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Sample records for chebyshev spectral methods

  1. Relaxation schemes for Chebyshev spectral multigrid methods

    NASA Technical Reports Server (NTRS)

    Kang, Yimin; Fulton, Scott R.

    1993-01-01

    Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

  2. Preconditioned minimal residual methods for Chebyshev spectral calculations

    NASA Technical Reports Server (NTRS)

    Canuto, C.; Quarteroni, A.

    1985-01-01

    The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

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

    NASA Technical Reports Server (NTRS)

    Johnson, Duane

    1996-01-01

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

  4. Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations

    NASA Technical Reports Server (NTRS)

    Canuto, C.; Quarteroni, A.

    1983-01-01

    The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

  5. Spectral methods for the Euler equations. II - Chebyshev methods and shock fitting

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

    1985-01-01

    The Chebyshev spectral collocation method for the Euler gasdynamic equations is described. It is used with shock fitting to compute several two-dimensional gasdynamic flows. Examples include a shock/acoustic wave interaction, a shock/vortex interaction, and the classical blunt-body problem. With shock fitting, the spectral method has a clear advantage over second-order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

  6. Spectral methods for the Euler equations: Chebyshev methods and shock-fitting

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

    1984-01-01

    The Chebyshev spectral collocation method for the Euler gas-dynamic equations is described. It is used with shock fitting to compute several two-dimensional, gas-dynamic flows. Examples include a shock-acoustic wave interaction, a shock/vortex interaction, and the classical blunt body problem. With shock fitting, the spectral method has a clear advantage over second order finite differences in that equivalent accuracy can be obtained with far fewer grid points.

  7. Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods

    NASA Astrophysics Data System (ADS)

    Julien, Keith; Watson, Mike

    2009-03-01

    A robust methodology is presented for efficiently solving partial differential equations using Chebyshev spectral techniques. It is well known that differential equations in one dimension can be solved efficiently with Chebyshev discretizations, O( N) operations for N unknowns, however this efficiency is lost in higher dimensions due to the coupling between modes. This paper presents the "quasi-inverse" technique (QIT), which combines optimizations of one-dimensional spectral differentiation matrices with Kronecker matrix products to build efficient multi-dimensional operators. This strategy results in O( N2 D-1 ) operations for ND unknowns, independent of the form of the differential operators. QIT is compared to the matrix diagonalization technique (MDT) of Haidvogel and Zang [D.B. Haidvogel, T. Zang, The accurate solution of Poisson's equation by expansion in Chebyshev polynomials, J. Comput. Phys. 30 (1979) 167-180] and Shen [J. Shen, Efficient spectral-Galerkin method. II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comp. 16 (1) (1995) 74-87]. While the cost for MDT and QIT are the same in two dimensions, there are significant differences. MDT utilizes an eigenvalue/eigenvector decomposition and can only be used for relatively simple differential equations. QIT is based upon intrinsic properties of the Chebyshev polynomials and is adaptable to linear PDEs with constant coefficients in simple domains. We present results for a standard suite of test problems, and discuss of the adaptability of QIT to more complicated problems.

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

    PubMed

    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.

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

    PubMed Central

    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. PMID:25254252

  10. Non-oscillatory spectral element Chebyshev method for shock wave calculations

    SciTech Connect

    Sidilkover, D.; Karniadakis, G.E.

    1993-07-01

    A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example. 20 refs., 10 figs.

  11. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1980-01-01

    New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

  12. Chebyshev collocation spectral method for one-dimensional radiative heat transfer in linearly anisotropic-scattering cylindrical medium

    NASA Astrophysics Data System (ADS)

    Zhou, Rui-Rui; Li, Ben-Wen

    2017-03-01

    In this study, the Chebyshev collocation spectral method (CCSM) is developed to solve the radiative integro-differential transfer equation (RIDTE) for one-dimensional absorbing, emitting and linearly anisotropic-scattering cylindrical medium. The general form of quadrature formulas for Chebyshev collocation points is deduced. These formulas are proved to have the same accuracy as the Gauss-Legendre quadrature formula (GLQF) for the F-function (geometric function) in the RIDTE. The explicit expressions of the Lagrange basis polynomials and the differentiation matrices for Chebyshev collocation points are also given. These expressions are necessary for solving an integro-differential equation by the CCSM. Since the integrand in the RIDTE is continuous but non-smooth, it is treated by the segments integration method (SIM). The derivative terms in the RIDTE are carried out to improve the accuracy near the origin. In this way, a fourth order accuracy is achieved by the CCSM for the RIDTE, whereas it's only a second order one by the finite difference method (FDM). Several benchmark problems (BPs) with various combinations of optical thickness, medium temperature distribution, degree of anisotropy, and scattering albedo are solved. The results show that present CCSM is efficient to obtain high accurate results, especially for the optically thin medium. The solutions rounded to seven significant digits are given in tabular form, and show excellent agreement with the published data. Finally, the solutions of RIDTE are used as benchmarks for the solution of radiative integral transfer equations (RITEs) presented by Sutton and Chen (JQSRT 84 (2004) 65-103). A non-uniform grid refined near the wall is advised to improve the accuracy of RITEs solutions.

  13. Cell averaging Chebyshev methods for hyperbolic problems

    NASA Technical Reports Server (NTRS)

    Wei, Cai; Gottlieb, David; Harten, Ami

    1990-01-01

    A cell averaging method for the Chebyshev approximations of first order hyperbolic equations in conservation form is described. Formulas are presented for transforming between pointwise data at the collocation points and cell averaged quantities, and vice-versa. This step, trivial for the finite difference and Fourier methods, is nontrivial for the global polynomials used in spectral methods. The cell averaging methods presented are proven stable for linear scalar hyperbolic equations and present numerical simulations of shock-density wave interaction using the new cell averaging Chebyshev methods.

  14. Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel

    NASA Technical Reports Server (NTRS)

    Karageorghis, Andreas; Phillips, Timothy N.

    1990-01-01

    The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further.

  15. Pseudo spectral Chebyshev representation of few-group cross sections on sparse grids

    SciTech Connect

    Bokov, P. M.; Botes, D.; Zimin, V. G.

    2012-07-01

    This paper presents a pseudo spectral method for representing few-group homogenised cross sections, based on hierarchical polynomial interpolation. The interpolation is performed on a multi-dimensional sparse grid built from Chebyshev nodes. The representation is assembled directly from the samples using basis functions that are constructed as tensor products of the classical one-dimensional Lagrangian interpolation functions. The advantage of this representation is that it combines the accuracy of Chebyshev interpolation with the efficiency of sparse grid methods. As an initial test, this interpolation method was used to construct a representation for the two-group macroscopic cross sections of a VVER pin cell. (authors)

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

    SciTech Connect

    Javaloyes, J.

    2015-10-01

    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.

  17. Solution of acoustic workshop problems by a spectral multidomain method

    NASA Technical Reports Server (NTRS)

    Kopriva, Davis A.; Kolias, John H.

    1995-01-01

    We use a new staggered grid Chebyshev spectral multidomain method to solve three of the Workshop benchmark problems. The method defines solution unknowns at the nodes of the Chebyshev Gauss quadrature, and the fluxes at the nodes of the Chebyshev Gauss-Lobatto quadrature. The Chebyshev spectral method gives exponentially convergent phase and dissipation errors. The multidomain approximation gives the method flexibility. Using the method, we solve problems in Categories 1 and 5 of the benchmark problems.

  18. Numerical approximation of Lévy-Feller fractional diffusion equation via Chebyshev-Legendre collocation method

    NASA Astrophysics Data System (ADS)

    Sweilam, N. H.; Abou Hasan, M. M.

    2016-08-01

    This paper reports a new spectral algorithm for obtaining an approximate solution for the Lévy-Feller diffusion equation depending on Legendre polynomials and Chebyshev collocation points. The Lévy-Feller diffusion equation is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative. A new formula expressing explicitly any fractional-order derivatives, in the sense of Riesz-Feller operator, of Legendre polynomials of any degree in terms of Jacobi polynomials is proved. Moreover, the Chebyshev-Legendre collocation method together with the implicit Euler method are used to reduce these types of differential equations to a system of algebraic equations which can be solved numerically. Numerical results with comparisons are given to confirm the reliability of the proposed method for the Lévy-Feller diffusion equation.

  19. Quadrature imposition of compatibility conditions in Chebyshev methods

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Streett, C. L.

    1990-01-01

    Often, in solving an elliptic equation with Neumann boundary conditions, a compatibility condition has to be imposed for well-posedness. This condition involves integrals of the forcing function. When pseudospectral Chebyshev methods are used to discretize the partial differential equation, these integrals have to be approximated by an appropriate quadrature formula. The Gauss-Chebyshev (or any variant of it, like the Gauss-Lobatto) formula can not be used here since the integrals under consideration do not include the weight function. A natural candidate to be used in approximating the integrals is the Clenshaw-Curtis formula, however it is shown that this is the wrong choice and it may lead to divergence if time dependent methods are used to march the solution to steady state. The correct quadrature formula is developed for these problems. This formula takes into account the degree of the polynomials involved. It is shown that this formula leads to a well conditioned Chebyshev approximation to the differential equations and that the compatibility condition is automatically satisfied.

  20. Modified Chebyshev-Picard Iteration Methods for Orbit Propagation

    NASA Astrophysics Data System (ADS)

    Bai, Xiaoli; Junkins, John L.

    2011-10-01

    Modified Chebyshev-Picard Iteration methods are presented for solving high precision, long-term orbit propagation problems. Fusing Chebyshev polynomials with the classical Picard iteration method, the proposed methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to traditional, step-wise, forward integration methods. Numerical results demonstrate that for orbit propagation problems, the presented methods are comparable to or superior to a state-of-the-art 12th order Runge-Kutta-Nystrom method in a serial processor as measured by both precision and efficiency. We have found revolutionary long solution arcs with more than eleven digit path approximations over one to three lower-case Earth orbit periods, multiple solution arcs can be patched continuously together to achieve very long-term propagation, leading to more than ten digit accuracy with built-in precise interpolation. Of revolutionary practical promise to much more efficiently solving high precision, long-term orbital trajectory propagation problems is the observation that the presented methods are well suited to massive parallelization because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed.

  1. Short-time Chebyshev wave packet method for molecular photoionization

    NASA Astrophysics Data System (ADS)

    Sun, Zhaopeng; Zheng, Yujun

    2016-08-01

    In this letter we present the extended usage of short-time Chebyshev wave packet method in the laser induced molecular photoionization dynamics. In our extension, the polynomial expansion of the exponential in the time evolution operator, the Hamiltonian operator can act on the wave packet directly which neatly avoids the matrix diagonalization. This propagation scheme is of obvious advantages when the dynamical system has large Hamiltonian matrix. Computational simulations are performed for the calculation of photoelectronic distributions from intense short pulse ionization of K2 and NaI which represent the Born-Oppenheimer (BO) model and Non-BO one, respectively.

  2. Topics in spectral methods

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1985-01-01

    After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

  3. A composite Chebyshev finite difference method for nonlinear optimal control problems

    NASA Astrophysics Data System (ADS)

    Marzban, H. R.; Hoseini, S. M.

    2013-06-01

    In this paper, a composite Chebyshev finite difference method is introduced and is successfully employed for solving nonlinear optimal control problems. The proposed method is an extension of the Chebyshev finite difference scheme. This method can be regarded as a non-uniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto points. The convergence of the method is established. The nice properties of hybrid functions are then used to convert the nonlinear optimal control problem into a nonlinear mathematical programming one that can be solved efficiently by a globally convergent algorithm. The validity and applicability of the proposed method are demonstrated through some numerical examples. The method is simple, easy to implement and yields very accurate results.

  4. Spectral methods for time dependent problems

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1990-01-01

    Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

  5. Modified Chebyshev-Picard Iteration Methods for Solution of Boundary Value Problems

    NASA Astrophysics Data System (ADS)

    Bai, Xiaoli; Junkins, John L.

    2011-10-01

    Modified Chebyshev-Picard iteration methods are presented for solving boundary value problems. Chebyshev polynomials are used to approximate the state trajectory in Picard iterations, while the boundary conditions are maintained by constraining the coefficients of the Chebyshev polynomials. Using Picard iteration and Clenshaw-Curtis quadrature, the presented methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to step-wise, forward integration approaches, which render the methods well-suited for parallel computation because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed. The presented methods solve optimal control problems through Pontryagin's principle without requiring shooting methods or gradient information. The methods are demonstrated to be computationally efficient and strikingly accurate when compared with Battin's method for a classical Lambert's problem and with a Chebyshev pseudospectral method for an optimal trajectory design problem. The reported simulation results obtained on a serial machine suggest a strong basis for optimism of using the presented methods for solving more challenging boundary value problems, especially when highly parallel architectures are fully exploited.

  6. A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation

    NASA Technical Reports Server (NTRS)

    Danabasoglu, G.; Biringen, S.

    1989-01-01

    The Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr-Sommerfeld equation for Poiseuille flow and the Blausius boundary layer. The problem is linearized by the companion matrix technique for semi-infinite domain using a mapping transformation. The method can be easily adapted to problems with different boundary conditions requiring different transformations.

  7. A Chebyshev condition for accelerating convergence of iterative tomographic methods-solving large least squares problems

    NASA Astrophysics Data System (ADS)

    Olson, Allen H.

    1987-08-01

    The Simultaneous Iterative Reconstruction Technique (SIRT) is a variation of Richardson's method for solving linear systems with positive definitive matrices, and can be used for solving any least squares problem. Previous SIRT methods used in tomography have suggested a constant normalization factor for the step size. With this normalization, the convergence rate of the eigencomponents decreases as the eigenvalue decreases, making these methods impractical for obtaining large bandwidth solutions. By allowing the normalization factor to change with each iteration, the error after k iterations is shown to be a k th order polynomial. The factors are then chosen to yield a Chebyshev polynomial so that the maximum error in the iterative method is minimized over a prescribed range of eigenvalues. Compared with k iterations using a constant normalization, the Chebyshev method requires only √ and has the property that all eigencomponents converge at the same rate. Simple expressions are given which permit the number of iterations to be determined in advanced based upon the desired accuracy and bandwidth. A stable ordering of the Chebyshev factors is also given which minimizes the effects of numerical roundoff. Since a good upper bound for the maximum eigenvalue of the normal matrix is essential to the calculations, the well known 'power method with shift of origin' is combined with the Chebyshev method to estimate its value.

  8. The rational Chebyshev of second kind collocation method for solving a class of astrophysics problems

    NASA Astrophysics Data System (ADS)

    Parand, K.; Khaleqi, S.

    2016-02-01

    The Lane-Emden equation has been used to model several phenomena in theoretical physics, mathematical physics and astrophysics such as the theory of stellar structure. This study is an attempt to utilize the collocation method with the rational Chebyshev function of Second kind (RCS) to solve the Lane-Emden equation over the semi-infinite interval [0,+∞[ . According to well-known results and comparing with previous methods, it can be said that this method is efficient and applicable.

  9. 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method

    NASA Astrophysics Data System (ADS)

    Zhou, D.; Lo, S. H.; Cheung, Y. K.

    2009-02-01

    The three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev-Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time.

  10. Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

    2013-01-01

    This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

  11. Sinc-Chebyshev Collocation Method for a Class of Fractional Diffusion-Wave Equations

    PubMed Central

    Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long

    2014-01-01

    This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed. PMID:24977177

  12. A Chebyshev Collocation Method for Moving Boundaries, Heat Transfer, and Convection During Directional Solidification

    NASA Technical Reports Server (NTRS)

    Zhang, Yiqiang; Alexander, J. I. D.; Ouazzani, J.

    1994-01-01

    Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and name propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectra collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

  13. A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries.

    PubMed

    Nielsen, S A; Hesthaven, J S

    2002-05-01

    The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral 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 derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE.

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

    NASA Astrophysics Data System (ADS)

    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.

  15. Spectral methods for time dependent partial differential equations

    NASA Technical Reports Server (NTRS)

    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.

  16. The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

    NASA Technical Reports Server (NTRS)

    Haidvogel, D. B.; Zang, T.

    1979-01-01

    A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

  17. Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Bernardi, Christine; Canuto, Claudio; Maday, Yvon

    1986-01-01

    An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

  18. On the boundary treatment in spectral methods for hyperbolic systems

    NASA Technical Reports Server (NTRS)

    Canuto, C.; Quarteroni, A.

    1986-01-01

    Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

  19. On the boundary treatment in spectral methods for hyperbolic systems

    NASA Technical Reports Server (NTRS)

    Canuto, Claudio; Quarteroni, Alfio

    1987-01-01

    Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

  20. Hydromagnetic Hiemenz flow of micropolar fluid over a nonlinearly stretching/shrinking sheet: Dual solutions by using Chebyshev Spectral Newton Iterative Scheme

    NASA Astrophysics Data System (ADS)

    Mahmood, Asad; Chen, Bin; Ghaffari, Abuzar

    2016-10-01

    Hydromagnetic stagnation point flow and heat transfer over a nonlinearly stretching/shrinking surface of micropolar fluid is investigated. The numerical simulation is carried out through Chebyshev Spectral Newton Iterative Scheme, after transforming the governing equations into dimensionless boundary layer form. The dual solutions are reported for different values of magnetic and material parameters against the limited range of stretching/shrinking parameter. It is also noted that second solution only occurs for the negative values of stretching/shrinking parameter, whereas for the positive values unique solution exists. The effects of dimensionless parameters are described through graphs. It is seen that the flow and heat transfer rates can be controlled through the material parameter and magnetic force.

  1. A conservative staggered-grid Chebyshev multidomain method for compressible flows

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.; Kolias, John H.

    1995-01-01

    We present a new multidomain spectral collocation method that uses staggered grids for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute.

  2. Spectral collocation methods

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

    1987-01-01

    This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

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

    PubMed Central

    Saberi Nik, Hassan; Rebelo, Paulo

    2014-01-01

    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. PMID:25386624

  4. Multistage spectral relaxation method for solving the hyperchaotic complex systems.

    PubMed

    Saberi Nik, Hassan; Rebelo, Paulo

    2014-01-01

    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.

  5. A conservative staggered-grid Chebyshev multidomain method for compressible flows

    SciTech Connect

    Kopriva, D.A.; Kolias, J.H.

    1996-04-01

    The authors present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems. The solution unknowns are defined at the nodes of a Gauss quadrature rule. The fluxes are evaluated at the nodes of a Gauss-Lobatto rule. The method is conservative, free-stream preserving, and exponentially accurate. A significant advantage of the method is that subdomain corners are not included in the approximation, making solutions in complex geometries easier to compute. 41 refs., 23 figs., 1 tab.

  6. Preconditioning matrices for Chebyshev derivative operators

    NASA Technical Reports Server (NTRS)

    Rothman, Ernest E.

    1986-01-01

    The problem of preconditioning the matrices arising from pseudo-spectral Chebyshev approximations of first order operators is considered in both one and two dimensions. In one dimension a preconditioner represented by a full matrix which leads to preconditioned eigenvalues that are real, positive, and lie between 1 and pi/2, is already available. Since there are cases in which it is not computationally convenient to work with such a preconditioner, a large number of preconditioners were studied which were more sparse (in particular three and four diagonal matrices). The eigenvalues of such preconditioned matrices are compared. The results were applied to the problem of finding the steady state solution to an equation of the type u sub t = u sub x + f, where the Chebyshev collocation is used for the spatial variable and time discretization is performed by the Richardson method. In two dimensions different preconditioners are proposed for the matrix which arises from the pseudo-spectral discretization of the steady state problem. Results are given for the CPU time and the number of iterations using a Richardson iteration method for the unpreconditioned and preconditioned cases.

  7. General relativistic neutrino transport using spectral methods

    NASA Astrophysics Data System (ADS)

    Peres, Bruno; Penner, Andrew Jason; Novak, Jérôme; Bonazzola, Silvano

    2014-02-01

    We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ɛ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.

  8. Spectral methods for the Euler equations - The blunt body problem revisited

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.; Zang, Thomas A.; Hussaini, M. Y.

    1991-01-01

    The present use of the Chebyshev spectral collocation method, in conjunction with shock-fitting, to solve the blunt-body problem gives attention to the boundary and the shock-acceleration equations. The crux of these procedures is the use of the characteristic compatibility relations to compute the body pressure and shock velocity. It is shown that converged solutions are obtainable without artificial smoothing, and that spectral accuracy is achieved.

  9. Milling Stability Analysis Based on Chebyshev Segmentation

    NASA Astrophysics Data System (ADS)

    HUANG, Jianwei; LI, He; HAN, Ping; Wen, Bangchun

    2016-09-01

    Chebyshev segmentation method was used to discretize the time period contained in delay differential equation, then the Newton second-order difference quotient method was used to calculate the cutter motion vector at each time endpoint, and the Floquet theory was used to determine the stability of the milling system after getting the transfer matrix of milling system. Using the above methods, a two degree of freedom milling system stability issues were investigated, and system stability lobe diagrams were got. The results showed that the proposed methods have the following advantages. Firstly, with the same calculation accuracy, the points needed to represent the time period are less by the Chebyshev Segmentation than those of the average segmentation, and the computational efficiency of the Chebyshev Segmentation is higher. Secondly, if the time period is divided into the same parts, the stability lobe diagrams got by Chebyshev segmentation method are more accurate than those of the average segmentation.

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

    NASA Astrophysics Data System (ADS)

    Cvitaš, Marko T.; Althorpe, Stuart C.

    2013-08-01

    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)], 10.1021/jp8111974 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.

  11. Accuracy and speed in computing the Chebyshev collocation derivative

    NASA Technical Reports Server (NTRS)

    Don, Wai-Sun; Solomonoff, Alex

    1991-01-01

    We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

  12. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations.

    PubMed

    Banerjee, Amartya S; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E

    2016-10-21

    The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

  13. Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations

    NASA Astrophysics Data System (ADS)

    Banerjee, Amartya S.; Lin, Lin; Hu, Wei; Yang, Chao; Pask, John E.

    2016-10-01

    The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

  14. Spectral methods for discontinuous problems

    NASA Technical Reports Server (NTRS)

    Abarbanel, S.; Gottlieb, D.; Tadmor, E.

    1985-01-01

    Spectral methods yield high-order accuracy even when applied to problems with discontinuities, though not in the sense of pointwise accuracy. Two different procedures are presented which recover pointwise accurate approximations from the spectral calculations.

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

    NASA Technical Reports Server (NTRS)

    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.

  16. Improved Parker's method for topographic models using Chebyshev series and low rank approximation

    NASA Astrophysics Data System (ADS)

    Wu, Leyuan; Lin, Qiang

    2017-03-01

    We present a new method to improve the convergence of the well-known Parker's formula for the modelling of gravity and magnetic fields caused by sources with complex topography. In the original Parker's formula, two approximations are made, which may cause considerable numerical errors and instabilities: 1) the approximation of the forward and inverse continuous Fourier transforms using their discrete counterparts, the forward and inverse Fast Fourier Transform (FFT) algorithms; 2) the approximation of the exponential function with its Taylor series expansion. In a previous paper of ours, we have made an effort addressing the first problem by applying the Gauss-FFT method instead of the standard FFT algorithm. The new Gauss-FFT based method shows improved numerical efficiency and agrees well with space-domain analytical or hybrid analytical-numerical algorithms. However, even under the simplifying assumption of a calculation surface being a level plane above all topographic sources, the method may still fail or become inaccurate under certain circumstances. When the peaks of the topography approach the observation surface too closely, the number of terms of the Taylor series expansion needed to reach a suitable precision becomes large and slows the calculation. We show in this paper that this problem is caused by the second approximation mentioned above, and it is due to the convergence property of the Taylor series expansion that the algorithm becomes inaccurate for certain topographic models with large amplitudes. Based on this observation, we present a modified Parker's method using low rank approximation (LRA) of the exponential function in virtue of the Chebfun software system. In this way, the optimal rate of convergence is achieved. Some pre-computation is needed but will not cause significant computational overheads. Synthetic and real model tests show that the method now works well for almost any practical topographic model, provided that the assumption

  17. A computationally efficient spectral method for modeling core dynamics

    NASA Astrophysics Data System (ADS)

    Marti, P.; Calkins, M. A.; Julien, K.

    2016-08-01

    An efficient, spectral numerical method is presented for solving problems in a spherical shell geometry that employs spherical harmonics in the angular dimensions and Chebyshev polynomials in the radial direction. We exploit the three-term recurrence relation for Chebyshev polynomials that renders all matrices sparse in spectral space. This approach is significantly more efficient than the collocation approach and is generalizable to both the Galerkin and tau methodologies for enforcing boundary conditions. The sparsity of the matrices reduces the computational complexity of the linear solution of implicit-explicit time stepping schemes to O(N) operations, compared to O>(N2>) operations for a collocation method. The method is illustrated by considering several example problems of important dynamical processes in the Earth's liquid outer core. Results are presented from both fully nonlinear, time-dependent numerical simulations and eigenvalue problems arising from the investigation of the onset of convection and the inertial wave spectrum. We compare the explicit and implicit temporal discretization of the Coriolis force; the latter becomes computationally feasible given the sparsity of the differential operators. We find that implicit treatment of the Coriolis force allows for significantly larger time step sizes compared to explicit algorithms; for hydrodynamic and dynamo problems at an Ekman number of E=10-5, time step sizes can be increased by a factor of 3 to 16 times that of the explicit algorithm, depending on the order of the time stepping scheme. The implementation with explicit Coriolis force scales well to at least 2048 cores, while the implicit implementation scales to 512 cores.

  18. Method of multivariate spectral analysis

    DOEpatents

    Keenan, Michael R.; Kotula, Paul G.

    2004-01-06

    A method of determining the properties of a sample from measured spectral data collected from the sample by performing a multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used to analyze X-ray spectral data generated by operating a Scanning Electron Microscope (SEM) with an attached Energy Dispersive Spectrometer (EDS).

  19. The Chebyshev Polynomials: Patterns and Derivation

    ERIC Educational Resources Information Center

    Sinwell, Benjamin

    2004-01-01

    The Chebyshev polynomials named after a Russian mathematician, Pafnuty Lvovich Chebyshev, have various mathematical applications. A process for obtaining Chebyshev polynomials, and a mathematical inquiry into the patterns they generate, is presented.

  20. Chebyshev matrix product state approach for time evolution

    NASA Astrophysics Data System (ADS)

    Halimeh, Jad C.; Kolley, Fabian; McCulloch, Ian P.

    2015-09-01

    We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011), 10.1103/PhysRevB.83.195115]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the nonprojective method and more efficient information storage, data compression, and less computational effort.

  1. Efficient modified Chebyshev differentiation matrices for fractional differential equations

    NASA Astrophysics Data System (ADS)

    Dabiri, Arman; Butcher, Eric A.

    2017-09-01

    This paper compares several fractional operational matrices for solving a system of linear fractional differential equations (FDEs) of commensurate or incommensurate order. For this purpose, three fractional collocation differentiation matrices (FCDMs) based on finite differences are first proposed and compared with Podlubny's matrix previously used in the literature, after which two new efficient FCDMs based on Chebyshev collocation are proposed. It is shown via an error analysis that the use of the well-known property of fractional differentiation of polynomial bases applied to these methods results in a limitation in the size of the obtained Chebyshev-based FCDMs. To compensate for this limitation, a new fast spectrally accurate FCDM for fractional differentiation which does not require the use of the gamma function is proposed. Then, the Schur-Pade and Schur decomposition methods are implemented to enhance and improve numerical stability. Therefore, this method overcomes the previous limitation regarding the size limitation. In several illustrative examples, the convergence and computation time of the proposed FCDMs are compared and their advantages and disadvantages are outlined.

  2. Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

    NASA Astrophysics Data System (ADS)

    Dutta, Ivy; Chowdhury, Anirban Roy; Kumbhakar, Dharmadas

    2013-03-01

    Using Chebyshev power series approach, accurate description for the first higher order (LP11) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP11 mode approximation present fairly accurate results, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

  3. Data compression using Chebyshev transform

    NASA Technical Reports Server (NTRS)

    Cheng, Andrew F. (Inventor); Hawkins, III, S. Edward (Inventor); Nguyen, Lillian (Inventor); Monaco, Christopher A. (Inventor); Seagrave, Gordon G. (Inventor)

    2007-01-01

    The present invention is a method, system, and computer program product for implementation of a capable, general purpose compression algorithm that can be engaged on the fly. This invention has particular practical application with time-series data, and more particularly, time-series data obtained form a spacecraft, or similar situations where cost, size and/or power limitations are prevalent, although it is not limited to such applications. It is also particularly applicable to the compression of serial data streams and works in one, two, or three dimensions. The original input data is approximated by Chebyshev polynomials, achieving very high compression ratios on serial data streams with minimal loss of scientific information.

  4. Thermal analysis of a fully wet porous radial fin with natural convection and radiation using the spectral collocation method

    NASA Astrophysics Data System (ADS)

    Khani, F.; Darvishi, M. T.; Gorla, R. S.. R.; Gireesha, B. J.

    2016-05-01

    Heat transfer with natural convection and radiation effect on a fully wet porous radial fin is considered. The radial velocity of the buoyancy driven flow at any radial location is obtained by applying Darcy's law. The obtained non-dimensionalized ordinary differential equation involving three highly nonlinear terms is solved numerically with the spectral collocation method. In this approach, the dimensionless temperature is approximated by Chebyshev polynomials and discretized by Chebyshev-Gausse-Lobatto collocation points. A particular algorithm is used to reduce the nonlinearity of the conservation of energy equation. The present analysis characterizes the effect of ambient temperature in different ways and it provides a better picture regarding the effect of ambient temperature on the thermal performance of the fin. The profiles for temperature distributions and dimensionless base heat flow are obtained for different parameters which influence the heat transfer rate.

  5. Spectral Methods for Numerical Relativity.

    PubMed

    Grandclément, Philippe; Novak, Jérôme

    2009-01-01

    Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole-binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole-binary mergers.

  6. Stability analysis of spectral methods for hyperbolic initial-boundary value systems

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Lustman, L.; Tadmor, E.

    1986-01-01

    A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

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

    SciTech Connect

    Giannakouros, J.; Karniadakis, G.E.

    1994-11-01

    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.

  8. Numerical relativity and spectral methods

    NASA Astrophysics Data System (ADS)

    Grandclement, P.

    2016-12-01

    The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.

  9. Shock capturing by the spectral viscosity method

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1989-01-01

    A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods than pollutes the unstable Gibbs oscillations overall the computational domain, and the lack of entropy dissipation prevents convergences in these cases. The Spectral Viscosity method, which is based on high frequency dependent vanishing viscosity regularization of the classical spectral methods is discussed. It is shown that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.

  10. On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.

    PubMed

    Magagula, Vusi M; Motsa, Sandile S; Sibanda, Precious; Dlamini, Phumlani G

    2016-01-01

    The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the SRM by applying the spectral method to discretize derivatives in both space and time variables. The new approach combines the relaxation scheme of the SRM, bivariate Lagrange interpolation as well as the Chebyshev spectral collocation method. The technique is tested on a system of four nonlinear partial differential equations that model unsteady three-dimensional magneto-hydrodynamic flow and mass transfer in a porous medium. Computed solutions are compared with previously published results obtained using the SRM, the spectral quasilinearization method and the Keller-box method. There is clear evidence that the new approach produces results that as good as, if not better than published results determined using the other methods. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The technique also leads to faster convergence to the required solution.

  11. Spectral Methods for Magnetic Anomalies

    NASA Astrophysics Data System (ADS)

    Parker, R. L.; Gee, J. S.

    2013-12-01

    Spectral methods, that is, those based in the Fourier transform, have long been employed in the analysis of magnetic anomalies. For example, Schouten and MaCamy's Earth filter is used extensively to map patterns to the pole, and Parker's Fourier transform series facilitates forward modeling and provides an efficient algorithm for inversion of profiles and surveys. From a different, and perhaps less familiar perspective, magnetic anomalies can be represented as the realization of a stationary stochastic process and then statistical theory can be brought to bear. It is vital to incorporate the full 2-D power spectrum, even when discussing profile data. For example, early analysis of long profiles failed to discover the small-wavenumber peak in the power spectrum predicted by one-dimensional theory. The long-wavelength excess is the result of spatial aliasing, when energy leaks into the along-track spectrum from the cross-track components of the 2-D spectrum. Spectral techniques may be used to improve interpolation and downward continuation of survey data. They can also evaluate the reliability of sub-track magnetization models both across and and along strike. Along-strike profiles turn out to be surprisingly good indicators of the magnetization directly under them; there is high coherence between the magnetic anomaly and the magnetization over a wide band. In contrast, coherence is weak at long wavelengths on across-strike lines, which is naturally the favored orientation for most studies. When vector (or multiple level) measurements are available, cross-spectral analysis can reveal the wavenumber interval where the geophysical signal resides, and where noise dominates. One powerful diagnostic is that the phase spectrum between the vertical and along-path components of the field must be constant 90 degrees. To illustrate, it was found that on some very long Project Magnetic lines, only the lowest 10% of the wavenumber band contain useful geophysical signal. In this

  12. Spectral Methods in General Relativistic MHD Simulations

    NASA Astrophysics Data System (ADS)

    Garrison, David

    2012-03-01

    In this talk I discuss the use of spectral methods in improving the accuracy of a General Relativistic Magnetohydrodynamic (GRMHD) computer code. I introduce SpecCosmo, a GRMHD code developed as a Cactus arrangement at UHCL, and show simulation results using both Fourier spectral methods and finite differencing. This work demonstrates the use of spectral methods with the FFTW 3.3 Fast Fourier Transform package integrated with the Cactus Framework to perform spectral differencing using MPI.

  13. A Multi-domain Spectral Method for Supersonic Reactive Flows

    NASA Technical Reports Server (NTRS)

    Don, Wai-Sun; Gottlieb, David; Jung, Jae-Hun; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    This paper has a dual purpose: it presents a multidomain Chebyshev method for the solution of the two-dimensional reactive compressible Navier-Stokes equations, and it reports the results of the application of this code to the numerical simulations of high Mach number reactive flows in recessed cavity. The computational method utilizes newly derived interface boundary conditions as well as an adaptive filtering technique to stabilize the computations. The results of the simulations are relevant to recessed cavity flameholders.

  14. Estrada index and Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Ginosar, Yuval; Gutman, Ivan; Mansour, Toufik; Schork, Matthias

    2008-03-01

    Let G be a graph whose eigenvalues are λ1, λ2,…, λn. The Estrada index of G is equal to ∑i=1ne. We point out certain classes of graphs whose characteristic polynomials are closely connected to the Chebyshev polynomials of the second kind. Various relations, in particular approximations, for the Estrada index of these graphs are obtained.

  15. A Multidomain Spectral Method for Scalar and Vectorial Poisson Equations with Noncompact Sources

    NASA Astrophysics Data System (ADS)

    Grandclément, P.; Bonazzola, S.; Gourgoulhon, E.; Marck, J.-A.

    2001-06-01

    We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ΔN/ +λ∇(nablaċ)=S, with λ≠-1. The source can extend in all the Euclidean space R3, provided it decays at least as r-3. A multidomain approach is used, along with spherical coordinates (r, θ, φ). In each domain, Chebyshev polynomials (in r or 1/r) and spherical harmonics (in θ and φ) expansions are used. If the source decays as r-k the error of the numerical solution is shown to decrease at least as N-2(k-2), where N is the number of Chebyshev coefficients. The error is even evanescents; i.e., it decreases as exp(-N), if the source does not contain any spherical harmonics of index l>=k-3 (scalar case) or l>=k-5 (vectorial case).

  16. Method of photon spectral analysis

    DOEpatents

    Gehrke, R.J.; Putnam, M.H.; Killian, E.W.; Helmer, R.G.; Kynaston, R.L.; Goodwin, S.G.; Johnson, L.O.

    1993-04-27

    A spectroscopic method to rapidly measure the presence of plutonium in soils, filters, smears, and glass waste forms by measuring the uranium L-shell x-ray emissions associated with the decay of plutonium. In addition, the technique can simultaneously acquire spectra of samples and automatically analyze them for the amount of americium and [gamma]-ray emitting activation and fission products present. The samples are counted with a large area, thin-window, n-type germanium spectrometer which is equally efficient for the detection of low-energy x-rays (10-2,000 keV), as well as high-energy [gamma] rays (>1 MeV). A 8,192- or 16,384 channel analyzer is used to acquire the entire photon spectrum at one time. A dual-energy, time-tagged pulser, that is injected into the test input of the preamplifier to monitor the energy scale, and detector resolution. The L x-ray portion of each spectrum is analyzed by a linear-least-squares spectral fitting technique. The [gamma]-ray portion of each spectrum is analyzed by a standard Ge [gamma]-ray analysis program. This method can be applied to any analysis involving x- and [gamma]-ray analysis in one spectrum and is especially useful when interferences in the x-ray region can be identified from the [gamma]-ray analysis and accommodated during the x-ray analysis.

  17. Method of photon spectral analysis

    DOEpatents

    Gehrke, Robert J.; Putnam, Marie H.; Killian, E. Wayne; Helmer, Richard G.; Kynaston, Ronnie L.; Goodwin, Scott G.; Johnson, Larry O.

    1993-01-01

    A spectroscopic method to rapidly measure the presence of plutonium in soils, filters, smears, and glass waste forms by measuring the uranium L-shell x-ray emissions associated with the decay of plutonium. In addition, the technique can simultaneously acquire spectra of samples and automatically analyze them for the amount of americium and .gamma.-ray emitting activation and fission products present. The samples are counted with a large area, thin-window, n-type germanium spectrometer which is equally efficient for the detection of low-energy x-rays (10-2000 keV), as well as high-energy .gamma. rays (>1 MeV). A 8192- or 16,384 channel analyzer is used to acquire the entire photon spectrum at one time. A dual-energy, time-tagged pulser, that is injected into the test input of the preamplifier to monitor the energy scale, and detector resolution. The L x-ray portion of each spectrum is analyzed by a linear-least-squares spectral fitting technique. The .gamma.-ray portion of each spectrum is analyzed by a standard Ge .gamma.-ray analysis program. This method can be applied to any analysis involving x- and .gamma.-ray analysis in one spectrum and is especially useful when interferences in the x-ray region can be identified from the .gamma.-ray analysis and accommodated during the x-ray analysis.

  18. Spectral methods for exterior elliptic problems

    NASA Technical Reports Server (NTRS)

    Canuto, C.; Hariharan, S. I.; Lustman, L.

    1984-01-01

    Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

  19. Numerical constructions involving Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Lyakhovsky, V. D.

    2017-02-01

    We propose a new algorithm for the character expansion of tensor products of finite-dimensional irreducible representations of simple Lie algebras. The algorithm produces valid results for the algebras B 3, C 3, and D 3. We use the direct correspondence between Weyl anti-invariant functions and multivariate second-kind Chebyshev polynomials. We construct the triangular trigonometric polynomials for the algebra D 3.

  20. Hybrid least squares multivariate spectral analysis methods

    DOEpatents

    Haaland, David M.

    2004-03-23

    A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following prediction or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The hybrid method herein means a combination of an initial calibration step with subsequent analysis by an inverse multivariate analysis method. A spectral shape herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The shape can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

  1. Hybrid least squares multivariate spectral analysis methods

    DOEpatents

    Haaland, David M.

    2002-01-01

    A set of hybrid least squares multivariate spectral analysis methods in which spectral shapes of components or effects not present in the original calibration step are added in a following estimation or calibration step to improve the accuracy of the estimation of the amount of the original components in the sampled mixture. The "hybrid" method herein means a combination of an initial classical least squares analysis calibration step with subsequent analysis by an inverse multivariate analysis method. A "spectral shape" herein means normally the spectral shape of a non-calibrated chemical component in the sample mixture but can also mean the spectral shapes of other sources of spectral variation, including temperature drift, shifts between spectrometers, spectrometer drift, etc. The "shape" can be continuous, discontinuous, or even discrete points illustrative of the particular effect.

  2. Spectral Methods for Computational Fluid Dynamics

    NASA Technical Reports Server (NTRS)

    Zang, T. A.; Streett, C. L.; Hussaini, M. Y.

    1994-01-01

    As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral

  3. Data Outlier Detection using the Chebyshev Theorem

    SciTech Connect

    Amidan, Brett G.; Ferryman, Thomas A.; Cooley, Scott K.

    2005-05-12

    During data collection and analysis, it is often necessary to identify and possibly remove outliers that exist. It is often critical to have an objective method of identifying outliers to be removed. There are many automated outlier detection methods, however, many are limited by assumptions of a distribution or they require upper and lower pre-defined boundaries in which the data should exist. If there is a known distribution for the data, then using that distribution can aid in finding outliers. Often, a distribution is not known, or the experimenter does not want to make an assumption about a certain distribution. Also, enough information may not exist about a set of data to be able to determine reliable upper and lower boundaries. For these cases, an outlier detection method, using the empirical data and based upon Chebyshev's inequality, was formed. This method also allows for detection of multiple outliers, not just one at a time.

  4. SPECTRAL RELATIVE ABSORPTION DIFFERENCE METHOD

    SciTech Connect

    Salaymeh, S.

    2010-06-17

    When analyzing field data, the uncertainty in the background continuum emission produces the majority of error in the final gamma-source analysis. The background emission typically dominates an observed spectrum in terms of counts and is highly variable spatially and temporally. The majority of the spectral shape of the background continuum is produced by combinations of cosmic rays, {sup 40}K, {sup 235}U, and {sup 220}Rn, and the continuum is similar in shape to the 15%-20% level for most field observations. However, the goal of spectroscopy analysis is to pick up subtle peaks (<%5) upon this large background. Because the continuum is falling off as energy increases, peak detection algorithms must first define the background surrounding the peak. This definition is difficult when the range of background shapes is considered. The full spectral template matching algorithms are heavily weighted to solving for the background continuum as it produces significant counts over much of the energy range. The most appropriate background mitigation technique is to take a separate background observation without the source of interest. But, it is frequently not possible to record a background observation in the exact location before (or after) a source has been detected. Thus, one uses approximate backgrounds that rely on spatially nearby locations or similar environments. Since the error in many field observations is dominated by the background, a technique that is less sensitive to the background would be quite beneficial. We report the result of an initial investigation into a novel observation scheme for gamma-emission detection in high background environments. Employing low resolution, NaI, detectors, we examine the different between the direct emission and the 'spectral-shadow' that the gamma emission produces when passed through a thin absorber. For this detection scheme to be competitive, it is required to count and analyze individual gamma-events. We describe the

  5. Spectral element methods: Algorithms and architectures

    NASA Technical Reports Server (NTRS)

    Fischer, Paul; Ronquist, Einar M.; Dewey, Daniel; Patera, Anthony T.

    1988-01-01

    Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling.

  6. Spectral ratio method for measuring emissivity

    USGS Publications Warehouse

    Watson, K.

    1992-01-01

    The spectral ratio method is based on the concept that although the spectral radiances are very sensitive to small changes in temperature the ratios are not. Only an approximate estimate of temperature is required thus, for example, we can determine the emissivity ratio to an accuracy of 1% with a temperature estimate that is only accurate to 12.5 K. Selecting the maximum value of the channel brightness temperatures is an unbiased estimate. Laboratory and field spectral data are easily converted into spectral ratio plots. The ratio method is limited by system signal:noise and spectral band-width. The images can appear quite noisy because ratios enhance high frequencies and may require spatial filtering. Atmospheric effects tend to rescale the ratios and require using an atmospheric model or a calibration site. ?? 1992.

  7. Standard methods for spectral estimation and prewhitening

    SciTech Connect

    Stearns, S.D.

    1986-07-01

    A standard FFT periodogram-averaging method for power spectral estimation is described in detail, with examples that the reader can use to verify his own software. The parameters that must be specified in order to repeat a given spectral estimate are listed. A standard technique for prewhitening is also described, again with repeatable examples and a summary of the parameters that must be specified.

  8. Improved Chebyshev series ephemeris generation capability of GTDS

    NASA Technical Reports Server (NTRS)

    Liu, S. Y.; Rogers, J.; Jacintho, J. J.

    1980-01-01

    An improved implementation of the Chebyshev ephemeris generation capability in the operational version of the Goddard Trajectory Determination System (GTDS) is described. Preliminary results of an evaluation of this orbit propagation method for three satellites of widely different orbit eccentricities are also discussed in terms of accuracy and computing efficiency with respect to the Cowell integration method. An empirical formula is deduced for determining an optimal fitting span which would give reasonable accuracy in the ephemeris with a reasonable consumption of computing resources.

  9. Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Geddes, K. O.

    1977-01-01

    If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

  10. A spectral mimetic least-squares method

    DOE PAGES

    Bochev, Pavel; Gerritsma, Marc

    2014-09-01

    We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are alsomore » satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.« less

  11. A spectral mimetic least-squares method

    SciTech Connect

    Bochev, Pavel; Gerritsma, Marc

    2014-09-01

    We present a spectral mimetic least-squares method for a model diffusion–reaction problem, which preserves key conservation properties of the continuum problem. Casting the model problem into a first-order system for two scalar and two vector variables shifts material properties from the differential equations to a pair of constitutive relations. We also use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also satisfied exactly. Additionally, the latter are reduced to purely topological relationships for the degrees of freedom that can be satisfied without reference to basis functions. Furthermore, numerical experiments confirm the spectral accuracy of the method and its local conservation.

  12. A fast and well-conditioned spectral method for singular integral equations

    NASA Astrophysics Data System (ADS)

    Slevinsky, Richard Mikael; Olver, Sheehan

    2017-03-01

    We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

  13. A spectral Phase-Amplitude method for propagating a wave function to large distances

    NASA Astrophysics Data System (ADS)

    Rawitscher, George

    2015-06-01

    The phase and amplitude (Ph-A) of a wave function vary slowly with distance, in contrast to the wave function that can be highly oscillatory. Hence the Ph-A representation of a wave function requires far fewer computational mesh points than the wave function itself. In 1930 Milne presented an equation for the phase and the amplitude functions (which is different from the one developed by Calogero), and in 1962 Seaton and Peach solved these equations iteratively. The objective of the present study is to implement Seaton and Peach's iteration procedure with a spectral Chebyshev expansion method, and at the same time present a non-iterative analytic solution to an approximate version of the iterative equations. The iterations converge rapidly for the case of attractive potentials. Two numerical examples are given: (1) for a potential that decreases with distance as 1 /r3, and (2) a Coulomb potential ∝ 1 / r. In both cases the whole radial range of [0-2000] requires only between 25 and 100 mesh points and the corresponding accuracy is between 10-3 and 10-6. The 0th iteration (which is the WKB approximation) gives an accuracy of 10-2. This spectral method permits one to calculate a wave function out to large distances reliably and economically.

  14. Logarithmic compression methods for spectral data

    DOEpatents

    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.

  15. Methods for peptide identification by spectral comparison

    PubMed Central

    Liu, Jian; Bell, Alexander W; Bergeron, John JM; Yanofsky, Corey M; Carrillo, Brian; Beaudrie, Christian EH; Kearney, Robert E

    2007-01-01

    Background Tandem mass spectrometry followed by database search is currently the predominant technology for peptide sequencing in shotgun proteomics experiments. Most methods compare experimentally observed spectra to the theoretical spectra predicted from the sequences in protein databases. There is a growing interest, however, in comparing unknown experimental spectra to a library of previously identified spectra. This approach has the advantage of taking into account instrument-dependent factors and peptide-specific differences in fragmentation probabilities. It is also computationally more efficient for high-throughput proteomics studies. Results This paper investigates computational issues related to this spectral comparison approach. Different methods have been empirically evaluated over several large sets of spectra. First, we illustrate that the peak intensities follow a Poisson distribution. This implies that applying a square root transform will optimally stabilize the peak intensity variance. Our results show that the square root did indeed outperform other transforms, resulting in improved accuracy of spectral matching. Second, different measures of spectral similarity were compared, and the results illustrated that the correlation coefficient was most robust. Finally, we examine how to assemble multiple spectra associated with the same peptide to generate a synthetic reference spectrum. Ensemble averaging is shown to provide the best combination of accuracy and efficiency. Conclusion Our results demonstrate that when combined, these methods can boost the sensitivity and specificity of spectral comparison. Therefore they are capable of enhancing and complementing existing tools for consistent and accurate peptide identification. PMID:17227583

  16. Advanced spectral methods for climatic time series

    USGS Publications Warehouse

    Ghil, M.; Allen, M.R.; Dettinger, M.D.; Ide, K.; Kondrashov, D.; Mann, M.E.; Robertson, A.W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.

    2002-01-01

    The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal- to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

  17. Spectral solution of the viscous blunt body problem. 2: Multidomain approximation

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.

    1994-01-01

    We present steady solutions of high speed viscous flows over blunt bodies using a multidomain Chebyshev spectral collocation method. The region with the shock layer is divided into subdomains so that internal layers can be well-resolved. In the interiors of the subdomains, the solution is approximated by Chebyshev collocation. At interfaces between subdomains, the advective terms are upwinded and the viscous terms are treated by a penalty method. The method is applied to five flows, the Mach number range 5-25 and Reynolds number range 2,000 - 83,000, based on nose radius. Results are compared to experimental data and to a finite difference result.

  18. Solution of the One-Dimensional Consolidation Equation for Saturated Clays Using a Spectral Method

    NASA Astrophysics Data System (ADS)

    Sepulveda, N.

    2003-12-01

    The nonlinear, one-dimensional consolidation equation of fully saturated clays interbedded in an aquifer, derived by Gibson and others in 1967, is solved using a spectral method. This equation considers the variation of soil compressibility and permeability during consolidation and recasts Darcy's law so that the relative velocity of the soil skeleton and the pore fluid are related to the excess pore fluid pressure gradient. The spectral solution presented herein uses the matrix representation with Chebyshev collocation to compute the spatial derivative of functions that depend on void ratio, vertical hydraulic conductivity, and the vertical gradient of effective stress. A fourth-order Runge-Kutta algorithm is used to solve the derivative of the void ratio with respect to time. The spectral method requires neither the linearization of the originally nonlinear equation nor the convergence of iterative processes of traditional numerical methods such as finite differences and finite elements. The solution identifies temporal changes in void ratio within the clay lenses occurring in the aquifer system. The compaction is calculated from void ratio changes accumulated throughout the simulated time periods. Laboratory data were used to obtain the mean value for the soil grain density and depth-dependent profiles for aquifer compressibility, hydraulic conductivity, and initial vertical distribution of void ratio for each clay lens. The vertical gradient of the effective stress, needed in the consolidation equation, was derived and the resulting expression was evaluated by using the depth-dependent void ratio profile and drawdown data from a well hydrograph. Compactions and expansions of the clay lens resulting from temporal variations in drawdown due to ground-water withdrawals and recharge periods were simulated for two observation wells in the Santa Clara Valley, California. The solution of the one-dimensional consolidation equation generated temporal changes in void

  19. LORENE: Spectral methods differential equations solver

    NASA Astrophysics Data System (ADS)

    Gourgoulhon, Eric; Grandclément, Philippe; Marck, Jean-Alain; Novak, Jérôme; Taniguchi, Keisuke

    2016-08-01

    LORENE (Langage Objet pour la RElativité NumériquE) solves various problems arising in numerical relativity, and more generally in computational astrophysics. It is a set of C++ classes and provides tools to solve partial differential equations by means of multi-domain spectral methods. LORENE classes implement basic structures such as arrays and matrices, but also abstract mathematical objects, such as tensors, and astrophysical objects, such as stars and black holes.

  20. Stochastic dynamic models and Chebyshev splines

    PubMed Central

    Fan, Ruzong; Zhu, Bin; Wang, Yuedong

    2015-01-01

    In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well-known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. PMID:26045632

  1. Evolutionary Computing Methods for Spectral Retrieval

    NASA Technical Reports Server (NTRS)

    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.

  2. The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

    NASA Technical Reports Server (NTRS)

    Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

    1995-01-01

    The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

  3. Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

    NASA Technical Reports Server (NTRS)

    Balachandar, S.; Yuen, D. A.

    1994-01-01

    A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

  4. A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations

    NASA Astrophysics Data System (ADS)

    Tarman, Hakan I.; Berberoğlu, Halil

    2009-04-01

    A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton's method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated on a case of the Raman propagation equations with strong nonlinearities. This is in contrast to algebraic accuracy obtained by typical solvers used in the literature. The resolving power and the efficiency of the underlying Chebyshev grid are demonstrated in comparison to a known BVP solver.

  5. Spectral method for a kinetic swarming model

    DOE PAGES

    Gamba, Irene M.; Haack, Jeffrey R.; Motsch, Sebastien

    2015-04-28

    Here we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. Lastly, we observe that the kinetic model captures key features such as vortex formation and traveling waves.

  6. Parallel algorithms for the spectral transform method

    SciTech Connect

    Foster, I.T.; Worley, P.H.

    1997-05-01

    The spectral transform method is a standard numerical technique for solving partial differential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, the authors describe these different parallel algorithms and report on computational experiments that they have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations on a sphere; considerable care was taken to ensure that the experiments provide a fair comparison of the different algorithms and that the results are relevant to global models. The authors focus on hypercube- and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but they also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional fast Fourier transforms (FFTs) and other parallel transforms.

  7. Spectral methods in edge-diffraction theories

    SciTech Connect

    Arnold, J.M. )

    1992-12-01

    Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are throughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [Proc. IEEE 62, 1468 (1974)] for circular apertures is deduced. 34 refs., 1 fig.

  8. Parallel algorithms for the spectral transform method

    SciTech Connect

    Foster, I.T.; Worley, P.H.

    1994-04-01

    The spectral transform method is a standard numerical technique for solving partial differential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identified several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the different algorithms has previously been attempted. In this paper, we describe these different parallel algorithms and report on computational experiments that we have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations or a sphere; considerable care was taken to ensure that the experiments provide a fair comparison of the different algorithms and that the results are relevant to global models. We focus on hypercube- and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional FFTs and other parallel transforms.

  9. On spectral relaxation method approach for steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating, viscous dissipation and suction/injection

    NASA Astrophysics Data System (ADS)

    Motsa, Sandile S.; Makukula, Zodwa G.

    2013-03-01

    In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.

  10. A new spectral method to compute FCN

    NASA Astrophysics Data System (ADS)

    Zhang, M.; Huang, C. L.

    2014-12-01

    Free core nutation (FCN) is a rotational modes of the earth with fluid core. All traditional theoretical methods produce FCN period near 460 days with PREM, while the precise observations (VLBI + SG tides) say it should be near 430 days. In order to fill this big gap, astronomers and geophysicists give various assumptions, e.g., increasing core-mantle-boundary (CMB) flattening by about 5%, a strong coupling between nutation and geomagnetic field near CMB, viscous coupling, or topographical coupling etc. Do we really need these unproved assumptions? or is it only the problem of these traditional theoretical methods themselves? Earth models (e.g. PREM) provide accurate and robust profiles of physical parameters, like density and Lame parameters, but their radial derivatives, which are also used in all traditional methods to calculate normal modes (e.g.. FCN), nutation and tides of non-rigid earth theoretically, are not so trustable as the parameters themselves. A new multiple layer spectral method is proposed and applied to the computation of normal modes, to avoid these problems. This new method can solve not only one order ellipsoid but also irregular asymmetric 3D earth model. Our primary result of the FCN period is 435 sidereal days.

  11. On obtaining spectrally accurate solutions of linear differential equations with complex interfaces using the immersed interface method

    NASA Astrophysics Data System (ADS)

    Ray, Sudipta; Saha, Sandeep

    2016-11-01

    Numerical solution of engineering problems with interfacial discontinuities requires exact implementation of the jump conditions else the accuracy deteriorates significantly; particularly, achieving spectral accuracy has been limited due to complex interface geometry and Gibbs phenomenon. We adopt a novel implementation of the immersed-interface method that satisfies the jump conditions at the interfaces exactly, in conjunction with the Chebyshev-collocation method. We consider solutions to linear second order ordinary and partial differential equations having a discontinuity in their zeroth and first derivatives across an interface traced by a complex curve. The solutions obtained demonstrate the ability of the proposed method to achieve spectral accuracy for discontinuous solutions across tortuous interfaces. The solution methodology is illustrated using two model problems: (i) an ordinary differential equation with jump conditions forced by an infinitely differentiable function, (ii) Poisson's equation having a discontinuous solution across interfaces that are ellipses of varying aspect ratio. The use of more polynomials in the direction of the major axis than the minor axis of the ellipse increases the convergence rate of the solution.

  12. Spectral solution of the viscous blunt-body problem

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.

    1993-01-01

    The viscous blunt-body problem is solved with a shock-fitted Chebyshev spectral method. No explicit artificial viscosity or filtering is needed to obtain smooth, converged solutions. The method is applied to two problems. First, results for the flow over a right circular cylinder in the Mach number range of 5.5-6.0 are compared with experimental data. Second, a solution for a Mach 25 flow over a hyperbolic cone is compared with a viscous shock-layer calculation.

  13. Two-dimensional Chebyshev pseudospectral modelling of cardiac propagation.

    PubMed

    Zhan, Z; Ng, K T

    2000-05-01

    Bidomain or monodomain modelling has been used widely to study various issues related to action potential propagation in cardiac tissue. In most of these previous studies, the finite difference method is used to solve the partial differential equations associated with the model. Though the finite difference approach has provided useful insight in many cases, adequate discretisation of cardiac tissue with realistic dimensions often requires a large number of nodes, making the numerical solution process difficult or impossible with available computer resources. Here, a Chebyshev pseudospectral method is presented that allows a significant reduction in the number of nodes required for a given solution accuracy. The new method is used to solve the governing nonlinear partial differential equation for the monodomain model representing a two-dimensional homogeneous sheet of cardiac tissue. The unknown transmembrane potential is expanded in terms of Chebyshev polynomial trial functions and the equation is enforced at the Gauss-Lobatto grid points. Spatial derivatives are obtained using the fast Fourier transform and the solution is advanced in time using an explicit technique. Numerical results indicate that the pseudospectral approach allows the number of nodes to be reduced by a factor of sixteen, while still maintaining the same error performance. This makes it possible to perform simulations with the same accuracy using about twelve times less CPU time and memory.

  14. On the convexity of N-Chebyshev sets

    NASA Astrophysics Data System (ADS)

    Borodin, Petr A.

    2011-10-01

    We define N-Chebyshev sets in a Banach space X for every positive integer N (when N=1, these are ordinary Chebyshev sets) and study conditions that guarantee their convexity. In particular, we prove that all N-Chebyshev sets are convex when N is even and X is uniformly convex or N\\ge 3 is odd and X is smooth uniformly convex.

  15. Spectral Properties and Dynamics of Gold Nanorods Revealed by EMCCD Based Spectral-Phasor Method

    PubMed Central

    Chen, Hongtao; Digman, Michelle A.

    2015-01-01

    Gold nanorods (NRs) with tunable plasmon-resonant absorption in the near-infrared region have considerable advantages over organic fluorophores as imaging agents. However, the luminescence spectral properties of NRs have not been fully explored at the single particle level in bulk due to lack of proper analytic tools. Here we present a global spectral phasor analysis method which allows investigations of NRs' spectra at single particle level with their statistic behavior and spatial information during imaging. The wide phasor distribution obtained by the spectral phasor analysis indicates spectra of NRs are different from particle to particle. NRs with different spectra can be identified graphically in corresponding spatial images with high spectral resolution. Furthermore, spectral behaviors of NRs under different imaging conditions, e.g. different excitation powers and wavelengths, were carefully examined by our laser-scanning multiphoton microscope with spectral imaging capability. Our results prove that the spectral phasor method is an easy and efficient tool in hyper-spectral imaging analysis to unravel subtle changes of the emission spectrum. Moreover, we applied this method to study the spectral dynamics of NRs during direct optical trapping and by optothermal trapping. Interestingly, spectral shifts were observed in both trapping phenomena. PMID:25684346

  16. Spectral properties and dynamics of gold nanorods revealed by EMCCD-based spectral phasor method.

    PubMed

    Chen, Hongtao; Gratton, Enrico; Digman, Michelle A

    2015-04-01

    Gold nanorods (NRs) with tunable plasmon-resonant absorption in the near-infrared region have considerable advantages over organic fluorophores as imaging agents due to their brightness and lack of photobleaching. However, the luminescence spectral properties of NRs have not been fully characterized at the single particle level due to lack of proper analytic tools. Here, we present a spectral phasor analysis method that allows investigations of NRs' spectra at single particle level showing the spectral variance and providing spatial information during imaging. The broad phasor distribution obtained by the spectral phasor analysis indicates that spectra of NRs are different from particle to particle. NRs with different spectra can be identified in images with high spectral resolution. The spectral behaviors of NRs under different imaging conditions, for example, different excitation powers and wavelengths, were revealed by our laser-scanning multiphoton microscope using a high-resolution spectrograph with imaging capability. Our results prove that the spectral phasor method is an easy and efficient tool in hyper-spectral imaging analysis to unravel subtle changes of the emission spectrum. We applied this method to study the spectral dynamics of NRs during direct optical trapping and by optothermal trapping. Interestingly, different spectral shifts were observed in both trapping phenomena.

  17. Method to analyze remotely sensed spectral data

    SciTech Connect

    Stork, Christopher L.; Van Benthem, Mark H.

    2009-02-17

    A fast and rigorous multivariate curve resolution (MCR) algorithm is applied to remotely sensed spectral data. The algorithm is applicable in the solar-reflective spectral region, comprising the visible to the shortwave infrared (ranging from approximately 0.4 to 2.5 .mu.m), midwave infrared, and thermal emission spectral region, comprising the thermal infrared (ranging from approximately 8 to 15 .mu.m). For example, employing minimal a priori knowledge, notably non-negativity constraints on the extracted endmember profiles and a constant abundance constraint for the atmospheric upwelling component, MCR can be used to successfully compensate thermal infrared hyperspectral images for atmospheric upwelling and, thereby, transmittance effects. Further, MCR can accurately estimate the relative spectral absorption coefficients and thermal contrast distribution of a gas plume component near the minimum detectable quantity.

  18. Chebyshev-based technique for automated restoration of digital copies of faded photographic prints

    NASA Astrophysics Data System (ADS)

    Uchaev, Dmitry V.; Uchaev, Denis V.; Malinnikov, Vasiliy A.

    2017-01-01

    We present a technique for automated restoration of digital images obtained from faded photographic prints. The proposed defading technique uses our early proposed image contrast enhancement algorithm based on a contrast measure of images in the Chebyshev moment transform domain. Obtained experimental results demonstrate some advantages of the technique as compared to other widely used image enhancement methods.

  19. Subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization

    NASA Astrophysics Data System (ADS)

    Motamarri, Phani; Gavini, Vikram

    2014-09-01

    We present a subspace projection technique to conduct large-scale Kohn-Sham density functional theory calculations using higher-order spectral finite-element discretization. The proposed method treats both metallic and insulating materials in a single framework and is applicable to both pseudopotential as well as all-electron calculations. The key ideas involved in the development of this method include: (i) employing a higher-order spectral finite-element basis that is amenable to mesh adaption; (ii) using a Chebyshev filter to construct a subspace, which is an approximation to the occupied eigenspace in a given self-consistent field iteration; (iii) using a localization procedure to construct a nonorthogonal localized basis spanning the Chebyshev filtered subspace; and (iv) using a Fermi-operator expansion in terms of the subspace-projected Hamiltonian represented in the nonorthogonal localized basis to compute relevant quantities like the density matrix, electron density, and band energy. We demonstrate the accuracy and efficiency of the proposed approach on benchmark systems involving pseudopotential calculations on aluminum nanoclusters up to 3430 atoms and on alkane chains up to 7052 atoms, as well as all-electron calculations on silicon nanoclusters up to 3920 electrons. The benchmark studies revealed that accuracies commensurate with chemical accuracy can be obtained with the proposed method, and a subquadratic-scaling with system size was observed for the range of materials systems studied. In particular, for the alkane chains—representing an insulating material—close to linear scaling is observed, whereas, for aluminum nanoclusters—representing a metallic material—the scaling is observed to be O (N1.46). For all-electron calculations on silicon nanoclusters, the scaling with the number of electrons is computed to be O (N1.75). In all the benchmark systems, significant computational savings have been realized with the proposed approach, with

  20. The Spectral Element Method for Geophysical Flows

    NASA Astrophysics Data System (ADS)

    Taylor, Mark

    1998-11-01

    We will describe SEAM, a Spectral Element Atmospheric Model. SEAM solves the 3D primitive equations used in climate modeling and medium range forecasting. SEAM uses a spectral element discretization for the surface of the globe and finite differences in the vertical direction. The model is spectrally accurate, as demonstrated by a variety of test cases. It is well suited for modern distributed-shared memory computers, sustaining over 24 GFLOPS on a 240 processor HP Exemplar. This performance has allowed us to run several interesting simulations in full spherical geometry at high resolution (over 22 million grid points).

  1. Single scattering from nonspherical Chebyshev particles: A compendium of calculations

    NASA Technical Reports Server (NTRS)

    Wiscombe, W. J.; Mugnai, A.

    1986-01-01

    A large set of exact calculations of the scattering from a class of nonspherical particles known as Chebyshev particles' has been performed. Phase function and degree of polarization in random orientation, and parallel and perpendicular intensities in fixed orientations, are plotted for a variety of particles shapes and sizes. The intention is to furnish a data base against which both experimental data, and the predictions of approximate methods, can be tested. The calculations are performed with the widely-used Extended Boundary Condition Method. An extensive discussion of this method is given, including much material that is not easily available elsewhere (especially the analysis of its convergence properties). An extensive review is also given of all extant methods for nonspherical scattering calculations, as well as of the available pool of experimental data.

  2. Advances and future directions of research on spectral methods

    NASA Technical Reports Server (NTRS)

    Patera, A. T.

    1986-01-01

    Recent advances in spectral methods are briefly reviewed and characterized with respect to their convergence and computational complexity. Classical finite element and spectral approaches are then compared, and spectral element (or p-type finite element) approximations are introduced. The method is applied to the full Navier-Stokes equations, and examples are given of the application of the technique to several transitional flows. Future directions of research in the field are outlined.

  3. Parallel computation with the spectral element method

    SciTech Connect

    Ma, Hong

    1995-12-01

    Spectral element models for the shallow water equations and the Navier-Stokes equations have been successfully implemented on a data parallel supercomputer, the Connection Machine model CM-5. The nonstaggered grid formulations for both models are described, which are shown to be especially efficient in data parallel computing environment.

  4. INSTRUMENTS AND METHODS OF INVESTIGATION: Spectral and spectral-frequency methods of investigating atmosphereless bodies of the Solar system

    NASA Astrophysics Data System (ADS)

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

    2007-06-01

    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.

  5. Digital spectral separation methods and systems for bioluminescence imaging.

    PubMed

    Wang, Ge; Shen, Haiou; Liu, Ying; Cong, Alex; Cong, Wenxiang; Wang, Yue; Dubey, Purnima

    2008-02-04

    We propose a digital spectral separation (DSS) system and methods to extract spectral information optimally from a weak multi-spectral signal such as in the bioluminescent imaging (BLI) studies. This system utilizes our newly invented spatially-translated spectral-image mixer (SSM), which consists of dichroic beam splitters, a mirror, and a DSS algorithm. The DSS approach overcomes the shortcomings of the data acquisition scheme used for the current BLI systems. Primarily, using our DSS scheme, spectral information will not be filtered out. Accordingly, truly parallel multi-spectral multi-view acquisition is enabled for the first time to minimize experimental time and optimize data quality. This approach also permits recovery of the bioluminescent signal time course, which is useful to study the kinetics of multiple bioluminescent probes using multi-spectral bioluminescence tomography (MSBT).

  6. Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D4 symmetry group; Interpolation within a squircle, Part I

    NASA Astrophysics Data System (ADS)

    Li, Shan; Boyd, John P.

    2014-02-01

    A domain is invariant under the eight-element D4 symmetry group if it is unchanged by reflection with respect to the x and y axes and also the diagonal line x=y. Previous treatments of group theory for spectral methods have generally demanded a semester's worth of group theory. We show this is unnecessary by providing explicit recipes for creating grids, etc. We show how to decompose an arbitrary function into six symmetry-invariant components, and thereby split the interpolation problem into six independent subproblems. We also show how to make symmetry-invariant basis functions from products of Chebyshev polynomials, from Zernike polynomials and from radial basis functions (RBFs) of any species. These recipes are completely general, and apply to any domain that is invariant under the dihedral group D4. These concepts are illustrated by RBF pseudospectral solutions of the Poisson equation in a domain bounded by a squircle, the square-with-rounded corners defined by x2ν+y2ν-1=0 where here ν=2. We also apply Chebyshev polynomials to compute eigenmodes of the Helmholtz equation on the square and show each mode belongs to one and only one of the six D4 classes. [F. Albert Cotton, in: Chemical Applications of Group Theory, John Wiley, New York, 1963, p. vii]Chebyshev polynomials in Cartesian coordinates. Znm(x,y), the Zernike polynomials. Radial basis functions (RBFs). We shall show how to rearrange each basis into six disjoint sets which are eigenfunctions of the operations of the group. We shall then explain how the interpolation problem with N points can be split into four problems of size N/8 and two problems of size N/4 with an enormous reduction of cost.First, though, we shall provide a brief overview of the D4 symmetry group.

  7. Methods of Spectral Analysis in C++ (MOSAIC)

    NASA Astrophysics Data System (ADS)

    Engesser, Michael

    2016-06-01

    Stellar spectroscopic classification is most often still done by hand. MOSAIC is a project focused on the collection and classification of astronomical spectra using a computerized algorithm. The code itself attempts to accurately classify stellar spectra according to the broad spectral classes within the Morgan-Keenan system of spectral classification, based on estimated temperature and the relative abundances of certain notable elements (Hydrogen, Helium, etc.) in the stellar atmosphere. The methodology includes calibrating the wavelength for pixels across the image by using the wavelength dispersion of pixels inherent with the spectrograph used. It then calculates the location of the peak in the star's Planck spectrum in order to roughly classify the star. Fitting the graph to a blackbody curve is the final step for a correct classification. Future work will involve taking a closer look at emission lines and luminosity classes.

  8. Evaluation of AMOEBA: a spectral-spatial classification method

    USGS Publications Warehouse

    Jenson, Susan K.; Loveland, Thomas R.; Bryant, J.

    1982-01-01

    Muitispectral remotely sensed images have been treated as arbitrary multivariate spectral data for purposes of clustering and classifying. However, the spatial properties of image data can also be exploited. AMOEBA is a clustering and classification method that is based on a spatially derived model for image data. In an evaluation test, Landsat data were classified with both AMOEBA and a widely used spectral classifier. The test showed that irrigated crop types can be classified as accurately with the AMOEBA method as with the generally used spectral method ISOCLS; the AMOEBA method, however, requires less computer time.

  9. A spectral and morphologic method for white blood cell classification

    NASA Astrophysics Data System (ADS)

    Wang, Qian; Chang, Li; Zhou, Mei; Li, Qingli; Liu, Hongying; Guo, Fangmin

    2016-10-01

    The identification of white blood cells is important as it provides an assay for diagnosis of various diseases. To overcome the complexity and inaccuracy of traditional methods based on light microscopy, we proposed a spectral and morphologic method based on hyperspectral blood images. We applied mathematical morphology-based methods to extract spatial information and supervised method is employed for spectral analysis. Experimental results show that white blood cells could be segmented and classified into five types with an overall accuracy of more than 90%. Moreover, the experiments including spectral features reached higher accuracy than the spatial-only cases, with a maximum improvement of nearly 20%. By combing both spatial and spectral features, the proposed method provides higher classification accuracy than traditional methods.

  10. A Spectral Method for the Equal Width Equation

    NASA Astrophysics Data System (ADS)

    García-Archilla, Bosco

    1996-05-01

    A spectral discretization of the equal width equation (EWE) is presented. The method is shown to be convergent and nonlinearly stable. Time-stepping is performed with high-order Adams methods. The spectral accuracy of the scheme reveals some features of the EWE that the methods previously used could not bare out properly. For instance, we may now study the changes in amplitude and velocity of solitary waves after collisions.

  11. Spectral analysis methods for automatic speech recognition applications

    NASA Astrophysics Data System (ADS)

    Parinam, Venkata Neelima Devi

    In this thesis, we evaluate the front-end of Automatic Speech Recognition (ASR) systems, with respect to different types of spectral processing methods that are extensively used. A filter bank approach for front end spectral analysis is one of the common methods used for spectral analysis. In this work we describe and evaluate spectral analysis based on Mel and Gammatone filter banks. These filtering methods are derived from auditory models and are thought to have some advantages for automatic speech recognition work. Experimentally, however, we show that direct use of FFT spectral values is just as effective as using either Mel or Gammatone filter banks, provided that the features extracted from the FFT spectral values take into account a Mel or Mel-like frequency scale. It is also shown that trajectory features based on sliding block of spectral features, computed using either FFT or filter bank spectral analysis are considerably more effective, in terms of ASR accuracy, than are delta and delta-delta terms often used for ASR. Although there is no major performance disadvantage to using a filter bank, simplicity of analysis is a reason to eliminate this step in speech processing. These assertions hold for both clean and noisy speech.

  12. Power Spectral Density Error Analysis of Spectral Subtraction Type of Speech Enhancement Methods

    NASA Astrophysics Data System (ADS)

    Händel, Peter

    2006-12-01

    A theoretical framework for analysis of speech enhancement algorithms is introduced for performance assessment of spectral subtraction type of methods. The quality of the enhanced speech is related to physical quantities of the speech and noise (such as stationarity time and spectral flatness), as well as to design variables of the noise suppressor. The derived theoretical results are compared with the outcome of subjective listening tests as well as successful design strategies, performed by independent research groups.

  13. FNAS/Rapid Spectral Inversion Methods

    NASA Technical Reports Server (NTRS)

    Poularikas, Alexander

    1997-01-01

    The purpose of this investigation was to study methods and ways for rapid inversion programs involving the correlated k-method, and to study the infrared observations of Saturn from the Cassini orbiter.

  14. Domain decomposition preconditioners for the spectral collocation method

    NASA Technical Reports Server (NTRS)

    Quarteroni, Alfio; Sacchilandriani, Giovanni

    1988-01-01

    Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate which does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor systems due to their high degree of parallelism.

  15. Orbital Tori Construction Using Trajectory Following Spectral Methods

    DTIC Science & Technology

    2010-09-01

    between the two methods, another approach to overcome the poor decomposition of Ω3 was thought to be an optimization method to correct those coef...Kolmogorov-Arnold-Moser (KAM) solution of a lightly perturbed integrable Hamiltonian system, this research focused on applying trajectory following spectral... approach focused on fitting local spectral structures, denoted as frequency clusters, within the sampled orbital data to the analytical form of the

  16. Application of the Spectral Element Method to Acoustic Radiation

    NASA Technical Reports Server (NTRS)

    Doyle, James F.; Rizzi, Stephen A. (Technical Monitor)

    2000-01-01

    This report summarizes research to develop a capability for analysis of interior noise in enclosed structures when acoustically excited by an external random source. Of particular interest was the application to the study of noise and vibration transmission in thin-walled structures as typified by aircraft fuselages. Three related topics are focused upon. The first concerns the development of a curved frame spectral element, the second shows how the spectral element method for wave propagation in folded plate structures is extended to problems involving curved segmented plates. These are of significance because by combining these curved spectral elements with previously presented flat spectral elements, the dynamic response of geometrically complex structures can be determined. The third topic shows how spectral elements, which incorporate the effect of fluid loading on the structure, are developed for analyzing acoustic radiation from dynamically loaded extended plates.

  17. Black hole evolution by spectral methods

    NASA Astrophysics Data System (ADS)

    Kidder, Lawrence E.; Scheel, Mark A.; Teukolsky, Saul A.; Carlson, Eric D.; Cook, Gregory B.

    2000-10-01

    Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast with finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.

  18. The chain collocation method: A spectrally accurate calculus of forms

    NASA Astrophysics Data System (ADS)

    Rufat, Dzhelil; Mason, Gemma; Mullen, Patrick; Desbrun, Mathieu

    2014-01-01

    Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.

  19. Complex Chebyshev-polynomial-based unified model (CCPBUM) neural networks

    NASA Astrophysics Data System (ADS)

    Jeng, Jin-Tsong; Lee, Tsu-Tian

    1998-03-01

    In this paper, we propose complex Chebyshev Polynomial Based unified model neural network for the approximation of complex- valued function. Based on this approximate transformable technique, we have derived the relationship between the single-layered neural network and multi-layered perceptron neural network. It is shown that the complex Chebyshev Polynomial Based unified model neural network can be represented as a functional link network that are based on Chebyshev polynomial. We also derived a new learning algorithm for the proposed network. It turns out that the complex Chebyshev Polynomial Based unified model neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional complex feedforward/recurrent neural network.

  20. A combined Galerkin/collocation spectral method for transient solution of flow past a spherical droplet

    SciTech Connect

    Nguyen, H.D.; Paik, S. ); Chung, J.N. . Dept. of Mechanical and Materials Engineering)

    1992-01-01

    A spectral model, based on the stream function and vorticity, is developed in order to calculate the time-dependent solution of flow past a spherical droplet. Both Chebyshev and Legendre polynomials are used to expand the stream fiinction and vorticity in the radial and angular directions, respectively, along with the backward Euler approximation to advance in time. Consistent treatment of boundary conditions is made to resolve the lack of vorticity boundary conditions by means of the influence matrix technique. The computed flow field, the drag coefficient, and the interfacial velocity are presented for Reynolds numbers in the range from 0.5 to 50 for both continuous and dispersed phases with viscosity ratios of 1 and 3. Comparison of the present results to those found in the literature indicate that the model is capable of predicting the correct nature of the flow associated with a droplet.

  1. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.

    2004-01-01

    A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

  2. Chebyshev-polynomial expansion of the localization length of Hermitian and non-Hermitian random chains

    NASA Astrophysics Data System (ADS)

    Hatano, Naomichi; Feinberg, Joshua

    2016-12-01

    We study Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as a function of energy. For Hermitian models, the expansion produces this energy-dependent function numerically in one run of the algorithm. This is in strong contrast to the standard transfer-matrix method, which produces the inverse localization length for a fixed energy in each run. For non-Hermitian models, as in the transfer-matrix method, our algorithm computes the inverse localization length for a fixed (complex) energy. We also find a formula of the Chebyshev-polynomial expansion of the density of states of non-Hermitian models. As explained in detail, our algorithm for non-Hermitian models may be the only available efficient algorithm for finding the density of states of models with interactions.

  3. Single-grid spectral collocation for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Bernardi, Christine; Canuto, Claudio; Maday, Yvon; Metivet, Brigitte

    1988-01-01

    The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

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

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

    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.

  5. Spectral methods for multiscale plasma-physics simulations

    NASA Astrophysics Data System (ADS)

    Delzanno, Gian Luca; Manzini, Gianmarco; Vencels, Juris; Markidis, Stefano; Roytershteyn, Vadim

    2016-10-01

    In this talk, we present the SpectralPlasmaSolver (SPS) simulation method for the numerical approximation of the Vlasov-Maxwell equations. SPS either uses spectral methods both in physical and velocity space or combines spectral methods for the velocity space and a Discontinuous Galerkin (DG) discretization in space. The spectral methods are based on generalized Hermite's functions or Legendre polynomials, thus resulting in a time-dependent hyperbolic system for the spectral coefficients. The DG method is applied to numerically solve this system after a characteristic decomposition that properly ensures the upwinding in the scheme. This numerical approach can be seen as a generalization of the method of moment expansion and makes it possible to incorporate microscopic kinetic effects in a macroscale fluid-like behavior. The numerical approximation error for a given computational cost and the computational costs for a prescribed accuracy are orders of magnitude less than those provided by the standard PIC method. Moreover, conservation of physical quantities like mass, momentum, and energy can be proved theoretically. Finally, numerical examples are shown to prove the effectiveness of the approach.

  6. A Spectral Conjugate Gradient Method for Unconstrained Optimization

    SciTech Connect

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

    2001-07-01

    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.

  7. A note on spectral properties of some gradient methods

    NASA Astrophysics Data System (ADS)

    di Serafino, Daniela; Ruggiero, Valeria; Toraldo, Gerardo; Zanni, Luca

    2016-10-01

    Starting from the work by Barzilai and Borwein, gradient methods have gained a great amount of attention, and efficient low-cost schemes are available nowadays. The acceleration strategies used by these methods are based on the definition of effective steplength updating rules, which capture spectral properties of the Hessian of the objective function. The methods arising from this idea represent effective computational tools, extremely appealing for a variety of large-scale optimization problems arising in applications. In this work we discuss the spectral properties of some recently proposed gradient methods with the aim of providing insight into their computational effectiveness. Numerical experiments supporting and illustrating the theoretical analysis are provided.

  8. Nonconforming mortar element methods: Application to spectral discretizations

    NASA Technical Reports Server (NTRS)

    Maday, Yvon; Mavriplis, Cathy; Patera, Anthony

    1988-01-01

    Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

  9. Spectral analysis method for detecting an element

    DOEpatents

    Blackwood, Larry G [Idaho Falls, ID; Edwards, Andrew J [Idaho Falls, ID; Jewell, James K [Idaho Falls, ID; Reber, Edward L [Idaho Falls, ID; Seabury, Edward H [Idaho Falls, ID

    2008-02-12

    A method for detecting an element is described and which includes the steps of providing a gamma-ray spectrum which has a region of interest which corresponds with a small amount of an element to be detected; providing nonparametric assumptions about a shape of the gamma-ray spectrum in the region of interest, and which would indicate the presence of the element to be detected; and applying a statistical test to the shape of the gamma-ray spectrum based upon the nonparametric assumptions to detect the small amount of the element to be detected.

  10. Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.

    PubMed

    Xie, Jiaquan; Huang, Qingxue; Yang, Xia

    2016-01-01

    In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.

  11. Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

    NASA Technical Reports Server (NTRS)

    Pavarino, Luca F.

    1996-01-01

    Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

  12. Adaptive mesh strategies for the spectral element method

    NASA Technical Reports Server (NTRS)

    Mavriplis, Catherine

    1992-01-01

    An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

  13. Non-Equilibrium Allele Frequency Spectra Via Spectral Methods

    PubMed Central

    Hey, Jody; Chen, Kevin

    2011-01-01

    A major challenge in the analysis of population genomics data consists of isolating signatures of natural selection from background noise caused by random drift and gene flow. Analyses of massive amounts of data from many related populations require high-performance algorithms to determine the likelihood of different demographic scenarios that could have shaped the observed neutral single nucleotide polymorphism (SNP) allele frequency spectrum. In many areas of applied mathematics, Fourier Transforms and Spectral Methods are firmly established tools to analyze spectra of signals and model their dynamics as solutions of certain Partial Differential Equations (PDEs). When spectral methods are applicable, they have excellent error properties and are the fastest possible in high dimension; see [15]. In this paper we present an explicit numerical solution, using spectral methods, to the forward Kolmogorov equations for a Wright-Fisher process with migration of K populations, influx of mutations, and multiple population splitting events. PMID:21376069

  14. Spectral methods for the Euler equations. I - Fourier methods and shock capturing

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

    1985-01-01

    Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collociation methods are put into historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock-capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem.

  15. Spectral methods for the Euler equations: Fourier methods and shock-capturing

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A.

    1984-01-01

    Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of Fourier spectral collocation methods are provided. Filtering strategies for shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one dimensional, periodic astrophysical ""nozzle'' problem.

  16. Methods for spectral image analysis by exploiting spatial simplicity

    DOEpatents

    Keenan, Michael R.

    2010-11-23

    Several full-spectrum imaging techniques have been introduced in recent years that promise to provide rapid and comprehensive chemical characterization of complex samples. One of the remaining obstacles to adopting these techniques for routine use is the difficulty of reducing the vast quantities of raw spectral data to meaningful chemical information. Multivariate factor analysis techniques, such as Principal Component Analysis and Alternating Least Squares-based Multivariate Curve Resolution, have proven effective for extracting the essential chemical information from high dimensional spectral image data sets into a limited number of components that describe the spectral characteristics and spatial distributions of the chemical species comprising the sample. There are many cases, however, in which those constraints are not effective and where alternative approaches may provide new analytical insights. For many cases of practical importance, imaged samples are "simple" in the sense that they consist of relatively discrete chemical phases. That is, at any given location, only one or a few of the chemical species comprising the entire sample have non-zero concentrations. The methods of spectral image analysis of the present invention exploit this simplicity in the spatial domain to make the resulting factor models more realistic. Therefore, more physically accurate and interpretable spectral and abundance components can be extracted from spectral images that have spatially simple structure.

  17. Methods for spectral image analysis by exploiting spatial simplicity

    DOEpatents

    Keenan, Michael R.

    2010-05-25

    Several full-spectrum imaging techniques have been introduced in recent years that promise to provide rapid and comprehensive chemical characterization of complex samples. One of the remaining obstacles to adopting these techniques for routine use is the difficulty of reducing the vast quantities of raw spectral data to meaningful chemical information. Multivariate factor analysis techniques, such as Principal Component Analysis and Alternating Least Squares-based Multivariate Curve Resolution, have proven effective for extracting the essential chemical information from high dimensional spectral image data sets into a limited number of components that describe the spectral characteristics and spatial distributions of the chemical species comprising the sample. There are many cases, however, in which those constraints are not effective and where alternative approaches may provide new analytical insights. For many cases of practical importance, imaged samples are "simple" in the sense that they consist of relatively discrete chemical phases. That is, at any given location, only one or a few of the chemical species comprising the entire sample have non-zero concentrations. The methods of spectral image analysis of the present invention exploit this simplicity in the spatial domain to make the resulting factor models more realistic. Therefore, more physically accurate and interpretable spectral and abundance components can be extracted from spectral images that have spatially simple structure.

  18. Spectral estimation of plasma fluctuations. I. Comparison of methods

    SciTech Connect

    Riedel, K.S.; Sidorenko, A. ); Thomson, D.J. )

    1994-03-01

    The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. The smoothed tapered periodogram is compared with the adaptive multiple taper methods and hybrid methods. It is found that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24% larger relative RMSE than the hybrid method. Two new adaptive multitaper weightings which outperform Thomson's original adaptive weighting are presented.

  19. The spectral-element method, Beowulf computing, and global seismology.

    PubMed

    Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen

    2002-11-29

    The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.

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

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

    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.

  1. Application of the Spectral Element Method to Interior Noise Problems

    NASA Technical Reports Server (NTRS)

    Doyle, James F.

    1998-01-01

    The primary effort of this research project was focused the development of analytical methods for the accurate prediction of structural acoustic noise and response. Of particular interest was the development of curved frame and shell spectral elements for the efficient computational of structural response and of schemes to match this to the surrounding fluid.

  2. Coupling finite element and spectral methods: First results

    NASA Technical Reports Server (NTRS)

    Bernardi, Christine; Debit, Naima; Maday, Yvon

    1987-01-01

    A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

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

    PubMed

    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.

  4. The convergence of spectral methods for nonlinear conservation laws

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1987-01-01

    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.

  5. Spectral method for obtaining three-dimensional magnetohydrodynamic equilibria

    SciTech Connect

    Hirshman, S.P.; Lee, D.K.

    1985-07-01

    A description is given of a new code, MOMCON (spectral moments with constraints), that obtains three-dimensional ideal magnetohydrodynamic (MHD) equilibria in a fixed toroidal domain using a Fourier expansion for the inverse coordinates (R,Z) representing nested magnetic surfaces. A set of nonlinear coupled ordinary differential equations for the spectral coefficients of (R,Z) is solved using an accelerated steepest descent method. A stream function lambda is introduced to improve the mode convergence properties of the Fourier series for R and Z. Constraint equations relating the m greater than or equal to 2 moments of R and Z are solved to define a unique poloidal angle.

  6. Solving incompressible flow problems with parallel spectral element methods

    SciTech Connect

    Ma, Hong

    1994-10-01

    Parallel spectral element models are built for the Navier-Stokes equations and the shallow water equations with nonstaggered grid formulations. The optimized computational efficiency of these parallel spectral element models comes not only from the exponential convergence of their numerical solutions, but also from their efficient usage of the powerful vector-processing units of the latest parallel architectures. Furthermore, the communication cost of the spectral element model is lower than that of the h-type finite element model, partly because many fewer redundant nodal values have to be stored. The nonstaggered grid formulations perform well in iterative procedures which are highly in parallel. Implementations of these models are carried out on the Connection Machine systems. The present work shows that the high-order domain decomposition methods can be efficiently applied in a data parallel programming environment.

  7. A review on spectral processing methods for geological remote sensing

    NASA Astrophysics Data System (ADS)

    Asadzadeh, Saeid; de Souza Filho, Carlos Roberto

    2016-05-01

    In this work, many of the fundamental and advanced spectral processing methods available to geologic remote sensing are reviewed. A novel categorization scheme is proposed that groups the techniques into knowledge-based and data-driven approaches, according to the type and availability of reference data. The two categories are compared and their characteristics and geologic outcomes are contrasted. Using an oil-sand sample scanned through the sisuCHEMA hyperspectral imaging system as a case study, the effectiveness of selected processing techniques from each category is demonstrated. The techniques used to bridge between the spectral data and other geoscience products are then discussed. Subsequently, the hybridization of the two approaches is shown to yield some of the most robust processing techniques available to multi- and hyperspectral remote sensing. Ultimately, current and future challenges that spectral analysis are expected to overcome and some potential trends are highlighted.

  8. Friedmann's equations in all dimensions and Chebyshev's theorem

    SciTech Connect

    Chen, Shouxin; Gibbons, Gary W.; Li, Yijun; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk E-mail: yisongyang@nyu.edu

    2014-12-01

    This short but systematic work demonstrates a link between Chebyshev's theorem and the explicit integration in cosmological time t and conformal time η of the Friedmann equations in all dimensions and with an arbitrary cosmological constant Λ. More precisely, it is shown that for spatially flat universes an explicit integration in t may always be carried out, and that, in the non-flat situation and when Λ is zero and the ratio w of the pressure and energy density in the barotropic equation of state of the perfect-fluid universe is rational, an explicit integration may be carried out if and only if the dimension n of space and w obey some specific relations among an infinite family. The situation for explicit integration in η is complementary to that in t. More precisely, it is shown in the flat-universe case with Λ ≠ 0 that an explicit integration in η can be carried out if and only if w and n obey similar relations among a well-defined family which we specify, and that, when Λ = 0, an explicit integration can always be carried out whether the space is flat, closed, or open. We also show that our method may be used to study more realistic cosmological situations when the equation of state is nonlinear.

  9. Circulating tumor cell detection using photoacoustic spectral methods

    NASA Astrophysics Data System (ADS)

    Strohm, Eric M.; Berndl, Elizabeth S. L.; Kolios, Michael C.

    2014-03-01

    A method to detect and differentiate circulating melanoma tumor cells (CTCs) from blood cells using ultrasound and photoacoustic signals with frequencies over 100 MHz is presented. At these frequencies, the acoustic wavelength is similar to the dimensions of a cell, which results in unique features in the signal; periodically varying minima and maxima occur throughout the power spectrum. The spacing between minima depends on the ratio of the size to sound speed of the cell. Using a 532 nm pulsed laser and a 375 MHz center frequency wide-bandwidth transducer, the ultrasound and photoacoustic signals were measured from single cells. A total of 80 cells were measured, 20 melanoma cells, 20 white blood cells (WBCs) and 40 red blood cells (RBCs). The photoacoustic spectral spacing Δf between minima was 95 +/- 15 MHz for melanoma cells and greater than 230 MHz for RBCs. No photoacoustic signal was detected from WBCs. The ultrasonic spectral spacing between minima was 46 +/- 9 MHz for melanoma cells and 98 +/- 11 for WBCs. Both photoacoustic and ultrasound signals were detected from melanoma cells, while only ultrasound signals were detected from WBCs. RBCs showed distinct photoacoustic spectral variations in comparison to any other type of cell. Using the spectral spacing and signal amplitudes, each cell type could be grouped together to aid in cell identification. This method could be used for label-free counting and classifying cells in a sample.

  10. Spectral methods and sum acceleration algorithms. Final report

    SciTech Connect

    Boyd, J.

    1995-03-01

    The principle investigator pursued his investigation of numerical algorithms during the period of the grant. The attached list of publications is so lengthy that it is impossible to describe them in detail. However, the author calls attention to the four articles on sequence acceleration and fourteen more on spectral methods, which fulfill the goals of the original proposal. He also continued his research on nonlinear waves, and wrote a dozen papers on this, too.

  11. Incompressible Spectral-Element Method-Derivation of Equations

    DTIC Science & Technology

    1993-04-01

    expansion functions. Not all orthogonal expansion functions provide high accuracy; however, the eigenfunctions of a singlar Sturm - Liouville operator allow...orthogonal functions p(x), q(x), w(x) = functions in Sturm - Liouville equation P = p/p + IV-V, dynamic pressure Pn = a system of orthogonal polynomials of...truncated series in approximating functions. 1.2 Sturm - Liouville Problems The importance of Sturm - Liouville problems for spectral methods lies in the fact

  12. Terminal Convergence Approximation Modified Chebyshev Picard Iteration for Efficient Orbit Propagation

    NASA Astrophysics Data System (ADS)

    Probe, A.; Macomber, B.; Kim, D.; Woollands, R.; Junkins, J.

    2014-09-01

    Modified Chebyshev Picard Iteration (MCPI) is a numerical method for approximating solutions of Ordinary Differential Equations (ODEs). MCPI uses Picard Iteration with Orthogonal Chebyshev Polynomial basis functions to recursively update approximate time histories of system states. Unlike stepping numerical integrators, such as explicit Runge-Kutta methods, MCPI approximates large segments of the trajectory by evaluating the forcing function at multiple nodes along the current approximation during each iteration. Importantly, the Picard sequence theoretically converges to the solution over large time intervals if the forces are continuous and once differentiable. Orthogonality of the basis functions and a vector-matrix formulation allow for low overhead cost, efficient iterations, and parallel evaluation of the forcing function. Despite these advantages MCPI only achieves a geometric rate of convergence. Depending on the quality of the starting approximation, MCPI sometimes requires more function evaluations than competing methods; for parallel applications, this is not a serious drawback, but may be for some serial applications. To improve efficiency, the Terminal Convergence Approximation Modified Chebyshev Picard Iteration (TCA-MCPI) was developed. TCA-MCPI takes advantage of the property that once moderate accuracy of the approximating trajectory has been achieved, the subsequent displacement of nodes asymptotically approaches zero. Applying judicious approximation methods to the force function at each node in the terminal convergence iterations is shown to dramatically reduce the computational cost to achieve accurate convergence. To illustrate this approach we consider high-order spherical-harmonic gravity for high accuracy orbital propagation. When combined with a starting approximation from the 2-body solution TCA-MCPI, is shown to outperform 2 current state-of-practice integration methods for astrodynamics. This paper presents the development of TCA

  13. Spectral method for pricing options in illiquid markets

    NASA Astrophysics Data System (ADS)

    Pindza, Edson; Patidar, Kailash C.

    2012-09-01

    We present a robust numerical method to solve a problem of pricing options in illiquid markets. The governing equation is described by a nonlinear Black-Scholes partial differential equation (BS-PDE) of the reaction-diffusion-advection type. To discretise this BS-PDE numerically, we use a spectral method in the asset (spatial) direction and couple it with a fifth order RADAU method for the discretisation in the time direction. Numerical experiments illustrate that our approach is very efficient for pricing financial options in illiquid markets.

  14. Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

    2011-01-01

    This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

  15. An Improved Spectral Background Subtraction Method Based on Wavelet Energy.

    PubMed

    Zhao, Fengkui; Wang, Jian; Wang, Aimin

    2016-12-01

    Most spectral background subtraction methods rely on the difference in frequency response of background compared with characteristic peaks. It is difficult to extract accurately the background components from the spectrum when characteristic peaks and background have overlaps in frequency domain. An improved background estimation algorithm based on iterative wavelet transform (IWT) is presented. The wavelet entropy principle is used to select the best wavelet basis. A criterion based on wavelet energy theory to determine the optimal iteration times is proposed. The case of energy dispersive X-ray spectroscopy is discussed for illustration. A simulated spectrum with a prior known background and an experimental spectrum are tested. The processing results of the simulated spectrum is compared with non-IWT and it demonstrates the superiority of the IWT. It has great significance to improve the accuracy for spectral analysis.

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

    SciTech Connect

    Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.

    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.

  17. Spectral analysis of mammographic images using a multitaper method

    SciTech Connect

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

    2012-02-15

    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.

  18. Application of Block Krylov Subspace Spectral Methods to Maxwell's Equations

    SciTech Connect

    Lambers, James V.

    2009-10-08

    Ever since its introduction by Kane Yee over forty years ago, the finite-difference time-domain (FDTD) method has been a widely-used technique for solving the time-dependent Maxwell's equations. This paper presents an alternative approach to these equations in the case of spatially-varying electric permittivity and/or magnetic permeability, based on Krylov subspace spectral (KSS) methods. These methods have previously been applied to the variable-coefficient heat equation and wave equation, and have demonstrated high-order accuracy, as well as stability characteristic of implicit time-stepping schemes, even though KSS methods are explicit. KSS methods for scalar equations compute each Fourier coefficient of the solution using techniques developed by Gene Golub and Gerard Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral, rather than physical, domain. We show how they can be generalized to coupled systems of equations, such as Maxwell's equations, by choosing appropriate basis functions that, while induced by this coupling, still allow efficient and robust computation of the Fourier coefficients of each spatial component of the electric and magnetic fields. We also discuss the implementation of appropriate boundary conditions for simulation on infinite computational domains, and how discontinuous coefficients can be handled.

  19. A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

    NASA Astrophysics Data System (ADS)

    Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

    2017-03-01

    Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

  20. Tomographic fluorescence reconstruction by a spectral projected gradient pursuit method

    NASA Astrophysics Data System (ADS)

    Ye, Jinzuo; An, Yu; Mao, Yamin; Jiang, Shixin; Yang, Xin; Chi, Chongwei; Tian, Jie

    2015-03-01

    In vivo fluorescence molecular imaging (FMI) has played an increasingly important role in biomedical research of preclinical area. Fluorescence molecular tomography (FMT) further upgrades the two-dimensional FMI optical information to three-dimensional fluorescent source distribution, which can greatly facilitate applications in related studies. However, FMT presents a challenging inverse problem which is quite ill-posed and ill-conditioned. Continuous efforts to develop more practical and efficient methods for FMT reconstruction are still needed. In this paper, a method based on spectral projected gradient pursuit (SPGP) has been proposed for FMT reconstruction. The proposed method was based on the directional pursuit framework. A mathematical strategy named the nonmonotone line search was associated with the SPGP method, which guaranteed the global convergence. In addition, the Barzilai-Borwein step length was utilized to build the new step length of the SPGP method, which was able to speed up the convergence of this gradient method. To evaluate the performance of the proposed method, several heterogeneous simulation experiments including multisource cases as well as comparative analyses have been conducted. The results demonstrated that, the proposed method was able to achieve satisfactory source localizations with a bias less than 1 mm; the computational efficiency of the method was one order of magnitude faster than the contrast method; and the fluorescence reconstructed by the proposed method had a higher contrast to the background than the contrast method. All the results demonstrated the potential for practical FMT applications with the proposed method.

  1. A spectral method for spatial downscaling | Science Inventory ...

    EPA Pesticide Factsheets

    Complex computer models play a crucial role in air quality research. These models are used to evaluate potential regulatory impacts of emission control strategies and to estimate air quality in areas without monitoring data. For both of these purposes, it is important to calibrate model output with monitoring data to adjust for model biases and improve spatial prediction. In this paper, we propose a new spectral method to study and exploit complex relationships between model output and monitoring data. Spectral methods allow us to estimate the relationship between model output and monitoring data separately at different spatial scales, and to use model output for prediction only at the appropriate scales. The proposed method is computationally efficient and can be implemented using standard software. We apply the method to compare Community Multiscale Air Quality (CMAQ) model output with ozone measurements in the United States in July, 2005. We find that CMAQ captures large-scale spatial trends, but has low correlation with the monitoring data at small spatial scales. The National Exposure Research Laboratory′s (NERL′s)Atmospheric Modeling Division (AMAD) conducts research in support of EPA′s mission to protect human health and the environment. AMAD′s research program is engaged in developing and evaluating predictive atmospheric models on all spatial and temporal scales for forecasting the Nation′s air quality and for assessing ch

  2. Time spectral method for rotorcraft flow with vorticity confinement

    NASA Astrophysics Data System (ADS)

    Butsuntorn, Nawee

    2008-10-01

    This thesis shows that simulation of helicopter flows can adhere to engineering accuracy without the need of massive computing resources or long turnaround time by choosing an alternative framework for rotorcraft simulation. The method works in both hovering and forward flight regimes. The new method has shown to be more computationally efficient and sufficiently accurate. By utilizing the periodic nature of the rotorcraft flow field, the Fourier based Time Spectral method lends itself to the problem and significantly increases the rate of convergence compared to traditional implicit time integration schemes such as the second order backward difference formula (BDF). A Vorticity Confinement method has been explored and has been shown to work well in subsonic and transonic simulations. Vortical structure can be maintained after long distances without resorting to the traditional mesh refinement technique.

  3. PSD computations using Welch's method. [Power Spectral Density (PSD)

    SciTech Connect

    Solomon, Jr, O M

    1991-12-01

    This report describes Welch's method for computing Power Spectral Densities (PSDs). We first describe the bandpass filter method which uses filtering, squaring, and averaging operations to estimate a PSD. Second, we delineate the relationship of Welch's method to the bandpass filter method. Third, the frequency domain signal-to-noise ratio for a sine wave in white noise is derived. This derivation includes the computation of the noise floor due to quantization noise. The signal-to-noise ratio and noise flood depend on the FFT length and window. Fourth, the variance the Welch's PSD is discussed via chi-square random variables and degrees of freedom. This report contains many examples, figures and tables to illustrate the concepts. 26 refs.

  4. Regularized discriminative spectral regression method for heterogeneous face matching.

    PubMed

    Huang, Xiangsheng; Lei, Zhen; Fan, Mingyu; Wang, Xiao; Li, Stan Z

    2013-01-01

    Face recognition is confronted with situations in which face images are captured in various modalities, such as the visual modality, the near infrared modality, and the sketch modality. This is known as heterogeneous face recognition. To solve this problem, we propose a new method called discriminative spectral regression (DSR). The DSR maps heterogeneous face images into a common discriminative subspace in which robust classification can be achieved. In the proposed method, the subspace learning problem is transformed into a least squares problem. Different mappings should map heterogeneous images from the same class close to each other, while images from different classes should be separated as far as possible. To realize this, we introduce two novel regularization terms, which reflect the category relationships among data, into the least squares approach. Experiments conducted on two heterogeneous face databases validate the superiority of the proposed method over the previous methods.

  5. A Fourier-Legendre spectral element method in polar coordinates

    NASA Astrophysics Data System (ADS)

    Qiu, Zhouhua; Zeng, Zhong; Mei, Huan; Li, Liang; Yao, Liping; Zhang, Liangqi

    2012-01-01

    In this paper, a new Fourier-Legendre spectral element method based on the Galerkin formulation is proposed to solve the Poisson-type equations in polar coordinates. The 1/ r singularity at r = 0 is avoided by using Gauss-Radau type quadrature points. In order to break the time-step restriction in the time-dependent problems, the clustering of collocation points near the pole is prevented through the technique of domain decomposition in the radial direction. A number of Poisson-type equations subject to the Dirichlet or Neumann boundary condition are computed and compared with the results in literature, which reveals a desirable result.

  6. Thermoacoustic tomography forward modeling with the spectral element method.

    PubMed

    Lim, Kim Hwa; Lee, Joon-Ho; Liu, Qing Huo

    2008-01-01

    A thermoacoustic tomography (TAT) forward solver based on the spectral element method (SEM) with perfectly matched layer absorbing boundary condition has been developed. The TAT forward solver is intended to model acoustically inhomogeneous media with high accuracy in the frequency domain. The high-order basis functions used in the SEM are Gauss-Lobatto-Legendre (GLL) polynomials. Due to the orthogonality of the GLL basis functions and GLL quadrature integration, the mass matrix is diagonal and the stiffness matrix is sparse. Thus, the proposed method greatly reduces the memory requirement and computational time in comparison with the conventional finite element method (FEM). Numerical results show that the high-order SEM is able to achieve the same accuracy as the FEM but with a much smaller number of unknowns. Therefore, the TAT forward solver based on SEM is able to simulate a large-scale and realistic TAT problem.

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

    NASA Technical Reports Server (NTRS)

    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.

  8. Near-infrared spectral methods for noninvasively measuring blood glucose

    NASA Astrophysics Data System (ADS)

    Fei, Sun; Kong, Deyi; Mei, Tao; Tao, Yongchun

    2004-05-01

    Determination of blood glucose concentrations in diabetic patients is a frequently occurring procedure and an important tool for diabetes management. Use of noninvasive detection techniques can relieve patients from the pain of frequent finger pokes and avoid the infection of disease via blood. This thesis discusses current research and analyzes the advantages and shortages of different measurement methods, including: optical methods (Transmission, Polarimetry and scattering), then, we give emphasis to analyze the technology of near-infrared (NIR) spectra. NIR spectral range 700 nm ~2300 nm was used because of its good transparency for biological tissue and presence of glucose absorption band. In this work, we present an outline of noninvasive blood glucose measurement. A near-infrared light beam is passed through the finger, and the spectral components of the emergent beam are measured using spectroscopic techniques. The device includes light sources having the wavelengths of 600 nm - 1800 nm to illuminate the tissue. Receptors associated with the light sources for receiving light and generating a transmission signal representing the light transmitted are also provided. Once a transmission signal is received by receptors, and the high and low values from each of the signals are stored in the device. The averaged values are then analyzed to determine the glucose concentration, which is displayed on the device.

  9. An improved Chebyshev distance metric for clustering medical images

    NASA Astrophysics Data System (ADS)

    Mousa, Aseel; Yusof, Yuhanis

    2015-12-01

    A metric or distance function is a function which defines a distance between elements of a set. In clustering, measuring the similarity between objects has become an important issue. In practice, there are various similarity measures used and this includes the Euclidean, Manhattan and Minkowski. In this paper, an improved Chebyshev similarity measure is introduced to replace existing metrics (such as Euclidean and standard Chebyshev) in clustering analysis. The proposed measure is later realized in analyzing blood cancer images. Results demonstrate that the proposed measure produces the smallest objective function value and converge at the lowest number of iteration. Hence, it can be concluded that the proposed distance metric contribute in producing better clusters.

  10. Spectral ordering techniques for incomplete LU preconditoners for CG methods

    NASA Technical Reports Server (NTRS)

    Clift, Simon S.; Simon, Horst D.; Tang, Wei-Pai

    1995-01-01

    The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.

  11. Spectral methods applied to fluidized-bed combustors

    SciTech Connect

    Brown, R.C.; Raines, T.S.; Thiede, T.D.

    1995-11-01

    The goal of this research is to characterize coals and sorbents during the normal operation of an industrial-scale circulating fluidized bed (CFB) boiler. The method determines coal or sorbent properties based on the analysis of transient CO{sub 2} or SO{sub 2} emissions from the boiler. Fourier Transform Infrared (FTIR) spectroscopy is used to qualitatively and quantitatively analyze the gaseous products of combustion. Spectral analysis applied to the transient response of CO{sub 2} and SO{sub 2} resulting from introduction of a batch of coal or limestone into the boiler yields characteristic time constants from which combustion or sorbent models are developed. The method is non-intrusive and is performed under realistic combustion conditions. Results are presented from laboratory studies and power plant monitoring.

  12. A Data Transfer Fusion Method for Discriminating Similar Spectral Classes

    PubMed Central

    Wang, Qingyan; Zhang, Junping

    2016-01-01

    Hyperspectral data provide new capabilities for discriminating spectrally similar classes, but such class signatures sometimes will be difficult to analyze. To incorporate reliable useful information could help, but at the same time, may also lead increased dimensionality of the feature vector making the hyperspectral data larger than expected. It is challenging to apply discriminative information from these training data to testing data that are not in the same feature space and with different data distributions. A data fusion method based on transfer learning is proposed, in which transfer learning is introduced into boosting algorithm, and other out-date data are used to instruct hyperspectral image classification. In order to validate the method, experiments are conducted on EO-1 Hyperion hyperspectral data and ROSIS hyperspectral data. Significant improvements have been achieved in terms of accuracy compared to the results generated by conventional classification approaches. PMID:27854238

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

    NASA Astrophysics Data System (ADS)

    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.

  14. Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    2004-01-01

    A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of

  15. Bivariate Chebyshev Expansion of the Pacejka's Tyre Model

    NASA Astrophysics Data System (ADS)

    López, Alberto; Vélez, Pilar; Moriano, Cristina

    2007-09-01

    Pacejka's tyre model is widely used and well-known by the community of automotive engineers. The magic formula basically describes the brake force, side force and self-aligning torque in terms of the longitudinal slip and slip angle, with corrections due to the variation of the load force and camber angle. Obtaining continuous approximate solutions in Chebyshev series expansions of full vehicle dynamics can help in the real time solving of vehicle equations, for collision avoidance purposes. We contribute to solve the specific problem of the tyre's model expansion and its integration with the longitudinal, lateral and vertical behaviour of the car. The present work describes the approximation of the magic formula with Chebyshev's series development of rational polynomials, maintaining a moderate error of the model respect to the original formula, with a triple objective: firstly to obtain a very fast processing of the formula, secondly to allow the inclusion of the formula in DAE systems of vehicular dynamic modelling solved continuously, not numerically, by means of the expansion of the complete system in Chebyshev's series, and thirdly, the final expressions can be evaluated, integrated and derived easily.

  16. Spectral Sensitivity Measured with Electroretinogram Using a Constant Response Method

    PubMed Central

    Rocha, Fernando Allan de Farias; Gomes, Bruno Duarte; Silveira, Luiz Carlos de Lima; Martins, Sonia Limara; Aguiar, Renata Genaro; de Souza, John Manuel; Ventura, Dora Fix

    2016-01-01

    A new method is presented to determine the retinal spectral sensitivity function S(λ) using the electroretinogram (ERG). S(λ)s were assessed in three different species of myomorph rodents, Gerbils (Meriones unguiculatus), Wistar rats (Ratus norvegicus), and mice (Mus musculus). The method, called AC Constant Method, is based on a computerized automatic feedback system that adjusts light intensity to maintain a constant-response amplitude to a flickering stimulus throughout the spectrum, as it is scanned from 300 to 700 nm, and back. The results are presented as the reciprocal of the intensity at each wavelength required to maintain a constant peak to peak response amplitude. The resulting S(λ) had two peaks in all three rodent species, corresponding to ultraviolet and M cones, respectively: 359 nm and 511 nm for mice, 362 nm and 493 nm for gerbils, and 362 nm and 502 nm for rats. Results for mouse and gerbil were similar to literature reports of S(λ) functions obtained with other methods, confirming that the ERG associated to the AC Constant-Response Method was effective to obtain reliable S(λ) functions. In addition, due to its fast data collection time, the AC Constant Response Method has the advantage of keeping the eye in a constant light adapted state. PMID:26800521

  17. A new automated spectral feature extraction method and its application in spectral classification and defective spectra recovery

    NASA Astrophysics Data System (ADS)

    Wang, Ke; Guo, Ping; Luo, A.-Li

    2017-03-01

    Spectral feature extraction is a crucial procedure in automated spectral analysis. This procedure starts from the spectral data and produces informative and non-redundant features, facilitating the subsequent automated processing and analysis with machine-learning and data-mining techniques. In this paper, we present a new automated feature extraction method for astronomical spectra, with application in spectral classification and defective spectra recovery. The basic idea of our approach is to train a deep neural network to extract features of spectra with different levels of abstraction in different layers. The deep neural network is trained with a fast layer-wise learning algorithm in an analytical way without any iterative optimization procedure. We evaluate the performance of the proposed scheme on real-world spectral data. The results demonstrate that our method is superior regarding its comprehensive performance, and the computational cost is significantly lower than that for other methods. The proposed method can be regarded as a new valid alternative general-purpose feature extraction method for various tasks in spectral data analysis.

  18. Method for detection and imaging over a broad spectral range

    SciTech Connect

    Yefremenko, Volodymyr; Gordiyenko, Eduard; Pishko, legal representative, Olga; Novosad, Valentyn; Pishko, deceased; Vitalii

    2007-09-25

    A method of controlling the coordinate sensitivity in a superconducting microbolometer employs localized light, heating or magnetic field effects to form normal or mixed state regions on a superconducting film and to control the spatial location. Electron beam lithography and wet chemical etching were applied as pattern transfer processes in epitaxial Y--Ba--Cu--O films. Two different sensor designs were tested: (i) a 3 millimeter long and 40 micrometer wide stripe and (ii) a 1.25 millimeters long, and 50 micron wide meandering-like structure. Scanning the laser beam along the stripe leads to physical displacement of the sensitive area, and, therefore, may be used as a basis for imaging over a broad spectral range. Forming the superconducting film as a meandering structure provides the equivalent of a two-dimensional detector array. Advantages of this approach are simplicity of detector fabrication, and simplicity of the read-out process requiring only two electrical terminals.

  19. Propane spectral resolution enhancement by the maximum entropy method

    NASA Technical Reports Server (NTRS)

    Bonavito, N. L.; Stewart, K. P.; Hurley, E. J.; Yeh, K. C.; Inguva, R.

    1990-01-01

    The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

  20. Spectral (Finite) Volume Method for One Dimensional Euler Equations

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2002-01-01

    Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

  1. Scalable implementation of spectral methods for the Dirac equation

    SciTech Connect

    Wells, J.C.

    1998-10-01

    The author discusses the implementation and performance on massively parallel, distributed-memory computers of a message-passing program to solve the time-dependent dirac equation in three Cartesian coordinates. Luses pseudo-spectral methods to obtain a discrete representation of the dirac spinor wavefunction and all coordinate-space operators. Algorithms for the solution of the discrete equations are iterative and depend critically on the dirac hamiltonian-wavefunction product, which he implements as a series of parallel matrix products using MPI. He investigated two communication algorithms, a ring algorithm and a collective-communication algorithm, and present performance results for each on a Paragon-MP (1024 nodes) and a Cray T3E-900 (512 nodes). The ring algorithm achieves very good performance, scaling up to the maximum number of nodes on each machine. However, the collective-communication algorithm scales effectively only on the Paragon.

  2. A spectral method for the computation of propeller acoustics

    NASA Astrophysics Data System (ADS)

    Schulten, J. B. H. M.

    1987-10-01

    An analytical description of the acoustic field of a propeller in a uniform flow is derived. Instead of applying the usual Ffowcs Williams-Hawkings version of the acoustic analogy, sources are formulated on a surface enclosing the propeller and its adjacent nonlinear flow field. This approach, which avoids the laborious evaluation of quadrupole source terms, is to be considered as a generalization of the Kirchhoff-Helmholtz theorem of acoustics. By describing the fundamental solution as a spectral Fourier-Bessel decomposition, the resulting sound field is readily given the appropriate series of harmonic amplitudes. The method is validated by a comparison of numerical results with experimental data of a propeller in an acoustic wind tunnel. A good agreement in amplitude and phase is found between theory and experiment.

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

    NASA Technical Reports Server (NTRS)

    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.

  4. A spectral boundary integral method for flowing blood cells

    NASA Astrophysics Data System (ADS)

    Zhao, Hong; Isfahani, Amir H. G.; Olson, Luke N.; Freund, Jonathan B.

    2010-05-01

    A spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated. The blood cells are modeled as finite-deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma, but the solver itself is independent of the particular constitutive model employed for the cell membranes. The surface integrals developed for solving the viscous flow, and thereby the motion of the massless membrane, are evaluated using an O(NlogN) particle-mesh Ewald (PME) approach. The cell shapes, which can become highly distorted under physiologic conditions, are discretized with spherical harmonics. The resolution of these global basis functions is, of course, excellent, but more importantly they facilitate an approximate de-aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step. Complex geometry no-slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine. The implementation is verified against solutions for axisymmetric flows reported in the literature, and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations. It is also used to simulate flow of blood cells at 30% volume fraction in tubes between 4.9 and 16.9 μm in diameter. For these, it is shown to reproduce the well-known non-monotonic dependence of the effective viscosity on the tube diameter.

  5. Effect of method and parameters of spectral analysis on selected indices of simulated Doppler spectra.

    PubMed

    Kaluzynski, K; Palko, T

    1993-05-01

    The sensitivity of Doppler spectral indices (mean frequency, maximum frequency, spectral broadening index and turbulence intensity) to the conditions of spectral analysis (estimation method, data window, smoothing window or model order) increases with decreasing signal bandwidth and growing index complexity. The bias of spectral estimate has a more important effect on these indices than its variance. A too low order, in the case of autoregressive modeling and minimum variance methods, and excessive smoothing, in the case of the FFT method, result in increased errors of Doppler spectral indices. There is a trade-off between the errors resulting from a short data window and those due to insufficient temporal resolution.

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

    SciTech Connect

    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.

  7. A method of determining spectral dye densities in color films

    NASA Technical Reports Server (NTRS)

    Friederichs, G. A.; Scarpace, F. L.

    1977-01-01

    A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

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

    PubMed

    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.

  9. Two-Time Green's Functions and the Spectral Density Method in Nonextensive Classical Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Cavallo, A.; Cosenza, F.; de Cesare, L.

    2001-12-01

    The two-time retarded and advanced Green's function technique is formulated in nonextensive classical statistical mechanics within the optimal Lagrange multiplier framework. The main spectral properties are presented and a spectral decomposition for the spectral density is obtained. Finally, the nonextensive version of the spectral density method is given and its effectiveness is tested by exploring the equilibrium properties of a classical ferromagnetic spin chain.

  10. Good Interpolation Points: Learning from Chebyshev, Fekete, Haar and Lebesgue

    NASA Astrophysics Data System (ADS)

    Cuyt, Annie; Ibrahimoglu, B. Ali; Yaman, Irem

    2011-09-01

    The search for sets of good interpolation points is highly motivated by the fact that, due to the finite precision of digital computers, valid results can only be expected when the interpolation problem is well-conditioned. The conditioning of polynomial interpolation and of rational interpolation with preassigned poles is measured by the respective Lebesgue constants. Here we summarize the main results with respect to the Lebesgue constant for polynomial interpolation and we present the best Lebesgue constants in existence for rational interpolation with preassigned poles. The new results are based on a fairly unknown rational analogue of the Chebyshev orthogonal polynomials. We compare with the results obtained in [1] and [2].

  11. Method and apparatus for measuring film spectral properties

    SciTech Connect

    Forrest, S.R.; Burrows, P.E.; Garbuzov, D.Z.; Bulovic, V.

    1999-12-21

    Film spectral properties are measured by projecting chopped monochromatic light onto a luminescent film sample deposited on a substrate, and coupling through use of immersion oil the reflection of light therefrom to a light detector.

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

    NASA Astrophysics Data System (ADS)

    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

  13. Chebyshev acceleration for lambda mode calculations

    SciTech Connect

    Belchior, A. Jr.; Moreira, J.M.L. )

    1992-01-01

    Coordenadoria para Projetos Especals (COPESP) has been making an effort to develop a power distribution mapping system utilizing self-powered neutron detectors. The scheme adopted to estimate the power distribution is based on an expansion of lambda modes for a given reactor state. Two-dimensional lambda modes were obtained previously with a modified version of the CITATION code. The method was based on the orthogonality properties of the lambda modes. Several modes could be obtained, but the convergence was slow because of the lack of an appropriate accelerating scheme in the CITATION code for calculating lambda modes. This work presents the acceleration scheme implemented into the CITATION code to obtain lambda modes.

  14. New spectral methods in cloud and aerosol remote sensing applications

    NASA Astrophysics Data System (ADS)

    Schmidt, K. Sebastian; McBride, Patrick; Pilewskie, Peter; Feingold, Graham; Jiang, Hongli

    2010-05-01

    We present new remote sensing techniques that rely on spectral observations of clouds and aerosols in the solar wavelength range. As a first example, we show how the effects of heterogeneous clouds, aerosols of changing optical properties, and the surface within one pixel can be distinguished by means of their spectral signatures. This example is based on data from the Gulf of Mexico Atmospheric Composition and Climate Study (GoMACCS, Houston, Texas, 2006), Large Eddy Simulations (LES) of polluted boundary layer clouds, and 3-dimensional radiative transfer calculations. In a second example, we show that the uncertainty of cloud retrievals can be improved considerably by exploiting the spectral information around liquid water absorption features in the near-infrared wavelength range. This is illustrated with spectral transmittance data from the NOAA International Chemistry Experiment in the Arctic LOwer Troposphere (ICEALOT, 2008). In contrast to reflected radiance, transmitted radiance is only weakly sensitive to cloud effective drop radius, and only cloud optical thickness can be obtained from the standard dual-channel technique. We show that effective radius and liquid water path can also be retrieved with the new spectral approach, and validate our results with microwave liquid water path measurements.

  15. Spectral multigrid methods for the solution of homogeneous turbulence problems

    NASA Technical Reports Server (NTRS)

    Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

    1987-01-01

    New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.

  16. PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise

    SciTech Connect

    Abdulle, Assyr; Vilmart, Gilles

    2013-06-01

    A partitioned implicit–explicit orthogonal Runge–Kutta method (PIROCK) is proposed for the time integration of diffusion–advection–reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise terms (solved explicitly) are integrated in the algorithm as finishing procedures. It is shown that the various coupling (between diffusion, reaction, advection and noise) can be stabilized in the PIROCK method. The method, implemented in a single black-box code that is fully adaptive, provides error estimators for the various terms present in the problem, and requires from the user solely the right-hand side of the differential equation. Numerical experiments and comparisons with existing Chebyshev methods, IMEX methods and partitioned methods show the efficiency and flexibility of our new algorithm.

  17. Spectral/HP Element Method With Hierarchical Reconstruction for Solving Hyperbolic Conservation Laws

    SciTech Connect

    Xu, Zhiliang; Lin, Guang

    2009-12-01

    Hierarchical reconstruction (HR) has been successfully applied to prevent oscillations in solutions computed by finite volume, discontinuous Galerkin, spectral volume schemes when solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element methods for solving hyperbolic conservation laws. We show that HR preserves the order of accuracy of spectral/hp element methods for smooth solutions and generate essentially non-oscillatory solution profiles for shock wave problems.

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

    NASA Astrophysics Data System (ADS)

    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.

  19. A multidomain spectral collocation method for the Stokes problem

    NASA Technical Reports Server (NTRS)

    Landriani, G. Sacchi; Vandeven, H.

    1989-01-01

    A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

  20. A spectral KRMI conjugate gradient method under the strong-Wolfe line search

    NASA Astrophysics Data System (ADS)

    Khadijah, Wan; Rivaie, Mohd.; Mamat, Mustafa; Jusoh, Ibrahim

    2016-06-01

    In this paper, a modification of spectral conjugate gradient (CG) method is proposed which combines the advantages of the spectral CG method and the RMIL method namely as spectral Khadijah-Rivaie-Mustafa-Ibrahim (SKRMI) to solve unconstrained optimization problems. Based on inexact line searches, the objective function generates a sufficient descent direction and the global convergence property for the proposed method has been proved. Moreover, the method reduces to the standard RMIL method if exact line search is applied. Numerical results are also presented to examine the efficiency of the proposed method.

  1. Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

    PubMed Central

    Bayındır, Cihan

    2016-01-01

    In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

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

    NASA Technical Reports Server (NTRS)

    Zorumski, William E.; Hodge, Steven L.

    1993-01-01

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

  3. Spectral element methods for transitional flows, in complex geometries.

    SciTech Connect

    Fischer, P. F.; Kruse, G. W.; Loth, F.; Mathematics and Computer Science; Juniata Coll.; Univ. of Illinois

    2002-01-01

    We describe the development and implementation of an efficient spectral element code for simulating transitional flows in complex three-dimensional domains. Critical to this effort is the use of geometrically nonconforming elements that allow localized refinement in regions of interest, coupled with a stabilized high-order time-split formulation of the semi-discrete Navier-Stokes equations. Simulations of transition in a model of an arteriovenous graft illustrate the potential of this approach in biomechanical applications.

  4. Spectral: Solving Schroedinger and Wheeler-DeWitt equations in the positive semi-axis by the spectral method

    NASA Astrophysics Data System (ADS)

    Corrêa Silva, E. V.; Monerat, G. A.; de Oliveira Neto, G.; Ferreira Filho, L. G.

    2014-01-01

    The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler-DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user.

  5. An efficient and secure Diffie-Hellman key agreement protocol based on Chebyshev chaotic map

    NASA Astrophysics Data System (ADS)

    Yoon, Eun-Jun; Jeon, Il-Soo

    2011-06-01

    This paper proposes a new efficient and secure Diffie-Hellman key agreement protocol based on Chebyshev chaotic map. The proposed key agreement protocol uses the semi-group property of Chebyshev polynomials to agree Diffie-Hellman based session key. The proposed protocol provides strong security compared with the previous related protocols. In addition, the proposed protocol does not require any timestamp information and greatly reduces computational costs between communication parties. As a result, the proposed protocol is more practical and provides computational/communicational efficiency compare with several previously proposed key agreement protocols based on Chebyshev chaotic map.

  6. The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

    NASA Astrophysics Data System (ADS)

    Degasperis, Antonio; Conforti, Matteo; Baronio, Fabio; Wabnitz, Stefan; Lombardo, Sara

    2011-06-01

    The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.

  7. A spectral-spatial kernel-based method for hyperspectral imagery classification

    NASA Astrophysics Data System (ADS)

    Li, Li; Ge, Hongwei; Gao, Jianqiang

    2017-02-01

    Spectral-based classification methods have gained increasing attention in hyperspectral imagery classification. Nevertheless, the spectral cannot fully represent the inherent spatial distribution of the imagery. In this paper, a spectral-spatial kernel-based method for hyperspectral imagery classification is proposed. Firstly, the spatial feature was extracted by using area median filtering (AMF). Secondly, the result of the AMF was used to construct spatial feature patch according to different window sizes. Finally, using the kernel technique, the spectral feature and the spatial feature were jointly used for the classification through a support vector machine (SVM) formulation. Therefore, for hyperspectral imagery classification, the proposed method was called spectral-spatial kernel-based support vector machine (SSF-SVM). To evaluate the proposed method, experiments are performed on three hyperspectral images. The experimental results show that an improvement is possible with the proposed technique in most of the real world classification problems.

  8. Quantum state-to-state cross sections for atom-diatom reactions: A Chebyshev real wave-packet approach

    SciTech Connect

    Lin Shiying; Guo Hua

    2006-08-15

    We describe the implementation of a quantum mechanical method to calculate state-to-state differential cross sections for atom-diatom reactive scattering processes. The key ingredient of this approach is the efficient and accurate propagation of a real scattering wave packet in the Chebyshev order domain, from which the S-matrix elements can be extracted. This approach is implemented with Open MP and applied to compute differential and integral cross sections for the direct H+H{sub 2} abstraction reaction and the more challenging N({sup 2}D)+H{sub 2} insertion reaction.

  9. A comparison of numerical methods for the Rayleigh equation in unbounded domains

    NASA Technical Reports Server (NTRS)

    Liou, W. W.; Morris, P. J.

    1991-01-01

    A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.

  10. Color constancy - A method for recovering surface spectral reflectance

    NASA Technical Reports Server (NTRS)

    Maloney, L. T.; Wandell, B. A.

    1986-01-01

    An algorithm has been developed for estimating the surface reflectance functions of objects in a scene with incomplete knowledge of the spectral power distribution of the ambient light. An image processing system employing this algorithm can assign colors that are constant despite changes in the lighting of the scene; this capability is essential to correct color rendering in photography, TV, and in the construction of artificial visual systems for robotics. Attention is given to the way in which constraints on lights and surfaces in the environment make color-constancy possible for a visual system, and the algorithm's implications for human color vision are discussed.

  11. Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

    PubMed

    Malachowski, George C; Clegg, Robert M; Redford, Glen I

    2007-12-01

    A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

  12. A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

    2001-01-01

    A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

  13. Analysis of the spectral vanishing viscosity method for periodic conservation laws

    NASA Technical Reports Server (NTRS)

    Maday, Yvon; Tadmor, Eitan

    1988-01-01

    The convergence of the spectral vanishing method for both the spectral and pseudospectral discretizations of the inviscid Burgers' equation is analyzed. It is proven that this kind of vanishing viscosity is responsible for a spectral decay of those Fourier coefficients located toward the end of the computed spectrum; consequently, the discretization error is shown to be spectrally small independent of whether the underlying solution is smooth or not. This in turn implies that the numerical solution remains uniformly bounded and convergence follows by compensated compactness arguments.

  14. [A method of hyperspectral quantificational identification of minerals based on infrared spectral artificial immune calculation].

    PubMed

    Liu, Qing-Jie; Jing, Lin-Hai; Li, Xin-Wu; Bi, Jian-Tao; Wang, Meng-Fei; Lin, Qi-Zhong

    2013-04-01

    Rapid identification of minerals based on near infrared (NIR) and shortwave infrared (SWIR) hyperspectra is vital to remote sensing mine exploration, remote sensing minerals mapping and field geological documentation of drill core, and have leaded to many identification methods including spectral angle mapping (SAM), spectral distance mapping (SDM), spectral feature fitting(SFF), linear spectral mixture model (LSMM), mathematical combination feature spectral linear inversion model(CFSLIM) etc. However, limitations of these methods affect their actual applications. The present paper firstly gives a unified minerals components spectral inversion (MCSI) model based on target sample spectrum and standard endmember spectral library evaluated by spectral similarity indexes. Then taking LSMM and SAM evaluation index for example, a specific formulation of unified MCSI model is presented in the form of a kind of combinatorial optimization. And then, an artificial immune colonial selection algorithm is used for solving minerals feature spectral linear inversion model optimization problem, which is named ICSFSLIM. Finally, an experiment was performed to use ICSFSLIM and CFSLIM to identify the contained minerals of 22 rock samples selected in Baogutu in Xinjiang China. The mean value of correctness and validness identification of ICSFSLIM are 34.22% and 54.08% respectively, which is better than that of CFSLIM 31.97% and 37.38%; the correctness and validness variance of ICSFSLIM are 0.11 and 0.13 smaller than that of CFSLIM, 0.15 and 0.25, indicating better identification stability.

  15. The research of a new test method about dynamic target infrared spectral signature

    NASA Astrophysics Data System (ADS)

    Wu, Jiang-hui; Gao, Jiao-bo; Chen, Qing; Luo, Yan-ling; Li, Jiang-jun; Gao, Ze-dong; Wang, Nan; Gao, Meng

    2014-11-01

    The research on infrared spectral target signature shows great military importance in the domain of IR detection Recognition, IRCM, IR image guide and ir stealth etc. The measurements of infrared spectral of tactical targets have been a direct but effective technique in providing signatures for both analysis and simulation to missile seeker designers for many years. In order to deal with the problem of dynamic target infrared spectral signature, this paper presents a new method for acquiring and testing ir spectral radiation signatures of dynamic objects, which is based on an IR imager guiding the target and acquiring the scene at the same time, a FOV chopping scan infrared spectral radiometer alternatively testing the target and its background around ir spectral signature.ir imager and spectral radiometer have the same optical axis. The raw test data was processed according to a new deal with method. Principles and data processing methods were described in detail, test error also analyzed. Field test results showed that the method described in the above is right; the test error was reduced smaller, and can better satisfy the needs of acquiring dynamic target ir spectral signature.

  16. A statistical evaluation of spectral fingerprinting methods using analysis of variance and principal component analysis

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Six methods were compared with respect to spectral fingerprinting of a well-characterized series of broccoli samples. Spectral fingerprints were acquired for finely-powdered solid samples using Fourier transform-infrared (IR) and Fourier transform-near infrared (NIR) spectrometry and for aqueous met...

  17. On spectral multigrid methods for the time-dependent Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Zang, T. A.; Hussaini, M. Y.

    1985-01-01

    A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.

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

    NASA Technical Reports Server (NTRS)

    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.

  19. A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching

    PubMed Central

    Mei, Xiaoguang; Ma, Yong; Li, Chang; Fan, Fan; Huang, Jun; Ma, Jiayi

    2015-01-01

    The state-of-the-art ultra-spectral sensor technology brings new hope for high precision applications due to its high spectral resolution. However, it also comes with new challenges, such as the high data dimension and noise problems. In this paper, we propose a real-time method for infrared ultra-spectral signature classification via spatial pyramid matching (SPM), which includes two aspects. First, we introduce an infrared ultra-spectral signature similarity measure method via SPM, which is the foundation of the matching-based classification method. Second, we propose the classification method with reference spectral libraries, which utilizes the SPM-based similarity for the real-time infrared ultra-spectral signature classification with robustness performance. Specifically, instead of matching with each spectrum in the spectral library, our method is based on feature matching, which includes a feature library-generating phase. We calculate the SPM-based similarity between the feature of the spectrum and that of each spectrum of the reference feature library, then take the class index of the corresponding spectrum having the maximum similarity as the final result. Experimental comparisons on two publicly-available datasets demonstrate that the proposed method effectively improves the real-time classification performance and robustness to noise. PMID:26205263

  20. A Real-Time Infrared Ultra-Spectral Signature Classification Method via Spatial Pyramid Matching.

    PubMed

    Mei, Xiaoguang; Ma, Yong; Li, Chang; Fan, Fan; Huang, Jun; Ma, Jiayi

    2015-07-03

    The state-of-the-art ultra-spectral sensor technology brings new hope for high precision applications due to its high spectral resolution. However, it also comes with new challenges, such as the high data dimension and noise problems. In this paper, we propose a real-time method for infrared ultra-spectral signature classification via spatial pyramid matching (SPM), which includes two aspects. First, we introduce an infrared ultra-spectral signature similarity measure method via SPM, which is the foundation of the matching-based classification method. Second, we propose the classification method with reference spectral libraries, which utilizes the SPM-based similarity for the real-time infrared ultra-spectral signature classification with robustness performance. Specifically, instead of matching with each spectrum in the spectral library, our method is based on feature matching, which includes a feature library-generating phase. We calculate the SPM-based similarity between the feature of the spectrum and that of each spectrum of the reference feature library, then take the class index of the corresponding spectrum having the maximum similarity as the final result. Experimental comparisons on two publicly-available datasets demonstrate that the proposed method effectively improves the real-time classification performance and robustness to noise.

  1. Estimates of the trace of the inverse of a symmetric matrix using the modified Chebyshev algorithm

    NASA Astrophysics Data System (ADS)

    Meurant, Gérard

    2009-07-01

    In this paper we study how to compute an estimate of the trace of the inverse of a symmetric matrix by using Gauss quadrature and the modified Chebyshev algorithm. As auxiliary polynomials we use the shifted Chebyshev polynomials. Since this can be too costly in computer storage for large matrices we also propose to compute the modified moments with a stochastic approach due to Hutchinson (Commun Stat Simul 18:1059-1076, 1989).

  2. Development and validation of a new fallout transport method using variable spectral winds. Doctoral thesis

    SciTech Connect

    Hopkins, A.T.

    1984-09-01

    The purpose of this research was to develop and validate a fallout prediction method using variable transport calculations. The new method uses National Meteorological Center (NMC) spectral coefficients to compute wind vectors along the space- and time-varying trajectories of falling particles. The method was validated by comparing computed and actual cloud trajectories from a Mount St. Helens volcanic eruption and a high dust cloud. In summary, this research demonstrated the feasibility of using spectral coefficients for fallout transport calculations, developed a two-step smearing model to treat variable winds, and showed that uncertainties in spectral winds do not contribute significantly to the error in computed dose rate.

  3. Research on method of infrared spectral imaging based on thermal imager

    NASA Astrophysics Data System (ADS)

    Huan, Ke-wei; Shi, Xiao-guang; Wu, Wei; Zheng, Feng; Liu, Xiao-xi

    2011-08-01

    In recent years, technology of thermal imager and spectral imaging is becoming mature, and the application of them is increased. The method is based on the blackbody radiation theory, make use of the infrared thermal imager to collect and analysis the thermal images, distill the temperature value of different pixel of the thermal images, use Matlab to deal blackbody radiation emitted curve fitting according with the temperature value of different pixels, and get the values of the degree of radiation emitted at the same wavelength from the different pixels, then make spectral imaging (1μm~10μm) according to the values. At last, do analysis to spectral imaging of different spectral bands; discuss the limitations of using this method to achieve spectral imaging.

  4. A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions

    PubMed Central

    Bhrawy, A. H.; Alghamdi, M. A.

    2014-01-01

    We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507

  5. Research on method of geometry and spectral calibration of pushbroom dispersive hyperspectral imager

    NASA Astrophysics Data System (ADS)

    He, Zhiping; Shu, Rong; Wang, Jianyu

    2012-11-01

    Development and application of airborne and aerospace hyperspectral imager press for high precision geometry and spectral calibration of pixels of image cube. The research of geometry and spectral calibration of pushbroom hyperspectral imager, its target is giving the coordinate of angle field of view and center wavelength of each detect unit in focal plane detector of hyperspectral imager, and achieves the high precision, full field of view, full channel geometry and spectral calibration. It is importance for imaging quantitative and deep application of hyperspectal imager. The paper takes the geometry and spectral calibration of pushbroom dispersive hyperspectral imager as case study, and research on the constitution and analysis of imaging mathematical model. Aimed especially at grating-dispersive hyperspectral imaging, the specialty of the imaging mode and dispersive method has been concretely analyzed. Based on the analysis, the theory and feasible method of geometry and spectral calibration of dispersive hyperspectral imager is set up. The key technique has been solved is As follows: 1). the imaging mathematical model and feasible method of geometry and spectral calibration for full pixels of image cube has been set up, the feasibility of the calibration method has been analyzed. 2). the engineering model and method of the geometry and spectral calibration of pushbroom dispersive hyperspectral imager has been set up and the calibration equipment has been constructed, and the calibration precision has been analyzed.

  6. Method for hyperspectral imagery exploitation and pixel spectral unmixing

    NASA Technical Reports Server (NTRS)

    Lin, Ching-Fang (Inventor)

    2003-01-01

    An efficiently hybrid approach to exploit hyperspectral imagery and unmix spectral pixels. This hybrid approach uses a genetic algorithm to solve the abundance vector for the first pixel of a hyperspectral image cube. This abundance vector is used as initial state in a robust filter to derive the abundance estimate for the next pixel. By using Kalman filter, the abundance estimate for a pixel can be obtained in one iteration procedure which is much fast than genetic algorithm. The output of the robust filter is fed to genetic algorithm again to derive accurate abundance estimate for the current pixel. The using of robust filter solution as starting point of the genetic algorithm speeds up the evolution of the genetic algorithm. After obtaining the accurate abundance estimate, the procedure goes to next pixel, and uses the output of genetic algorithm as the previous state estimate to derive abundance estimate for this pixel using robust filter. And again use the genetic algorithm to derive accurate abundance estimate efficiently based on the robust filter solution. This iteration continues until pixels in a hyperspectral image cube end.

  7. Spectral methods and cluster structure in correlation-based networks

    NASA Astrophysics Data System (ADS)

    Heimo, Tapio; Tibély, Gergely; Saramäki, Jari; Kaski, Kimmo; Kertész, János

    2008-10-01

    We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and focus specifically on the spectral properties of weight W=|-δ and diffusion matrices D=W/sj-δ, where C is the correlation matrix and si=∑jW the strength of node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix are ranked in descending order. As in the earlier observations, the first eigenvector stands for a measure of the market correlations. Its components are, to first approximation, equal to the strengths of the nodes and there is a second order, roughly linear, correction. The high ranking eigenvectors, excluding the highest ranking one, are usually assigned to market sectors and industrial branches. Our study shows that both for weight and diffusion matrices the eigenpair analysis is not capable of easily deducing the cluster structure of the network without a priori knowledge. In addition we have studied the clustering of stocks using the asset graph approach with and without spectrum based noise filtering. It turns out that asset graphs are quite insensitive to noise and there is no sharp percolation transition as a function of the ratio of bonds included, thus no natural threshold value for that ratio seems to exist. We suggest that these observations can be of use for other correlation based networks as well.

  8. On the Convergence of Galerkin Spectral Methods for a Bioconvective Flow

    NASA Astrophysics Data System (ADS)

    de Aguiar, R.; Climent-Ezquerra, B.; Rojas-Medar, M. A.; Rojas-Medar, M. D.

    2017-03-01

    Convergence rates of the spectral Galerkin method are obtained for a system consisting of the Navier-Stokes equation coupled with a linear convection-diffusion equation modeling the concentration of microorganisms in a culture fluid.

  9. Source depth estimation of self-potential anomalies by spectral methods

    NASA Astrophysics Data System (ADS)

    Di Maio, Rosa; Piegari, Ester; Rani, Payal

    2017-01-01

    Spectral analysis of the self-potential (SP) field for geometrically simple anomalous bodies is studied. In particular, three spectral techniques, i.e. Periodogram (PM), Multi Taper (MTM) and Maximum Entropy (MEM) methods, are proposed to derive the depth of the anomalous bodies. An extensive numerical analysis at varying the source parameters outlines that MEM is successful in determining the source depth with a percent error less than 5%. The application of the proposed spectral approach to the interpretation of field datasets has provided depth estimations of the SP anomaly sources in very good agreement with those obtained by other numerical methods.

  10. Computationally efficient algorithms for incorporation of hydrodynamic and excluded volume interactions in Brownian dynamics simulations: A comparative study of the Krylov subspace and Chebyshev based techniques

    NASA Astrophysics Data System (ADS)

    Saadat, Amir; Khomami, Bamin

    2014-05-01

    Excluded volume and hydrodynamic interactions play a central role in macromolecular dynamics under equilibrium and non-equilibrium settings. The high computational cost of incorporating the influence of hydrodynamic interaction in meso-scale simulation of polymer dynamics has motivated much research on development of high fidelity and cost efficient techniques. Among them, the Chebyshev polynomial based techniques and the Krylov subspace methods are most promising. To this end, in this study we have developed a series of semi-implicit predictor-corrector Brownian dynamics algorithms for bead-spring chain micromechanical model of polymers that utilizes either the Chebyshev or the Krylov framework. The efficiency and fidelity of these new algorithms in equilibrium (radius of gyration and diffusivity) and non-equilibrium conditions (transient planar extensional flow) are demonstrated with particular emphasis on the new enhancements of the Chebyshev polynomial and the Krylov subspace methods. In turn, the algorithm with the highest efficiency and fidelity, namely, the Krylov subspace method, is used to simulate dilute solutions of high molecular weight polystyrene in uniaxial extensional flow. Finally, it is demonstrated that the bead-spring Brownian dynamics simulation with appropriate inclusion of excluded volume and hydrodynamic interactions can quantitatively predict the observed extensional hardening of polystyrene dilute solutions over a broad molecular weight range.

  11. Application of spectral methods for high-frequency financial data to quantifying states of market participants

    NASA Astrophysics Data System (ADS)

    Sato, Aki-Hiro

    2008-06-01

    Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A 382 (2007) 258-270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation of the earth, and that the similarities among best quotation rates are associated with those among quotation frequencies. Furthermore, it is shown that the Jensen-Shannon spectral divergence is proportional to a mean of the Kullback-Leibler spectral distance both empirically and numerically. It is confirmed that these spectral distances are connected with distributions for behavioural parameters of the market participants from numerical simulation. This concludes that spectral distances of representative quantities of financial markets are related into diversification of behavioural parameters of the market participants.

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

    NASA Astrophysics Data System (ADS)

    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 <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.

  13. Postprocessing Fourier spectral methods: The case of smooth solutions

    SciTech Connect

    Garcia-Archilla, B.; Novo, J.; Titi, E.S.

    1998-11-01

    A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is analyzed and a refined postprocessing technique is proposed.

  14. A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Gong, Yuezheng; Wang, Qi; Wang, Yushun; Cai, Jiaxiang

    2017-01-01

    A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O (N-r +τ2) in the discrete L2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and τ is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method.

  15. Spectrum-based method to generate good decoy libraries for spectral library searching in peptide identifications.

    PubMed

    Cheng, Chia-Ying; Tsai, Chia-Feng; Chen, Yu-Ju; Sung, Ting-Yi; Hsu, Wen-Lian

    2013-05-03

    As spectral library searching has received increasing attention for peptide identification, constructing good decoy spectra from the target spectra is the key to correctly estimating the false discovery rate in searching against the concatenated target-decoy spectral library. Several methods have been proposed to construct decoy spectral libraries. Most of them construct decoy peptide sequences and then generate theoretical spectra accordingly. In this paper, we propose a method, called precursor-swap, which directly constructs decoy spectral libraries directly at the "spectrum level" without generating decoy peptide sequences by swapping the precursors of two spectra selected according to a very simple rule. Our spectrum-based method does not require additional efforts to deal with ion types (e.g., a, b or c ions), fragment mechanism (e.g., CID, or ETD), or unannotated peaks, but preserves many spectral properties. The precursor-swap method is evaluated on different spectral libraries and the results of obtained decoy ratios show that it is comparable to other methods. Notably, it is efficient in time and memory usage for constructing decoy libraries. A software tool called Precursor-Swap-Decoy-Generation (PSDG) is publicly available for download at http://ms.iis.sinica.edu.tw/PSDG/.

  16. A DFFD simulation method combined with the spectral element method for solid-fluid-interaction problems

    NASA Astrophysics Data System (ADS)

    Chen, Li-Chieh; Huang, Mei-Jiau

    2017-02-01

    A 2D simulation method for a rigid body moving in an incompressible viscous fluid is proposed. It combines one of the immersed-boundary methods, the DFFD (direct forcing fictitious domain) method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. A pseudo body force is imposed within the solid domain to enforce the rigid body motion and a Lagrangian mesh composed of triangular elements is employed for tracing the rigid body. In particular, a so called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures.

  17. Spectral methods for some singularly perturbed third order ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Temsah, R.

    2008-01-01

    Spectral methods with interface point are presented to deal with some singularly perturbed third order boundary value problems of reaction-diffusion and convection-diffusion types. First, linear equations are considered and then non-linear equations. To solve non-linear equations, Newton?s method of quasi-linearization is applied. The problem is reduced to two systems of ordinary differential equations. And, then, each system is solved using spectral collocation methods. Our numerical experiments show that the proposed methods are produce highly accurate solutions in little computer time when compared with the other methods available in the literature.

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

    NASA Astrophysics Data System (ADS)

    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.

  19. Spectral methods applied to fluidized bed combustors. Final report

    SciTech Connect

    Brown, R.C.; Christofides, N.J.; Junk, K.W.; Raines, T.S.; Thiede, T.D.

    1996-08-01

    The objective of this project was to develop methods for characterizing fuels and sorbents from time-series data obtained during transient operation of fluidized bed boilers. These methods aimed at determining time constants for devolatilization and char burnout using carbon dioxide (CO{sub 2}) profiles and from time constants for the calcination and sulfation processes using CO{sub 2} and sulfur dioxide (SO{sub 2}) profiles.

  20. Stepwise method based on Wiener estimation for spectral reconstruction in spectroscopic Raman imaging.

    PubMed

    Chen, Shuo; Wang, Gang; Cui, Xiaoyu; Liu, Quan

    2017-01-23

    Raman spectroscopy has demonstrated great potential in biomedical applications. However, spectroscopic Raman imaging is limited in the investigation of fast changing phenomena because of slow data acquisition. Our previous studies have indicated that spectroscopic Raman imaging can be significantly sped up using the approach of narrow-band imaging followed by spectral reconstruction. A multi-channel system was built to demonstrate the feasibility of fast wide-field spectroscopic Raman imaging using the approach of simultaneous narrow-band image acquisition followed by spectral reconstruction based on Wiener estimation in phantoms. To further improve the accuracy of reconstructed Raman spectra, we propose a stepwise spectral reconstruction method in this study, which can be combined with the earlier developed sequential weighted Wiener estimation to improve spectral reconstruction accuracy. The stepwise spectral reconstruction method first reconstructs the fluorescence background spectrum from narrow-band measurements and then the pure Raman narrow-band measurements can be estimated by subtracting the estimated fluorescence background from the overall narrow-band measurements. Thereafter, the pure Raman spectrum can be reconstructed from the estimated pure Raman narrow-band measurements. The result indicates that the stepwise spectral reconstruction method can improve spectral reconstruction accuracy significantly when combined with sequential weighted Wiener estimation, compared with the traditional Wiener estimation. In addition, qualitatively accurate cell Raman spectra were successfully reconstructed using the stepwise spectral reconstruction method from the narrow-band measurements acquired by a four-channel wide-field Raman spectroscopic imaging system. This method can potentially facilitate the adoption of spectroscopic Raman imaging to the investigation of fast changing phenomena.

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

    NASA Technical Reports Server (NTRS)

    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.

  2. FOCUSR: Feature Oriented Correspondence using Spectral Regularization–A Method for Precise Surface Matching

    PubMed Central

    Lombaert, Herve; Grady, Leo; Polimeni, Jonathan R.; Cheriet, Farida

    2013-01-01

    Existing methods for surface matching are limited by the trade-off between precision and computational efficiency. Here we present an improved algorithm for dense vertex-to-vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization. This algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision (distance errors of 1.4%). The method, FOCUSR, incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest-frequency harmonics of a graph Laplacian to spatially regularize the features. In its simplest form, FOCUSR is an improved spectral correspondence method that nonrigidly deforms spectral embeddings. We provide here a full realization of spectral correspondence where virtually any feature can be used as additional information using weights on graph edges, but also on graph nodes and as extra embedded coordinates. As an example, the full power of FOCUSR is demonstrated in a real case scenario with the challenging task of brain surface matching across several individuals. Our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision (to a sub-millimeter level) while performing at much greater speed than existing methods. PMID:23868776

  3. FOCUSR: feature oriented correspondence using spectral regularization--a method for precise surface matching.

    PubMed

    Lombaert, Herve; Grady, Leo; Polimeni, Jonathan R; Cheriet, Farida

    2013-09-01

    Existing methods for surface matching are limited by the tradeoff between precision and computational efficiency. Here, we present an improved algorithm for dense vertex-to-vertex correspondence that uses direct matching of features defined on a surface and improves it by using spectral correspondence as a regularization. This algorithm has the speed of both feature matching and spectral matching while exhibiting greatly improved precision (distance errors of 1.4 percent). The method, FOCUSR, incorporates implicitly such additional features to calculate the correspondence and relies on the smoothness of the lowest-frequency harmonics of a graph Laplacian to spatially regularize the features. In its simplest form, FOCUSR is an improved spectral correspondence method that nonrigidly deforms spectral embeddings. We provide here a full realization of spectral correspondence where virtually any feature can be used as an additional information using weights on graph edges, but also on graph nodes and as extra embedded coordinates. As an example, the full power of FOCUSR is demonstrated in a real-case scenario with the challenging task of brain surface matching across several individuals. Our results show that combining features and regularizing them in a spectral embedding greatly improves the matching precision (to a submillimeter level) while performing at much greater speed than existing methods.

  4. Tracking perturbations in Boolean networks with spectral methods

    NASA Astrophysics Data System (ADS)

    Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli

    2005-08-01

    In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks.

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

    SciTech Connect

    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.

  6. A spectral method for halo particle definition in intense mismatched beams

    SciTech Connect

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

    2011-04-15

    An advanced spectral analysis of a mismatched 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.

  7. Fast Spectral Collocation Method for Surface Integral Equations of Potential Problems in a Spheroid

    PubMed Central

    Xu, Zhenli; Cai, Wei

    2009-01-01

    This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the proposed technique, the computation cost of collocation matrix entries is reduced from 𝒪(M2N4) to 𝒪(MN4), where N2 is the number of spherical harmonics (i.e., size of the matrix) and M is the number of one-dimensional integration quadrature points. Numerical results demonstrate the spectral accuracy of the method. PMID:20414359

  8. Weak turbulence simulations with the Hermite-Fourier spectral method

    NASA Astrophysics Data System (ADS)

    Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Roytershteyn, Vadim; Markidis, Stefano

    2015-11-01

    Recently, a new (transform) method based on a Fourier-Hermite (FH) discretization of the Vlasov-Maxwell equations has been developed. The resulting set of moment equations is discretized implicitly in time with a Crank-Nicolson scheme and solved with a nonlinear Newton-Krylov technique. For periodic boundary conditions, this discretization delivers a scheme that conserves the total mass, momentum and energy of the system exactly. In this work, we apply the FH method to study a problem of Langmuir turbulence, where a low signal-to-noise ratio is important to follow the turbulent cascade and might require a lot of computational resources if studied with PIC. We simulate a weak (low density) electron beam moving in a Maxwellian plasma and subject to an instability that generates Langmuir waves and a weak turbulence field. We also discuss some optimization techniques to optimally select the Hermite basis in terms of its shift and scaling argument, and show that this technique improve the overall accuracy of the method. Finally, we discuss the applicability of the HF method for studying kinetic plasma turbulence. This work was funded by LDRD under the auspices of the NNSA of the U.S. by LANL under contract DE-AC52-06NA25396 and by EC through the EPiGRAM project (grant agreement no. 610598. epigram-project.eu).

  9. A method extracting solar cell parameters from spectral response by inverse laplace transform

    NASA Astrophysics Data System (ADS)

    Tuominen, E.; Acerbis, M.; Hovinen, A.; Siirtola, T.; Sinkkonen, J.

    1997-01-01

    A mathematical method to interpret spectral responses measured from solar cells has been developed. Taking an inverse Laplace transform from the spectral response of a solar cell the spatial dependent collection efficiency of the cell can be obtained. Several important material parameters of the solar cell can be extracted from this function. Applying this method the properties of the solar cell can be investigated without applying characterization methods to the cell itself. We have applied the method both to simulated solar cells andto real solar cells.

  10. Incompressible spectral-element method: Derivation of equations

    NASA Technical Reports Server (NTRS)

    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.

  11. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors.

    PubMed

    Kawamoto, Tatsuro; Kabashima, Yoshiyuki

    2015-06-01

    Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

  12. Limitations in the spectral method for graph partitioning: Detectability threshold and localization of eigenvectors

    NASA Astrophysics Data System (ADS)

    Kawamoto, Tatsuro; Kabashima, Yoshiyuki

    2015-06-01

    Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

  13. GPU Accelerated Spectral Element Methods: 3D Euler equations

    NASA Astrophysics Data System (ADS)

    Abdi, D. S.; Wilcox, L.; Giraldo, F.; Warburton, T.

    2015-12-01

    A GPU accelerated nodal discontinuous Galerkin method for the solution of three dimensional Euler equations is presented. The Euler equations are nonlinear hyperbolic equations that are widely used in Numerical Weather Prediction (NWP). Therefore, acceleration of the method plays an important practical role in not only getting daily forecasts faster but also in obtaining more accurate (high resolution) results. The equation sets used in our atomospheric model NUMA (non-hydrostatic unified model of the atmosphere) take into consideration non-hydrostatic effects that become more important with high resolution. We use algorithms suitable for the single instruction multiple thread (SIMT) architecture of GPUs to accelerate solution by an order of magnitude (20x) relative to CPU implementation. For portability to heterogeneous computing environment, we use a new programming language OCCA, which can be cross-compiled to either OpenCL, CUDA or OpenMP at runtime. Finally, the accuracy and performance of our GPU implementations are veried using several benchmark problems representative of different scales of atmospheric dynamics.

  14. Generalized spectral method for near-field optical microscopy

    SciTech Connect

    Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M.; Castro Neto, A. H.

    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.

  15. Generalized spectral method for near-field optical microscopy

    NASA Astrophysics Data System (ADS)

    Jiang, B.-Y.; Zhang, L. M.; Castro Neto, A. H.; Basov, D. N.; Fogler, M. M.

    2016-02-01

    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.

  16. Spectral responsivity calibrations of two types of pyroelectric radiometers using three different methods

    NASA Astrophysics Data System (ADS)

    Zeng, J.; Eppeldauer, G. P.; Hanssen, L. M.; Podobedov, V. B.

    2012-06-01

    Spectral responsivity calibrations of two different types of pyroelectric radiometers have been made in the infrared region up to 14 μm in power mode using three different calibration facilities at NIST. One pyroelectric radiometer is a temperature-controlled low noise-equivalent-power (NEP) single-element pyroelectric radiometer with an active area of 5 mm in diameter. The other radiometer is a prototype using the same type of pyroeletric detector with dome-input optics, which was designed to increase absorptance and to minimize spectral structures to obtain a constant spectral responsivity. Three calibration facilities at NIST were used to conduct direct and indirect responsivity calibrations tied to absolute scales in the infrared spectral regime. We report the calibration results for the single-element pyroelectric radiometer using a new Infrared Spectral Comparator Facility (IRSCF) for direct calibration. Also, a combined method using the Fourier Transform Infrared Spectrophotometry (FTIS) facility and single wavelength laser tie-points are described to calibrated standard detectors with an indirect approach. For the dome-input pyroelectric radiometer, the results obtained from another direct calibration method using a circular variable filter (CVF) spectrometer and the FTIS are also presented. The inter-comparison of different calibration methods enables us to improve the responsivity uncertainty performed by the different facilities. For both radiometers, consistent results of the spectral power responsivity have been obtained applying different methods from 1.5 μm to 14 μm with responsivity uncertainties between 1 % and 2 % (k = 2). Relevant characterization results, such as spatial uniformity, linearity, and angular dependence of responsivity, are shown. Validation of the spectral responsivity calibrations, uncertainty sources, and improvements for each method will also be discussed.

  17. Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

    NASA Technical Reports Server (NTRS)

    Siegel, R.; Spuckler, C. M.

    1994-01-01

    Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

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

    SciTech Connect

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

    2013-06-15

    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.

  19. Binding characteristics of salbutamol with DNA by spectral methods.

    PubMed

    Bi, Shuyun; Pang, Bo; Zhao, Tingting; Wang, Tianjiao; Wang, Yu; Yan, Lili

    2013-07-01

    Salbutamol interacting with deoxyribonucleic acid (DNA) was examined by fluorescence, UV absorption, viscosity measurements, and DNA melting techniques. The binding constants and binding sites were obtained at different temperatures by fluorescence quenching. The Stern-Volmer plots showed that the quenching of fluorescence of salbutamol by DNA was a static quenching. To probe the binding mode, various analytical methods were performed and the results were as follows: hyperchromic effect was shown in the absorption spectra of salbutamol upon addition of DNA; there was no appreciable increase in melting temperature of DNA when salbutamol was presented in DNA solution; the fluorescence intensity of salbutamol-DNA decrease with the increasing ionic strength; the relative viscosity of DNA did not change in the presence of salbutamol; the binding constant of salbutamol with double strand DNA (dsDNA) was much higher than that of it with single strand DNA (ssDNA). All these results indicated that the binding mode of salbutamol to DNA should be groove binding. The thermodynamic parameters suggested that hydrogen bond or van der Waals force might play an important role in salbutamol binding to DNA. According to the Förster energy transference theory, the binding distance between the acceptor and donor was 3.70 nm.

  20. Binding characteristics of salbutamol with DNA by spectral methods

    NASA Astrophysics Data System (ADS)

    Bi, Shuyun; Pang, Bo; Zhao, Tingting; Wang, Tianjiao; Wang, Yu; Yan, Lili

    2013-07-01

    Salbutamol interacting with deoxyribonucleic acid (DNA) was examined by fluorescence, UV absorption, viscosity measurements, and DNA melting techniques. The binding constants and binding sites were obtained at different temperatures by fluorescence quenching. The Stern-Volmer plots showed that the quenching of fluorescence of salbutamol by DNA was a static quenching. To probe the binding mode, various analytical methods were performed and the results were as follows: hyperchromic effect was shown in the absorption spectra of salbutamol upon addition of DNA; there was no appreciable increase in melting temperature of DNA when salbutamol was presented in DNA solution; the fluorescence intensity of salbutamol-DNA decrease with the increasing ionic strength; the relative viscosity of DNA did not change in the presence of salbutamol; the binding constant of salbutamol with double strand DNA (dsDNA) was much higher than that of it with single strand DNA (ssDNA). All these results indicated that the binding mode of salbutamol to DNA should be groove binding. The thermodynamic parameters suggested that hydrogen bond or van der Waals force might play an important role in salbutamol binding to DNA. According to the Förster energy transference theory, the binding distance between the acceptor and donor was 3.70 nm.

  1. A comparison of vortex and pseudo-spectral methods at high Reynolds numbers

    NASA Astrophysics Data System (ADS)

    Leonard, Anthony; van Rees, Wim; Koumoutsakos, Petros

    2010-11-01

    We validate the hybrid particle-mesh vortex method against a pseudo-spectral method in simulations of the Taylor-Green vortex and colliding vortex tubes at Re = 1600 - 10,000. The spectral method uses the smooth filter introduced in [1]. In the case of the Taylor-Green vortex, we observe very good agreement in the evolution of the vortical structures albeit small discrepancies in the energy spectrum only for the smallest length scales. In the collision of two anti-parallel vortex tubes at Re = 10 000, there is very good agreement between the two methods in terms of the simulated vortical structures throughout the first reconnection of the tubes. The maximum error in the effective viscosity is below 2.5% and 1% for the vortex method and the pseudo-spectral method respectively. At later times the agreement between the two methods in the vortical structures deteriorates even though there is good agreement in the energy spectrum. Both methods resolve an unexpected vortex breakdown during the second reconnection of the vortex tubes.[4pt] [1] Hou, T. and Li, R., 2007. Computing nearly singular solutions using pseudo-spectral methods. J. of Comput. Phys., 226:379-397.

  2. Semi-implicit spectral deferred correction methods for ordinary differential equations

    SciTech Connect

    Minion, Michael L.

    2002-10-06

    A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for ordinary differential equations with both stiff and non-stiff terms is presented. Several modifications and variations to the original spectral deferred corrections method by Dutt, Greengard, and Rokhlin concerning the choice of integration points and the form of the correction iteration are presented. The stability and accuracy of the resulting ODE methods are explored analytically and numerically. The SISDC methods are intended to be combined with the method of lines approach to yield a flexible framework for creating higher-order semi-implicit methods for partial differential equations. A discussion and numerical examples of the SISDC method applied to advection-diffusion type equations are included. The results suggest that higher-order SISDC methods are more efficient than semi-implicit Runge-Kutta methods for moderately stiff problems in terms of accuracy per function evaluation.

  3. A novel edge-preserving nonnegative matrix factorization method for spectral unmixing

    NASA Astrophysics Data System (ADS)

    Bao, Wenxing; Ma, Ruishi

    2015-12-01

    Spectral unmixing technique is one of the key techniques to identify and classify the material in the hyperspectral image processing. A novel robust spectral unmixing method based on nonnegative matrix factorization(NMF) is presented in this paper. This paper used an edge-preserving function as hypersurface cost function to minimize the nonnegative matrix factorization. To minimize the hypersurface cost function, we constructed the updating functions for signature matrix of end-members and abundance fraction respectively. The two functions are updated alternatively. For evaluation purpose, synthetic data and real data have been used in this paper. Synthetic data is used based on end-members from USGS digital spectral library. AVIRIS Cuprite dataset have been used as real data. The spectral angle distance (SAD) and abundance angle distance(AAD) have been used in this research for assessment the performance of proposed method. The experimental results show that this method can obtain more ideal results and good accuracy for spectral unmixing than present methods.

  4. Performance evaluation of spectral analysis and Werner deconvolution interpretation techniques in magnetic method

    NASA Astrophysics Data System (ADS)

    Subrahmanyam, M.; Gebissa, Fekadu Tamiru

    2017-03-01

    Determining the depth of anomalous geological subsurface structure is an important parameter in any of geophysical methods. Though, numerous magnetic interpretation techniques are available in literature for locating depth to the causative source, no specific information is found on the performance of any of the techniques. Werner deconvolution and Spectral methods are widely used to determine the approximate depth to the causative sources, which are then used in modeling methods. An attempt has been made in this study to evaluate the performance of Werner and spectral methods. Synthetic magnetic anomalies are generated over sheet, dyke and fault models for different combinations of geometric dimensions of the bodies and magnetization angles. These anomalies were interpreted with the two methods: Werner deconvolution and Spectral analysis. The error percentages are calculated as the difference between the theoretical and interpreted values. In addition, the results are discussed for their performance. It is observed that Werner method yields more reasonable values for depth compared to spectral methods particularly when body widths are more and deep seated or faulting is deep. In case of dyke model, the Werner method determines width also reliably.

  5. Finite and spectral cell method for wave propagation in heterogeneous materials

    NASA Astrophysics Data System (ADS)

    Joulaian, Meysam; Duczek, Sascha; Gabbert, Ulrich; Düster, Alexander

    2014-09-01

    In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring [1-3], quantitative ultrasound applications [4], or the active control of vibrations and noise [5, 6].

  6. A note on the accuracy of spectral method applied to nonlinear conservation laws

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang; Wong, Peter S.

    1994-01-01

    Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

  7. High-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding

    NASA Astrophysics Data System (ADS)

    Lai, Hong; Orgun, Mehmet A.; Pieprzyk, Josef; Li, Jing; Luo, Mingxing; Xiao, Jinghua; Xiao, Fuyuan

    2016-11-01

    We propose an approach that achieves high-capacity quantum key distribution using Chebyshev-map values corresponding to Lucas numbers coding. In particular, we encode a key with the Chebyshev-map values corresponding to Lucas numbers and then use k-Chebyshev maps to achieve consecutive and flexible key expansion and apply the pre-shared classical information between Alice and Bob and fountain codes for privacy amplification to solve the security of the exchange of classical information via the classical channel. Consequently, our high-capacity protocol does not have the limitations imposed by orbital angular momentum and down-conversion bandwidths, and it meets the requirements for longer distances and lower error rates simultaneously.

  8. Improved Fault Classification in Series Compensated Transmission Line: Comparative Evaluation of Chebyshev Neural Network Training Algorithms.

    PubMed

    Vyas, Bhargav Y; Das, Biswarup; Maheshwari, Rudra Prakash

    2016-08-01

    This paper presents the Chebyshev neural network (ChNN) as an improved artificial intelligence technique for power system protection studies and examines the performances of two ChNN learning algorithms for fault classification of series compensated transmission line. The training algorithms are least-square Levenberg-Marquardt (LSLM) and recursive least-square algorithm with forgetting factor (RLSFF). The performances of these algorithms are assessed based on their generalization capability in relating the fault current parameters with an event of fault in the transmission line. The proposed algorithm is fast in response as it utilizes postfault samples of three phase currents measured at the relaying end corresponding to half-cycle duration only. After being trained with only a small part of the generated fault data, the algorithms have been tested over a large number of fault cases with wide variation of system and fault parameters. Based on the studies carried out in this paper, it has been found that although the RLSFF algorithm is faster for training the ChNN in the fault classification application for series compensated transmission lines, the LSLM algorithm has the best accuracy in testing. The results prove that the proposed ChNN-based method is accurate, fast, easy to design, and immune to the level of compensations. Thus, it is suitable for digital relaying applications.

  9. Research on high resolution spectral method of hyperspectral LiDAR

    NASA Astrophysics Data System (ADS)

    Li, Feng; Jiang, Chenghao; Zhu, Jingguo; Li, Menglin; Meng, Zhe

    2016-10-01

    Hyperspectral LiDAR using supercontinuum laser as light source, applying spectroscopic technology gets backscattered reflectance of different wavelengths, and can acquire both the geometry and spectral information on the target. Due to the development of the photoelectric sensor, hyperspectral LiDAR has fewer spectral channels, which limits its application in physical properties detection. To solve this problem, this paper proposes a new method based on the micro mirror array. By blaze grating, the supercontinuum laser is grating into monochromatic light in space, first projected to the micro mirror array, by controlling the micro mirror array flip, specific spectrum and reflection to corresponding photoelectric sensor channels, improve the spectral resolution. The micro mirror array photoelectric sensor resolution is much higher than the number of channels, through this method, can greatly improve the spectral resolution. In this paper, based on the micro mirror array, the simulation design is carried out and the feasibility of the method is verified by experiments. The simulation and experimental results show that the spectral resolution can be improved greatly by controlling the turning of the micro mirror.

  10. Color image segmentation using watershed and Nyström method based spectral clustering

    NASA Astrophysics Data System (ADS)

    Bai, Xiaodong; Cao, Zhiguo; Yu, Zhenghong; Zhu, Hu

    2011-11-01

    Color image segmentation draws a lot of attention recently. In order to improve efficiency of spectral clustering in color image segmentation, a novel two-stage color image segmentation method is proposed. In the first stage, we use vector gradient approach to detect color image gradient information, and watershed transformation to get the pre-segmentation result. In the second stage, Nyström extension based spectral clustering is used to get the final result. To verify the proposed algorithm, it is applied to color images from the Berkeley Segmentation Dataset. Experiments show our method can bring promising results and reduce the runtime significantly.

  11. Application of Modified Chebyshev Picard Iteration to Differential Correction for Improved Robustness and Computation Time

    NASA Astrophysics Data System (ADS)

    Swenson, Travis; Woollands, Robyn; Junkins, John; Lo, Martin

    2017-01-01

    A novel application of Modified Chebyshev Picard Iteration (MCPI) to differential correction is presented. By leveraging the Chebyshev basis functions of MCPI, interpolation in 1 dimension may be used to target plane crossing events, instead of integrating the 42 dimensional variational equation required for standard step integrators. This results in dramatically improved performance over traditional differential correctors. MCPI was tested against the Runge-Kutta 7/8 integrator on over 45,000 halo orbits in three different three-body problems, and was found to be up to an order of magnitude faster, while simultaneously increasing robustness.

  12. A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

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

    NASA Astrophysics Data System (ADS)

    Ostachowicz, W.; Kudela, P.

    2010-06-01

    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.

  14. 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

    NASA Astrophysics Data System (ADS)

    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

  15. An Extension of the Time-Spectral Method to Overset Solvers

    NASA Technical Reports Server (NTRS)

    Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas

    2013-01-01

    Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

  16. [Study on the absolute spectral irradiation calibration method for far ultraviolet spectrometer in remote sensing].

    PubMed

    Yu, Lei; Lin, Guan-Yu; Chen, Bin

    2013-01-01

    The present paper studied spectral irradiation responsivities calibration method which can be applied to the far ultraviolet spectrometer for upper atmosphere remote sensing. It is difficult to realize the calibration for far ultraviolet spectrometer for many reasons. Standard instruments for far ultraviolet waveband calibration are few, the degree of the vacuum experiment system is required to be high, the stabilities of the experiment are hardly maintained, and the limitation of the far ultraviolet waveband makes traditional diffuser and the integrating sphere radiance calibration method difficult to be used. To solve these problems, a new absolute spectral irradiance calibration method was studied, which can be applied to the far ultraviolet calibration. We build a corresponding special vacuum experiment system to verify the calibration method. The light source system consists of a calibrated deuterium lamp, a vacuum ultraviolet monochromater and a collimating system. We used the calibrated detector to obtain the irradiance responsivities of it. The three instruments compose the calibration irradiance source. We used the "calibration irradiance source" to illuminate the spectrometer prototype and obtained the spectral irradiance responsivities. It realized the absolute spectral irradiance calibration for the far ultraviolet spectrometer utilizing the calibrated detector. The absolute uncertainty of the calibration is 7.7%. The method is significant for the ground irradiation calibration of the far ultraviolet spectrometer in upper atmosphere remote sensing.

  17. A quaternion-based spectral clustering method for color image segmentation

    NASA Astrophysics Data System (ADS)

    Li, Xiang; Jin, Lianghai; Liu, Hong; He, Zeng

    2011-11-01

    Spectral clustering method has been widely used in image segmentation. A key issue in spectral clustering is how to build the affinity matrix. When it is applied to color image segmentation, most of the existing methods either use Euclidean metric to define the affinity matrix, or first converting color-images into gray-level images and then use the gray-level images to construct the affinity matrix (component-wise method). However, it is known that Euclidean distances can not represent the color differences well and the component-wise method does not consider the correlation between color channels. In this paper, we propose a new method to produce the affinity matrix, in which the color images are first represented in quaternion form and then the similarities between color pixels are measured by quaternion rotation (QR) mechanism. The experimental results show the superiority of the new method.

  18. Development and Validation of a New Fallout Transport Method Using Variable Spectral Winds

    NASA Astrophysics Data System (ADS)

    Hopkins, Arthur Thomas

    A new method has been 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 specgtral 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. Further validation was performed by comparing computed and actual trajectories of a high explosive dust cloud (DIRECT COURSE). Using an error propagation formula, it was determined that uncertainties in spectral wind components produce less than four percent of the total dose rate variance. In summary, this research demonstrated the feasibility of using spectral coefficients for fallout transport calculations, developed a two-step smearing model to treat variable winds, and showed that uncertainties in spectral winds do not contribute significantly to the error in computed dose rate.

  19. Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

    NASA Technical Reports Server (NTRS)

    Casarin, Mario

    1996-01-01

    Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

  20. Study on Raman spectral imaging method for simultaneous estimation of ingredients concentration in food powder

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This study investigated the potential of point scan Raman spectral imaging method for estimation of different ingredients and chemical contaminant concentration in food powder. Food powder sample was prepared by mixing sugar, vanillin, melamine and non-dairy cream at 5 different concentrations in a ...

  1. Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems

    NASA Astrophysics Data System (ADS)

    Marchandise, Emilie; Chevaugeon, Nicolas; Remacle, Jean-Francois

    2008-06-01

    In this paper, we analyze the spatial and spectral superconvergence properties of one-dimensional hyperbolic conservation law by a discontinuous Galerkin (DG) method. The analyses combine classical mathematical arguments with MATLAB experiments. Some properties of the DG schemes are discovered using discrete Fourier analyses: superconvergence of the numerical wave numbers, Radau structure of the X spatial error.

  2. Finite-difference, spectral and Galerkin methods for time-dependent problems

    NASA Technical Reports Server (NTRS)

    Tadmor, E.

    1983-01-01

    Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.

  3. Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method

    NASA Technical Reports Server (NTRS)

    Mcmurtry, Patrick A.; Givi, Peyman

    1992-01-01

    An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.

  4. Variational multiscale turbulence modelling in a high order spectral element method

    SciTech Connect

    Wasberg, Carl Erik Gjesdal, Thor Reif, Bjorn Anders Pettersson Andreassen, Oyvind

    2009-10-20

    In the variational multiscale (VMS) approach to large eddy simulation (LES), the governing equations are projected onto an a priori scale partitioning of the solution space. This gives an alternative framework for designing and analyzing turbulence models. We describe the implementation of the VMS LES methodology in a high order spectral element method with a nodal basis, and discuss the properties of the proposed scale partitioning. The spectral element code is first validated by doing a direct numerical simulation of fully developed plane channel flow. The performance of the turbulence model is then assessed by several coarse grid simulations of channel flow at different Reynolds numbers.

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

    DOE PAGES

    Yu, Hua-Gen

    2014-12-28

    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 originalmore » 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 HO₂, and compared to previous calculations.« less

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

    SciTech Connect

    Yu, Hua-Gen

    2014-12-28

    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 HO₂, and compared to previous calculations.

  7. Spectral methods based on new formulations for coupled Stokes and Darcy equations

    NASA Astrophysics Data System (ADS)

    Wang, Weiwei; Xu, Chuanju

    2014-01-01

    In this paper we consider the numerical solution of the Stokes and Darcy coupled equations, which frequently appears in porous media modeling. The main contribution of this work is as follows: First, we introduce a new formulation for the Stokes/Darcy coupled equations, subject respectively to the Beavers-Joseph-Saffman interface condition and an alternative matching interface condition. Secondly, we prove the well-posedness of these weak problems by using the classical saddle point theory. Thirdly, some spectral approximations to the weak problems are proposed and analyzed, and some error estimates are provided. It is found that the new formulations significantly simplify the error analysis and numerical implementation. Finally, some two-dimensional spectral and spectral element numerical examples are provided to demonstrate the efficiency of our methods.

  8. Method for Removing Spectral Contaminants to Improve Analysis of Raman Imaging Data

    PubMed Central

    Zhang, Xun; Chen, Sheng; Ling, Zhe; Zhou, Xia; Ding, Da-Yong; Kim, Yoon Soo; Xu, Feng

    2017-01-01

    The spectral contaminants are inevitable during micro-Raman measurements. A key challenge is how to remove them from the original imaging data, since they can distort further results of data analysis. Here, we propose a method named “automatic pre-processing method for Raman imaging data set (APRI)”, which includes the adaptive iteratively reweighted penalized least-squares (airPLS) algorithm and the principal component analysis (PCA). It eliminates the baseline drifts and cosmic spikes by using the spectral features themselves. The utility of APRI is illustrated by removing the spectral contaminants from a Raman imaging data set of a wood sample. In addition, APRI is computationally efficient, conceptually simple and potential to be extended to other methods of spectroscopy, such as infrared (IR), nuclear magnetic resonance (NMR), X-Ray Diffraction (XRD). With the help of our approach, a typical spectral analysis can be performed by a non-specialist user to obtain useful information from a spectroscopic imaging data set. PMID:28054587

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

    SciTech Connect

    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.

  10. Two-time Green's functions and spectral density method in nonextensive quantum statistical mechanics.

    PubMed

    Cavallo, A; Cosenza, F; De Cesare, L

    2008-05-01

    We extend the formalism of the thermodynamic two-time Green's functions to nonextensive quantum statistical mechanics. Working in the optimal Lagrangian multiplier representation, the q -spectral properties and the methods for a direct calculation of the two-time q Green's functions and the related q -spectral density ( q measures the nonextensivity degree) for two generic operators are presented in strict analogy with the extensive (q=1) counterpart. Some emphasis is devoted to the nonextensive version of the less known spectral density method whose effectiveness in exploring equilibrium and transport properties of a wide variety of systems has been well established in conventional classical and quantum many-body physics. To check how both the equations of motion and the spectral density methods work to study the q -induced nonextensivity effects in nontrivial many-body problems, we focus on the equilibrium properties of a second-quantized model for a high-density Bose gas with strong attraction between particles for which exact results exist in extensive conditions. Remarkably, the contributions to several thermodynamic quantities of the q -induced nonextensivity close to the extensive regime are explicitly calculated in the low-temperature regime by overcoming the calculation of the q grand-partition function.

  11. From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

    ERIC Educational Resources Information Center

    Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

    2006-01-01

    Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

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

    NASA Astrophysics Data System (ADS)

    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.

  13. Energy conserving discontinuous Galerkin spectral element method for the Vlasov-Poisson system

    NASA Astrophysics Data System (ADS)

    Madaule, Éric; Restelli, Marco; Sonnendrücker, Eric

    2014-12-01

    We propose a new, energy conserving, spectral element, discontinuous Galerkin method for the approximation of the Vlasov-Poisson system in arbitrary dimension, using Cartesian grids. The method is derived from the one proposed in [4], with two modifications: energy conservation is obtained by a suitable projection operator acting on the solution of the Poisson problem, rather than by solving multiple Poisson problems, and all the integrals appearing in the finite element formulation are approximated with Gauss-Lobatto quadrature, thereby yielding a spectral element formulation. The resulting method has the following properties: exact energy conservation (up to errors introduced by the time discretization), stability (thanks to the use of upwind numerical fluxes), high order accuracy and high locality. For the time discretization, we consider both Runge-Kutta methods and exponential integrators, and show results for 1D and 2D cases (2D and 4D in phase space, respectively).

  14. Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

    NASA Technical Reports Server (NTRS)

    Quarteroni, Alfio

    1989-01-01

    Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

  15. Strong and Weak Lagrange-Galerkin Spectral Element Methods for the Shallow Water Equations

    DTIC Science & Technology

    2003-02-01

    Galerkin Spectral Element Methods for the Shallow Water Equations F . X. GIRALDO Naval Research Laboratory Monterey, CA 93943, U.S.A...edged. 0898-1221/03/$ - see front matter © 2003 Published by Elsevier Science Ltd. PII: 80898-1221(02)00330-9 Typeset by ANfS-TEX 98 F . X...resulting operator is then discretized using the standard finite-element method. This is the approach used by Bercovier and Pironneau [4], Bermejo [5

  16. Determination of rare-earth elements in Luna 16 regolith sample by chemical spectral method

    NASA Technical Reports Server (NTRS)

    Stroganova, N. S.; Ryabukhin, V. A.; Laktinova, N. V.; Ageyeva, L. V.; Galkina, I. P.; Gatinskaya, N. G.; Yermakov, A. N.; Karyakin, A. V.

    1974-01-01

    An analysis was made of regolith from layer A of the Luna 16 sample for rare earth elements, by a chemical spectral method. Chemical and ion exchange concentrations were used to determine the content of 12 elements and Y at the level 0.001 to 0.0001 percent with 10 to 15 percent reproducibility of the emission determination. Results within the limits of reproducibility agree with data obtained by mass spectra, activation, and X-ray fluorescent methods.

  17. Axisymmetric fully spectral code for hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Panosso Macedo, Rodrigo; Ansorg, Marcus

    2014-11-01

    We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.

  18. Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

    NASA Technical Reports Server (NTRS)

    Vanel, Florence O.

    1995-01-01

    Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the

  19. Comment on ``Spectral filters in quantum mechanics: A measurement theory perspective''

    NASA Astrophysics Data System (ADS)

    Mandelshtam, Vladimir A.; Carrington, Tucker

    2002-02-01

    We criticize a paper by Vijay and Wyatt [Phys. Rev. E 63, 4351 (2000)], in which the authors suggest that energy levels computed, from the same set of matrix-vector products, with the filter diagonalization method (FDM) and the Fourier spectral analysis using the same Chebyshev correlation function are of comparable accuracy. We explain why the FDM is superior and demonstrate it numerically, using the same test matrix as that employed in the above paper. We also compare the FDM with the Lanczos method, another commonly used iterative technique for computing eigenvalues. We find that eigenvalues in a low-density region near the middle of the spectrum converge more quickly with the FDM, but that the Lanczos method requires fewer matrix-vector products to converge all the eigenvalues.

  20. Stress drop of earthquakes from the Multi-Window Spectral Ratio method in a regional network

    NASA Astrophysics Data System (ADS)

    D'Alessio, M. A.; Imanishi, K.; Ellsworth, W. L.

    2006-12-01

    Insight into the mechanics of faulting comes from seismologically determined parameters such as earthquake stress drop. To produce higher precision estimates of stress drop on regional networks like the Parkfield HRSN borehole network, we use the multi-window spectral ratio (MWSR) method to determine the corner frequency and relative moment of earthquake pairs. This method assumes that the frequency distribution of spectral power is the same for direct arrivals and later arriving scattered energy. By taking the power spectra of individual time windows, we collect multiple, quasi-independent estimates of the power spectra for a given earthquake. For pairs of earthquakes located within a few hundred meters of one another, the ratio of their power spectra at a given station provides better estimates of their relative moments and corner frequencies by eliminating some of the path-dependent effects. We calculate the spectral ratio for each time window at each station in a regional borehole network and stack the ratios to cancel out noise and determine a robust estimate of the true power spectral ratio. Systematic differences between the spectral ratio at stations with different azimuths can be interpreted as evidence for directivity in the earthquake pulses or frequency- dependent attenuation along the source-receiver path. Because the method is based on a collection of quasi- independent spectral ratio observations, we can quantify the uncertainty in the estimates of corner frequency and moment for each earthquake pair. We use a bootstrap analysis with noise selected from the distribution of scatter from individual time windows about the mean spectral ratio to quantify the range of moment and corner frequencies that fit each station. By assuming that the earthquakes are simple circular cracks, we convert these parameters into stress drop with estimates of uncertainty. We evaluate the reliability of the technique in a regional network for different earthquake spacings

  1. A wavelet-based computational method for solving stochastic Itô–Volterra integral equations

    SciTech Connect

    Mohammadi, Fakhrodin

    2015-10-01

    This paper presents a computational method based on the Chebyshev wavelets for solving stochastic Itô–Volterra integral equations. First, a stochastic operational matrix for the Chebyshev wavelets is presented and a general procedure for forming this matrix is given. Then, the Chebyshev wavelets basis along with this stochastic operational matrix are applied for solving stochastic Itô–Volterra integral equations. Convergence and error analysis of the Chebyshev wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.

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

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei; Liu, Na; Liu, Qing Huo

    2016-12-01

    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.

  4. Deterministic numerical solutions of the Boltzmann equation using the fast spectral method

    NASA Astrophysics Data System (ADS)

    Wu, Lei; White, Craig; Scanlon, Thomas J.; Reese, Jason M.; Zhang, Yonghao

    2013-10-01

    The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those corresponding to the soft, Lennard-Jones, and rigid attracting potentials. The accuracy of the fast spectral method is checked by comparing our numerical solutions of the space-homogeneous Boltzmann equation with the exact Bobylev-Krook-Wu solutions for a gas of Maxwell molecules. It is found that the accuracy is improved by replacing the trapezoidal rule with Gauss-Legendre quadrature in the calculation of the kernel mode, and the conservation of momentum and energy are ensured by the Lagrangian multiplier method without loss of spectral accuracy. The relax-to-equilibrium processes of different collision kernels with the same value of shear viscosity are then compared; the numerical results indicate that different forms of the collision kernels can be used as long as the shear viscosity (not only the value, but also its temperature dependence) is recovered. An iteration scheme is employed to obtain stationary solutions of the space-inhomogeneous Boltzmann equation, where the numerical errors decay exponentially. Four classical benchmarking problems are investigated: the normal shock wave, and the planar Fourier/Couette/force-driven Poiseuille flows. For normal shock waves, our numerical results are compared with a finite difference solution of the Boltzmann equation for hard sphere molecules, experimental data, and molecular dynamics simulation of argon using the realistic Lennard-Jones potential. For planar Fourier/Couette/force-driven Poiseuille flows, our results are compared with the direct simulation Monte Carlo method. Excellent agreements are observed in all test cases

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

    PubMed Central

    Putz, Ana-Maria; Putz, Mihai V.

    2012-01-01

    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. PMID:23443102

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

    NASA Astrophysics Data System (ADS)

    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.

  7. A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows

    NASA Astrophysics Data System (ADS)

    Min, Misun; Lee, Taehun

    2011-01-01

    We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.

  8. A spectral-element discontinuous Galerkin lattice Boltzmann method for incompressible flows.

    SciTech Connect

    Min, M.; Lee, T.; Mathematics and Computer Science; City Univ. of New York

    2011-01-01

    We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss-Lobatto-Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge-Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400-5000 and flows around an impulsively started cylinder for Re = 550-9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.

  9. [Research on Accuracy and Stability of Inversing Vegetation Chlorophyll Content by Spectral Index Method].

    PubMed

    Jiang, Hai-ling; Yang, Hang; Chen, Xiao-ping; Wang, Shu-dong; Li, Xue-ke; Liu, Kai; Cen, Yi

    2015-04-01

    Spectral index method was widely applied to the inversion of crop chlorophyll content. In the present study, PSR3500 spectrometer and SPAD-502 chlorophyll fluorometer were used to acquire the spectrum and relative chlorophyll content (SPAD value) of winter wheat leaves on May 2nd 2013 when it was at the jointing stage of winter wheat. Then the measured spectra were resampled to simulate TM multispectral data and Hyperion hyperspectral data respectively, using the Gaussian spectral response function. We chose four typical spectral indices including normalized difference vegetation index (NDVD, triangle vegetation index (TVI), the ratio of modified transformed chlorophyll absorption ratio index (MCARI) to optimized soil adjusted vegetation index (OSAVI) (MCARI/OSAVI) and vegetation index based on universal pattern decomposition (VIUPD), which were constructed with the feature bands sensitive to the vegetation chlorophyll. After calculating these spectral indices based on the resampling TM and Hyperion data, the regression equation between spectral indices and chlorophyll content was established. For TM, the result indicates that VIUPD has the best correlation with chlorophyll (R2 = 0.819 7) followed by NDVI (R2 = 0.791 8), while MCARI/OSAVI and TVI also show a good correlation with R2 higher than 0.5. For the simulated Hyperion data, VIUPD again ranks first with R2 = 0.817 1, followed by MCARI/OSAVI (R2 = 0.658 6), while NDVI and TVI show very low values with R2 less than 0.2. It was demonstrated that VIUPD has the best accuracy and stability to estimate chlorophyll of winter wheat whether using simulated TM data or Hyperion data, which reaffirms that VIUPD is comparatively sensor independent. The chlorophyll estimation accuracy and stability of MCARI/OSAVI also works well, partly because OSAVI could reduce the influence of backgrounds. Two broadband spectral indices NDVI and TVI are weak for the chlorophyll estimation of simulated Hyperion data mainly because of

  10. Applications of spectral methods to turbulent magnetofluids in space and fusion research

    NASA Technical Reports Server (NTRS)

    Montgomery, D.; Voigt, R. G. (Editor); Gottlieb, D. (Editor); Hussaini, M. Y. (Editor)

    1984-01-01

    Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas.

  11. A Quadrilateral Spectral Multidomain Penalty Method Model For High Reynolds Number Incompressible Stratified Flows

    NASA Astrophysics Data System (ADS)

    Escobar-Vargas, Jorge; Diamessis, Peter

    2011-11-01

    We present a spectral multidomain penalty method-based incompressible Navier Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains. Within the solver, time is discretized with a fractional-step method, and, in space, a Gauss-Lobatto-Legendre collocation approach is used in discontinuous quadrilateral subdomains. Stability of the numerical scheme is guaranteed through a penalty scheme and spectral filtering, further buttressed by a overintegration-based dealiasing technique. The efficient iterative solution of the associated discrete pressure Poisson equation is ensured through a Kronecker product based computation of the null vector associated with the global matrix, plus a two-level preconditioner within a GMRES solver. Efficiency and accuracy of the Navier Stokes solver are assessed through the solution of the lid-driven cavity flow, Taylor vortex and double shear layer. The canonical lock exchange problem is also presented to assess the potential of the solver for the study of environmental stratified flows.

  12. A Comparison of Analytical and Data Preprocessing Methods for Spectral Fingerprinting

    PubMed Central

    LUTHRIA, DEVANAND L.; MUKHOPADHYAY, SUDARSAN; LIN, LONG-ZE; HARNLY, JAMES M.

    2013-01-01

    Spectral fingerprinting, as a method of discriminating between plant cultivars and growing treatments for a common set of broccoli samples, was compared for six analytical instruments. Spectra were acquired for finely powdered solid samples using Fourier transform infrared (FT-IR) and Fourier transform near-infrared (NIR) spectrometry. Spectra were also acquired for unfractionated aqueous methanol extracts of the powders using molecular absorption in the ultraviolet (UV) and visible (VIS) regions and mass spectrometry with negative (MS−) and positive (MS+) ionization. The spectra were analyzed using nested one-way analysis of variance (ANOVA) and principal component analysis (PCA) to statistically evaluate the quality of discrimination. All six methods showed statistically significant differences between the cultivars and treatments. The significance of the statistical tests was improved by the judicious selection of spectral regions (IR and NIR), masses (MS+ and MS−), and derivatives (IR, NIR, UV, and VIS). PMID:21352644

  13. Spectral transmittance of organic dye-doped glass films obtained by the solgel method

    NASA Astrophysics Data System (ADS)

    Nemoto, Shojiro; Hirokawa, Naoyuki

    1996-06-01

    The spectral transmittance of colored glass films synthesized by the solgel method is presented. The film was formed on a glass slide by dipping it into an organic dye-doped solution and, thereafter, by putting it into a furnace for solidification. Three dyes, Methylene Blue, Eosin, and Uranine, were used that exhibit transparent blue, pink, and yellow colors, respectively, when they are dissolved in the starting solution. We clarify how the spectral transmittance of the films varies with the solidification temperature. The films doped with two of the three dyes that exhibit violet, orange, and green colors are also synthesized, and their transmittance is measured. Moreover, the chemical durability of the films and the transmittance change caused by aging and illumination are examined. organic dye, solgel method.

  14. Spectral collocation and a two-level continuation scheme for dipolar Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Jeng, B.-W.; Chien, C.-S.; Chern, I.-L.

    2014-01-01

    We exploit the high accuracy of spectral collocation methods in the context of a two-level continuation scheme for computing ground state solutions of dipolar Bose-Einstein condensates (BEC), where the first kind Chebyshev polynomials and Fourier sine functions are used as the basis functions for the trial function space. The governing Gross-Pitaevskii equation (or Schrödinger equation) can be reformulated as a Schrödinger-Poisson (SP) type system [13]. The two-level continuation scheme is developed for tracing the first solution curves of the SP system, which in turn provide an appropriate initial guess for the Newton method to compute ground state solutions for 3D dipolar BEC. Extensive numerical experiments on 3D dipolar BEC and dipolar BEC in optical lattices are reported.

  15. Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries

    NASA Technical Reports Server (NTRS)

    Maday, Yvon; Ronquist, Einar M.

    1989-01-01

    The numerical analysis of spectral methods when non-constant coefficients appear in the equation, either due to the original statement of the equations or to take into account the deformed geometry, is presented. Particular attention is devoted to the optimality of the discretization even for low values of the discretization parameter. The effect of some overintegration is also addressed, in order to possibly improve the accuracy of the discretization.

  16. A comparative study of the performance of different spectral estimation methods for classification of mental tasks.

    PubMed

    Diez, Pablo F; Laciar, Eric; Mut, Vicente; Avila, Enrique; Torres, Abel

    2008-01-01

    In this paper we compare three different spectral estimation techniques for the classification of mental tasks. These techniques are the standard periodogram, the Welch periodogram and the Burg method, applied to electroencephalographic (EEG) signals. For each one of these methods we compute two parameters: the mean power and the root mean square (RMS), in various frequency bands. The classification of the mental tasks was conducted with a linear discriminate analysis. The Welch periodogram and the Burg method performed better than the standard periodogram. The use of the RMS allows better classification accuracy than the obtained with the power of EEG signals.

  17. Method for separation of homogeneous and inhomogeneous components of spectral broadening of rigid systems

    SciTech Connect

    Litvinyuk, I.V.

    1997-01-30

    A method is suggested that allows separation of the contributions from homogeneous and inhomogeneous broadening (IB) to a total spectral contour of rigid systems. Based upon a simple convolution model of inhomogeneous broadening, the method allows calculation of homogeneously broadened spectra and an inhomogeneous distribution function (IDF) from the measured excitation-wavelength-dependent fluorescence spectra of the system. The method is applied successfully to the solid solution of coumarin 334 (C334) in poly(methyl methacrylate) (PMMA) glass at 293 K. 16 refs., 5 figs.

  18. Comparison of outburst danger criteria of coal seams for acoustic spectral and instrumental forecast methods

    NASA Astrophysics Data System (ADS)

    Shadrin, A. V.; Bireva, Yu A.

    2016-10-01

    Outburst danger criteria for the two methods of current coal seam outburst forecast are considered: instrumental - by the initial outgassing rate and chippings outlet during test boreholes drilling, and geo-physical - by relation of high frequency and low frequency components of noise caused by cutting tool of operating equipment probing the face area taking into consideration the outburst criteria correction based on methane concentration at the face area and the coal strength. The conclusion is made on “adjustment” possibility of acoustic spectral forecast method criterion amended by control of methane concentration at the coal face and the coal strength taken from the instrumental method forecast results.

  19. A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory

    SciTech Connect

    Nintcheu Fata, Sylvain; Gray, Leonard J

    2009-01-01

    This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.

  20. Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation

    SciTech Connect

    Mitra, S.; Dhurandhar, S.V.; Finn, L.S.

    2005-11-15

    Inspiraling compact-object binary systems are promising gravitational wave sources for ground and space-based detectors. The time-dependent signature of these sources is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched filtering and maximum likelihood methods. As the parameters that characterize the source model vary, so do the templates against which the detector data are compared in the matched filter. For small variations in the parameters, the filter responses are closely correlated. Current analysis methodology samples a bank of filters whose parameter values are chosen so that the correlation between successive samples from successive filters in the bank is 97%. Correspondingly, the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we investigate the use of Chebyshev interpolation for reducing the number of templates that must be evaluated to obtain the same analysis sensitivity. Additionally, rather than focus on the 'loss' of signal-to-noise associated with the finite number of filters in the template bank, we evaluate the receiver operating characteristic (ROC) as a measure of the effectiveness of an analysis technique. The ROC relates the false alarm probability to the false dismissal probability of an analysis, which are the quantities that bear most directly on the effectiveness of an analysis scheme. As a demonstration, we compare the present 'dense sampling' analysis methodology with the 'interpolation' methodology using Chebyshev polynomials, restricted to one dimension of the multidimensional analysis problem by plotting the ROC curves. We find that the interpolated search can be

  1. The automatic solution of partial differential equations using a global spectral method

    NASA Astrophysics Data System (ADS)

    Townsend, Alex; Olver, Sheehan

    2015-10-01

    A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method. If a partial differential operator is of splitting rank 2, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree (nx ,ny) is computed in O ((nxny) 3 / 2) operations. Partial differential operators of splitting rank ≥3 are solved via a linear system involving a block-banded matrix in O (min ⁡ (nx3 ny ,nx ny3)) operations. Numerical examples demonstrate the applicability of our 2D spectral method to a broad class of PDEs, which includes elliptic and dispersive time-evolution equations. The resulting PDE solver is written in MATLAB and is publicly available as part of CHEBFUN. It can resolve solutions requiring over a million degrees of freedom in under 60 seconds. An experimental implementation in the JULIA language can currently perform the same solve in 10 seconds.

  2. a High-Efficiency Fusion Method of Multi-Spectral Image and Panchromatic Image

    NASA Astrophysics Data System (ADS)

    Xue, X.; Wang, J. P.; Wang, H.; Xiang, F.

    2013-07-01

    With the development of modern remote sensing technology, a variety of earth observation satellites could continue to tremendously provide image data of different spatial resolution, time resolution, spectral resolution remote sensing, and the remote sensing data obtained is increasing with great capacity, which forms multi-source image pyramid in the same area. To play the advantages of a variety of remote sensing data, the application of remote sensing image fusion is a very important choice. When remote sensing data is large, fusion is large in computing capacity and time-consuming, so it is difficult to carry out rapid, real-time fusion. However, in some remote sensing applications, such as disaster prevention and relief quick, etc., timely fusion is required. Based on image fusion method of principal component analysis (PCA) and the advantage of parallel computing, a high-efficiency fusion method of multi-spectral image and panchromatic image is proposed. Beijing-1 Micro-satellite is a high-performance small satellite for earth observation,With Beijing-1 Micro-satellite remote sensing images as the experimental data, it is proved that good fusion results of multi-spectral image and panchromatic image can be obtained with the proposed method, and the fusion speed is also fast. At the same time, some measures of improving the efficiency of parallel image fusion are also discussed.

  3. Imaging Earth's Interior based on Spectral-Element and Adjoint Methods (Invited)

    NASA Astrophysics Data System (ADS)

    Tromp, J.; Zhu, H.; Bozdag, E.

    2013-12-01

    We use spectral-element and adjoint methods to iteratively improve 3D tomographic images of Earth's interior, ranging from global to continental to exploration scales. The spectral-element method, a high-order finite-element method with the advantage of a diagonal mass matrix, is used to accurately calculate three-component synthetic seismograms in a complex 3D Earth model. An adjoint method is used to numerically compute Frechét derivatives of a misfit function based on the interaction between the wavefield for a reference Earth model and a wavefield obtained by using time-reversed differences between data and synthetics at all receivers as simultaneous sources. In combination with gradient-based optimization methods, such as a preconditioned conjugate gradient or L-BSGF method, we are able to iteratively improve 3D images of Earth's interior and gradually minimize discrepancies between observed and simulated seismograms. Various misfit functions may be chosen to quantify these discrepancies, such as cross-correlation traveltime differences, frequency-dependent phase and amplitude anomalies as well as full-waveform differences. Various physical properties of the Earth are constrained based on this method, such as elastic wavespeeds, radial anisotropy, shear attenuation and impedance contrasts. We apply this method to study seismic inverse problems at various scales, from global- and continental-scale seismic tomography to exploration-scale full-waveform inversion.

  4. Spectral Element Method Simulation of Linear and Nonlinear Electromagnetic Field in Semiconductor Nanostructures

    NASA Astrophysics Data System (ADS)

    Luo, Ma

    The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics. The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver. For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented. The second harmonic generation, which is a kind of nonlinear optical effect

  5. Using Spectral Methods to Quantify Changes in Temperature Variability across Frequencies

    NASA Astrophysics Data System (ADS)

    Sun, S.; McInerney, D.; Stein, M.; Leeds, W.; Poppick, A. N.; Nazarenko, L.; Schmidt, G. A.; Moyer, E. J.

    2014-12-01

    Changes in future surface temperature variability are of great scientific and societal interest. Since the impact of variability on human society depends on not only the magnitude but also the frequency of variations, shifts in the marginal distribution of temperatures do not provide enough information for impacts assessment. Leeds et al (2014) proposed a method to quantify changes in variability of temperature at distinct temporal frequencies by estimating the ratio of the spectral densities of temperature between pre-industrial and equilibrated future climates. This spectral ratio functions well as a metric to quantify temperature variability shifts in climate model output. In this study, we apply the method of Leeds et al (2014) to explore the temperature variability changes under increased radiative forcing. We compare changes in variability in higher-CO2 climates across two different climate models (CCSM3 from the National Center for Atmospheric Research and GISS-E2-R from NASA Goddard Institute for Space Studies), and changes driven by two different forcing agents (CO2 and solar radiation) within the same model (CCSM3). In all cases we use only the equilibrium stages of model runs extended several thousand years after an abrupt forcing change is imposed. We find a number of results. First, changes in temperature variability differ by frequency in most regions, confirming the need for spectral methods. Second, changes are similar regardless of forcing agents. In experiments with abruptly increased CO2 and solar forcing designed to produce the same change in global mean temperature, the distributions and magnitudes of spectral ratio changes are nearly identical. Finally, projections of variability changes differ across models. In CCSM3, temperature variability decreases in most regions and at most frequencies. Conversely, in GISS-E2-R, temperature variability tends to increase over land. The discrepancy between CCSM3 and the GISS-E-R highlights the need for

  6. Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

    NASA Astrophysics Data System (ADS)

    Ren, Z. X.; Zhang, S. Q.; Meng, J.

    2017-02-01

    A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in a 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single-particle energy are smaller than 10-4 MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial-deformed, nonaxial-deformed, and octupole-deformed potential are provided and discussed.

  7. Multispectral image compression methods for improvement of both colorimetric and spectral accuracy

    NASA Astrophysics Data System (ADS)

    Liang, Wei; Zeng, Ping; Xiao, Zhaolin; Xie, Kun

    2016-07-01

    We propose that both colorimetric and spectral distortion in compressed multispectral images can be reduced by a composite model, named OLCP(W)-X (OptimalLeaders_Color clustering-PCA-W weighted-X coding). In the model, first the spectral-colorimetric clustering is designed for sparse equivalent representation by generating spatial basis. Principal component analysis (PCA) is subsequently used in the manipulation of spatial basis for spectral redundancy removal. Then error compensation mechanism is presented to produce predicted difference image, and finally combined with visual characteristic matrix W, and the created image is compressed by traditional multispectral image coding schemes. We introduce four model-based algorithms to explain their validity. The first two algorithms are OLCPWKWS (OLC-PCA-W-KLT-WT-SPIHT) and OLCPKWS, in which Karhunen-Loeve transform, wavelet transform, and set partitioning in hierarchical trees coding are applied for the created image compression. And the latter two methods are OLCPW-JPEG2000-MCT and OLCP-JPEG2000-MCT. Experimental results show that, compared with the corresponding traditional coding, the proposed OLCPW-X schemes can significantly improve the colorimetric accuracy of rebuilding images under various illumination conditions and generally achieve satisfactory peak signal-to-noise ratio under the same compression ratio. And OLCP-X methods could always ensure superior spectrum reconstruction. Furthermore, our model has excellent performance on user interaction.

  8. Study of Site Response in the Seattle and Tacoma Basins, Washington, Using Spectral Ratio Methods

    NASA Astrophysics Data System (ADS)

    Keshvardoost, R.; Wolf, L. W.

    2014-12-01

    Sedimentary basins are known to have a pronounced influence on earthquake-generated ground motions, affecting both predominant frequencies and wave amplification. These site characteristics are important elements in estimating ground shaking and seismic hazard. In this study, we use three-component broadband and strong motion seismic data from three recent earthquakes to determine site response characteristics in the Seattle and Tacoma basins, Washington. Resonant frequencies and relative amplification of ground motions were determined using Fourier spectral ratios of velocity and acceleration records from the 2012 Mw 6.1 Vancouver Island earthquake, the 2012 Mw 7.8 Queen Charlotte Island earthquake, and the 2014 Mw 6.6 Vancouver Island earthquake. Recordings from sites within and adjacent to the Seattle and Tacoma basins were selected for the study based on their signal to noise ratios. Both the Standard Spectral Ratio (SSR) and the Horizontal-to-Vertical Spectral Ratio (HVSR) methods were used in the analysis, and results from each were compared to examine their agreement and their relation to local geology. Although 57% of the sites (27 out of 48) exhibited consistent results between the two methods, other sites varied considerably. In addition, we use data from the Seattle Liquefaction Array (SLA) to evaluate the site response at 4 different depths. Results indicate that resonant frequencies remain the same at different depths but amplification decreases significantly over the top 50 m.

  9. Using the nonstationary spectral method to analyze asymptotic macrodispersion in uniformly recharged heterogeneous aquifers

    NASA Astrophysics Data System (ADS)

    Chang, Ching-Min; Yeh, Hund-Der

    2008-02-01

    SummaryThis paper describes an investigation of the influence of uniformly distributed groundwater recharge on asymptotic macrodispersion in two-dimensional heterogeneous media. This is performed using a nonstationary spectral approach [Li, S.-G., McLaughlin, D., 1991. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour. Res. 27 (7), 1589-1605; Li, S.-G., McLaughlin, D., 1995. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour. Res. 31 (3), 541-551] based on Fourier-Stieltjes representations for the perturbed quantities. To solve the problem analytically, focus is placed on the case where the local longitudinal dispersivity αL is much smaller than the integral scale of log transmissivity λ (i.e., αL/ λ ≪ 1). The closed-form expressions are obtained for describing the spectrum of flow velocity, the variability of flow velocity and asymptotic macrodispersion, in terms of the statistical properties and the integral scale of log transmissivity, local transport parameters and a parameter β [Rubin, Y., Bellin, A., 1994. The effects of recharge on flow nonuniformity and macrodispersion. Water Resour. Res. 30 (4), 939-948] used to characterize the degree of flow nonuniformity due to the groundwater recharge. The impact of β on these results is examined.

  10. Application of Spectral Ratio Methods to an Investigation of Site Response in the Los Angeles Basin

    NASA Astrophysics Data System (ADS)

    Ng, R.; Polet, J.

    2015-12-01

    It is well established that sedimentary basins can increase the amplification and duration of earthquake ground motion. Past earthquakes have shown that site effects have a major influence on seismic damage and loss in urban areas. However, the response at any given site can vary significantly, even within the LA basin. We aim to investigate site response within the LA Basin through the application of the Horizontal-to-Vertical (H/V) spectral ratio method. This method was applied to 3-component broadband waveforms from the Los Angeles Syncline Seismic Interferometry Experiment (LASSIE). LASSIE is a collaborative, temporary, and dense array of 73 broadband seismometers that were active for a two month period starting October 2014 until November 2014, transecting the Los Angeles basin from Long Beach to La Puente. We use the Geopsy software to measure the fundamental frequency and minimum site amplification at each station. Data analysis and interpretation were conducted in accordance to the Site Effects Assessment Using Ambient Excitations (SESAME) guidelines for implementing the H/V ratio technique for investigations of site effects. Results from our initial data analysis indicate an average fundamental period at the basin center of 6 s - 12 s and peaks in the spectral ratio curves at much shorter periods for sites the basin edge of. We will show maps of the amplification and fundamental frequencies based on our spectral ratio analysis of the LASSIE data and compare our results with damage patterns of historic earthquakes, as well as models of the LA basin.

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

    PubMed

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

    2016-05-21

    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.

  12. Comparison of spectral estimation methods in reconstruction of parametric ultrasound images

    NASA Astrophysics Data System (ADS)

    Chaturvedi, Pawan; Insana, Michael F.; Hall, Timothy J.

    1996-04-01

    The application of inverse scattering methods to diagnostic ultrasound echo signals has provided us with detailed information about renal microstructure and function. In particular, the average scatterer size has been used to follow changes in microvascular perfusion that occur early in many renal disease processes. This paper shows that by introducing prior knowledge of the tissue state into the process, uncertainty in the spectral estimate is reduced for low SNR situations, and the contrast and range-resolution in scatterer size images can be improved without increasing the noise. Prior information used in the estimation technique is obtained from the histology of biological tissue. Maximum a posteriori and constrained least squares estimators are designed to obtain images for different levels of noise and for different gate-durations. Prior knowledge about the noise properties and the nature of the echo spectrum is used to obtain the order of an autoregressive model for estimating the power spectral density.

  13. A spectral multidomain penalty method model for high Reynolds number incompressible flows

    NASA Astrophysics Data System (ADS)

    Escobar-Vargas, Jorge; Diamessis, Peter

    2010-11-01

    We present the latest results of a spectral multidomain penalty method-based incompressible Navier Stokes solver for high Reynolds number stratified turbulent flows in doubly non-periodic domains that is currently under development. Time is discretized with a high-order stiffly stable scheme, whereas space is discretized with a Gauss-Lobatto-Legendre collocation approach in discontinuous quadrilateral subdomains. Numerical stability is guaranteed through a penalty scheme, spectral filtering and dealiasing techniques. The Poisson system of equations that arises from the temporal discretization is analyzed in detail as well as different preconditioning strategies to solve it efficiently, such as Kronecker product, deflation, multigrid, Jacobi, and finite difference based techniques. The efficiency and accuracy of the Navier Stokes solver are assessed through the solution of the driven cavity flow, Taylor vortex, and Couette flow.

  14. Spectral Decomposition Using the CEEMD Method: A Case Study from the Carpathian Foredeep

    NASA Astrophysics Data System (ADS)

    Kwietniak, Anna; Cichostępski, Kamil; Kasperska, Monika

    2016-10-01

    The purpose of this work is to select the optimal spectral decomposition (SD) method for channel detection in the Miocene strata of the Carpathian Fordeep, SE Poland. For analysis, two spectral decomposition algorithms were tested on 3D seismic data: the first, based on Fast Fourier Transform (FFT), and second, on Complete Ensemble Empirical Mode Decomposition (CEEMD). Additionally the results of instantaneous frequency (IF) were compared with the results of peak frequency (PF) computed after the CEEMD. Both algorithms of SD enabled us to interpret channels, but the results are marginally different, i.e. the FFT shows more coarse, linear structures, that are desirable for channel interpretation, whereas the CEEMD does not highlight these structures as clearly and shows more, what the authors believe to be, noise.

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

    SciTech Connect

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

    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)

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    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.

  17. Reconstruction of fluorescence molecular tomography via a nonmonotone spectral projected gradient pursuit method

    NASA Astrophysics Data System (ADS)

    Ye, Jinzuo; Du, Yang; An, Yu; Chi, Chongwei; Tian, Jie

    2014-12-01

    Fluorescence molecular tomography (FMT) is a promising imaging technique in preclinical research, enabling three-dimensional location of the specific tumor position for small animal imaging. However, FMT presents a challenging inverse problem that is quite ill-posed and ill-conditioned. Thus, the reconstruction of FMT faces various challenges in its robustness and efficiency. We present an FMT reconstruction method based on nonmonotone spectral projected gradient pursuit (NSPGP) with l1-norm optimization. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. A nonmonotone line search strategy is utilized to get the appropriate updating direction, which guarantees global convergence. Additionally, the Barzilai-Borwein step length is applied to build the optimal step length, further improving the convergence speed of the proposed method. Several numerical simulation studies, including multisource cases as well as comparative analyses, have been performed to evaluate the performance of the proposed method. The results indicate that the proposed NSPGP method is able to ensure the accuracy, robustness, and efficiency of FMT reconstruction. Furthermore, an in vivo experiment based on a heterogeneous mouse model was conducted, and the results demonstrated that the proposed method held the potential for practical applications of FMT.

  18. Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics

    NASA Astrophysics Data System (ADS)

    Layton, Anita T.; Minion, Michael L.

    2004-03-01

    In most models of reacting gas dynamics, the characteristic time scales of chemical reactions are much shorter than the hydrodynamic and diffusive time scales, rendering the reaction part of the model equations stiff. Moreover, nonlinear forcings may introduce into the solutions sharp gradients or shocks, the robust behavior and correct propagation of which require the use of specialized spatial discretization procedures. This study presents high-order conservative methods for the temporal integration of model equations of reacting flows. By means of a method of lines discretization on the flux difference form of the equations, these methods compute approximations to the cell-averaged or finite-volume solution. The temporal discretization is based on a multi-implicit generalization of spectral deferred correction methods. The advection term is integrated explicitly, and the diffusion and reaction terms are treated implicitly but independently, with the splitting errors reduced via the spectral deferred correction procedure. To reduce computational cost, different time steps may be used to integrate processes with widely-differing time scales. Numerical results show that the conservative nature of the methods allows a robust representation of discontinuities and sharp gradients; the results also demonstrate the expected convergence rates for the methods of orders three, four, and five for smooth problems.

  19. Legendre spectral-collocation method for solving some types of fractional optimal control problems.

    PubMed

    Sweilam, Nasser H; Al-Ajami, Tamer M

    2015-05-01

    In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques.

  20. Legendre spectral-collocation method for solving some types of fractional optimal control problems

    PubMed Central

    Sweilam, Nasser H.; Al-Ajami, Tamer M.

    2014-01-01

    In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh–Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937

  1. Significance of parametric spectral ratio methods in detection and recognition of whispered speech

    NASA Astrophysics Data System (ADS)

    Mathur, Arpit; Reddy, Shankar M.; Hegde, Rajesh M.

    2012-12-01

    In this article the significance of a new parametric spectral ratio method that can be used to detect whispered speech segments within normally phonated speech is described. Adaptation methods based on the maximum likelihood linear regression (MLLR) are then used to realize a mismatched train-test style speech recognition system. This proposed parametric spectral ratio method computes a ratio spectrum of the linear prediction (LP) and the minimum variance distortion-less response (MVDR) methods. The smoothed ratio spectrum is then used to detect whispered segments of speech within neutral speech segments effectively. The proposed LP-MVDR ratio method exhibits robustness at different SNRs as indicated by the whisper diarization experiments conducted on the CHAINS and the cell phone whispered speech corpus. The proposed method also performs reasonably better than the conventional methods for whisper detection. In order to integrate the proposed whisper detection method into a conventional speech recognition engine with minimal changes, adaptation methods based on the MLLR are used herein. The hidden Markov models corresponding to neutral mode speech are adapted to the whispered mode speech data in the whispered regions as detected by the proposed ratio method. The performance of this method is first evaluated on whispered speech data from the CHAINS corpus. The second set of experiments are conducted on the cell phone corpus of whispered speech. This corpus is collected using a set up that is used commercially for handling public transactions. The proposed whisper speech recognition system exhibits reasonably better performance when compared to several conventional methods. The results shown indicate the possibility of a whispered speech recognition system for cell phone based transactions.

  2. Numerical methods for problems in computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Mead, Jodi Lorraine

    1998-12-01

    A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev

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

    NASA Astrophysics Data System (ADS)

    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.

  4. Study on structural and spectral properties of isobavachalcone and 4-hydroxyderricin by computational method

    NASA Astrophysics Data System (ADS)

    Rong, Yuzhi; Wu, Jinhong; Liu, Xing; Zhao, Bo; Wang, Zhengwu

    Isobavachalcone and 4-hydroxyderricin, two major chalcone constituents isolated from the roots of Angelica keiskei KOIDZUMI, exhibit numerous biological activities. Quantum chemical methods have been employed to investigate their structural and spectral properties. The ground state structures were optimized using density functional B3LYP method with 6-311G (d, p) basis set in both gas and solvent phases. Based on the optimized geometries, the harmonic vibrational frequency, the 1H and 13C nuclear magnetic resonance (NMR) chemical shift using the GIAO method were calculated at the same level of theory, with the aim of verifying the experimental values. Results reveal that B3LYP has been a good method to study their vibrational spectroscopic and NMR spectral properties of the two chalcones. The electronic absorption spectra were calculated using the time-dependent density functional theory (TDDFT) method. The solvent polarity effects were considered and calculated using the polarizable continuum model (PCM). Results also show that substitutions of different electron donating groups can alter the absorption properties and shift the spectra to a higher wavelength region.

  5. Time and spectral analysis methods with machine learning for the authentication of digital audio recordings.

    PubMed

    Korycki, Rafal

    2013-07-10

    This paper addresses the problem of tampering detection and discusses new methods that can be used for authenticity analysis of digital audio recordings. Nowadays, the only method referred to digital audio files commonly approved by forensic experts is the ENF criterion. It consists in fluctuation analysis of the mains frequency induced in electronic circuits of recording devices. Therefore, its effectiveness is strictly dependent on the presence of mains signal in the recording, which is a rare occurrence. This article presents the existing methods of time and spectral analysis along with their modifications as proposed by the author involving spectral analysis of residual signal enhanced by machine learning algorithms. The effectiveness of tampering detection methods described in this paper is tested on a predefined music database. The results are compared graphically using ROC-like curves. Furthermore, time-frequency plots are presented and enhanced by reassignment method in purpose of visual inspection of modified recordings. Using this solution, enables analysis of minimal changes of background sounds, which may indicate tampering.

  6. Models of spectral unmixing: simplex versus least squares method of resolution

    NASA Astrophysics Data System (ADS)

    Lavreau, Johan

    1995-01-01

    Spectral unmixing is referred to in textbooks as a straightforward technique the application of which encounters apparently no problem. Operational applications are however scarce in the literature. The method usually used is based on the least square method of minimizing the error in search of the best fit solution. This method, however, poses problems when applied to real data when the number of end-members increases and/or the composition of end-members is similar. An alternative method based on linear algebra has several advantages: (1) no inversion of matrix is required, no meaningless values are thus generated; (2) not only a condition of the closed system can be introduced, but the end-members remain independent (i.e., the last one is not the complement to 1 of the sum of the other, as in the least square method); (3) a condition of positive value of the weights can be imposed. The latter condition yields a supplementary equation to the system, one more end-member may be taken into account, thus improving both the qualitative and the quantitative aspects of the mixture problem. Examples based on Landsat TM imagery are shown in the fields of vegetation monitoring (subtraction of the vegetal component in the landscape) and spectral geology in arid terrains (end-members being defined through a principal components analysis of the image).

  7. Spectral element method for band structures of two-dimensional anisotropic photonic crystals.

    PubMed

    Luo, Ma; Liu, Qing Huo; Li, Zhibing

    2009-02-01

    A spectral element method (SEM) is proposed for the accurate calculation of band structures of two-dimensional anisotropic photonic crystals. It uses Gauss-Lobatto-Legendre polynomials as the basis functions in the finite-element framework with curvilinear quadrilateral elements. Coordination mapping is introduced to make the curved quadrilateral elements conformal with the problem geometry. Mixed order basis functions are used in the vector SEM for full vector calculation. The numerical convergence speed of the method is investigated with both square and triangular lattices, and with isotropic and in-plane anisotropic media. It is shown that this method has spectral accuracy, i.e., the numerical error decreases exponentially with the order of basis functions. With only four points per wavelength, the SEM can achieve a numerical error smaller than 0.1%. The full vector calculation method can suppress all spurious modes with nonzero eigenvalues, thus making it easy to filter out real modes. It is thus demonstrated that the SEM is an efficient alternative method for accurate determination of band structures of two-dimensional photonic crystals.

  8. Spectral element method for band structures of two-dimensional anisotropic photonic crystals

    NASA Astrophysics Data System (ADS)

    Luo, Ma; Liu, Qing Huo; Li, Zhibing

    2009-02-01

    A spectral element method (SEM) is proposed for the accurate calculation of band structures of two-dimensional anisotropic photonic crystals. It uses Gauss-Lobatto-Legendre polynomials as the basis functions in the finite-element framework with curvilinear quadrilateral elements. Coordination mapping is introduced to make the curved quadrilateral elements conformal with the problem geometry. Mixed order basis functions are used in the vector SEM for full vector calculation. The numerical convergence speed of the method is investigated with both square and triangular lattices, and with isotropic and in-plane anisotropic media. It is shown that this method has spectral accuracy, i.e., the numerical error decreases exponentially with the order of basis functions. With only four points per wavelength, the SEM can achieve a numerical error smaller than 0.1%. The full vector calculation method can suppress all spurious modes with nonzero eigenvalues, thus making it easy to filter out real modes. It is thus demonstrated that the SEM is an efficient alternative method for accurate determination of band structures of two-dimensional photonic crystals.

  9. Spectral element method-based parabolic equation for EM-scattering problems

    NASA Astrophysics Data System (ADS)

    He, Zi; Fan, Zhen-Hong; Chen, Ru-Shan

    2016-01-01

    The traditional parabolic equation (PE) method is based on the finite difference (FD) scheme. However, the scattering object cannot be well approximated for complex geometries. As a result, a large number of meshes are needed to discretize the complex scattering objects. In this paper, the spectral element method is introduced to better approximate the complex geometry in each transverse plane, while the FD scheme is used along the paraxial direction. This proposed algorithm begins with expanding the reduced scattered fields with the Gauss-Lobatto-Legendre polynomials and testing them by the Galerkin's method in each transverse plane. Then, the calculation can be taken plane by plane along the paraxial direction. Numerical results demonstrate that the accuracy can be improved by the proposed method with larger meshes when compared with the traditional PE method.

  10. Hybrid Lanczos-type product methods

    SciTech Connect

    Ressel, K.J.

    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.

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

    SciTech Connect

    Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

    2015-09-08

    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 oper- ator. 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 approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks 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 in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

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

    DOE PAGES

    Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

    2015-09-08

    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 oper- ator. 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 approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks 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 in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

  13. Structure-preserving spectral element method in attenuating seismic wave modeling

    NASA Astrophysics Data System (ADS)

    Cai, Wenjun; Zhang, Huai

    2016-04-01

    This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive

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

    NASA Astrophysics Data System (ADS)

    Engsig-Karup, A. P.; Eskilsson, C.; Bigoni, D.

    2016-08-01

    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 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 removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order - possibly adapted - spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.

  15. Pipelined chebyshev functional link artificial recurrent neural network for nonlinear adaptive filter.

    PubMed

    Zhao, Haiquan; Zhang, Jiashu

    2010-02-01

    A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously be performed in a pipelined parallelism fashion, and this would lead to a significant improvement in its total computational efficiency. Furthermore, contrasted with the architecture of a pipelined RNN (PRNN), each module of PCFLARNN is a CFLARNN whose nonlinearity is introduced by enhancing the input pattern with Chebyshev functional expansion, whereas the RNN of each module in PRNN utilizing linear input and first-order recurrent term only fails to utilize the high-order terms of inputs. Therefore, the performance of PCFLARNN can further be improved at the cost of a slightly increased computational complexity. In addition, due to the introduced nonlinear functional expansion of each module in PRNN, the number of input signals can be reduced. Computer simulations have demonstrated that the proposed filter performs better than PRNN and RNN for nonlinear colored signal prediction, nonstationary speech signal prediction, and chaotic time series prediction.

  16. Stieltjes polynomials and Gauss-Kronrod quadrature formulae for measures induced by Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Notaris, Sotirios

    1995-03-01

    Given a fixed n≥1, and a (monic) orthogonal polynomial πn(·)Dπn(·;dσ) relative to a positive measuredσ on the interval [a, b], one can define the nonnegative measure , to which correspond the (monic) orthogonal polynomials . The coefficients in the three-term recurrence relation for , whendσ is a Chebyshev measure of any of the four kinds, were obtained analytically in closed form by Gautschi and Li. Here, we give explicit formulae for the Stieltjes polynomials whendσ is any of the four Chebyshev measures. In addition, we show that the corresponding Gauss-Kronrod quadrature formulae for each of these , based on the zeros of and , have all the desirable properties of the interlacing of nodes, their inclusion in [-1, 1], and the positivity of all quadrature weights. Exceptions occur only for the Chebyshev measuredσ of the third or fourth kind andn even, in which case the inclusion property fails. The precise degree of exactness for each of these formulae is also determined.

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

    SciTech Connect

    Gamba, Irene M.; Haack, Jeffrey R.

    2014-08-01

    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.

  18. A spectral boundary integral equation method for the 2-D Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

  19. Methods Development for Spectral Simplification of Room-Temperature Rotational Spectra

    NASA Astrophysics Data System (ADS)

    Kent, Erin B.; Shipman, Steven

    2014-06-01

    Room-temperature rotational spectra are dense and difficult to assign, and so we have been working to develop methods to accelerate this process. We have tested two different methods with our waveguide-based spectrometer, which operates from 8.7 to 26.5 GHz. The first method, based on previous work by Medvedev and De Lucia, was used to estimate lower state energies of transitions by performing relative intensity measurements at a range of temperatures between -20 and +50 °C. The second method employed hundreds of microwave-microwave double resonance measurements to determine level connectivity between rotational transitions. The relative intensity measurements were not particularly successful in this frequency range (the reasons for this will be discussed), but the information gleaned from the double-resonance measurements can be incorporated into other spectral search algorithms (such as autofit or genetic algorithm approaches) via scoring or penalty functions to help with the spectral assignment process. I.R. Medvedev, F.C. De Lucia, Astrophys. J. 656, 621-628 (2007).

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

    PubMed

    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.

  1. A spectral method for retrieving cloud optical thickness and effective radius from surface-based transmittance measurements

    NASA Astrophysics Data System (ADS)

    McBride, P. J.; Schmidt, K. S.; Pilewskie, P.; Kittelman, A. S.; Wolfe, D. E.

    2011-07-01

    We introduce a new spectral method for the retrieval of optical thickness and effective radius from cloud transmittance that relies on the spectral slope of the normalized transmittance between 1565 nm and 1634 nm, and on cloud transmittance at a visible wavelength. The standard dual-wavelength technique, which is traditionally used in reflectance-based retrievals, is ill-suited for transmittance because it lacks sensitivity to effective radius, especially for optically thin clouds. Using the spectral slope rather than the transmittance itself enhances the sensitivity of transmittance observations with respect to the effective radius. This is demonstrated by applying it to the moderate spectral resolution observations from the Solar Spectral Flux Radiometer (SSFR) and Shortwave Spectroradiometer (SWS), and by examining the retrieval uncertainties of the standard and the spectral method for data from the DOE ARM Southern Great Plains (SGP) site and a NOAA ship cruise (ICEALOT). The liquid water path (LWP) is derived from the retrieved optical thickness and effective radius, based on two different assumptions about the cloud vertical profile, and compared to the simultaneous observations from a microwave radiometer. Optical thickness and effective radius is also compared to MODIS retrievals. In general, the effective radius uncertainties were much larger for the standard retrieval than for the spectral retrieval, particularly for thin clouds. When defining 2 μm as upper limit for the tolerable uncertainty of the effective radius, the standard method returned only very few valid retrievals for clouds with an optical thickness below 25. For the analyzed ICEALOT data (mean optical thickness 23), the spectral method provided valid retrievals for 84 % of the data (24 % for the standard method). For the SGP data (mean optical thickness 44), both methods provided a high return of 90 % for the spectral method and 78 % for the standard method.

  2. Fourier spectral method for higher order space fractional reaction-diffusion equations

    NASA Astrophysics Data System (ADS)

    Pindza, Edson; Owolabi, Kolade M.

    2016-11-01

    Evolution equations containing fractional derivatives can provide suitable mathematical models for describing important physical phenomena. In this paper, we propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The proposed method is based on an exponential integrator scheme in time and the Fourier spectral method in space. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency, and a completely straightforward extension to high spatial dimensions. Although, in general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives, we introduce them to describe fractional hyper-diffusions in reaction diffusion. The scheme justified by a number of computational experiments, this includes two and three dimensional partial differential equations. Numerical experiments are provided to validate the effectiveness of the proposed approach.

  3. On shifted Jacobi spectral method for high-order multi-point boundary value problems

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

    2012-10-01

    This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

  4. Damage detection by a FE model updating method using power spectral density: Numerical and experimental investigation

    NASA Astrophysics Data System (ADS)

    Pedram, Masoud; Esfandiari, Akbar; Khedmati, Mohammad Reza

    2017-06-01

    This paper investigates the viability of damage detection using power spectral density (PSD) of structural response both numerically and experimentally. The paper establishes a sensitivity based damage detection method to use PSD. The advantages of PSD as a model updating metric are explained and its challenges are addressed. An approximate frequency response function of damaged model is used to redeem the method for the effect of incomplete measurement. The robust solution of the developed sensitivity equation is achieved through a least-squares error minimization scheme, and the challenging issues are discussed. The ability of the method in localizing and quantifying the damage and its robustness against measurement and modeling errors is investigated by a numerical example. Experimental vibration test data of a laboratory concrete beam with various level of distributed damage is used to probe the method in practical conditions. The results show that PSD of response can be used to detect damages in lower frequency ranges with acceptable accuracy.

  5. A hybrid classification method using spectral, spatial, and textural features for remotely sensed images based on morphological filtering

    NASA Astrophysics Data System (ADS)

    Okumura, Hiroshi; Yamaura, Makoto; Arai, Kohei

    2007-10-01

    "HYCLASS", a new hybrid classification method for remotely sensed multi-spectral images is proposed. This method consists of two procedures, the textural edge detection and texture classification. In the textural edge detection, the maximum likelihood classification (MLH) method is employed to find "the spectral edges", and the morphological filtering is employed to process the spectral edges into "the textural edges" by sharpening the opened curve parts of the spectral edges. In the texture classification, the supervised texture classification method based on normalized Zernike moment vector that the authors have already proposed. Some experiments using a simulated texture image and an actual airborne sensor image are conducted to evaluate the classification accuracy of the HYCLASS. The experimental results show that the HYCLASS can provide reasonable classification results in comparison with those by the conventional classification method.

  6. A spectral method determination of the first critical Rayleigh number for a low-Prandtl number crystal melt in a cylindrical container

    NASA Technical Reports Server (NTRS)

    Dietz, C. M., Jr.; Diplas, P.

    1993-01-01

    The onset of laminar axisymmetric Rayleigh-Benard convection is investigated for a low-Prandtl number liquid metal in a cylindrical container. All surfaces are considered to be solid and no-slip. Two separate cases are examined for the thermal boundary conditions at the side wall, one with conducting and the other with insulated surface. The governing Boussinesq system is first perturbed and then simplified by introducing a Stokes stream function. Subsequently, a Chebyshev Galerkin spectral model is employed to reduce the simplified system to a system of first-order nonlinear ordinary differential equations. A local stability analysis determines the two values of the first critical Rayleigh number, Ra(sub cl), for the insulated and conducting side walls. As expected, the conducting Ra(sub cl) value of 2882.5 obtained from the present approach exceeded the corresponding insulated Ra(sub cl) value of 2331.6. For the insulated case, an earlier study using a different numerical approach suggests that Ra(sub cl) = 2261.9, while an experimental study measured Ra(sub cl) = 2700.

  7. Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

    2002-01-01

    Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve

  8. Method and system for calibrating acquired spectra for use in spectral analysis

    DOEpatents

    Reber, Edward L.; Rohde, Kenneth W.; Blackwood, Larry G.

    2010-09-14

    A method for calibrating acquired spectra for use in spectral analysis includes performing Gaussian peak fitting to spectra acquired by a plurality of NaI detectors to define peak regions. A Na and annihilation doublet may be located among the peak regions. A predetermined energy level may be applied to one of the peaks in the doublet and a location of a hydrogen peak may be predicted based on the location of at least one of the peaks of the doublet. Control systems for calibrating spectra are also disclosed.

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

    DOEpatents

    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.

  10. On the simulation of industrial gas dynamic applications with the discontinuous Galerkin spectral element method

    NASA Astrophysics Data System (ADS)

    Hempert, F.; Hoffmann, M.; Iben, U.; Munz, C.-D.

    2016-06-01

    In the present investigation, we demonstrate the capabilities of the discontinuous Galerkin spectral element method for high order accuracy computation of gas dynamics. The internal flow field of a natural gas injector for bivalent combustion engines is investigated under its operating conditions. The simulations of the flow field and the aeroacoustic noise emissions were in a good agreement with the experimental data. We tested several shock-capturing techniques for the discontinuous Galerkin scheme. Based on the validated framework, we analyzed the development of the supersonic jets during different opening procedures of a compressed natural gas injector. The results suggest that a more gradual injector opening decreases the noise emission.

  11. Spectral-domain moment-method analysis of coplanar microstrip parasitic subarrays

    NASA Technical Reports Server (NTRS)

    Chen, Wei; Lee, Kai-Fong; Lee, R. Q.

    1993-01-01

    Basic characteristics of several configurations of coplanar microstrip parasitic subarrays consisting of one fed patch and two or more parasitic patches were investigated by means of a spectral-domain full-wave analysis and the moment method analysis. Results are presented for radiating- and nonradiating edge-coupled three-element linear subarrays and for a five-patch cross. A comparison of the theoretical input impedance results obtained by the analysis of a three-element linear array showed a reasonable agreement between computed and measured R and X values.

  12. Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

    NASA Astrophysics Data System (ADS)

    Andretta, Marina; Birgin, Ernesto; Martínez, J.

    2010-01-01

    A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/˜egbirgin/tango/.

  13. Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation

    NASA Astrophysics Data System (ADS)

    Carella, Alfredo Raúl; Dorao, Carlos Alberto

    2013-01-01

    Fractional derivatives provide a general approach for modeling transport phenomena occurring in diverse fields. This article describes a Least Squares Spectral Method for solving advection-dispersion equations using Caputo or Riemann-Liouville fractional derivatives. A Gauss-Lobatto-Jacobi quadrature is implemented to approximate the singularities in the integrands arising from the fractional derivative definition. Exponential convergence rate of the operator is verified when increasing the order of the approximation. Solutions are calculated for fractional-time and fractional-space differential equations. Comparisons with finite difference schemes are included. A significant reduction in storage space is achieved by lowering the resolution requirements in the time coordinate.

  14. A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices

    NASA Astrophysics Data System (ADS)

    Li, Z.-C.; Chen, S.-Y.; Chien, C.-S.; Chen, H.-S.

    2011-06-01

    We extend the study of spectral collocation methods (SCM) in Li et al. (2009) [1] for semilinear elliptic eigenvalue problems to that for a rotating Bose-Einstein condensation (BEC) and a rotating BEC in optical lattices. We apply the Lagrange interpolants using the Legendre-Gauss-Lobatto points to derive error bounds for the SCM. The optimal error bounds are derived for both H-norm and L-norm. Extensive numerical experiments on a rotating Bose-Einstein condensation and a rotating BEC in optical lattices are reported. Our numerical results show that the convergence rate of the SCM is exponential, and is independent of the collocation points we choose.

  15. Suppression of spectral anomalies in SSFP-NMR signal by the Krylov Basis Diagonalization Method

    NASA Astrophysics Data System (ADS)

    Moraes, Tiago Bueno; Santos, Poliana Macedo; Magon, Claudio Jose; Colnago, Luiz Alberto

    2014-06-01

    Krylov Basis Diagonalization Method (KBDM) is a numerical procedure used to fit time domain signals as a sum of exponentially damped sinusoids. In this work KBDM is used as an alternative spectral analysis tool, complimentary to Fourier transform. We report results obtained from 13C Nuclear Magnetic Resonance (NMR) by Steady State Free Precession (SSFP) measurements in brucine, C23H26N2O4. Results lead to the conclusion that the KBDM can be successfully applied, mainly because it is not influenced by truncation or phase anomalies, as observed in the Fourier transform spectra.

  16. Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

    2016-01-01

    The perfectly matched layer (PML) technique is developed in the context of a high- order spectral-element Discontinuous-Galerkin (DG) method. The technique is applied to a range of test cases and is shown to be superior compared to other approaches, such as those based on using characteristic boundary conditions and sponge layers, for treating the inflow and outflow boundaries of computational domains. In general, the PML technique improves the quality of the numerical results for simulations of practical flow configurations, but it also exhibits some instabilities for large perturbations. A preliminary analysis that attempts to understand the source of these instabilities is discussed.

  17. A shortcut through the Coulomb gas method for spectral linear statistics on random matrices

    NASA Astrophysics Data System (ADS)

    Deelan Cunden, Fabio; Facchi, Paolo; Vivo, Pierpaolo

    2016-04-01

    In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two-dimensional Coulomb gas analogy is available. We present a critical revision of the Coulomb gas method in random matrix theory (RMT) borrowing language and tools from large deviations theory. This allows us to formalize an equivalent, but more effective and quicker route toward RMT free energy calculations. Moreover, we argue that this more modern viewpoint is likely to shed further light on the interesting issues of weak phase transitions and evaporation phenomena recently observed in RMT.

  18. A spectral collocation time-domain solver for Maxwell's equations of electromagnetics with application to radar cross-section computation

    NASA Astrophysics Data System (ADS)

    Kabakian, Adour Vahe

    1998-12-01

    Most time-domain solvers of Maxwell's equations that are applied to electromagnetic wave scattering problems are based on second- or third-order finite-difference and finite-volume schemes. Since linear wave propagation phenomena tend to be very susceptible to numerical dissipation and dispersion errors, they place high accuracy demands on the numerical methods employed. Starting with the premise that the required accuracy can be achieved more efficiently with high-order methods, a new numerical scheme based on spectral collocation is developed for solving Maxwell's equations in the time domain. The three-dimensional method is formulated over generalized curvilinear coordinates. It employs Fourier and Chebyshev spectral collocation for the spatial derivatives, while time advancement is achieved by the explicit third-order Adams-Moulton-Bashforth scheme. A domain decomposition method supplementing the spectral solver is also developed, extending its range of applications to geometries more complex than those traditionally associated with spectral methods. Reflective and absorbing boundary conditions are developed specifically for the spectral scheme. Finally, a grid stretching function is incorporated into the solver, which can be used, when needed, to relieve the stability restriction associated with the Chebyshev spacing of the collocation points, at the expense of only moderate loss in accuracy. The numerical method is applied to solve electromagnetic wave scattering problems from perfectly conducting solid targets, using both single and multi-domain grids. The geometries considered are the circular cylinder, the square cylinder, and the sphere. Solutions are evaluated and validated by the accuracy of the radar cross-section and, in some instances, the surface currents. Compared to commonly used finite-difference and finite-volume solvers, the spectral scheme produces results that are one to two orders of magnitude more accurate, using grids that are an order of

  19. Spectral methods in general relativity and large Randall-Sundrum II black holes

    SciTech Connect

    Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; Yaghoobpour-Tari, Shima E-mail: celine.cattoen-gilbert@canterbury.ac.nz E-mail: yaghoobp@ualberta.ca

    2013-06-01

    Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS{sub 5}-CFT{sub 4} solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS{sub 5}-CFT{sub 4} solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(−ΛM{sup 2}), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(−Λ)

  20. A multiple criteria-based spectral partitioning method for remotely sensed hyperspectral image classification

    NASA Astrophysics Data System (ADS)

    Liu, Yi; Li, Jun; Plaza, Antonio; Sun, Yanli

    2016-10-01

    Hyperspectral remote sensing offers a powerful tool in many different application contexts. The imbalance between the high dimensionality of the data and the limited availability of training samples calls for the need to perform dimensionality reduction in practice. Among traditional dimensionality reduction techniques, feature extraction is one of the most widely used approaches due to its flexibility to transform the original spectral information into a subspace. In turn, band selection is important when the application requires preserving the original spectral information (especially the physically meaningful information) for the interpretation of the hyperspectral scene. In the case of hyperspectral image classification, both techniques need to discard most of the original features/bands in order to perform the classification using a feature set with much lower dimensionality. However, the discriminative information that allows a classifier to provide good performance is usually classdependent and the relevant information may live in weak features/bands that are usually discarded or lost through subspace transformation or band selection. As a result, in practice, it is challenging to use either feature extraction or band selection for classification purposes. Relevant lines of attack to address this problem have focused on multiple feature selection aiming at a suitable fusion of diverse features in order to provide relevant information to the classifier. In this paper, we present a new dimensionality reduction technique, called multiple criteria-based spectral partitioning, which is embedded in an ensemble learning framework to perform advanced hyperspectral image classification. Driven by the use of a multiple band priority criteria that is derived from classic band selection techniques, we obtain multiple spectral partitions from the original hyperspectral data that correspond to several band subgroups with much lower spectral dimensionality as compared with

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

    NASA Astrophysics Data System (ADS)

    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

  2. A new method for spatial resolution enhancement of hyperspectral images using sparse coding and linear spectral unmixing

    NASA Astrophysics Data System (ADS)

    Hashemi, Nezhad Z.; Karami, A.

    2015-10-01

    Hyperspectral images (HSI) have high spectral and low spatial resolutions. However, multispectral images (MSI) usually have low spectral and high spatial resolutions. In various applications HSI with high spectral and spatial resolutions are required. In this paper, a new method for spatial resolution enhancement of HSI using high resolution MSI based on sparse coding and linear spectral unmixing (SCLSU) is introduced. In the proposed method (SCLSU), high spectral resolution features of HSI and high spatial resolution features of MSI are fused. In this case, the sparse representation of some high resolution MSI and linear spectral unmixing (LSU) model of HSI and MSI is simultaneously used in order to construct high resolution HSI (HRHSI). The fusion process of HSI and MSI is formulated as an ill-posed inverse problem. It is solved by the Split Augmented Lagrangian Shrinkage Algorithm (SALSA) and an orthogonal matching pursuit (OMP) algorithm. Finally, the proposed algorithm is applied to the Hyperion and ALI datasets. Compared with the other state-of-the-art algorithms such as Coupled Nonnegative Matrix Factorization (CNMF) and local spectral unmixing, the SCLSU has significantly increased the spatial resolution and in addition the spectral content of HSI is well maintained.

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

    PubMed

    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.

  4. Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes

    SciTech Connect

    Mayeda, K; Malagnini, L; Walter, W R

    2007-03-16

    This study is motivated by renewed interest within the seismic source community to resolve the long-standing question on energy scaling of earthquakes, specifically, 'Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones?' This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. Estimating the total radiated energy (ER) from earthquakes requires significant broadband corrections for path and site effects. Moreover, source radiation pattern and directivity corrections can be equally significant and also must be accounted for. Regional studies have used a number of different methods, each with their own advantages and disadvantages. These methods include: integration of squared shear wave moment-rate spectra, direct integration of broadband velocity-squared waveforms, empirical Green's function deconvolution, and spectral ratio techniques. The later two approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In spite of this, a number of such studies find very large amplitude variance across a network of stations. In this paper we test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing a better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy. The local and regional coda is virtually insensitive to lateral crustal heterogeneity and source radiation pattern, and the use of the coda might allow for more stable amplitude ratios to better constrain source differences between event pairs. We first compared amplitude ratio performance between local and near-regional S and coda waves in the San Francisco Bay region for

  5. Mapping Site Response Parameters on Cal Poly Pomona Campus Using the Spectral Ratio Method

    NASA Astrophysics Data System (ADS)

    HO, K. Y. K.; Polet, J.

    2014-12-01

    Site characteristics are an important factor in earthquake hazard assessment. To better understand site response differences on a small scale, as well as the seismic hazard of the area, we develop site response parameter maps of Cal Poly Pomona campus. Cal Poly Pomona is located in southern California about 40 km east of Los Angeles, within 50 km of San Andreas Fault. The campus is situated on top of the San Jose Fault. With about twenty two thousand students on campus, it is important to know the site response in this area. To this end, we apply the Horizontal-to-Vertical (H/V) spectral ratio technique, which is an empirical method that can be used in an urban environment with no environmental impact. This well-established method is based on the computation of the ratio of vertical ambient noise ground motion over horizontal ambient noise ground motion as a function of frequency. By applying the spectral ratio method and the criteria from Site Effects Assessment Using Ambient Excitations (SESAME) guidelines, we can determine fundamental frequency and a minimum site amplification factor. We installed broadband seismometers throughout the Cal Poly Pomona campus, with an initial number of about 15 sites. The sites are approximately 50 to 150 meters apart and about two hours of waveforms were recorded at each site. We used the Geopsy software to make measurements of the peak frequency and the amplitude of the main peak from the spectral ratio. These two parameters have been determined to be estimates of fundamental frequency and a minimum site amplification factor, respectively. Based on the geological map from the U.S. Geological Survey (USGS) and our data collected from Cal Poly Pomona campus, our preliminary results suggest that the area of campus that is covered by alluvial fan material tends to have a single significant spectral peak with a fundamental frequency of ~1Hz and a minimum amplification factor of ~3.7. The minimum depth of the surface layer is about 56

  6. Spectral solution of acoustic wave-propagation problems

    NASA Technical Reports Server (NTRS)

    Kopriva, David A.

    1990-01-01

    The Chebyshev spectral collocation solution of acoustic wave propagation problems is considered. It is shown that the phase errors decay exponentially fast and that the number of points per wavelength is not sufficient to estimate the phase accuracy. Applications include linear propagation of a sinusoidal acoustic wavetrain in two space dimensions, and the interaction of a sound wave with the bow shock formed by placing a cylinder in a uniform Mach 4 supersonic free stream.

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

    PubMed Central

    Vu, Trung Nghia; Laukens, Kris

    2013-01-01

    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. PMID:24957991

  8. Precision of the IAS monitoring system based on the elapsed time method in the spectral domain

    NASA Astrophysics Data System (ADS)

    André, H.; Girardin, F.; Bourdon, A.; Antoni, J.; Rémond, D.

    2014-02-01

    Instantaneous Angular Speed (IAS) has recently appeared as an original and promising tool for monitoring mechanical parts of rotating machines. Mechanisms running under non-stationary conditions, such as wind turbine, are especially suited to this method since the issued signal is intrinsically sampled in the angular domain. Although processing tools are developed to enhance its use in the industry, this method is lacking a proper identification of its limitations and this paper aims at precisely understanding two of its main shortcomings: the aliasing and the quantization phenomena. After having presented the measurement method, both the aliasing and the quantization error are theoretically dissected. Formula is proposed to estimate their influence in the spectral observation of the IAS, and a good signal-to-noise ratio appraisal for this measurement technique is finally obtained. It can eventually be used as a first guide to conveniently design an IAS based control/monitoring system.

  9. Computing the Periods of Light Variation of Blazar Objects 3C279 and OJ 287 with Autoregressive Spectral Analysis Method

    NASA Astrophysics Data System (ADS)

    Tang, Jie; Zhang, Xiao-juan; Pang, Qiao; Zhang, Hao-Jing; Zheng, Yong-Gang; Zhang, Xiong

    2010-04-01

    The light variability is one of the main characteristics of blazar objects. Because of the complexity of their light curves, the present periodicity analysis methods are not yet perfect. Based on the modern spectral estimate theory, this paper has described in details the principles of the maximum entropy spectral estimate and autoregressive (AR) spectral estimate, analyzed the effect of the order number selection on the resultant model. Applying these methods to the periodicity analysis of the quasar 3C 279 and BL Lac object OJ 287, their light periods are obtained to be 7.14 and 11.76 yr, respectively. As is verified by experiments, the AR spectral estimate has a high resolution and is a rather good periodicity analysis method. Finally, the items noteworthy for the application of these spectrum estimation methods to the periodicity analysis of the light variations of blazars are mentioned.

  10. Methods of dynamic spectral analysis by self-exciting autoregressive moving average models and their application to analysing biosignals.

    PubMed

    Schack, B; Bareshova, E; Grieszbach, G; Witte, H

    1995-05-01

    Dynamic methods in the spectral domain are necessary to analyse biological signals because of the frequently nonstationary character of the signals. The paper presents an adaptive procedure of fitting time-dependent ARMA models to nonstationary signals, which is suitable for on-line calculations. The properties of the model parameter estimations are examined, and in the stationary case are compared with the results of convergent estimation methods. On this basis time-varying spectral parameters with high temporal and spectral resolution are calculated, and the possibility of their application is shown in EEG analysis and laser-Doppler-flowmetry.

  11. [The research on separating and extracting overlapping spectral feature lines in LIBS using damped least squares method].

    PubMed

    Wang, Yin; Zhao, Nan-jing; Liu, Wen-qing; Yu, Yang; Fang, Li; Meng, De-shuo; Hu, Li; Zhang, Da-hai; Ma, Min-jun; Xiao, Xue; Wang, Yu; Liu, Jian-guo

    2015-02-01

    In recent years, the technology of laser induced breakdown spectroscopy has been developed rapidly. As one kind of new material composition detection technology, laser induced breakdown spectroscopy can simultaneously detect multi elements fast and simply without any complex sample preparation and realize field, in-situ material composition detection of the sample to be tested. This kind of technology is very promising in many fields. It is very important to separate, fit and extract spectral feature lines in laser induced breakdown spectroscopy, which is the cornerstone of spectral feature recognition and subsequent elements concentrations inversion research. In order to realize effective separation, fitting and extraction of spectral feature lines in laser induced breakdown spectroscopy, the original parameters for spectral lines fitting before iteration were analyzed and determined. The spectral feature line of' chromium (Cr I : 427.480 nm) in fly ash gathered from a coal-fired power station, which was overlapped with another line(FeI: 427.176 nm), was separated from the other one and extracted by using damped least squares method. Based on Gauss-Newton iteration, damped least squares method adds damping factor to step and adjust step length dynamically according to the feedback information after each iteration, in order to prevent the iteration from diverging and make sure that the iteration could converge fast. Damped least squares method helps to obtain better results of separating, fitting and extracting spectral feature lines and give more accurate intensity values of these spectral feature lines: The spectral feature lines of chromium in samples which contain different concentrations of chromium were separated and extracted. And then, the intensity values of corresponding spectral lines were given by using damped least squares method and least squares method separately. The calibration curves were plotted, which showed the relationship between spectral

  12. Measuring method of diffraction efficiency for plane grating based on Fourier spectral technology.

    PubMed

    Ma, Zhenyu; Qi, Xiangdong; Li, Xiaotian; Zhang, Shanwen; Bayanheshig; Yu, Hongzhu; Yu, Haili; Jiao, Qingbin

    2016-01-20

    A traditional double monochromatic measurement instrument of diffraction efficiency for a plane grating involves two major problems: one is the differences of output spectrum bandwidths during measurement of a standard reflection mirror and the tested grating; the other is overlapping of diffracted spectra, which influence testing accuracy of diffraction efficiency. In this paper, a new measuring method of diffraction efficiency based on Fourier spectral technology is presented. The mathematical model of diffraction efficiency is first deduced and then verified by ray tracing and Fourier optics simulation. The influences of the moving cube corner's tilt error, lateral shift error, and maximal moving distance error on the measurement accuracy are analyzed in detail. The analyses provide theoretical references for designing diffraction efficiency instruments. Compared with the traditional diffraction efficiency measurement instrument with double monochromator structure, our method not only improves the measurement accuracy of diffraction efficiency but also has the advantage of high luminous flux, high spectral resolution, multiwavelength measurement in mean time, and high wavenumber accuracy.

  13. Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method

    NASA Astrophysics Data System (ADS)

    Lee, Usik; Kim, Daehwan; Park, Ilwook

    2013-03-01

    The health of thin laminated composite beams is often monitored using the ultrasonic guided waves excited by wafer-type piezoelectric transducers (PZTs). Thus, for the smart composite beams which consist of a laminated composite base beam and PZT layers, it is very important to develop a very reliable mathematical model and to use a very accurate computational method to predict accurate dynamic characteristics at very high ultrasonic frequency. In this paper, the axial-bending-shear-lateral contraction coupled differential equations of motion are derived first by the Hamilton's principle with Lagrange multipliers. The smart composite beam is represented by a Timoshenko beam model by adopting the first-order shear deformation theory (FSDT) for the laminated composite base beam. The axial deformation of smart composite beam is improved by taking into account the effects of lateral contraction by adopting the concept of Mindlin-Herrmann rod theory. The spectral element model is then formulated by the variation approach from coupled differential equations of motion transformed into the frequency domain via the discrete Fourier transform. The high accuracy of the present spectral element model is verified by comparing with other solution methods: the finite element model developed in this paper and the commercial FEA package ANSYS. Finally the dynamics and wave characteristics of some example smart composite beams are investigated through the numerical studies.

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

    PubMed

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

    2016-08-19

    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.

  15. Spectral and structural studies of the anti-cancer drug Flutamide by density functional theoretical method.

    PubMed

    Mariappan, G; Sundaraganesan, N

    2014-01-03

    A comprehensive screening of the more recent DFT theoretical approach to structural analysis is presented in this section of theoretical structural analysis. The chemical name of 2-methyl-N-[4-nitro-3-(trifluoromethyl)phenyl]-propanamide is usually called as Flutamide (In the present study it is abbreviated as FLT) and is an important and efficacious drug in the treatment of anti-cancer resistant. The molecular geometry, vibrational spectra, electronic and NMR spectral interpretation of Flutamide have been studied with the aid of density functional theory method (DFT). The vibrational assignments of the normal modes were performed on the basis of the PED calculations using the VEDA 4 program. Comparison of computational results with X-ray diffraction results of Flutamide allowed the evaluation of structure predictions and confirmed B3LYP/6-31G(d,p) as accurate for structure determination. Application of scaling factors for IR and Raman frequency predictions showed good agreement with experimental values. This is supported the assignment of the major contributors of the vibration modes of the title compound. Stability of the molecule arising from hyperconjugative interactions leading to its bioactivity, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. NMR chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. The comparison of measured FTIR, FT-Raman, and UV-Visible data to calculated values allowed assignment of major spectral features of the title molecule. Besides, Frontier molecular orbital analyze was also investigated using theoretical calculations.

  16. Spectral and structural studies of the anti-cancer drug Flutamide by density functional theoretical method

    NASA Astrophysics Data System (ADS)

    Mariappan, G.; Sundaraganesan, N.

    2014-01-01

    A comprehensive screening of the more recent DFT theoretical approach to structural analysis is presented in this section of theoretical structural analysis. The chemical name of 2-methyl-N-[4-nitro-3-(trifluoromethyl)phenyl]-propanamide is usually called as Flutamide (In the present study it is abbreviated as FLT) and is an important and efficacious drug in the treatment of anti-cancer resistant. The molecular geometry, vibrational spectra, electronic and NMR spectral interpretation of Flutamide have been studied with the aid of density functional theory method (DFT). The vibrational assignments of the normal modes were performed on the basis of the PED calculations using the VEDA 4 program. Comparison of computational results with X-ray diffraction results of Flutamide allowed the evaluation of structure predictions and confirmed B3LYP/6-31G(d,p) as accurate for structure determination. Application of scaling factors for IR and Raman frequency predictions showed good agreement with experimental values. This is supported the assignment of the major contributors of the vibration modes of the title compound. Stability of the molecule arising from hyperconjugative interactions leading to its bioactivity, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. NMR chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. The comparison of measured FTIR, FT-Raman, and UV-Visible data to calculated values allowed assignment of major spectral features of the title molecule. Besides, Frontier molecular orbital analyze was also investigated using theoretical calculations.

  17. Spectral analysis methods for the robust measurement of the flexural rigidity of biopolymers.

    PubMed

    Valdman, David; Atzberger, Paul J; Yu, Dezhi; Kuei, Steve; Valentine, Megan T

    2012-03-07

    The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules.

  18. Imaging the slab beneath central Chile using the Spectral Elements Method and adjoint techniques

    NASA Astrophysics Data System (ADS)

    Mercerat, E. D.; Nolet, G.; Marot, M.; Deshayes, P.; Monfret, T.

    2010-12-01

    This work focuses on imaging the subducting slab beneath Central Chile using novel inversion techniques based on the adjoint method and accurate wave propagation simulations using the Spectral Elements Method. The study area comprises the flat slab portion of the Nazca plate between 29 S and 34 S subducting beneath South America. We will use a database of regional seismicity consisting of both crustal and deep slab earthquakes with magnitude 3 < Mw < 6 recorded by different temporary and permanent seismological networks. Our main goal is to determine both the kinematics and the geometry of the subducting slab in order to help the geodynamical interpretation of such particular active margin. The Spectral Elements Method (SPECFEM3D code) is used to generate the synthetic seismograms and it will be applied for the iterative minimization based on adjoint techniques. The numerical mesh is 600 km x 600 km in horizontal coordinates and 220 km depth. As a first step, we are faced to well-known issues concerning mesh generation (resolution, quality, absorbing boundary conditions). In particular, we must evaluate the influence of free surface topography, as well as the MOHO and other geological interfaces in the synthetic seismograms. The initial velocity model from a previous travel-time tomography study, is linearly interpolated to the Gauss-Lobatto-Legendre grid. The comparison between the first forward simulations (up to 4 seconds minimum period) validate the initial velocity model of the study area, although many features not reproduced by the initial model have already been identified. Next step will concentrate in the comparison between finite-frequency kernels calculated by travel-time methods with ones based on adjoint methods, in order to highlight advantages and disadvantages in terms of resolution, accuracy, but also computational cost.

  19. Novel selective TOCSY method enables NMR spectral elucidation of metabolomic mixtures

    NASA Astrophysics Data System (ADS)

    MacKinnon, Neil; While, Peter T.; Korvink, Jan G.

    2016-11-01

    Complex mixture analysis is routinely encountered in NMR-based investigations. With the aim of component identification, spectral complexity may be addressed chromatographically or spectroscopically, the latter being favored to reduce sample handling requirements. An attractive experiment is selective total correlation spectroscopy (sel-TOCSY), which is capable of providing tremendous spectral simplification and thereby enhancing assignment capability. Unfortunately, isolating a well resolved resonance is increasingly difficult as the complexity of the mixture increases and the assumption of single spin system excitation is no longer robust. We present TOCSY optimized mixture elucidation (TOOMIXED), a technique capable of performing spectral assignment particularly in the case where the assumption of single spin system excitation is relaxed. Key to the technique is the collection of a series of 1D sel-TOCSY experiments as a function of the isotropic mixing time (τm), resulting in a series of resonance intensities indicative of the underlying molecular structure. By comparing these τm -dependent intensity patterns with a library of pre-determined component spectra, one is able to regain assignment capability. After consideration of the technique's robustness, we tested TOOMIXED firstly on a model mixture. As a benchmark we were able to assign a molecule with high confidence in the case of selectively exciting an isolated resonance. Assignment confidence was not compromised when performing TOOMIXED on a resonance known to contain multiple overlapping signals, and in the worst case the method suggested a follow-up sel-TOCSY experiment to confirm an ambiguous assignment. TOOMIXED was then demonstrated on two realistic samples (whisky and urine), where under our conditions an approximate limit of detection of 0.6 mM was determined. Taking into account literature reports for the sel-TOCSY limit of detection, the technique should reach on the order of 10 μ M

  20. Compound faults detection in gearbox via meshing resonance and spectral kurtosis methods

    NASA Astrophysics Data System (ADS)

    Wang, Tianyang; Chu, Fulei; Han, Qinkai; Kong, Yun

    2017-03-01

    Kurtosis-based impulsive component identification is one of the most effective algorithms in detecting localized faults in both gearboxes and rolling bearings. However, if localized faults exist in both gear tooth and rolling bearing simultaneously it is difficult to tell the differences between the two types of defects. As such, this study proposes a new method to solve the problem by using the meshing resonance and spectral kurtosis (SK) algorithms together. In specific, the raw signal is first decomposed into different frequency bands and levels, and then the corresponding Kurtogram and MRgram are calculated via the fault SK analysis and the meshing index. Furthermore, the resonance frequency bands induced by localized faults of the gear tooth and rolling bearing are separately identified by comparing the Kurtogram and the MRgram. Finally, the compound faults are respectively detected using envelope analysis. The effectiveness of the proposed method has been validated via both simulated and experimental gearboxes vibration signals with compound faults.

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

    SciTech Connect

    Tamarchenko, T.

    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.

  2. A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system

    NASA Astrophysics Data System (ADS)

    Manzini, G.; Delzanno, G. L.; Vencels, J.; Markidis, S.

    2016-07-01

    We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov-Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank-Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton-Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre-Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.

  3. A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

    SciTech Connect

    Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; Markidis, Stefano

    2016-04-22

    In this study, we present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.

  4. A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

    DOE PAGES

    Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

    2016-04-22

    In this study, we present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iterativelymore » solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

  5. Spectral modeling of Ceres VIR data from Dawn: Method and Result

    NASA Astrophysics Data System (ADS)

    Raponi, Andrea; De Sanctis, M. C.; Ciarniello, M.; Carrozzo, F. G.; Ammannito, E.; Capaccioni, F.; Capria, M. T.; Frigeri, A.; Fonte, S.; Giardino, M.; Longobardo, A.; Magni, G.; Marchi, S.; Palomba, E.; Pieters, C. M.; Tosi, F.; Turrini, D.; Zambon, F.; Raymond, C. A.; Russell, C. T.

    2015-11-01

    The Dawn spacecraft [1] is at Ceres, the closest of the IAU-defined dwarf planets to the Sun. This work focuses on the interpretation of Ceres’ surface composition based on the data from the VIR instrument [2] onboard Dawn. The Visible InfraRed (VIR) mapping spectrometer combines high spectral and spatial resolution in the VIS (0.25-1mm) and IR (1-5mm) spectral ranges. VIR will provide a very good coverage of the surface during its orbital mission at Ceres.In order to model the measured spectra, we have utilized Hapke's radiative transfer model [3], which allows estimation of the mineral composition, the relative abundances of the spectral end-members, and the grain size. Optical constants of the spectral end-members are approximated by applying the methodology described in [4] to IR spectra reflectance obtained from the RELAB database.The observed spectra of Ceres surface are affected by a thermal emission component that prevents direct comparison with laboratory data at longer wavelengths. Thus to model the whole wavelength range measured by VIR, the thermal emission is modeled together with the reflectance. Calibrated spectra are first cleaned by removing artefacts. A best fit is obtained with a least square optimization algorithm. For further details on the method, see reference [5].The range 2.5 - 2.9 μm is severely hindered by Earth's atmosphere, but it contains a strong absorption band that dominates the IR Ceres’ spectrum. Thanks to the VIR instrument we can obtain a compositional model for the whole IR range [6]. We used several different combinations of materials hypothesized to be representative of the Ceres’ surface including phyllosilicates, ices, carbonaceous chondrites and salts. The results will be discussed.Acknowledgements This work is supported by the Italian Space Agencies and NASA. Enabling contributions from the Dawn Instrument, Operations, and Science Teams are gratefully acknowledged.Reference[1] Russell et al., Space Sci. Rev., 163

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

    NASA Astrophysics Data System (ADS)

    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

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

    PubMed

    Novosad, Philip; Reader, Andrew J

    2016-06-21

    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 [(18)F]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

  8. Post-earthquake relaxation using a spectral element method: 2.5-D case

    USGS Publications Warehouse

    Pollitz, Fred

    2014-01-01

    The computation of quasi-static deformation for axisymmetric viscoelastic structures on a gravitating spherical earth is addressed using the spectral element method (SEM). A 2-D spectral element domain is defined with respect to spherical coordinates of radius and angular distance from a pole of symmetry, and 3-D viscoelastic structure is assumed to be azimuthally symmetric with respect to this pole. A point dislocation source that is periodic in azimuth is implemented with a truncated sequence of azimuthal order numbers. Viscoelasticity is limited to linear rheologies and is implemented with the correspondence principle in the Laplace transform domain. This leads to a series of decoupled 2-D problems which are solved with the SEM. Inverse Laplace transform of the independent 2-D solutions leads to the time-domain solution of the 3-D equations of quasi-static equilibrium imposed on a 2-D structure. The numerical procedure is verified through comparison with analytic solutions for finite faults embedded in a laterally homogeneous viscoelastic structure. This methodology is applicable to situations where the predominant structure varies in one horizontal direction, such as a structural contrast across (or parallel to) a long strike-slip fault.

  9. Post-earthquake relaxation using a spectral element method: 2.5-D case

    NASA Astrophysics Data System (ADS)

    Pollitz, F. F.

    2014-07-01

    The computation of quasi-static deformation for axisymmetric viscoelastic structures on a gravitating spherical earth is addressed using the spectral element method (SEM). A 2-D spectral element domain is defined with respect to spherical coordinates of radius and angular distance from a pole of symmetry, and 3-D viscoelastic structure is assumed to be azimuthally symmetric with respect to this pole. A point dislocation source that is periodic in azimuth is implemented with a truncated sequence of azimuthal order numbers. Viscoelasticity is limited to linear rheologies and is implemented with the correspondence principle in the Laplace transform domain. This leads to a series of decoupled 2-D problems which are solved with the SEM. Inverse Laplace transform of the independent 2-D solutions leads to the time-domain solution of the 3-D equations of quasi-static equilibrium imposed on a 2-D structure. The numerical procedure is verified through comparison with analytic solutions for finite faults embedded in a laterally homogeneous viscoelastic structure. This methodology is applicable to situations where the predominant structure varies in one horizontal direction, such as a structural contrast across (or parallel to) a long strike-slip fault.

  10. A multi-similarity spectral clustering method for community detection in dynamic networks.

    PubMed

    Qin, Xuanmei; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun; Yuan, Ning

    2016-08-16

    Community structure is one of the fundamental characteristics of complex networks. Many methods have been proposed for community detection. However, most of these methods are designed for static networks and are not suitable for dynamic networks that evolve over time. Recently, the evolutionary clustering framework was proposed for clustering dynamic data, and it can also be used for community detection in dynamic networks. In this paper, a multi-similarity spectral (MSSC) method is proposed as an improvement to the former evolutionary clustering method. To detect the community structure in dynamic networks, our method considers the different similarity metrics of networks. First, multiple similarity matrices are constructed for each snapshot of dynamic networks. Then, a dynamic co-training algorithm is proposed by bootstrapping the clustering of different similarity measures. Compared with a number of baseline models, the experimental results show that the proposed MSSC method has better performance on some widely used synthetic and real-world datasets with ground-truth community structure that change over time.

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

    NASA Technical Reports Server (NTRS)

    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.

  12. A multi-similarity spectral clustering method for community detection in dynamic networks

    PubMed Central

    Qin, Xuanmei; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun; Yuan, Ning

    2016-01-01

    Community structure is one of the fundamental characteristics of complex networks. Many methods have been proposed for community detection. However, most of these methods are designed for static networks and are not suitable for dynamic networks that evolve over time. Recently, the evolutionary clustering framework was proposed for clustering dynamic data, and it can also be used for community detection in dynamic networks. In this paper, a multi-similarity spectral (MSSC) method is proposed as an improvement to the former evolutionary clustering method. To detect the community structure in dynamic networks, our method considers the different similarity metrics of networks. First, multiple similarity matrices are constructed for each snapshot of dynamic networks. Then, a dynamic co-training algorithm is proposed by bootstrapping the clustering of different similarity measures. Compared with a number of baseline models, the experimental results show that the proposed MSSC method has better performance on some widely used synthetic and real-world datasets with ground-truth community structure that change over time. PMID:27528179

  13. Comparison of the STA/LTA and power spectral density methods for microseismic event detection

    NASA Astrophysics Data System (ADS)

    Vaezi, Yoones; Van der Baan, Mirko

    2015-12-01

    Robust event detection and picking is a prerequisite for reliable (micro-) seismic interpretations. Detection of weak events is a common challenge among various available event detection algorithms. In this paper we compare the performance of two event detection methods, the short-term average/long-term average (STA/LTA) method, which is the most commonly used technique in industry, and a newly introduced method that is based on the power spectral density (PSD) measurements. We have applied both techniques to a 1-hr long segment of the vertical component of some raw continuous data recorded at a borehole geophone in a hydraulic fracturing experiment. The PSD technique outperforms the STA/LTA technique by detecting a higher number of weak events while keeping the number of false alarms at a reasonable level. The time-frequency representations obtained through the PSD method can also help define a more suitable bandpass filter which is usually required for the STA/LTA method. The method offers thus much promise for automated event detection in industrial, local, regional and global seismological data sets.

  14. A multi-similarity spectral clustering method for community detection in dynamic networks

    NASA Astrophysics Data System (ADS)

    Qin, Xuanmei; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun; Yuan, Ning

    2016-08-01

    Community structure is one of the fundamental characteristics of complex networks. Many methods have been proposed for community detection. However, most of these methods are designed for static networks and are not suitable for dynamic networks that evolve over time. Recently, the evolutionary clustering framework was proposed for clustering dynamic data, and it can also be used for community detection in dynamic networks. In this paper, a multi-similarity spectral (MSSC) method is proposed as an improvement to the former evolutionary clustering method. To detect the community structure in dynamic networks, our method considers the different similarity metrics of networks. First, multiple similarity matrices are constructed for each snapshot of dynamic networks. Then, a dynamic co-training algorithm is proposed by bootstrapping the clustering of different similarity measures. Compared with a number of baseline models, the experimental results show that the proposed MSSC method has better performance on some widely used synthetic and real-world datasets with ground-truth community structure that change over time.

  15. A method for atmospheric correction based on the MERIS spectral and spatial variability

    NASA Astrophysics Data System (ADS)

    Béal, D.; Baret, F.; Bacour, C.; Gu, X.; Regner, P.

    Atmospheric correction is necessary to estimate the surface reflectance required within biophysical algorithms used to estimate canopy characteristics. Aerosol characterization is obviously one of the main problem in atmospheric correction because aerosol may vary rapidly with time and space. The objective of this study is to develop an autonomous aerosol correction method exploiting the information content in MERIS images. The spectral variation of the radiance signal, when enough sampled by the sensor, allows decoupling aerosol effects from that of the surface because of the very different spectral features exhibited. We thus propose to use (i) 13 over the 15 MERIS bands, (ii) the geometry of the scene and (iii) the atmospheric pressure and ozone and water vapour contents to estimate the aerosol optical thickness (AOT) assuming only continental aerosol type in this prototype algorithm. For this purpose, several dedicated neural networks were trained to retrieve aerosol AOT from the top of atmosphere signal contained in MERIS level 1B products. The training database was generated with radiative transfer model simulations, SMAC coupled to SAIL and PROSPECT. Performances demonstrate the pertinence of the method for the median of 5 neural networks, with a 0.047 Root Mean Square Error associated to the estimation of the AOT at 550nm. This induces a RMSE on the estimated top of canopy reflectance better than 0.005. In addition, assuming that the aerosol vary typically over scales of few tenths of kilometers, while the surface varies at shorter distances, allows to smooth out the AOT values for all pixels of an image using a moving window. The method was applied to actual MERIS data (more than 50 scenes) over AERONET sites for its validation with a 0.07 Root Mean Square Error associated to the estimation of the AOT. Conclusions are drawn on possible improvements of the database and of the neural network's architecture like the number of entries and the inclusion of

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

    NASA Technical Reports Server (NTRS)

    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.

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

    NASA Astrophysics Data System (ADS)

    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.

  18. CONTROL OF LASER RADIATION PARAMETERS: New method to control the shape of spectral characteristics of Bragg gratings in electrooptical materials

    NASA Astrophysics Data System (ADS)

    Shamrai, A. V.; Kozlov, A. S.; Il'ichev, I. V.; Petrov, Mikhail P.

    2005-08-01

    A new method is proposed to control the shape of spectral characteristics of Bragg gratings, which is based on the introduction of electrically controlled shifts of the average refractive index. The shape of the spectral characteristics of Bragg gratings with a complex step structure of the spatial distribution of the average refractive index is calculated. The operative electric control of their shape in a channel optical LiNbO3 crystal waveguide is experimentally demonstrated.

  19. Use of a Remote Sensing Method to Estimate the Influence of Anthropogenic Factors on the Spectral Reflectance of Plant Species

    NASA Astrophysics Data System (ADS)

    Krezhova, Dora D.; Yanev, Tony K.

    2007-04-01

    Results from a remote sensing study of the influence of stress factors on the leaf spectral reflectance of wheat and tomato plants contaminated by viruses and pea plants treated with herbicides are presented and discussed. The changes arising in the spectral reflectance characteristics of control and treated plants are estimated through statistical methods as well as through derivative analysis to determine specific reflectance features in the red edge region.

  20. A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers

    NASA Astrophysics Data System (ADS)

    van Rees, Wim M.; Leonard, Anthony; Pullin, D. I.; Koumoutsakos, Petros

    2011-04-01

    We present a validation study for the hybrid particle-mesh vortex method against a pseudo-spectral method for the Taylor-Green vortex at ReΓ = 1600 as well as in the collision of two antiparallel vortex tubes at ReΓ = 10,000. In this study we present diagnostics such as energy spectra and enstrophy as computed by both methods as well as point-wise comparisons of the vorticity field. Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases. For the Taylor-Green vortex, the vorticity contours computed by both methods around the time of the energy dissipation peak overlap. The energy spectrum shows that only the smallest length scales in the flow are not captured by the vortex method. In the second flow case, where we compute the collision of two anti-parallel vortex tubes at Reynolds number 10,000, the vortex method results and the pseudo-spectral method results are in very good agreement up to and including the first reconnection of the tubes. The maximum error in the effective viscosity is about 2.5% for the vortex method and about 1% for the pseudo-spectral method. At later times the flows computed with the different methods show the same qualitative features, but the quantitative agreement on vortical structures is lost.

  1. Shifted Jacobi spectral collocation method for solving two-sided fractional water wave models

    NASA Astrophysics Data System (ADS)

    Abdelkawy, M. A.; Alqahtani, Rubayyi T.

    2017-01-01

    This paper presents the spectral collocation technique to solve the two-sided fractional water wave models (TSF-WWMs). The shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods are developed to approximate the TSF-WWMs. The main idea in the novel algorithm is to reduce the TSF-WWM to a systems of algebraic equations. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is a simple and very accurate numerical scheme for solving TSF-WWMs.

  2. SPECTRAL REFLECTANCE METHOD TO MEASURE ACID DEPOSITION EFFECTS ON BUILDING STONE.

    USGS Publications Warehouse

    Kingston, Marguerite J.; Ager, Cathy M.

    1985-01-01

    As part of the National Acid Precipitation Assessment Program (NAPAP), the U. S. Geological Survey is cooperating with other agencies to test the effects of acid deposition on building stone. A 10-year test-site study has been organized for the purpose of correlating possible stone deterioration with environmental factors. In Summer 1984, slabs of building stone, 3 by 2 by 2 inches, were exposed to the atmosphere at four test sites where the pH of precipitation and other meteorological variables are continuously monitored. This paper examines the development of one experimental technique used in this study - the application of diffuse spectral reflectance methods for laboratory and in situ measurement of those properties of stone which may be affected by acid deposition.

  3. A new resonance Rayleigh scattering spectral method for determination of O3 with victoria blue B

    NASA Astrophysics Data System (ADS)

    Wen, Guiqing; Yang, Duo; Jiang, Zhiliang

    2014-01-01

    Ozone (O3) could be absorbed by boric acid-potassium iodide (BKI) absorbent solution to produce tri-iodine ion (I3-) that react with victoria blue B (VBB) to form the associated particle (VBB-I3)n and exhibited a strong resonance Rayleigh scattering (RRS) peak at 722 nm. Under the chosen conditions, the RRS peak intensity was linear with O3 concentration in the range of 0.2-50 μmol/L, with a linear regression equation of ΔI722 = 17.9c - 45.4 and detection limit of 0.057 μmol/L. Accordingly, a simple, rapid and sensitive RRS spectral method was set up for determination of trace O3 in air, with satisfactory results.

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

    NASA Astrophysics Data System (ADS)

    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.

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

    SciTech Connect

    Keating, Kristina; Slater, Lee; Ntarlagiannis, Dimitris; Williams, Kenneth H.

    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

  6. On Bernstein type inequalities and a weighted Chebyshev approximation problem on ellipses

    NASA Technical Reports Server (NTRS)

    Freund, Roland

    1989-01-01

    A classical inequality due to Bernstein which estimates the norm of polynomials on any given ellipse in terms of their norm on any smaller ellipse with the same foci is examined. For the uniform and a certain weighted uniform norm, and for the case that the two ellipses are not too close, sharp estimates of this type were derived and the corresponding extremal polynomials were determined. These Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Some new results were also presented for a weighted approximation problem of this type.

  7. Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map

    PubMed Central

    2014-01-01

    We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10113 key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970

  8. A nodal triangle-based spectral element method for the shallow water equations on the sphere

    NASA Astrophysics Data System (ADS)

    Giraldo, F. X.; Warburton, T.

    2005-07-01

    A nodal triangle-based spectral element (SE) method for the shallow water equations on the sphere is presented. The original SE method uses quadrilateral elements and high-order nodal Lagrange polynomials, constructed from a tensor-product of the Legendre-Gauss-Lobatto points. In this work, we construct the high-order Lagrange polynomials directly on the triangle using nodal sets obtained from the electrostatics principle [J.S. Hesthaven, From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex, SIAM Journal on Numerical Analysis 35 (1998) 655-676] and Fekete points [M.A. Taylor, B.A. Wingate, R.E. Vincent, An algorithm for computing Fekete points in the triangle, SIAM Journal on Numerical Analysis 38 (2000) 1707-1720]. These points have good approximation properties and far better Lebesgue constants than any other nodal set derived for the triangle. By employing triangular elements as the basic building-blocks of the SE method and the Cartesian coordinate form of the equations, we can use any grid imaginable including adaptive unstructured grids. Results for six test cases are presented to confirm the accuracy and stability of the method. The results show that the triangle-based SE method yields the expected exponential convergence and that it can be more accurate than the quadrilateral-based SE method even while using 30-60% fewer grid points especially when adaptive grids are used to align the grid with the flow direction. However, at the moment, the quadrilateral-based SE method is twice as fast as the triangle-based SE method because the latter does not yield a diagonal mass matrix.

  9. Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

    NASA Technical Reports Server (NTRS)

    Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.

    1997-01-01

    A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

  10. Investigations of spectral resolution and angle dependency in a 2-D tracking Doppler method.

    PubMed

    Fredriksen, Tonje D; Avdal, Jorgen; Ekroll, Ingvild K; Dahl, Torbjorn; Lovstakken, Lasse; Torp, Hans

    2014-07-01

    An important source of error in velocity measurements from conventional pulsed wave (PW) Doppler is the angle used for velocity calibration. Because there are great uncertainties and interobserver variability in the methods used for Doppler angle correction in the clinic today, it is desirable to develop new and more robust methods. In this work, we have investigated how a previously presented method, 2-D tracking Doppler, depends on the tracking angle. A signal model was further developed to include tracking along any angle, providing velocity spectra which showed good agreement with both experimental data and simulations. The full-width at half-maximum (FWHM) bandwidth and the peak value of predicted power spectra were calculated for varying tracking angles. It was shown that the spectra have lowest bandwidth and maximum power when the tracking angle is equal to the beam-to-flow angle. This may facilitate new techniques for velocity calibration, e.g., by manually adjusting the tracking angle, while observing the effect on the spectral display. An in vitro study was performed in which the Doppler angles were predicted by the minimum FWHM and the maximum power of the 2-D tracking Doppler spectra for 3 different flow angles. The estimated Doppler angles had an overall error of 0.24° ± 0.75° when using the minimum FWHM. With an in vivo example, it was demonstrated that the 2-D tracking Doppler method is suited for measurements in a patient with carotid stenosis.

  11. The Hybrid Search: A Mass Spectral Library Search Method for Discovery of Modifications in Proteomics.

    PubMed

    Burke, Meghan Catherine; Mirokhin, Yuri A; Tchekhovskoi, Dmitrii V; Markey, Sanford P; Heidbrink Thompson, Jenny L; Larkin, Christopher; Stein, Stephen E

    2017-04-03

    We present a mass spectral library based method to identify tandem mass spectra of peptides that contain unanticipated modifications and amino acid variants. We describe this as a 'hybrid' method because it combines matching both ion m/z and mass losses. The losses are differences in mass between an ion peak and its precursor mass. This difference, termed DeltaMass, is used to shift the product ions in the library spectrum that contain the modification, thereby allowing library product ions that contain the unexpected modification to match the query spectrum. Clustered unidentified spectra from the Clinical Proteomic Tumor Analysis Consortium (CPTAC) and Chinese hamster ovary cells were used to evaluate this method. Results demonstrate the ability of the hybrid method to identify unanticipated modifications, insertions and deletions, which may include those due to an incomplete protein sequence database or to search settings that exclude the correct identification, in high resolution tandem mass spectra without regard of their precursor mass. This has been made possible by indexing of m/z values of each fragment ion and their difference in mass from their precursor ion.

  12. Seismic Attenuation in the Rupture Zone of the 2010 Maule, Chile, Earthquake: Two Spectral Ratio Methods

    NASA Astrophysics Data System (ADS)

    Torpey, M.; Russo, R. M.; Beck, S. L.; Meltzer, A.; Roecker, S. W.

    2013-12-01

    We used data from the IRIS CHAMP temporary seismic network, deployed for 6 months following the February 2010 Mw 8.8 Maule earthquake, to estimate differential attenuation of P and S waves in the Maule rupture zone, 33°S - 38°S. We used two complementary spectral ratio methods both of which assume identical source-to-station travel paths which allowed us to neglect the source-time function and instrument response of each P-S phase pair. The first method iteratively determines 400 individual Qs values and uncertainties for each phase pair and the second method stacks the spectra of each of the 400 measurements to yield a composite spectrum from which we derive a single Qs. Measurements are deemed acceptable when the two methods agree. We examined 235 local events yielding a total of 1083 Qs measurements.The majority of ray paths evaluated show low Qs values (100-400) with an average Qs over the entire rupture zone of 350 and an average standard deviation of +/- 569. We are evaluating spatial and temporal variability in Qs; however, from our preliminary measurements we do not observe a temporal variability in Qs throughout the rupture zone nor do we recognize any consistent spatial pattern in the measurements. Tomographic inversion of the Qs measurements made along ray paths spanning the upper mantle wedge and South American crust above the Maule rupture region will allow us to interpret the observed Qs variability.

  13. Propagation of 3D nonlinear waves over complex bathymetry using a High-Order Spectral method

    NASA Astrophysics Data System (ADS)

    Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

    2016-04-01

    Scattering of regular and irregular surface gravity waves propagating over a region of arbitrary three-dimensional varying bathymetry is considered here. The three-dimensional High-Order Spectral method (HOS) with an extension to account for a variable bathymetry is used. The efficiency of the model has been proved to be conserved even with this extension. The method is first applied to a bathymetry consisting of an elliptical lens, as used in the Vincent and Briggs (1989) experiment. Incident waves passing across the lens are transformed and a strong convergence region is observed after the elliptical mound. The wave amplification depends on the incident wave. Numerical results for regular and irregular waves are analysed and compared with other methods and experimental data demonstrating the efficiency and practical applicability of the present approach. Then the method is used to model waves propagating over a real bathymetry: the canyons of Scripps/La Jolla in California. The implementation of this complex bathymetry in the model is presented, as well as the first results achieved. They will be compared to the ones obtained with another numerical model.

  14. Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel; Wang, Z. J.

    2004-01-01

    A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of

  15. High-Order Moving Overlapping Grid Methodology in a Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Merrill, Brandon E.

    A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies

  16. Comparison between two methods for forward calculation of ambient noise H/V spectral ratios

    NASA Astrophysics Data System (ADS)

    Garcia-Jerez, A.; Luzón, F.; Sanchez-Sesma, F. J.; Santoyo, M. A.; Albarello, D.; Lunedei, E.; Campillo, M.; Iturrarán-Viveros, U.

    2011-12-01

    The analysis of horizontal-to-vertical spectral ratios of ambient noise (NHVSR) is a valuable tool for seismic prospecting, particularly if both a dense spatial sampling and a low-cost procedure are required. Unfortunately, the computation method still lacks of a unanimously accepted theoretical basis and different approaches are currently being used for inversion of the ground structure from the measured H/V curves. Two major approaches for forward calculation of NHVSRs in a layered medium are compared in this work. The first one was developed by Arai and Tokimatsu (2004) and recently improved by Albarello and Lunedei (2011). It consists of a description of the wavefield as generated by Far Surface point Forces (FSF method). The second one is based on the work of Sánchez-Sesma et al. (2011) who consider ambient noise as a Diffuse WaveField (DWF method), taking advantage of the proportionality between its Fourier-transformed autocorrelation (power spectrum) and the imaginary part of the Green function when source and receiver are the same. In both methods, the NHVSR is written as (PH/PV)1/2, where PH and PV are the horizontal and vertical power spectra. In the FSF method these quantities are given by PV∝⊙m(1+1/2χm2α2)(ARm/kRm)2 PH∝⊙m{(1+1/2χm2α2)(ARm/kRm)2χm2+1/2α2(ALm/kLm)2} where kRm, χm and ARm are wavenumber, ellipticity and medium response of the m-th Rayleigh wave mode; kLm and ALm correspond to the m-th Love wave mode and α is the horizontal-to-vertical load ratio of the ambient noise sources. Some common factors are omitted in the expressions of PV and PH. On the other hand, the DWF method deals with the full wavefield including both surface and body waves. In order to make the comparison easier, and taking into account that surface waves are often the dominant components in wide spectral ranges, body wave contributions are neglected here. In this case, the PH and PV power spectra for the DWF method are reduced to the simple expressions: PV

  17. Specific CT 3D rendering of the treatment zone after Irreversible Electroporation (IRE) in a pig liver model: the “Chebyshev Center Concept” to define the maximum treatable tumor size

    PubMed Central

    2014-01-01

    Background Size and shape of the treatment zone after Irreversible electroporation (IRE) can be difficult to depict due to the use of multiple applicators with complex spatial configuration. Exact geometrical definition of the treatment zone, however, is mandatory for acute treatment control since incomplete tumor coverage results in limited oncological outcome. In this study, the “Chebyshev Center Concept” was introduced for CT 3d rendering to assess size and position of the maximum treatable tumor at a specific safety margin. Methods In seven pig livers, three different IRE protocols were applied to create treatment zones of different size and shape: Protocol 1 (n = 5 IREs), Protocol 2 (n = 5 IREs), and Protocol 3 (n = 5 IREs). Contrast-enhanced CT was used to assess the treatment zones. Technique A consisted of a semi-automated software prototype for CT 3d rendering with the “Chebyshev Center Concept” implemented (the “Chebyshev Center” is the center of the largest inscribed sphere within the treatment zone) with automated definition of parameters for size, shape and position. Technique B consisted of standard CT 3d analysis with manual definition of the same parameters but position. Results For Protocol 1 and 2, short diameter of the treatment zone and diameter of the largest inscribed sphere within the treatment zone were not significantly different between Technique A and B. For Protocol 3, short diameter of the treatment zone and diameter of the largest inscribed sphere within the treatment zone were significantly smaller for Technique A compared with Technique B (41.1 ± 13.1 mm versus 53.8 ± 1.1 mm and 39.0 ± 8.4 mm versus 53.8 ± 1.1 mm; p < 0.05 and p < 0.01). For Protocol 1, 2 and 3, sphericity of the treatment zone was significantly larger for Technique A compared with B. Conclusions Regarding size and shape of the treatment zone after IRE, CT 3d rendering with the “Chebyshev Center Concept” implemented provides

  18. Verification of a Non-Hydrostatic Dynamical Core Using Horizontally Spectral Element Vertically Finite Difference Method: 2D Aspects

    DTIC Science & Technology

    2014-04-01

    ranges of ′θ ∈ −1.51×10−3,2.78 ×10−3⎡⎣ ⎤⎦ from the model based on 351 the spectral element and discontinuous Galerkin method. Also Li et al. (2013...2008: A study of spectral element and discontinuous Galerkin 457 methods for the Navier-Stokes equations in nonhydrostatic mesoscale 458 atmospheric...of Computational Physics, 117, 35-46. 467 468 Kelly, J. F. and F. X. Giraldo, 2012: Continuous and discontinuous Galerkin methods for a 469

  19. Numerical study of electromagnetic wave propagation in twisted birefringent layers by the spectral moments method

    NASA Astrophysics Data System (ADS)

    Lakhliai, Z.; Chenouni, D.; Benoit, C.; Poussigue, G.; Brunet, M.; Quentel, S.; Sakout, A.

    1996-11-01

    This paper presents a first attempt at using the spectral moments method (SMM) to solve Maxwell's equations in twisted anisotropic media in the presence of defects. This numerical method, previously developed in condensed matter physics, allows computation of Green functions for very large systems. The dynamic matrix of the discretized system is built from the medium parameters. Green functions, calculated for a given source, representing a point source at infinity and given receiver, are developed as a continued fraction whose coefficients are related to the moments and directly computed from the dynamic matrix. In this study we compute the light transmitted through thin surface-stabilized ferroelectric liquid crystal cells with a chevron structure and a twisted director distribution. The efficiency and accuracy of the method are analysed by comparing the results obtained by SMM with the analytical solution obtained using the Jones matrix formalism. Finally, we apply SMM to compute the transmitted light with different director configurations. We show, by comparisons with experimental data, that the simplest director configuration is certainly the most probable.

  20. Geothermal reservoir monitoring based upon spectral-element and adjoint methods

    NASA Astrophysics Data System (ADS)

    Morency, C.; Templeton, D. C.; Harris, D.; Mellors, R. J.

    2011-12-01

    Induced seismicity associated with CO2 sequestration, enhanced oil recovery, and enhanced geothermal systems is triggered by fracturing during fluid injection. These events range from magnitude -1 (microseismicity) up to 3.5, for induced seismicity on pre-existing faults. In our approach, we are using seismic data collected at the Salton Sea geothermal field, to improve the current structural model (SCEC CVM4.0 including a 10m resolution topography) and to invert for the moment tensor and source location of the microseismic events. The key here is to refine the velocity model to then precisely invert for the location and mechanism (tensile or shear) of fracture openings. This information is crucial for geothermal reservoir assessment, especially in an unconventional setting where hydrofracturing is used to enhance productivity. The location of pre-existing and formed fractures as well as their type of openings are important elements for strategic decisions. Numerical simulations are performed using a spectral-element method, which contrary to finite-element methods (FEM), uses high degree Lagrange polynomials, allowing the technique to not only handle complex geometries, like the FEM, but also to retain the strength of exponential convergence and accuracy due to the use of high degree polynomials. Finite-frequency sensitivity kernels, used in the non-linear iterative inversions, are calculated based on an adjoint method.

  1. Phase Difference Correction Method for Phase and Frequency in Spectral Analysis

    NASA Astrophysics Data System (ADS)

    Kang, D.; Ming, X.; Xiaofei, Z.

    2000-09-01

    A new method, phase difference corrections method is developed to correct the frequency and phase of spectrum peak. The continuous time-domain signal is separated into two segments and fast Fourier translation (FFT) is carried out for them, respectively. The frequency and phase are corrected using the phase difference of corresponding discrete spectral lines. Furthermore, the amplitude can also be rectified using the formula of window function spectrum. This method, with good adaptability, high speed and accuracy, is theoretically simple. It can resolve the frequency by means of phase difference directly without the formula of window function. Simulation shows that the single-component frequency, phase and amplitude of theoretical signal can be corrected satisfactorily, with frequency error less than 0.0002 frequency resolution, phase 0.1° and amplitude 0.0002. If the signal involves noise, the mean corrected errors are less than 0.001 frequency resolution, 1° for phase, and 0.01 for amplitude, respectively, and the maximum corrected errors of one segment are less than 0.01 frequency resolution, 1° and 0.03, respectively.

  2. SEDEBLEND: a new method for deblending spectral energy distributions in confused imaging

    NASA Astrophysics Data System (ADS)

    MacKenzie, Todd P.; Scott, Douglas; Swinbank, Mark

    2016-11-01

    For high-redshift submillimetre or millimetre sources detected with single-dish telescopes, interferometric follow-up has shown that many are multiple submillimetre galaxies blended together. Confusion-limited Herschel observations of such targets are also available, and these sample the peak of their spectral energy distribution (SED) in the far-infrared. Many methods for analysing these data have been adopted, but most follow the traditional approach of extracting fluxes before model SEDs are fit, which has the potential to erase important information on degeneracies among fitting parameters and glosses over the intricacies of confusion noise. Here, we adapt the forward-modelling method that we originally developed to disentangle a high-redshift strongly lensed galaxy group, in order to tackle this general problem in a more statistically rigorous way, by combining source deblending and SED fitting into the same procedure. We call this method `SEDeblend'. As an application, we derive constraints on far-infrared luminosities and dust temperatures for sources within the ALMA follow-up of the LABOCA Extended Chandra Deep Field South Submillimetre Survey. We find an average dust temperature for an 870-μm-selected sample of (33.9 ± 2.4) K for the full survey. When selection effects of the sample are considered, we find no evidence that the average dust temperature evolves with redshift for sources with redshifts greater than about 1.5, when compared to those with redshifts between 0.1 and 1.5.

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

    SciTech Connect

    Sidler, Rolf; Carcione, José M.; Holliger, Klaus

    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.

  4. Preliminary study on soil to rock spectral ratio method of microtremor measurement in Taipei Basin, Taiwan

    NASA Astrophysics Data System (ADS)

    Huang, Jyun Yan; Wen, Kuo Liang; Te Chen, Chun; Chang, Shun Chiang

    2014-05-01

    Taipei city is the capital of Taiwan which located in Taipei basin and covered with hundreds meter of alluvial layer that might cause serious damage during huge earthquake. Prediction of possible strong motion levels occurred in the basin then became popular. Engineers most like to use Ground Motion Prediction Equation (GMPEs) as common tool for seismic hazard calculation but GMPEs were usually debated that it can only give one prediction value (PGA, PGV, Sa etc.) rather than time history or spectrum. Seismologists tried theoretical simulation (1D, 2D, 3D method) but could only give low frequency (usually less than 1 Hz) results restricted to that the shallow structures were not clear enough. Resent years, wide frequency simulation techniques such as empirical green's function added stochastic simulation method (hybrid method) were applied to several different purposes but site effect still plays an important role that need to be considered. Traditionally soil to rock spectral ratio of shear wave (denoted as S/R) was widely applied to check basin effect for decades but the technique needs lots of permanent stations and several years to get enough records. If some site located within strong motion network but not close enough to the strong motion stations, interpolate or extrapolate results needed to be used. Wen and Huang (2012) conducted a dense microtremor measurement network in whole Taiwan and applied microtremor H/V to discuss dominant frequency with traditional transfer functions from earthquake shear wave and found good agreement between them. Furthermore, in this study, the ability of soil to rock spectral ratio of microtremor (denoted as MS/R) measurement was tested in Taipei basin. The preliminary results showed MS/R had good agreement with S/R between 0.2 to 5 Hz. And distance from soil site to reference rock site should no greater than 8 to 10 km base on degree of spectrum difference (DSPD) calculation. If the MS/R works that site effect study from this

  5. Iterative method for optimal design of flat-spectral-response arrayed waveguide gratings.

    PubMed

    Park, Shin-Woong; Park, Yohan; Yi, Yun; Kim, Hwi

    2013-10-20

    A novel iterative projection-type optimal design algorithm of arrayed waveguide gratings (AWGs) with a flat spectral response is proposed based on the Fourier optics model of AWG. The enhancement of the spectral-response flatness of the AWG is demonstrated, with an analysis on the trade-off relationship between band flatness and crosstalk.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. A 2D wavelet-based spectral finite element method for elastic wave propagation

    NASA Astrophysics Data System (ADS)

    Pahlavan, L.; Kassapoglou, C.; Suiker, A. S. J.; Gürdal, Z.

    2012-10-01

    A wavelet-based spectral finite element method (WSFEM) is presented that may be used for an accurate and efficient analysis of elastic wave propagation in two-dimensional (2D) structures. The approach is characterised by a temporal transformation of the governing equations to the wavelet domain using a wavelet-Galerkin approach, and subsequently performing the spatial discretisation in the wavelet domain with the finite element method (FEM). The final solution is obtained by transforming the nodal displacements computed in the wavelet domain back to the time domain. The method straightforwardly eliminates artificial temporal edge effects resulting from the discrete wavelet transform and allows for the modelling of structures with arbitrary geometries and boundary conditions. The accuracy and applicability of the method is demonstrated through (i) the analysis of a benchmark problem on axial and flexural waves (Lamb waves) propagating in an isotropic layer, and (ii) the study of a plate subjected to impact loading. The wave propagation response for the impact problem is compared to the result computed with standard FEM equipped with a direct time-integration scheme. The effect of anisotropy on the response is demonstrated by comparing the numerical result for an isotropic plate to that of an orthotropic plate, and to that of a plate made of two dissimilar materials, with and without a cut-out at one of the plate corners. The decoupling of the time-discretised equations in the wavelet domain makes the method inherently suitable for parallel computation, and thus an appealing candidate for efficiently studying high-frequency wave propagation in engineering structures with a large number of degrees of freedom.

  8. Spectral element method for band structures of three-dimensional anisotropic photonic crystals

    NASA Astrophysics Data System (ADS)

    Luo, Ma; Liu, Qing Huo

    2009-11-01

    A spectral element method (SEM) is introduced for accurate calculation of band structures of three-dimensional anisotropic photonic crystals. The method is based on the finite-element framework with curvilinear hexahedral elements. Gauss-Lobatto-Legendre polynomials are used to construct the basis functions. In order to suppress spurious modes, mixed-order vector basis functions are employed and the Bloch periodic boundary condition is imposed into the basis functions with tangential components at the boundary by multiplying a Bloch phase factor. The fields and coordinates in the curvilinear hexahedral elements are mapped to the reference domain by covariant mapping, which preserves the continuity of tangential components of the field. Numerical results show that the SEM has exponential convergence for both square-lattice and triangular-lattice photonic crystals. The sampling density as small as 3.4 points per wavelength can achieve accuracy as high as 99.9%. The band structures of several modified woodpile photonic crystals are calculated by using the SEM.

  9. Development and evaluation of a hydrostatic dynamical core using the spectral element/discontinuous Galerkin methods

    NASA Astrophysics Data System (ADS)

    Choi, S.-J.; Giraldo, F. X.

    2014-06-01

    In this paper, we present a dynamical core for the atmospheric primitive hydrostatic equations using a unified formulation of spectral element (SE) and discontinuous Galerkin (DG) methods in the horizontal direction with a finite difference (FD) method in the radial direction. The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points, which define the common machinery. The atmospheric primitive hydrostatic equations are solved on the cubed-sphere grid using the flux form governing equations in a three-dimensional (3-D) Cartesian space. By using Cartesian space, we can avoid the pole singularity problem due to spherical coordinates and this also allows us to use any quadrilateral-based grid naturally. In order to consider an easy way for coupling the dynamics with existing physics packages, we use a FD in the radial direction. The models are verified by conducting conventional benchmark test cases: the Rossby-Haurwitz wavenumber 4, Jablonowski-Williamson tests for balanced initial state and baroclinic instability, and Held-Suarez tests. The results from those tests demonstrate that the present dynamical core can produce numerical solutions of good quality comparable to other models.

  10. Spectral element method for band structures of three-dimensional anisotropic photonic crystals.

    PubMed

    Luo, Ma; Liu, Qing Huo

    2009-11-01

    A spectral element method (SEM) is introduced for accurate calculation of band structures of three-dimensional anisotropic photonic crystals. The method is based on the finite-element framework with curvilinear hexahedral elements. Gauss-Lobatto-Legendre polynomials are used to construct the basis functions. In order to suppress spurious modes, mixed-order vector basis functions are employed and the Bloch periodic boundary condition is imposed into the basis functions with tangential components at the boundary by multiplying a Bloch phase factor. The fields and coordinates in the curvilinear hexahedral elements are mapped to the reference domain by covariant mapping, which preserves the continuity of tangential components of the field. Numerical results show that the SEM has exponential convergence for both square-lattice and triangular-lattice photonic crystals. The sampling density as small as 3.4 points per wavelength can achieve accuracy as high as 99.9%. The band structures of several modified woodpile photonic crystals are calculated by using the SEM.

  11. Using the power spectral density method to characterise the surface topography of optical surfaces

    NASA Astrophysics Data System (ADS)

    Alcock, Simon G.; Ludbrook, Geoff D.; Owen, Tommy; Dockree, Richard

    2010-08-01

    Power Spectral Density (PSD) is an alternative method for specifying optical surfaces, and quantifies the contribution of each spatial regime to the total surface error. This approach naturally includes mid-range spatial frequency errors, which are often overlooked. The PSD method has recently been adopted by the Space and Astronomy industries, but has not yet received general acceptance within the synchrotron community. To assess the suitability for specifying synchrotron optics using PSD, Fast Fourier Transforms were performed on topography data from a range of optical surfaces of varying quality and manufacturing techniques. For each grade of optic, the entire regime ({100nm to {50mm) of surface errors was measured, with overlapping bandwidths, using a micro-interferometer and a Fizeau interferometer. From this heuristic information, root-mean square "roughness" can be predicted over any desired spatial range, thus allowing direct comparison of metrology data obtained by instruments with different spatial bandwidths. We present an efficient approach for calculating 1-D and 2-D PSDs using MATLAB algorithms, and discuss analysis considerations, including "field of view" effects and instrument calibration.

  12. Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method

    NASA Astrophysics Data System (ADS)

    Choi, S. J.; Kim, J.; Shin, S.

    2014-12-01

    In this presentation, a new non-hydrostatic (NH) dynamical core using the spectral element method (SEM) in the horizontal discretization and the finite difference method (FDM) in the vertical discretization will be presented. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, we can achieve a high level of scalability. Also by using vertical FDM, we provide an easy way for coupling the dynamics and existing physics packages. The Euler equations used here are in a flux form based on the hybrid sigma hydrostatic pressure vertical coordinate, which are similar to those used in the Weather Research and Forecasting (WRF) model. Within these Euler equations, we use a time-split third-order Runge-Kutta (RK3) for the time discretization. In order to establish robustness, firstly the NH dynamical core is verified in a simplified two dimensional (2D) slice framework by conducting widely used standard benchmark tests, and then we verify the global three dimensional (3D) dynamical core on the cubed-sphere grid with several test cases introduced by Dynamical Core Model Intercomparison Project (DCMIP).

  13. Vibration analysis of coupled conical-cylindrical-spherical shells using a Fourier spectral element method.

    PubMed

    Su, Zhu; Jin, Guoyong

    2016-11-01

    This paper presents a Fourier spectral element method (FSEM) to analyze the free vibration of conical-cylindrical-spherical shells with arbitrary boundary conditions. Cylindrical-conical and cylindrical-spherical shells as special cases are also considered. In this method, each fundamental shell component (i.e., cylindrical, conical, and spherical shells) is divided into appropriate elements. The variational principle in conjunction with first-order shear deformation shell theory is employed to model the shell elements. Since the displacement and rotation components of each element are expressed as a linear superposition of nodeless Fourier sine functions and nodal Lagrangian polynomials, the global equations of the coupled shell structure can be obtained by adopting the assembly procedure. The Fourier sine series in the displacement field is introduced to enhance the accuracy and convergence of the solution. Numerical results show that the FSEM can be effectively applied to vibration analysis of the coupled shell structures. Numerous results for coupled shell structures with general boundary conditions are presented. Furthermore, the effects of geometric parameters and boundary conditions on the frequencies are investigated.

  14. High-accuracy measurement of low-water-content in liquid using NIR spectral absorption method

    NASA Astrophysics Data System (ADS)

    Peng, Bao-Jin; Wan, Xu; Jin, Hong-Zhen; Zhao, Yong; Mao, He-Fa

    2005-01-01

    Water content measurement technologies are very important for quality inspection of food, medicine products, chemical products and many other industry fields. In recent years, requests for accurate low-water-content measurement in liquid are more and more exigent, and great interests have been shown from the research and experimental work. With the development and advancement of modern production and control technologies, more accurate water content technology is needed. In this paper, a novel experimental setup based on near-infrared (NIR) spectral technology and fiber-optic sensor (OFS) is presented. It has a good measurement accuracy about -/+ 0.01%, which is better, to our knowledge, than most other methods published until now. It has a high measurement resolution of 0.001% in the measurement range from zero to 0.05% for water-in-alcohol measurement, and the water-in-oil measurement is carried out as well. In addition, the advantages of this method also include pollution-free to the measured liquid, fast measurement and so on.

  15. Analysis of the Spectral Singularities of Schrödinger Operator with Complex Potential by Means of the SPPS Method

    NASA Astrophysics Data System (ADS)

    Barrera Figueroa, V.

    2016-03-01

    In this work we present an effective way of finding the spectral singularities of the one-dimensional Schrödinger operator with a complex-valued potential defined in the half-axis [0, ∞). The spectral singularities are certain poles in the kernel of the resolvent, which are not eigenvalues of the operator. In this work, the spectral singularities are calculated from the real zeros of ϰ (ϱ) = 0, where ϰ (ϱ) is an analytic function of the complex variable ϱ, which is obtained by means of the Spectral Parameter Power Series Method. This representation is convenient from a numerical point of view since its numerical implementation implies truncating the series up to a M-th term. Hence, finding the approximate spectral singularities is equivalent to finding the real roots of a certain polynomial of degree 2M. In addition, we provide explicit formulas for calculating the eigenvalues of the operator, as well as the eigenfunctions and generalized eigenfunctions associated to both the continuous spectrum and the spectral singularities.

  16. Model-free methods to study membrane environmental probes: a comparison of the spectral phasor and generalized polarization approaches

    PubMed Central

    Malacrida, Leonel; Gratton, Enrico; Jameson, David M

    2016-01-01

    In this note, we present a discussion of the advantages and scope of model-free analysis methods applied to the popular solvatochromic probe LAURDAN, which is widely used as an environmental probe to study dynamics and structure in membranes. In particular, we compare and contrast the generalized polarization approach with the spectral phasor approach. To illustrate our points we utilize several model membrane systems containing pure lipid phases and, in some cases, cholesterol or surfactants. We demonstrate that the spectral phasor method offers definitive advantages in the case of complex systems. PMID:27182438

  17. Model-free methods to study membrane environmental probes: a comparison of the spectral phasor and generalized polarization approaches.

    PubMed

    Malacrida, Leonel; Gratton, Enrico; Jameson, David M

    2015-12-01

    In this note, we present a discussion of the advantages and scope of model-free analysis methods applied to the popular solvatochromic probe LAURDAN, which is widely used as an environmental probe to study dynamics and structure in membranes. In particular, we compare and contrast the generalized polarization approach with the spectral phasor approach. To illustrate our points we utilize several model membrane systems containing pure lipid phases and, in some cases, cholesterol or surfactants. We demonstrate that the spectral phasor method offers definitive advantages in the case of complex systems.

  18. Centaur feedline dynamics study using power spectral methods. [fundamental mode resonant frequencies of RL-10 oxygen and hydrogen feed lines

    NASA Technical Reports Server (NTRS)

    Lorenzo, C. F.

    1974-01-01

    Tests were conducted to determine the dynamic characteristics of the Centaur/RL-10 oxygen and hydrogen feedlines. The fundamental-mode resonant frequencies were determined by applying power spectral methods to noise-generated data from hot firings of the RL-10 engine. The effect of net positive suction pressure of the main feed pumps on resonant frequency characteristics was determined to be a straight-line relation. Power spectral methods were also used to determine the dynamic characteristics of the boost pumps.

  19. A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow

    NASA Technical Reports Server (NTRS)

    Moser, R. D.; Moin, P.; Leonard, A.

    1983-01-01

    A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.

  20. A general spectral method for the numerical simulation of one-dimensional interacting fermions

    NASA Astrophysics Data System (ADS)

    Clason, Christian; von Winckel, Gregory

    2012-02-01

    This work introduces 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. Program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_0.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.: 102 No. of bytes in distributed program, including test data, etc.: 2294 Distribution format: tar.gz Programming language: MATLAB Computer: Any architecture supported by MATLAB Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6) RAM: Depends on the data Classification: 4.3, 2.2 Nature of problem: The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Solution method: A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave

  1. A Tape Method for Fast Characterization and Identification of Active Pharmaceutical Ingredients in the 2-18 THz Spectral Range

    NASA Astrophysics Data System (ADS)

    Kissi, Eric Ofosu; Bawuah, Prince; Silfsten, Pertti; Peiponen, Kai-Erik

    2015-03-01

    In order to find counterfeit drugs quickly and reliably, we have developed `tape method' a transmission spectroscopic terahertz (THz) measurement technique and compared it with a standard attenuated total reflection (ATR) THz spectroscopic measurement. We used well-known training samples, which include commercial paracetamol and aspirin tablets to check the validity of these two measurement techniques. In this study, the spectral features of some active pharmaceutical ingredients (APIs), such as aspirin and paracetamol are characterized for identification purpose. This work covers a wide THz spectral range namely, 2-18 THz. This proposed simple but novel technique, the tape method, was used for characterizing API and identifying their presence in their dosage forms. By comparing the spectra of the APIs to their dosage forms (powder samples), all distinct fingerprints present in the APIs are also present in their respective dosage forms. The positions of the spectral features obtained with the ATR techniques were akin to that obtained from the tape method. The ATR and the tape method therefore, complement each other. The presence of distinct fingerprints in this spectral range has highlighted the possibility of developing fast THz sensors for the screening of pharmaceuticals. It is worth noting that, the ATR method is applicable to flat faced tablets whereas the tape method is suitable for powders in general (e.g. curved surface tablets that require milling before measurement). Finally, we have demonstrated that ATR techniques can be used to screen counterfeit antimalarial tablets.

  2. The Features of the Frequency-Modulation Method When Studying the Shapes of the Spectral Lines of Nonlinear Absorption

    NASA Astrophysics Data System (ADS)

    Golubiatnikov, G. Yu.; Belov, S. P.; Lapinov, A. V.

    2017-01-01

    We briefly consider the method of the frequency (phase) modulation and signal detection at the second harmonic of the modulation frequency for recording and analyzing the spectral-line shapes. The precision sub-Doppler spectrometer in the millimeter- and submillimeter-wave ranges, which operated in the regime of nonlinear saturation of the spectral transitions in a standing wave (the Lamb-dip method), was used during the measurements. The influence of the saturation degree on the value and shape of the recorded frequency-modulated signals in the quadrature channels during the synchronous detection is demonstrated. Variation in the relationships among the signals determined by dispersion and absorption was observed. The necessity of allowance for the influence of the group-velocity dispersion and coherent effects on the shape of the recorded spectral lines is experimentally shown.

  3. High precision computing with charge domain devices and a pseudo-spectral method therefor

    NASA Technical Reports Server (NTRS)

    Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor); Fijany, Amir (Inventor); Zak, Michail (Inventor)

    1997-01-01

    The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

  4. Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows

    NASA Astrophysics Data System (ADS)

    Chaudhuri, A.; Jacobs, G. B.; Don, W. S.; Abbassi, H.; Mashayek, F.

    2017-03-01

    A spatio-temporal adaptive artificial viscosity (AV) based shock-capturing scheme is proposed for the solution of both inviscid and viscous compressible flows using a high-order parallel Discontinuous Spectral Element Method (DSEM). The artificial viscosity and artificial thermal conduction coefficients are proportional to the viscous and thermal entropy generating terms, respectively, in the viscous entropy conservation law. The magnitude of AV is limited based on the explicit stable CFL criterion, so that the stable artificial viscous time step size is greater than the convective stable time step size. To further ensure the stability of this explicit approach, an adaptive variable order exponential filter is applied, if necessary, in elements where the AV has been limited. In viscous flow computations a modified Jameson's sensor (Ducros et al., 1999 [61]) limits the AV to small values in viscous shear regions, so as to maintain a high-order resolution in smooth regions and an essentially non-oscillatory behavior near sharp gradients/shocks regions. We have performed a systematic and extensive validation of the algorithm with one-dimensional problems (inviscid moving shock and viscous shock-structure interaction), two-dimensional problems (inviscid steady and unsteady shocked flows and viscous shock-boundary layer interaction), and a three-dimensional supersonic turbulent flow over a ramped cavity. These examples demonstrate that the explicit DSEM scheme with adaptive artificial viscosity terms is stable, accurate and efficient.

  5. Magnetic control of natural convection in the horizontal Bridgman configuration using a spectral method: transversal plan

    NASA Astrophysics Data System (ADS)

    Baaziz, Inès; Ben Salah, Nizar; Kaddeche, Slim

    2014-07-01

    The present study investigates the electromagnetic braking of buoyancy convective flows occurring in differentially heated cavities, filled with low Prandtl, dilute, incompressible and electrically conducting alloys, and subjected to a constant horizontal temperature gradient. In practice, such flows known as 'Hadley circulation' are relevant in material processing technologies, such as the horizontal Bridgman configuration. A collocation spectral numerical method is developed to solve the two-dimensional Navier-Stokes equations, modelling the flow phenomena occurring in such configurations, using a vorticity-stream function formulation. The two components of the velocity are deduced from the stream function and the temperature distribution is obtained through the resolution of the energy conservation equation. The results in terms of velocity and temperature distributions for a given Grashof number are obtained for various Hartmann numbers and show that as the Hartmann number increases, the electromagnetic braking of the flow is observed. Moreover, the results illustrate the changes affecting the flow structure which becomes quasi-parallel in the core region of the cavity for sufficiently high values of Ha and the onset of the Hartmann and parallel layers along the boundaries. Also, with increasing Ha, the isotherms are less affected by the convective flow and become parallel to the vertical walls indicating that heat transfer is mainly achieved by conduction.

  6. Applications methods of spectral ratios in the estimation of site effects: Case Damien (Haiti)

    NASA Astrophysics Data System (ADS)

    Jean, B. J.; ST Fleur, S.

    2014-12-01

    Measurements of H/V type were carried out on the Damien site with Tromino hardware an « all in one » station which includes both the sensor and the integrated digitizer. A total of 32 measurements of seismic noise have been completed on this site in order to see if lithological site effects are detectable with this H/V method. After checking the H/V curve reliability criteria (length of the window to be analyzed, the number of windows analyzed, standard deviation) and the criteria for clear peaks in H/V (conditions for the amplitude, conditions for stability) found in the SESAME project in 2004, the results of the H/V spectra obtained are generally very consistent and clearly indicate site effects with peak resonance frequencies between 3 and 14 Hz. The presence of these well defined frequency peaks in the H/V spectral ratio indicates that the ground motion can be amplified by geomorphological site effects. Comparative analyzes of these H/V measurements with Grilla and Geopsy software were made in this paper to estimate the amplification magnitude of these effects. Graphical comparisons between the Grilla and Geopsy H/V maps were completed in this study and allow us to identify typical areas and their associated fundamental resonance frequencies.

  7. Simulations of Ground Motion in Southern California based upon the Spectral-Element Method

    NASA Astrophysics Data System (ADS)

    Tromp, J.; Komatitsch, D.; Liu, Q.

    2003-12-01

    We use the spectral-element method to simulate ground motion generated by recent well-recorded small earthquakes in Southern California. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum industry well logs and more than twenty thousand kilometers of seismic reflection profiles. The numerical simulations account for 3D variations of seismic wave speeds and density, topography and bathymetry, and attenuation. Simulations for several small recent events demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 seconds and longer inside the Los Angeles basin and 6 seconds and longer elsewhere. Peak ground displacement, velocity and acceleration maps illustrate that significant amplification occurs in the basin. Centroid-Moment Tensor mechanisms are obtained based upon Pnl and surface waveforms and numerically calculated 3D Frechet derivatives. We use a combination of waveform and waveform-envelope misfit criteria, and facilitate pure double-couple or zero-trace moment-tensor inversions.

  8. Nuclear spatial and spectral features based evolutionary method for meningioma subtypes classification in histopathology.

    PubMed

    Fatima, Kiran; Majeed, Hammad; Irshad, Humayun

    2017-04-05

    Meningioma subtypes classification is a real-world multiclass problem from the realm of neuropathology. The major challenge in solving this problem is the inherent complexity due to high intra-class variability and low inter-class variation in tissue samples. The development of computational methods to assist pathologists in characterization of these tissue samples would have great diagnostic and prognostic value. In this article, we proposed an optimized evolutionary framework for the classification of benign meningioma into four subtypes. This framework investigates the imperative role of RGB color channels for discrimination of tumor subtypes and compute structural, statistical and spectral phenotypes. An evolutionary technique, Genetic Algorithm, in combination with Support Vector Machine is applied to tune classifier parameters and to select the best possible combination of extracted phenotypes that improved the classification accuracy (94.88%) on meningioma histology dataset, provided by the Institute of Neuropathology, Bielefeld. These statistics show that computational framework can robustly discriminate four subtypes of benign meningioma and may aid pathologists in the diagnosis and classification of these lesions.

  9. Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators

    DOE PAGES

    Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

    2015-12-02

    We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less

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

    PubMed Central

    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. PMID:28050197

  11. Spectral Quadrature method for accurate O(N) electronic structure calculations of metals and insulators

    NASA Astrophysics Data System (ADS)

    Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

    2016-03-01

    We present the Clenshaw-Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw-Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N3) planewave results. Finally, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.

  12. Analysis of iterative methods for the viscous/inviscid coupled problem via a spectral element approximation

    NASA Astrophysics Data System (ADS)

    Xu, Chuanju; Lin, Yumin

    2000-03-01

    Based on a new global variational formulation, a spectral element approximation of the incompressible Navier-Stokes/Euler coupled problem gives rise to a global discrete saddle problem. The classical Uzawa algorithm decouples the original saddle problem into two positive definite symmetric systems. Iterative solutions of such systems are feasible and attractive for large problems. It is shown that, provided an appropriate pre-conditioner is chosen for the pressure system, the nested conjugate gradient methods can be applied to obtain rapid convergence rates. Detailed numerical examples are given to prove the quality of the pre-conditioner. Thanks to the rapid iterative convergence, the global Uzawa algorithm takes advantage of this as compared with the classical iteration by sub-domain procedures. Furthermore, a generalization of the pre-conditioned iterative algorithm to flow simulation is carried out. Comparisons of computational complexity between the Navier-Stokes/Euler coupled solution and the full Navier-Stokes solution are made. It is shown that the gain obtained by using the Navier-Stokes/Euler coupled solution is generally considerable. Copyright

  13. Chebyshev-polynomial-based (CPB) unified model neural network for the worst-case identification of nonlinear systems H∞ problem

    NASA Astrophysics Data System (ADS)

    Jeng, Jin-Tsong; Lee, Tsu-Tian

    1998-03-01

    In this paper, we propose a neural network model with a faster learning speed and a good approximate capability in the function approximation for solving worst-case identification of nonlinear systems H(infinity ) problems. Specifically, via the approximate transformable technique, we develop a Chebyshev Polynomials Based unified model neural network for solving the worst-case identification of nonlinear systems H(infinity ) problems. Based on this approximate transformable technique, the relationship between the single-layered neural network and multi-layered perceptron neural network is derived. It is shown that the Chebyshev Polynomials Based unified model neural network can be represented as a functional link network that is based on Chebyshev polynomials. We also derive a new learning algorithm such that the infinity norm of the transfer function from the input to the output is under a prescribed level. It turns out that the Chebyshev Polynomials Based unified model neural network not only has the same capability of universal approximator, but also has a faster learning speed than multi-layered perceptron or the recurrent neural network in the deterministic worst-case identification of nonlinear systems H(infinity ) problems.

  14. Validation of 3D Seismic Velocity Models Using the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Maceira, M.; Larmat, C. S.; Porritt, R. W.; Higdon, D.; Allen, R. M.

    2012-12-01

    For over a decade now, many research institutions have been focusing on addressing the Earth's 3D heterogeneities and complexities by improving tomographic methods. Utilizing dense array datasets, these efforts have led to unprecedented 3D seismic images, but little is done in terms of model validation or to provide any absolute assessment of model uncertainty. Furthermore, the question of "How good is a 3D geophysical model at representing the Earth's true physics? " remains largely not addressed in a time when 3D Earth models are used for societal and energy security. In the last few years, new horizons have opened up in earth structure imaging, with the advent of new numerical and mathematical methods in computational seismology and statistical sciences. We use these methods to tackle the question of model validation taking advantage of unique and extensive High Performance Computing resources available at Los Alamos National Laboratory. We present results from a study focused on validating 3D models for the Western USA generated using both ray-theoretical and finite-frequency approximations. In this manner we do not validate just the model but also the imaging technique. For this test case, we utilize the Dynamic North America (DNA) model family of UC Berkeley, as they are readily available in both formulations. We evaluate model performances by comparing observed and synthetic seismograms generated using the Spectral Element Method. Results show that both, finite-frequency and ray-theoretical DNA09 models, predict the observations well. Waveform cross-correlation coefficients show a difference in performance between models obtained with the finite-frequency or ray-theory limited to smallest periods (<15s), with no perceptible difference at longer periods (50-200s). At those shortest periods, and based on statistical analyses on S-wave phase delay measurements, finite-frequency shows an improvement over ray theory. We are also investigating the breakdown of ray

  15. Simulations of Strong Ground Motion in the Los Angeles Basin Using the Spectral-Element Method

    NASA Astrophysics Data System (ADS)

    Komatitsch, D.; Liu, Q.; Tromp, J.; Suess, P.; Shaw, J.

    2003-04-01

    We use the spectral-element method (SEM) to simulate strong ground motion in the Los Angeles basin. Our basin velocity model was constructed using sonic log and stacking velocity information provided by oil industry sources. The method includes effects due to attenuation, topography and bathymetry. The basin model is embedded into the regional model of Hauksson (2000). Our mesh honors the bottom part of the 8.5 km deep sedimentary pocket underneath downtown Los Angeles, as well as topography and bathymetry, and the Moho map of Zhu and Kanamori (2000). We double the mesh twice in the vertical direction based upon a conforming doubling `brick'. This allows us to increase the resolution of the SEM calculations near the surface, in low-velocity sediments. We obtain a high-quality mesh based upon a heuristic rule to prevent elements in the doubling regions from becoming too flat. The SEM is implemented on a parallel computer based upon a message-passing algorithm (MPI), and run on a large PC cluster, a so-called Beowulf machine. This allows us to model wave propagation in a large region that includes most of the TriNet stations. Results are shown for two small events (M = 4.2) that can be treated as point sources, the September 2001 Hollywood earthquake, and the September 2002 Yorba Linda event. We use a three-dimensional centroid-moment tensor inversion based upon the SEM and the basin model to determine the mechanisms and locations of these events. Excellent agreement is obtained for the three components of the data down to a period of 2 seconds.

  16. Seismic waves modeling with the Fourier pseudo-spectral method on massively parallel machines.

    NASA Astrophysics Data System (ADS)

    Klin, Peter

    2015-04-01

    The Fourier pseudo-spectral method (FPSM) is an approach for the 3D numerical modeling of the wave propagation, which is based on the discretization of the spatial domain in a structured grid and relies on global spatial differential operators for the solution of the wave equation. This last peculiarity is advantageous from the accuracy point of view but poses difficulties for an efficient implementation of the method to be run on parallel computers with distributed memory architecture. The 1D spatial domain decomposition approach has been so far commonly adopted in the parallel implementations of the FPSM, but it implies an intensive data exchange among all the processors involved in the computation, which can degrade the performance because of communication latencies. Moreover, the scalability of the 1D domain decomposition is limited, since the number of processors can not exceed the number of grid points along the directions in which the domain is partitioned. This limitation inhibits an efficient exploitation of the computational environments with a very large number of processors. In order to overcome the limitations of the 1D domain decomposition we implemented a parallel version of the FPSM based on a 2D domain decomposition, which allows to achieve a higher degree of parallelism and scalability on massively parallel machines with several thousands of processing elements. The parallel programming is essentially achieved using the MPI protocol but OpenMP parts are also included in order to exploit the single processor multi - threading capabilities, when available. The developed tool is aimed at the numerical simulation of the seismic waves propagation and in particular is intended for earthquake ground motion research. We show the scalability tests performed up to 16k processing elements on the IBM Blue Gene/Q computer at CINECA (Italy), as well as the application to the simulation of the earthquake ground motion in the alluvial plain of the Po river (Italy).

  17. Quantitative measurement of speech sound distortions with the aid of minimum variance spectral estimation method for dentistry use.

    PubMed

    Bereteu, L; Drăgănescu, G E; Stănescu, D; Sinescu, C

    2011-12-01

    In this paper, we search an adequate quantitative method based on minimum variance spectral analysis in order to reflect the dependence of the speech quality on the correct positioning of the dental prostheses. We also search some quantitative parameters, which reflect the correct position of dental prostheses in a sensitive manner.

  18. Effects of leaf excision and sample storage methods on spectral reflectance by foliage of giant reed, Arundo donax

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Research was conducted to evaluate the effects of leaf excision and sample storage methods on spectral reflectance by foliage of giant reed, Arundo donax, an invasive weed which has caused extensive damage in many areas of the Rio Grande Basin in Texas and Mexico. Within 24 hours of excision, A. d...

  19. Effects of leaf excision and sample storage methods on spectral reflectance by foliage of Giant Reed, Arundo donax

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Research was conducted to evaluate the effects of leaf excision and sample storage methods on spectral reflectance by foliage of giant reed, Arundo donax, an invasive weed which has caused extensive damage in many areas of the Rio Grande Basin in Texas and Mexico. Within 24 hours of excision, A. don...

  20. New method for removal of spectral interferences for beryllium assay using inductively coupled plasma atomic emission spectrometry.

    PubMed

    Maxwell, Sherrod L; Bernard, Maureen A; Nelson, Matthew R; Youmans, Linda D

    2008-07-15

    Beryllium (Be) has been used widely in specific areas of nuclear technology. Frequent monitoring of air and possible contaminated surfaces in U.S. Department of Energy (DOE) facilities is required to identify potential health risks and to protect U.S. DOE workers from beryllium-contaminated dust. A new method has been developed to rapidly remove spectral interferences prior to beryllium measurement by inductively coupled plasma atomic emission spectrometry (ICP-AES) that allows lower detection limits. The ion exchange separation removes uranium (U), plutonium (Pu), thorium (Th), niobium (Nb), vanadium (V), molybdenum (Mo), zirconium (Zr), tungsten (W), iron (Fe), chromium (Cr), cerium (Ce), erbium (Er) and titanium (Ti). A stacked column consisting of Diphonix Resin and TEVA Resin reduces the levels of the spectral interferences so that low level Be measurements can be performed accurately. If necessary, an additional anion exchange separation can be used for further removal of interferences, particularly chromium. The method has been tested using spiked filters, spiked wipe samples and certified reference material (CRM) standards with high levels of interferences added. The method provides very efficient removal of spectral interferences with very good accuracy and precision for beryllium on filters or wipes. This new method offers improvements over other separation methods that have been used by removing large amounts of all the significant spectral interferences with greater simplicity and effectiveness. The effective removal of spectral interferences allows lower method detection limits (MDL) using inductively coupled atomic emission spectrometry. A vacuum box system is employed to reduce analytical time and reduce labor costs.