaction for J = 0 show that the new version of the method is as efficient as the previously developed split-operator version. The advantages of the Chebyshev propagator (most notably the ease of parallelization for J > 0) can now be fully exploited in state-to-state reactive scattering calculations on 4-atom reactions.

  13. On the use of a spatial Chebyshev polynomials together with the collocation method in solving radiative transfer problem in a slab

    International Nuclear Information System (INIS)

    Haggag, M.H.; Al-Gorashi, A.K.; Machali, H.M.

    2013-01-01

    In this study, the integral form of the radiative transfer equation in planar slab with isotropic scattering has been studied by using the Chebyshev polynomial approximation which is called TN method. The scalar flux is expanded in terms of Chebyshev polynomials in the space variable. The expansion coefficients are solutions to a system of linear algebraic equations. Analytical expressions are given for the scalar and angular flux everywhere in the slab. Numerical calculations are done for the transmissivity and reflectivity of slabs with various values of the single scattering albedo. Calculations are also carried out for the transmitted and reflected angular intensity at the slab boundaries. Our numerical results are in a very good agreement with other results, as shown in the tables

  14. Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

    Science.gov (United States)

    Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.

    1998-01-01

    We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

  15. Cosmographic analysis with Chebyshev polynomials

    Science.gov (United States)

    Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

    2018-05-01

    The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

  16. Spectral element method for vector radiative transfer equation

    International Nuclear Information System (INIS)

    Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

    2010-01-01

    A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

  17. A spectral element-FCT method for the compressible Euler equations

    International Nuclear Information System (INIS)

    Giannakouros, J.; Karniadakis, G.E.

    1994-01-01

    A new algorithm based on spectral element discretizations and flux-corrected transport concepts is developed for the solution of the Euler equations of inviscid compressible fluid flow. A conservative formulation is proposed based on one- and two-dimensional cell-averaging and reconstruction procedures, which employ a staggered mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev collocation points. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensions. It is demonstrated through shock-tube problems and two-dimensional simulations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. Of particular importance is the fact that dispersion errors are minimal, as show through experiments. From the operational point of view, casting the method in a spectral element formulation provides flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements

  18. Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

    KAUST Repository

    Chu, Chunlei

    2012-07-01

    Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency. © 2012 Society of Exploration Geophysicists.

  19. A new Identity Based Encryption (IBE) scheme using extended Chebyshev polynomial over finite fields Zp

    International Nuclear Information System (INIS)

    Benasser Algehawi, Mohammed; Samsudin, Azman

    2010-01-01

    We present a method to extract key pairs needed for the Identity Based Encryption (IBE) scheme from extended Chebyshev polynomial over finite fields Z p . Our proposed scheme relies on the hard problem and the bilinear property of the extended Chebyshev polynomial over Z p . The proposed system is applicable, secure, and reliable.

  20. Spectral methods. Fundamentals in single domains

    International Nuclear Information System (INIS)

    Canuto, C.

    2006-01-01

    Since the publication of ''Spectral Methods in Fluid Dynamics'' 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded. (orig.)

  1. Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

    Science.gov (United States)

    Temel, Burcin; Mills, Greg; Metiu, Horia

    2008-03-27

    We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.

  2. Spectral Methods in Numerical Plasma Simulation

    DEFF Research Database (Denmark)

    Coutsias, E.A.; Hansen, F.R.; Huld, T.

    1989-01-01

    An introduction is given to the use of spectral methods in numerical plasma simulation. As examples of the use of spectral methods, solutions to the two-dimensional Euler equations in both a simple, doubly periodic region, and on an annulus will be shown. In the first case, the solution is expanded...

  3. Chebyshev-Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications

    Science.gov (United States)

    Mireles James, J. D.; Murray, Maxime

    2017-12-01

    This paper develops a Chebyshev-Taylor spectral method for studying stable/unstable manifolds attached to periodic solutions of differential equations. The work exploits the parameterization method — a general functional analytic framework for studying invariant manifolds. Useful features of the parameterization method include the fact that it can follow folds in the embedding, recovers the dynamics on the manifold through a simple conjugacy, and admits a natural notion of a posteriori error analysis. Our approach begins by deriving a recursive system of linear differential equations describing the Taylor coefficients of the invariant manifold. We represent periodic solutions of these equations as solutions of coupled systems of boundary value problems. We discuss the implementation and performance of the method for the Lorenz system, and for the planar circular restricted three- and four-body problems. We also illustrate the use of the method as a tool for computing cycle-to-cycle connecting orbits.

  4. Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials

    Directory of Open Access Journals (Sweden)

    Tingting Wang

    2015-01-01

    Full Text Available We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015.

  5. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2011-07-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  6. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2009-10-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  7. Spectral/hp element methods for CFD

    CERN Document Server

    Karniadakis, George Em

    1999-01-01

    Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.

  8. A numerical investigation of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet via rational Chebyshev functions

    Science.gov (United States)

    Parand, Kourosh; Mahdi Moayeri, Mohammad; Latifi, Sobhan; Delkhosh, Mehdi

    2017-07-01

    In this paper, a spectral method based on the four kinds of rational Chebyshev functions is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. First, by using the quasilinearization method (QLM), the model which is a nonlinear ordinary differential equation is converted to a sequence of linear ordinary differential equations (ODEs). By applying the proposed method on the ODEs in each iteration, the equations are converted to a system of linear algebraic equations. The results indicate the high accuracy and convergence of our method. Moreover, the effects of the Eyring-Powell fluid material parameters are discussed.

  9. Spectral shift reactor control method

    International Nuclear Information System (INIS)

    Impink, A.J. Jr.

    1981-01-01

    A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core wherein is established a reator coolant temperature set point at which it is desired to operate said reactor and first reactor coolant temperature band limits are provided within which said set point is located and it is desired to operate said reactor charactrized in that said reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in said core as said reactor coolant temperature approaches said first band limits thereby to maintain said reactor coolant temperature near said set point and within said first band limits

  10. Spectral shift reactor control method

    International Nuclear Information System (INIS)

    Impink, A.J.

    1982-01-01

    A method of operating a nuclear reactor having a core and coolant displacer elements arranged in the core where there is established a reactor coolant temperature set point at which it is desired to operate the reactor and first reactor coolant temperature band limits within which the set point is characterized. The reactor coolant displacer elements are moved relative to the reactor core for adjusting the volume of reactor coolant in the core as the reactor coolant temperature approaches the first band limits to maintain the reactor coolant temperature near the set point and within the first band limits. The reactivity charges associated with movement of respective coolant displacer element clusters is calculated and compared with a calculated derived reactivity charge in order to select the cluster to be moved. (author)

  11. Logarithmic compression methods for spectral data

    Science.gov (United States)

    Dunham, Mark E.

    2003-01-01

    A method is provided for logarithmic compression, transmission, and expansion of spectral data. A log Gabor transformation is made of incoming time series data to output spectral phase and logarithmic magnitude values. The output phase and logarithmic magnitude values are compressed by selecting only magnitude values above a selected threshold and corresponding phase values to transmit compressed phase and logarithmic magnitude values. A reverse log Gabor transformation is then performed on the transmitted phase and logarithmic magnitude values to output transmitted time series data to a user.

  12. Superiority of legendre polynomials to Chebyshev polynomial in ...

    African Journals Online (AJOL)

    In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev ...

  13. Stochastic Spectral and Conjugate Descent Methods

    KAUST Repository

    Kovalev, Dmitry

    2018-02-11

    The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.

  14. Stochastic Spectral and Conjugate Descent Methods

    KAUST Repository

    Kovalev, Dmitry; Gorbunov, Eduard; Gasanov, Elnur; Richtarik, Peter

    2018-01-01

    The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.

  15. Spectral-element Method for 3D Marine Controlled-source EM Modeling

    Science.gov (United States)

    Liu, L.; Yin, C.; Zhang, B., Sr.; Liu, Y.; Qiu, C.; Huang, X.; Zhu, J.

    2017-12-01

    As one of the predrill reservoir appraisal methods, marine controlled-source EM (MCSEM) has been widely used in mapping oil reservoirs to reduce risk of deep water exploration. With the technical development of MCSEM, the need for improved forward modeling tools has become evident. We introduce in this paper spectral element method (SEM) for 3D MCSEM modeling. It combines the flexibility of finite-element and high accuracy of spectral method. We use Galerkin weighted residual method to discretize the vector Helmholtz equation, where the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as vector basis functions. As a kind of high-order complete orthogonal polynomials, the GLC have the characteristic of exponential convergence. This helps derive the matrix elements analytically and improves the modeling accuracy. Numerical 1D models using SEM with different orders show that SEM method delivers accurate results. With increasing SEM orders, the modeling accuracy improves largely. Further we compare our SEM with finite-difference (FD) method for a 3D reservoir model (Figure 1). The results show that SEM method is more effective than FD method. Only when the mesh is fine enough, can FD achieve the same accuracy of SEM. Therefore, to obtain the same precision, SEM greatly reduces the degrees of freedom and cost. Numerical experiments with different models (not shown here) demonstrate that SEM is an efficient and effective tool for MSCEM modeling that has significant advantages over traditional numerical methods.This research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900).

  16. Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

    Directory of Open Access Journals (Sweden)

    M. Tavassoli Kajani

    2012-01-01

    Full Text Available Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞. This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method.

  17. Evolutionary Computing Methods for Spectral Retrieval

    Science.gov (United States)

    Terrile, Richard; Fink, Wolfgang; Huntsberger, Terrance; Lee, Seugwon; Tisdale, Edwin; VonAllmen, Paul; Tinetti, Geivanna

    2009-01-01

    A methodology for processing spectral images to retrieve information on underlying physical, chemical, and/or biological phenomena is based on evolutionary and related computational methods implemented in software. In a typical case, the solution (the information that one seeks to retrieve) consists of parameters of a mathematical model that represents one or more of the phenomena of interest. The methodology was developed for the initial purpose of retrieving the desired information from spectral image data acquired by remote-sensing instruments aimed at planets (including the Earth). Examples of information desired in such applications include trace gas concentrations, temperature profiles, surface types, day/night fractions, cloud/aerosol fractions, seasons, and viewing angles. The methodology is also potentially useful for retrieving information on chemical and/or biological hazards in terrestrial settings. In this methodology, one utilizes an iterative process that minimizes a fitness function indicative of the degree of dissimilarity between observed and synthetic spectral and angular data. The evolutionary computing methods that lie at the heart of this process yield a population of solutions (sets of the desired parameters) within an accuracy represented by a fitness-function value specified by the user. The evolutionary computing methods (ECM) used in this methodology are Genetic Algorithms and Simulated Annealing, both of which are well-established optimization techniques and have also been described in previous NASA Tech Briefs articles. These are embedded in a conceptual framework, represented in the architecture of the implementing software, that enables automatic retrieval of spectral and angular data and analysis of the retrieved solutions for uniqueness.

  18. High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

    Energy Technology Data Exchange (ETDEWEB)

    Pieper, Andreas [Ernst-Moritz-Arndt-Universität Greifswald (Germany); Kreutzer, Moritz [Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany); Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de [Ernst-Moritz-Arndt-Universität Greifswald (Germany); Galgon, Martin [Bergische Universität Wuppertal (Germany); Fehske, Holger [Ernst-Moritz-Arndt-Universität Greifswald (Germany); Hager, Georg [Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany); Lang, Bruno [Bergische Universität Wuppertal (Germany); Wellein, Gerhard [Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

    2016-11-15

    We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.

  19. Spectral Analysis Methods of Social Networks

    Directory of Open Access Journals (Sweden)

    P. G. Klyucharev

    2017-01-01

    Full Text Available Online social networks (such as Facebook, Twitter, VKontakte, etc. being an important channel for disseminating information are often used to arrange an impact on the social consciousness for various purposes - from advertising products or services to the full-scale information war thereby making them to be a very relevant object of research. The paper reviewed the analysis methods of social networks (primarily, online, based on the spectral theory of graphs. Such methods use the spectrum of the social graph, i.e. a set of eigenvalues of its adjacency matrix, and also the eigenvectors of the adjacency matrix.Described measures of centrality (in particular, centrality based on the eigenvector and PageRank, which reflect a degree of impact one or another user of the social network has. A very popular PageRank measure uses, as a measure of centrality, the graph vertices, the final probabilities of the Markov chain, whose matrix of transition probabilities is calculated on the basis of the adjacency matrix of the social graph. The vector of final probabilities is an eigenvector of the matrix of transition probabilities.Presented a method of dividing the graph vertices into two groups. It is based on maximizing the network modularity by computing the eigenvector of the modularity matrix.Considered a method for detecting bots based on the non-randomness measure of a graph to be computed using the spectral coordinates of vertices - sets of eigenvector components of the adjacency matrix of a social graph.In general, there are a number of algorithms to analyse social networks based on the spectral theory of graphs. These algorithms show very good results, but their disadvantage is the relatively high (albeit polynomial computational complexity for large graphs.At the same time it is obvious that the practical application capacity of the spectral graph theory methods is still underestimated, and it may be used as a basis to develop new methods.The work

  20. Analytical theory for artificial satellites. [nominal orbit expressed by means of Chebyshev polynomials

    Science.gov (United States)

    Deprit, A.

    1975-01-01

    A theory for generating segmented ephemerides is discussed as a means for fast generation and simple retrieval of nominal orbit data. Over a succession of finite intervals of time, the orbit is represented by a best approximation expressed by Chebyshev polynomials. Storage of coefficients tables for Chebyshev polynomials is seen as a method to reduce data and decrease transmission costs. A general algorithm was constructed and computer programs were designed. The possibility of storing an ephemeris for a few days in the on-board computer, or in microprocessors attached to the data collectors is suggested.

  1. Introduction to finite and spectral element methods using Matlab

    CERN Document Server

    Pozrikidis, Constantine

    2014-01-01

    The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.

  2. Spectral and spectral-frequency methods of investigating atmosphereless bodies of the Solar system

    International Nuclear Information System (INIS)

    Busarev, Vladimir V; Prokof'eva-Mikhailovskaya, Valentina V; Bochkov, Valerii V

    2007-01-01

    A method of reflectance spectrophotometry of atmosphereless bodies of the Solar system, its specificity, and the means of eliminating basic spectral noise are considered. As a development, joining the method of reflectance spectrophotometry with the frequency analysis of observational data series is proposed. The combined spectral-frequency method allows identification of formations with distinctive spectral features, and estimations of their sizes and distribution on the surface of atmospherelss celestial bodies. As applied to investigations of asteroids 21 Lutetia and 4 Vesta, the spectral frequency method has given us the possibility of obtaining fundamentally new information about minor planets. (instruments and methods of investigation)

  3. Numerical Methods for Stochastic Computations A Spectral Method Approach

    CERN Document Server

    Xiu, Dongbin

    2010-01-01

    The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth

  4. Derivation of reduced model for control system design using Chebyshev techniques

    International Nuclear Information System (INIS)

    Bistritz, Y.

    1978-07-01

    New methods are developed for reduced-order modelling of high-order, linear, time-invariant systems characterized by a transfer function. The first method is based on manipulating two Chebyshev polynomial series, one representing the frequency characteristics of the high-order system and the other representing the approximating low-order model. The proposed method can be viewed as generalizing the classical Pade approximation problem, with Chebyshev polynomial series being over a desired frequency interval instead of a power series about a single frequency point. The second method is based on approximating the high-order transfer function in terms of best Chebyshev approximation on a desired domain in the complex plane. An algorithm to find for a complex function best Chebyshev rational approximations in the complex plane is suggested and its theoretical basis confirmed. The algorithm is based on a complex version of Lawson algorithm that is applied to a complex version of a rational least square approximation program. (author)

  5. Orthogonal feature selection method. [For preprocessing of man spectral data

    Energy Technology Data Exchange (ETDEWEB)

    Kowalski, B R [Univ. of Washington, Seattle; Bender, C F

    1976-01-01

    A new method of preprocessing spectral data for extraction of molecular structural information is desired. This SELECT method generates orthogonal features that are important for classification purposes and that also retain their identity to the original measurements. A brief introduction to chemical pattern recognition is presented. A brief description of the method and an application to mass spectral data analysis follow. (BLM)

  6. Digital spectral analysis parametric, non-parametric and advanced methods

    CERN Document Server

    Castanié, Francis

    2013-01-01

    Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature.The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models.An entire chapter is devoted to the non-parametric methods most widely used in industry.High resolution methods a

  7. Developement of the method for realization of spectral irradiance scale featuring system of spectral comparisons

    International Nuclear Information System (INIS)

    Skerovic, V; Zarubica, V; Aleksic, M; Zekovic, L; Belca, I

    2010-01-01

    Realization of the scale of spectral responsivity of the detectors in the Directorate of Measures and Precious Metals (DMDM) is based on silicon detectors traceable to LNE-INM. In order to realize the unit of spectral irradiance in the laboratory for photometry and radiometry of the Bureau of Measures and Precious Metals, the new method based on the calibration of the spectroradiometer by comparison with standard detector has been established. The development of the method included realization of the System of Spectral Comparisons (SSC), together with the detector spectral responsivity calibrations by means of a primary spectrophotometric system. The linearity testing and stray light analysis were preformed to characterize the spectroradiometer. Measurement of aperture diameter and calibration of transimpedance amplifier were part of the overall experiment. In this paper, the developed method is presented and measurement results with the associated measurement uncertainty budget are shown.

  8. Developement of the method for realization of spectral irradiance scale featuring system of spectral comparisons

    Energy Technology Data Exchange (ETDEWEB)

    Skerovic, V; Zarubica, V; Aleksic, M [Directorate of measures and precious metals, Optical radiation Metrology department, Mike Alasa 14, 11000 Belgrade (Serbia); Zekovic, L; Belca, I, E-mail: vladanskerovic@dmdm.r [Faculty of Physics, Department for Applied physics and metrology, Studentski trg 12-16, 11000 Belgrade (Serbia)

    2010-10-15

    Realization of the scale of spectral responsivity of the detectors in the Directorate of Measures and Precious Metals (DMDM) is based on silicon detectors traceable to LNE-INM. In order to realize the unit of spectral irradiance in the laboratory for photometry and radiometry of the Bureau of Measures and Precious Metals, the new method based on the calibration of the spectroradiometer by comparison with standard detector has been established. The development of the method included realization of the System of Spectral Comparisons (SSC), together with the detector spectral responsivity calibrations by means of a primary spectrophotometric system. The linearity testing and stray light analysis were preformed to characterize the spectroradiometer. Measurement of aperture diameter and calibration of transimpedance amplifier were part of the overall experiment. In this paper, the developed method is presented and measurement results with the associated measurement uncertainty budget are shown.

  9. Stability estimates for hp spectral element methods for general ...

    Indian Academy of Sciences (India)

    We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-conforming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are ...

  10. Pseudo-random bit generator based on Chebyshev map

    Science.gov (United States)

    Stoyanov, B. P.

    2013-10-01

    In this paper, we study a pseudo-random bit generator based on two Chebyshev polynomial maps. The novel derivative algorithm shows perfect statistical properties established by number of statistical tests.

  11. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

    Directory of Open Access Journals (Sweden)

    Paul Barry

    2013-01-01

    Full Text Available The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.

  12. The spectral volume method as applied to transport problems

    International Nuclear Information System (INIS)

    McClarren, Ryan G.

    2011-01-01

    We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)

  13. The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

    International Nuclear Information System (INIS)

    Borzov, V. V.; Damaskinsky, E. V.

    2014-01-01

    In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators

  14. Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

    Directory of Open Access Journals (Sweden)

    Fakhrodin Mohammadi

    2017-10-01

    Full Text Available ‎Stochastic fractional differential equations (SFDEs have been used for modeling many physical problems in the fields of turbulance‎, ‎heterogeneous‎, ‎flows and matrials‎, ‎viscoelasticity and electromagnetic theory‎. ‎In this paper‎, ‎an‎ efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs‎. ‎In ‎this ‎app‎roach‎‎, ‎o‎perational matrices of the second kind Chebyshev wavelets ‎are used ‎for reducing SFDEs to a linear system of algebraic equations that can be solved easily‎. ‎C‎onvergence and error analysis of the proposed method is ‎considered‎.‎ ‎Some numerical examples are performed to confirm the applicability and efficiency of the proposed method‎.

  15. Improvements to the Chebyshev expansion of attenuation correction factors for cylindrical samples

    International Nuclear Information System (INIS)

    Mildner, D.F.R.; Carpenter, J.M.

    1990-01-01

    The accuracy of the Chebyshev expansion coefficients used for the calculation of attenuation correction factors for cylinderical samples has been improved. An increased order of expansion allows the method to be useful over a greater range of attenuation. It is shown that many of these coefficients are exactly zero, others are rational numbers, and others are rational frations of π -1 . The assumptions of Sears in his asymptotic expression of the attenuation correction factor are also examined. (orig.)

  16. Performance of spectral fitting methods for vegetation fluorescence quantification

    NARCIS (Netherlands)

    Meroni, M.; Busetto, D.; Colombo, R.; Guanter, L.; Moreno, J.; Verhoef, W.

    2010-01-01

    The Fraunhofer Line Discriminator (FLD) principle has long been considered as the reference method to quantify solar-induced chlorophyll fluorescence (F) from passive remote sensing measurements. Recently, alternative retrieval algorithms based on the spectral fitting of hyperspectral radiance

  17. Spectral Methods for Immunization of Large Networks

    Directory of Open Access Journals (Sweden)

    Muhammad Ahmad

    2017-11-01

    Full Text Available Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbour nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint that are immunized (vaccinated, screened, filtered so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic and efficiency (runtime and space complexity.

  18. A divisive spectral method for network community detection

    International Nuclear Information System (INIS)

    Cheng, Jianjun; Li, Longjie; Yao, Yukai; Chen, Xiaoyun; Leng, Mingwei; Lu, Weiguo

    2016-01-01

    Community detection is a fundamental problem in the domain of complex network analysis. It has received great attention, and many community detection methods have been proposed in the last decade. In this paper, we propose a divisive spectral method for identifying community structures from networks which utilizes a sparsification operation to pre-process the networks first, and then uses a repeated bisection spectral algorithm to partition the networks into communities. The sparsification operation makes the community boundaries clearer and sharper, so that the repeated spectral bisection algorithm extract high-quality community structures accurately from the sparsified networks. Experiments show that the combination of network sparsification and a spectral bisection algorithm is highly successful, the proposed method is more effective in detecting community structures from networks than the others. (paper: interdisciplinary statistical mechanics)

  19. A Spectral Conjugate Gradient Method for Unconstrained Optimization

    International Nuclear Information System (INIS)

    Birgin, E. G.; Martinez, J. M.

    2001-01-01

    A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribiere and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented

  20. Spectral method and its high performance implementation

    KAUST Repository

    Wu, Zedong

    2014-01-01

    We have presented a new method that can be dispersion free and unconditionally stable. Thus the computational cost and memory requirement will be reduced a lot. Based on this feature, we have implemented this algorithm on GPU based CUDA for the anisotropic Reverse time migration. There is almost no communication between CPU and GPU. For the prestack wavefield extrapolation, it can combine all the shots together to migration. However, it requires to solve a bigger dimensional problem and more meory which can\\'t fit into one GPU cards. In this situation, we implement it based on domain decomposition method and MPI for distributed memory system.

  1. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis

    2011-04-01

    The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

  2. Analysis of spectral methods for the homogeneous Boltzmann equation

    KAUST Repository

    Filbet, Francis; Mouhot, Clé ment

    2011-01-01

    The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation of spectrally accurate schemes for the Boltzmann equation, but very few of them were concerned with the stability analysis of the method. In particular there was no result of stability except when the method was modified in order to enforce the positivity preservation, which destroys the spectral accuracy. In this paper we propose a new method to study the stability of homogeneous Boltzmann equations perturbed by smoothed balanced operators which do not preserve positivity of the distribution. This method takes advantage of the "spreading" property of the collision, together with estimates on regularity and entropy production. As an application we prove stability and convergence of spectral methods for the Boltzmann equation, when the discretization parameter is large enough (with explicit bound). © 2010 American Mathematical Society.

  3. Modeling Belt-Servomechanism by Chebyshev Functional Recurrent Neuro-Fuzzy Network

    Science.gov (United States)

    Huang, Yuan-Ruey; Kang, Yuan; Chu, Ming-Hui; Chang, Yeon-Pun

    A novel Chebyshev functional recurrent neuro-fuzzy (CFRNF) network is developed from a combination of the Takagi-Sugeno-Kang (TSK) fuzzy model and the Chebyshev recurrent neural network (CRNN). The CFRNF network can emulate the nonlinear dynamics of a servomechanism system. The system nonlinearity is addressed by enhancing the input dimensions of the consequent parts in the fuzzy rules due to functional expansion of a Chebyshev polynomial. The back propagation algorithm is used to adjust the parameters of the antecedent membership functions as well as those of consequent functions. To verify the performance of the proposed CFRNF, the experiment of the belt servomechanism is presented in this paper. Both of identification methods of adaptive neural fuzzy inference system (ANFIS) and recurrent neural network (RNN) are also studied for modeling of the belt servomechanism. The analysis and comparison results indicate that CFRNF makes identification of complex nonlinear dynamic systems easier. It is verified that the accuracy and convergence of the CFRNF are superior to those of ANFIS and RNN by the identification results of a belt servomechanism.

  4. Spectral/ hp element methods: Recent developments, applications, and perspectives

    Science.gov (United States)

    Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

    2018-02-01

    The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

  5. Spectral methods for quantum Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Szehr, Oleg

    2014-05-08

    The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

  6. Spectral methods for quantum Markov chains

    International Nuclear Information System (INIS)

    Szehr, Oleg

    2014-01-01

    The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.

  7. Spectral methods in quantum field theory

    International Nuclear Information System (INIS)

    Graham, Noah; Quandt, Markus; Weigel, Herbert

    2009-01-01

    This concise text introduces techniques from quantum mechanics, especially scattering theory, to compute the effects of an external background on a quantum field in general, and on the properties of the quantum vacuum in particular. This approach can be succesfully used in an increasingly large number of situations, ranging from the study of solitons in field theory and cosmology to the determination of Casimir forces in nano-technology. The method introduced and applied in this book is shown to give an unambiguous connection to perturbation theory, implementing standard renormalization conditions even for non-perturbative backgrounds. It both gives new theoretical insights, for example illuminating longstanding questions regarding Casimir stresses, and also provides an efficient analytic and numerical tool well suited to practical calculations. Last but not least, it elucidates in a concrete context many of the subtleties of quantum field theory, such as divergences, regularization and renormalization, by connecting them to more familiar results in quantum mechanics. While addressed primarily at young researchers entering the field and nonspecialist researchers with backgrounds in theoretical and mathematical physics, introductory chapters on the theoretical aspects of the method make the book self-contained and thus suitable for advanced graduate students. (orig.)

  8. [An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

    Science.gov (United States)

    Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

    2016-04-01

    Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

  9. Spectral radiative property control method based on filling solution

    International Nuclear Information System (INIS)

    Jiao, Y.; Liu, L.H.; Hsu, P.-F.

    2014-01-01

    Controlling thermal radiation by tailoring spectral properties of microstructure is a promising method, can be applied in many industrial systems and have been widely researched recently. Among various property tailoring schemes, geometry design of microstructures is a commonly used method. However, the existing radiation property tailoring is limited by adjustability of processed microstructures. In other words, the spectral radiative properties of microscale structures are not possible to change after the gratings are fabricated. In this paper, we propose a method that adjusts the grating spectral properties by means of injecting filling solution, which could modify the thermal radiation in a fabricated microstructure. Therefore, this method overcomes the limitation mentioned above. Both mercury and water are adopted as the filling solution in this study. Aluminum and silver are selected as the grating materials to investigate the generality and limitation of this control method. The rigorous coupled-wave analysis is used to investigate the spectral radiative properties of these filling solution grating structures. A magnetic polaritons mechanism identification method is proposed based on LC circuit model principle. It is found that this control method could be used by different grating materials. Different filling solutions would enable the high absorption peak to move to longer or shorter wavelength band. The results show that the filling solution grating structures are promising for active control of spectral radiative properties. -- Highlights: • A filling solution grating structure is designed to adjust spectral radiative properties. • The mechanism of radiative property control is studied for engineering utilization. • Different grating materials are studied to find multi-functions for grating

  10. Convergence analysis of spectral element method for electromechanical devices

    NARCIS (Netherlands)

    Curti, M.; Jansen, J.W.; Lomonova, E.A.

    2017-01-01

    This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with the

  11. Convergence analysis of spectral element method for magnetic devices

    NARCIS (Netherlands)

    Curti, M.; Jansen, J.W.; Lomonova, E.A.

    2018-01-01

    This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for modeling a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with

  12. A conjugate gradient method for the spectral partitioning of graphs

    NARCIS (Netherlands)

    Kruyt, Nicolaas P.

    1997-01-01

    The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and

  13. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

    Science.gov (United States)

    Li, Weidong

    2017-09-01

    This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

  14. The spectral cell method in nonlinear earthquake modeling

    Science.gov (United States)

    Giraldo, Daniel; Restrepo, Doriam

    2017-12-01

    This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

  15. Spectral anomaly methods for aerial detection using KUT nuisance rejection

    International Nuclear Information System (INIS)

    Detwiler, R.S.; Pfund, D.M.; Myjak, M.J.; Kulisek, J.A.; Seifert, C.E.

    2015-01-01

    This work discusses the application and optimization of a spectral anomaly method for the real-time detection of gamma radiation sources from an aerial helicopter platform. Aerial detection presents several key challenges over ground-based detection. For one, larger and more rapid background fluctuations are typical due to higher speeds, larger field of view, and geographically induced background changes. As well, the possible large altitude or stand-off distance variations cause significant steps in background count rate as well as spectral changes due to increased gamma-ray scatter with detection at higher altitudes. The work here details the adaptation and optimization of the PNNL-developed algorithm Nuisance-Rejecting Spectral Comparison Ratios for Anomaly Detection (NSCRAD), a spectral anomaly method previously developed for ground-based applications, for an aerial platform. The algorithm has been optimized for two multi-detector systems; a NaI(Tl)-detector-based system and a CsI detector array. The optimization here details the adaptation of the spectral windows for a particular set of target sources to aerial detection and the tailoring for the specific detectors. As well, the methodology and results for background rejection methods optimized for the aerial gamma-ray detection using Potassium, Uranium and Thorium (KUT) nuisance rejection are shown. Results indicate that use of a realistic KUT nuisance rejection may eliminate metric rises due to background magnitude and spectral steps encountered in aerial detection due to altitude changes and geographically induced steps such as at land–water interfaces

  16. A modified sliding spectral method and its application to COSMIC ...

    Indian Academy of Sciences (India)

    A modified sliding spectral method and its application to COSMIC radio occultation data 1751. The window length with 300 samples is supposed to provide a reasonable resolution. In a spherically symmetric atmosphere, the refractive index n as a function of tangent radius r0 can be computed from the bending angle α as.

  17. Deconvolution of EPR spectral lines with an approximate method

    International Nuclear Information System (INIS)

    Jimenez D, H.; Cabral P, A.

    1990-10-01

    A recently reported approximation expression to deconvolution Lorentzian-Gaussian spectral lines. with small Gaussian contribution, is applied to study an EPR line shape. The potassium-ammonium solution line reported in the literature by other authors was used and the results are compared with those obtained by employing a precise method. (Author)

  18. Nonconforming h-p spectral element methods for elliptic problems

    Indian Academy of Sciences (India)

    In [6,7,13,14] h-p spectral element methods for solving elliptic boundary value problems on polygonal ... Let M denote the number of corner layers and W denote the number of degrees of .... β is given by Theorem 2.2 of [3] which can be stated.

  19. Spectral calculations in magnetohydrodynamics using the Jacobi-Davidson method

    NARCIS (Netherlands)

    Belien, A. J. C.; van der Holst, B.; Nool, M.; van der Ploeg, A.; Goedbloed, J. P.

    2001-01-01

    For the solution of the generalized complex non-Hermitian eigenvalue problems Ax = lambda Bx occurring in the spectral study of linearized resistive magnetohydrodynamics (MHD) a new parallel solver based on the recently developed Jacobi-Davidson [SIAM J. Matrix Anal. Appl. 17 (1996) 401] method has

  20. [An improved low spectral distortion PCA fusion method].

    Science.gov (United States)

    Peng, Shi; Zhang, Ai-Wu; Li, Han-Lun; Hu, Shao-Xing; Meng, Xian-Gang; Sun, Wei-Dong

    2013-10-01

    Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance.

  1. Convergence of spectral methods for nonlinear conservation laws. Final report

    International Nuclear Information System (INIS)

    Tadmor, E.

    1987-08-01

    The convergence of the Fourier method for scalar nonlinear conservation laws which exhibit spontaneous shock discontinuities is discussed. Numerical tests indicate that the convergence may (and in fact in some cases must) fail, with or without post-processing of the numerical solution. Instead, a new kind of spectrally accurate vanishing viscosity is introduced to augment the Fourier approximation of such nonlinear conservation laws. Using compensated compactness arguments, it is shown that this spectral viscosity prevents oscillations, and convergence to the unique entropy solution follows

  2. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

    Science.gov (United States)

    Freund, Roland

    1989-01-01

    Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

  3. INTEGRATED FUSION METHOD FOR MULTIPLE TEMPORAL-SPATIAL-SPECTRAL IMAGES

    Directory of Open Access Journals (Sweden)

    H. Shen

    2012-08-01

    Full Text Available Data fusion techniques have been widely researched and applied in remote sensing field. In this paper, an integrated fusion method for remotely sensed images is presented. Differently from the existed methods, the proposed method has the performance to integrate the complementary information in multiple temporal-spatial-spectral images. In order to represent and process the images in one unified framework, two general image observation models are firstly presented, and then the maximum a posteriori (MAP framework is used to set up the fusion model. The gradient descent method is employed to solve the fused image. The efficacy of the proposed method is validated using simulated images.

  4. Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

    Energy Technology Data Exchange (ETDEWEB)

    Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

    1996-12-31

    The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

  5. High order spectral volume and spectral difference methods on unstructured grids

    Science.gov (United States)

    Kannan, Ravishekar

    The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed

  6. International Conference on Spectral and High-Order Methods

    CERN Document Server

    Dumont, Ney; Hesthaven, Jan

    2017-01-01

    This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

  7. A NEW TOOL FOR IMAGE ANALYSIS BASED ON CHEBYSHEV RATIONAL FUNCTIONS: CHEF FUNCTIONS

    International Nuclear Information System (INIS)

    Jiménez-Teja, Y.; Benítez, N.

    2012-01-01

    We introduce a new approach to the modeling of the light distribution of galaxies, an orthonormal polar basis formed by a combination of Chebyshev rational functions and Fourier polynomials that we call CHEF functions, or CHEFs. We have developed an orthonormalization process to apply this basis to pixelized images, and implemented the method as a Python pipeline. The new basis displays remarkable flexibility, being able to accurately fit all kinds of galaxy shapes, including irregulars, spirals, ellipticals, highly compact, and highly elongated galaxies. It does this while using fewer components than similar methods, as shapelets, and without producing artifacts, due to the efficiency of the rational Chebyshev polynomials to fit quickly decaying functions like galaxy profiles. The method is linear and very stable, and therefore is capable of processing large numbers of galaxies in a fast and automated way. Due to the high quality of the fits in the central parts of the galaxies, and the efficiency of the CHEF basis modeling galaxy profiles up to very large distances, the method provides highly accurate estimates of total galaxy fluxes and ellipticities. Future papers will explore in more detail the application of the method to perform multiband photometry, morphological classification, and weak shear measurements.

  8. Spectral analysis of mammographic images using a multitaper method

    International Nuclear Information System (INIS)

    Wu Gang; Mainprize, James G.; Yaffe, Martin J.

    2012-01-01

    Purpose: Power spectral analysis in radiographic images is conventionally performed using a windowed overlapping averaging periodogram. This study describes an alternative approach using a multitaper technique and compares its performance with that of the standard method. This tool will be valuable in power spectrum estimation of images, whose content deviates significantly from uniform white noise. The performance of the multitaper approach will be evaluated in terms of spectral stability, variance reduction, bias, and frequency precision. The ultimate goal is the development of a useful tool for image quality assurance. Methods: A multitaper approach uses successive data windows of increasing order. This mitigates spectral leakage allowing one to calculate a reduced-variance power spectrum. The multitaper approach will be compared with the conventional power spectrum method in several typical situations, including the noise power spectra (NPS) measurements of simulated projection images of a uniform phantom, NPS measurement of real detector images of a uniform phantom for two clinical digital mammography systems, and the estimation of the anatomic noise in mammographic images (simulated images and clinical mammograms). Results: Examination of spectrum variance versus frequency resolution and bias indicates that the multitaper approach is superior to the conventional single taper methods in the prevention of spectrum leakage and variance reduction. More than four times finer frequency precision can be achieved with equivalent or less variance and bias. Conclusions: Without any shortening of the image data length, the bias is smaller and the frequency resolution is higher with the multitaper method, and the need to compromise in the choice of regions of interest size to balance between the reduction of variance and the loss of frequency resolution is largely eliminated.

  9. Solution of the Schroedinger equation by a spectral method

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.

    1982-01-01

    A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential

  10. High temperature spectral emissivity measurement using integral blackbody method

    Science.gov (United States)

    Pan, Yijie; Dong, Wei; Lin, Hong; Yuan, Zundong; Bloembergen, Pieter

    2016-10-01

    Spectral emissivity is a critical material's thermos-physical property for heat design and radiation thermometry. A prototype instrument based upon an integral blackbody method was developed to measure material's spectral emissivity above 1000 °. The system was implemented with an optimized commercial variable-high-temperature blackbody, a high speed linear actuator, a linear pyrometer, and an in-house designed synchronization circuit. A sample was placed in a crucible at the bottom of the blackbody furnace, by which the sample and the tube formed a simulated blackbody which had an effective total emissivity greater than 0.985. During the measurement, the sample was pushed to the end opening of the tube by a graphite rod which was actuated through a pneumatic cylinder. A linear pyrometer was used to monitor the brightness temperature of the sample surface through the measurement. The corresponding opto-converted voltage signal was fed and recorded by a digital multi-meter. A physical model was proposed to numerically evaluate the temperature drop along the process. Tube was discretized as several isothermal cylindrical rings, and the temperature profile of the tube was measurement. View factors between sample and rings were calculated and updated along the whole pushing process. The actual surface temperature of the sample at the end opening was obtained. Taking advantages of the above measured voltage profile and the calculated true temperature, spectral emissivity under this temperature point was calculated.

  11. Spectral/hp element methods: Recent developments, applications, and perspectives

    DEFF Research Database (Denmark)

    Xu, Hui; Cantwell, Chris; Monteserin, Carlos

    2018-01-01

    regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral...... is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain...

  12. Terahertz spectral unmixing based method for identifying gastric cancer

    Science.gov (United States)

    Cao, Yuqi; Huang, Pingjie; Li, Xian; Ge, Weiting; Hou, Dibo; Zhang, Guangxin

    2018-02-01

    At present, many researchers are exploring biological tissue inspection using terahertz time-domain spectroscopy (THz-TDS) techniques. In this study, based on a modified hard modeling factor analysis method, terahertz spectral unmixing was applied to investigate the relationships between the absorption spectra in THz-TDS and certain biomarkers of gastric cancer in order to systematically identify gastric cancer. A probability distribution and box plot were used to extract the distinctive peaks that indicate carcinogenesis, and the corresponding weight distributions were used to discriminate the tissue types. The results of this work indicate that terahertz techniques have the potential to detect different levels of cancer, including benign tumors and polyps.

  13. Damage Identification of Bridge Based on Chebyshev Polynomial Fitting and Fuzzy Logic without Considering Baseline Model Parameters

    Directory of Open Access Journals (Sweden)

    Yu-Bo Jiao

    2015-01-01

    Full Text Available The paper presents an effective approach for damage identification of bridge based on Chebyshev polynomial fitting and fuzzy logic systems without considering baseline model data. The modal curvature of damaged bridge can be obtained through central difference approximation based on displacement modal shape. Depending on the modal curvature of damaged structure, Chebyshev polynomial fitting is applied to acquire the curvature of undamaged one without considering baseline parameters. Therefore, modal curvature difference can be derived and used for damage localizing. Subsequently, the normalized modal curvature difference is treated as input variable of fuzzy logic systems for damage condition assessment. Numerical simulation on a simply supported bridge was carried out to demonstrate the feasibility of the proposed method.

  14. Spectral Element Method for the Simulation of Unsteady Compressible Flows

    Science.gov (United States)

    Diosady, Laslo Tibor; Murman, Scott M.

    2013-01-01

    This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.

  15. The spectral method and ergodic theorems for general Markov chains

    International Nuclear Information System (INIS)

    Nagaev, S V

    2015-01-01

    We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space

  16. Spectral Karyotyping. An new method for chromosome analysis

    International Nuclear Information System (INIS)

    Zhou Liying; Qian Jianxin; Guo Xiaokui; Dai Hong; Liu Yulong; Zhou Jianying

    2006-01-01

    Spectral Karyotyping (SKY) can reveal fine changes in Chromosome structure which could not be detected by G, R, Q banding before, has become an accurate, sensitive and reliable method for karyotyping, promoted the development of cell genetics to molecular level and has been used in medicine and radiological injury research. It also has the ability of analyzing 24 chromosomes on its once test run and, find implicated structure of chromosome changes, such as metathesis, depletion, amplification, rearrangement, dikinetochore, equiarm and maker-body, detect the abnormal change of stable Chromosome and calculate the bio-dose curve; The abnormal Chromosome detected by SKY can be adopted as early diagnosis, effective indexes of minor remaining changes for use of monitor of treatment and in the duration of follow up. This technique provides us a more advanced and effective method for relative gene cloning and the study of pathological mechanism of cancer. (authors)

  17. Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank

    DEFF Research Database (Denmark)

    Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2013-01-01

    A new hybrid-spectral solution strategy is proposed for the simulation of the fully nonlinear free surface equations based on potential flow theory. A Fourier collocation method is adopted horisontally for the discretization of the free surface equations. This is combined with a modal Chebyshev Tau...... method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...... wave problem, ensuring fast convergence and optimal scaling with the problem size. Preliminary results for very nonlinear waves show expected convergence rates and a clear advantage of using spectral schemes....

  18. Spectral analysis methods for vehicle interior vibro-acoustics identification

    Science.gov (United States)

    Hosseini Fouladi, Mohammad; Nor, Mohd. Jailani Mohd.; Ariffin, Ahmad Kamal

    2009-02-01

    Noise has various effects on comfort, performance and health of human. Sound are analysed by human brain based on the frequencies and amplitudes. In a dynamic system, transmission of sound and vibrations depend on frequency and direction of the input motion and characteristics of the output. It is imperative that automotive manufacturers invest a lot of effort and money to improve and enhance the vibro-acoustics performance of their products. The enhancement effort may be very difficult and time-consuming if one relies only on 'trial and error' method without prior knowledge about the sources itself. Complex noise inside a vehicle cabin originated from various sources and travel through many pathways. First stage of sound quality refinement is to find the source. It is vital for automotive engineers to identify the dominant noise sources such as engine noise, exhaust noise and noise due to vibration transmission inside of vehicle. The purpose of this paper is to find the vibro-acoustical sources of noise in a passenger vehicle compartment. The implementation of spectral analysis method is much faster than the 'trial and error' methods in which, parts should be separated to measure the transfer functions. Also by using spectral analysis method, signals can be recorded in real operational conditions which conduce to more consistent results. A multi-channel analyser is utilised to measure and record the vibro-acoustical signals. Computational algorithms are also employed to identify contribution of various sources towards the measured interior signal. These achievements can be utilised to detect, control and optimise interior noise performance of road transport vehicles.

  19. Wind Turbine Driving a PM Synchronous Generator Using Novel Recurrent Chebyshev Neural Network Control with the Ideal Learning Rate

    Directory of Open Access Journals (Sweden)

    Chih-Hong Lin

    2016-06-01

    Full Text Available A permanent magnet (PM synchronous generator system driven by wind turbine (WT, connected with smart grid via AC-DC converter and DC-AC converter, are controlled by the novel recurrent Chebyshev neural network (NN and amended particle swarm optimization (PSO to regulate output power and output voltage in two power converters in this study. Because a PM synchronous generator system driven by WT is an unknown non-linear and time-varying dynamic system, the on-line training novel recurrent Chebyshev NN control system is developed to regulate DC voltage of the AC-DC converter and AC voltage of the DC-AC converter connected with smart grid. Furthermore, the variable learning rate of the novel recurrent Chebyshev NN is regulated according to discrete-type Lyapunov function for improving the control performance and enhancing convergent speed. Finally, some experimental results are shown to verify the effectiveness of the proposed control method for a WT driving a PM synchronous generator system in smart grid.

  20. Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

    Science.gov (United States)

    Streett, C. L.

    1987-01-01

    Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

  1. Transport survey calculations using the spectral collocation method

    International Nuclear Information System (INIS)

    Painter, S.L.; Lyon, J.F.

    1989-01-01

    A novel transport survey code has been developed and is being used to study the sensitivity of stellarator reactor performance to various transport assumptions. Instead of following one of the usual approaches, the steady-state transport equation are solved in integral form using the spectral collocation method. This approach effectively combine the computational efficiency of global models with the general nature of 1-D solutions. A compact torsatron reactor test case was used to study the convergence properties and flexibility of the new method. The heat transport model combined Shaing's model for ripple-induced neoclassical transport, the Chang-Hinton model for axisymmetric neoclassical transport, and neoalcator scaling for anomalous electron heat flux. Alpha particle heating, radiation losses, classical electron-ion heat flow, and external heating were included. For the test problem, the method exhibited some remarkable convergence properties. As the number of basis functions was increased, the maximum, pointwise error in the integrated power balance decayed exponentially until the numerical noise level as reached. Better than 10% accuracy in the globally-averaged quantities was achieved with only 5 basis functions; better than 1% accuracy was achieved with 10 basis functions. The numerical method was also found to be very general. Extreme temperature gradients at the plasma edge which sometimes arise from the neoclassical models and are difficult to resolve with finite-difference methods were easily resolved. 8 refs., 6 figs

  2. Genetic Algorithms: A New Method for Neutron Beam Spectral Characterization

    International Nuclear Information System (INIS)

    David W. Freeman

    2000-01-01

    A revolutionary new concept for solving the neutron spectrum unfolding problem using genetic algorithms (GAs) has recently been introduced. GAs are part of a new field of evolutionary solution techniques that mimic living systems with computer-simulated chromosome solutions that mate, mutate, and evolve to create improved solutions. The original motivation for the research was to improve spectral characterization of neutron beams associated with boron neutron capture therapy (BNCT). The GA unfolding technique has been successfully applied to problems with moderate energy resolution (up to 47 energy groups). Initial research indicates that the GA unfolding technique may well be superior to popular unfolding methods in common use. Research now under way at Kansas State University is focused on optimizing the unfolding algorithm and expanding its energy resolution to unfold detailed beam spectra based on multiple foil measurements. Indications are that the final code will significantly outperform current, state-of-the-art codes in use by the scientific community

  3. Methods of total spectral radiant flux realization at VNIIOFI

    Science.gov (United States)

    Ivashin, Evgeniy; Lalek, Jan; Rybczyński, Andrzej; Ogarev, Sergey; Khlevnoy, Boris; Dobroserdov, Dmitry; Sapritsky, Victor

    2018-02-01

    VNIIOFI carries out works on realization of independent methods for realization of the total spectral radiant flux (TSRF) of incoherent optical radiation sources - reference high-temperature blackbodies (BB), halogen lamps, and LED with quasi-Lambert spatial distribution of radiance. The paper describes three schemes for measuring facilities using photometers, spectroradiometers and computer-controlled high class goniometer. The paper describes different approaches for TSRF realization at the VNIIOFI National radiometric standard on the basis of high-temperature BB and LED sources, and gonio-spectroradiometer. Further, they are planned to be compared, and the use of fixed-point cells (in particular, based on the high-temperature δ(MoC)-C metal-carbon eutectic with a phase transition temperature of 2583 °C corresponding to the metrological optical “source-A”) as an option instead of the BB is considered in order to enhance calibration accuracy.

  4. Standard Test Method for Normal Spectral Emittance at Elevated Temperatures

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    1972-01-01

    1.1 This test method describes a highly accurate technique for measuring the normal spectral emittance of electrically conducting materials or materials with electrically conducting substrates, in the temperature range from 600 to 1400 K, and at wavelengths from 1 to 35 μm. 1.2 The test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is suitable for research laboratories where the highest precision and accuracy are desired, but is not recommended for routine production or acceptance testing. However, because of its high accuracy this test method can be used as a referee method to be applied to production and acceptance testing in cases of dispute. 1.3 The values stated in SI units are to be regarded as the standard. The values in parentheses are for information only. 1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this stan...

  5. The use of spectral methods in bidomain studies.

    Science.gov (United States)

    Trayanova, N; Pilkington, T

    1992-01-01

    A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

  6. Variational Multi-Scale method with spectral approximation of the sub-scales.

    KAUST Repository

    Dia, Ben Mansour

    2015-01-07

    A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a nite number of modes.

  7. Spectral-Product Methods for Electronic Structure Calculations (Preprint)

    National Research Council Canada - National Science Library

    Langhoff, P. W; Mills, J. E; Boatz, J. A

    2006-01-01

    .... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...

  8. Spectral-Product Methods for Electronic Structure Calculations (Postprint)

    National Research Council Canada - National Science Library

    Langhoff, P. W; Hinde, R. J; Mills, J. D; Boatz, J. A

    2007-01-01

    .... The spectral-product approach to molecular electronic structure avoids the repeated evaluations of the one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices...

  9. An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

    Science.gov (United States)

    Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

    2014-09-01

    Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the

  10. Method for estimating effects of unknown correlations in spectral irradiance data on uncertainties of spectrally integrated colorimetric quantities

    Science.gov (United States)

    Kärhä, Petri; Vaskuri, Anna; Mäntynen, Henrik; Mikkonen, Nikke; Ikonen, Erkki

    2017-08-01

    Spectral irradiance data are often used to calculate colorimetric properties, such as color coordinates and color temperatures of light sources by integration. The spectral data may contain unknown correlations that should be accounted for in the uncertainty estimation. We propose a new method for estimating uncertainties in such cases. The method goes through all possible scenarios of deviations using Monte Carlo analysis. Varying spectral error functions are produced by combining spectral base functions, and the distorted spectra are used to calculate the colorimetric quantities. Standard deviations of the colorimetric quantities at different scenarios give uncertainties assuming no correlations, uncertainties assuming full correlation, and uncertainties for an unfavorable case of unknown correlations, which turn out to be a significant source of uncertainty. With 1% standard uncertainty in spectral irradiance, the expanded uncertainty of the correlated color temperature of a source corresponding to the CIE Standard Illuminant A may reach as high as 37.2 K in unfavorable conditions, when calculations assuming full correlation give zero uncertainty, and calculations assuming no correlations yield the expanded uncertainties of 5.6 K and 12.1 K, with wavelength steps of 1 nm and 5 nm used in spectral integrations, respectively. We also show that there is an absolute limit of 60.2 K in the error of the correlated color temperature for Standard Illuminant A when assuming 1% standard uncertainty in the spectral irradiance. A comparison of our uncorrelated uncertainties with those obtained using analytical methods by other research groups shows good agreement. We re-estimated the uncertainties for the colorimetric properties of our 1 kW photometric standard lamps using the new method. The revised uncertainty of color temperature is a factor of 2.5 higher than the uncertainty assuming no correlations.

  11. Use of new spectral analysis methods in gamma spectra deconvolution

    International Nuclear Information System (INIS)

    Pinault, J.L.

    1991-01-01

    A general deconvolution method applicable to X and gamma ray spectrometry is proposed. Using new spectral analysis methods, it is applied to an actual case: the accurate on-line analysis of three elements (Ca, Si, Fe) in a cement plant using neutron capture gamma rays. Neutrons are provided by a low activity (5 μg) 252 Cf source; the detector is a BGO 3 in.x8 in. scintillator. The principle of the methods rests on the Fourier transform of the spectrum. The search for peaks and determination of peak areas are worked out in the Fourier representation, which enables separation of background and peaks and very efficiently discriminates peaks, or elements represented by several peaks. First the spectrum is transformed so that in the new representation the full width at half maximum (FWHM) is independent of energy. Thus, the spectrum is arranged symmetrically and transformed into the Fourier representation. The latter is multiplied by a function in order to transform original Gaussian into Lorentzian peaks. An autoregressive filter is calculated, leading to a characteristic polynomial whose complex roots represent both the location and the width of each peak, provided that the absolute value is lower than unit. The amplitude of each component (the area of each peak or the sum of areas of peaks characterizing an element) is fitted by the weighted least squares method, taking into account that errors in spectra are independent and follow a Poisson law. Very accurate results are obtained, which would be hard to achieve by other methods. The DECO FORTRAN code has been developed for compatible PC microcomputers. Some features of the code are given. (orig.)

  12. Martian Radiative Transfer Modeling Using the Optimal Spectral Sampling Method

    Science.gov (United States)

    Eluszkiewicz, J.; Cady-Pereira, K.; Uymin, G.; Moncet, J.-L.

    2005-01-01

    The large volume of existing and planned infrared observations of Mars have prompted the development of a new martian radiative transfer model that could be used in the retrievals of atmospheric and surface properties. The model is based on the Optimal Spectral Sampling (OSS) method [1]. The method is a fast and accurate monochromatic technique applicable to a wide range of remote sensing platforms (from microwave to UV) and was originally developed for the real-time processing of infrared and microwave data acquired by instruments aboard the satellites forming part of the next-generation global weather satellite system NPOESS (National Polarorbiting Operational Satellite System) [2]. As part of our on-going research related to the radiative properties of the martian polar caps, we have begun the development of a martian OSS model with the goal of using it to perform self-consistent atmospheric corrections necessary to retrieve caps emissivity from the Thermal Emission Spectrometer (TES) spectra. While the caps will provide the initial focus area for applying the new model, it is hoped that the model will be of interest to the wider Mars remote sensing community.

  13. Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

    Science.gov (United States)

    Riva, Fabio; Milanese, Lucio; Ricci, Paolo

    2017-10-01

    To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

  14. The use of the spectral method within the fast adaptive composite grid method

    Energy Technology Data Exchange (ETDEWEB)

    McKay, S.M.

    1994-12-31

    The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.

  15. Rapid simulation of spatial epidemics: a spectral method.

    Science.gov (United States)

    Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J

    2015-04-07

    Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel. Copyright © 2015 Elsevier Ltd. All rights reserved.

  16. Efficiency of High Order Spectral Element Methods on Petascale Architectures

    KAUST Repository

    Hutchinson, Maxwell; Heinecke, Alexander; Pabst, Hans; Henry, Greg; Parsani, Matteo; Keyes, David E.

    2016-01-01

    High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.

  17. Efficiency of High Order Spectral Element Methods on Petascale Architectures

    KAUST Repository

    Hutchinson, Maxwell

    2016-06-14

    High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.

  18. Chebyshev approximations for the transmission integral for one single line in Moessbauer spectroscopy

    International Nuclear Information System (INIS)

    Flores-Lamas, H.

    1994-01-01

    An analytic expansion, to arbitrary accuracy, of the transmission integral (TI) for a single Moessbauer line is presented. This serves for calculating the effective thickness (T a ) of an absorber in Moessbauer spectroscopy even for T a >10. The new analytic expansion arises from substituting in the TI expression the exponential function by a Chebyshev polynomials series. A very fast converging series for TI is obtained and used as a test function in a least squares fit to a simulated spectrum. The test yields satisfactory results. The area and height parameters calculated were found to be in good agreement with earlier results. The present analytic method assumes that the source and absorber widths are different. ((orig.))

  19. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

    Science.gov (United States)

    Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

    2017-02-01

    Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

  20. Visual Method for Spectral Energy Distribution Calculation of ...

    Indian Academy of Sciences (India)

    Abstract. In this work, we propose to use 'The Geometer's Sketchpad' to the fitting of a spectral energy distribution of blazar based on three effective spectral indices, αRO, αOX, and αRX and the flux density in the radio band. It can make us to see the fitting in detail with both the peak frequency and peak luminosity given ...

  1. Towards spectral geometric methods for Euclidean quantum gravity

    Science.gov (United States)

    Panine, Mikhail; Kempf, Achim

    2016-04-01

    The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.

  2. Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet

    Directory of Open Access Journals (Sweden)

    Fuqiang Zhao

    2017-01-01

    Full Text Available In the current study, a numerical technique for solving one-dimensional fractional nonsteady heat transfer model is presented. We construct the second kind Chebyshev wavelet and then derive the operational matrix of fractional-order integration. The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. Lastly, illustrated examples are included to demonstrate the validity and applicability of the technique.

  3. hp Spectral element methods for three dimensional elliptic problems

    Indian Academy of Sciences (India)

    This is the first of a series of papers devoted to the study of h-p spec- .... element functions defined on mesh elements in the new system of variables with a uni- ... the spectral element functions on these elements and give construction of the stability .... By Hm( ), we denote the usual Sobolev space of integer order m ≥ 0 ...

  4. hp Spectral element methods for three dimensional elliptic problems

    Indian Academy of Sciences (India)

    elliptic boundary value problems on non-smooth domains in R3. For Dirichlet problems, ... of variable degree bounded by W. Let N denote the number of layers in the geomet- ric mesh ... We prove a stability theorem for mixed problems when the spectral element functions vanish ..... Applying Theorem 3.1,. ∫ r l. |Mu|2dx −.

  5. An Improved Variational Method for Hyperspectral Image Pansharpening with the Constraint of Spectral Difference Minimization

    Science.gov (United States)

    Huang, Z.; Chen, Q.; Shen, Y.; Chen, Q.; Liu, X.

    2017-09-01

    Variational pansharpening can enhance the spatial resolution of a hyperspectral (HS) image using a high-resolution panchromatic (PAN) image. However, this technology may lead to spectral distortion that obviously affect the accuracy of data analysis. In this article, we propose an improved variational method for HS image pansharpening with the constraint of spectral difference minimization. We extend the energy function of the classic variational pansharpening method by adding a new spectral fidelity term. This fidelity term is designed following the definition of spectral angle mapper, which means that for every pixel, the spectral difference value of any two bands in the HS image is in equal proportion to that of the two corresponding bands in the pansharpened image. Gradient descent method is adopted to find the optimal solution of the modified energy function, and the pansharpened image can be reconstructed. Experimental results demonstrate that the constraint of spectral difference minimization is able to preserve the original spectral information well in HS images, and reduce the spectral distortion effectively. Compared to original variational method, our method performs better in both visual and quantitative evaluation, and achieves a good trade-off between spatial and spectral information.

  6. A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula

    KAUST Repository

    Hale, Nicholas; Townsend, Alex

    2014-01-01

    -known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency

  7. Solution of linear transport equation using Chebyshev polynomials and Laplace transform

    International Nuclear Information System (INIS)

    Cardona, A.V.; Vilhena, M.T.M.B. de

    1994-01-01

    The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

  8. A Fast, Simple, and Stable Chebyshev--Legendre Transform Using an Asymptotic Formula

    KAUST Repository

    Hale, Nicholas

    2014-02-06

    A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(log N)2/ log log N) operations is derived. The fundamental idea of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid. © 2014 Society for Industrial and Applied Mathematics.

  9. Assessment of modern spectral analysis methods to improve wavenumber resolution of F-K spectra

    International Nuclear Information System (INIS)

    Shirley, T.E.; Laster, S.J.; Meek, R.A.

    1987-01-01

    The improvement in wavenumber spectra obtained by using high resolution spectral estimators is examined. Three modern spectral estimators were tested, namely the Autoregressive/Maximum Entropy (AR/ME) method, the Extended Prony method, and an eigenstructure method. They were combined with the conventional Fourier method by first transforming each trace with a Fast Fourier Transform (FFT). A high resolution spectral estimator was applied to the resulting complex spatial sequence for each frequency. The collection of wavenumber spectra thus computed comprises a hybrid f-k spectrum with high wavenumber resolution and less spectral ringing. Synthetic and real data records containing 25 traces were analyzed by using the hybrid f-k method. The results show an FFT-AR/ME f-k spectrum has noticeably better wavenumber resolution and more spectral dynamic range than conventional spectra when the number of channels is small. The observed improvement suggests the hybrid technique is potentially valuable in seismic data analysis

  10. An experimental method for making spectral emittance and surface temperature measurements of opaque surfaces

    International Nuclear Information System (INIS)

    Moore, Travis J.; Jones, Matthew R.; Tree, Dale R.; Daniel Maynes, R.; Baxter, Larry L.

    2011-01-01

    An experimental procedure has been developed to make spectral emittance and temperature measurements. The spectral emittance of an object is calculated using measurements of the spectral emissive power and of the surface temperature of the object obtained using a Fourier transform infrared (FTIR) spectrometer. A calibration procedure is described in detail which accounts for the temperature dependence of the detector. The methods used to extract the spectral emissive power and surface temperature from measured infrared spectra were validated using a blackbody radiator at known temperatures. The average error in the measured spectral emittance was 2.1% and the average difference between the temperature inferred from the recorded spectra and the temperature indicated on the blackbody radiator was 1.2%. The method was used to measure the spectral emittance of oxidized copper at various temperatures.

  11. Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain

    International Nuclear Information System (INIS)

    Judin, Mika; Nylander, Jari; Larkiola, Jari; Verho, Martti

    2011-01-01

    The thickness profile of hot strip is of importance to profile, flatness and shape of the final cold rolled product. In this work, strip thickness and flatness profiles are decomposed into independent components by solving Chebyshev polynomials coefficients using matrix calculation. Four terms are used to characterize most common shapes of thickness and flatness profile. The calculated Chebyshev coefficients from different line measurements are combined together and analysed using neural network tools. The most common types of shapes are classified.

  12. Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

    KAUST Repository

    Winokur, J.; Kim, D.; Bisetti, Fabrizio; Le Maî tre, O. P.; Knio, Omar

    2015-01-01

    We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a

  13. 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.

  14. Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

    KAUST Repository

    Zou, Peng; Cheng, Jiubing

    2017-01-01

    -difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using

  15. Variational Multi-Scale method with spectral approximation of the sub-scales.

    KAUST Repository

    Dia, Ben Mansour; Chá con-Rebollo, Tomas

    2015-01-01

    A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base

  16. Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

    Directory of Open Access Journals (Sweden)

    Jinkui Liu

    2012-01-01

    Full Text Available A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995 in contrast to the famous CD method, FR method, and PRP method.

  17. A Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results

    Science.gov (United States)

    Larsen, Curtis E.; Irvine, Tom

    2013-01-01

    A comprehensive review of the available methods for estimating fatigue damage from variable amplitude loading is presented. The dependence of fatigue damage accumulation on power spectral density (psd) is investigated for random processes relevant to real structures such as in offshore or aerospace applications. Beginning with the Rayleigh (or narrow band) approximation, attempts at improved approximations or corrections to the Rayleigh approximation are examined by comparison to rainflow analysis of time histories simulated from psd functions representative of simple theoretical and real world applications. Spectral methods investigated include corrections by Wirsching and Light, Ortiz and Chen, the Dirlik formula, and the Single-Moment method, among other more recent proposed methods. Good agreement is obtained between the spectral methods and the time-domain rainflow identification for most cases, with some limitations. Guidelines are given for using the several spectral methods to increase confidence in the damage estimate.

  18. Discrete Chebyshev nets and a universal permutability theorem

    International Nuclear Information System (INIS)

    Schief, W K

    2007-01-01

    The Pohlmeyer-Lund-Regge system which was set down independently in the contexts of Lagrangian field theories and the relativistic motion of a string and which played a key role in the development of a geometric interpretation of soliton theory is known to appear in a variety of important guises such as the vectorial Lund-Regge equation, the O(4) nonlinear σ-model and the SU(2) chiral model. Here, it is demonstrated that these avatars may be discretized in such a manner that both integrability and equivalence are preserved. The corresponding discretization procedure is geometric and algebraic in nature and based on discrete Chebyshev nets and generalized discrete Lelieuvre formulae. In connection with the derivation of associated Baecklund transformations, it is shown that a generalized discrete Lund-Regge equation may be interpreted as a universal permutability theorem for integrable equations which admit commuting matrix Darboux transformations acting on su(2) linear representations. Three-dimensional coordinate systems and lattices of 'Lund-Regge' type related to particular continuous and discrete Zakharov-Manakov systems are obtained as a by-product of this analysis

  19. Establishing a method to measure bone structure using spectral CT

    Science.gov (United States)

    Ramyar, M.; Leary, C.; Raja, A.; Butler, A. P. H.; Woodfield, T. B. F.; Anderson, N. G.

    2017-03-01

    Combining bone structure and density measurement in 3D is required to assess site-specific fracture risk. Spectral molecular imaging can measure bone structure in relation to bone density by measuring macro and microstructure of bone in 3D. This study aimed to optimize spectral CT methodology to measure bone structure in excised bone samples. MARS CT with CdTe Medipix3RX detector was used in multiple energy bins to calibrate bone structure measurements. To calibrate thickness measurement, eight different thicknesses of Aluminium (Al) sheets were scanned one in air and the other around a falcon tube and then analysed. To test if trabecular thickness measurements differed depending on scan plane, a bone sample from sheep proximal tibia was scanned in two orthogonal directions. To assess the effect of air on thickness measurement, two parts of the same human femoral head were scanned in two conditions (in the air and in PBS). The results showed that the MARS scanner (with 90μm voxel size) is able to accurately measure the Al (in air) thicknesses over 200μm but it underestimates the thicknesses below 200μm because of partial volume effect in Al-air interface. The Al thickness measured in the highest energy bin is overestimated at Al-falcon tube interface. Bone scanning in two orthogonal directions gives the same trabecular thickness and air in the bone structure reduced measurement accuracy. We have established a bone structure assessment protocol on MARS scanner. The next step is to combine this with bone densitometry to assess bone strength.

  20. $h - p$ Spectral element methods for elliptic problems on non-smooth domains using parallel computers

    NARCIS (Netherlands)

    Tomar, S.K.

    2002-01-01

    It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.

  1. Fourier spectral methods for fractional-in-space reaction-diffusion equations

    KAUST Repository

    Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin

    2014-01-01

    approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction

  2. An Improved Spectral Analysis Method for Fatigue Damage Assessment of Details in Liquid Cargo Tanks

    Science.gov (United States)

    Zhao, Peng-yuan; Huang, Xiao-ping

    2018-03-01

    Errors will be caused in calculating the fatigue damages of details in liquid cargo tanks by using the traditional spectral analysis method which is based on linear system, for the nonlinear relationship between the dynamic stress and the ship acceleration. An improved spectral analysis method for the assessment of the fatigue damage in detail of a liquid cargo tank is proposed in this paper. Based on assumptions that the wave process can be simulated by summing the sinusoidal waves in different frequencies and the stress process can be simulated by summing the stress processes induced by these sinusoidal waves, the stress power spectral density (PSD) is calculated by expanding the stress processes induced by the sinusoidal waves into Fourier series and adding the amplitudes of each harmonic component with the same frequency. This analysis method can take the nonlinear relationship into consideration and the fatigue damage is then calculated based on the PSD of stress. Take an independent tank in an LNG carrier for example, the accuracy of the improved spectral analysis method is proved much better than that of the traditional spectral analysis method by comparing the calculated damage results with the results calculated by the time domain method. The proposed spectral analysis method is more accurate in calculating the fatigue damages in detail of ship liquid cargo tanks.

  3. Quantitative method to assess caries via fluorescence imaging from the perspective of autofluorescence spectral analysis

    International Nuclear Information System (INIS)

    Chen, Q G; Xu, Y; Zhu, H H; Chen, H; Lin, B

    2015-01-01

    A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565–750 nm. The spectral parameter, defined as the ratio of wavebands at 565–750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as <0.66, 0.66–1.06, 1.06–1.62, and >1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems. (paper)

  4. Quantitative method to assess caries via fluorescence imaging from the perspective of autofluorescence spectral analysis

    Science.gov (United States)

    Chen, Q. G.; Zhu, H. H.; Xu, Y.; Lin, B.; Chen, H.

    2015-08-01

    A quantitative method to discriminate caries lesions for a fluorescence imaging system is proposed in this paper. The autofluorescence spectral investigation of 39 teeth samples classified by the International Caries Detection and Assessment System levels was performed at 405 nm excitation. The major differences in the different caries lesions focused on the relative spectral intensity range of 565-750 nm. The spectral parameter, defined as the ratio of wavebands at 565-750 nm to the whole spectral range, was calculated. The image component ratio R/(G + B) of color components was statistically computed by considering the spectral parameters (e.g. autofluorescence, optical filter, and spectral sensitivity) in our fluorescence color imaging system. Results showed that the spectral parameter and image component ratio presented a linear relation. Therefore, the image component ratio was graded as 1.62 to quantitatively classify sound, early decay, established decay, and severe decay tissues, respectively. Finally, the fluorescence images of caries were experimentally obtained, and the corresponding image component ratio distribution was compared with the classification result. A method to determine the numerical grades of caries using a fluorescence imaging system was proposed. This method can be applied to similar imaging systems.

  5. Multi-spectral lifetime imaging: methods and applications

    NARCIS (Netherlands)

    Fereidouni, F.

    2013-01-01

    The aim of this PhD project is to further develop multispectral life time imaging hardware and analyses methods. The hardware system, Lambda-Tau, generates a considerable amount of data at high speed. To fully exploit the power of this new hardware, fast and reliable data analyses methods are

  6. Methods for Enhancing Geological Structures in Spectral Spatial Difference-Based on Remote-Sensing Image

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    @@In this paper, some image processing methods such as directional template (mask) matching enhancement, pseudocolor or false color enhancement, K-L transform enhancement are used to enhance a geological structure, one of important ore-controlling factors, shown in the remote-sensing images.This geological structure is regarded as image anomaly in the remote-sensing image, since considerable differences, based on the spatial spectral distribution pattern, in gray values (spectral), color tones and texture, are always present between the geological structure and background. Therefore,the enhancement of the geological structure in the remotesensing image is that of the spectral spatial difference.

  7. Modified Spectral Fatigue Methods for S-N Curves With MIL-HDBK-5J Coefficients

    Science.gov (United States)

    Irvine, Tom; Larsen, Curtis

    2016-01-01

    The rainflow method is used for counting fatigue cycles from a stress response time history, where the fatigue cycles are stress-reversals. The rainflow method allows the application of Palmgren-Miner's rule in order to assess the fatigue life of a structure subject to complex loading. The fatigue damage may also be calculated from a stress response power spectral density (PSD) using the semi-empirical Dirlik, Single Moment, Zhao-Baker and other spectral methods. These methods effectively assume that the PSD has a corresponding time history which is stationary with a normal distribution. This paper shows how the probability density function for rainflow stress cycles can be extracted from each of the spectral methods. This extraction allows for the application of the MIL-HDBK-5J fatigue coefficients in the cumulative damage summation. A numerical example is given in this paper for the stress response of a beam undergoing random base excitation, where the excitation is applied separately by a time history and by its corresponding PSD. The fatigue calculation is performed in the time domain, as well as in the frequency domain via the modified spectral methods. The result comparison shows that the modified spectral methods give comparable results to the time domain rainflow counting method.

  8. Continuous non-invasive blood glucose monitoring by spectral image differencing method

    Science.gov (United States)

    Huang, Hao; Liao, Ningfang; Cheng, Haobo; Liang, Jing

    2018-01-01

    Currently, the use of implantable enzyme electrode sensor is the main method for continuous blood glucose monitoring. But the effect of electrochemical reactions and the significant drift caused by bioelectricity in body will reduce the accuracy of the glucose measurements. So the enzyme-based glucose sensors need to be calibrated several times each day by the finger-prick blood corrections. This increases the patient's pain. In this paper, we proposed a method for continuous Non-invasive blood glucose monitoring by spectral image differencing method in the near infrared band. The method uses a high-precision CCD detector to switch the filter in a very short period of time, obtains the spectral images. And then by using the morphological method to obtain the spectral image differences, the dynamic change of blood sugar is reflected in the image difference data. Through the experiment proved that this method can be used to monitor blood glucose dynamically to a certain extent.

  9. New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams

    Energy Technology Data Exchange (ETDEWEB)

    Dorf, Mikhail A.; Davidson, Ronald C.; Startsev, Edward A.

    2011-04-27

    An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.

  10. Multi-spectral temperature measurement method for gas turbine blade

    Science.gov (United States)

    Gao, Shan; Feng, Chi; Wang, Lixin; Li, Dong

    2016-02-01

    One of the basic methods to improve both the thermal efficiency and power output of a gas turbine is to increase the firing temperature. However, gas turbine blades are easily damaged in harsh high-temperature and high-pressure environments. Therefore, ensuring that the blade temperature remains within the design limits is very important. There are unsolved problems in blade temperature measurement, relating to the emissivity of the blade surface, influences of the combustion gases, and reflections of radiant energy from the surroundings. In this study, the emissivity of blade surfaces has been measured, with errors reduced by a fitting method, influences of the combustion gases have been calculated for different operational conditions, and a reflection model has been built. An iterative computing method is proposed for calculating blade temperatures, and the experimental results show that this method has high precision.

  11. A time-spectral approach to numerical weather prediction

    Science.gov (United States)

    Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

    2018-05-01

    Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

  12. Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

    KAUST Repository

    Ait-Haddou, Rachid

    2013-08-01

    The notion of a blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Müntz spaces with integer exponents, the notion of a Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Müntz spaces in terms of Schur functions. We derive an explicit expression for the Chebyshev-Bernstein basis via an inductive argument on nested Müntz spaces. We also reveal a simple algorithm for dimension elevation. Free-form design schemes in Müntz spaces with Young diagrams as shape parameters are discussed. © 2013 Elsevier Ltd. All rights reserved.

  13. Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

    KAUST Repository

    Ait-Haddou, Rachid; Sakane, Yusuke; Nomura, Taishin

    2013-01-01

    The notion of a blossom in extended Chebyshev spaces offers adequate generalizations and extra-utilities to the tools for free-form design schemes. Unfortunately, such advantages are often overshadowed by the complexity of the resulting algorithms. In this work, we show that for the case of Müntz spaces with integer exponents, the notion of a Chebyshev blossom leads to elegant algorithms whose complexities are embedded in the combinatorics of Schur functions. We express the blossom and the pseudo-affinity property in Müntz spaces in terms of Schur functions. We derive an explicit expression for the Chebyshev-Bernstein basis via an inductive argument on nested Müntz spaces. We also reveal a simple algorithm for dimension elevation. Free-form design schemes in Müntz spaces with Young diagrams as shape parameters are discussed. © 2013 Elsevier Ltd. All rights reserved.

  14. Methods for deconvoluting and interpreting complex gamma- and x-ray spectral regions

    International Nuclear Information System (INIS)

    Gunnink, R.

    1983-06-01

    Germanium and silicon detectors are now widely used for the detection and measurement of x and gamma radiation. However, some analysis situations and spectral regions have heretofore been too complex to deconvolute and interpret by techniques in general use. One example is the L x-ray spectrum of an element taken with a Ge or Si detector. This paper describes some new tools and methods that were developed to analyze complex spectral regions; they are illustrated with examples

  15. Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mesiar, Radko; Ouyang, Y.

    2010-01-01

    Roč. 46, č. 1 (2010), s. 83-95 ISSN 0023-5954 R&D Projects: GA ČR GA402/08/0618 Institutional research plan: CEZ:AV0Z10750506 Keywords : Sugeno integral * fuzzy measure * comonotone functions * Chebyshev's inequality Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/E/mesiar-further development of chebyshev type inequalities for sugeno integrals and t-(s-)evaluators.pdf

  16. Incompressible spectral-element method: Derivation of equations

    Science.gov (United States)

    Deanna, Russell G.

    1993-01-01

    A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

  17. Spectral Analysis of Large Finite Element Problems by Optimization Methods

    Directory of Open Access Journals (Sweden)

    Luca Bergamaschi

    1994-01-01

    Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.

  18. Spectral methods in chemistry and physics applications to kinetic theory and quantum mechanics

    CERN Document Server

    Shizgal, Bernard

    2015-01-01

    This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficient...

  19. A stabilised nodal spectral element method for fully nonlinear water waves

    DEFF Research Database (Denmark)

    Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele

    2016-01-01

    can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...

  20. A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

    International Nuclear Information System (INIS)

    Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.

    2013-01-01

    Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods

  1. Generalized spectral method for near-field optical microscopy

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M. [Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093 (United States); Castro Neto, A. H. [Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States); Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore 117542 (Singapore)

    2016-02-07

    Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.

  2. Methodes spectrales paralleles et applications aux simulations de couches de melange compressibles

    OpenAIRE

    Male , Jean-Michel; Fezoui , Loula ,

    1993-01-01

    La resolution des equations de Navier-Stokes en methodes spectrales pour des ecoulements compressibles peut etre assez gourmande en temps de calcul. On etudie donc ici la parallelisation d'un tel algorithme et son implantation sur une machine massivement parallele, la connection-machine CM-2. La methode spectrale s'adapte bien aux exigences du parallelisme massif, mais l'un des outils de base de cette methode, la transformee de Fourier rapide (lorsqu'elle doit etre appliquee sur les deux dime...

  3. Spectral methods for a nonlinear initial value problem involving pseudo differential operators

    International Nuclear Information System (INIS)

    Pasciak, J.E.

    1982-01-01

    Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed

  4. A Spectral-Texture Kernel-Based Classification Method for Hyperspectral Images

    Directory of Open Access Journals (Sweden)

    Yi Wang

    2016-11-01

    Full Text Available Classification of hyperspectral images always suffers from high dimensionality and very limited labeled samples. Recently, the spectral-spatial classification has attracted considerable attention and can achieve higher classification accuracy and smoother classification maps. In this paper, a novel spectral-spatial classification method for hyperspectral images by using kernel methods is investigated. For a given hyperspectral image, the principle component analysis (PCA transform is first performed. Then, the first principle component of the input image is segmented into non-overlapping homogeneous regions by using the entropy rate superpixel (ERS algorithm. Next, the local spectral histogram model is applied to each homogeneous region to obtain the corresponding texture features. Because this step is performed within each homogenous region, instead of within a fixed-size image window, the obtained local texture features in the image are more accurate, which can effectively benefit the improvement of classification accuracy. In the following step, a contextual spectral-texture kernel is constructed by combining spectral information in the image and the extracted texture information using the linearity property of the kernel methods. Finally, the classification map is achieved by the support vector machines (SVM classifier using the proposed spectral-texture kernel. Experiments on two benchmark airborne hyperspectral datasets demonstrate that our method can effectively improve classification accuracies, even though only a very limited training sample is available. Specifically, our method can achieve from 8.26% to 15.1% higher in terms of overall accuracy than the traditional SVM classifier. The performance of our method was further compared to several state-of-the-art classification methods of hyperspectral images using objective quantitative measures and a visual qualitative evaluation.

  5. Application of Least-Squares Spectral Element Methods to Polynomial Chaos

    NARCIS (Netherlands)

    Vos, P.E.J.; Gerritsma, M.I.

    2006-01-01

    This papers describes the use of the Least-Squares Spectral Element Method to polynomial Chaos to solve stochastic partial differential equations. The method will be described in detail and a comparison will be presented between the least-squares projection and the conventional Galerkin projection.

  6. A Legendre Wavelet Spectral Collocation Method for Solving Oscillatory Initial Value Problems

    Directory of Open Access Journals (Sweden)

    A. Karimi Dizicheh

    2013-01-01

    wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.

  7. Application of the spectral correction method to reanalysis data in South Africa

    DEFF Research Database (Denmark)

    Larsén, Xiaoli Guo; Kruger, Andries C.

    2014-01-01

    of this study is to evaluate the applicability of the method to the relevant region. The impacts from the two aspects are investigated for interior and coastal locations. Measurements from five stations from South Africa are used to evaluate the results from the spectral model S(f)=af−5/3 together...... with the hourly time series of the Climate Forecast System Reanalysis (CFSR) 10 m wind at 38 km resolution over South Africa. The results show that using the spectral correction method to the CFSR wind data produce extreme wind atlases in acceptable agreement with the atlas made from limited measurements across...

  8. The analysis of toxic connections content in water by spectral methods

    Science.gov (United States)

    Plotnikova, I. V.; Chaikovskaya, O. N.; Sokolova, I. V.; Artyushin, V. R.

    2017-08-01

    The current state of ecology means the strict observance of measures for the utilization of household and industrial wastes that is connected with very essential expenses of means and time. Thanks to spectroscopic devices usage the spectral methods allow to carry out the express quantitative and qualitative analysis in a workplace and field conditions. In a work the application of spectral methods by studying the degradation of toxic organic compounds after preliminary radiation of various sources is shown. Experimental data of optical density of water at various influences are given.

  9. SOLUTION OF A MULTIVARIATE STRATIFIED SAMPLING PROBLEM THROUGH CHEBYSHEV GOAL PROGRAMMING

    Directory of Open Access Journals (Sweden)

    Mohd. Vaseem Ismail

    2010-12-01

    Full Text Available In this paper, we consider the problem of minimizing the variances for the various characters with fixed (given budget. Each convex objective function is first linearised at its minimal point where it meets the linear cost constraint. The resulting multiobjective linear programming problem is then solved by Chebyshev goal programming. A numerical example is given to illustrate the procedure.

  10. Site Characterization in the Urban Area of Tijuana, B. C., Mexico by Means of: H/V Spectral Ratios, Spectral Analysis of Surface Waves, and Random Decrement Method

    Science.gov (United States)

    Tapia-Herrera, R.; Huerta-Lopez, C. I.; Martinez-Cruzado, J. A.

    2009-05-01

    Results of site characterization for an experimental site in the metropolitan area of Tijuana, B. C., Mexico are presented as part of the on-going research in which time series of earthquakes, ambient noise, and induced vibrations were processed with three different methods: H/V spectral ratios, Spectral Analysis of Surface Waves (SASW), and the Random Decrement Method, (RDM). Forward modeling using the wave propagation stiffness matrix method (Roësset and Kausel, 1981) was used to compute the theoretical SH/P, SV/P spectral ratios, and the experimental H/V spectral ratios were computed following the conventional concepts of Fourier analysis. The modeling/comparison between the theoretical and experimental H/V spectral ratios was carried out. For the SASW method the theoretical dispersion curves were also computed and compared with the experimental one, and finally the theoretical free vibration decay curve was compared with the experimental one obtained with the RDM. All three methods were tested with ambient noise, induced vibrations, and earthquake signals. Both experimental spectral ratios obtained with ambient noise as well as earthquake signals agree quite well with the theoretical spectral ratios, particularly at the fundamental vibration frequency of the recording site. Differences between the fundamental vibration frequencies are evident for sites located at alluvial fill (~0.6 Hz) and at sites located at conglomerate/sandstones fill (0.75 Hz). Shear wave velocities for the soft soil layers of the 4-layer discrete soil model ranges as low as 100 m/s and up to 280 m/s. The results with the SASW provided information that allows to identify low velocity layers, not seen before with the traditional seismic methods. The damping estimations obtained with the RDM are within the expected values, and the dominant frequency of the system also obtained with the RDM correlates within the range of plus-minus 20 % with the one obtained by means of the H/V spectral

  11. Spectral analysis of an algebraic collapsing acceleration for the characteristics method

    International Nuclear Information System (INIS)

    Le Tellier, R.; Hebert, A.

    2005-01-01

    A spectral analysis of a diffusion synthetic acceleration called Algebraic Collapsing Acceleration (ACA) was carried out in the context of the characteristics method to solve the neutron transport equation. Two analysis were performed in order to assess the ACA performances. Both a standard Fourier analysis in a periodic and infinite slab-geometry and a direct spectral analysis for a finite slab-geometry were investigated. In order to evaluate its performance, ACA was compared with two competing techniques used to accelerate the convergence of the characteristics method, the Self-Collision Re-balancing technique and the Asymptotic Synthetic Acceleration. In the restricted framework of 1-dimensional slab-geometries, we conclude that ACA offers a good compromise between the reduction of the spectral radius of the iterative matrix and the resources to construct, store and solve the corrective system. A comparison on a monoenergetic 2-dimensional benchmark was performed and tends to confirm these conclusions. (authors)

  12. Wave propagation numerical models in damage detection based on the time domain spectral element method

    International Nuclear Information System (INIS)

    Ostachowicz, W; Kudela, P

    2010-01-01

    A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.

  13. 3D registration method for assessing the gastrointestinal motility using spectral reflectance estimation

    Science.gov (United States)

    Nobe, Kazuki; Yoshimoto, Kayo; Yamada, Kenji; Takahashi, Hideya

    2018-02-01

    Functional gastrointestinal disorders (FGID) are the most common gastrointestinal disorders. The term "functional" is generally applied to disorders where there are no structural abnormalities. One of the major factors for FGID is abnormal gastrointestinal motility. We have proposed a system for assessing the function of gastric motility using a 3D endoscope. In this previous study, we established a method for estimating characteristics of contraction wave extracted from a 3D shape include contraction wave obtained from stereo endoscope. Because it is difficult to fix the tip position of the endoscope during the examination, estimation of the 3D position between the endoscope and the gastric wall is necessary for the accurate assessment. Then, we have proposed a motion compensation method using 3D scene flow. However, since mucosa has few feature points, it is difficult to obtain 3D scene flow from RGB images. So, we focused on spectral imaging that can enhance visualization of mucosal structure. Spectral image can be obtained without switching optical filters by using technique to estimate spectral reflectance by image processing. In this paper, we propose registration method of measured 3D shape in time series using estimated spectral image. The spectral image is estimated from the RGB image for each frame. 3D scene flow of feature points, that is, enhanced mucosal structure calculated by spectral images in a time series. The position change between the endoscope and gastric wall is estimated by 3D scene flow. We experimented to confirm the validity of the proposed method using papers with a grid of colors close to the background color.

  14. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  15. The next step in coastal numerical models: spectral/hp element methods?

    DEFF Research Database (Denmark)

    Eskilsson, Claes; Engsig-Karup, Allan Peter; Sherwin, Spencer J.

    2005-01-01

    In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations....

  16. A new approach to passivity preserving model reduction : the dominant spectral zero method

    NARCIS (Netherlands)

    Ionutiu, R.; Rommes, J.; Antoulas, A.C.; Roos, J.; Costa, L.R.J.

    2010-01-01

    A new model reduction method for circuit simulation is presented, which preserves passivity by interpolating dominant spectral zeros. These are computed as poles of an associated Hamiltonian system, using an iterative solver: the subspace accelerated dominant pole algorithm (SADPA). Based on a

  17. Mass anomalous dimension of SU(2) with Nf=8 using the spectral density method

    DEFF Research Database (Denmark)

    Suorsa, Joni M.; Leino, Viljami; Rantaharju, Jarno

    2015-01-01

    SU(2) with Nf=8 is believed to have an infrared conformal fixed point. We use the spectral density method to evaluate the coupling constant dependence of the mass anomalous dimension for massless HEX smeared, clover improved Wilson fermions with Schr\\"odinger functional boundary conditions....

  18. Spectral mimetic least-squares method for div-curl systems

    NARCIS (Netherlands)

    Gerritsma, Marc; Palha, Artur; Lirkov, I.; Margenov, S.

    2018-01-01

    In this paper the spectral mimetic least-squares method is applied to a two-dimensional div-curl system. A test problem is solved on orthogonal and curvilinear meshes and both h- and p-convergence results are presented. The resulting solutions will be pointwise divergence-free for these test

  19. Stability Estimates for h-p Spectral Element Methods for Elliptic Problems

    NARCIS (Netherlands)

    Dutt, Pravir; Tomar, S.K.; Kumar, B.V. Rathish

    2002-01-01

    In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which

  20. The spectral method and the central limit theorem for general Markov chains

    Science.gov (United States)

    Nagaev, S. V.

    2017-12-01

    We consider Markov chains with an arbitrary phase space and develop a modification of the spectral method that enables us to prove the central limit theorem (CLT) for non-uniformly ergodic Markov chains. The conditions imposed on the transition function are more general than those by Athreya-Ney and Nummelin. Our proof of the CLT is purely analytical.

  1. Evaluation of methods to determine the spectral variations of aerosol optical thickness

    Digital Repository Service at National Institute of Oceanography (India)

    Suresh, T.; Talaulikar, M.; Rodrigues, A.; Desa, E.; Chauhan, P.

    The methods used to derive spectral variations of aerosol optical thickness, AOT are evaluated. For our analysis we have used the AOT measured using a hand held sunphotometer at the coastal station on the west coast of India, Dona-Paula, Goa...

  2. Testing the accuracy and stability of spectral methods in numerical relativity

    International Nuclear Information System (INIS)

    Boyle, Michael; Lindblom, Lee; Pfeiffer, Harald P.; Scheel, Mark A.; Kidder, Lawrence E.

    2007-01-01

    The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the Kidder, Scheel, and Teukolsky (KST) representation of the Einstein evolution equations. The basic 'Mexico City tests' widely adopted by the numerical relativity community are adapted here for codes based on spectral methods. Exponential convergence of the spectral code is established, apparently limited only by numerical roundoff error or by truncation error in the time integration. A general expression for the growth of errors due to finite machine precision is derived, and it is shown that this limit is achieved here for the linear plane-wave test

  3. Spectral density analysis of time correlation functions in lattice QCD using the maximum entropy method

    International Nuclear Information System (INIS)

    Fiebig, H. Rudolf

    2002-01-01

    We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss the practical issues of the approach

  4. A complex guided spectral transform Lanczos method for studying quantum resonance states

    International Nuclear Information System (INIS)

    Yu, Hua-Gen

    2014-01-01

    A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO, and compared to previous calculations

  5. Multiscale finite element methods for high-contrast problems using local spectral basis functions

    KAUST Repository

    Efendiev, Yalchin

    2011-02-01

    In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ*)1/2, where Λ* is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings. © 2010.

  6. Development and validation of a new fallout transport method using variable spectral winds

    International Nuclear Information System (INIS)

    Hopkins, A.T.

    1984-01-01

    A new method was developed to incorporate variable winds into fallout transport calculations. The method uses spectral coefficients derived by the National Meteorological Center. Wind vector components are computed with the coefficients along the trajectories of falling particles. Spectral winds are used in the two-step method to compute dose rate on the ground, downwind of a nuclear cloud. First, the hotline is located by computing trajectories of particles from an initial, stabilized cloud, through spectral winds to the ground. The connection of particle landing points is the hotline. Second, dose rate on and around the hotline is computed by analytically smearing the falling cloud's activity along the ground. The feasibility of using spectral winds for fallout particle transport was validated by computing Mount St. Helens ashfall locations and comparing calculations to fallout data. In addition, an ashfall equation was derived for computing volcanic ash mass/area on the ground. Ashfall data and the ashfall equation were used to back-calculate an aggregated particle size distribution for the Mount St. Helens eruption cloud

  7. A hybrid spatial-spectral denoising method for infrared hyperspectral images using 2DPCA

    Science.gov (United States)

    Huang, Jun; Ma, Yong; Mei, Xiaoguang; Fan, Fan

    2016-11-01

    The traditional noise reduction methods for 3-D infrared hyperspectral images typically operate independently in either the spatial or spectral domain, and such methods overlook the relationship between the two domains. To address this issue, we propose a hybrid spatial-spectral method in this paper to link both domains. First, principal component analysis and bivariate wavelet shrinkage are performed in the 2-D spatial domain. Second, 2-D principal component analysis transformation is conducted in the 1-D spectral domain to separate the basic components from detail ones. The energy distribution of noise is unaffected by orthogonal transformation; therefore, the signal-to-noise ratio of each component is used as a criterion to determine whether a component should be protected from over-denoising or denoised with certain 1-D denoising methods. This study implements the 1-D wavelet shrinking threshold method based on Stein's unbiased risk estimator, and the quantitative results on publicly available datasets demonstrate that our method can improve denoising performance more effectively than other state-of-the-art methods can.

  8. High-precision solution to the moving load problem using an improved spectral element method

    Science.gov (United States)

    Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li

    2018-02-01

    In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

  9. [A cloud detection algorithm for MODIS images combining Kmeans clustering and multi-spectral threshold method].

    Science.gov (United States)

    Wang, Wei; Song, Wei-Guo; Liu, Shi-Xing; Zhang, Yong-Ming; Zheng, Hong-Yang; Tian, Wei

    2011-04-01

    An improved method for detecting cloud combining Kmeans clustering and the multi-spectral threshold approach is described. On the basis of landmark spectrum analysis, MODIS data is categorized into two major types initially by Kmeans method. The first class includes clouds, smoke and snow, and the second class includes vegetation, water and land. Then a multi-spectral threshold detection is applied to eliminate interference such as smoke and snow for the first class. The method is tested with MODIS data at different time under different underlying surface conditions. By visual method to test the performance of the algorithm, it was found that the algorithm can effectively detect smaller area of cloud pixels and exclude the interference of underlying surface, which provides a good foundation for the next fire detection approach.

  10. Ultrafast method of calculating the dynamic spectral line shapes for integrated modelling of plasmas

    International Nuclear Information System (INIS)

    Lisitsa, V.S.

    2009-01-01

    An ultrafast code for spectral line shape calculations is presented to be used in the integrated modelling of plasmas. The code is based on the close analogy between two mechanisms: (i) Dicke narrowing of the Doppler-broadened spectral lines and (ii) transition from static to impact regime in the Stark broadening. The analogy makes it possible to describe the dynamic Stark broadening in terms of an analytical functional of the static line shape. A comparison of new method with the widely used Frequency Fluctuating Method (FFM) developed by the Marseille University group (B. Talin, R. Stamm, et al.) shows good agreement, with the new method being faster than the standard FFM by nearly two orders of magnitude. The method proposed may significantly simplify the radiation transport modeling and opens new possibilities for integrated modeling of the edge and divertor plasma in tokamaks. (author)

  11. A sparse-mode spectral method for the simulation of turbulent flows

    International Nuclear Information System (INIS)

    Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.

    1996-01-01

    We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows

  12. Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Z. Pashazadeh Atabakan

    2013-01-01

    Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

  13. Reduction of Musical Noise in Spectral Subtraction Method Using Subframe Phase Randomization

    Energy Technology Data Exchange (ETDEWEB)

    Seok, J.W.; Bae, K.S. [Kyungpook National University, Taegu (Korea)

    1999-06-01

    The Subframe phase randomization method is applied to the spectral subtraction method to reduce the musical noise in nonvoicing region after speech enhancement. The musical noise in the spectral subtraction method is the result of the narrowband tonal components that appearing somewhat periodically in the spectrogram of unvoiced and silence regions. Thus each synthesis frame in nonvoicing region is divided into several subframes to broaden the narrowband spectrum, and then phases of silence and unvoiced regions are randomized to eliminate the tonal components in the spectrum while keeping the shape of the amplitude spectrum. Performance assessments based on visual inspection of spectrogram, objective measure, and informal subjective listening tests demonstrate the superiority of the proposed algorithm. (author). 7 refs., 5 figs.

  14. Color quality improvement of reconstructed images in color digital holography using speckle method and spectral estimation

    Science.gov (United States)

    Funamizu, Hideki; Onodera, Yusei; Aizu, Yoshihisa

    2018-05-01

    In this study, we report color quality improvement of reconstructed images in color digital holography using the speckle method and the spectral estimation. In this technique, an object is illuminated by a speckle field and then an object wave is produced, while a plane wave is used as a reference wave. For three wavelengths, the interference patterns of two coherent waves are recorded as digital holograms on an image sensor. Speckle fields are changed by moving a ground glass plate in an in-plane direction, and a number of holograms are acquired to average the reconstructed images. After the averaging process of images reconstructed from multiple holograms, we use the Wiener estimation method for obtaining spectral transmittance curves in reconstructed images. The color reproducibility in this method is demonstrated and evaluated using a Macbeth color chart film and staining cells of onion.

  15. [Study of near infrared spectral preprocessing and wavelength selection methods for endometrial cancer tissue].

    Science.gov (United States)

    Zhao, Li-Ting; Xiang, Yu-Hong; Dai, Yin-Mei; Zhang, Zhuo-Yong

    2010-04-01

    Near infrared spectroscopy was applied to measure the tissue slice of endometrial tissues for collecting the spectra. A total of 154 spectra were obtained from 154 samples. The number of normal, hyperplasia, and malignant samples was 36, 60, and 58, respectively. Original near infrared spectra are composed of many variables, for example, interference information including instrument errors and physical effects such as particle size and light scatter. In order to reduce these influences, original spectra data should be performed with different spectral preprocessing methods to compress variables and extract useful information. So the methods of spectral preprocessing and wavelength selection have played an important role in near infrared spectroscopy technique. In the present paper the raw spectra were processed using various preprocessing methods including first derivative, multiplication scatter correction, Savitzky-Golay first derivative algorithm, standard normal variate, smoothing, and moving-window median. Standard deviation was used to select the optimal spectral region of 4 000-6 000 cm(-1). Then principal component analysis was used for classification. Principal component analysis results showed that three types of samples could be discriminated completely and the accuracy almost achieved 100%. This study demonstrated that near infrared spectroscopy technology and chemometrics method could be a fast, efficient, and novel means to diagnose cancer. The proposed methods would be a promising and significant diagnosis technique of early stage cancer.

  16. Rapid screening of guar gum using portable Raman spectral identification methods.

    Science.gov (United States)

    Srivastava, Hirsch K; Wolfgang, Steven; Rodriguez, Jason D

    2016-01-25

    Guar gum is a well-known inactive ingredient (excipient) used in a variety of oral pharmaceutical dosage forms as a thickener and stabilizer of suspensions and as a binder of powders. It is also widely used as a food ingredient in which case alternatives with similar properties, including chemically similar gums, are readily available. Recent supply shortages and price fluctuations have caused guar gum to come under increasing scrutiny for possible adulteration by substitution of cheaper alternatives. One way that the U.S. FDA is attempting to screen pharmaceutical ingredients at risk for adulteration or substitution is through field-deployable spectroscopic screening. Here we report a comprehensive approach to evaluate two field-deployable Raman methods--spectral correlation and principal component analysis--to differentiate guar gum from other gums. We report a comparison of the sensitivity of the spectroscopic screening methods with current compendial identification tests. The ability of the spectroscopic methods to perform unambiguous identification of guar gum compared to other gums makes them an enhanced surveillance alternative to the current compendial identification tests, which are largely subjective in nature. Our findings indicate that Raman spectral identification methods perform better than compendial identification methods and are able to distinguish guar gum from other gums with 100% accuracy for samples tested by spectral correlation and principal component analysis. Published by Elsevier B.V.

  17. Spectral element method for elastic and acoustic waves in frequency domain

    Energy Technology Data Exchange (ETDEWEB)

    Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)

    2016-12-15

    Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

  18. Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems

    International Nuclear Information System (INIS)

    Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da

    2001-01-01

    Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)

  19. Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

    Science.gov (United States)

    Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

    2018-04-01

    The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

  20. Development of spectral history methods for pin-by-pin core analysis method using three-dimensional direct response matrix

    International Nuclear Information System (INIS)

    Mitsuyasu, T.; Ishii, K.; Hino, T.; Aoyama, M.

    2009-01-01

    Spectral history methods for pin-by-pin core analysis method using the three-dimensional direct response matrix have been developed. The direct response matrix is formalized by four sub-response matrices in order to respond to a core eigenvalue k and thus can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the burn-up effect related to spectral history. One of the methods is to evaluate the nodal burn-up spectrum obtained using the out-going neutron current. The other is to correct the fuel rod neutron production rates obtained the pin-by-pin correction. These spectral history methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error can be reduced by half during burn-up, the nodal neutron production rates errors can be reduced by 30% or more. The root-mean-square differences between the relative fuel rod neutron production rate distributions can be reduced within 1.1% error. This means that these methods can accurately reflect the effects of intra- and inter-assembly heterogeneities during burn-up and can be used for core analysis. Core analysis with the DRM method was carried out for an ABWR quarter core and it was found that both thermal power and coolant-flow distributions were smoothly converged. (authors)

  1. Spectral Inverse Quantum (Spectral-IQ Method for Modeling Mesoporous Systems: Application on Silica Films by FTIR

    Directory of Open Access Journals (Sweden)

    Mihai V. Putz

    2012-11-01

    Full Text Available The present work advances the inverse quantum (IQ structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings to more wave behavior (free or covalent bindings. This so-called spectral inverse quantum (Spectral-IQ particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB and cetyltrimethylammonium bromide (CTAB and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature.

  2. Advances in Spectral Nodal Methods applied to SN Nuclear Reactor Global calculations in Cartesian Geometry

    International Nuclear Information System (INIS)

    Barros, R.C.; Filho, H.A.; Oliveira, F.B.S.; Silva, F.C. da

    2004-01-01

    Presented here are the advances in spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: (i) the use of the standard discretized spatial balance SN equations; (ii) the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and (iii) the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. Moreover, we describe in this paper the progress of the approximate SN albedo boundary conditions for substituting the non-multiplying regions around the nuclear reactor core. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (Author)

  3. Spectral feature characterization methods for blood stain detection in crime scene backgrounds

    Science.gov (United States)

    Yang, Jie; Mathew, Jobin J.; Dube, Roger R.; Messinger, David W.

    2016-05-01

    Blood stains are one of the most important types of evidence for forensic investigation. They contain valuable DNA information, and the pattern of the stains can suggest specifics about the nature of the violence that transpired at the scene. Blood spectral signatures containing unique reflectance or absorption features are important both for forensic on-site investigation and laboratory testing. They can be used for target detection and identification applied to crime scene hyperspectral imagery, and also be utilized to analyze the spectral variation of blood on various backgrounds. Non-blood stains often mislead the detection and can generate false alarms at a real crime scene, especially for dark and red backgrounds. This paper measured the reflectance of liquid blood and 9 kinds of non-blood samples in the range of 350 nm - 2500 nm in various crime scene backgrounds, such as pure samples contained in petri dish with various thicknesses, mixed samples with different colors and materials of fabrics, and mixed samples with wood, all of which are examined to provide sub-visual evidence for detecting and recognizing blood from non-blood samples in a realistic crime scene. The spectral difference between blood and non-blood samples are examined and spectral features such as "peaks" and "depths" of reflectance are selected. Two blood stain detection methods are proposed in this paper. The first method uses index to denote the ratio of "depth" minus "peak" over"depth" add"peak" within a wavelength range of the reflectance spectrum. The second method uses relative band depth of the selected wavelength ranges of the reflectance spectrum. Results show that the index method is able to discriminate blood from non-blood samples in most tested crime scene backgrounds, but is not able to detect it from black felt. Whereas the relative band depth method is able to discriminate blood from non-blood samples on all of the tested background material types and colors.

  4. Methods for measuring the spectral reflectivity of advanced materials at high temperature

    International Nuclear Information System (INIS)

    Salikhov, T.P.; Kan, V.V.

    1993-01-01

    For investigation in the domain of advanced materials as well as for new technologies there is an urgent need for knowledge of the spectral reflectivity of the materials specially at high temperatures. However the methods available are mostly intended for measuring the model materials with specular or diffuse reflection surface. This is not quite correct since advanced materials have mixed specular diffuse reflection surfaces. New methods for reflectivity measurements of materials in the visible, near and middle infrared range at high temperature, regardless of surface texture, have been developed. The advantages of the methods proposed are as flows: (a) the facility of performing the reflectivity measurements for materials with mixed specular diffuse reflectance; (b) wide spectral range 0,38-8 micro m; (c) wide temperature range 300-3000 K; (d) high accuracy and rapid measurements. The methods are based on the following principals (i) Diffuse irradiation of the sample surface and the use of Helkholtz reciprocity principle to determine the directional hemispherical reflectivity ii) Pulse polychromatic probing of the sample by additional light source. The first principle excludes the influence of the angular reflection distribution of sample surface on data obtained. The second principle gives the possibility of simultaneous measurements of the reflectivity. The second principle gives the possibility of simultaneous measurements of the reflectivity in wide spectral range. On the basis of these principles for high temperature reflectometers have been developed and discussed here. (author)

  5. Spectral decomposition in advection-diffusion analysis by finite element methods

    International Nuclear Information System (INIS)

    Nickell, R.E.; Gartling, D.K.; Strang, G.

    1978-01-01

    In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies

  6. A spectral measurement method for determining white OLED average junction temperatures

    Science.gov (United States)

    Zhu, Yiting; Narendran, Nadarajah

    2016-09-01

    The objective of this study was to investigate an indirect method of measuring the average junction temperature of a white organic light-emitting diode (OLED) based on temperature sensitivity differences in the radiant power emitted by individual emitter materials (i.e., "blue," "green," and "red"). The measured spectral power distributions (SPDs) of the white OLED as a function of temperature showed amplitude decrease as a function of temperature in the different spectral bands, red, green, and blue. Analyzed data showed a good linear correlation between the integrated radiance for each spectral band and the OLED panel temperature, measured at a reference point on the back surface of the panel. The integrated radiance ratio of the spectral band green compared to red, (G/R), correlates linearly with panel temperature. Assuming that the panel reference point temperature is proportional to the average junction temperature of the OLED panel, the G/R ratio can be used for estimating the average junction temperature of an OLED panel.

  7. High-order multi-implicit spectral deferred correction methods for problems of reactive flow

    International Nuclear Information System (INIS)

    Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.

    2003-01-01

    Models for reacting flow are typically based on advection-diffusion-reaction (A-D-R) partial differential equations. Many practical cases correspond to situations where the relevant time scales associated with each of the three sub-processes can be widely different, leading to disparate time-step requirements for robust and accurate time-integration. In particular, interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection. The numerical strategy introduced in this paper is a general procedure to account for this time-scale disparity. The proposed methods are high-order multi-implicit generalizations of spectral deferred correction methods (MISDC methods), constructed for the temporal integration of A-D-R equations. Spectral deferred correction methods compute a high-order approximation to the solution of a differential equation by using a simple, low-order numerical method to solve a series of correction equations, each of which increases the order of accuracy of the approximation. The key feature of MISDC methods is their flexibility in handling several sub-processes implicitly but independently, while avoiding the splitting errors present in traditional operator-splitting methods and also allowing for different time steps for each process. The stability, accuracy, and efficiency of MISDC methods are first analyzed using a linear model problem and the results are compared to semi-implicit spectral deferred correction methods. Furthermore, numerical tests on simplified reacting flows demonstrate the expected convergence rates for MISDC methods of orders three, four, and five. The gain in efficiency by independently controlling the sub-process time steps is illustrated for nonlinear problems, where reaction and diffusion are much stiffer than advection. Although the paper focuses on this specific time-scales ordering, the generalization to any ordering combination is straightforward

  8. Operation analysis of a Chebyshev-Pantograph leg mechanism for a single DOF biped robot

    Science.gov (United States)

    Liang, Conghui; Ceccarelli, Marco; Takeda, Yukio

    2012-12-01

    In this paper, operation analysis of a Chebyshev-Pantograph leg mechanism is presented for a single degree of freedom (DOF) biped robot. The proposed leg mechanism is composed of a Chebyshev four-bar linkage and a pantograph mechanism. In contrast to general fully actuated anthropomorphic leg mechanisms, the proposed leg mechanism has peculiar features like compactness, low-cost, and easy-operation. Kinematic equations of the proposed leg mechanism are formulated for a computer oriented simulation. Simulation results show the operation performance of the proposed leg mechanism with suitable characteristics. A parametric study has been carried out to evaluate the operation performance as function of design parameters. A prototype of a single DOF biped robot equipped with two proposed leg mechanisms has been built at LARM (Laboratory of Robotics and Mechatronics). Experimental test shows practical feasible walking ability of the prototype, as well as drawbacks are discussed for the mechanical design.

  9. Applications of the semiclassical spectral method to nuclear, atomic, molecular, and polymeric dynamics

    International Nuclear Information System (INIS)

    Koszykowski, M.L.; Pfeffer, G.A.; Noid, D.W.

    1987-01-01

    Nonlinear dynamics plays a dominant role in a variety of important problems in chemical physics. Examples are unimolecular reactions, infrared multiphoton decomposition of molecules, the pumping process of the gamma ray laser, dissociation of vibrationally excited state-selected van der Waals's complexes, and many other chemical and atomic processes. The present article discusses recent theoretical studies on the quasi-periodic and chaotic dynamic aspects of vibrational-rotational states of atomic, nuclear, and molecular systems using the semiclassical spectral method (SSM). The authors note that the coordinates, momenta, and so on, are found using classical mechanics in the studies included in this review. They outline the semiclassical spectral method and a wide variety of applications. Although this technique was first developed ten years ago, it has proved to be tremendously successful as a tool used in dynamics problems. Applications include problems in nonlinear dynamics, molecular and atomic spectra, surface science, astronomy and stellar dynamics, nuclear physics, and polymer physics

  10. Stable multi-domain spectral penalty methods for fractional partial differential equations

    Science.gov (United States)

    Xu, Qinwu; Hesthaven, Jan S.

    2014-01-01

    We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

  11. Simple spectral method for solving propagation problems in cylindrical geometry with fast Fourier transforms

    International Nuclear Information System (INIS)

    Feit, M.D.; Fleck, J.A. Jr.

    1989-01-01

    We describe a spectral method for solving the paraxial wave equation in cylindrical geometry that is based on expansion of the exponential evolution operator in a Taylor series and use of fast Fourier transforms to evaluate derivatives. A fourth-order expansion gives excellent agreement with a two-transverse-dimensional split-operator calculation at a fraction of the cost in computation time per z step and at a considerable savings in storage

  12. Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models

    OpenAIRE

    MURILLO, Carol Andrea; THOREL, Luc; CAICEDO, Bernardo

    2009-01-01

    The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge test...

  13. Application of the spectral-correlation method for diagnostics of cellulose paper

    Science.gov (United States)

    Kiesewetter, D.; Malyugin, V.; Reznik, A.; Yudin, A.; Zhuravleva, N.

    2017-11-01

    The spectral-correlation method was described for diagnostics of optically inhomogeneous biological objects and materials of natural origin. The interrelation between parameters of the studied objects and parameters of the cross correlation function of speckle patterns produced by scattering of coherent light at different wavelengths is shown for thickness, optical density and internal structure of the material. A detailed study was performed for cellulose electric insulating paper with different parameters.

  14. Perturbation method utilization in the analysis of the Convertible Spectral Shift Reactor (RCVS)

    International Nuclear Information System (INIS)

    Bruna, G.B; Legendre, J.F.; Porta, J.; Doriath, J.Y.

    1988-01-01

    In the framework of the preliminary faisability studies on a new core concept, techniques derived from perturbation theory show-up very useful in the calculation and physical analysis of project parameters. We show, in the present work, some applications of these methods to the RCVS (Reacteur Convertible a Variation de Spectre - Convertible Spectral Shift Reactor) Concept studies. Actually, we present here the search of a few group project type energy structure and the splitting of reactivity effects into individual components [fr

  15. The spectral induced polarisation method and its application to hydrogeological problems

    International Nuclear Information System (INIS)

    Hoerdt, A.

    2007-01-01

    The spectral induced polarisation (SIP) method is an extension of the DC resistivity technique, where an alternating current is injected and the phase shift between voltage and current is measured in addition to the amplitude. In unconsolidated sediments, the phase shift includes complementary information on the structure of the pore space, and thus it should be possible to estimate hydraulic parameters from SIP measurements. Here, I describe some recent developments and give one example where hydraulic conductivity was estimated at the field scale

  16. Performance Evaluation of the Spectral Centroid Downshift Method for Attenuation Estimation

    OpenAIRE

    Samimi, Kayvan; Varghese, Tomy

    2015-01-01

    Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequency-domain approaches applied to this problem. In this study, a statistical analysis of this method’s performance was carried out based on a parametric m...

  17. Rigorous Integration of Non-Linear Ordinary Differential Equations in Chebyshev Basis

    Czech Academy of Sciences Publication Activity Database

    Dzetkulič, Tomáš

    2015-01-01

    Roč. 69, č. 1 (2015), s. 183-205 ISSN 1017-1398 R&D Projects: GA MŠk OC10048; GA ČR GD201/09/H057 Institutional research plan: CEZ:AV0Z10300504 Keywords : Initial value problem * Rigorous integration * Taylor model * Chebyshev basis Subject RIV: IN - Informatics, Computer Science Impact factor: 1.366, year: 2015

  18. The comparative metrological estimation of methods of emission spectral analysis for wear products in aviation oils

    Energy Technology Data Exchange (ETDEWEB)

    Alchimov, A B; Drobot, S I; Drokov, V G; Zarubin, V P; Kazmirov, A D; Skodaev, Y D; Podrezov, A M [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)

    1998-12-31

    The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.

  19. The comparative metrological estimation of methods of emission spectral analysis for wear products in aviation oils

    Energy Technology Data Exchange (ETDEWEB)

    Alchimov, A.B.; Drobot, S.I.; Drokov, V.G.; Zarubin, V.P.; Kazmirov, A.D.; Skodaev, Y.D.; Podrezov, A.M. [Applied Physics Institute of Irkutsk State University, Irkutsk (Russian Federation)

    1997-12-31

    The comparison of different spectral methods of analysis for wear diagnostics of aircraft engines has been carried out. It is shown that known techniques of determination of metals content in aviation oils with the use the spectrometers MFS (Russia) and MOA (USA) give a low accuracy of measurements. As an alternative the method of wear diagnostics on the base of a scintillation spectrometer is suggested. This method possess far better metrological properties in comparison with those on the base of the spectrometer MFS and MOA. (orig.) 6 refs.

  20. Detection of the power lines in UAV remote sensed images using spectral-spatial methods.

    Science.gov (United States)

    Bhola, Rishav; Krishna, Nandigam Hari; Ramesh, K N; Senthilnath, J; Anand, Gautham

    2018-01-15

    In this paper, detection of the power lines on images acquired by Unmanned Aerial Vehicle (UAV) based remote sensing is carried out using spectral-spatial methods. Spectral clustering was performed using Kmeans and Expectation Maximization (EM) algorithm to classify the pixels into the power lines and non-power lines. The spectral clustering methods used in this study are parametric in nature, to automate the number of clusters Davies-Bouldin index (DBI) is used. The UAV remote sensed image is clustered into the number of clusters determined by DBI. The k clustered image is merged into 2 clusters (power lines and non-power lines). Further, spatial segmentation was performed using morphological and geometric operations, to eliminate the non-power line regions. In this study, UAV images acquired at different altitudes and angles were analyzed to validate the robustness of the proposed method. It was observed that the EM with spatial segmentation (EM-Seg) performed better than the Kmeans with spatial segmentation (Kmeans-Seg) on most of the UAV images. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Predicting the effective response of bulk polycrystalline ferroelectric ceramics via improved spectral phase field methods

    Science.gov (United States)

    Vidyasagar, A.; Tan, W. L.; Kochmann, D. M.

    2017-09-01

    Understanding the electromechanical response of bulk polycrystalline ferroelectric ceramics requires scale-bridging approaches. Recent advances in fast numerical methods to compute the homogenized mechanical response of materials with heterogeneous microstructure have enabled the solution of hitherto intractable systems. In particular, the use of a Fourier-based spectral method as opposed to the traditional finite element method has gained significant interest in the homogenization of periodic microstructures. Here, we solve the periodic, electro-mechanically-coupled boundary value problem at the mesoscale of polycrystalline ferroelectrics in order to extract the effective response of barium titanate (BaTiO3) and lead zirconate titanate (PZT) under applied electric fields. Results include the effective electric hysteresis and the associated butterfly curve of strain vs. electric field for mean stress-free electric loading. Computational predictions of the 3D polycrystalline response show convincing agreement with our experimental electric cycling and strain hysteresis data for PZT-5A. In addition to microstructure-dependent effective physics, we also show how finite-difference-based approximations in the spectral solution scheme significantly reduce instability and ringing phenomena associated with spectral techniques and lead to spatial convergence with h-refinement, which have been major challenges when modeling high-contrast systems such as polycrystals.

  2. Mapping Landslides in Lunar Impact Craters Using Chebyshev Polynomials and Dem's

    Science.gov (United States)

    Yordanov, V.; Scaioni, M.; Brunetti, M. T.; Melis, M. T.; Zinzi, A.; Giommi, P.

    2016-06-01

    Geological slope failure processes have been observed on the Moon surface for decades, nevertheless a detailed and exhaustive lunar landslide inventory has not been produced yet. For a preliminary survey, WAC images and DEM maps from LROC at 100 m/pixels have been exploited in combination with the criteria applied by Brunetti et al. (2015) to detect the landslides. These criteria are based on the visual analysis of optical images to recognize mass wasting features. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sections in order to obtain a parametric characterization useful for classification into different morphological shapes. Here a new implementation of Chebyshev polynomial approximation is proposed, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analyzing the absolute values off odd coefficients of estimated Chebyshev polynomials. A case study on the Cassini A crater has demonstrated the key-points of the proposed methodology and outlined the required future development to carry out.

  3. The Fundamental Blossoming Inequality in Chebyshev Spaces—I: Applications to Schur Functions

    KAUST Repository

    Ait-Haddou, Rachid

    2016-10-19

    A classical theorem by Chebyshev says how to obtain the minimum and maximum values of a symmetric multiaffine function of n variables with a prescribed sum. We show that, given two functions in an Extended Chebyshev space good for design, a similar result can be stated for the minimum and maximum values of the blossom of the first function with a prescribed value for the blossom of the second one. We give a simple geometric condition on the control polygon of the planar parametric curve defined by the pair of functions ensuring the uniqueness of the solution to the corresponding optimization problem. This provides us with a fundamental blossoming inequality associated with each Extended Chebyshev space good for design. This inequality proves to be a very powerful tool to derive many classical or new interesting inequalities. For instance, applied to Müntz spaces and to rational Müntz spaces, it provides us with new inequalities involving Schur functions which generalize the classical MacLaurin’s and Newton’s inequalities. This work definitely demonstrates that, via blossoms, CAGD techniques can have important implications in other mathematical domains, e.g., combinatorics.

  4. A spectral nodal method for discrete ordinates problems in x,y geometry

    International Nuclear Information System (INIS)

    Barros, R.C. de; Larsen, E.W.

    1991-06-01

    A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)

  5. Sparse grid spectral methods for the numerical solution of partial differential equations with periodic boundary conditions

    International Nuclear Information System (INIS)

    Kupka, F.

    1997-11-01

    This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)

  6. Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients.

    Science.gov (United States)

    Chen, Weitian; Sica, Christopher T; Meyer, Craig H

    2008-11-01

    Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

  7. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)

    2013-07-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  8. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    International Nuclear Information System (INIS)

    Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.

    2013-01-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  9. Analysing flow structures around a blade using spectral/hp method and HPIV

    International Nuclear Information System (INIS)

    Stoevesandt, Bernhard; Steigerwald, Christian; Shishkin, Andrei; Wagner, Claus; Peinke, Joachim

    2007-01-01

    A still difficult, yet pressing task for blade manufacturers and turbine producers is the correct prediction of the effects of turbulent winds on the blade. Reynolds Averaged Numerical Simulations (RANS) are a limited tool for calculating the effects. For large eddy simulations (LES) boundary layer calculation are still difficult therefore the spectral element method seems to be an approach to improve numerical calculations of flow separation. The flow field around an fx79-w151a airfoil has been calculated by the spectral element code NεκTαrusing a direct numerical simulation (DNS) solver. In a first step a laminar inflow on the airfoil at angle of attack of α = 12 0 and a Reynolds number of Re= 33000 was simulated using the 2D Version of the code. The flow pattern was compared to measurements using holographic particle induced velocimetry (HPIV) in a wind tunnel

  10. Spectral element method for band-structure calculations of 3D phononic crystals

    International Nuclear Information System (INIS)

    Shi, Linlin; Liu, Na; Zhou, Jianyang; Zhou, Yuanguo; Wang, Jiamin; Liu, Qing Huo

    2016-01-01

    The spectral element method (SEM) is a special kind of high-order finite element method (FEM) which combines the flexibility of a finite element method with the accuracy of a spectral method. In contrast to the traditional FEM, the SEM exhibits advantages in the high-order accuracy as the error decreases exponentially with the increase of interpolation degree by employing the Gauss–Lobatto–Legendre (GLL) polynomials as basis functions. In this study, the spectral element method is developed for the first time for the determination of band structures of 3D isotropic/anisotropic phononic crystals (PCs). Based on the Bloch theorem, we present a novel, intuitive discretization formulation for Navier equation in the SEM scheme for periodic media. By virtue of using the orthogonal Legendre polynomials, the generalized eigenvalue problem is converted to a regular one in our SEM implementation to improve the efficiency. Besides, according to the specific geometry structure, 8-node and 27-node hexahedral elements as well as an analytic mesh have been used to accurately capture curved PC models in our SEM scheme. To verify its accuracy and efficiency, this study analyses the phononic-crystal plates with square and triangular lattice arrangements, and the 3D cubic phononic crystals consisting of simple cubic (SC), bulk central cubic (BCC) and faced central cubic (FCC) lattices with isotropic or anisotropic scatters. All the numerical results considered demonstrate that SEM is superior to the conventional FEM and can be an efficient alternative method for accurate determination of band structures of 3D phononic crystals. (paper)

  11. Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equation

    Science.gov (United States)

    Khan, Sami Ullah; Ali, Ishtiaq

    2018-03-01

    Explicit solutions to delay differential equation (DDE) and stochastic delay differential equation (SDDE) can rarely be obtained, therefore numerical methods are adopted to solve these DDE and SDDE. While on the other hand due to unstable nature of both DDE and SDDE numerical solutions are also not straight forward and required more attention. In this study, we derive an efficient numerical scheme for DDE and SDDE based on Legendre spectral-collocation method, which proved to be numerical methods that can significantly speed up the computation. The method transforms the given differential equation into a matrix equation by means of Legendre collocation points which correspond to a system of algebraic equations with unknown Legendre coefficients. The efficiency of the proposed method is confirmed by some numerical examples. We found that our numerical technique has a very good agreement with other methods with less computational effort.

  12. Measurement of reactor parameters of the 'Nora' reactor by noise analysis method - power spectral density

    International Nuclear Information System (INIS)

    Jovanovic, S.; Stormark, E.

    1966-01-01

    Measurements of reactor parameters the Nora reactor by Power Spectral Density (PSD) method are described. In case of critical reactor this method was applied for direct measurement of β/l ratio, β is the effective yield of delayed neutrons and l is the neutron lifetime. In case of subcritical reactor values of α+β-ρ/l were measured, ρ is the negative reactivity. Out coming PSD was measured by a filter or by ISAC. PSD was registered by ISAC as well as the auto-correlation function [sr

  13. Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models

    Science.gov (United States)

    Murillo, Carol Andrea; Thorel, Luc; Caicedo, Bernardo

    2009-06-01

    The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge testing is a relevant method to characterize VS near the surface.

  14. Optimized low-order explicit Runge-Kutta schemes for high- order spectral difference method

    KAUST Repository

    Parsani, Matteo

    2012-01-01

    Optimal explicit Runge-Kutta (ERK) schemes with large stable step sizes are developed for method-of-lines discretizations based on the spectral difference (SD) spatial discretization on quadrilateral grids. These methods involve many stages and provide the optimal linearly stable time step for a prescribed SD spectrum and the minimum leading truncation error coefficient, while admitting a low-storage implementation. Using a large number of stages, the new ERK schemes lead to efficiency improvements larger than 60% over standard ERK schemes for 4th- and 5th-order spatial discretization.

  15. The Spectral/hp-Finite Element Method for Partial Differential Equations

    DEFF Research Database (Denmark)

    Engsig-Karup, Allan Peter

    2009-01-01

    dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...

  16. An efficient spatial spectral integral-equation method for EM scattering from finite objects in layered media

    NARCIS (Netherlands)

    Dilz, R.J.; van Beurden, M.C.

    2016-01-01

    We propose a mixed spatial spectral method aimed directly at aperiodic, finite scatterers in a layered medium. By using a Gabor frame to discretize the problem a straightforward and fast way to Fourier transform is available. The poles and branchcuts in the spectral-domain Green function can be

  17. Hybrid Lanczos-type product methods

    Energy Technology Data Exchange (ETDEWEB)

    Ressel, K.J. [Swiss Center for Scientific Computing, Zuerich (Switzerland)

    1996-12-31

    A general framework is proposed to construct hybrid iterative methods for the solution of large nonsymmetric systems of linear equations. This framework is based on Lanczos-type product methods, whose iteration polynomial consists of the Lanczos polynomial multiplied by some other arbitrary, {open_quotes}shadow{close_quotes} polynomial. By using for the shadow polynomial Chebyshev (more general Faber) polynomials or L{sup 2}-optimal polynomials, hybrid (Chebyshev-like) methods are incorporated into Lanczos-type product methods. In addition, to acquire spectral information on the system matrix, which is required for such a choice of shadow polynomials, the Lanczos-process can be employed either directly or in an QMR-like approach. The QMR like approach allows the cheap computation of the roots of the B-orthogonal polynomials and the residual polynomials associated with the QMR iteration. These roots can be used as a good approximation for the spectrum of the system matrix. Different choices for the shadow polynomials and their construction are analyzed. The resulting hybrid methods are compared with standard Lanczos-type product methods, like BiOStab, BiOStab({ell}) and BiOS.

  18. The spectral element method for static neutron transport in AN approximation. Part I

    International Nuclear Information System (INIS)

    Barbarino, A.; Dulla, S.; Mund, E.H.; Ravetto, P.

    2013-01-01

    Highlights: ► Spectral elements methods (SEMs) are extended for the neutronics of nuclear reactor cores. ► The second-order, A N formulation of neutron trasport is adopted. ► Results for classical benchmark cases in 2D are presented and compared to finite elements. ► The advantages of SEM in terms of precision and convergence rate are illustrated. ► SEM consitutes a promising approach for the solution of neutron transport problems. - Abstract: Spectral elements methods provide very accurate solutions of elliptic problems. In this paper we apply the method to the A N (i.e. SP 2N−1 ) approximation of neutron transport. Numerical results for classical benchmark cases highlight its performance in comparison with finite element computations, in terms of accuracy per degree of freedom and convergence rate. All calculations presented in this paper refer to two-dimensional problems. The method can easily be extended to three-dimensional cases. The results illustrate promising features of the method for more complex transport problems

  19. A spatial discretization of the MHD equations based on the finite volume - spectral method

    International Nuclear Information System (INIS)

    Miyoshi, Takahiro

    2000-05-01

    Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)

  20. Validation of spectral methods for the seismic analysis of multi-supported structures

    International Nuclear Information System (INIS)

    Viola, B.

    1999-01-01

    There are many methodologies for the seismic analysis of buildings. When a seism occurs, structures such piping systems in nuclear power plants are subjected to motions that may be different at each support point. Therefore it is necessary to develop methods that take into account the multi-supported effect. In a first time, a bibliography analysis on the different methods that exist has been carried out. The aim was to find a particular method applicable to the study of piping systems. The second step of this work consisted in developing a program that may be used to test and make comparisons on different selected methods. So spectral methods have the advantage to give an estimation of the maximum values for strain in the structure, in reduced calculation time. The time history analysis is used as the reference for the tests. (author)

  1. Spectral methods for the detection of network community structure: a comparative analysis

    International Nuclear Information System (INIS)

    Shen, Hua-Wei; Cheng, Xue-Qi

    2010-01-01

    Spectral analysis has been successfully applied to the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlation matrix and several other variants of these matrices. However, the comparison between these spectral methods is less reported. More importantly, it is still unclear which matrix is more appropriate for the detection of community structure. This paper answers the question by evaluating the effectiveness of these five matrices against benchmark networks with heterogeneous distributions of node degree and community size. Test results demonstrate that the normalized Laplacian matrix and the correlation matrix significantly outperform the other three matrices at identifying the community structure of networks. This indicates that it is crucial to take into account the heterogeneous distribution of node degree when using spectral analysis for the detection of community structure. In addition, to our surprise, the modularity matrix exhibits very similar performance to the adjacency matrix, which indicates that the modularity matrix does not gain benefits from using the configuration model as a reference network with the consideration of the node degree heterogeneity

  2. Overdetermined shooting methods for computing standing water waves with spectral accuracy

    International Nuclear Information System (INIS)

    Wilkening, Jon; Yu Jia

    2012-01-01

    A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge–Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly

  3. A Guide on Spectral Methods Applied to Discrete Data in One Dimension

    Directory of Open Access Journals (Sweden)

    Martin Seilmayer

    2017-01-01

    Full Text Available This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment R prior to this article.

  4. Standard Test Method for Normal Spectral Emittance at Elevated Temperatures of Nonconducting Specimens

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    1971-01-01

    1.1 This test method describes an accurate technique for measuring the normal spectral emittance of electrically nonconducting materials in the temperature range from 1000 to 1800 K, and at wavelengths from 1 to 35 μm. It is particularly suitable for measuring the normal spectral emittance of materials such as ceramic oxides, which have relatively low thermal conductivity and are translucent to appreciable depths (several millimetres) below the surface, but which become essentially opaque at thicknesses of 10 mm or less. 1.2 This test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is particularly suitable for research laboratories, where the highest precision and accuracy are desired, and is not recommended for routine production or acceptance testing. Because of its high accuracy, this test method may be used as a reference method to be applied to production and acceptance testing in case of dispute. 1.3 This test metho...

  5. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Haack, Jeffrey R.

    2014-01-01

    We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation

  6. An Excel‐based implementation of the spectral method of action potential alternans analysis

    Science.gov (United States)

    Pearman, Charles M.

    2014-01-01

    Abstract Action potential (AP) alternans has been well established as a mechanism of arrhythmogenesis and sudden cardiac death. Proper interpretation of AP alternans requires a robust method of alternans quantification. Traditional methods of alternans analysis neglect higher order periodicities that may have greater pro‐arrhythmic potential than classical 2:1 alternans. The spectral method of alternans analysis, already widely used in the related study of microvolt T‐wave alternans, has also been used to study AP alternans. Software to meet the specific needs of AP alternans analysis is not currently available in the public domain. An AP analysis tool is implemented here, written in Visual Basic for Applications and using Microsoft Excel as a shell. This performs a sophisticated analysis of alternans behavior allowing reliable distinction of alternans from random fluctuations, quantification of alternans magnitude, and identification of which phases of the AP are most affected. In addition, the spectral method has been adapted to allow detection and quantification of higher order regular oscillations. Analysis of action potential morphology is also performed. A simple user interface enables easy import, analysis, and export of collated results. PMID:25501439

  7. An Excel-based implementation of the spectral method of action potential alternans analysis.

    Science.gov (United States)

    Pearman, Charles M

    2014-12-01

    Action potential (AP) alternans has been well established as a mechanism of arrhythmogenesis and sudden cardiac death. Proper interpretation of AP alternans requires a robust method of alternans quantification. Traditional methods of alternans analysis neglect higher order periodicities that may have greater pro-arrhythmic potential than classical 2:1 alternans. The spectral method of alternans analysis, already widely used in the related study of microvolt T-wave alternans, has also been used to study AP alternans. Software to meet the specific needs of AP alternans analysis is not currently available in the public domain. An AP analysis tool is implemented here, written in Visual Basic for Applications and using Microsoft Excel as a shell. This performs a sophisticated analysis of alternans behavior allowing reliable distinction of alternans from random fluctuations, quantification of alternans magnitude, and identification of which phases of the AP are most affected. In addition, the spectral method has been adapted to allow detection and quantification of higher order regular oscillations. Analysis of action potential morphology is also performed. A simple user interface enables easy import, analysis, and export of collated results. © 2014 The Author. Physiological Reports published by Wiley Periodicals, Inc. on behalf of the American Physiological Society and The Physiological Society.

  8. A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate

    Science.gov (United States)

    Djenidi, L.; Antonia, R. A.

    2012-10-01

    We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a -5/3 inertial subrange only when the Taylor microscale Reynods number R λ is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30 ≤ R λ ≤ 400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of < \\varepsilon rangle in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall.

  9. Performance evaluation of the spectral centroid downshift method for attenuation estimation.

    Science.gov (United States)

    Samimi, Kayvan; Varghese, Tomy

    2015-05-01

    Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequencydomain approaches applied to this problem. In this study, a statistical analysis of this method's performance was carried out based on a parametric model of the signal power spectrum in the presence of electronic noise. The parametric model used for the power spectrum of received RF data assumes a Gaussian spectral profile for the transmit pulse, and incorporates effects of attenuation, windowing, and electronic noise. Spectral moments were calculated and used to estimate second-order centroid statistics. A theoretical expression for the variance of a maximum likelihood estimator of attenuation coefficient was derived in terms of the centroid statistics and other model parameters, such as transmit pulse center frequency and bandwidth, RF data window length, SNR, and number of regression points. Theoretically predicted estimation variances were compared with experimentally estimated variances on RF data sets from both computer-simulated and physical tissue-mimicking phantoms. Scan parameter ranges for this study were electronic SNR from 10 to 70 dB, transmit pulse standard deviation from 0.5 to 4.1 MHz, transmit pulse center frequency from 2 to 8 MHz, and data window length from 3 to 17 mm. Acceptable agreement was observed between theoretical predictions and experimentally estimated values with differences smaller than 0.05 dB/cm/MHz across the parameter ranges investigated. This model helps predict the best attenuation estimation variance achievable with the CDS method, in terms of said scan parameters.

  10. A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

    International Nuclear Information System (INIS)

    Xu, Jin; Yu, Yaming; Van Dyk, David A.; Kashyap, Vinay L.; Siemiginowska, Aneta; Drake, Jeremy; Ratzlaff, Pete; Connors, Alanna; Meng, Xiao-Li

    2014-01-01

    Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use a principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.

  11. Method and apparatus for simultaneously measuring a plurality of spectral wavelengths present in electromagnetic radiation

    Science.gov (United States)

    Buican, Tudor N.; Martin, John C.

    1990-01-01

    An apparatus and method simultaneously measures a plurality of spectral wavelengths present in electromagnetic radiation. A modulatable birefringent optical element is employed to divide a polarized light beam into two components, thereby producing a phase difference in two resulting light beams such that the two beams can be made to interfere with one another when recombined, the interference pattern providing the wavelength information required for the analysis of the incident light. The interferometer thus created performs in a similar manner to a Michelson interferometer, but with no moving parts, and with a resolution dependent on the degree of phase shift introduced by the modulator.

  12. Spectral methods in machine learning and new strategies for very large datasets

    Science.gov (United States)

    Belabbas, Mohamed-Ali; Wolfe, Patrick J.

    2009-01-01

    Spectral methods are of fundamental importance in statistics and machine learning, because they underlie algorithms from classical principal components analysis to more recent approaches that exploit manifold structure. In most cases, the core technical problem can be reduced to computing a low-rank approximation to a positive-definite kernel. For the growing number of applications dealing with very large or high-dimensional datasets, however, the optimal approximation afforded by an exact spectral decomposition is too costly, because its complexity scales as the cube of either the number of training examples or their dimensionality. Motivated by such applications, we present here 2 new algorithms for the approximation of positive-semidefinite kernels, together with error bounds that improve on results in the literature. We approach this problem by seeking to determine, in an efficient manner, the most informative subset of our data relative to the kernel approximation task at hand. This leads to two new strategies based on the Nyström method that are directly applicable to massive datasets. The first of these—based on sampling—leads to a randomized algorithm whereupon the kernel induces a probability distribution on its set of partitions, whereas the latter approach—based on sorting—provides for the selection of a partition in a deterministic way. We detail their numerical implementation and provide simulation results for a variety of representative problems in statistical data analysis, each of which demonstrates the improved performance of our approach relative to existing methods. PMID:19129490

  13. A New Pansharpening Method Based on Spatial and Spectral Sparsity Priors.

    Science.gov (United States)

    He, Xiyan; Condat, Laurent; Bioucas-Diaz, Jose; Chanussot, Jocelyn; Xia, Junshi

    2014-06-27

    The development of multisensor systems in recent years has led to great increase in the amount of available remote sensing data. Image fusion techniques aim at inferring high quality images of a given area from degraded versions of the same area obtained by multiple sensors. This paper focuses on pansharpening, which is the inference of a high spatial resolution multispectral image from two degraded versions with complementary spectral and spatial resolution characteristics: a) a low spatial resolution multispectral image; and b) a high spatial resolution panchromatic image. We introduce a new variational model based on spatial and spectral sparsity priors for the fusion. In the spectral domain we encourage low-rank structure, whereas in the spatial domain we promote sparsity on the local differences. Given the fact that both panchromatic and multispectral images are integrations of the underlying continuous spectra using different channel responses, we propose to exploit appropriate regularizations based on both spatial and spectral links between panchromatic and the fused multispectral images. A weighted version of the vector Total Variation (TV) norm of the data matrix is employed to align the spatial information of the fused image with that of the panchromatic image. With regard to spectral information, two different types of regularization are proposed to promote a soft constraint on the linear dependence between the panchromatic and the fused multispectral images. The first one estimates directly the linear coefficients from the observed panchromatic and low resolution multispectral images by Linear Regression (LR) while the second one employs the Principal Component Pursuit (PCP) to obtain a robust recovery of the underlying low-rank structure. We also show that the two regularizers are strongly related. The basic idea of both regularizers is that the fused image should have low-rank and preserve edge locations. We use a variation of the recently proposed

  14. Spectral triangulation: a 3D method for locating single-walled carbon nanotubes in vivo

    Science.gov (United States)

    Lin, Ching-Wei; Bachilo, Sergei M.; Vu, Michael; Beckingham, Kathleen M.; Bruce Weisman, R.

    2016-05-01

    Nanomaterials with luminescence in the short-wave infrared (SWIR) region are of special interest for biological research and medical diagnostics because of favorable tissue transparency and low autofluorescence backgrounds in that region. Single-walled carbon nanotubes (SWCNTs) show well-known sharp SWIR spectral signatures and therefore have potential for noninvasive detection and imaging of cancer tumours, when linked to selective targeting agents such as antibodies. However, such applications face the challenge of sensitively detecting and localizing the source of SWIR emission from inside tissues. A new method, called spectral triangulation, is presented for three dimensional (3D) localization using sparse optical measurements made at the specimen surface. Structurally unsorted SWCNT samples emitting over a range of wavelengths are excited inside tissue phantoms by an LED matrix. The resulting SWIR emission is sampled at points on the surface by a scanning fibre optic probe leading to an InGaAs spectrometer or a spectrally filtered InGaAs avalanche photodiode detector. Because of water absorption, attenuation of the SWCNT fluorescence in tissues is strongly wavelength-dependent. We therefore gauge the SWCNT-probe distance by analysing differential changes in the measured SWCNT emission spectra. SWCNT fluorescence can be clearly detected through at least 20 mm of tissue phantom, and the 3D locations of embedded SWCNT test samples are found with sub-millimeter accuracy at depths up to 10 mm. Our method can also distinguish and locate two embedded SWCNT sources at distinct positions.Nanomaterials with luminescence in the short-wave infrared (SWIR) region are of special interest for biological research and medical diagnostics because of favorable tissue transparency and low autofluorescence backgrounds in that region. Single-walled carbon nanotubes (SWCNTs) show well-known sharp SWIR spectral signatures and therefore have potential for noninvasive detection and

  15. A practical material decomposition method for x-ray dual spectral computed tomography.

    Science.gov (United States)

    Hu, Jingjing; Zhao, Xing

    2016-03-17

    X-ray dual spectral CT (DSCT) scans the measured object with two different x-ray spectra, and the acquired rawdata can be used to perform the material decomposition of the object. Direct calibration methods allow a faster material decomposition for DSCT and can be separated in two groups: image-based and rawdata-based. The image-based method is an approximative method, and beam hardening artifacts remain in the resulting material-selective images. The rawdata-based method generally obtains better image quality than the image-based method, but this method requires geometrically consistent rawdata. However, today's clinical dual energy CT scanners usually measure different rays for different energy spectra and acquire geometrically inconsistent rawdata sets, and thus cannot meet the requirement. This paper proposes a practical material decomposition method to perform rawdata-based material decomposition in the case of inconsistent measurement. This method first yields the desired consistent rawdata sets from the measured inconsistent rawdata sets, and then employs rawdata-based technique to perform material decomposition and reconstruct material-selective images. The proposed method was evaluated by use of simulated FORBILD thorax phantom rawdata and dental CT rawdata, and simulation results indicate that this method can produce highly quantitative DSCT images in the case of inconsistent DSCT measurements.

  16. A Method of Particle Swarm Optimized SVM Hyper-spectral Remote Sensing Image Classification

    International Nuclear Information System (INIS)

    Liu, Q J; Jing, L H; Wang, L M; Lin, Q Z

    2014-01-01

    Support Vector Machine (SVM) has been proved to be suitable for classification of remote sensing image and proposed to overcome the Hughes phenomenon. Hyper-spectral sensors are intrinsically designed to discriminate among a broad range of land cover classes which may lead to high computational time in SVM mutil-class algorithms. Model selection for SVM involving kernel and the margin parameter values selection which is usually time-consuming, impacts training efficiency of SVM model and final classification accuracies of SVM hyper-spectral remote sensing image classifier greatly. Firstly, based on combinatorial optimization theory and cross-validation method, particle swarm algorithm is introduced to the optimal selection of SVM (PSSVM) kernel parameter σ and margin parameter C to improve the modelling efficiency of SVM model. Then an experiment of classifying AVIRIS in India Pine site of USA was performed for evaluating the novel PSSVM, as well as traditional SVM classifier with general Grid-Search cross-validation method (GSSVM). And then, evaluation indexes including SVM model training time, classification Overall Accuracy (OA) and Kappa index of both PSSVM and GSSVM are all analyzed quantitatively. It is demonstrated that OA of PSSVM on test samples and whole image are 85% and 82%, the differences with that of GSSVM are both within 0.08% respectively. And Kappa indexes reach 0.82 and 0.77, the differences with that of GSSVM are both within 0.001. While the modelling time of PSSVM can be only 1/10 of that of GSSVM, and the modelling. Therefore, PSSVM is an fast and accurate algorithm for hyper-spectral image classification and is superior to GSSVM

  17. A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

    Science.gov (United States)

    Terrana, S.; Vilotte, J. P.; Guillot, L.

    2018-04-01

    We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm

  18. Getting Your Peaks in Line: A Review of Alignment Methods for NMR Spectral Data

    Directory of Open Access Journals (Sweden)

    Trung Nghia Vu

    2013-04-01

    Full Text Available One of the most significant challenges in the comparative analysis of Nuclear Magnetic Resonance (NMR metabolome profiles is the occurrence of shifts between peaks across different spectra, for example caused by fluctuations in pH, temperature, instrument factors and ion content. Proper alignment of spectral peaks is therefore often a crucial preprocessing step prior to downstream quantitative analysis. Various alignment methods have been developed specifically for this purpose. Other methods were originally developed to align other data types (GC, LC, SELDI-MS, etc., but can also be applied to NMR data. This review discusses the available methods, as well as related problems such as reference determination or the evaluation of alignment quality. We present a generic alignment framework that allows for comparison and classification of different alignment approaches according to their algorithmic principles, and we discuss their performance.

  19. Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method

    International Nuclear Information System (INIS)

    Zhang Xu; Tan Duowang

    2009-01-01

    A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)

  20. A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

    KAUST Repository

    Efendiev, Yalchin R.

    2015-08-01

    We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

  1. Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method

    International Nuclear Information System (INIS)

    Xu, Zhang; Duo-Wang, Tan

    2009-01-01

    A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))

  2. A multi-domain spectral method for time-fractional differential equations

    Science.gov (United States)

    Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

    2015-07-01

    This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

  3. Spectral finite element method wave propagation, diagnostics and control in anisotropic and inhomogeneous structures

    CERN Document Server

    Gopalakrishnan, Srinivasan; Roy Mahapatra, Debiprosad

    2008-01-01

    The use of composites and Functionally Graded Materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and have many uses in structural engineering. However, the behaviour of these structures under high-impact loading is not well understood. This book is the first to apply the Spectral Finite Element Method (SFEM) to inhomogeneous and anisotropic structures in a unified and systematic manner. It focuses on some of the problems with this media which were previously thought unmanageable. Types of SFEM for regular and damaged 1-D and 2-D waveguides, solution techniques, methods of detecting the presence of damages and their locations, and methods for controlling the wave propagation responses are discussed. Tables, figures and graphs support the theory and case studies are included. This book is of value to senior undergraduates and postgraduates studying in this field, and researchers and practicing engineers in structural integrity.

  4. A method for spectral DNS of low Rm channel flows based on the least dissipative modes

    Science.gov (United States)

    Kornet, Kacper; Pothérat, Alban

    2015-10-01

    We put forward a new type of spectral method for the direct numerical simulation of flows where anisotropy or very fine boundary layers are present. The main idea is to take advantage of the fact that such structures are dissipative and that their presence should reduce the number of degrees of freedom of the flow, when paradoxically, their fine resolution incurs extra computational cost in most current methods. The principle of this method is to use a functional basis with elements that already include these fine structures so as to avoid these extra costs. This leads us to develop an algorithm to implement a spectral method for arbitrary functional bases, and in particular, non-orthogonal ones. We construct a basic implementation of this algorithm to simulate magnetohydrodynamic (MHD) channel flows with an externally imposed, transverse magnetic field, where very thin boundary layers are known to develop along the channel walls. In this case, the sought functional basis can be built out of the eigenfunctions of the dissipation operator, which incorporate these boundary layers, and it turns out to be non-orthogonal. We validate this new scheme against numerical simulations of freely decaying MHD turbulence based on a finite volume code and it is found to provide accurate results. Its ability to fully resolve wall-bounded turbulence with a number of modes close to that required by the dynamics is demonstrated on a simple example. This opens the way to full-blown simulations of MHD turbulence under very high magnetic fields. Until now such simulations were too computationally expensive. In contrast to traditional methods the computational cost of the proposed method, does not depend on the intensity of the magnetic field.

  5. A spectral nudging method for the ACCESS1.3 atmospheric model

    Science.gov (United States)

    Uhe, P.; Thatcher, M.

    2015-06-01

    A convolution-based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS) version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow for flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10-30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.

  6. Multivariat least-squares methods applied to the quantitative spectral analysis of multicomponent samples

    International Nuclear Information System (INIS)

    Haaland, D.M.; Easterling, R.G.; Vopicka, D.A.

    1985-01-01

    In an extension of earlier work, weighted multivariate least-squares methods of quantitative FT-IR analysis have been developed. A linear least-squares approximation to nonlinearities in the Beer-Lambert law is made by allowing the reference spectra to be a set of known mixtures, The incorporation of nonzero intercepts in the relation between absorbance and concentration further improves the approximation of nonlinearities while simultaneously accounting for nonzero spectra baselines. Pathlength variations are also accommodated in the analysis, and under certain conditions, unknown sample pathlengths can be determined. All spectral data are used to improve the precision and accuracy of the estimated concentrations. During the calibration phase of the analysis, pure component spectra are estimated from the standard mixture spectra. These can be compared with the measured pure component spectra to determine which vibrations experience nonlinear behavior. In the predictive phase of the analysis, the calculated spectra are used in our previous least-squares analysis to estimate sample component concentrations. These methods were applied to the analysis of the IR spectra of binary mixtures of esters. Even with severely overlapping spectral bands and nonlinearities in the Beer-Lambert law, the average relative error in the estimated concentration was <1%

  7. A spectral element method with adaptive segmentation for accurately simulating extracellular electrical stimulation of neurons.

    Science.gov (United States)

    Eiber, Calvin D; Dokos, Socrates; Lovell, Nigel H; Suaning, Gregg J

    2017-05-01

    The capacity to quickly and accurately simulate extracellular stimulation of neurons is essential to the design of next-generation neural prostheses. Existing platforms for simulating neurons are largely based on finite-difference techniques; due to the complex geometries involved, the more powerful spectral or differential quadrature techniques cannot be applied directly. This paper presents a mathematical basis for the application of a spectral element method to the problem of simulating the extracellular stimulation of retinal neurons, which is readily extensible to neural fibers of any kind. The activating function formalism is extended to arbitrary neuron geometries, and a segmentation method to guarantee an appropriate choice of collocation points is presented. Differential quadrature may then be applied to efficiently solve the resulting cable equations. The capacity for this model to simulate action potentials propagating through branching structures and to predict minimum extracellular stimulation thresholds for individual neurons is demonstrated. The presented model is validated against published values for extracellular stimulation threshold and conduction velocity for realistic physiological parameter values. This model suggests that convoluted axon geometries are more readily activated by extracellular stimulation than linear axon geometries, which may have ramifications for the design of neural prostheses.

  8. Research on the strong optical feedback effects based on spectral analysis method

    Science.gov (United States)

    Zeng, Zhaoli; Qu, XueMin; Li, Weina; Zhang, Min; Wang, Hao; Li, Tuo

    2018-01-01

    The strong optical feedback has the advantage of generating high resolution fringes. However, these feedback fringes usually seem like the noise signal when the feedback level is high. This defect severely limits its practical application. In this paper, the generation mechanism of noise fringes with strong optical feedback is studied by using spectral analysis method. The spectral analysis results show that, in most cases, the noise-like fringes are observed owing to the strong multiple high-order feedback. However, at certain feedback cavity condition, there may be only one high-order feedback beam goes back to the laser cavity, the noise-like fringes can change to the cosine-like fringes. And the resolution of this fringe is dozens times than that of the weak optical feedback. This research provides a method to obtain high resolution cosine-like fringes rather than noise signal in the strong optical feedback, which makes it possible to be used in nanoscale displacement measurements.

  9. A spectral nudging method for the ACCESS1.3 atmospheric model

    Directory of Open Access Journals (Sweden)

    P. Uhe

    2015-06-01

    Full Text Available A convolution-based method of spectral nudging of atmospheric fields is developed in the Australian Community Climate and Earth Systems Simulator (ACCESS version 1.3 which uses the UK Met Office Unified Model version 7.3 as its atmospheric component. The use of convolutions allow for flexibility in application to different atmospheric grids. An approximation using one-dimensional convolutions is applied, improving the time taken by the nudging scheme by 10–30 times compared with a version using a two-dimensional convolution, without measurably degrading its performance. Care needs to be taken in the order of the convolutions and the frequency of nudging to obtain the best outcome. The spectral nudging scheme is benchmarked against a Newtonian relaxation method, nudging winds and air temperature towards ERA-Interim reanalyses. We find that the convolution approach can produce results that are competitive with Newtonian relaxation in both the effectiveness and efficiency of the scheme, while giving the added flexibility of choosing which length scales to nudge.

  10. Pseudo-spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

    KAUST Repository

    Zou, Peng

    2017-05-10

    Staggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finite-difference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggered-grid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.

  11. NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

    OpenAIRE

    NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI

    2017-01-01

    In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...

  12. Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol

    Directory of Open Access Journals (Sweden)

    Hong Lai

    2012-01-01

    Full Text Available We apply semigroup property of enhanced Chebyshev polynomials to present an anonymous authentication protocol. This paper aims at improving security and reducing computational and storage overhead. The proposed scheme not only has much lower computational complexity and cost in the initialization phase but also allows the users to choose their passwords freely. Moreover, it can provide revocation of lost or stolen smart card, which can resist man-in-the-middle attack and off-line dictionary attack together with various known attacks.

  13. A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate

    Energy Technology Data Exchange (ETDEWEB)

    Djenidi, L.; Antonia, R.A. [The University of Newcastle, School of Engineering, Newcastle, NSW (Australia)

    2012-10-15

    We present an empirical but simple and practical spectral chart method for determining the mean turbulent kinetic energy dissipation rate left angle {epsilon}right angle in a variety of turbulent flows. The method relies on the validity of the first similarity hypothesis of Kolmogorov (C R (Doklady) Acad Sci R R SS, NS 30:301-305, 1941) (or K41) which implies that spectra of velocity fluctuations scale on the kinematic viscosity {nu} and left angle {epsilon}right angle at large Reynolds numbers. However, the evidence, based on the DNS spectra, points to this scaling being also valid at small Reynolds numbers, provided effects due to inhomogeneities in the flow are negligible. The methods avoid the difficulty associated with estimating time or spatial derivatives of the velocity fluctuations. It also avoids using the second hypothesis of K41, which implies the existence of a -5/3 inertial subrange only when the Taylor microscale Reynolds number R{sub {lambda}} is sufficiently large. The method is in fact applied to the lower wavenumber end of the dissipative range thus avoiding most of the problems due to inadequate spatial resolution of the velocity sensors and noise associated with the higher wavenumber end of this range.The use of spectral data (30 {<=} R{sub {lambda}}{<=} 400) in both passive and active grid turbulence, a turbulent mixing layer and the turbulent wake of a circular cylinder indicates that the method is robust and should lead to reliable estimates of left angle {epsilon}right angle in flows or flow regions where the first similarity hypothesis should hold; this would exclude, for example, the region near a wall. (orig.)

  14. Frequency-dependant homogenized properties of composite using spectral analysis method

    International Nuclear Information System (INIS)

    Ben Amor, M; Ben Ghozlen, M H; Lanceleur, P

    2010-01-01

    An inverse procedure is proposed to determine the material constants of multilayered composites using a spectral analysis homogenization method. Recursive process gives interfacial displacement perpendicular to layers in term of deepness. A fast-Fourier transform (FFT) procedure has been used in order to extract the wave numbers propagating in the multilayer. The upper frequency bound of this homogenization domain is estimated. Inside the homogenization domain, we discover a maximum of three planes waves susceptible to propagate in the medium. A consistent algorithm is adopted to develop an inverse procedure for the determination of the materials constants of multidirectional composite. The extracted wave numbers are used as the inputs for the procedure. The outputs are the elastic constants of multidirectional composite. Using this method, the frequency dependent effective elastic constants are obtained and example for [0/90] composites is given.

  15. Parallelizing the spectral transform method: A comparison of alternative parallel algorithms

    International Nuclear Information System (INIS)

    Foster, I.; Worley, P.H.

    1993-01-01

    The spectral transform method is a standard numerical technique for solving partial differential equations on the sphere and is widely used in global climate modeling. In this paper, we outline different approaches to parallelizing the method and describe experiments that we are conducting to evaluate the efficiency of these approaches on parallel computers. The experiments are conducted using a testbed code that solves the nonlinear shallow water equations on a sphere, but are designed to permit evaluation in the context of a global model. They allow us to evaluate the relative merits of the approaches as a function of problem size and number of processors. The results of this study are guiding ongoing work on PCCM2, a parallel implementation of the Community Climate Model developed at the National Center for Atmospheric Research

  16. Application of spectral Lanczos decomposition method to large scale problems arising geophysics

    Energy Technology Data Exchange (ETDEWEB)

    Tamarchenko, T. [Western Atlas Logging Services, Houston, TX (United States)

    1996-12-31

    This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.

  17. Membership determination of open clusters based on a spectral clustering method

    Science.gov (United States)

    Gao, Xin-Hua

    2018-06-01

    We present a spectral clustering (SC) method aimed at segregating reliable members of open clusters in multi-dimensional space. The SC method is a non-parametric clustering technique that performs cluster division using eigenvectors of the similarity matrix; no prior knowledge of the clusters is required. This method is more flexible in dealing with multi-dimensional data compared to other methods of membership determination. We use this method to segregate the cluster members of five open clusters (Hyades, Coma Ber, Pleiades, Praesepe, and NGC 188) in five-dimensional space; fairly clean cluster members are obtained. We find that the SC method can capture a small number of cluster members (weak signal) from a large number of field stars (heavy noise). Based on these cluster members, we compute the mean proper motions and distances for the Hyades, Coma Ber, Pleiades, and Praesepe clusters, and our results are in general quite consistent with the results derived by other authors. The test results indicate that the SC method is highly suitable for segregating cluster members of open clusters based on high-precision multi-dimensional astrometric data such as Gaia data.

  18. Standard Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    2010-01-01

    1.1 This test method covers a procedure for the determination of a spectral mismatch parameter used in performance testing of photovoltaic devices. 1.2 The spectral mismatch parameter is a measure of the error, introduced in the testing of a photovoltaic device, caused by mismatch between the spectral responses of the photovoltaic device and the photovoltaic reference cell, as well as mismatch between the test light source and the reference spectral irradiance distribution to which the photovoltaic reference cell was calibrated. Examples of reference spectral irradiance distributions are Tables E490 or G173. 1.3 The spectral mismatch parameter can be used to correct photovoltaic performance data for spectral mismatch error. 1.4 This test method is intended for use with linear photovoltaic devices. 1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. 1.6 This standard does not purport to address all of the safety concerns, if any, a...

  19. MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions

    Science.gov (United States)

    Novosad, Philip; Reader, Andrew J.

    2016-06-01

    Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [18F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral

  20. Rapid estimation of compost enzymatic activity by spectral analysis method combined with machine learning.

    Science.gov (United States)

    Chakraborty, Somsubhra; Das, Bhabani S; Ali, Md Nasim; Li, Bin; Sarathjith, M C; Majumdar, K; Ray, D P

    2014-03-01

    The aim of this study was to investigate the feasibility of using visible near-infrared (VisNIR) diffuse reflectance spectroscopy (DRS) as an easy, inexpensive, and rapid method to predict compost enzymatic activity, which traditionally measured by fluorescein diacetate hydrolysis (FDA-HR) assay. Compost samples representative of five different compost facilities were scanned by DRS, and the raw reflectance spectra were preprocessed using seven spectral transformations for predicting compost FDA-HR with six multivariate algorithms. Although principal component analysis for all spectral pretreatments satisfactorily identified the clusters by compost types, it could not separate different FDA contents. Furthermore, the artificial neural network multilayer perceptron (residual prediction deviation=3.2, validation r(2)=0.91 and RMSE=13.38 μg g(-1) h(-1)) outperformed other multivariate models to capture the highly non-linear relationships between compost enzymatic activity and VisNIR reflectance spectra after Savitzky-Golay first derivative pretreatment. This work demonstrates the efficiency of VisNIR DRS for predicting compost enzymatic as well as microbial activity. Copyright © 2013 Elsevier Ltd. All rights reserved.

  1. Making of a solar spectral irradiance dataset I: observations, uncertainties, and methods

    Directory of Open Access Journals (Sweden)

    Schöll Micha

    2016-01-01

    Full Text Available Context. Changes in the spectral solar irradiance (SSI are a key driver of the variability of the Earth’s environment, strongly affecting the upper atmosphere, but also impacting climate. However, its measurements have been sparse and of different quality. The “First European Comprehensive Solar Irradiance Data Exploitation project” (SOLID aims at merging the complete set of European irradiance data, complemented by archive data that include data from non-European missions. Aims. As part of SOLID, we present all available space-based SSI measurements, reference spectra, and relevant proxies in a unified format with regular temporal re-gridding, interpolation, gap-filling as well as associated uncertainty estimations. Methods. We apply a coherent methodology to all available SSI datasets. Our pipeline approach consists of the pre-processing of the data, the interpolation of missing data by utilizing the spectral coherency of SSI, the temporal re-gridding of the data, an instrumental outlier detection routine, and a proxy-based interpolation for missing and flagged values. In particular, to detect instrumental outliers, we combine an autoregressive model with proxy data. We independently estimate the precision and stability of each individual dataset and flag all changes due to processing in an accompanying quality mask. Results. We present a unified database of solar activity records with accompanying meta-data and uncertainties. Conclusions. This dataset can be used for further investigations of the long-term trend of solar activity and the construction of a homogeneous SSI record.

  2. First application of the spectral difference method for lifetime measurements of doppler attenuated line shapes

    Energy Technology Data Exchange (ETDEWEB)

    Duckwitz, Hannah [Institut fuer Kernphysik, Koeln Univ. (Germany); Petkov, Pavel [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)

    2016-07-01

    In this new approach to lifetime measurements via Doppler attenuated line shapes, the spectra of a feeding f and a deexciting transition d of the level of interest are used to determine the lifetime without any lineshape analysis of the feeding transition (direct or indirect). Similarly to the DDC method, the decay function λ{sub d}n{sub d}(t) of the deexciting transition is determined. The feeding of the level is included via the spectral difference of the two successive decays. Consequently, the determined lifetime is the real lifetime. After transforming both transitions into the same energy region, their spectral difference D(v{sub θ}) = S{sub d}(v{sub θ})-S{sub f}(v{sub θ}) = ∫{sub 0}{sup ∞}(∂P{sub θ}(t,v{sub θ}))/(∂t)n{sub d}(t) dt, is solved for n{sub d}(t). Dividing n{sub d}(t) by the decay function λ{sub d}n{sub d}(t) should yield a constant τ value for the level lifetime as a function of the time t. After the development and test of the procedure in 2015, it is now applied for the first time. Two level lifetimes are determined in {sup 86}Sr for the 2{sup +}{sub 2} and the 2{sup +}{sub 3} levels.

  3. Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

    Science.gov (United States)

    Vanel, Florence O.; Baysal, Oktay

    1995-01-01

    Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

  4. A spectral scheme for Kohn–Sham density functional theory of clusters

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Amartya S., E-mail: baner041@umn.edu; Elliott, Ryan S., E-mail: relliott@umn.edu; James, Richard D., E-mail: james@umn.edu

    2015-04-15

    Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

  5. A spectral scheme for Kohn-Sham density functional theory of clusters

    Science.gov (United States)

    Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.

    2015-04-01

    Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems - the plane-wave method - is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed.

  6. A spectral scheme for Kohn–Sham density functional theory of clusters

    International Nuclear Information System (INIS)

    Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.

    2015-01-01

    Starting from the observation that one of the most successful methods for solving the Kohn–Sham equations for periodic systems – the plane-wave method – is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn–Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn–Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed

  7. Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

    KAUST Repository

    Le Maitre, Olivier

    2014-01-06

    In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

  8. Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

    KAUST Repository

    Le Maitre, Olivier

    2014-01-01

    In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

  9. A numerical study of viscous vortex rings using a spectral method

    Science.gov (United States)

    Stanaway, S. K.; Cantwell, B. J.; Spalart, Philippe R.

    1988-01-01

    Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.

  10. Spectral methods for study of the G-protein-coupled receptor rhodopsin. II. Magnetic resonance methods

    Science.gov (United States)

    Struts, A. V.; Barmasov, A. V.; Brown, M. F.

    2016-02-01

    This article continues our review of spectroscopic studies of G-protein-coupled receptors. Magnetic resonance methods including electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) provide specific structural and dynamical data for the protein in conjunction with optical methods (vibrational, electronic spectroscopy) as discussed in the accompanying article. An additional advantage is the opportunity to explore the receptor proteins in the natural membrane lipid environment. Solid-state 2H and 13C NMR methods yield information about both the local structure and dynamics of the cofactor bound to the protein and its light-induced changes. Complementary site-directed spin-labeling studies monitor the structural alterations over larger distances and correspondingly longer time scales. A multiscale reaction mechanism describes how local changes of the retinal cofactor unlock the receptor to initiate large-scale conformational changes of rhodopsin. Activation of the G-protein-coupled receptor involves an ensemble of conformational substates within the rhodopsin manifold that characterize the dynamically active receptor.

  11. Introduction to the spectral distribution method. Application example to the subspaces with a large number of quasi particles

    International Nuclear Information System (INIS)

    Arvieu, R.

    The assumptions and principles of the spectral distribution method are reviewed. The object of the method is to deduce information on the nuclear spectra by constructing a frequency function which has the same first few moments, as the exact frequency function, these moments being then exactly calculated. The method is applied to subspaces containing a large number of quasi particles [fr

  12. Spatially adaptive hp refinement approach for PN neutron transport equation using spectral element method

    International Nuclear Information System (INIS)

    Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.

    2015-01-01

    Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks

  13. A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

    Science.gov (United States)

    Liu, X.; Banerjee, J. R.

    2017-03-01

    A highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J0) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

  14. Spectral Imaging by Upconversion

    DEFF Research Database (Denmark)

    Dam, Jeppe Seidelin; Pedersen, Christian; Tidemand-Lichtenberg, Peter

    2011-01-01

    We present a method to obtain spectrally resolved images using upconversion. By this method an image is spectrally shifted from one spectral region to another wavelength. Since the process is spectrally sensitive it allows for a tailored spectral response. We believe this will allow standard...... silicon based cameras designed for visible/near infrared radiation to be used for spectral images in the mid infrared. This can lead to much lower costs for such imaging devices, and a better performance....

  15. Using spectral element method to solve variational inequalities with applications in finance

    International Nuclear Information System (INIS)

    Moradipour, M.; Yousefi, S.A.

    2015-01-01

    Under the Black–Scholes model, the value of an American option solves a time dependent variational inequality problem (VIP). In this paper, first we discretize the variational inequality of American option in temporal direction by applying the Rannacher time stepping and achieve a sequence of elliptic variational inequalities. Second we discretize the spatial domain of variational inequalities by using spectral element methods with high order Lagrangian polynomials introduced on Gauss–Legendre–Lobatto points. Also by computing integrals by the Gauss–Legendre–Lobatto quadrature rule we derive a sequence of the linear complementarity problems (LCPs) having a positive definite sparse coefficient matrix. To find the unique solutions of the LCPs, we use the projected successive over-relaxation (PSOR) algorithm. Furthermore we present some existence and uniqueness theorems for the variational inequalities and LCPs. Finally, theoretical results are verified on the relevant numerical examples.

  16. Statistical learning method in regression analysis of simulated positron spectral data

    International Nuclear Information System (INIS)

    Avdic, S. Dz.

    2005-01-01

    Positron lifetime spectroscopy is a non-destructive tool for detection of radiation induced defects in nuclear reactor materials. This work concerns the applicability of the support vector machines method for the input data compression in the neural network analysis of positron lifetime spectra. It has been demonstrated that the SVM technique can be successfully applied to regression analysis of positron spectra. A substantial data compression of about 50 % and 8 % of the whole training set with two and three spectral components respectively has been achieved including a high accuracy of the spectra approximation. However, some parameters in the SVM approach such as the insensitivity zone e and the penalty parameter C have to be chosen carefully to obtain a good performance. (author)

  17. Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Youshan, E-mail: ysliu@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Teng, Jiwen, E-mail: jwteng@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); Xu, Tao, E-mail: xutao@mail.iggcas.ac.cn [State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 (China); CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, 100101 (China); Badal, José, E-mail: badal@unizar.es [Physics of the Earth, Sciences B, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza (Spain)

    2017-05-01

    The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational

  18. Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

    Science.gov (United States)

    Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

    2017-05-01

    The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant-Friedrichs-Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational

  19. Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

    International Nuclear Information System (INIS)

    Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José

    2017-01-01

    The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational

  20. Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

    Energy Technology Data Exchange (ETDEWEB)

    Carella, Alfredo Raul

    2012-09-15

    Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)

  1. 3D airborne EM modeling based on the spectral-element time-domain (SETD) method

    Science.gov (United States)

    Cao, X.; Yin, C.; Huang, X.; Liu, Y.; Zhang, B., Sr.; Cai, J.; Liu, L.

    2017-12-01

    In the field of 3D airborne electromagnetic (AEM) modeling, both finite-difference time-domain (FDTD) method and finite-element time-domain (FETD) method have limitations that FDTD method depends too much on the grids and time steps, while FETD requires large number of grids for complex structures. We propose a time-domain spectral-element (SETD) method based on GLL interpolation basis functions for spatial discretization and Backward Euler (BE) technique for time discretization. The spectral-element method is based on a weighted residual technique with polynomials as vector basis functions. It can contribute to an accurate result by increasing the order of polynomials and suppressing spurious solution. BE method is a stable tine discretization technique that has no limitation on time steps and can guarantee a higher accuracy during the iteration process. To minimize the non-zero number of sparse matrix and obtain a diagonal mass matrix, we apply the reduced order integral technique. A direct solver with its speed independent of the condition number is adopted for quickly solving the large-scale sparse linear equations system. To check the accuracy of our SETD algorithm, we compare our results with semi-analytical solutions for a three-layered earth model within the time lapse 10-6-10-2s for different physical meshes and SE orders. The results show that the relative errors for magnetic field B and magnetic induction are both around 3-5%. Further we calculate AEM responses for an AEM system over a 3D earth model in Figure 1. From numerical experiments for both 1D and 3D model, we draw the conclusions that: 1) SETD can deliver an accurate results for both dB/dt and B; 2) increasing SE order improves the modeling accuracy for early to middle time channels when the EM field diffuses fast so the high-order SE can model the detailed variation; 3) at very late time channels, increasing SE order has little improvement on modeling accuracy, but the time interval plays

  2. Integrated Geophysical Measurements for Bioremediation Monitoring: Combining Spectral Induced Polarization, Nuclear Magnetic Resonance and Magnetic Methods

    Energy Technology Data Exchange (ETDEWEB)

    Keating, Kristina [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Slater, Lee [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Ntarlagiannis, Dimitris [Rutgers Univ., Newark, NJ (United States). Dept. of Earth and Environmental Sciences; Williams, Kenneth H. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Earth Sciences Division

    2015-02-24

    This documents contains the final report for the project "Integrated Geophysical Measurements for Bioremediation Monitoring: Combining Spectral Induced Polarization, Nuclear Magnetic Resonance and Magnetic Methods" (DE-SC0007049) Executive Summary: Our research aimed to develop borehole measurement techniques capable of monitoring subsurface processes, such as changes in pore geometry and iron/sulfur geochemistry, associated with remediation of heavy metals and radionuclides. Previous work has demonstrated that geophysical method spectral induced polarization (SIP) can be used to assess subsurface contaminant remediation; however, SIP signals can be generated from multiple sources limiting their interpretation value. Integrating multiple geophysical methods, such as nuclear magnetic resonance (NMR) and magnetic susceptibility (MS), with SIP, could reduce the ambiguity of interpretation that might result from a single method. Our research efforts entails combining measurements from these methods, each sensitive to different mineral forms and/or mineral-fluid interfaces, providing better constraints on changes in subsurface biogeochemical processes and pore geometries significantly improving our understanding of processes impacting contaminant remediation. The Rifle Integrated Field Research Challenge (IFRC) site was used as a test location for our measurements. The Rifle IFRC site is located at a former uranium ore-processing facility in Rifle, Colorado. Leachate from spent mill tailings has resulted in residual uranium contamination of both groundwater and sediments within the local aquifer. Studies at the site include an ongoing acetate amendment strategy, native microbial populations are stimulated by introduction of carbon intended to alter redox conditions and immobilize uranium. To test the geophysical methods in the field, NMR and MS logging measurements were collected before, during, and after acetate amendment. Next, laboratory NMR, MS, and SIP measurements

  3. Substructure identification for shear structures: cross-power spectral density method

    International Nuclear Information System (INIS)

    Zhang, Dongyu; Johnson, Erik A

    2012-01-01

    In this paper, a substructure identification method for shear structures is proposed. A shear structure is divided into many small substructures; utilizing the dynamic equilibrium of a one-floor substructure, an inductive identification problem is formulated, using the cross-power spectral densities between structural floor accelerations and a reference response, to estimate the parameters of that one story. Repeating this procedure, all story parameters of the shear structure are identified from top to bottom recursively. An identification error analysis is performed for the proposed substructure method, revealing how uncertain factors (e.g. measurement noise) in the identification process affect the identification accuracy. According to the error analysis, a smart reference selection rule is designed to choose the optimal reference response that further enhances the identification accuracy. Moreover, based on the identification error analysis, explicit formulae are developed to calculate the variances of the parameter identification errors. A ten-story shear structure is used to illustrate the effectiveness of the proposed substructure method. The simulation results show that the method, combined with the reference selection rule, can very accurately identify structural parameters despite large measurement noise. Furthermore, the proposed formulae provide good predictions for the variances of the parameter identification errors, which are vital for providing accurate warnings of structural damage. (paper)

  4. A new physics-based method for detecting weak nuclear signals via spectral decomposition

    International Nuclear Information System (INIS)

    Chan, Kung-Sik; Li, Jinzheng; Eichinger, William; Bai, Erwei

    2012-01-01

    We propose a new physics-based method to determine the presence of the spectral signature of one or more nuclides from a poorly resolved spectra with weak signatures. The method is different from traditional methods that rely primarily on peak finding algorithms. The new approach considers each of the signatures in the library to be a linear combination of subspectra. These subspectra are obtained by assuming a signature consisting of just one of the unique gamma rays emitted by the nuclei. We propose a Poisson regression model for deducing which nuclei are present in the observed spectrum. In recognition that a radiation source generally comprises few nuclear materials, the underlying Poisson model is sparse, i.e. most of the regression coefficients are zero (positive coefficients correspond to the presence of nuclear materials). We develop an iterative algorithm for a penalized likelihood estimation that prompts sparsity. We illustrate the efficacy of the proposed method by simulations using a variety of poorly resolved, low signal-to-noise ratio (SNR) situations, which show that the proposed approach enjoys excellent empirical performance even with SNR as low as to -15 db.

  5. Spectral-ratio radon background correction method in airborne γ-ray spectrometry based on compton scattering deduction

    International Nuclear Information System (INIS)

    Gu Yi; Xiong Shengqing; Zhou Jianxin; Fan Zhengguo; Ge Liangquan

    2014-01-01

    γ-ray released by the radon daughter has severe impact on airborne γ-ray spectrometry. The spectral-ratio method is one of the best mathematical methods for radon background deduction in airborne γ-ray spectrometry. In this paper, an advanced spectral-ratio method was proposed which deducts Compton scattering ray by the fast Fourier transform rather than tripping ratios, the relationship between survey height and correction coefficient of the advanced spectral-ratio radon background correction method was studied, the advanced spectral-ratio radon background correction mathematic model was established, and the ground saturation model calibrating technology for correction coefficient was proposed. As for the advanced spectral-ratio radon background correction method, its applicability and correction efficiency are improved, and the application cost is saved. Furthermore, it can prevent the physical meaning lost and avoid the possible errors caused by matrix computation and mathematical fitting based on spectrum shape which is applied in traditional correction coefficient. (authors)

  6. Chebyshev Distance

    OpenAIRE

    Coghetto Roland

    2016-01-01

    In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of ℰTn${\\cal E}_T^n $ and in [20] he has formalized that ℰTn${\\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23]) a denumerable base of ℰTn${\\cal E}_T^n $.

  7. Chebyshev Distance

    Directory of Open Access Journals (Sweden)

    Coghetto Roland

    2016-06-01

    Full Text Available In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26] of ℰTn${\\cal E}_T^n $ and in [20] he has formalized that ℰTn${\\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23] a denumerable base of ℰTn${\\cal E}_T^n $.

  8. Spectral map-analysis: a method to analyze gene expression data

    OpenAIRE

    Bijnens, Luc J.M.; Lewi, Paul J.; Göhlmann, Hinrich W.; Molenberghs, Geert; Wouters, Luc

    2004-01-01

    bioinformatics; biplot; correspondence factor analysis; data mining; data visualization; gene expression data; microarray data; multivariate exploratory data analysis; principal component analysis; Spectral map analysis

  9. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    International Nuclear Information System (INIS)

    Dufresne, L.; Dumas, G.

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r→∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions

  10. Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

    Directory of Open Access Journals (Sweden)

    Omar Eldwaik

    2018-01-01

    Full Text Available Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.

  11. A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Sidler, Rolf, E-mail: rsidler@gmail.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, José M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)

    2013-02-15

    We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

  12. Uncertainty quantification in reactor physics using adjoint/perturbation techniques and adaptive spectral methods

    NARCIS (Netherlands)

    Gilli, L.

    2013-01-01

    This thesis presents the development and the implementation of an uncertainty propagation algorithm based on the concept of spectral expansion. The first part of the thesis is dedicated to the study of uncertainty propagation methodologies and to the analysis of spectral techniques. The concepts

  13. Complex method for angular-spectral analysis of volume phase diffraction gratings recorded in photopolymers

    Czech Academy of Sciences Publication Activity Database

    Vojtíšek, Petr; Květoň, M.; Richter, I.

    2016-01-01

    Roč. 11, February (2016), č. článku 16009. ISSN 1990-2573 R&D Projects: GA MŠk(CZ) LO1206 Institutional support: RVO:61389021 Keywords : Photopolymers * diffraction gratings * angular-spectral maps * spectral selectivity * angular selectivity Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.975, year: 2016

  14. Data preprocessing methods of FT-NIR spectral data for the classification cooking oil

    Science.gov (United States)

    Ruah, Mas Ezatul Nadia Mohd; Rasaruddin, Nor Fazila; Fong, Sim Siong; Jaafar, Mohd Zuli

    2014-12-01

    This recent work describes the data pre-processing method of FT-NIR spectroscopy datasets of cooking oil and its quality parameters with chemometrics method. Pre-processing of near-infrared (NIR) spectral data has become an integral part of chemometrics modelling. Hence, this work is dedicated to investigate the utility and effectiveness of pre-processing algorithms namely row scaling, column scaling and single scaling process with Standard Normal Variate (SNV). The combinations of these scaling methods have impact on exploratory analysis and classification via Principle Component Analysis plot (PCA). The samples were divided into palm oil and non-palm cooking oil. The classification model was build using FT-NIR cooking oil spectra datasets in absorbance mode at the range of 4000cm-1-14000cm-1. Savitzky Golay derivative was applied before developing the classification model. Then, the data was separated into two sets which were training set and test set by using Duplex method. The number of each class was kept equal to 2/3 of the class that has the minimum number of sample. Then, the sample was employed t-statistic as variable selection method in order to select which variable is significant towards the classification models. The evaluation of data pre-processing were looking at value of modified silhouette width (mSW), PCA and also Percentage Correctly Classified (%CC). The results show that different data processing strategies resulting to substantial amount of model performances quality. The effects of several data pre-processing i.e. row scaling, column standardisation and single scaling process with Standard Normal Variate indicated by mSW and %CC. At two PCs model, all five classifier gave high %CC except Quadratic Distance Analysis.

  15. Validation and application of an high-order spectral difference method for flow induced noise simulation

    KAUST Repository

    Parsani, Matteo

    2011-09-01

    The main goal of this paper is to develop an efficient numerical algorithm to compute the radiated far field noise provided by an unsteady flow field from bodies in arbitrary motion. The method computes a turbulent flow field in the near fields using a high-order spectral difference method coupled with large-eddy simulation approach. The unsteady equations are solved by advancing in time using a second-order backward difference formulae scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lowerupper symmetric GaussSeidel algorithm. In the second step, the method calculates the far field sound pressure based on the acoustic source information provided by the first step simulation. The method is based on the Ffowcs WilliamsHawkings approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10 3 and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional turbulent flow in a muffler at Re = 4.665 × 10 4 and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately. © 2011 IMACS.

  16. A method of incident angle estimation for high resolution spectral recovery in filter-array-based spectrometers

    Science.gov (United States)

    Kim, Cheolsun; Lee, Woong-Bi; Ju, Gun Wu; Cho, Jeonghoon; Kim, Seongmin; Oh, Jinkyung; Lim, Dongsung; Lee, Yong Tak; Lee, Heung-No

    2017-02-01

    In recent years, there has been an increasing interest in miniature spectrometers for research and development. Especially, filter-array-based spectrometers have advantages of low cost and portability, and can be applied in various fields such as biology, chemistry and food industry. Miniaturization in optical filters causes degradation of spectral resolution due to limitations on spectral responses and the number of filters. Nowadays, many studies have been reported that the filter-array-based spectrometers have achieved resolution improvements by using digital signal processing (DSP) techniques. The performance of the DSP-based spectral recovery highly depends on the prior information of transmission functions (TFs) of the filters. The TFs vary with respect to an incident angle of light onto the filter-array. Conventionally, it is assumed that the incident angle of light on the filters is fixed and the TFs are known to the DSP. However, the incident angle is inconstant according to various environments and applications, and thus TFs also vary, which leads to performance degradation of spectral recovery. In this paper, we propose a method of incident angle estimation (IAE) for high resolution spectral recovery in the filter-array-based spectrometers. By exploiting sparse signal reconstruction of the L1- norm minimization, IAE estimates an incident angle among all possible incident angles which minimizes the error of the reconstructed signal. Based on IAE, DSP effectively provides a high resolution spectral recovery in the filter-array-based spectrometers.

  17. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    CERN Document Server

    Dufresne, L

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...

  18. The Sternheimer-GW method and the spectral signatures of plasmonic polarons

    Science.gov (United States)

    Giustino, Feliciano

    During the past three decades the GW method has emerged among the most promising electronic structure techniques for predictive calculations of quasiparticle band structures. In order to simplify the GW work-flow while at the same time improving the calculation accuracy, we developed the Sternheimer-GW method. In Sternheimer-GW both the screened Coulomb interaction and the electron Green's function are evaluated by using exclusively occupied Kohn-Sham states, as in density-functional perturbation theory. In this talk I will review the basics of Sternheimer-GW, and I will discuss two recent applications to semiconductors and superconductors. In the case of semiconductors we calculated complete energy- and momentum-resolved spectral functions by combining Sternheimer-GW with the cumulant expansion approach. This study revealed the existence of band structure replicas which arise from electron-plasmon interactions. In the case of superconductors we calculated the Coulomb pseudo-potential from first principles, and combined this approach with the Eliashberg theory of the superconducting critical temperature. This work was supported by the Leverhulme Trust (RL-2012-001), the European Research Council (EU FP7/ERC 239578), the UK Engineering and Physical Sciences Research Council (EP/J009857/1), and the Graphene Flagship (EU FP7/604391).

  19. Using Linear Spectral Method when Calculating Seismic Resistance of Large-Capacity Vertical Steel Tanks

    Directory of Open Access Journals (Sweden)

    Tarasenko Alexandr

    2016-01-01

    Full Text Available The paper is aimed at determining the possibility of applying the simplified method proposed by the authors to calculate the tank seismic resistance in compliance with current regulations and scientific provisions. The authors propose a highly detailed numerical model for a common oil storage tank RVSPK-50000 that enables static operational loads and dynamic action of earthquakes to be calculated. Within the modal analysis the natural oscillation frequencies in the range of 0-10 Hz were calculated; the results are given for the first ten modes. The model takes into account the effect of impulsive and convective components of hydrodynamic pressure during earthquakes. Within the spectral analysis by generalized response spectra was calculated a general stress-strain state of a structure during earthquakes of 7, 8, 9 intensity degrees on the MSK-64 scale for a completely filled up, a half-filled up to the mark of 8.5 m and an empty RVSPK-50000 tank. The developed finite element model can be used to perform calculations of seismic resistance by the direct dynamic method, which will give further consideration to the impact of individual structures (floating roof, support posts, adjoined elements of added stiffness on the general stress-strain state of a tank.

  20. A Wavelet-Modified ESPRIT Hybrid Method for Assessment of Spectral Components from 0 to 150 kHz

    Directory of Open Access Journals (Sweden)

    Luisa Alfieri

    2017-01-01

    Full Text Available Waveform distortions are an important issue in distribution systems. In particular, the assessment of very wide spectra, that include also components in the 2–150 kHz range, has recently become an issue of great interest. This is due to the increasing presence of high-spectral emission devices like end-user devices and distributed generation systems. This study proposed a new sliding-window wavelet-modified estimation of signal parameters by rotational invariance technique (ESPRIT method, particularly suitable for the spectral analysis of waveforms that have very wide spectra. The method is very accurate and requires reduced computational effort. It can be applied successfully to detect spectral components in the range of 0–150 kHz introduced both by distributed power plants, such as wind and photovoltaic generation systems, and by end-user equipment connected to grids through static converters, such as fluorescent lamps.

  1. Task-oriented comparison of power spectral density estimation methods for quantifying acoustic attenuation in diagnostic ultrasound using a reference phantom method.

    Science.gov (United States)

    Rosado-Mendez, Ivan M; Nam, Kibo; Hall, Timothy J; Zagzebski, James A

    2013-07-01

    Reported here is a phantom-based comparison of methods for determining the power spectral density (PSD) of ultrasound backscattered signals. Those power spectral density values are then used to estimate parameters describing α(f), the frequency dependence of the acoustic attenuation coefficient. Phantoms were scanned with a clinical system equipped with a research interface to obtain radiofrequency echo data. Attenuation, modeled as a power law α(f)= α0 f (β), was estimated using a reference phantom method. The power spectral density was estimated using the short-time Fourier transform (STFT), Welch's periodogram, and Thomson's multitaper technique, and performance was analyzed when limiting the size of the parameter-estimation region. Errors were quantified by the bias and standard deviation of the α0 and β estimates, and by the overall power-law fit error (FE). For parameter estimation regions larger than ~34 pulse lengths (~1 cm for this experiment), an overall power-law FE of 4% was achieved with all spectral estimation methods. With smaller parameter estimation regions as in parametric image formation, the bias and standard deviation of the α0 and β estimates depended on the size of the parameter estimation region. Here, the multitaper method reduced the standard deviation of the α0 and β estimates compared with those using the other techniques. The results provide guidance for choosing methods for estimating the power spectral density in quantitative ultrasound methods.

  2. Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

    KAUST Repository

    Winokur, J.

    2015-12-19

    We investigate two methods to build a polynomial approximation of a model output depending on some parameters. The two approaches are based on pseudo-spectral projection (PSP) methods on adaptively constructed sparse grids, and aim at providing a finer control of the resolution along two distinct subsets of model parameters. The control of the error along different subsets of parameters may be needed for instance in the case of a model depending on uncertain parameters and deterministic design variables. We first consider a nested approach where an independent adaptive sparse grid PSP is performed along the first set of directions only, and at each point a sparse grid is constructed adaptively in the second set of directions. We then consider the application of aPSP in the space of all parameters, and introduce directional refinement criteria to provide a tighter control of the projection error along individual dimensions. Specifically, we use a Sobol decomposition of the projection surpluses to tune the sparse grid adaptation. The behavior and performance of the two approaches are compared for a simple two-dimensional test problem and for a shock-tube ignition model involving 22 uncertain parameters and 3 design parameters. The numerical experiments indicate that whereas both methods provide effective means for tuning the quality of the representation along distinct subsets of parameters, PSP in the global parameter space generally requires fewer model evaluations than the nested approach to achieve similar projection error. In addition, the global approach is better suited for generalization to more than two subsets of directions.

  3. Fourier spectral methods for fractional-in-space reaction-diffusion equations

    KAUST Repository

    Bueno-Orovio, Alfonso

    2014-04-01

    © 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

  4. Analysis of China's real estate prices and macroeconomy based on evolutionary co-spectral method

    Directory of Open Access Journals (Sweden)

    Juan Li

    2015-04-01

    Full Text Available Purpose: This paper investigates the dynamic interaction between the real estate market and the macroeconomic environment of China by use of dynamic coherence function based on co-spectral analysis. Design/methodology/approach: Through a theoretical perspective, the dynamic interrelationship among economic variables at different time intervals (both long and short terms is analyzed. Findings: The empirical results show that China’s real estate market features a high coherence with the change of the long-term interest rate, employment rate and money supply, while there is a moderate coherence between the real estate market and the inflation rate and economic growth rate, and the coherence between the short-term rate of interest and the real estate market is the lowest. Research implications: Previous researches have some shortcomings. They do not consider the dependence between nonlinear series, but the latter is crucial to avoid the deviation of results. In this paper, we proposed a new method of experience to overcome these shortcomings. Originality/value: The paper provides a reasonable explanation accordingly to different coherences between the real estate market and the macroeconomic variables.

  5. Quasiparticle self-consistent GW method for the spectral properties of complex materials.

    Science.gov (United States)

    Bruneval, Fabien; Gatti, Matteo

    2014-01-01

    The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.

  6. A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method

    Energy Technology Data Exchange (ETDEWEB)

    Hsu, Li-Chieh; Chen, Chien-Lin; Ye, Jian-Zhi [National Yunlin University of Science and Technology, Taiwan (China)

    2017-06-15

    This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.

  7. Spectral Analysis Method of Plastic Scintillator-based Radiation Detector against Nuclear/Radiological Terrorism

    International Nuclear Information System (INIS)

    Kwak, Sung-Woo; Yoo, Ho-Sik; Jang, Sung Soon; Kim, Jung-Soo; Yoon, Wan-Ki

    2008-01-01

    In these days, the threats relating to nuclear or radioactive materials have become a matter of internationally increased grave concern. A plastic scintillation detector in radiation portal monitoring (RPM) application has been used to detect radioactive sources in steel scrap entering reprocessing facilities, and to detect illicit transport of radioactive material across border ports-of-entry. The detection systems for RPM application usually are large and can not easily be moved to a different location. For some situations, an inconspicuous and mobile system for the radioactive or nuclear material during road transport is needed. The mobile radiation detection system has employed a NaI- based radiation detector to detect and identify the material hidden in vehicle. There are some operational constraints - short measuring time, weak activity due to heavy shield of illegal source, long distance - of inspection system in such nuclear security applications. Due to these constraints, large area sensor is required to maximize its sensitivity. Large NaI material, however, is extremely expensive. In designing a radiation detector for prevention of illicit trafficking of nuclear or radioactive materials, the trade-off should be carefully optimized between performance and cost in order to achieve cost-effective inspection system. For the cost-effective mobile radiation detection system, this paper describes new spectral analysis method to use the crude spectroscopic information available from a plastic detector to discriminate other man-made radiation source from NORM

  8. Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

    KAUST Repository

    Liu, Shaolin

    2017-09-28

    The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

  9. Spectral Analysis of Dynamic PET Studies: A Review of 20 Years of Method Developments and Applications.

    Science.gov (United States)

    Veronese, Mattia; Rizzo, Gaia; Bertoldo, Alessandra; Turkheimer, Federico E

    2016-01-01

    In Positron Emission Tomography (PET), spectral analysis (SA) allows the quantification of dynamic data by relating the radioactivity measured by the scanner in time to the underlying physiological processes of the system under investigation. Among the different approaches for the quantification of PET data, SA is based on the linear solution of the Laplace transform inversion whereas the measured arterial and tissue time-activity curves of a radiotracer are used to calculate the input response function of the tissue. In the recent years SA has been used with a large number of PET tracers in brain and nonbrain applications, demonstrating that it is a very flexible and robust method for PET data analysis. Differently from the most common PET quantification approaches that adopt standard nonlinear estimation of compartmental models or some linear simplifications, SA can be applied without defining any specific model configuration and has demonstrated very good sensitivity to the underlying kinetics. This characteristic makes it useful as an investigative tool especially for the analysis of novel PET tracers. The purpose of this work is to offer an overview of SA, to discuss advantages and limitations of the methodology, and to inform about its applications in the PET field.

  10. A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations

    KAUST Repository

    Chacó n Rebollo, Tomá s; Dia, Ben Mansour

    2015-01-01

    This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.

  11. A variational multi-scale method with spectral approximation of the sub-scales: Application to the 1D advection-diffusion equations

    KAUST Repository

    Chacón Rebollo, Tomás

    2015-03-01

    This paper introduces a variational multi-scale method where the sub-grid scales are computed by spectral approximations. It is based upon an extension of the spectral theorem to non necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces. This allows to element-wise calculate the sub-grid scales by means of the associated spectral expansion. We propose a feasible VMS-spectral method by truncation of this spectral expansion to a finite number of modes. We apply this general framework to the convection-diffusion equation, by analytically computing the family of eigenfunctions. We perform a convergence and error analysis. We also present some numerical tests that show the stability of the method for an odd number of spectral modes, and an improvement of accuracy in the large resolved scales, due to the adding of the sub-grid spectral scales.

  12. Seismoelectric Effects based on Spectral-Element Method for Subsurface Fluid Characterization

    Science.gov (United States)

    Morency, C.

    2017-12-01

    Present approaches for subsurface imaging rely predominantly on seismic techniques, which alone do not capture fluid properties and related mechanisms. On the other hand, electromagnetic (EM) measurements add constraints on the fluid phase through electrical conductivity and permeability, but EM signals alone do not offer information of the solid structural properties. In the recent years, there have been many efforts to combine both seismic and EM data for exploration geophysics. The most popular approach is based on joint inversion of seismic and EM data, as decoupled phenomena, missing out the coupled nature of seismic and EM phenomena such as seismoeletric effects. Seismoelectric effects are related to pore fluid movements with respect to the solid grains. By analyzing coupled poroelastic seismic and EM signals, one can capture a pore scale behavior and access both structural and fluid properties.Here, we model the seismoelectric response by solving the governing equations derived by Pride and Garambois (1994), which correspond to Biot's poroelastic wave equations and Maxwell's electromagnetic wave equations coupled electrokinetically. We will show that these coupled wave equations can be numerically implemented by taking advantage of viscoelastic-electromagnetic mathematical equivalences. These equations will be solved using a spectral-element method (SEM). The SEM, in contrast to finite-element methods (FEM) uses high degree Lagrange polynomials. Not only does this allow the technique to handle complex geometries similarly to FEM, but it also retains exponential convergence and accuracy due to the use of high degree polynomials. Finally, we will discuss how this is a first step toward full coupled seismic-EM inversion to improve subsurface fluid characterization. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  13. Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods

    Science.gov (United States)

    Ma, Xiaoke; Wang, Bingbo; Yu, Liang

    2018-01-01

    Community detection is fundamental for revealing the structure-functionality relationship in complex networks, which involves two issues-the quantitative function for community as well as algorithms to discover communities. Despite significant research on either of them, few attempt has been made to establish the connection between the two issues. To attack this problem, a generalized quantification function is proposed for community in weighted networks, which provides a framework that unifies several well-known measures. Then, we prove that the trace optimization of the proposed measure is equivalent with the objective functions of algorithms such as nonnegative matrix factorization, kernel K-means as well as spectral clustering. It serves as the theoretical foundation for designing algorithms for community detection. On the second issue, a semi-supervised spectral clustering algorithm is developed by exploring the equivalence relation via combining the nonnegative matrix factorization and spectral clustering. Different from the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the spectral algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method improves the accuracy of the traditional spectral algorithms in community detection.

  14. Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics

    International Nuclear Information System (INIS)

    Beyer, Florian; Daszuta, Boris; Frauendiener, Jörg; Whale, Ben

    2014-01-01

    Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through the use of integer spin-weighted spherical harmonics, we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2 + 1 Maxwell equations on a deformed sphere. (paper)

  15. A general spectral method for the numerical simulation of one-dimensional interacting fermions

    Science.gov (United States)

    Clason, Christian; von Winckel, Gregory

    2012-08-01

    This software implements a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient Matlab program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. The new version includes a Python implementation of the presented approach. New version program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 332 No. of bytes in distributed program, including test data, etc.: 5418 Distribution format: tar.gz Programming language: MATLAB/GNU Octave, Python Computer: Any architecture supported by MATLAB, GNU Octave or Python Operating system: Any supported by MATLAB, GNU Octave or Python RAM: Depends on the data Classification: 4.3, 2.2. External routines: Python 2.7+, NumPy 1.3+, SciPy 0.10+ Catalogue identifier of previous version: AEKO_v1_0 Journal reference of previous version: Comput. Phys. Commun. 183 (2012) 405 Does the new version supersede the previous version?: Yes Nature of problem: The direct numerical

  16. Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

    Science.gov (United States)

    Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

    2014-12-01

    Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

  17. Synthesis and spectral characterization of hydrazone derivative of furfural using experimental and DFT methods.

    Science.gov (United States)

    Babu, N Ramesh; Subashchandrabose, S; Ali Padusha, M Syed; Saleem, H; Erdoğdu, Y

    2014-01-01

    The Spectral Characterization of (E)-1-(Furan-2-yl) methylene)-2-(1-phenylvinyl) hydrazine (FMPVH) were carried out by using FT-IR, FT-Raman and UV-Vis., Spectrometry. The B3LYP/6-311++G(d,p) level of optimization has been performed on the title compound. The conformational analysis was performed for this molecule, in which the cis and trans conformers were studied for spectral characterization. The recorded spectral results were compared with calculated results. The optimized bond parameters of FMPVH molecule was compared with X-ray diffraction data of related molecule. To study the intra-molecular charge transfers within the molecule the Lewis (bonding) and Non-Lewis (anti-bonding) structural calculation was performed. The Non-linear optical behavior of the title compound was measured using first order hyperpolarizability calculation. The atomic charges were calculated and analyzed. Copyright © 2013 Elsevier B.V. All rights reserved.

  18. A new method of organizing spectral line intensity ratio fluctuations of nightglow emissions

    International Nuclear Information System (INIS)

    Thelin, B.

    1986-02-01

    In this paper a new kind of linearization effect between the atmospheric night airglow emissions is presented. The same kind of linearization effect has previously been studied with spectrochemical light sources together with a spectrometer. A linear graph was obtained for atomic spectral lines and vibrational bandspectra when the spectral line intensity ratio fluctuations were plotted versus the photon energies of these emissions. To study this effect data from a number of different photometer investigations of night airglow emissions at different times and places have been used. (author)

  19. Using spectral methods to obtain particle size information from optical data: applications to measurements from CARES 2010

    Science.gov (United States)

    Atkinson, Dean B.; Pekour, Mikhail; Chand, Duli; Radney, James G.; Kolesar, Katheryn R.; Zhang, Qi; Setyan, Ari; O'Neill, Norman T.; Cappa, Christopher D.

    2018-04-01

    Multi-wavelength in situ aerosol extinction, absorption and scattering measurements made at two ground sites during the 2010 Carbonaceous Aerosols and Radiative Effects Study (CARES) are analyzed using a spectral deconvolution method that allows extraction of particle-size-related information, including the fraction of extinction produced by the fine-mode particles and the effective radius of the fine mode. The spectral deconvolution method is typically applied to analysis of remote sensing measurements. Here, its application to in situ measurements allows for comparison with more direct measurement methods and validation of the retrieval approach. Overall, the retrieved fine-mode fraction and effective radius compare well with other in situ measurements, including size distribution measurements and scattering and absorption measurements made separately for PM1 and PM10, although there were some periods during which the different methods yielded different results. One key contributor to differences between the results obtained is the alternative, spectrally based definitions of fine and coarse modes from the optical methods, relative to instruments that use a physically defined cut point. These results indicate that for campaigns where size, composition and multi-wavelength optical property measurements are made, comparison of the results can result in closure or can identify unusual circumstances. The comparison here also demonstrates that in situ multi-wavelength optical property measurements can be used to determine information about particle size distributions in situations where direct size distribution measurements are not available.

  20. Using spectral methods to obtain particle size information from optical data: applications to measurements from CARES 2010

    Directory of Open Access Journals (Sweden)

    D. B. Atkinson

    2018-04-01

    Full Text Available Multi-wavelength in situ aerosol extinction, absorption and scattering measurements made at two ground sites during the 2010 Carbonaceous Aerosols and Radiative Effects Study (CARES are analyzed using a spectral deconvolution method that allows extraction of particle-size-related information, including the fraction of extinction produced by the fine-mode particles and the effective radius of the fine mode. The spectral deconvolution method is typically applied to analysis of remote sensing measurements. Here, its application to in situ measurements allows for comparison with more direct measurement methods and validation of the retrieval approach. Overall, the retrieved fine-mode fraction and effective radius compare well with other in situ measurements, including size distribution measurements and scattering and absorption measurements made separately for PM1 and PM10, although there were some periods during which the different methods yielded different results. One key contributor to differences between the results obtained is the alternative, spectrally based definitions of fine and coarse modes from the optical methods, relative to instruments that use a physically defined cut point. These results indicate that for campaigns where size, composition and multi-wavelength optical property measurements are made, comparison of the results can result in closure or can identify unusual circumstances. The comparison here also demonstrates that in situ multi-wavelength optical property measurements can be used to determine information about particle size distributions in situations where direct size distribution measurements are not available.

  1. Systems and methods for selective detection and imaging in coherent Raman microscopy by spectral excitation shaping

    Science.gov (United States)

    Xie, Xiaoliang Sunney; Freudiger, Christian; Min, Wei

    2016-03-15

    A microscopy imaging system is disclosed that includes a light source system, a spectral shaper, a modulator system, an optics system, an optical detector and a processor. The light source system is for providing a first train of pulses and a second train of pulses. The spectral shaper is for spectrally modifying an optical property of at least some frequency components of the broadband range of frequency components such that the broadband range of frequency components is shaped producing a shaped first train of pulses to specifically probe a spectral feature of interest from a sample, and to reduce information from features that are not of interest from the sample. The modulator system is for modulating a property of at least one of the shaped first train of pulses and the second train of pulses at a modulation frequency. The optical detector is for detecting an integrated intensity of substantially all optical frequency components of a train of pulses of interest transmitted or reflected through the common focal volume. The processor is for detecting a modulation at the modulation frequency of the integrated intensity of substantially all of the optical frequency components of the train of pulses of interest due to the non-linear interaction of the shaped first train of pulses with the second train of pulses as modulated in the common focal volume, and for providing an output signal for a pixel of an image for the microscopy imaging system.

  2. Tailoring Spectral Properties of Binary PT-Symmetric Gratings by Duty-Cycle Methods

    DEFF Research Database (Denmark)

    Lupu, Anatole T.; Benisty, Henri; Lavrinenko, Andrei

    2016-01-01

    We explore the frequency selective functionalities of a nonuniform PT-symmetric Bragg grating with modulated complex index profile. We start by assessing the possibility to achieve an efficient apodization of the PT-symmetric Bragg grating spectral response by using direct adaptations of the conv...

  3. A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

    Science.gov (United States)

    Taneja, Ankur; Higdon, Jonathan

    2018-01-01

    A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

  4. Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

    Science.gov (United States)

    Karaoǧlu, Haydar; Romanowicz, Barbara

    2018-06-01

    We present a global upper-mantle shear wave attenuation model that is built through a hybrid full-waveform inversion algorithm applied to long-period waveforms, using the spectral element method for wavefield computations. Our inversion strategy is based on an iterative approach that involves the inversion for successive updates in the attenuation parameter (δ Q^{-1}_μ) and elastic parameters (isotropic velocity VS, and radial anisotropy parameter ξ) through a Gauss-Newton-type optimization scheme that employs envelope- and waveform-type misfit functionals for the two steps, respectively. We also include source and receiver terms in the inversion steps for attenuation structure. We conducted a total of eight iterations (six for attenuation and two for elastic structure), and one inversion for updates to source parameters. The starting model included the elastic part of the relatively high-resolution 3-D whole mantle seismic velocity model, SEMUCB-WM1, which served to account for elastic focusing effects. The data set is a subset of the three-component surface waveform data set, filtered between 400 and 60 s, that contributed to the construction of the whole-mantle tomographic model SEMUCB-WM1. We applied strict selection criteria to this data set for the attenuation iteration steps, and investigated the effect of attenuation crustal structure on the retrieved mantle attenuation structure. While a constant 1-D Qμ model with a constant value of 165 throughout the upper mantle was used as starting model for attenuation inversion, we were able to recover, in depth extent and strength, the high-attenuation zone present in the depth range 80-200 km. The final 3-D model, SEMUCB-UMQ, shows strong correlation with tectonic features down to 200-250 km depth, with low attenuation beneath the cratons, stable parts of continents and regions of old oceanic crust, and high attenuation along mid-ocean ridges and backarcs. Below 250 km, we observe strong attenuation in the

  5. Fatigue Life Prediction of the Keel Structure of a Tsunami Buoy Using Spectral Fatigue Analysis Method

    Directory of Open Access Journals (Sweden)

    Angga Yustiawan

    2013-09-01

    Full Text Available One  of  the  components  of  the  Indonesia  Tsunami  Early  Warning  System  (InaTEWS  is  a  surface  buoy.  The  surface buoy  is  exposed  to  dynamic  and  random  loadings  while  operating  at  sea,  particularly  due  to  waves.  Because  of  the cyclic  nature  of  the  wave  load,  this  may  result  in  a fatigue  damage  of  the  keel  structure,  which  connects  the  mooring line  with  the  buoy  hull.  The  operating  location  of  the buoy  is  off  the  Java  South  Coast  at  the  coordinate (10.3998  S, 108.3417  E. To  determine  the  stress  transfer  function, model  tests  were  performed,  measuring  the  buoy  motions  and the stress at the mooring line. A spectral fatigue analysis method is applied for the purpose of estimating the fatigue life of the keel structure. Utilizing the  model-test results, the S-N curve obtained in a previous study and the  wave data at the buoy location, it is found that the fatigue life of the keel structure is approximately 11 years.

  6. Study of old ecological hazards, oil seeps and contaminations using earth observation methodsspectral library for oil seep

    Directory of Open Access Journals (Sweden)

    Smejkalová Eva

    2017-03-01

    Full Text Available The possibilities of remote sensing techniques in the field of the Earth surface monitoring and protection specifically for the problems caused by petroleum contaminations, for the mapping of insufficiently plugged and abandoned old oil wells and for the analysis of onshore oil seeps are described. Explained is the methodology for analyzing and detection of potential hydrocarbon contaminations using the Earth observation in the area of interest in Slovakia (Korňa and in Czech Republic (Nesyt, mainly building and calibrating the spectral library for oil seeps. The acquisition of the in-situ field data (ASD, Cropscan spectroradiometers for this purpose, the successful building and verification of hydrocarbon spectral library, the application of hydrocarbon indexes and use of shift in red-edge part of electromagnetic spectra, the spectral analysis of input data are clarified in the paper. Described is approach which could innovate the routine methods for investigating the occurrence of hydrocarbons and can assist during the mapping and locating the potential oil seep sites. Important outcome is the successful establishment of a spectral library (database with calibration data suitable for further application in data classification for identifying the occurrence of hydrocarbons.

  7. Testing of the method for water microleakage detection from OH hydroxyl spectral lines at the L-2M stellarator

    International Nuclear Information System (INIS)

    Voronov, G. S.; Berezhetskii, M. S.; Bondar’, Yu. F.; Vafin, I. Yu.; Vasil’kov, D. G.; Voronova, E. V.; Grebenshchikov, S. E.; Grishina, I. A.; Larionova, N. F.; Letunov, A. A.; Logvinenko, V. P.; Meshcheryakov, A. I.; Pleshkov, E. I.; Khol’nov, Yu. V.; Fedyanin, O. I.; Tsygankov, V. A.; Shchepetov, S. V.; Kurnaev, V. A.; Vizgalov, I. V.; Urusov, V. A.

    2013-01-01

    Results are presented from L-2M stellarator experiments on testing a possible method for detection of water microleakages in the cooling system of the first wall and vacuum chamber of ITER. The method consists in the spectroscopic detection of spectral lines of the OH hydroxyl, which forms via the dissociation of water molecules in plasma. Emission in the spectral band of 305–310 nm can be detected even at water leakage rates less than 10 −4 Pa m 3 /s. Chemical reactions between water and boron compounds on the vacuum chamber wall delay the detection of leakages up to ∼2000 s. A similar phenomenon can be expected when a leakage will occur in ITER, where the materials suggested for the first wall (Be, Li) can also chemically react with water.

  8. Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

    International Nuclear Information System (INIS)

    Gamba, Irene M.; Tharkabhushanam, Sri Harsha

    2009-01-01

    We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S d-1 . The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ( )]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously

  9. 3D anisotropic modeling and identification for airborne EM systems based on the spectral-element method

    Science.gov (United States)

    Huang, Xin; Yin, Chang-Chun; Cao, Xiao-Yue; Liu, Yun-He; Zhang, Bo; Cai, Jing

    2017-09-01

    The airborne electromagnetic (AEM) method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element (SE) method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell's equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic

  10. A New Six-Parameter Model Based on Chebyshev Polynomials for Solar Cells

    Directory of Open Access Journals (Sweden)

    Shu-xian Lun

    2015-01-01

    Full Text Available This paper presents a new current-voltage (I-V model for solar cells. It has been proved that series resistance of a solar cell is related to temperature. However, the existing five-parameter model ignores the temperature dependence of series resistance and then only accurately predicts the performance of monocrystalline silicon solar cells. Therefore, this paper uses Chebyshev polynomials to describe the relationship between series resistance and temperature. This makes a new parameter called temperature coefficient for series resistance introduced into the single-diode model. Then, a new six-parameter model for solar cells is established in this paper. This new model can improve the accuracy of the traditional single-diode model and reflect the temperature dependence of series resistance. To validate the accuracy of the six-parameter model in this paper, five kinds of silicon solar cells with different technology types, that is, monocrystalline silicon, polycrystalline silicon, thin film silicon, and tripe-junction amorphous silicon, are tested at different irradiance and temperature conditions. Experiment results show that the six-parameter model proposed in this paper is an I-V model with moderate computational complexity and high precision.

  11. Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport Systems

    Energy Technology Data Exchange (ETDEWEB)

    Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)

    2012-08-01

    An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.

  12. Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

    Science.gov (United States)

    Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

    2010-09-01

    This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

  13. Spectral fitting method for the solution of time-dependent Schroedinger equations: Applications to atoms in intense laser fields

    International Nuclear Information System (INIS)

    Qiao Haoxue; Cai Qingyu; Rao Jianguo; Li Baiwen

    2002-01-01

    A spectral fitting method for solving the time-dependent Schroedinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of Δt. Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields

  14. A new method of organizing spectral line intensity ratio fluctuations of auroral emissions

    International Nuclear Information System (INIS)

    Thelin, B.

    1986-02-01

    In this paper a new kind of linearization effect between the atmospheric auroral emissions is presented. The same kind of linearization effect has previously been found in nightglow emissions from photometer measurements and in the spectrochemical field from studies of optical light sources. Linear graphs have been obtained for atomic spectral lines and vibrational bandspectra when the spectral line ratio fluctuations were plotted versus the photon energies of these emissions. This new effect has been studied with a spectrophotometer in auroral emissions, where linear graphs have been obtained on different auroral occasions. By doing such studies of auroral light it is possible to see the importance of the inelastic scattering cross section between electrons - atoms and electrons - molecules. In this way it has shown to be possible to determine the mean energy of the interacting thermal electrons that are active in the different auroral phases. (author)

  15. A method to decompose spectral changes in Synechocystis PCC 6803 during light-induced state transitions

    Czech Academy of Sciences Publication Activity Database

    Acuna, A.M.; Kaňa, Radek; Gwizdala, M.; Snellenburg, J.J.; van Alphen, P.; van Oort, B.; Kirilovsky, D.; van Grondelle, R.; van Stokkum, I.H.M.

    2016-01-01

    Roč. 130, 1-3 SI (2016), s. 237-249 ISSN 0166-8595 R&D Projects: GA ČR GBP501/12/G055; GA MŠk(CZ) LO1416; GA MŠk(CZ) ED2.1.00/19.0392 Institutional support: RVO:61388971 Keywords : Cyanobacteria * Spectrally resolved fluorometry * Singular value decomposition Subject RIV: EF - Botanics Impact factor: 3.864, year: 2016

  16. The optimized gradient method for full waveform inversion and its spectral implementation

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2016-01-01

    At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.

  17. The optimized gradient method for full waveform inversion and its spectral implementation

    KAUST Repository

    Wu, Zedong

    2016-03-28

    At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.

  18. SCPS: a fast implementation of a spectral method for detecting protein families on a genome-wide scale

    Directory of Open Access Journals (Sweden)

    Paccanaro Alberto

    2010-03-01

    Full Text Available Abstract Background An important problem in genomics is the automatic inference of groups of homologous proteins from pairwise sequence similarities. Several approaches have been proposed for this task which are "local" in the sense that they assign a protein to a cluster based only on the distances between that protein and the other proteins in the set. It was shown recently that global methods such as spectral clustering have better performance on a wide variety of datasets. However, currently available implementations of spectral clustering methods mostly consist of a few loosely coupled Matlab scripts that assume a fair amount of familiarity with Matlab programming and hence they are inaccessible for large parts of the research community. Results SCPS (Spectral Clustering of Protein Sequences is an efficient and user-friendly implementation of a spectral method for inferring protein families. The method uses only pairwise sequence similarities, and is therefore practical when only sequence information is available. SCPS was tested on difficult sets of proteins whose relationships were extracted from the SCOP database, and its results were extensively compared with those obtained using other popular protein clustering algorithms such as TribeMCL, hierarchical clustering and connected component analysis. We show that SCPS is able to identify many of the family/superfamily relationships correctly and that the quality of the obtained clusters as indicated by their F-scores is consistently better than all the other methods we compared it with. We also demonstrate the scalability of SCPS by clustering the entire SCOP database (14,183 sequences and the complete genome of the yeast Saccharomyces cerevisiae (6,690 sequences. Conclusions Besides the spectral method, SCPS also implements connected component analysis and hierarchical clustering, it integrates TribeMCL, it provides different cluster quality tools, it can extract human-readable protein

  19. SCPS: a fast implementation of a spectral method for detecting protein families on a genome-wide scale.

    Science.gov (United States)

    Nepusz, Tamás; Sasidharan, Rajkumar; Paccanaro, Alberto

    2010-03-09

    An important problem in genomics is the automatic inference of groups of homologous proteins from pairwise sequence similarities. Several approaches have been proposed for this task which are "local" in the sense that they assign a protein to a cluster based only on the distances between that protein and the other proteins in the set. It was shown recently that global methods such as spectral clustering have better performance on a wide variety of datasets. However, currently available implementations of spectral clustering methods mostly consist of a few loosely coupled Matlab scripts that assume a fair amount of familiarity with Matlab programming and hence they are inaccessible for large parts of the research community. SCPS (Spectral Clustering of Protein Sequences) is an efficient and user-friendly implementation of a spectral method for inferring protein families. The method uses only pairwise sequence similarities, and is therefore practical when only sequence information is available. SCPS was tested on difficult sets of proteins whose relationships were extracted from the SCOP database, and its results were extensively compared with those obtained using other popular protein clustering algorithms such as TribeMCL, hierarchical clustering and connected component analysis. We show that SCPS is able to identify many of the family/superfamily relationships correctly and that the quality of the obtained clusters as indicated by their F-scores is consistently better than all the other methods we compared it with. We also demonstrate the scalability of SCPS by clustering the entire SCOP database (14,183 sequences) and the complete genome of the yeast Saccharomyces cerevisiae (6,690 sequences). Besides the spectral method, SCPS also implements connected component analysis and hierarchical clustering, it integrates TribeMCL, it provides different cluster quality tools, it can extract human-readable protein descriptions using GI numbers from NCBI, it interfaces with

  20. A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

    DEFF Research Database (Denmark)

    Nielsen, S.A.; Hesthaven, J.S.

    2002-01-01

    elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial...

  1. Standard Test Methods for Measurement of Electrical Performance and Spectral Response of Nonconcentrator Multijunction Photovoltaic Cells and Modules

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    2010-01-01

    1.1 These test methods provide special techniques needed to determine the electrical performance and spectral response of two-terminal, multijunction photovoltaic (PV) devices, both cell and modules. 1.2 These test methods are modifications and extensions of the procedures for single-junction devices defined by Test Methods E948, E1021, and E1036. 1.3 These test methods do not include temperature and irradiance corrections for spectral response and current-voltage (I-V) measurements. Procedures for such corrections are available in Test Methods E948, E1021, and E1036. 1.4 These test methods may be applied to cells and modules intended for concentrator applications. 1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. 1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and ...

  2. Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

    KAUST Repository

    Parsani, Matteo

    2013-04-10

    Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

  3. Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems

    KAUST Repository

    Parsani, Matteo; Ketcheson, David I.; Deconinck, W.

    2013-01-01

    Explicit Runge--Kutta schemes with large stable step sizes are developed for integration of high-order spectral difference spatial discretizations on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge--Kutta schemes available in the literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.

  4. Dynamic analysis of smart composite beams by using the frequency domain spectral element method

    Energy Technology Data Exchange (ETDEWEB)

    Park, Il Wook; Lee, Usik [Inha Univ., Incheon (Korea, Republic of)

    2012-08-15

    To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafertype piezoelectric transducers are often bonded on the surface of the composite structure to form a multi layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two layer smart composite beams by using the Hamilton's principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay up of composite laminates and surface bonded wafer type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.

  5. A postprocessing method based on high-resolution spectral estimation for FDTD calculation of phononic band structures

    Energy Technology Data Exchange (ETDEWEB)

    Su Xiaoxing, E-mail: xxsu@bjtu.edu.c [School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044 (China); Li Jianbao; Wang Yuesheng [Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044 (China)

    2010-05-15

    If the energy bands of a phononic crystal are calculated by the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome this difficulty. Numerical simulation results for three-dimensional acoustic and two-dimensional elastic systems show that, compared with the classic FFT-based postprocessing method, the proposed method can give much better estimation of the eigenfrequencies when the FDTD is run with relatively few iterations.

  6. A postprocessing method based on high-resolution spectral estimation for FDTD calculation of phononic band structures

    International Nuclear Information System (INIS)

    Su Xiaoxing; Li Jianbao; Wang Yuesheng

    2010-01-01

    If the energy bands of a phononic crystal are calculated by the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome this difficulty. Numerical simulation results for three-dimensional acoustic and two-dimensional elastic systems show that, compared with the classic FFT-based postprocessing method, the proposed method can give much better estimation of the eigenfrequencies when the FDTD is run with relatively few iterations.

  7. A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements

    Energy Technology Data Exchange (ETDEWEB)

    Li, Mao; Qiu, Zihua; Liang, Chunlei; Sprague, Michael; Xu, Min

    2017-01-13

    In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.

  8. Combined FVTD/PSTD Schemes with Enhanced Spectral Accuracy for the Design of Large-Scale EMC Applications

    Directory of Open Access Journals (Sweden)

    N. V. Kantartzis

    2012-10-01

    Full Text Available A generalized conformal time-domain method with adjustable spectral accuracy is introduced in this paper for the consistent analysis of large-scale electromagnetic compatibility problems. The novel 3-D hybrid schemes blend a stencil-optimized finite-volume time-domain and a multimodal Fourier-Chebyshev pseudo-spectral time-domain algorithm that split the overall space into smaller and flexible areas. A key asset is that both techniques are updated independently and interconnected by robust boundary conditions. Also, combining a family of spatial derivative approximators with controllable precision in general curvilinear coordinates, the proposed method launches a conformal field flux formulation to derive electromagnetic quantities in regions with fine details. For advanced grid reliability at dissimilar media interfaces, dispersion-reduced adaptive operators, which assign the proper weights to each spatial increment, are developed. So, the resulting discretization yields highly rigorous and computationally affordable simulations, devoid of lattice errors. Numerical results, addressing detailed comparisons of various realistic applications with reference or measurement data verify our methodology and reveal its significant applicability.

  9. Estimation of Melanin and Hemoglobin Using Spectral Reflectance Images Reconstructed from a Digital RGB Image by the Wiener Estimation Method

    Directory of Open Access Journals (Sweden)

    Yoshihisa Aizu

    2013-06-01

    Full Text Available A multi-spectral diffuse reflectance imaging method based on a single snap shot of Red-Green-Blue images acquired with the exposure time of 65 ms (15 fps was investigated for estimating melanin concentration, blood concentration, and oxygen saturation in human skin tissue. The technique utilizes the Wiener estimation method to deduce spectral reflectance images instantaneously from an RGB image. Using the resultant absorbance spectrum as a response variable and the extinction coefficients of melanin, oxygenated hemoglobin and deoxygenated hemoglobin as predictor variables, multiple regression analysis provides regression coefficients. Concentrations of melanin and total blood are then determined from the regression coefficients using conversion vectors that are numerically deduced in advance by the Monte Carlo simulations for light transport in skin. Oxygen saturation is obtained directly from the regression coefficients. Experiments with a tissue-like agar gel phantom validated the method. In vivo experiments on fingers during upper limb occlusion demonstrated the ability of the method to evaluate physiological reactions of human skin.

  10. Modified Spectral Projected Subgradient Method: Convergence Analysis and Momentum Parameter Heuristics

    Directory of Open Access Journals (Sweden)

    Milagros Loreto

    2016-09-01

    Full Text Available The Modified Spectral Projected Subgradient (MSPS was proposed to solve Langrangen Dual Problems, and its convergence was shown when the momentum term was zero. The MSPS uses a momentum term in order to speed up its convergence. The momentum term is built on the multiplication of a momentum parameter and the direction of the previous iterate. In this work, we show convergence when the momentum parameter is a non-zero constant. We also propose heuristics to choose the momentum parameter intended to avoid the Zigzagging Phenomenon of Kind I. This phenomenon is present in the MSPS when at an iterate the subgradient forms an obtuse angle with the previous direction. We identify and diminish the Zigzagging Phenomenon of Kind I on Setcovering problems, and compare our numerical results to those of the original MSPS algorithm.

  11. Laser systems configured to output a spectrally-consolidated laser beam and related methods

    Science.gov (United States)

    Koplow, Jeffrey P [San Ramon, CA

    2012-01-10

    A laser apparatus includes a plurality of pumps each of which is configured to emit a corresponding pump laser beam having a unique peak wavelength. The laser apparatus includes a spectral beam combiner configured to combine the corresponding pump laser beams into a substantially spatially-coherent pump laser beam having a pump spectrum that includes the unique peak wavelengths, and first and second selectively reflective elements spaced from each other to define a lasing cavity including a lasing medium therein. The lasing medium generates a plurality of gain spectra responsive to absorbing the pump laser beam. Each gain spectrum corresponds to a respective one of the unique peak wavelengths of the substantially spatially-coherent pump laser beam and partially overlaps with all other ones of the gain spectra. The reflective elements are configured to promote emission of a laser beam from the lasing medium with a peak wavelength common to each gain spectrum.

  12. Apparatus and method using a holographic optical element for converting a spectral distribution to image points

    Science.gov (United States)

    McGill, Matthew J. (Inventor); Scott, Vibart S. (Inventor); Marzouk, Marzouk (Inventor)

    2001-01-01

    A holographic optical element transforms a spectral distribution of light to image points. The element comprises areas, each of which acts as a separate lens to image the light incident in its area to an image point. Each area contains the recorded hologram of a point source object. The image points can be made to lie in a line in the same focal plane so as to align with a linear array detector. A version of the element has been developed that has concentric equal areas to match the circular fringe pattern of a Fabry-Perot interferometer. The element has high transmission efficiency, and when coupled with high quantum efficiency solid state detectors, provides an efficient photon-collecting detection system. The element may be used as part of the detection system in a direct detection Doppler lidar system or multiple field of view lidar system.

  13. Calculation of isotope selective excitation of uranium isotopes using spectral simulation method

    International Nuclear Information System (INIS)

    Al-Hassanieh, O.

    2009-06-01

    Isotope ratio enhancement factor and isotope selectivity of 235 U in five excitation schemes (I: 0→10069 cm - 1 →IP, II: 0 →10081 cm - 1 →IP, III: 0 →25349 cm - 1→ IP, IV: 0→28650 cm - 1 →IP, V: 0→16900 cm - 1 →34659 cm - 1 →IP), were computed by a spectral simulation approach. The effect of laser bandwidth and Doppler width on the isotope ratio enhancement factor and isotope selectivity of 235 U has been studied. The photoionization scheme V gives the highest isotope ratio enhancement factor. The main factors which effect the separation possibility are the isotope shift and the relative intensity of the transitions between hyperfine levels. The isotope ratio enhancement factor decreases exponentially by increasing the Doppler width and the laser bandwidth, where the effect of Doppler width is much greater than the effect of the laser bandwidth. (author)

  14. A novel diagnostic method (spectral computed tomography of sacroiliac joints) for axial spondyloarthritis.

    Science.gov (United States)

    Zhang, Ping; Yu, Kai Hu; Guo, Rui Min; Ran, Jun; Liu, Yao; Morelli, John; Runge, Val M; Li, Xiao Ming

    2016-08-01

    To evaluate the diagnostic value of spectral computed tomography (CT) of sacroiliac joints for axial spondyloarthritis (SpA). We retrospectively analyzed the records of 125 patients with low back pain (LBP) suspected of having SpA. Each patient underwent sacroiliac joint spectral CT examination. Water- and calcium-based material decomposition images were reconstructed. After 3-6 months of follow-up, 76 were diagnosed with SpA, and the remaining 49 patients were diagnosed with nonspecific LBP (nLBP). The slope of sacroiliac bone marrow HU (Hounsfield unit) curve (λHU), CT value, and bone marrow to normal muscle ratios of water and calcium concentrations in the ilium and sacrum were calculated and compared between nLBP and SpA patients. The iliac λHU was 8.26 ± 3.91 for nLBP and 9.81 ± 4.92 for SpA. The mean iliac ratios of water and calcium concentrations were 1.04 ± 0.03 and 21.67 ± 4.40, respectively, for nLBP, and 1.07 ± 0.04 and 111.5 ± 358.98, respectively, for SpA. The mean iliac CT values were 311.12 ± 86.52 HU for nLBP and 423.97 ± 127.51 HU for SpA. There were statistically significant differences in iliac ratios of water and calcium concentrations, CT value, and λHU between nLBP and SpA patients (p sacroiliac joints of SpA patients. Copyright © 2015. Published by Elsevier B.V.

  15. Spectral Resolution for Five-Element, Filtered, X-Ray Detector (XRD) Arrays Using the Methods of Backus and Gilbert

    International Nuclear Information System (INIS)

    FEHL, DAVID LEE; BIGGS, F.; CHANDLER, GORDON A.; STYGAR, WILLIAM A.

    2000-01-01

    The generalized method of Backus and Gilbert (BG) is described and applied to the inverse problem of obtaining spectra from a 5-channel, filtered array of x-ray detectors (XRD's). This diagnostic is routinely fielded on the Z facility at Sandia National Laboratories to study soft x-ray photons ((le)2300 eV), emitted by high density Z-pinch plasmas. The BG method defines spectral resolution limits on the system of response functions that are in good agreement with the unfold method currently in use. The resolution so defined is independent of the source spectrum. For noise-free, simulated data the BG approximating function is also in reasonable agreement with the source spectrum (150 eV black-body) and the unfold. This function may be used as an initial trial function for iterative methods or a regularization model

  16. Comparison of the Performance of Two Advanced Spectral Methods for the Analysis of Times Series in Paleoceanography

    Directory of Open Access Journals (Sweden)

    Eulogio Pardo-Igúzquiza

    2015-08-01

    Full Text Available Many studies have revealed the cyclicity of past ocean/atmosphere dynamics at a wide range of time scales (from decadal to millennial time scales, based on the spectral analysis of time series of climate proxies obtained from deep sea sediment cores. Among the many techniques available for spectral analysis, the maximum entropy method and the Thomson multitaper approach have frequently been used because of their good statistical properties and high resolution with short time series. The novelty of the present study is that we compared the two methods by according to the performance of their statistical tests to assess the statistical significance of their power spectrum estimates. The statistical significance of maximum entropy estimates was assessed by a random permutation test (Pardo-Igúzquiza and Rodríguez-Tovar, 2000, while the statistical significance of the Thomson multitaper method was assessed by an F-test (Thomson, 1982. We compared the results obtained in a case study using simulated data where the spectral content of the time series was known and in a case study with real data. In both cases the results are similar: while the cycles identified as significant by maximum entropy and the permutation test have a clear physical interpretation, the F-test with the Thomson multitaper estimator tends to find as no significant the peaks in the low frequencies and tends to give as significant more spurious peaks in the middle and high frequencies. Nevertheless, the best strategy is to use both techniques and to use the advantages of each of them.

  17. A comparison of dimension reduction methods with application to multi-spectral images of sand used in concrete

    DEFF Research Database (Denmark)

    Clemmensen, Line Katrine Harder; Hansen, M. E.; Ersbøll, Bjarne Kjær

    2010-01-01

    This paper presents a comparison of dimension reduction methods based on a novel machine vision application for estimating moisture content in sand used to make concrete. For the application in question it is very important to know the moisture content of the sand so as to ensure good-quality...... sand types were examined with 20-60 images for each type. To reduce the amount of data, features were extracted from the multi-spectral images; the features were summary statistics on single bands and pairs of bands as well as morphological summaries. The number of features (2,016) is high in relation...

  18. Comparison between statistical and optimization methods in accessing unmixing of spectrally similar materials

    CSIR Research Space (South Africa)

    Debba, Pravesh

    2010-11-01

    Full Text Available This paper reports on the results from ordinary least squares and ridge regression as statistical methods, and is compared to numerical optimization methods such as the stochastic method for global optimization, simulated annealing, particle swarm...

  19. Performance evaluation of high rate space–time trellis-coded modulation using Gauss–Chebyshev quadrature technique

    CSIR Research Space (South Africa)

    Sokoya, O

    2008-05-01

    Full Text Available combines both simplicity and accuracy in finding the closed form expression of the PEP. The paper is organised as follows. In Section 2, we discuss the general transmission model of the HR-STTCM and the channel model. In Section 3, we describe... the derivation of the PEP using the Gauss–Chebyshev quadrature technique and also give a numerical example. In Section 4, we use the PEP obtained in Section 3 to estimate the average BEP for slow fading channels. Section 5 concludes the paper with discussion...

  20. Assessing NIR & MIR Spectral Analysis as a Method for Soil C Estimation Across a Network of Sampling Sites

    Science.gov (United States)

    Spencer, S.; Ogle, S.; Borch, T.; Rock, B.

    2008-12-01

    Monitoring soil C stocks is critical to assess the impact of future climate and land use change on carbon sinks and sources in agricultural lands. A benchmark network for soil carbon monitoring of stock changes is being designed for US agricultural lands with 3000-5000 sites anticipated and re-sampling on a 5- to10-year basis. Approximately 1000 sites would be sampled per year producing around 15,000 soil samples to be processed for total, organic, and inorganic carbon, as well as bulk density and nitrogen. Laboratory processing of soil samples is cost and time intensive, therefore we are testing the efficacy of using near-infrared (NIR) and mid-infrared (MIR) spectral methods for estimating soil carbon. As part of an initial implementation of national soil carbon monitoring, we collected over 1800 soil samples from 45 cropland sites in the mid-continental region of the U.S. Samples were processed using standard laboratory methods to determine the variables above. Carbon and nitrogen were determined by dry combustion and inorganic carbon was estimated with an acid-pressure test. 600 samples are being scanned using a bench- top NIR reflectance spectrometer (30 g of 2 mm oven-dried soil and 30 g of 8 mm air-dried soil) and 500 samples using a MIR Fourier-Transform Infrared Spectrometer (FTIR) with a DRIFT reflectance accessory (0.2 g oven-dried ground soil). Lab-measured carbon will be compared to spectrally-estimated carbon contents using Partial Least Squares (PLS) multivariate statistical approach. PLS attempts to develop a soil C predictive model that can then be used to estimate C in soil samples not lab-processed. The spectral analysis of soil samples either whole or partially processed can potentially save both funding resources and time to process samples. This is particularly relevant for the implementation of a national monitoring network for soil carbon. This poster will discuss our methods, initial results and potential for using NIR and MIR spectral

  1. Spectral encoding method for measuring the relative arrival time between x-ray/optical pulses

    International Nuclear Information System (INIS)

    Bionta, M. R.; Hartmann, N.; Weaver, M.; French, D.; Glownia, J. M.; Bostedt, C.; Chollet, M.; Ding, Y.; Fritz, D. M.; Fry, A. R.; Krzywinski, J.; Lemke, H. T.; Messerschmidt, M.; Schorb, S.; Zhu, D.; White, W. E.; Nicholson, D. J.; Cryan, J. P.; Baker, K.; Kane, D. J.

    2014-01-01

    The advent of few femtosecond x-ray light sources brings promise of x-ray/optical pump-probe experiments that can measure chemical and structural changes in the 10–100 fs time regime. Widely distributed timing systems used at x-ray Free-Electron Laser facilities are typically limited to above 50 fs fwhm jitter in active x-ray/optical synchronization. The approach of single-shot timing measurements is used to sort results in the event processing stage. This has seen wide use to accommodate the insufficient precision of active stabilization schemes. In this article, we review the current technique for “measure-and-sort” at the Linac Coherent Light Source at the SLAC National Accelerator Laboratory. The relative arrival time between an x-ray pulse and an optical pulse is measured near the experimental interaction region as a spectrally encoded cross-correlation signal. The cross-correlation provides a time-stamp for filter-and-sort algorithms used for real-time sorting. Sub-10 fs rms resolution is common in this technique, placing timing precision at the same scale as the duration of the shortest achievable x-ray pulses

  2. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, Aidan P. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Multiscale Science Dept.; Swiler, Laura P. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Optimization and Uncertainty Quantification Dept.; Trott, Christian R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Scalable Algorithms Dept.; Foiles, Stephen M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Materials and Data Science Dept.; Tucker, Garritt J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Materials and Data Science Dept.; Drexel Univ., Philadelphia, PA (United States). Dept. of Materials Science and Engineering

    2015-03-15

    Here, we present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.

  3. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials

    Energy Technology Data Exchange (ETDEWEB)

    Thompson, A.P., E-mail: athomps@sandia.gov [Multiscale Science Department, Sandia National Laboratories, PO Box 5800, MS 1322, Albuquerque, NM 87185 (United States); Swiler, L.P., E-mail: lpswile@sandia.gov [Optimization and Uncertainty Quantification Department, Sandia National Laboratories, PO Box 5800, MS 1318, Albuquerque, NM 87185 (United States); Trott, C.R., E-mail: crtrott@sandia.gov [Scalable Algorithms Department, Sandia National Laboratories, PO Box 5800, MS 1322, Albuquerque, NM 87185 (United States); Foiles, S.M., E-mail: foiles@sandia.gov [Computational Materials and Data Science Department, Sandia National Laboratories, PO Box 5800, MS 1411, Albuquerque, NM 87185 (United States); Tucker, G.J., E-mail: gtucker@coe.drexel.edu [Computational Materials and Data Science Department, Sandia National Laboratories, PO Box 5800, MS 1411, Albuquerque, NM 87185 (United States); Department of Materials Science and Engineering, Drexel University, Philadelphia, PA 19104 (United States)

    2015-03-15

    We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum.

  4. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials

    International Nuclear Information System (INIS)

    Thompson, A.P.; Swiler, L.P.; Trott, C.R.; Foiles, S.M.; Tucker, G.J.

    2015-01-01

    We present a new interatomic potential for solids and liquids called Spectral Neighbor Analysis Potential (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected onto a basis of hyperspherical harmonics in four dimensions. The bispectrum components are the same bond-orientational order parameters employed by the GAP potential [1]. The SNAP potential, unlike GAP, assumes a linear relationship between atom energy and bispectrum components. The linear SNAP coefficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. We demonstrate that a previously unnoticed symmetry property can be exploited to reduce the computational cost of the force calculations by more than one order of magnitude. We present results for a SNAP potential for tantalum, showing that it accurately reproduces a range of commonly calculated properties of both the crystalline solid and the liquid phases. In addition, unlike simpler existing potentials, SNAP correctly predicts the energy barrier for screw dislocation migration in BCC tantalum

  5. A COMPARISON STUDY OF DIFFERENT MARKER SELECTION METHODS FOR SPECTRAL-SPATIAL CLASSIFICATION OF HYPERSPECTRAL IMAGES

    Directory of Open Access Journals (Sweden)

    D. Akbari

    2015-12-01

    Full Text Available An effective approach based on the Minimum Spanning Forest (MSF, grown from automatically selected markers using Support Vector Machines (SVM, has been proposed for spectral-spatial classification of hyperspectral images by Tarabalka et al. This paper aims at improving this approach by using image segmentation to integrate the spatial information into marker selection process. In this study, the markers are extracted from the classification maps, obtained by both SVM and segmentation algorithms, and then are used to build the MSF. The segmentation algorithms are the watershed, expectation maximization (EM and hierarchical clustering. These algorithms are used in parallel and independently to segment the image. Moreover, the pixels of each class, with the largest population in the classification map, are kept for each region of the segmentation map. Lastly, the most reliable classified pixels are chosen from among the exiting pixels as markers. Two benchmark urban hyperspectral datasets are used for evaluation: Washington DC Mall and Berlin. The results of our experiments indicate that, compared to the original MSF approach, the marker selection using segmentation algorithms leads in more accurate classification maps.

  6. Spectral difference method applied in determination of beta-carotene, chlorophyll a and b from irradiated seeds of Calendula Officinalis

    International Nuclear Information System (INIS)

    Cucu, Delia-Irina; Dorobantu, Ioan

    2002-01-01

    Beta-carotene is part of the class of the carotenoid pigments that have a special function in the pigmentation of flowers and fruits. These pigments are essential in photosynthesis where they are retaining energy and are photoprotectors by forming the redox system. They are also precursors of vitamin A, pigments involved in the process of seeing. Beta-carotene is responsible for the growth and development of organisms, for the protection and recovery of epithelial tissue, etc. Next to chlorophyll, carotenoids are the major components of the complex pigment-protein from the thylacoide membrane, and some of them, such as beta-carotene, were for a long time considered to be protecting the membrane against destructive events caused by the over excitement of the chlorophyll. This paper presents spectral difference method for physico-chemical characterisation of three components (beta-carotene, chlorophyll a and b) from Calendula officinalis leaves and stalks, after irradiation of germinated seeds. The germinated seeds of Calendula officinalis has been irradiated at 8 different doses ( 1 k Rad, 3 k Rad, 5 k Rad, 10 k Rad, 20 k Rad, 50 k Rad, 100 k Rad, 500 krad), one set of seeds remaining unirradiated for comparison. The plants had been grown in the same conditions of light, temperature and humidity. The identification of beta-carotene was performed through thin layer chromatography. The chemical concentrations of beta-carotene, chlorophyll a and b were determined by spectral difference method. (authors)

  7. Nuclear techniques and cross-correlation methods for spectral analysis in two-phase flow measurements in mineral pipelines

    Energy Technology Data Exchange (ETDEWEB)

    Brandao, Luis E.B.; Salgado, Cesar M., E-mail: brandaos@ien.gov.br, E-mail: otero@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil). Divisao de Radiofarmacos; Sicilliano, Umberto C.C.S., E-mail: umberto.cassara@poli.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, RJ (Brazil). Dept. de Metalurgia

    2013-07-01

    In mineral industry is common to use water to transport pellets inside pipes. In these units, the correct measurement of flow (both solid and liquid phase) is important to guarantee a safe operation. Cross correlation flow meters are devices specially suited to be used in dual-phase flow and they are based on measure the transit time due the disturbances registered between two points, in our case gamma attenuation from radioactive sources. The emphasis of this work is the application of gamma transmission and scattering technique associated with spectral analysis methods to measure the flow of solid phase in a liquid fluid in side the pipe. The detectors and the sources are out side of the tube and are positioned 10.0 cm distant one from the other. The photons of transmission/scattering gamma radiation were registered, and across-correlation method was applied to measure the flow and spectral analysis was used to study the flow profile inside the pipe. (author)

  8. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

    KAUST Repository

    Bä ck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

    2010-01-01

    Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods

  9. An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials

    Directory of Open Access Journals (Sweden)

    Jianping Liu

    2016-01-01

    Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.

  10. Spatio-Spectral Method for Estimating Classified Regions with High Confidence using MODIS Data

    International Nuclear Information System (INIS)

    Katiyal, Anuj; Rajan, Dr K S

    2014-01-01

    In studies like change analysis, the availability of very high resolution (VHR)/high resolution (HR) imagery for a particular period and region is a challenge due to the sensor revisit times and high cost of acquisition. Therefore, most studies prefer lower resolution (LR) sensor imagery with frequent revisit times, in addition to their cost and computational advantages. Further, the classification techniques provide us a global estimate of the class accuracy, which limits its utility if the accuracy is low. In this work, we focus on the sub-classification problem of LR images and estimate regions of higher confidence than the global classification accuracy within its classified region. The spectrally classified data was mined into spatially clustered regions and further refined and processed using statistical measures to arrive at local high confidence regions (LHCRs), for every class. Rabi season MODIS data of January 2006 and 2007 was used for this study and the evaluation of LHCR was done using the APLULC 2005 classified data. For Jan-2007, the global class accuracies for water bodies (WB), forested regions (FR) and Kharif crops and barren lands (KB) were 89%, 71.7% and 71.23% respectively, while the respective LHCRs had accuracies of 96.67%, 89.4% and 80.9% covering an area of 46%, 29% and 14.5% of the initially classified areas. Though areas are reduced, LHCRs with higher accuracies help in extracting more representative class regions. Identification of such regions can facilitate in improving the classification time and processing for HR images when combined with the more frequently acquired LR imagery, isolate pure vs. mixed/impure pixels and as training samples locations for HR imagery

  11. Using a Spectral Method to Evaluate Hyporheic Exchange and its Effect on Reach Scale Nitrate Removal.

    Science.gov (United States)

    Moren, I.; Worman, A. L. E.; Riml, J.

    2017-12-01

    Previous studies have shown that hyporheic exchange processes can be of great importance for the transport, retention and mass removal of nutrients in streams. Specifically, the flow of surface water through the hyporheic zone enhances redox-sensitive reactions such as coupled nitrification-denitrification. This self-cleaning capacity of streams can be utilized in stream restoration projects aiming to improve water quality by reconstructing the geomorphology of the streams. To optimize the effect of restoration actions we need quantitative understanding of the linkage between stream geomorphology, hyporheic exchange processes and the desired water quality targets. Here we propose an analytical, spectral methodology to evaluate how different stream geomorphologies induce hyporheic exchange on a wide range of spatial and temporal scales. Measurements of streambed topographies and surface water profiles from agricultural streams were used to calculate the average hyporheic exchange velocity and residence times and the result was compared with in-stream tracer test. Furthermore, the hyporheic exchange induced by steps in the surface water profile was derived as a comparison of the theoretical capacity of the system. Based on differences in hyporheic exchange, the mass removal of nitrate could be derived for the different geomorphologies. The maximum nitrate mass removal was found to be related to a specific Damkhöler number, which reflects that the mass removal can be either reaction or transport controlled. Therefore, although hyporheic exchange induced by steps in the surface water profile was generally larger than the hyporheic exchange in the observed natural reaches, this would not necessarily lead a larger nitrate mass removal provided that the hyporheic residence times are not long enough to facilitate denitrification processes. The study illustrates the importance to investigate a stream thoroughly before any remediation actions are implemented, specifically

  12. A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell

    KAUST Repository

    Wright, G. B.

    2010-07-01

    A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth\\'s mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 103 and 105. Results from a Ra = 106 simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature. Copyright 2010 by the American Geophysical Union.

  13. Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system for prediction of financial and energy market data

    Directory of Open Access Journals (Sweden)

    A.K. Parida

    2016-09-01

    Full Text Available In this paper Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system is presented for the prediction and analysis of financial and electrical energy market data. The normally used TSK-type feedforward fuzzy neural network is unable to take the full advantage of the use of the linear fuzzy rule base in accurate input–output mapping and hence the consequent part of the rule base is made nonlinear using polynomial or arithmetic basis functions. Further the Chebyshev polynomial functions provide an expanded nonlinear transformation to the input space thereby increasing its dimension for capturing the nonlinearities and chaotic variations in financial or energy market data streams. Also the locally recurrent neuro-fuzzy information system (LRNFIS includes feedback loops both at the firing strength layer and the output layer to allow signal flow both in forward and backward directions, thereby making the LRNFIS mimic a dynamic system that provides fast convergence and accuracy in predicting time series fluctuations. Instead of using forward and backward least mean square (FBLMS learning algorithm, an improved Firefly-Harmony search (IFFHS learning algorithm is used to estimate the parameters of the consequent part and feedback loop parameters for better stability and convergence. Several real world financial and energy market time series databases are used for performance validation of the proposed LRNFIS model.

  14. Health State Monitoring of Bladed Machinery with Crack Growth Detection in BFG Power Plant Using an Active Frequency Shift Spectral Correction Method

    Directory of Open Access Journals (Sweden)

    Weifang Sun

    2017-08-01

    Full Text Available Power generation using waste-gas is an effective and green way to reduce the emission of the harmful blast furnace gas (BFG in pig-iron producing industry. Condition monitoring of mechanical structures in the BFG power plant is of vital importance to guarantee their safety and efficient operations. In this paper, we describe the detection of crack growth of bladed machinery in the BFG power plant via vibration measurement combined with an enhanced spectral correction technique. This technique enables high-precision identification of amplitude, frequency, and phase information (the harmonic information belonging to deterministic harmonic components within the vibration signals. Rather than deriving all harmonic information using neighboring spectral bins in the fast Fourier transform spectrum, this proposed active frequency shift spectral correction method makes use of some interpolated Fourier spectral bins and has a better noise-resisting capacity. We demonstrate that the identified harmonic information via the proposed method is of suppressed numerical error when the same level of noises is presented in the vibration signal, even in comparison with a Hanning-window-based correction method. With the proposed method, we investigated vibration signals collected from a centrifugal compressor. Spectral information of harmonic tones, related to the fundamental working frequency of the centrifugal compressor, is corrected. The extracted spectral information indicates the ongoing development of an impeller blade crack that occurred in the centrifugal compressor. This method proves to be a promising alternative to identify blade cracks at early stages.

  15. Health State Monitoring of Bladed Machinery with Crack Growth Detection in BFG Power Plant Using an Active Frequency Shift Spectral Correction Method.

    Science.gov (United States)

    Sun, Weifang; Yao, Bin; He, Yuchao; Chen, Binqiang; Zeng, Nianyin; He, Wangpeng

    2017-08-09

    Power generation using waste-gas is an effective and green way to reduce the emission of the harmful blast furnace gas (BFG) in pig-iron producing industry. Condition monitoring of mechanical structures in the BFG power plant is of vital importance to guarantee their safety and efficient operations. In this paper, we describe the detection of crack growth of bladed machinery in the BFG power plant via vibration measurement combined with an enhanced spectral correction technique. This technique enables high-precision identification of amplitude, frequency, and phase information (the harmonic information) belonging to deterministic harmonic components within the vibration signals. Rather than deriving all harmonic information using neighboring spectral bins in the fast Fourier transform spectrum, this proposed active frequency shift spectral correction method makes use of some interpolated Fourier spectral bins and has a better noise-resisting capacity. We demonstrate that the identified harmonic information via the proposed method is of suppressed numerical error when the same level of noises is presented in the vibration signal, even in comparison with a Hanning-window-based correction method. With the proposed method, we investigated vibration signals collected from a centrifugal compressor. Spectral information of harmonic tones, related to the fundamental working frequency of the centrifugal compressor, is corrected. The extracted spectral information indicates the ongoing development of an impeller blade crack that occurred in the centrifugal compressor. This method proves to be a promising alternative to identify blade cracks at early stages.

  16. Proposal of a New Method for Neutron Dosimetry Based on Spectral Information Obtained by Application of Artificial Neural Networks

    International Nuclear Information System (INIS)

    Fehrenbacher, G.; Schuetz, R.; Hahn, K.; Sprunck, M.; Cordes, E.; Biersack, J.P.; Wahl, W.

    1999-01-01

    A new method for the monitoring of neutron radiation is proposed. It is based on the determination of spectral information on the neutron field in order to derive dose quantities like the ambient dose equivalent, the dose equivalent, or other dose quantities which depend on the neutron energy. The method uses a multi-element system consisting of converter type silicon detectors. The unfolding procedure is based on an artificial neural network (ANN). The response function of each element is determined by a computational model considering the neutron interaction with the dosemeter layers and the subsequent transport of produced ions. An example is given for a multi-element system. The ANN is trained by a given set of neutron spectra and then applied to count responses obtained in neutron fields. Four examples of spectra unfolded using the ANN are presented. (author)

  17. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

    Science.gov (United States)

    Khader, M M

    2013-10-01

    In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

  18. Spectral algorithms for multiple scale localized eigenfunctions in infinitely long, slightly bent quantum waveguides

    Science.gov (United States)

    Boyd, John P.; Amore, Paolo; Fernández, Francisco M.

    2018-03-01

    -channel coordinate, X ∈ [ - ∞ , ∞ ] , Fourier domain truncation using the change of coordinate X = sinh(Lt) is considerably more efficient than rational Chebyshev functions TBn(X ; L) . All the spectral methods, however, yielded the required accuracy on a desktop computer.

  19. Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

    Science.gov (United States)

    Nguyen, Vu-Hieu; Naili, Salah

    2012-08-01

    This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

  20. Parallel Programming Application to Matrix Algebra in the Spectral Method for Control Systems Analysis, Synthesis and Identification

    Directory of Open Access Journals (Sweden)

    V. Yu. Kleshnin

    2016-01-01

    Full Text Available The article describes the matrix algebra libraries based on the modern technologies of parallel programming for the Spectrum software, which can use a spectral method (in the spectral form of mathematical description to analyse, synthesise and identify deterministic and stochastic dynamical systems. The developed matrix algebra libraries use the following technologies for the GPUs: OmniThreadLibrary, OpenMP, Intel Threading Building Blocks, Intel Cilk Plus for CPUs nVidia CUDA, OpenCL, and Microsoft Accelerated Massive Parallelism.The developed libraries support matrices with real elements (single and double precision. The matrix dimensions are limited by 32-bit or 64-bit memory model and computer configuration. These libraries are general-purpose and can be used not only for the Spectrum software. They can also find application in the other projects where there is a need to perform operations with large matrices.The article provides a comparative analysis of the libraries developed for various matrix operations (addition, subtraction, scalar multiplication, multiplication, powers of matrices, tensor multiplication, transpose, inverse matrix, finding a solution of the system of linear equations through the numerical experiments using different CPU and GPU. The article contains sample programs and performance test results for matrix multiplication, which requires most of all computational resources in regard to the other operations.

  1. A Hybrid Finite Element-Fourier Spectral Method for Vibration Analysis of Structures with Elastic Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Wan-You Li

    2014-01-01

    Full Text Available A novel hybrid method, which simultaneously possesses the efficiency of Fourier spectral method (FSM and the applicability of the finite element method (FEM, is presented for the vibration analysis of structures with elastic boundary conditions. The FSM, as one type of analytical approaches with excellent convergence and accuracy, is mainly limited to problems with relatively regular geometry. The purpose of the current study is to extend the FSM to problems with irregular geometry via the FEM and attempt to take full advantage of the FSM and the conventional FEM for structural vibration problems. The computational domain of general shape is divided into several subdomains firstly, some of which are represented by the FSM while the rest by the FEM. Then, fictitious springs are introduced for connecting these subdomains. Sufficient details are given to describe the development of such a hybrid method. Numerical examples of a one-dimensional Euler-Bernoulli beam and a two-dimensional rectangular plate show that the present method has good accuracy and efficiency. Further, one irregular-shaped plate which consists of one rectangular plate and one semi-circular plate also demonstrates the capability of the present method applied to irregular structures.

  2. Spectral isotopic methods of determining nitrogen and carbon in plant specimens with laser volatization

    International Nuclear Information System (INIS)

    Lazeeva, G.S.

    1986-01-01

    Methods have been devised for the local determination of nitrogen and carbon isotope compositions in plant specimens, which provide separate and joint determination. Local laser evaporation has been combined with spectroscopic determination of the isotope compositions in the gas phase. A continuous-wave CO 2 laser is preferable for the local evaporation; the carbon isotope composition may be determined directly on the sum of the evaporation products, whereas nitrogen must first be separated as N 2 . Methods have also been developed for the local determination of total nitrogen and carbon in a sample with isotope dilution on the basis of laser evaporation. In order to eliminate systematic errors in determining total carbon in plant material, an evaporation method free from a rim has been devised. These methods have been used in determining isotope concentration profiles in plant specimens grown in experiments employing labeled nitrogen and carbon

  3. Validation and application of an high-order spectral difference method for flow induced noise simulation

    KAUST Repository

    Parsani, Matteo; Ghorbaniasl, Ghader; Lacor, C.

    2011-01-01

    . The method is based on the Ffowcs WilliamsHawkings approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases

  4. Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

    KAUST Repository

    Bäck, Joakim

    2010-09-17

    Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.

  5. Tremor Detection Using Parametric and Non-Parametric Spectral Estimation Methods: A Comparison with Clinical Assessment

    Science.gov (United States)

    Martinez Manzanera, Octavio; Elting, Jan Willem; van der Hoeven, Johannes H.; Maurits, Natasha M.

    2016-01-01

    In the clinic, tremor is diagnosed during a time-limited process in which patients are observed and the characteristics of tremor are visually assessed. For some tremor disorders, a more detailed analysis of these characteristics is needed. Accelerometry and electromyography can be used to obtain a better insight into tremor. Typically, routine clinical assessment of accelerometry and electromyography data involves visual inspection by clinicians and occasionally computational analysis to obtain objective characteristics of tremor. However, for some tremor disorders these characteristics may be different during daily activity. This variability in presentation between the clinic and daily life makes a differential diagnosis more difficult. A long-term recording of tremor by accelerometry and/or electromyography in the home environment could help to give a better insight into the tremor disorder. However, an evaluation of such recordings using routine clinical standards would take too much time. We evaluated a range of techniques that automatically detect tremor segments in accelerometer data, as accelerometer data is more easily obtained in the home environment than electromyography data. Time can be saved if clinicians only have to evaluate the tremor characteristics of segments that have been automatically detected in longer daily activity recordings. We tested four non-parametric methods and five parametric methods on clinical accelerometer data from 14 patients with different tremor disorders. The consensus between two clinicians regarding the presence or absence of tremor on 3943 segments of accelerometer data was employed as reference. The nine methods were tested against this reference to identify their optimal parameters. Non-parametric methods generally performed better than parametric methods on our dataset when optimal parameters were used. However, one parametric method, employing the high frequency content of the tremor bandwidth under consideration

  6. On application of ion-photon emission method in spectral analysis of surface of different materials

    International Nuclear Information System (INIS)

    Bazhin, A.I.; Buravlev, Yu.M.; Ryzhov, V.N.

    1983-01-01

    Possibilities of application of ion-photom emission (IPE) method for determining element composition of the aluminium bronzes surface and profiles of distribution of hydrogen and helium implanted in metals (Mon Wn Cun Aln OKh18N10T steel) by ion bombardment have been studied. As ion source duoplasmatron which permits to obtain ions of inert (helium, argon) and active (hydrogenn oxygen) gases with current density 0.1-1 mA/cm 2 in the beam and energy from 5 to 25 keV has been applied. The photomultiplier PEM-79 has been used as a detector of optical radiation arising in the course of ion bombardment of the sample. For spectra recording the two-coordinate recorder has been used. Calibration charts which permit to determine the concentration of the investigated elements with 3-5% accuracy are obtained. The method sensitivity depends on excitation energy of transition observed in the spectrum. By known volumetric element concentration in the sample one can determine its concentration on a sUrface without resorting to a calibration chart in the coUrse of target sputtering. It has been found that the target impurity sputtering coefficient becomes nonselective to their relatiVe content. At wide incidence angles of ion beam. In contrast to other excitation methods (arc, spark) the IPE method possesses locality which constitutes 1 μm at a quite simple method of ion beam focussing (single lens)

  7. Adaptive Spectral Doppler Estimation

    DEFF Research Database (Denmark)

    Gran, Fredrik; Jakobsson, Andreas; Jensen, Jørgen Arendt

    2009-01-01

    . The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to pro- vide good spectral resolution and contrast even when the ob- servation window is very short. The 2 adaptive techniques are tested......In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence...... and compared with the averaged periodogram (Welch’s method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set...

  8. Joint image reconstruction method with correlative multi-channel prior for x-ray spectral computed tomography

    Science.gov (United States)

    Kazantsev, Daniil; Jørgensen, Jakob S.; Andersen, Martin S.; Lionheart, William R. B.; Lee, Peter D.; Withers, Philip J.

    2018-06-01

    Rapid developments in photon-counting and energy-discriminating detectors have the potential to provide an additional spectral dimension to conventional x-ray grayscale imaging. Reconstructed spectroscopic tomographic data can be used to distinguish individual materials by characteristic absorption peaks. The acquired energy-binned data, however, suffer from low signal-to-noise ratio, acquisition artifacts, and frequently angular undersampled conditions. New regularized iterative reconstruction methods have the potential to produce higher quality images and since energy channels are mutually correlated it can be advantageous to exploit this additional knowledge. In this paper, we propose a novel method which jointly reconstructs all energy channels while imposing a strong structural correlation. The core of the proposed algorithm is to employ a variational framework of parallel level sets to encourage joint smoothing directions. In particular, the method selects reference channels from which to propagate structure in an adaptive and stochastic way while preferring channels with a high data signal-to-noise ratio. The method is compared with current state-of-the-art multi-channel reconstruction techniques including channel-wise total variation and correlative total nuclear variation regularization. Realistic simulation experiments demonstrate the performance improvements achievable by using correlative regularization methods.

  9. Estimate of Small Stiffness and Damping Ratio in Residual Soil Using Spectral Analysis of Surface Wave Method

    Directory of Open Access Journals (Sweden)

    Bawadi Nor Faizah

    2016-01-01

    Full Text Available Research in the important parameters for modeling the dynamic behavior of soils has led to rapid development of the small strain stiffness and damping ratio for use in the seismic method. It is because, the experimental determination of the damping ratio is problematic, especially for hard soils sample. Many researchers have proved that the surface wave method is a reliable tool to determine shear wave velocity and damping ratio profiles at a site with very small strains level. Surface wave methods based on Rayleigh waves propagation and the resulting attenuation curve can become erroneous when higher modes contribute to the soil’s response. In this study, two approaches has been used to determine the shear strain amplitude and damping ratio of residual soils at small strain level using Spectral Analysis of Surface Wave (SASW method. One is to derive shear strain amplitude from the frequency-response curve and the other is to derive damping ratio from travel-time data. Then, the results are compared to the conventional method.

  10. Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

    Science.gov (United States)

    Antoine, Xavier; Levitt, Antoine; Tang, Qinglin

    2017-08-01

    We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.

  11. Studies on the arctiin and its interaction with DNA by spectral methods

    International Nuclear Information System (INIS)

    Sun Yantao; Zhang Hanqi; Bi Shuyun; Zhou Xiaofu; Wang Liang; Yan Yongsheng

    2011-01-01

    The emission spectra of arctiin were determined under various experimental conditions. In addition, a fluorescence method was developed to obtain the binding constants and sites of the interaction between arctiin and DNA. A competitive binding experiment and melting temperature mensuration were carried out to investigate the binding mechanism of arctiin and DNA. The experimental results showed that the interaction between arctiin and DNA belongs to a groove binding mode. - Highlights: → Determined the emission spectra of arctiin by fluorescence spectrometry. → Obtain the binding constants and sites of interaction between arctiin and DNA. → Calculate the binding parameters according an improved calculation method.

  12. A cloud shadow detection method combined with cloud height iteration and spectral analysis for Landsat 8 OLI data

    Science.gov (United States)

    Sun, Lin; Liu, Xinyan; Yang, Yikun; Chen, TingTing; Wang, Quan; Zhou, Xueying

    2018-04-01

    Although enhanced over prior Landsat instruments, Landsat 8 OLI can obtain very high cloud detection precisions, but for the detection of cloud shadows, it still faces great challenges. Geometry-based cloud shadow detection methods are considered the most effective and are being improved constantly. The Function of Mask (Fmask) cloud shadow detection method is one of the most representative geometry-based methods that has been used for cloud shadow detection with Landsat 8 OLI. However, the Fmask method estimates cloud height employing fixed temperature rates, which are highly uncertain, and errors of large area cloud shadow detection can be caused by errors in estimations of cloud height. This article improves the geometry-based cloud shadow detection method for Landsat OLI from the following two aspects. (1) Cloud height no longer depends on the brightness temperature of the thermal infrared band but uses a possible dynamic range from 200 m to 12,000 m. In this case, cloud shadow is not a specific location but a possible range. Further analysis was carried out in the possible range based on the spectrum to determine cloud shadow location. This effectively avoids the cloud shadow leakage caused by the error in the height determination of a cloud. (2) Object-based and pixel spectral analyses are combined to detect cloud shadows, which can realize cloud shadow detection from two aspects of target scale and pixel scale. Based on the analysis of the spectral differences between the cloud shadow and typical ground objects, the best cloud shadow detection bands of Landsat 8 OLI were determined. The combined use of spectrum and shape can effectively improve the detection precision of cloud shadows produced by thin clouds. Several cloud shadow detection experiments were carried out, and the results were verified by the results of artificial recognition. The results of these experiments indicated that this method can identify cloud shadows in different regions with correct

  13. Remote Determination of Cloud Temperature and Transmittance from Spectral Radiance Measurements: Method and Results

    Science.gov (United States)

    1996-10-01

    atmospherics temperatura and humidity profiles. Validation tests performed on experimental spectra demonstrate the occuracy of the method with typical...indicated as with the title.) Passive Remota Sensing Infrared Spectra Cloud Temperatura Cloud Transmittance FTIR Spectrometer Icing Hazard Detection (DCD03E.IFO - 95.02.22) UNCLASSIFIED SECURITY CLASSIFICATION OF FORM

  14. Spectral analysis of charcoal on soils: Implications for wildland fire severity mapping methods

    Science.gov (United States)

    Alistair M. S. Smith; Jan U. H. Eitel; Andrew T. Hudak

    2010-01-01

    Recent studies in the Western United States have supported climate scenarios that predict a higher occurrence of large and severe wildfires. Knowledge of the severity is important to infer long-term biogeochemical, ecological, and societal impacts, but understanding the sensitivity of any severity mapping method to variations in soil type and increasing charcoal (char...

  15. Quasistatic field simulations based on finite elements and spectral methods applied to superconducting magnets

    International Nuclear Information System (INIS)

    Koch, Stephan

    2009-01-01

    This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The

  16. Expert systems for structure elucidation of organic molecules by spectral methods

    International Nuclear Information System (INIS)

    Elyashberg, Mikhail E

    1999-01-01

    The state-of-the-art of the investigations aimed at creating expert systems for establishing the structure of organic molecules from IR, 1 H and 13 C NMR spectra is analysed. Computer methods used for identification of molecular fragments, generation of their structure and spectra prediction are considered. Principles of the creation of modern expert systems and general strategy of solving structural problems are discussed. The bibliography includes 174 references.

  17. A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

    Directory of Open Access Journals (Sweden)

    D. Baleanu

    2013-01-01

    fractional derivatives is based on modified generalized Laguerre polynomials Li(α,β(x with x∈Λ=(0,∞, α>−1, and β>0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

  18. Spectrally accurate contour dynamics

    International Nuclear Information System (INIS)

    Van Buskirk, R.D.; Marcus, P.S.

    1994-01-01

    We present an exponentially accurate boundary integral method for calculation the equilibria and dynamics of piece-wise constant distributions of potential vorticity. The method represents contours of potential vorticity as a spectral sum and solves the Biot-Savart equation for the velocity by spectrally evaluating a desingularized contour integral. We use the technique in both an initial-value code and a newton continuation method. Our methods are tested by comparing the numerical solutions with known analytic results, and it is shown that for the same amount of computational work our spectral methods are more accurate than other contour dynamics methods currently in use

  19. Numerical resolution of the Navier-Stokes equations for a low Mach number by a spectral method

    International Nuclear Information System (INIS)

    Frohlich, Jochen

    1990-01-01

    The low Mach number approximation of the Navier-Stokes equations, also called isobar, is an approximation which is less restrictive than the one due to Boussinesq. It permits strong density variations while neglecting acoustic phenomena. We present a numerical method to solve these equations in the unsteady, two dimensional case with one direction of periodicity. The discretization uses a semi-implicit finite difference scheme in time and a Fourier-Chebycheff pseudo-spectral method in space. The solution of the equations of motion is based on an iterative algorithm of Uzawa type. In the Boussinesq limit we obtain a direct method. A first application is concerned with natural convection in the Rayleigh-Benard setting. We compare the results of the low Mach number equations with the ones in the Boussinesq case and consider the influence of variable fluid properties. A linear stability analysis based on a Chebychev-Tau method completes the study. The second application that we treat is a case of isobaric combustion in an open domain. We communicate results for the hydrodynamic Darrieus-Landau instability of a plane laminar flame front. [fr

  20. Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

    Science.gov (United States)

    Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; Tohyama, Takami

    2018-04-01

    We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003), 10.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013), 10.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S =1 /2 , we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

  1. Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures.

    Science.gov (United States)

    Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; Tohyama, Takami

    2018-04-01

    We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)PRBMDO0163-182910.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S=1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

  2. A spectral method to detect community structure based on distance modularity matrix

    Science.gov (United States)

    Yang, Jin-Xuan; Zhang, Xiao-Dong

    2017-08-01

    There are many community organizations in social and biological networks. How to identify these community structure in complex networks has become a hot issue. In this paper, an algorithm to detect community structure of networks is proposed by using spectra of distance modularity matrix. The proposed algorithm focuses on the distance of vertices within communities, rather than the most weakly connected vertex pairs or number of edges between communities. The experimental results show that our method achieves better effectiveness to identify community structure for a variety of real-world networks and computer generated networks with a little more time-consumption.

  3. Study of spectral response of a neutron filter. Design of a method to adjust spectra

    International Nuclear Information System (INIS)

    Colomb-Dolci, F.

    1999-02-01

    The first part of this thesis describes an experimental method which intends to determine a neutron spectrum in the epithermal range [1 eV -10 keV]. Based on measurements of reaction rates provided by activation foils, it gives flux level in each energy range corresponding to each probe. This method can be used in any reactor location or in a neutron beam. It can determine scepter on eight energy groups, five groups in the epithermal range. The second part of this thesis presents a study of an epithermal neutron beam design, in the frame of Neutron Capture Therapy. A beam tube was specially built to test filters made up of different materials. Its geometry was designed to favour epithermal neutron crossing and to cut thermal and fast neutrons. A code scheme was validated to simulate the device response with a Monte Carlo code. Measurements were made at ISIS reactor and experimental spectra were compared to calculated ones. This validated code scheme was used to simulate different materials usable as shields in the tube. A study of these shields is presented at the end of this thesis. (author)

  4. Blind Forensics of Successive Geometric Transformations in Digital Images Using Spectral Method: Theory and Applications.

    Science.gov (United States)

    Chen, Chenglong; Ni, Jiangqun; Shen, Zhaoyi; Shi, Yun Qing

    2017-06-01

    Geometric transformations, such as resizing and rotation, are almost always needed when two or more images are spliced together to create convincing image forgeries. In recent years, researchers have developed many digital forensic techniques to identify these operations. Most previous works in this area focus on the analysis of images that have undergone single geometric transformations, e.g., resizing or rotation. In several recent works, researchers have addressed yet another practical and realistic situation: successive geometric transformations, e.g., repeated resizing, resizing-rotation, rotation-resizing, and repeated rotation. We will also concentrate on this topic in this paper. Specifically, we present an in-depth analysis in the frequency domain of the second-order statistics of the geometrically transformed images. We give an exact formulation of how the parameters of the first and second geometric transformations influence the appearance of periodic artifacts. The expected positions of characteristic resampling peaks are analytically derived. The theory developed here helps to address the gap left by previous works on this topic and is useful for image security and authentication, in particular, the forensics of geometric transformations in digital images. As an application of the developed theory, we present an effective method that allows one to distinguish between the aforementioned four different processing chains. The proposed method can further estimate all the geometric transformation parameters. This may provide useful clues for image forgery detection.

  5. A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

    Science.gov (United States)

    Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

    2005-01-01

    Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

  6. A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

    International Nuclear Information System (INIS)

    Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

    2005-01-01

    Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem

  7. Dual-energy approach to contrast-enhanced mammography using the balanced filter method: spectral optimization and preliminary phantom measurement.

    Science.gov (United States)

    Saito, Masatoshi

    2007-11-01

    Dual-energy contrast agent-enhanced mammography is a technique of demonstrating breast cancers obscured by a cluttered background resulting from the contrast between soft tissues in the breast. The technique has usually been implemented by exploiting two exposures to different x-ray tube voltages. In this article, another dual-energy approach using the balanced filter method without switching the tube voltages is described. For the spectral optimization of dual-energy mammography using the balanced filters, we applied a theoretical framework reported by Lemacks et al. [Med. Phys. 29, 1739-1751 (2002)] to calculate the signal-to-noise ratio (SNR) in an iodinated contrast agent subtraction image. This permits the selection of beam parameters such as tube voltage and balanced filter material, and the optimization of the latter's thickness with respect to some critical quantity-in this case, mean glandular dose. For an imaging system with a 0.1 mm thick CsI:T1 scintillator, we predict that the optimal tube voltage would be 45 kVp for a tungsten anode using zirconium, iodine, and neodymium balanced filters. A mean glandular dose of 1.0 mGy is required to obtain an SNR of 5 in order to detect 1.0 mg/cm2 iodine in the resulting clutter-free image of a 5 cm thick breast composed of 50% adipose and 50% glandular tissue. In addition to spectral optimization, we carried out phantom measurements to demonstrate the present dual-energy approach for obtaining a clutter-free image, which preferentially shows iodine, of a breast phantom comprising three major components-acrylic spheres, olive oil, and an iodinated contrast agent. The detection of iodine details on the cluttered background originating from the contrast between acrylic spheres and olive oil is analogous to the task of distinguishing contrast agents in a mixture of glandular and adipose tissues.

  8. Dual-energy approach to contrast-enhanced mammography using the balanced filter method: Spectral optimization and preliminary phantom measurement

    International Nuclear Information System (INIS)

    Saito, Masatoshi

    2007-01-01

    Dual-energy contrast agent-enhanced mammography is a technique of demonstrating breast cancers obscured by a cluttered background resulting from the contrast between soft tissues in the breast. The technique has usually been implemented by exploiting two exposures to different x-ray tube voltages. In this article, another dual-energy approach using the balanced filter method without switching the tube voltages is described. For the spectral optimization of dual-energy mammography using the balanced filters, we applied a theoretical framework reported by Lemacks et al. [Med. Phys. 29, 1739-1751 (2002)] to calculate the signal-to-noise ratio (SNR) in an iodinated contrast agent subtraction image. This permits the selection of beam parameters such as tube voltage and balanced filter material, and the optimization of the latter's thickness with respect to some critical quantity--in this case, mean glandular dose. For an imaging system with a 0.1 mm thick CsI:Tl scintillator, we predict that the optimal tube voltage would be 45 kVp for a tungsten anode using zirconium, iodine, and neodymium balanced filters. A mean glandular dose of 1.0 mGy is required to obtain an SNR of 5 in order to detect 1.0 mg/cm 2 iodine in the resulting clutter-free image of a 5 cm thick breast composed of 50% adipose and 50% glandular tissue. In addition to spectral optimization, we carried out phantom measurements to demonstrate the present dual-energy approach for obtaining a clutter-free image, which preferentially shows iodine, of a breast phantom comprising three major components - acrylic spheres, olive oil, and an iodinated contrast agent. The detection of iodine details on the cluttered background originating from the contrast between acrylic spheres and olive oil is analogous to the task of distinguishing contrast agents in a mixture of glandular and adipose tissues

  9. Multitaper spectral method to estimate the elastic thickness of South China: Implications for intracontinental deformation

    Directory of Open Access Journals (Sweden)

    Yangfan Deng

    2014-03-01

    Full Text Available The effective elastic thickness (Te represents the thickness of the elastic layer or the flexural rigidity of the lithosphere, the equivalent of which can be calculated from the spectral analysis of gravity and topographic data. Studies of Te have profound influence on intracontinental deformation, and coupling of the tectonic blocks. In this paper, we use the multitaper spectral estimation method to calculate the coherence between Bouguer gravity and topography data, and to obtain the Te map of South China. Through the process of correction, we discuss the relationships of Te versus heat flow, and Te versus seismicity. The results show that Te distribution of South China is affected by three factors: the original age, which controls the basic feature; the Mesozoic evolution, which affects the Te distribution; and the neotectonic movement, which shaped the final distribution. The crust age has a positive correlation with the first-order Te distribution; thus the Yangtze Craton has a relatively higher Te (about 50 km whereas the Te in Cathaysia block is only 10–20 km. By analysis and comparison among the tectonic models of South China, the Te distribution can be well explained using the flat-subduction model. As is typical with neotectonics, the region with a higher heat flow is related with a lower Te. The seismicity does not have a clear relationship with Te, but the strong seismicity could cause a low Te. Seismogenic layer (Ts has a similar trend as Te in the craton, whereas in other areas the relationship is complex.

  10. The spectral analysis of fuel oils using terahertz radiation and chemometric methods

    Science.gov (United States)

    Zhan, Honglei; Zhao, Kun; Zhao, Hui; Li, Qian; Zhu, Shouming; Xiao, Lizhi

    2016-10-01

    The combustion characteristics of fuel oils are closely related to both engine efficiency and pollutant emissions, and the analysis of oils and their additives is thus important. These oils and additives have been found to generate distinct responses to terahertz (THz) radiation as the result of various molecular vibrational modes. In the present work, THz spectroscopy was employed to identify a number of oils, including lubricants, gasoline and diesel, with different additives. The identities of dozens of these oils could be readily established using statistical models based on principal component analysis. The THz spectra of gasoline, diesel, sulfur and methyl methacrylate (MMA) were acquired and linear fittings were obtained. By using chemometric methods, including back propagation, artificial neural network and support vector machine techniques, typical concentrations of sulfur in gasoline (ppm-grade) could be detected, together with MMA in diesel below 0.5%. The absorption characteristics of the oil additives were also assessed using 2D correlation spectroscopy, and several hidden absorption peaks were discovered. The technique discussed herein should provide a useful new means of analyzing fuel oils with various additives and impurities in a non-destructive manner and therefore will be of benefit to the field of chemical detection and identification.

  11. Enhanced spectral resolution by high-dimensional NMR using the filter diagonalization method and "hidden" dimensions.

    Science.gov (United States)

    Meng, Xi; Nguyen, Bao D; Ridge, Clark; Shaka, A J

    2009-01-01

    High-dimensional (HD) NMR spectra have poorer digital resolution than low-dimensional (LD) spectra, for a fixed amount of experiment time. This has led to "reduced-dimensionality" strategies, in which several LD projections of the HD NMR spectrum are acquired, each with higher digital resolution; an approximate HD spectrum is then inferred by some means. We propose a strategy that moves in the opposite direction, by adding more time dimensions to increase the information content of the data set, even if only a very sparse time grid is used in each dimension. The full HD time-domain data can be analyzed by the filter diagonalization method (FDM), yielding very narrow resonances along all of the frequency axes, even those with sparse sampling. Integrating over the added dimensions of HD FDM NMR spectra reconstitutes LD spectra with enhanced resolution, often more quickly than direct acquisition of the LD spectrum with a larger number of grid points in each of the fewer dimensions. If the extra-dimensions do not appear in the final spectrum, and are used solely to boost information content, we propose the moniker hidden-dimension NMR. This work shows that HD peaks have unmistakable frequency signatures that can be detected as single HD objects by an appropriate algorithm, even though their patterns would be tricky for a human operator to visualize or recognize, and even if digital resolution in an HD FT spectrum is very coarse compared with natural line widths.

  12. The spectral analysis of fuel oils using terahertz radiation and chemometric methods

    International Nuclear Information System (INIS)

    Zhan, Honglei; Zhao, Kun; Xiao, Lizhi; Zhao, Hui; Li, Qian; Zhu, Shouming

    2016-01-01

    The combustion characteristics of fuel oils are closely related to both engine efficiency and pollutant emissions, and the analysis of oils and their additives is thus important. These oils and additives have been found to generate distinct responses to terahertz (THz) radiation as the result of various molecular vibrational modes. In the present work, THz spectroscopy was employed to identify a number of oils, including lubricants, gasoline and diesel, with different additives. The identities of dozens of these oils could be readily established using statistical models based on principal component analysis. The THz spectra of gasoline, diesel, sulfur and methyl methacrylate (MMA) were acquired and linear fittings were obtained. By using chemometric methods, including back propagation, artificial neural network and support vector machine techniques, typical concentrations of sulfur in gasoline (ppm-grade) could be detected, together with MMA in diesel below 0.5%. The absorption characteristics of the oil additives were also assessed using 2D correlation spectroscopy, and several hidden absorption peaks were discovered. The technique discussed herein should provide a useful new means of analyzing fuel oils with various additives and impurities in a non-destructive manner and therefore will be of benefit to the field of chemical detection and identification. (paper)

  13. Comparison of matrix exponential methods for fuel burnup calculations

    International Nuclear Information System (INIS)

    Oh, Hyung Suk; Yang, Won Sik

    1999-01-01

    Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7. (author). 11 refs., 4 figs., 2 tabs

  14. Three-dimensional free boundary calculations using a spectral Green's function method

    International Nuclear Information System (INIS)

    Hirshman, S.P.; van Rij, W.I.; Merkel, P.

    1986-01-01

    The plasma energy W/sub p/ = integral Ω/sub p/(1/2B 2 + p)dV is minimized over a toroidal domain Ω/sub p/ using an inverse representation for the cylindrical coordinates R = ΣR/sub mn/(s)cos(mθ - n zeta) and Z = ΣZ/sub mn/(s)sin(mθ - n zeta), where (s,θ,zeta) are radial, poloidal, and toroidal flux coordinates, respectively. The radial resolution of the MHD equations is significantly improved by separating R and Z into contributions from even and odd poloidal harmonics which are individually analytic near the magnetic axis. A free boundary equilibrium results when Ω/sub p/ is varied to make the total pressure 1/2B 2 + p continuous at the plasma surface Σ/sub p/ and when the vacuum magnetic field B/sub ν/ satisfies the Neumann condition B/sub ν/ x dΣ/sub p/ = 0. The vacuum field is decomposed as B/sub ν/ = B 0 + del Phi, where B 0 is the field arising from plasma currents and external coils and Phi is a single-valued potential necessary to satisfy B/sub ν/ x dΣ/sub p/ = 0 when p not equal to 0. A Green's function method is used to obtain an integral equation over Σ/sub p/ for the scalar magnetic potential Phi = ΣPhi/sub mn/sin(mθ - n zeta). A linear matrix equation is solved for Phi/sub mn/ to determine 1/2 B/sub ν/ 2 on the boundary. Real experimental conditions are simulated by keeping the external and net plasma currents constant during the iteration. Applications to l = 2 stellarator equilibria are presented

  15. Coastline change mapping using a spectral band method and Sobel edge operator

    Science.gov (United States)

    Al-Mansoori, Saeed; Al-Marzouqi, Fatima

    2016-10-01

    Coastline extraction has become an essential activity in wake of the natural disasters taking place in some regions such as tsunami, flooding etc. Salient feature of such catastrophes is lack of reaction time available for combating emergency, thus it is the endeavor of any country to develop constant monitoring mechanism of shorelines. This is a challenging task because of the magnitude of changes taking place to the coastline regularly. Previous research findings highlight a need of formulating automation driven methodology for timely and accurate detection of alterations in the coastline impacting sustainability of mankind operating in the coastal zone. In this study, we propose a new approach for automatic extraction of the coastline using remote sensing data. This approach is composed of three main stages. Firstly, classifying pixels of the image into two categories i.e. land and water body by applying two normalized difference indices i.e. Normalized Difference Vegetation Index (NDVI) and Normalized Difference Water Index (NDWI). Then, the process of binary conversion of classified image takes place using a local threshold method. Finally, the coastline is extracted by applying Sobel edge operator with a pair of (3×3) kernels. The approach is tested using 2.5m DubaiSat-1 (DS1) and DubaiSat-2 (DS2) images captured to detect and monitor the changes occurring along Dubai coastal zone within a period of six years from 2009 till 2015. Experimental results prove that the approach is capable of extracting the coastlines from DS1 and DS2 images with moderate human interaction. The results of the study show an increase of 6% in Dubai shoreline resulting on account of numerous man-made infrastructure development projects in tourism and allied sectors.

  16. Improvement to the PhytoDOAS method for identification of coccolithophores using hyper-spectral satellite data

    Directory of Open Access Journals (Sweden)

    A. Sadeghi

    2012-11-01

    Full Text Available The goal of this study was to improve PhytoDOAS, which is a new retrieval method for quantitative identification of major phytoplankton functional types (PFTs using hyper-spectral satellite data. PhytoDOAS is an extension of the Differential Optical Absorption Spectroscopy (DOAS, a method for detection of atmospheric trace gases, developed for remote identification of oceanic phytoplankton groups. Thus far, PhytoDOAS has been successfully exploited to identify cyanobacteria and diatoms over the global ocean from SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY hyper-spectral data. This study aimed to improve PhytoDOAS for remote identification of coccolithophores, another functional group of phytoplankton. The main challenge for retrieving more PFTs by PhytoDOAS is to overcome the correlation effects between different PFT absorption spectra. Different PFTs are composed of different types and amounts of pigments, but also have pigments in common, e.g. chl a, causing correlation effects in the usual performance of the PhytoDOAS retrieval. Two ideas have been implemented to improve PhytoDOAS for the PFT retrieval of more phytoplankton groups. Firstly, using the fourth-derivative spectroscopy, the peak positions of the main pigment components in each absorption spectrum have been derived. After comparing the corresponding results of major PFTs, the optimized fit-window for the PhytoDOAS retrieval of each PFT was determined. Secondly, based on the results from derivative spectroscopy, a simultaneous fit of PhytoDOAS has been proposed and tested for a selected set of PFTs (coccolithophores, diatoms and dinoflagellates within an optimized fit-window, proven by spectral orthogonality tests. The method was then applied to the processing of SCIAMACHY data over the year 2005. Comparisons of the PhytoDOAS coccolithophore retrievals in 2005 with other coccolithophore-related data showed similar patterns in their

  17. A NEW MULTI-SPECTRAL THRESHOLD NORMALIZED DIFFERENCE WATER INDEX (MST-NDWI WATER EXTRACTION METHOD – A CASE STUDY IN YANHE WATERSHED

    Directory of Open Access Journals (Sweden)

    Y. Zhou

    2018-05-01

    Full Text Available Accurate remote sensing water extraction is one of the primary tasks of watershed ecological environment study. Since the Yanhe water system has typical characteristics of a small water volume and narrow river channel, which leads to the difficulty for conventional water extraction methods such as Normalized Difference Water Index (NDWI. A new Multi-Spectral Threshold segmentation of the NDWI (MST-NDWI water extraction method is proposed to achieve the accurate water extraction in Yanhe watershed. In the MST-NDWI method, the spectral characteristics of water bodies and typical backgrounds on the Landsat/TM images have been evaluated in Yanhe watershed. The multi-spectral thresholds (TM1, TM4, TM5 based on maximum-likelihood have been utilized before NDWI water extraction to realize segmentation for a division of built-up lands and small linear rivers. With the proposed method, a water map is extracted from the Landsat/TM images in 2010 in China. An accuracy assessment is conducted to compare the proposed method with the conventional water indexes such as NDWI, Modified NDWI (MNDWI, Enhanced Water Index (EWI, and Automated Water Extraction Index (AWEI. The result shows that the MST-NDWI method generates better water extraction accuracy in Yanhe watershed and can effectively diminish the confusing background objects compared to the conventional water indexes. The MST-NDWI method integrates NDWI and Multi-Spectral Threshold segmentation algorithms, with richer valuable information and remarkable results in accurate water extraction in Yanhe watershed.

  18. Spectral methods for study of the G-protein-coupled receptor rhodopsin: I. Vibrational and electronic spectroscopy

    Science.gov (United States)

    Struts, A. V.; Barmasov, A. V.; Brown, M. F.

    2015-05-01

    Here we review the application of modern spectral methods for the study of G-protein-coupled receptors (GPCRs) using rhodopsin as a prototype. Because X-ray analysis gives us immobile snapshots of protein conformations, it is imperative to apply spectroscopic methods for elucidating their function: vibrational (Raman, FTIR), electronic (UV-visible absorption, fluorescence) spectroscopies, and magnetic resonance (electron paramagnetic resonance, EPR), and nuclear magnetic resonance (NMR). In the first of the two companion articles, we discuss the application of optical spectroscopy for studying rhodopsin in a membrane environment. Information is obtained regarding the time-ordered sequence of events in rhodopsin activation. Isomerization of the chromophore and deprotonation of the retinal Schiff base leads to a structural change of the protein involving the motion of helices H5 and H6 in a pH-dependent process. Information is obtained that is unavailable from X-ray crystallography, which can be combined with spectroscopic studies to achieve a more complete understanding of GPCR function.

  19. Numerical Simulations of Microseisms in a NE Atlantic 3D Geological Model, using a Spectral-Element Method

    Science.gov (United States)

    Ying, Yingzi; Bean, Christopher J.

    2014-05-01

    Ocean-generated microseisms are faint Earth tremors associated with the interaction between ocean water waves and the solid Earth. The microseism noise recorded as low frequency ground vibrations by seismometers contains significant information about the Earth's interior and the sea states. In this work, we first aim to investigate the forward propagation of microseisms in a deep-ocean environment. We employ a 3D North-East Atlantic geological model and simulate wave propagation in a coupled fluid-solid domain, using a spectral-element method. The aim is to investigate the effects of the continental shelf on microseism wave propagation. A second goal of this work is to perform noise simulation to calculate synthetic ensemble averaged cross-correlations of microseism noise signals with time reversal method. The algorithm can relieve computational cost by avoiding time stacking and get cross-correlations between the designated master station and all the remaining slave stations, at one time. The origins of microseisms are non-uniform, so we also test the effect of simulated noise source distribution on the determined cross-correlations.

  20. Automated 3-D method for the correction of axial artifacts in spectral-domain optical coherence tomography images

    Science.gov (United States)

    Antony, Bhavna; Abràmoff, Michael D.; Tang, Li; Ramdas, Wishal D.; Vingerling, Johannes R.; Jansonius, Nomdo M.; Lee, Kyungmoo; Kwon, Young H.; Sonka, Milan; Garvin, Mona K.

    2011-01-01

    The 3-D spectral-domain optical coherence tomography (SD-OCT) images of the retina often do not reflect the true shape of the retina and are distorted differently along the x and y axes. In this paper, we propose a novel technique that uses thin-plate splines in two stages to estimate and correct the distinct axial artifacts in SD-OCT images. The method was quantitatively validated using nine pairs of OCT scans obtained with orthogonal fast-scanning axes, where a segmented surface was compared after both datasets had been corrected. The mean unsigned difference computed between the locations of this artifact-corrected surface after the single-spline and dual-spline correction was 23.36 ± 4.04 μm and 5.94 ± 1.09 μm, respectively, and showed a significant difference (p < 0.001 from two-tailed paired t-test). The method was also validated using depth maps constructed from stereo fundus photographs of the optic nerve head, which were compared to the flattened top surface from the OCT datasets. Significant differences (p < 0.001) were noted between the artifact-corrected datasets and the original datasets, where the mean unsigned differences computed over 30 optic-nerve-head-centered scans (in normalized units) were 0.134 ± 0.035 and 0.302 ± 0.134, respectively. PMID:21833377

  1. Band-gap analysis of a novel lattice with a hierarchical periodicity using the spectral element method

    Science.gov (United States)

    Wu, Zhijing; Li, Fengming; Zhang, Chuanzeng

    2018-05-01

    Inspired by the hierarchical structures of butterfly wing surfaces, a new kind of lattice structures with a two-order hierarchical periodicity is proposed and designed, and the band-gap properties are investigated by the spectral element method (SEM). The equations of motion of the whole structure are established considering the macro and micro periodicities of the system. The efficiency of the SEM is exploited in the modeling process and validated by comparing the results with that of the finite element method (FEM). Based on the highly accurate results in the frequency domain, the dynamic behaviors of the proposed two-order hierarchical structures are analyzed. An original and interesting finding is the existence of the distinct macro and micro stop-bands in the given frequency domain. The mechanisms for these two types of band-gaps are also explored. Finally, the relations between the hierarchical periodicities and the different types of the stop-bands are investigated by analyzing the parametrical influences.

  2. Biopsy Diagnosis of Oral Carcinoma by the Combination of Morphological and Spectral Methods Based on Embedded Relay Lens Microscopic Hyperspectral Imaging System.

    Science.gov (United States)

    Ou-Yang, Mang; Hsieh, Yao-Fang; Lee, Cheng-Chung

    Cytopathological examination through biopsy is very important for carcinoma detection. The embedded relay lens microscopic hyperspectral imaging system (ERL-MHIS) provides a morphological image of a biopsy sample and the spectrum of each pixel in the image simultaneously. Based on the ERL-MHIS, this work develops morphological and spectral methods to diagnose oral carcinoma biopsy. In morphological discrimination, the fractal dimension method is applied to differentiate between normal and abnormal tissues. In spectral identification, normal and cancerous cells are distinguished using five methods. However, the spectra of normal and cancerous cells vary with patient. The diagnostic performances of the five methods are thus not ideal. Hence, the proposed cocktail approach is used to determine the effectiveness of the spectral methods in correlating with the sampling conditions. And then we use a combination of effective spectral methods according to the sample conditions for diagnosing a sample. A total of 68 biopsies from 34 patients are analyzed using the ERL-MHIS. The results demonstrate a sensitivity of 90 ± 4.53 % and a specificity of 87.8 ± 5.21 %. Furthermore, in our survey, this system is the first time utilized to study oral carcinoma biopsies.

  3. DO WE REALLY KNOW THE DUST? SYSTEMATICS AND UNCERTAINTIES OF THE MID-INFRARED SPECTRAL ANALYSIS METHODS

    International Nuclear Information System (INIS)

    Juhasz, A.; Henning, Th.; Bouwman, J.; Dullemond, C. P.; Pascucci, I.; Apai, D.

    2009-01-01

    The spectral region around 10 μm, showing prominent emission bands from various dust species is commonly used for the evaluation of the chemical composition of protoplanetary dust. Different methods of analysis have been proposed for this purpose, but so far, no comparative test has been performed to test the validity of their assumptions. In this paper, we evaluate how good the various methods are in deriving the chemical composition of dust grains from infrared spectroscopy. Synthetic spectra of disk models with different geometries and central sources were calculated, using a two-dimensional radiative transfer code. These spectra were then fitted in a blind test by four spectral decomposition methods. We studied the effect of disk structure (flared versus flat), inclination angle, size of an inner disk hole, and stellar luminosity on the fitted chemical composition. Our results show that the dust parameters obtained by all methods deviate systematically from the input data of the synthetic spectra. The dust composition fitted by the new two-layer temperature distribution method, described in this paper, differs the least from the input dust composition and the results show the weakest systematic effects. The reason for the deviations of the results given by the previously used methods lies in their simplifying assumptions. Due to the radial extent of the 10 μm emitting region there is dust at different temperatures contributing to the flux in the silicate feature. Therefore, the assumption of a single averaged grain temperature can be a strong limitation of the previously used methods. The continuum below the feature can consist of multiple components (e.g., star, inner rim, and disk midplane), which cannot simply be described by a Planck function at a single temperature. In addition, the optically thin emission of 'featureless' grains (e.g., carbon in the considered wavelength range) produces a degeneracy in the models with the optically thick emission of the

  4. Application of the finite-element method and the eigenmode expansion method to investigate the periodic and spectral characteristic of discrete phase-shift fiber Bragg grating

    Science.gov (United States)

    He, Yue-Jing; Hung, Wei-Chih; Syu, Cheng-Jyun

    2017-12-01

    The finite-element method (FEM) and eigenmode expansion method (EEM) were adopted to analyze the guided modes and spectrum of phase-shift fiber Bragg grating at five phase-shift degrees (including zero, 1/4π, 1/2π, 3/4π, and π). In previous studies on optical fiber grating, conventional coupled-mode theory was crucial. This theory contains abstruse knowledge about physics and complex computational processes, and thus is challenging for users. Therefore, a numerical simulation method was coupled with a simple and rigorous design procedure to help beginners and users to overcome difficulty in entering the field; in addition, graphical simulation results were presented. To reduce the difference between the simulated context and the actual context, a perfectly matched layer and perfectly reflecting boundary were added to the FEM and the EEM. When the FEM was used for grid cutting, the object meshing method and the boundary meshing method proposed in this study were used to effectively enhance computational accuracy and substantially reduce the time required for simulation. In summary, users can use the simulation results in this study to easily and rapidly design an optical fiber communication system and optical sensors with spectral characteristics.

  5. Spectral gamuts and spectral gamut mapping

    Science.gov (United States)

    Rosen, Mitchell R.; Derhak, Maxim W.

    2006-01-01

    All imaging devices have two gamuts: the stimulus gamut and the response gamut. The response gamut of a print engine is typically described in CIE colorimetry units, a system derived to quantify human color response. More fundamental than colorimetric gamuts are spectral gamuts, based on radiance, reflectance or transmittance units. Spectral gamuts depend on the physics of light or on how materials interact with light and do not involve the human's photoreceptor integration or brain processing. Methods for visualizing a spectral gamut raise challenges as do considerations of how to utilize such a data-set for producing superior color reproductions. Recent work has described a transformation of spectra reduced to 6-dimensions called LabPQR. LabPQR was designed as a hybrid space with three explicit colorimetric axes and three additional spectral reconstruction axes. In this paper spectral gamuts are discussed making use of LabPQR. Also, spectral gamut mapping is considered in light of the colorimetric-spectral duality of the LabPQR space.

  6. A case study of forward calculations of the gravity anomaly by spectral method for a three-dimensional parameterised fault model

    Science.gov (United States)

    Xu, Weimin; Chen, Shi

    2018-02-01

    Spectral methods provide many advantages for calculating gravity anomalies. In this paper, we derive a kernel function for a three-dimensional (3D) fault model in the wave number domain, and present the full Fortran source code developed for the forward computation of the gravity anomalies and related derivatives obtained from the model. The numerical error and computing speed obtained using the proposed spectral method are compared with those obtained using a 3D rectangular prism model solved in the space domain. The error obtained using the spectral method is shown to be dependent on the sequence length employed in the fast Fourier transform. The spectral method is applied to some examples of 3D fault models, and is demonstrated to be a straightforward and alternative computational approach to enhance computational speed and simplify the procedures for solving many gravitational potential forward problems involving complicated geological models. The proposed method can generate a great number of feasible geophysical interpretations based on a 3D model with only a few variables, and can thereby improve the efficiency of inversion.

  7. A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

    Science.gov (United States)

    Zhan, Lei; Xiong, Juntao; Liu, Feng

    2016-05-01

    The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

  8. The Application of Spectral Analysis of Surface Wave (SASW) Method as a New Rock Mass Classification Technique in Engineering Geology

    International Nuclear Information System (INIS)

    Abdul Rahim Samsuddin; Abdul Ghani Rafek; Umar Hamzah; Suharsono; Khairul Anuar Mohd Nayan

    2008-01-01

    Spectral analysis of surface waves (SASW) is a seismic method that uses the dispersive characteristics of Rayleigh waves propagating through layered material to evaluate S-wave velocity profile. The SASW is an in situ non intrusive method for geotechnical site characterization which is cost effective as compared to the conventional drilling method. In this study, a total of 20 stations from 13 sites were selected. A software (WINSASW 2.0) was used for the inversion process to produce S-wave velocity versus depth profiles. These profiles were then separately analyzed in relation to several engineering rock mass geological parameters such as stiffness, rock quality designation (RQD), anisotropy and the excavability properties. The analysis of the SASW data was based on the assumption that the rock mass is an isotropic homogeneous material with various intensity of discontinuity which influenced the velocity of surface wave propagation within the rock mass. Measurement of dynamic soil properties was carried out employing the shear wave velocities and the N values of the Standard Penetration Test (N SPT ) from borehole data. A new linear equation V s = 4.44 N SPT + 213.84 which relates S-wave and N SPT was deduced. An empirical equation is also proposed to calculate Rock Quality Designation (RQD) values based on S-wave velocity derived from SASW and that of ultrasonic tests. The result of this equation was found to be less than 10% in comparison to the RQD obtained from actual borehole data. An isotropic analysis of the rock mass was carried out using S-wave velocities derived from SASW measurements in four directions. The plots of S-wave - ultrasonic velocity ratio versus ultrasonic velocity were used to evaluate the excavability properties of rock mass. Five classes of rock mass excavability curves were finally proposed in relation to easy digging, easy ripping, hard ripping, hydraulic breaking and blasting. (author)

  9. Modeling of the Through-the-Thickness Electric Potentials of a Piezoelectric Bimorph Using the Spectral Element Method

    Directory of Open Access Journals (Sweden)

    Xingjian Dong

    2014-02-01

    Full Text Available An efficient spectral element (SE with electric potential degrees of freedom (DOF is proposed to investigate the static electromechanical responses of a piezoelectric bimorph for its actuator and sensor functions. A sublayer model based on the piecewise linear approximation for the electric potential is used to describe the nonlinear distribution of electric potential through the thickness of the piezoelectric layers. An equivalent single layer (ESL model based on first-order shear deformation theory (FSDT is used to describe the displacement field. The Legendre orthogonal polynomials of order 5 are used in the element interpolation functions. The validity and the capability of the present SE model for investigation of global and local responses of the piezoelectric bimorph are confirmed by comparing the present solutions with those obtained from coupled 3-D finite element (FE analysis. It is shown that, without introducing any higher-order electric potential assumptions, the current method can accurately describe the distribution of the electric potential across the thickness even for a rather thick bimorph. It is revealed that the effect of electric potential is significant when the bimorph is used as sensor while the effect is insignificant when the bimorph is used as actuator, and therefore, the present study may provide a better understanding of the nonlinear induced electric potential for bimorph sensor and actuator.

  10. Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

    Science.gov (United States)

    Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

    2017-05-01

    The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

  11. A hybrid artificial bee colony algorithm and pattern search method for inversion of particle size distribution from spectral extinction data

    Science.gov (United States)

    Wang, Li; Li, Feng; Xing, Jian

    2017-10-01

    In this paper, a hybrid artificial bee colony (ABC) algorithm and pattern search (PS) method is proposed and applied for recovery of particle size distribution (PSD) from spectral extinction data. To be more useful and practical, size distribution function is modelled as the general Johnson's ? function that can overcome the difficulty of not knowing the exact type beforehand encountered in many real circumstances. The proposed hybrid algorithm is evaluated through simulated examples involving unimodal, bimodal and trimodal PSDs with different widths and mean particle diameters. For comparison, all examples are additionally validated by the single ABC algorithm. In addition, the performance of the proposed algorithm is further tested by actual extinction measurements with real standard polystyrene samples immersed in water. Simulation and experimental results illustrate that the hybrid algorithm can be used as an effective technique to retrieve the PSDs with high reliability and accuracy. Compared with the single ABC algorithm, our proposed algorithm can produce more accurate and robust inversion results while taking almost comparative CPU time over ABC algorithm alone. The superiority of ABC and PS hybridization strategy in terms of reaching a better balance of estimation accuracy and computation effort increases its potentials as an excellent inversion technique for reliable and efficient actual measurement of PSD.

  12. Investigation on the pH-dependent binding of Eosin Y and bovine serum albumin by spectral methods

    International Nuclear Information System (INIS)

    Gao Dejiang; Tian Yuan; Liang Fanghui; Jin Danhong; Chen Yanhua; Zhang Hanqi; Yu Aimin

    2007-01-01

    In this paper, the pH-dependent binding of Eosin Y and bovine serum albumin (BSA) was investigated by spectral methods, including resonance light scattering (RLS), absorption and fluorescence spectrometry. Due to the pH-dependent structure of Eosin Y and BSA, the interaction of BSA and Eosin Y depended on the solution pH value. Especially at pH 2.6 and 9.2, the RLS intensity of BSA was obviously enhanced in the presence of Eosin Y. However, the fluorescence intensity of BSA was quenched in the presence of Eosin Y. To fully understand the pH-dependent binding of BSA and Eosin Y, fluorescence quenching technique was introduced. Based on the fluorescence data obtained, the style of binding, the binding constant, the binding site number and the thermodynamic parameters for the interaction of BSA and Eosin Y were studied. Based on Foerster non-radiation energy transfer theory, the distance between donor BSA and acceptor Eosin Y was obtained

  13. SQDFT: Spectral Quadrature method for large-scale parallel O(N) Kohn-Sham calculations at high temperature

    Science.gov (United States)

    Suryanarayana, Phanish; Pratapa, Phanisri P.; Sharma, Abhiraj; Pask, John E.

    2018-03-01

    We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for O(N) Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect O(N) scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.

  14. Investigation on the pH-dependent binding of Eosin Y and bovine serum albumin by spectral methods

    Energy Technology Data Exchange (ETDEWEB)

    Gao Dejiang; Tian Yuan [College of Chemistry, Jilin University, Changchun 130012 (China); Liang Fanghui; Jin Danhong [Changchun Medical College, Changchun 130031 (China); Chen Yanhua; Zhang Hanqi [College of Chemistry, Jilin University, Changchun 130012 (China); Yu Aimin [College of Chemistry, Jilin University, Changchun 130012 (China)], E-mail: analchem@mail.jlu.edu.cn

    2007-12-15

    In this paper, the pH-dependent binding of Eosin Y and bovine serum albumin (BSA) was investigated by spectral methods, including resonance light scattering (RLS), absorption and fluorescence spectrometry. Due to the pH-dependent structure of Eosin Y and BSA, the interaction of BSA and Eosin Y depended on the solution pH value. Especially at pH 2.6 and 9.2, the RLS intensity of BSA was obviously enhanced in the presence of Eosin Y. However, the fluorescence intensity of BSA was quenched in the presence of Eosin Y. To fully understand the pH-dependent binding of BSA and Eosin Y, fluorescence quenching technique was introduced. Based on the fluorescence data obtained, the style of binding, the binding constant, the binding site number and the thermodynamic parameters for the interaction of BSA and Eosin Y were studied. Based on Foerster non-radiation energy transfer theory, the distance between donor BSA and acceptor Eosin Y was obtained.

  15. A method of noise reduction in heterodyne interferometric vibration metrology by combining auto-correlation analysis and spectral filtering

    Science.gov (United States)

    Hao, Hongliang; Xiao, Wen; Chen, Zonghui; Ma, Lan; Pan, Feng

    2018-01-01

    Heterodyne interferometric vibration metrology is a useful technique for dynamic displacement and velocity measurement as it can provide a synchronous full-field output signal. With the advent of cost effective, high-speed real-time signal processing systems and software, processing of the complex signals encountered in interferometry has become more feasible. However, due to the coherent nature of the laser sources, the sequence of heterodyne interferogram are corrupted by a mixture of coherent speckle and incoherent additive noise, which can severely degrade the accuracy of the demodulated signal and the optical display. In this paper, a new heterodyne interferometric demodulation method by combining auto-correlation analysis and spectral filtering is described leading to an expression for the dynamic displacement and velocity of the object under test that is significantly more accurate in both the amplitude and frequency of the vibrating waveform. We present a mathematical model of the signals obtained from interferograms that contain both vibration information of the measured objects and the noise. A simulation of the signal demodulation process is presented and used to investigate the noise from the system and external factors. The experimental results show excellent agreement with measurements from a commercial Laser Doppler Velocimetry (LDV).

  16. Uncertainty of long-term CO2 flux estimates due to the choice of the spectral correction method

    Science.gov (United States)

    Ibrom, Andreas; Geißler, Simon; Pilegaard, Kim

    2010-05-01

    The eddy covariance system at the Danish beech forest long-term flux observation site at Sorø has been intensively examined. Here we investigate which systematic and non-systematic effects the choice of the spectral correction method has on long-term net CO2 flux estimates and their components. Ibrom et al. (2007) gave an overview over different ways to correct for low-pass filtering of the atmospheric turbulent signal by a closed path eddy covariance system. They used degraded temperature time series for spectral correction of low-pass filtered signals. In this new study, correction for high-pass filtering was also included, which made it anyway necessary to use model co-spectra. We compared different ways of adapting different kinds of model co-spectra to the wealth of 14 years high frequency raw data. As the trees grew, the distance between the sonic anemometer and the displacement height decreased over time. The study enabled us to compare the two approaches and different variants of them to give recommendations on their use. The analysis showed that model spectra should not be derived from co-spectra between the vertical wind speed (w) and the scalars measured with the closed path system, i.e. CO2 and H20 concentrations, but instead with sonic temperature (T) w cospectra, to avoid low-pass filtering effects on the estimation of the co-spectral peak frequency (fx). This concern was already expressed earlier in the above mentioned study, but here we show the quantitative effects. The wT co-spectra did not show any height effect on fx as it was suggested in generally used parameterizations. A possible reason for this difference is that measurements, like in all forest flux sites, took place in the roughness sub-layer and not in the inertial sub-layer. At the same time the shape of the relationship between fx and the stability parameter ? differed much from that of often used parameterizations (e.g. from Horst, 1997). The shift of fx towards higher frequencies at

  17. On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and Particle-in-Cell methods

    NARCIS (Netherlands)

    E. Camporeale (Enrico); G.L. Delzanno; B.K. Bergen; J.D. Moulton

    2016-01-01

    htmlabstractWe describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time

  18. method for ranging and noise reduction of low coherence interferometry LCI and optical coherence tomography OCT signals by parallel detection of spectral bands

    NARCIS (Netherlands)

    Boer, JF De; Tearney, G. J.; Bouma, BE

    2008-01-01

    Apparatus and method for increasing the sensitivity in the detection of optical coherence tomography and loW coher ence interferometry (“LCI”) signals by detecting a parallel set of spectral bands, each band being a unique combination of optical frequencies. The LCI broad bandwidth source is split

  19. Universal bounds on spectral measures of one-dimensional Schrödinger operators

    CERN Document Server

    Remling, C

    2002-01-01

    Consider a Schrödinger operator $H=-d^2/dx^2+V(x)$ on $L_2(0,\\infty)$ and suppose that an initial piece of the potential $V(x)$, $0spectral measure of intervals with a certain minimum length. This length scale is set by the eigenvalues of the problems on $[0,N]$. So in a sense (and perhaps somewhat surprisingly) the behavior of $V(x)$ becomes less important if $x$ grows. The results of this paper are developments of classical work of Chebyshev and Markov on orthogonal polynomials.

  20. The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

    KAUST Repository

    Schillinger, Dominik

    2013-07-01

    The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed. © 2013 Elsevier Ltd.

  1. [Experimental Methods and Result Analysis of a Variety of Spectral Reflectance Properties of the Thin Oil Film].

    Science.gov (United States)

    Ye, Zhou; Liu, Li; Wei, Chuan-xin; Gu, Qun; An, Ping-ao; Zhao, Yue-jiao; Yin, Da-yi

    2015-06-01

    In order to analysis the oil spill situation based on the obtained data in airborne aerial work, it's needed to get the spectral reflectance characteristics of the oil film of different oils and thickness as support and to select the appropriate operating band. An experiment is set up to measure the reflectance spectroscopy from ultraviolet to near-infrared for the film of five target samples, which means petrol, diesel, lubricating oil, kerosene and fossil, using spectral measurement device. The result is compared with the reflectance spectra of water in the same experimental environment, which shows that the spectral reflection characteristics of the oil film are related to the thickness and the type of the oil film. In case of the same thickness, the spectral reflectance curve of different types of film is far different, and for the same type of film, the spectral reflectance curve changes accordingly with the change of film thickness, therefore in terms of the single film, different film thickness can be distinguished by reflectance curves. It also shows that in terms of the same film thickness, the reflectance of diesel, kerosene, lubricants reaches peak around 380 nm wavelength, obviously different from the reflectance of water, and that the reflectance of crude oil is far less than that of water in more than 340 nm wavelength, and the obtained reflection spectrum can be used to distinguish between different types of oil film to some extent. The experiment covers main types of spilled oil, with data comprehensively covering commonly used detect spectral bands, and quantitative description of the spectral reflectance properties of film. It provides comprehensive theoretical and data support for the selection of airborne oil spill detection working band and the detection and analysis of water-surface oil spill.

  2. A calibration method for the measurement of IR detector spectral responses using a FTIR spectrometer equipped with a DTGS reference cell

    Science.gov (United States)

    Gravrand, Olivier; Wlassow, J.; Bonnefond, L.

    2014-07-01

    transfert function of the DTGS has to be qualified and taken into account. The usual way is to measure it directly by means of an optical shopper and a locking amplifier for different shopping frequencies. We present here an alternative method to estimate this DTGS transfer function, based on the fact that a FTIR continuous scan interfergram contains the different spectral frequencies of interest. Such a calibration method doesn't need a specific setup as it can be performed in standard configuration, playing only with spectrometer parameters. It allows for the precise estimation of detector spectral shapes. However, this measurement is not absolute and the peak response needs therefore to be estimated using a calibrated black body cavity. The method, its results and limits is presented and discussed for a set of different DTGS cells.

  3. Method for estimation of the spectral distribution that influence electric power of PV module; Taiyo denchi shutsuryoku ni eikyo wo ataeru bunko nissha bunpu no suiteiho

    Energy Technology Data Exchange (ETDEWEB)

    Yamagami, Y.; Tani, T. [Science University of Tokyo, Tokyo (Japan)

    1997-11-25

    A method was proposed for estimating the spectral distribution using air mass, precipitable water, and clear indexes which are generally obtainable, and a comparative study was made between the spectral distribution obtained by this method and the measured data using output power of PV modules, etc. as indexes. When solar light comes into the atmosphere, it dissipates receiving scattering/absorption by various gases and aerosols. Direct light component and scattered light component which arrive at the earth surface become functions of air mass and precipitable water. The wavelength distribution of scattered light in cloudy sky is not dependent upon air mass, but affected strongly by absorption band by steam of clouds. By relational equations considered of these, output power and short-circuit current of PV modules are obtained to make a comparison with the measured data. As a result, it was found that this method estimated the spectral distribution with accuracy. Further, seasonal changes in the spectral distribution were well reproduced. The simulation of the module output in Sapporo and Okinawa brought a result that the output in Okinawa is 1.93% larger than in Okinawa. 5 refs., 5 figs., 6 tabs.

  4. Rectangular spectral collocation

    KAUST Repository

    Driscoll, Tobin A.; Hale, Nicholas

    2015-01-01

    Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon

  5. A theoretical-experimental methodology for assessing the sensitivity of biomedical spectral imaging platforms, assays, and analysis methods.

    Science.gov (United States)

    Leavesley, Silas J; Sweat, Brenner; Abbott, Caitlyn; Favreau, Peter; Rich, Thomas C

    2018-01-01

    Spectral imaging technologies have been used for many years by the remote sensing community. More recently, these approaches have been applied to biomedical problems, where they have shown great promise. However, biomedical spectral imaging has been complicated by the high variance of biological data and the reduced ability to construct test scenarios with fixed ground truths. Hence, it has been difficult to objectively assess and compare biomedical spectral imaging assays and technologies. Here, we present a standardized methodology that allows assessment of the performance of biomedical spectral imaging equipment, assays, and analysis algorithms. This methodology incorporates real experimental data and a theoretical sensitivity analysis, preserving the variability present in biomedical image data. We demonstrate that this approach can be applied in several ways: to compare the effectiveness of spectral analysis algorithms, to compare the response of different imaging platforms, and to assess the level of target signature required to achieve a desired performance. Results indicate that it is possible to compare even very different hardware platforms using this methodology. Future applications could include a range of optimization tasks, such as maximizing detection sensitivity or acquisition speed, providing high utility for investigators ranging from design engineers to biomedical scientists. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  6. Structural and vibrational spectral investigations of melaminium glutarate monohydrate by FTIR, FT-Raman and DFT methods

    Science.gov (United States)

    Arjunan, V.; Marchewka, M. K.; Raj, Arushma; Yang, Haifeng; Mohan, S.

    2015-01-01

    Melaminium glutarate monohydrate has been synthesised and FTIR and FT-Raman spectral investigations are carried out. The molecular geometry and vibrational frequencies of melaminium glutarate monohydrate in the ground state have been determined by using B3LYP method with 6-31++G**, 6-31++G and cc-pVDZ basis sets. The stability of the system, inter molecular hydrogen bonding and the electron donor-acceptor interactions of the complex have been investigated by using natural bonding orbital analysis. It reveals that the Nsbnd H⋯O and Osbnd H⋯O intermolecular interactions significantly influence crystal packing of this molecular complex. The glutarate anion forms hydrogen bonds to the melaminium cation as the proton donor of the type Nsbnd H⋯O with a distance (N⋯O) = 2.51 Å. It is also linked by other hydrogen bonds to the water molecule of the type Osbnd H⋯O with (O⋯O) = 2.82 Å and to the amino (sbnd NH2) group of melaminium cation of the type Nsbnd H⋯O with (N⋯O) = 2.82 Å as the proton acceptor. The electrostatic potential of the complex is in the range +1.892e × 10-2 to -1.892e × 10-2. The limits of total electron density of the complex is +6.679e × 10-2 to -6.679e × 10-2.

  7. Structural and vibrational spectral investigations of melaminium glutarate monohydrate by FTIR, FT-Raman and DFT methods.

    Science.gov (United States)

    Arjunan, V; Marchewka, M K; Raj, Arushma; Yang, Haifeng; Mohan, S

    2015-01-25

    Melaminium glutarate monohydrate has been synthesised and FTIR and FT-Raman spectral investigations are carried out. The molecular geometry and vibrational frequencies of melaminium glutarate monohydrate in the ground state have been determined by using B3LYP method with 6-31++G(**), 6-31++G and cc-pVDZ basis sets. The stability of the system, inter molecular hydrogen bonding and the electron donor-acceptor interactions of the complex have been investigated by using natural bonding orbital analysis. It reveals that the N-H⋯O and O-H⋯O intermolecular interactions significantly influence crystal packing of this molecular complex. The glutarate anion forms hydrogen bonds to the melaminium cation as the proton donor of the type N-H⋯O with a distance (N⋯O)=2.51 Å. It is also linked by other hydrogen bonds to the water molecule of the type O-H⋯O with (O⋯O)=2.82 Å and to the amino (NH2) group of melaminium cation of the type N-H⋯O with (N⋯O)=2.82 Å as the proton acceptor. The electrostatic potential of the complex is in the range +1.892e×10(-2) to -1.892e×10(-2). The limits of total electron density of the complex is +6.679e×10(-2) to -6.679e×10(-2). Copyright © 2014 Elsevier B.V. All rights reserved.

  8. Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

    International Nuclear Information System (INIS)

    Oliveira, J.V.P. de; Cardona, A.V.; Vilhena, M.T.M.B. de

    2002-01-01

    In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations

  9. Dispersive heterodyne probing method for laser frequency stabilization based on spectral hole burning in rare-earth doped crystals

    DEFF Research Database (Denmark)

    Gobron, Olivier; Jung, K.; Galland, N.

    2017-01-01

    Frequency-locking a laser to a spectral hole in rare-earth doped crystals at cryogenic temperature has been shown to be a promising alternative to the use of high finesse Fabry-Perot cavities when seeking a very high short term stability laser (M. J. Thorpe et al., Nature Photonics 5, 688 (2011......)). We demonstrate here a novel technique for achieving such stabilization, based on generating a heterodyne beat-note between a master laser and a slave laser whose dephasing caused by propagation near a spectral hole generate the error signal of the frequency lock. The master laser is far detuned from...

  10. A spectral nodal method for eigenvalue S{sub N} transport problems in two-dimensional rectangular geometry for energy multigroup nuclear reactor global calculations

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Programa de Pos-Graduacao em Modelagem Computacional

    2015-07-01

    A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S{sub N}) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S{sub N} discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S{sub N} transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S{sub N} eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)

  11. A spectral nodal method for eigenvalue SN transport problems in two-dimensional rectangular geometry for energy multigroup nuclear reactor global calculations

    International Nuclear Information System (INIS)

    Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C.

    2015-01-01

    A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S N ) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S N discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S N transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S N eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)

  12. NURBS-SEM: a hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces

    OpenAIRE

    Pitton, Giuseppe; Heltai, Luca

    2018-01-01

    Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p

  13. Automated 3-D method for the correction of axial artifacts in spectral-domain optical coherence tomography images

    NARCIS (Netherlands)

    B. Antony (Bhavna); M.D. Abràmoff (Michael); L. Tang (Li); W.D. Ramdas (Wishal); J.R. Vingerling (Hans); N.M. Jansonius (Nomdo); K. Lee (Kyungmoo); Y.H. Kwon (Young); M. Sonka (Milan); M.K. Garvin (Mona)

    2011-01-01

    textabstractThe 3-D spectral-domain optical coherence tomography (SD-OCT) images of the retina often do not reflect the true shape of the retina and are distorted differently along the x and y axes. In this paper, we propose a novel technique that uses thin-plate splines in two stages to estimate

  14. Automated 3-D method for the correction of axial artifacts in spectral-domain optical coherence tomography images

    NARCIS (Netherlands)

    Antony, Bhavna; Abramoff, Michael D.; Tang, Li; Ramdas, Wishal D.; Vingerling, Johannes R.; Jansonius, Nomdo M.; Lee, Kyungmoo; Kwon, Young H.; Sonka, Milan; Garvin, Mona K.

    2011-01-01

    The 3-D spectral-domain optical coherence tomography (SD-OCT) images of the retina often do not reflect the true shape of the retina and are distorted differently along the x and y axes. In this paper, we propose a novel technique that uses thin-plate splines in two stages to estimate and correct

  15. Spectral stratigraphy

    Science.gov (United States)

    Lang, Harold R.

    1991-01-01

    A new approach to stratigraphic analysis is described which uses photogeologic and spectral interpretation of multispectral remote sensing data combined with topographic information to determine the attitude, thickness, and lithology of strata exposed at the surface. The new stratigraphic procedure is illustrated by examples in the literature. The published results demonstrate the potential of spectral stratigraphy for mapping strata, determining dip and strike, measuring and correlating stratigraphic sequences, defining lithofacies, mapping biofacies, and interpreting geological structures.

  16. Robust chemical and chemical-resistant material detection using hyper-spectral imager and a new bend interpolation and local scaling HSI sharpening method

    Science.gov (United States)

    Chen, Hai-Wen; McGurr, Michael; Brickhouse, Mark

    2015-05-01

    We present new results from our ongoing research activity for chemical threat detection using hyper-spectral imager (HSI) detection techniques by detecting nontraditional threat spectral signatures of agent usage, such as protective equipment, coatings, paints, spills, and stains that are worn by human or on trucks or other objects. We have applied several current state-of-the-art HSI target detection methods such as Matched Filter (MF), Adaptive Coherence Estimator (ACE), Constrained Energy Minimization (CEM), and Spectral Angle Mapper (SAM). We are interested in detecting several chemical related materials: (a) Tyvek clothing is chemical resistance and Tyvek coveralls are one-piece garments for protecting human body from harmful chemicals, and (b) ammonium salts from background could be representative of spills from scrubbers or related to other chemical activities. The HSI dataset that we used for detection covers a chemical test field with more than 50 different kinds of chemicals, protective materials, coatings, and paints. Among them, there are four different kinds of Tyvek material, three types of ammonium salts, and one yellow jugs. The imagery cube data were collected by a HSI sensor with a spectral range of 400-2,500nm. Preliminary testing results are promising, and very high probability of detection (Pd) and low probability of false detection are achieved with the usage of full spectral range (400- 2,500nm). In the second part of this paper, we present our newly developed HSI sharpening technique. A new Band Interpolation and Local Scaling (BILS) method has been developed to improve HSI spatial resolution by 4-16 times with a low-cost high-resolution pen-chromatic camera and a RGB camera. Preliminary results indicate that this new technique is promising.

  17. A comparison of random forest and its Gini importance with standard chemometric methods for the feature selection and classification of spectral data

    Directory of Open Access Journals (Sweden)

    Himmelreich Uwe

    2009-07-01

    Full Text Available Abstract Background Regularized regression methods such as principal component or partial least squares regression perform well in learning tasks on high dimensional spectral data, but cannot explicitly eliminate irrelevant features. The random forest classifier with its associated Gini feature importance, on the other hand, allows for an explicit feature elimination, but may not be optimally adapted to spectral data due to the topology of its constituent classification trees which are based on orthogonal splits in feature space. Results We propose to combine the best of both approaches, and evaluated the joint use of a feature selection based on a recursive feature elimination using the Gini importance of random forests' together with regularized classification methods on spectral data sets from medical diagnostics, chemotaxonomy, biomedical analytics, food science, and synthetically modified spectral data. Here, a feature selection using the Gini feature importance with a regularized classification by discriminant partial least squares regression performed as well as or better than a filtering according to different univariate statistical tests, or using regression coefficients in a backward feature elimination. It outperformed the direct application of the random forest classifier, or the direct application of the regularized classifiers on the full set of features. Conclusion The Gini importance of the random forest provided superior means for measuring feature relevance on spectral data, but – on an optimal subset of features – the regularized classifiers might be preferable over the random forest classifier, in spite of their limitation to model linear dependencies only. A feature selection based on Gini importance, however, may precede a regularized linear classification to identify this optimal subset of features, and to earn a double benefit of both dimensionality reduction and the elimination of noise from the classification task.

  18. Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

    Science.gov (United States)

    Seiffert, Betsy R.; Ducrozet, Guillaume

    2018-01-01

    We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642-658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation

  19. Generalization of Spectral Green's Function nodal method for slab-geometry fixed-source adjoint transport problems in S{sub N} formulation

    Energy Technology Data Exchange (ETDEWEB)

    Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-graduacao em Modelagem Computacional; Garcia, Carlos R., E-mail: cgh@instec.cu [Departamento de Ingenieria Nuclear, Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)

    2017-07-01

    Presented here is the application of the adjoint technique for solving source-detector discrete ordinates (S{sub N}) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF{sup †}) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non-zero prescribed boundary conditions for the forward S{sub N} transport problems. The SGF{sup †} method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF{sup †} equations, we use the partial adjoint one-node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)

  20. Generalization of Spectral Green's Function nodal method for slab-geometry fixed-source adjoint transport problems in SN formulation

    International Nuclear Information System (INIS)

    Curbelo, Jesus P.; Silva, Odair P. da; Barros, Ricardo C.

    2017-01-01

    Presented here is the application of the adjoint technique for solving source{detector discrete ordinates (S N ) transport problems by using a spectral nodal method. For slab-geometry adjoint S-N model, the adjoint spectral Green's function method (SGF † ) is extended to multigroup problems considering arbitrary L'th-order of scattering anisotropy, and the possibility of non{zero prescribed boundary conditions for the forward S N transport problems. The SGF † method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF † equations, we use the partial adjoint one{node block inversion (NBI) iterative scheme. Partial adjoint NBI scheme uses the most recent estimates for the node-edge adjoint angular Fluxes in the outgoing directions of a given discretization node, to solve the resulting adjoint SN problem in that node for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent node in the sweeping directions. Numerical results are given to illustrate the present spectral nodal method features and some advantages of using the adjoint technique in source-detector problems. author)