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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. Elimination of spurious eigenvalues in the Chebyshev tau spectral method

    NASA Technical Reports Server (NTRS)

    Mcfadden, G. B.; Murray, B. T.; Boisvert, R. F.

    1989-01-01

    Spectral methods have been used to great advantage in hydrodynamic stability calculations; the concepts are described in Orszag's seminal application of the Chebyshev tau method to the Orr-Sommerfeld equation for plane Poiseuille flow in 1971. Orszag discusses both the Chebyshev Galerkin and the Chebyshev tau methods, but presents results for the tau method, which is easier to implement than the Galerkin method. The tau method has the disadvantage that two unstable eigenvalues are produced that are artifacts of the discretization. An extremely simple modification to the Chebyshev tau method is presented which eliminates the spurious eigenvalues. First a simplified model of the Orr-Sommerfeld equation discussed by Gottlieb and Orszag was studied. Then the Chebyshev tau method is considered, which has two spurious eigenvalues, and then a modification which eliminates them is described. Finally, results for the Orr-Sommerfeld equation are considered where the modified tau method also eliminates the spurious eigenvalues. The simplicity of the modification makes it a convenient alternative to other approaches to the problem.

  3. Elimination of spurious eigenvalues in the Chebyshev tau spectral method

    NASA Technical Reports Server (NTRS)

    Mcfadden, G. B.; Murray, B. T.; Boisvert, R. F.

    1990-01-01

    A very simple modification is presented for the Chebyshev tau method which can eliminate spurious eigenvalues, proceeding from a consideration of the vorticity-streamfunction reformulation of the Chebyshev tau method and the Chebyshev-Galerkin method, which have no spurious modes. Consideration of a model problem indicates that these two approaches are equivalent, and that they reduce to the present modification of the tau method. This modified tau method also eliminates spurious eigenvalues from the Orr-Sommerfeld equation.

  4. Chebyshev-Fourier spectral methods in bipolar coordinates

    NASA Astrophysics Data System (ADS)

    Huang, Zhu; Boyd, John P.

    2015-08-01

    Bipolar coordinates provide an efficient cartography for a variety of geometries: the exterior of two disks or cylinders, a half-plane containing a disk, an eccentric annulus with a small disk offset from the center of an outer boundary that is a large circle, and so on. A pseudospectral method that employs a tensor product basis of Fourier functions in the cyclic coordinate η and Chebyshev polynomials in the quasi-radial coordinate ξ gives easy-to-program spectral accuracy. We show, however, that as the inner disk becomes more and more offset from the center of the outer boundary circle, the grid is increasingly non-uniform, and the rate of exponential convergence increasingly slow. One-dimensional coordinate mappings significantly reduce the non-uniformity. In spite of this non-uniformity, the Chebyshev-Fourier method is quite effective in an idealized model of the wind-driven ocean circulation, resolving both internal and boundary layers. Bipolar coordinates are also a good starting point for solving problems in a domain which is not one of the "bipolar-compatible" domains listed above, but is a sufficiently small perturbation of such. This is illustrated by applying boundary collocation with bipolar harmonics to solve Laplace's equation in a perturbed eccentric annulus in which the disk-shaped island has been replaced by an island bounded by an ellipse. Similarly a perturbed bipolar domain can be mapped to an eccentric annulus by a smooth change of coordinates.

  5. 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.

  6. A new iterative Chebyshev spectral method for solving the elliptic equation [del] [center dot] ([sigma] [del]u) = f

    SciTech Connect

    Zhao, Shengkai; Yedlin, M.J. )

    1994-08-01

    We present a new iterative Chebyshev spectral method for solving the elliptic equation [del] [center dot] ([sigma] [del]u) = f. We rewrite the equation in the form of a Poisson's equation [del][sup 2]u = (f - [del]u [center dot] [del][sigma]/[sigma]). In each iteration we compute the right-hand side terms from the guess values first. Then we solve the resultant Poisson equation by a direct method to obtain the updated values. Three numerical examples are presented. For the sam number of iterations, the accuracy of the present method is about 6-8 orders better than the Chebyshev spectral multigrid method. On a SPARC Station 2 computer, the CPU time of the new method is about one-third of the Chebyshev spectral multigrid method. To obtain the same accuracy, the CPU time of the present method is about one-tenth of the Chebyshev spectral multigrid method. 17 refs., 5 figs., 3 tabs.

  7. 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. PMID:25254252

  8. 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

  9. A third-order multistep time discretization for a Chebyshev tau spectral method

    NASA Astrophysics Data System (ADS)

    Vreman, A. W.; Kuerten, J. G. M.

    2016-01-01

    A time discretization scheme based on the third-order backward difference formula has been embedded into a Chebyshev tau spectral method for the Navier-Stokes equations. The time discretization is a variant of the second-order backward scheme proposed by Krasnov et al. (2008) [3]. High-resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the Runge-Kutta scheme proposed by Spalart et al. (1991) [2]. It is shown that the Runge-Kutta scheme leads to a poor convergence of some third-order spatial derivatives in the direct vicinity of the wall, derivatives that represent the diffusion of wall-tangential vorticity. The convergence at the wall is shown to be significantly improved if the backward scheme is applied.

  10. Chebyshev collocation spectral lattice Boltzmann method for simulation of low-speed flows.

    PubMed

    Hejranfar, Kazem; Hajihassanpour, Mahya

    2015-01-01

    In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used. An iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows. The main advantage of using the CCSLBM over other high-order accurate lattice Boltzmann method (LBM)-based flow solvers is the decay of the error at exponential rather than at polynomial rates. Note also that the CCSLBM applied does not need any numerical dissipation or filtering for the solution to be stable, leading to highly accurate solutions. Three two-dimensional (2D) test cases are simulated herein that are a regularized cavity, the Taylor vortex problem, and doubly periodic shear layers. The results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement. The computational efficiency of the proposed solution methodology based on the CCSLBM is also examined by comparison with those of the standard streaming-collision (classical) LBM and two finite-difference LBM solvers. The study indicates that the CCSLBM provides more accurate and efficient solutions than these LBM solvers in terms of CPU and memory usage and an exponential

  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. Boundary conditions in Chebyshev and Legendre methods

    NASA Technical Reports Server (NTRS)

    Canuto, C.

    1984-01-01

    Two different ways of treating non-Dirichlet boundary conditions in Chebyshev and Legendre collocation methods are discussed for second order differential problems. An error analysis is provided. The effect of preconditioning the corresponding spectral operators by finite difference matrices is also investigated.

  13. 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.

  14. A poly-grid approach for wave propagation modelling in highly heterogeneous media by using a Chebyshev spectral element method

    NASA Astrophysics Data System (ADS)

    Su, C.; Seriani, G.

    2012-04-01

    Many physical problems require the modelling of wave phenomena in media having variable properties, while highly accurate algorithms are needed in order to avoid unphysical effects. Often the property fluctuations may be very high compared to the minimum wavelength, leading to an extremely large problem, since a grid resolution down to the finest scales is required and the much larger wavelength scale of interest cannot be exploited in order to reduce the computational burden. Here, like in multiscale methods, efficiency can be increased only by solving the macroscopic behavior without solving explicitly the microscopic one. Spectral element methods (SEM) have excellent properties of accuracy and flexibility in describing complex models and are used as well for wave modelling. In the standard SEM approach, the computational domain is discretized by using very coarse meshes and constant-property elements, which makes it inappropriate for solving the above mentioned problem. A convenient solution approach is provided by a poly-grid Chebyshev spectral element method, which allows to overcome this limitation. The domain decomposition is built by using composite elements having a set of local grids, or poly-grid. The main grid is used for wave propagation, whereas the remaining auxiliary grids are used for describing the physical parameters. As a consequence, SEM accuracy and efficiency is maintained in wave field computations while dealing with small scale property fluctuations. Moreover, interfaces between different materials can be easily handled internally to each element without the need of their edges be aligned with the interfaces.

  15. Chebyshev moment problems: Maximum entropy and kernel polynomial methods

    SciTech Connect

    Silver, R.N.; Roeder, H.; Voter, A.F.; Kress, J.D.

    1995-12-31

    Two Chebyshev recursion methods are presented for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are applicable to physical properties involving large numbers of eigenstates such as densities of states, spectral functions, thermodynamics, total energies for Monte Carlo simulations and forces for tight binding molecular dynamics. this paper emphasizes efficient algorithms.

  16. The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points

    NASA Technical Reports Server (NTRS)

    Don, Wai Sun; Gottlieb, David

    1993-01-01

    We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.

  17. 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.

  18. Weighted Chebyshev distance classification method for hyperspectral imaging

    NASA Astrophysics Data System (ADS)

    Demirci, S.; Erer, I.; Ersoy, O.

    2015-06-01

    The main objective of classification is to partition the surface materials into non-overlapping regions by using some decision rules. For supervised classification, the hyperspectral imagery (HSI) is compared with the reflectance spectra of the material containing similar spectral characteristic. As being a spectral similarity based classification method, prediction of different level of upper and lower spectral boundaries of all classes spectral signatures across spectral bands constitutes the basic principles of the Multi-Scale Vector Tunnel Algorithm (MS-VTA) classification algorithm. The vector tunnel (VT) scaling parameters obtained from means and standard deviations of the class references are used. In this study, MS-VT method is improved and a spectral similarity based technique referred to as Weighted Chebyshev Distance (WCD) method for the supervised classification of HSI is introduced. This is also shown to be equivalent to the use of the WCD in which the weights are chosen as an inverse power of the standard deviation per spectral band. The use of WCD measures in terms of the inverse power of standard deviations and optimization of power parameter constitute the most important side of the study. The algorithms are trained with the same kinds of training sets, and their performances are calculated for the power of the standard deviation. During these studies, various levels of the power parameters are evaluated based on the efficiency of the algorithms for choosing the best values of the weights.

  19. Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics

    NASA Astrophysics Data System (ADS)

    Junkins, John L.; Bani Younes, Ahmad; Woollands, Robyn M.; Bai, Xiaoli

    2013-12-01

    This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics. Using Chebyshev polynomials, as the orthogonal approximation basis, it is straightforward to distribute the computation of force functions needed in MCPI to generate the polynomial coefficients (approximating the path iterations) to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refines path estimates over large time intervals chosen to be within the domain of convergence of Picard iteration. The developed vector-matrix form makes MCPI methods computationally efficient and a more systematic approach is given, leading to a modest correction to results in the published dissertation by Bai. The power of MCPI methods for solving IVPs is clearly illustrated using a simple nonlinear differential equation with a known analytical solution. Compared with the most common integration scheme, the standard Runge-Kutta 4-5 method as implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, on a serial machine. MCPI performance is also compared to state of the art integrators such as the Runge-Kutta Nystrom 12(10) methods applied to the relevant orbit mechanics problems. The MCPI method is shown to be well-suited to solving these problems in serial processors with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. When used in conjunction with the recently developed local gravity approximations in conjunction with parallel computation, we anticipate MCPI will enable revolutionary speedups while ensuring

  20. An error embedded method based on generalized Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung

    2016-02-01

    In this paper, we develop an error embedded method based on generalized Chebyshev polynomials for solving stiff initial value problems. The solution and the error at each integration step are calculated by generalized Chebyshev polynomials of two consecutive degrees having overlapping zeros, which enables us to minimize overall computational costs. Further the errors at each integration step are embedded in the algorithm itself. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 6th order convergence and an almost L-stability. We assess the proposed method with several numerical results, showing that it uses larger time step sizes and is numerically more efficient.

  1. Exponential time differencing methods with Chebyshev collocation for polymers confined by interacting surfaces

    SciTech Connect

    Liu, Yi-Xin Zhang, Hong-Dong

    2014-06-14

    We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourth-order accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules 45, 2905 (2012)], non-periodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.

  2. 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.

  3. Numerical modeling of wave propagation in functionally graded materials using time-domain spectral Chebyshev elements

    NASA Astrophysics Data System (ADS)

    Hedayatrasa, Saeid; Bui, Tinh Quoc; Zhang, Chuanzeng; Lim, Chee Wah

    2014-02-01

    Numerical modeling of the Lamb wave propagation in functionally graded materials (FGMs) by a two-dimensional time-domain spectral finite element method (SpFEM) is presented. The high-order Chebyshev polynomials as approximation functions are used in the present formulation, which provides the capability to take into account the through thickness variation of the material properties. The efficiency and accuracy of the present model with one and two layers of 5th order spectral elements in modeling wave propagation in FGM plates are analyzed. Different excitation frequencies in a wide range of 28-350 kHz are investigated, and the dispersion properties obtained by the present model are verified by reference results. The through thickness wave structure of two principal Lamb modes are extracted and analyzed by the symmetry and relative amplitude of the vertical and horizontal oscillations. The differences with respect to Lamb modes generated in homogeneous plates are explained. Zero-crossing and wavelet signal processing-spectrum decomposition procedures are implemented to obtain phase and group velocities and their dispersion properties. So it is attested how this approach can be practically employed for simulation, calibration and optimization of Lamb wave based nondestructive evaluation techniques for the FGMs. The capability of modeling stress wave propagation through the thickness of an FGM specimen subjected to impact load is also investigated, which shows that the present method is highly accurate as compared with other existing reference data.

  4. 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.

  5. Hubbell rectangular source integral calculation using a fast Chebyshev wavelets method.

    PubMed

    Manai, K; Belkadhi, K

    2016-07-01

    An integration method based on Chebyshev wavelets is presented and used to calculate the Hubbell rectangular source integral. A study of the convergence and the accuracy of the method was carried out by comparing it to previous studies. PMID:27152913

  6. Spectral multigrid methods for elliptic equations II

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

    A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

  7. Spectral multigrid methods for elliptic equations 2

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

  8. 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.

  9. An efficient implementation of the Chebyshev Rational Approximation Method (CRAM) for solving the burnup equations

    SciTech Connect

    Pusa, M.; Leppaenen, J.

    2012-07-01

    The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. Fast Chebyshev-polynomial method for simulating the time evolution of linear dynamical systems.

    PubMed

    Loh, Y L; Taraskin, S N; Elliott, S R

    2001-05-01

    We present a fast method for simulating the time evolution of any linear dynamical system possessing eigenmodes. This method does not require an explicit calculation of the eigenvectors and eigenfrequencies, and is based on a Chebyshev polynomial expansion of the formal operator matrix solution in the eigenfrequency domain. It does not suffer from the limitations of ordinary time-integration methods, and can be made accurate to almost machine precision. Among its possible applications are harmonic classical mechanical systems, quantum diffusion, and stochastic transport theory. An example of its use is given for the problem of vibrational wave-packet propagation in a disordered lattice. PMID:11415044

  15. 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.

  16. Modified Chebyshev pseudospectral method with O(N exp -1) time step restriction

    NASA Technical Reports Server (NTRS)

    Kosloff, Dan; Tal-Ezer, Hillel

    1989-01-01

    The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N exp 2) where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N exp -2) which, in many cases, is much below the time step dictated by the physics of the partial differential equation. A new set of interpolating points is introduced such that the eigenvalues of the differentiation operator are O(N) and the allowable time step is O(N exp -1). The properties of the new algorithm are similar to those of the Fourier method. The new algorithm also provides a highly accurate solution for non-periodic boundary value problems.

  17. Comparison of the Chebyshev Method and the Generalized Crank-Nicholson Method for time Propagation in Quantum Mechanics

    SciTech Connect

    Formanek, Martin; Vana, Martin; Houfek, Karel

    2010-09-30

    We compare efficiency of two methods for numerical solution of the time-dependent Schroedinger equation, namely the Chebyshev method and the recently introduced generalized Crank-Nicholson method. As a testing system the free propagation of a particle in one dimension is used. The space discretization is based on the high-order finite diferences to approximate accurately the kinetic energy operator in the Hamiltonian. We show that the choice of the more effective method depends on how many wave functions must be calculated during the given time interval to obtain relevant and reasonably accurate information about the system, i.e. on the choice of the time step.

  18. Preconditioners for the spectral multigrid method

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

  19. Preconditioners for the spectral multigrid method

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

    The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

  20. Accuracy considerations for Chebyshev rational approximation method (CRAM) in Burnup calculations

    SciTech Connect

    Pusa, M.

    2013-07-01

    The burnup equations can in principle be solved by computing the exponential of the burnup matrix. However, due to the difficult numerical characteristics of burnup matrices, the problem is extremely stiff and the matrix exponential solution has previously been considered infeasible for an entire burnup system containing over a thousand nuclides. It was recently discovered by the author that the eigenvalues of burnup matrices are generally located near the negative real axis, which prompted introducing the Chebyshev rational approximation method (CRAM) for solving the burnup equations. CRAM can be characterized as the best rational approximation on the negative real axis and it has been shown to be capable of simultaneously solving an entire burnup system both accurately and efficiently. In this paper, the accuracy of CRAM is further studied in the context of burnup equations. The approximation error is analyzed based on the eigenvalue decomposition of the burnup matrix. It is deduced that the relative accuracy of CRAM may be compromised if a nuclide concentration diminishes significantly during the considered time step. Numerical results are presented for two test cases, the first one representing a small burnup system with 36 nuclides and the second one a full a decay system with 1531 nuclides. (authors)

  1. 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.

  2. 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.

  3. An adaptive pseudo-spectral method for reaction diffusion problems

    NASA Technical Reports Server (NTRS)

    Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.

    1987-01-01

    The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

  4. Spectral methods for CFD

    NASA Technical Reports Server (NTRS)

    Zang, Thomas A.; Streett, Craig L.; Hussaini, M. Yousuff

    1989-01-01

    One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched.

  5. 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.

  6. 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. PMID:25386624

  7. 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

  8. Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn–Sham equation

    SciTech Connect

    Zhou, Yunkai; Chelikowsky, James R.; Saad, Yousef

    2014-10-01

    First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn–Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.

  9. Spectral methods for modeling supersonic chemically reacting flow fields

    NASA Technical Reports Server (NTRS)

    Drummond, J. P.; Hussaini, M. Y.; Zang, T. A.

    1985-01-01

    A numerical algorithm was developed for solving the equations describing chemically reacting supersonic flows. The algorithm employs a two-stage Runge-Kutta method for integrating the equations in time and a Chebyshev spectral method for integrating the equations in space. The accuracy and efficiency of the technique were assessed by comparison with an existing implicit finite-difference procedure for modeling chemically reacting flows. The comparison showed that the procedure presented yields equivalent accuracy on much coarser grids as compared to the finite-difference procedure with resultant significant gains in computational efficiency.

  10. Mapping implicit spectral methods to distributed memory architectures

    NASA Technical Reports Server (NTRS)

    Overman, Andrea L.; Vanrosendale, John

    1991-01-01

    Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

  11. Chebyshev Expansion Applied to Dissipative Quantum Systems.

    PubMed

    Popescu, Bogdan; Rahman, Hasan; Kleinekathöfer, Ulrich

    2016-05-19

    To determine the dynamics of a molecular aggregate under the influence of a strongly time-dependent perturbation within a dissipative environment is still, in general, a challenge. The time-dependent perturbation might be, for example, due to external fields or explicitly treated fluctuations within the environment. Methods to calculate the dynamics in these cases do exist though some of these approaches assume that the corresponding correlation functions can be written as a weighted sum of exponentials. One such theory is the hierarchical equations of motion approach. If the environment, however, is described by a complex spectral density or if its temperature is low, these approaches become very inefficient. Therefore, we propose a scheme based on a Chebyshev decomposition of the bath correlation functions and detail the respective quantum master equations within second-order perturbation theory in the environmental coupling. Similar approaches have recently been proposed for systems coupled to Fermionic reservoirs. The proposed scheme is tested for a simple two-level system and compared to existing results. Furthermore, the advantages and disadvantages of the present Chebyshev approach are discussed. PMID:26845380

  12. 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.

  13. 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.

  14. 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.

  15. A spectral element method for the simulation of unsteady incompressible flows with heat transfer

    NASA Technical Reports Server (NTRS)

    Karniadakis, George E.; Patera, Anthony T.

    1986-01-01

    The spectral element method is a high-order finite element technique for solution of the Navier-Stokes and energy equations. In the isoparametric spectral element discretization, the domain is broken up into general brick elements, and the dependent and independent variables represented as high-order tensor-product Lagrangian interpolants through Chebyshev collocation points. The nonlinear and convective terms in the governing equations are treated with explicit collocation, while the pressure and diffusive contributions are handled implicitly using variational projection operators. The method is applied to flow past a cylinder, flow in grooved channels, and natural convection in an enclosure.

  16. Spectral methods on arbitrary grids

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David

    1995-01-01

    Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

  17. 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).

  18. 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.

  19. Spectral methods in fluid dynamics

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

    Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

  20. 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.

  1. A linear-scaling spectral-element method for computing electrostatic potentials.

    PubMed

    Watson, Mark A; Hirao, Kimihiko

    2008-11-14

    A new linear-scaling method is presented for the fast numerical evaluation of the electronic Coulomb potential. Our approach uses a simple real-space partitioning of the system into cubic cells and a spectral-element representation of the density in a tensorial basis of high-order Chebyshev polynomials. Electrostatic interactions between non-neighboring cells are described using the fast multipole method. The remaining near-field interactions are computed in the tensorial basis as a sum of differential contributions by exploiting the numerical low-rank separability of the Coulomb operator. The method is applicable to arbitrary charge densities, avoids the Poisson equation, and does not involve the solution of any systems of linear equations. Above all, an adaptive resolution of the Chebyshev basis in each cell facilitates the accurate and efficient treatment of molecular systems. We demonstrate the performance of our implementation for quantum chemistry with benchmark calculations on the noble gas atoms, long-chain alkanes, and diamond fragments. We conclude that the spectral-element method can be a competitive tool for the accurate computation of electrostatic potentials in large-scale molecular systems. PMID:19045386

  2. 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. PMID:27119059

  3. 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.

  4. Spectral Methods for Thesaurus Construction

    NASA Astrophysics Data System (ADS)

    Shimizu, Nobuyuki; Sugiyama, Masashi; Nakagawa, Hiroshi

    Traditionally, popular synonym acquisition methods are based on the distributional hypothesis, and a metric such as Jaccard coefficients is used to evaluate the similarity between the contexts of words to obtain synonyms for a query. On the other hand, when one tries to compile and clean a thesaurus, one often already has a modest number of synonym relations at hand. Could something be done with a half-built thesaurus alone? We propose the use of spectral methods and discuss their relation to other network-based algorithms in natural language processing (NLP), such as PageRank and Bootstrapping. Since compiling a thesaurus is very laborious, we believe that adding the proposed method to the toolkit of thesaurus constructors would significantly ease the pain in accomplishing this task.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. Spectral methods for inviscid, compressible flows

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. Best quadrature formula on Sobolev class with Chebyshev weight

    NASA Astrophysics Data System (ADS)

    Xie, Congcong

    2008-05-01

    Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f[set membership, variant]KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples.

  19. Efficient Conjunction Assessment using Modified Chebyshev Picard Iteration

    NASA Astrophysics Data System (ADS)

    Probe, A.; Macomber, B.; Read, J.; Woollands, R.; Masher, A.; Junkins, J.

    Conjunction Assessment is one of the most important and computationally expensive components of modern SSA efforts. Timely warnings of potential conjunctions are critical for the protection of valuable space assets. Upgrades to the US Space Surveillance Network (SSN) such as the Space Surveillance Telescope and the new Space Fence become operational, the influx of newly trackable objects will exacerbate the current issues of computational tractability. Modified Chebyshev Picard Iteration (MCPI) is a numerical method for solving ordinary differential equations that can be utilized to efficiently proximate orbits with high accuracy. Unlike, more traditional stepping based integrators; MCPI uses recursive approximation using Chebyshev polynomials to estimate segments of an orbit. The end result of the propagation is orthogonal Chebyshev polynomial approximation of the orbital trajectory; this approximation is analytically differentiable and potentially accurate to machine precision. Once computed, these approximations provide an efficient method for evaluating and comparing the positions of space objects. The reduced cost of catalog propagation and subsequent conjunction probability analysis when using MCPI, allows for significant reduction in the cost to perform high fidelity conjunction assessment. A method for catalog propagation and conjunction assessment using MCPI is presented, along with results from implementation running in a compute cluster environment are presented.

  20. Spectral multigrid methods for elliptic equations

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

    An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.

  1. Some Theoretical Aspects for Elastic Wave Modeling in a Recently Developed Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Wang, X. M.; Seriani, G.; Lin, W. J.

    2006-10-01

    A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media and by the Galerkin approach applied to a partition, in small subdomains, of the original physical domain under investigation. In the present work some mathematical aspects of the method and of the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobbatto collocation points, used in reference element quadrature, are introduced. The related analytical integration formulas are obtained. The standard error estimations and expansion convergence are discussed. In order to improve the computation accuracy and efficiency, an element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence neither the global matrices, nor the effective force vector is assembled. When analytical formula are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without loosing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes spectral element methods much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The second part will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the modelling example comparison of the proposed spectral element method with a conventional finite-element method and a staggered pseudo-spectral method that is to be reported in the other work.

  2. Spectral methods to detect surface mines

    NASA Astrophysics Data System (ADS)

    Winter, Edwin M.; Schatten Silvious, Miranda

    2008-04-01

    Over the past five years, advances have been made in the spectral detection of surface mines under minefield detection programs at the U. S. Army RDECOM CERDEC Night Vision and Electronic Sensors Directorate (NVESD). The problem of detecting surface land mines ranges from the relatively simple, the detection of large anti-vehicle mines on bare soil, to the very difficult, the detection of anti-personnel mines in thick vegetation. While spatial and spectral approaches can be applied to the detection of surface mines, spatial-only detection requires many pixels-on-target such that the mine is actually imaged and shape-based features can be exploited. This method is unreliable in vegetated areas because only part of the mine may be exposed, while spectral detection is possible without the mine being resolved. At NVESD, hyperspectral and multi-spectral sensors throughout the reflection and thermal spectral regimes have been applied to the mine detection problem. Data has been collected on mines in forest and desert regions and algorithms have been developed both to detect the mines as anomalies and to detect the mines based on their spectral signature. In addition to the detection of individual mines, algorithms have been developed to exploit the similarities of mines in a minefield to improve their detection probability. In this paper, the types of spectral data collected over the past five years will be summarized along with the advances in algorithm development.

  3. A semi-implicit spectral method for compressible convection of rotating and density-stratified flows in Cartesian geometry

    NASA Astrophysics Data System (ADS)

    Cai, Tao

    2016-04-01

    In this paper, we have described a 'stratified' semi-implicit spectral method to study compressible convection in Cartesian geometry. The full set of compressible hydrodynamic equations are solved in conservative forms. The numerical scheme is accurate and efficient, based on fast Fourier/sin/cos spectral transforms in the horizontal directions, Chebyshev spectral transform or second-order finite difference scheme in the vertical direction, and second order semi-implicit scheme in time marching of linear terms. We have checked the validity of both the fully pseudo-spectral scheme and the mixed finite-difference pseudo-spectral scheme by studying the onset of compressible convection. The difference of the critical Rayleigh number between our numerical result and the linear stability analysis is within two percent. Besides, we have computed the Mach numbers with different Rayleigh numbers in compressible convection. It shows good agreement with the numerical results of finite difference methods and finite volume method. This model has wide application in studying laminar and turbulent flow. Illustrative examples of application on horizontal convection, gravity waves, and long-lived vortex are given in this paper.

  4. 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.

  5. Quasioptimality of some spectral mixed methods

    NASA Astrophysics Data System (ADS)

    Gopalakrishnan, Jayadeep; Demkowicz, L. F. Leszek F.

    2004-05-01

    In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectral mixed methods, including the Raviart-Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.

  6. A spectral mimetic least-squares method

    DOE PAGESBeta

    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

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. Image contrast enhancement using Chebyshev wavelet moments

    NASA Astrophysics Data System (ADS)

    Uchaev, Dm. V.; Uchaev, D. V.; Malinnikov, V. A.

    2015-12-01

    A new algorithm for image contrast enhancement in the Chebyshev moment transform (CMT) domain is introduced. This algorithm is based on a contrast measure that is defined as the ratio of high-frequency to zero-frequency content in the bands of CMT matrix. Our algorithm enables to enhance a large number of high-spatial-frequency coefficients, that are responsible for image details, without severely degrading low-frequency contributions. To enhance high-frequency Chebyshev coefficients we use a multifractal spectrum of scaling exponents (SEs) for Chebyshev wavelet moment (CWM) magnitudes, where CWMs are multiscale realization of Chebyshev moments (CMs). This multifractal spectrum is very well suited to extract meaningful structures on images of natural scenes, because these images have a multifractal character. Experiments with test images show some advantages of the proposed algorithm as compared to other widely used image enhancement algorithms. The main advantage of our algorithm is the following: the algorithm very well highlights image details during image contrast enhancement.

  12. 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.

  13. 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.

  14. 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.

  15. Fuzzy stochastic elements method. Spectral approach

    NASA Astrophysics Data System (ADS)

    Sniady, Pawel; Mazur-Sniady, Krystyna; Sieniawska, Roza; Zukowski, Stanislaw

    2013-05-01

    We study a complex dynamic problem, which concerns a structure with uncertain parameters subjected to a stochastic excitation. Formulation of such a problem introduces fuzzy random variables for parameters of the structure and fuzzy stochastic processes for the load process. The uncertainty has two sources, namely the randomness of structural parameters such as geometry characteristics, material and damping properties, load process and imprecision of the theoretical model and incomplete information or uncertain data. All of these have a great influence on the response of the structure. By analyzing such problems we describe the random variability using the probability theory and the imprecision by use of fuzzy sets. Due to the fact that it is difficult to find an analytic expression for the inversion of the stochastic operator in the stochastic differential equation, a number of approximate methods have been proposed in the literature which can be connected to the finite element method. To evaluate the effects of excitation in the frequency domain we use the spectral density function. The spectral analysis is widely used in stochastic dynamics field of linear systems for stationary random excitation. The concept of the evolutionary spectral density is used in the case of non-stationary random excitation. We solve the considered problem using fuzzy stochastic finite element method. The solution is based on the idea of a fuzzy random frequency response vector for stationary input excitation and a transient fuzzy random frequency response vector for the fuzzy non-stationary one. We use the fuzzy random frequency response vector and the transient fuzzy random frequency response vector in the context of spectral analysis in order to determine the influence of structural uncertainty on the fuzzy random response of the structure. We study a linear system with random parameters subjected to two particular cases of stochastic excitation in a frequency domain. The first one

  16. Spectral methods for the equations of classical density-functional theory: relaxation dynamics of microscopic films.

    PubMed

    Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim

    2012-03-28

    We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying. PMID:22462841

  17. 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.

  18. Chebyshev Polynomials Are Not Always Optimal

    NASA Technical Reports Server (NTRS)

    Fischer, B.; Freund, E.

    1989-01-01

    The authors are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.

  19. A spectral method for spatial downscaling.

    PubMed

    Reich, Brian J; Chang, Howard H; Foley, Kristen M

    2014-12-01

    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 article, 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. PMID:24965037

  20. A Spectral Method for Spatial Downscaling

    PubMed Central

    Reich, Brian J.; Chang, Howard H.; Foley, Kristen M.

    2014-01-01

    Summary 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 article, 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. PMID:24965037

  1. A spectral projection method for transmission eigenvalues

    NASA Astrophysics Data System (ADS)

    Zeng, Fang; Sun, JiGuang; Xu, LiWei

    2016-08-01

    In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides if the region contains eigenvalue(s) or not. It is particularly suitable to test if zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.

  2. Spectral method for a kinetic swarming model

    SciTech Connect

    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.

  3. Spectral method for a kinetic swarming model

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    In this paper 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. We observe that the kinetic model captures key features such as vortex formation and traveling waves.

  4. The iterative solution of the problem of orbit determination using Chebyshev series

    NASA Technical Reports Server (NTRS)

    Feagin, T.

    1975-01-01

    A method of orbit determination is investigated which employs Picard iteration and Chebyshev series. The method is applied to the problem of determining the orbit of an earth satellite from range and range-rate observations contaminated by noise. It is shown to be readily applicable and to possess linear convergence.

  5. Modelling the post-Newtonian test-mass gravitational wave flux function for compact binary systems using Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Porter, Edward K.

    2006-10-01

    We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these intermediate mass ratio inspiral events (IMRI) are expected to be seen in both the ground- and space-based detectors. Starting with the post-Newtonian expansion from black hole perturbation theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster convergence than either post-Newtonian- or Padé-based methods. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. We find that at the last stable orbit, the error between the Chebyshev approximation and a numerically calculated flux is reduced, <1.8%, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general >0.99, and smaller errors, <1/10%, in the estimation of the chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the intermediate test-mass case, the new Chebyshev template is superior to both PN and Padé approximant templates, especially at lower orders of approximation.

  6. 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.

  7. 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.

  8. Spectral Methods Using Rational Basis Functions on an Infinite Interval

    NASA Astrophysics Data System (ADS)

    Boyd, John P.

    1987-03-01

    By using the map y = L cot( t) where L is a constant, differential equations on the interval yɛ [- ∞, ∞] can be transformed into tɛ [0, π] and solved by an ordinary Fourier series. In this article, earlier work by Grosch and Orszag ( J. Comput. Phys.25, 273 (1977)), Cain, Ferziger, and Reynolds ( J. Comput. Phys.56, 272 (1984)), and Boyd ( J. Comput. Phys.25, 43 (1982); 57, 454 (1985); SIAM J. Numer. Anal. (1987)) is extended in several ways. First, the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y-plane. Second, Galerkin's method will convert differential equations with polynomial or rational coefficients into banded matrix problems. Third, with orthogonal rational functions it is possible to obtain exponential convergence even for u( y) that asymptote to a constant although this behavior would wreck alternatives such as Hermite or sinc expansions. Fourth, boundary conditions are usually "natural" rather than "essential" in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions. Fifth, mapping a finite interval to an infinite one and then applying the rational Chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities. These concepts are illustrated by five numerical examples.

  9. Spectral density method to Anderson-Holstein model

    SciTech Connect

    Chebrolu, Narasimha Raju Chatterjee, Ashok

    2015-06-24

    Two-parameter spectral density function of a magnetic impurity electron in a non-magnetic metal is calculated within the framework of the Anderson-Holstein model using the spectral density approximation method. The effect of electron-phonon interaction on the spectral function is investigated.

  10. Method to analyze remotely sensed spectral data

    DOEpatents

    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.

  11. Spectral distributed Lagrange multiplier method: algorithm and benchmark tests

    NASA Astrophysics Data System (ADS)

    Dong, Suchuan; Liu, Dong; Maxey, Martin R.; Karniadakis, George Em

    2004-04-01

    We extend the formulation of the distributed Lagrange multiplier (DLM) approach for particulate flows to high-order methods within the spectral/ hp element framework. We implement the rigid-body motion constraint inside the particle via a penalty method. The high-order DLM method demonstrates spectral convergence rate, i.e. discretization errors decrease exponentially as the order of spectral polynomials increases. We provide detailed comparisons between the spectral DLM method, direct numerical simulations, and the force coupling method for a number of 2D and 3D benchmark flow problems. We also validate the spectral DLM method with available experimental data for a transient problem. The new DLM method can potentially be very effective in many-moving body problems, where a smaller number of grid points is required in comparison with low-order methods.

  12. 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.

  13. 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.

  14. A broadband spectral inversion method for spatial heterodyne spectroscopy

    NASA Astrophysics Data System (ADS)

    Cai, Qisheng; Bin, Xiangli; Du, Shusong

    2014-11-01

    Spatial heterodyne spectroscopy (SHS) is a Fourier-transform spectroscopic technique with many advantages, such as high throughput, good robustness (no moving parts), and high resolving power. However, in the basic theory of SHS, the relationship between the wavenumber and the frequency of the interferogram is approximated to be linear. This approximation limits the spectral range of a spatial heterodyne spectrometer to a narrow band near the Littrow wavenumber. Several methods have been developed to extend the spectral range of the SHS. They use echelle gratings or tunable pilot mirrors to make a SHS instrument work at multiple narrow spectral bands near different Littrow wavenumbers. These solutions still utilize the linear relationship between the wavenumber and the frequency of the interferogram. But they need to separate different spectral bands, and this will increase the difficulty of post processing and the complexity of the SHS system. Here, we solve this problem from another perspective: making a SHS system work at one broad spectral band instead of multiple narrow spectral bands. As in a broad spectral range, the frequency of the interferogram will not be linear with respect to the wavenumber anymore. According to this non-linear relationship, we propose a broadband spectral inversion method based on the stationary phase theory. At first, we describe the principles and the basic characters of SHS. Then, the narrow band limitation is analyzed and the broadband spectral inversion method is elaborated. In the end, we present a parameter design example of the SHS system according to a given spectral range, and the effectiveness of this method is validated with a spectral simulation example. This broadband spectral inversion method can be applied to the existing SHS system without changing or inserting any moving components. This method retains the advantages of SHS and there is almost no increase in complexity for post processing.

  15. 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.

  16. Spectral methods for electromagnetic propagation and diffraction

    NASA Astrophysics Data System (ADS)

    Felsen, L. B.

    1990-03-01

    Analysis of source-excited time-harmonic and transient electromagnetic wave propagation in complicated environments, wave scattering by complicated targets, or wave penetration into complex structures generally requires decomposition of the incident field into elementary constituents, tracking each constituent through the environment or past the scatter, and recombining at the observer. The elementary constituents are spectral objects such as plane waves, cylindrical waves, conical waves, modal fields, ray field, etc. Under transient conditions, the recombination is conventionally performed first on the time-harmonic constituents, with frequency synthesis performed thereafter, but one may alternatively, by a less conventional approach, employ transient constituents (transient plane or cylindrical waves, etc.) and perform the remaining spatial synthesis thereafter. Viewed from this general perspective, there exists an enormous flexibility in the selection of the spectral objects, and of hybrid combinations, for analysis of a particular propagation or scattering problem. It is the objective of the proposed research to examine the various spectral options in their most fundamental terms, study the relation between them, and then assess which option best addresses a particular propagation or scattering phenomenon.

  17. Feature Transformation Detection Method with Best Spectral Band Selection Process for Hyper-spectral Imaging

    NASA Astrophysics Data System (ADS)

    Chen, Hai-Wen; McGurr, Mike; Brickhouse, Mark

    2015-11-01

    We present a newly developed feature transformation (FT) detection method for hyper-spectral imagery (HSI) sensors. In essence, the FT method, by transforming the original features (spectral bands) to a different feature domain, may considerably increase the statistical separation between the target and background probability density functions, and thus may significantly improve the target detection and identification performance, as evidenced by the test results in this paper. We show that by differentiating the original spectral, one can completely separate targets from the background using a single spectral band, leading to perfect detection results. In addition, we have proposed an automated best spectral band selection process with a double-threshold scheme that can rank the available spectral bands from the best to the worst for target detection. Finally, we have also proposed an automated cross-spectrum fusion process to further improve the detection performance in lower spectral range (<1000 nm) by selecting the best spectral band pair with multivariate analysis. Promising detection performance has been achieved using a small background material signature library for concept-proving, and has then been further evaluated and verified using a real background HSI scene collected by a HYDICE sensor.

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

    SciTech Connect

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

    2014-10-15

    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.

  19. Inflationary reheating classes via spectral methods

    NASA Astrophysics Data System (ADS)

    Bassett, Bruce A.

    1998-07-01

    Inflationary reheating is almost completely controlled by the Floquet indices, μk. Using spectral theory, we demonstrate that the stability bands (where μk=0) of the Mathieu and Lamé equations are destroyed even in Minkowski spacetime, leaving a fractal Cantor set or a measure zero set of stable modes in the cases, where the inflaton evolves in an almost-periodic or stochastic manner, respectively. These two types of potential model the expected multi-field and quantum back reaction effects during reheating.

  20. 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.

  1. Modified Chebyshev Picard Iteration for Efficient Numerical Integration of Ordinary Differential Equations

    NASA Astrophysics Data System (ADS)

    Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.

    2013-09-01

    Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are

  2. 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. PMID:27504247

  3. 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.

  4. 3D parallel computations of turbofan noise propagation using a spectral element method

    NASA Astrophysics Data System (ADS)

    Taghaddosi, Farzad

    2006-12-01

    A three-dimensional code has been developed for the simulation of tone noise generated by turbofan engine inlets using computational aeroacoustics. The governing equations are the linearized Euler equations, which are further simplified to a set of equations in terms of acoustic potential, using the irrotational flow assumption, and subsequently solved in the frequency domain. Due to the special nature of acoustic wave propagation, the spatial discretization is performed using a spectral element method, where a tensor product of the nth-degree polynomials based on Chebyshev orthogonal functions is used to approximate variations within hexahedral elements. Non-reflecting boundary conditions are imposed at the far-field using a damping layer concept. This is done by augmenting the continuity equation with an additional term without modifying the governing equations as in PML methods. Solution of the linear system of equations for the acoustic problem is based on the Schur complement method, which is a nonoverlapping domain decomposition technique. The Schur matrix is first solved using a matrix-free iterative method, whose convergence is accelerated with a novel local preconditioner. The solution in the entire domain is then obtained by finding solutions in smaller subdomains. The 3D code also contains a mean flow solver based on the full potential equation in order to take into account the effects of flow variations around the nacelle on the scattering of the radiated sound field. All aspects of numerical simulations, including building and assembling the coefficient matrices, implementation of the Schur complement method, and solution of the system of equations for both the acoustic and mean flow problems are performed on multiprocessors in parallel using the resources of the CLUMEQ Supercomputer Center. A large number of test cases are presented, ranging in size from 100 000-2 000 000 unknowns for which, depending on the size of the problem, between 8-48 CPU's are

  5. [Spectral discrimination method information divergence combined with gradient angle].

    PubMed

    Zhang, Xiu-bao; Yuan, Yan; Jing, Juan-juan; Sun, Cheng-ming; Wang, Qian

    2011-03-01

    The present paper proposes a spectral discrimination method combining spectral information divergence with spectral gradient angle (SID x tan(SGA(pi/2)) which overcomes the shortages of the existing methods which can not take the whole spectral shape and local characteristics into account simultaneously. Using the simulation spectra as input data, according to the interferogram acquirement principle and spectrum recovery algorithm of the temporally and spatially modulated Fourier transform imaging spectrometer (TSMFTIS), we simulated the distortion spectra recovery process of the TMSFTIS in different maximum mix ratio and distinguished the difference between the recovered spectra and the true spectrum by different spectral discrimination methods. The experiment results show that the SID x tan(SGA(pi/2)) can not only identify the similarity of the whole spectral shapes, but also distinguish local differences of the spectral characteristics. A comparative study was conducted among the different discrimination methods. The results have validated that the SID x tan(SGA(pi/2)) has a significant improvement in the discriminatory ability. PMID:21595255

  6. 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.

  7. 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.

  8. A divisive spectral method for network community detection

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

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

  9. Comparison of spectral analysis methods for characterizing brain oscillations

    PubMed Central

    van Vugt, Marieke K.; Sederberg, Per B.; Kahana, Michael J.

    2007-01-01

    Spectral analysis methods are now routinely used in electrophysiological studies of human and animal cognition. Although a wide variety of spectral methods has been used, the ways in which these methods differ are not generally understood. Here we use simulation methods to characterize the similarities and differences between three spectral analysis methods: wavelets, multitapers and Pepisode. Pepisode is a novel method that quantifies the fraction of time that oscillations exceed amplitude and duration thresholds. We show that wavelets and Pepisode used side-by-side helps to disentangle length and amplitude of a signal. Pepisode is especially sensitive to fluctuations around its thresholds, puts frequencies on a more equal footing, and is sensitive to long but low-amplitude signals. In contrast, multitaper methods are less sensitive to weak signals, but are very frequency-specific. If frequency-specificity is not essential, then wavelets and Pepisode are recommended. PMID:17292478

  10. 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.

  11. 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.

  12. Spectral radiative property control method based on filling solution

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  13. Spectral multigrid methods with applications to transonic potential flow

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.

  14. Spectral multigrid methods with applications to transonic potential flow

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    Spectral multigrid methods are demonstrated to be a competitive technique for solving the transonic potential flow equation. The spectral discretization, the relaxation scheme, and the multigrid techniques are described in detail. Significant departures from current approaches are first illustrated on several linear problems. The principal applications and examples, however, are for compressible potential flow. These examples include the relatively challenging case of supercritical flow over a lifting airfoil.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. Spatio-spectral Maximum Entropy Method. I. Formulation and Test

    NASA Astrophysics Data System (ADS)

    Bong, Su-Chan; Lee, Jeongwoo; Gary, Dale E.; Yun, Hong Sik

    2006-01-01

    The spatio-spectral maximum entropy method (SSMEM) has been developed by Komm and coworkers in 1997 for use with solar multifrequency interferometric observation. In this paper we further improve the formulation of the SSMEM to establish it as a tool for astronomical imaging spectroscopy. We maintain their original idea that spectral smoothness at neighboring frequencies can be used as an additional a priori assumption in astrophysical problems and that this can be implemented by adding a spectral entropy term to the usual maximum entropy method (MEM) formulation. We, however, address major technical difficulties in introducing the spectral entropy into the imaging problem that are not encountered in the conventional MEM. These include calculation of the spectral entropy in a generally frequency-dependent map grid, simultaneous adjustment of the temperature variables and Lagrangian multipliers in the spatial and spectral domain, and matching the solutions to the observational constraints at a large number of frequencies. We test the performance of the SSMEM in comparison with the conventional MEM.

  1. Preconditioned conjugate residual methods for the solution of spectral equations

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

    Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

  2. 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.

  3. 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.

  4. 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

  5. Radon transforms and Gegenbauer-Chebyshev integrals, I

    NASA Astrophysics Data System (ADS)

    Rubin, Boris

    2016-04-01

    We suggest new modifications of the Helgason's support theorem and description of the kernel for the hyperplane Radon transform and its dual. The assumptions for functions are formulated in integral terms and close to minimal. The proofs rely on the properties of the Gegenbauer-Chebyshev integrals which generalize Abel type fractional integrals on the positive half-line.

  6. 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.

  7. [High Precision Spectral Calibration Method of Fourier Interferometric Spectrometer].

    PubMed

    Lin, Jun; Shao, Jun; Song, Chao-yu; Li, Yun-wei; Lei, Yu-fei

    2015-12-01

    The Fourier interferometric spectrometer (FIS) acquires the interference data information of the spectrum and during the spectrum data processing, a series of spectrum reconstruction will be performed on the interference information to obtain the final spectrum information data. The spectral calibration is the key step to spectrum reconstruction of FIS, which directly determines accuracy and availability of the spectrum results. This paper introduces the basic ideas and calibration accuracy about the spectral calibration for the FIS and puts forward a new spectral calibration method based on calculating the precise value of the total optical path difference (TOPD). The TOPD of FIS is difficult to be precisely measured, but it is the core and key to the spectral calibration. In order to calculate the precise TOPD, this paper proposes the idea how to traverse the TOPD and analyzes the spectrum drift. During the calibration, all the possible values of the TOPD participate in the spectrum reconstruction flow to carry out spectrum recovery and analysis. Ultimately the TOPD with the minimum spectrum drift will be achieved, namely solution value of the TOPD. This method can accurately resolve the TOPD of the FIS and then calibrate the spectrum with high accuracy. In addition, the paper introduces the detailed and complete spectral calibration flow and obtains the center wavelength value of every band and wavenumber resolution. Moreover, the paper designs the main parameters of the typical FIS and generates its simulation interference data. Using the above method to calibrate the simulation data, the analysis and verification of the spectral calibration results proves that the calibration precision of wavenumber resolution achieves 0.000 25 cm⁻¹ or above. PMID:26964245

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Hyperspectral image-based methods for spectral diversity

    NASA Astrophysics Data System (ADS)

    Sotomayor, Alejandro; Medina, Ollantay; Chinea, J. D.; Manian, Vidya

    2015-05-01

    Hyperspectral images are an important tool to assess ecosystem biodiversity. To obtain more precise analysis of biodiversity indicators that agree with indicators obtained using field data, analysis of spectral diversity calculated from images have to be validated with field based diversity estimates. The plant species richness is one of the most important indicators of biodiversity. This indicator can be measured in hyperspectral images considering the Spectral Variation Hypothesis (SVH) which states that the spectral heterogeneity is related to spatial heterogeneity and thus to species richness. The goal of this research is to capture spectral heterogeneity from hyperspectral images for a terrestrial neo tropical forest site using Vector Quantization (VQ) method and then use the result for prediction of plant species richness. The results are compared with that of Hierarchical Agglomerative Clustering (HAC). The validation of the process index is done calculating the Pearson correlation coefficient between the Shannon entropy from actual field data and the Shannon entropy computed in the images. One of the advantages of developing more accurate analysis tools would be the extension of the analysis to larger zones. Multispectral image with a lower spatial resolution has been evaluated as a prospective tool for spectral diversity.

  14. 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.

  15. A Spectral Adaptive Mesh Refinement Method for the Burgers equation

    NASA Astrophysics Data System (ADS)

    Nasr Azadani, Leila; Staples, Anne

    2013-03-01

    Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh.

  16. 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.

  17. Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials

    NASA Astrophysics Data System (ADS)

    Shakiba, Ali; Hooshmandasl, Mohammad Reza; Meybodi, Mohsen Alambardar

    2016-06-01

    In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.

  18. Calculating the spectrum of anisotropic waveguides using a spectral method.

    PubMed

    Zharnikov, T V; Syresin, D E; Hsu, C-J

    2013-09-01

    The computation of the spectrum of a waveguide with arbitrary anisotropy with spatial dependence is a challenging task due to the coupling between axial and azimuthal harmonics. This problem is tackled in cylindrical coordinates by extending a spectral method for the general case. By considering the matrix representation of the operator on the right-hand side of the governing equations, the latter are exactly reformulated as an infinite set of integro-differential equations. Essential part of this study is taking into account the coupling of different harmonics, which becomes evident from the kernels of these equations. Provided a waveguide is translationally invariant in the axial direction, the coupling of axial harmonics vanishes. A practical approximation and truncation procedure yields a generalized eigenvalue problem, which can be solved numerically to obtain the entire spectrum of the operator and to construct the dispersion curves for the eigenmodes. The spectral method is tested against the results from the measurements of dispersion curves for the monopole, dipole, and quadrupole normal modes of scaled boreholes in tilted transverse isotropy anisotropic rock sample. Besides, the comparison of dispersion curves calculated by the spectral method and those computed from the synthetic data is discussed. PMID:23967909

  19. Power spectrum of the fluctuation of Chebyshev's prime counting function

    NASA Astrophysics Data System (ADS)

    Lan, Boon Leong; Yong, Shaohen

    2006-02-01

    The one-sided power spectrum of the fluctuation of Chebyshev's weighted prime counting function is numerically estimated based on samples of the fluctuating function of different sizes. The power spectrum is also estimated analytically for large frequency based on Riemann hypothesis and the exact formula for the fluctuating function in terms of all the non-trivial Riemann zeroes. Our analytical estimate is consistent with our numerical estimate of a 1/f2 power spectrum.

  20. 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.

  1. On a spectral method for forward gravity field modelling

    NASA Astrophysics Data System (ADS)

    Root, B. C.; Novák, P.; Dirkx, D.; Kaban, M.; van der Wal, W.; Vermeersen, L. L. A.

    2016-07-01

    This article reviews a spectral forward gravity field modelling method that was initially designed for topographic/isostatic mass reduction of gravity data. The method transforms 3D spherical density models into gravitational potential fields using a spherical harmonic representation. The binomial series approximation in the approach, which is crucial for its computational efficiency, is examined and an error analysis is performed. It is shown that, this method cannot be used for density layers in crustal and upper mantle regions, because it results in large errors in the modelled potential field. Here, a correction is proposed to mitigate this erroneous behaviour. The improved method is benchmarked with a tesseroid gravity field modelling method and is shown to be accurate within ±4 mGal for a layer representing the Moho density interface, which is below other errors in gravity field studies. After the proposed adjustment the method can be used for the global gravity modelling of the complete Earth's density structure.

  2. Spatial and Spectral Methods for Weed Detection and Localization

    NASA Astrophysics Data System (ADS)

    Vioix, Jean-Baptiste; Douzals, Jean-Paul; Truchetet, Frédéric; Assémat, Louis; Guillemin, Jean-Philippe

    2002-12-01

    This study concerns the detection and localization of weed patches in order to improve the knowledge on weed-crop competition. A remote control aircraft provided with a camera allowed to obtain low cost and repetitive information. Different processings were involved to detect weed patches using spatial then spectral methods. First, a shift of colorimetric base allowed to separate the soil and plant pixels. Then, a specific algorithm including Gabor filter was applied to detect crop rows on the vegetation image. Weed patches were then deduced from the comparison of vegetation and crop images. Finally, the development of a multispectral acquisition device is introduced. First results for the discrimination of weeds and crops using the spectral properties are shown from laboratory tests. Application of neural networks were mostly studied.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

    NASA Astrophysics Data System (ADS)

    Garbanzo-Salas, Marcial; Hocking, Wayne. K.

    2015-09-01

    In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.

  8. Method for evaluating moisture tensions of soils using spectral data

    NASA Technical Reports Server (NTRS)

    Peterson, John B. (Inventor)

    1982-01-01

    A method is disclosed which permits evaluation of soil moisture utilizing remote sensing. Spectral measurements at a plurality of different wavelengths are taken with respect to sample soils and the bidirectional reflectance factor (BRF) measurements produced are submitted to regression analysis for development therefrom of predictable equations calculated for orderly relationships. Soil of unknown reflective and unknown soil moisture tension is thereafter analyzed for bidirectional reflectance and the resulting data utilized to determine the soil moisture tension of the soil as well as providing a prediction as to the bidirectional reflectance of the soil at other moisture tensions.

  9. A GIHS-based spectral preservation fusion method for remote sensing images using edge restored spectral modulation

    NASA Astrophysics Data System (ADS)

    Zhou, Xiran; Liu, Jun; Liu, Shuguang; Cao, Lei; Zhou, Qiming; Huang, Huawen

    2014-02-01

    High spatial resolution and spectral fidelity are basic standards for evaluating an image fusion algorithm. Numerous fusion methods for remote sensing images have been developed. Some of these methods are based on the intensity-hue-saturation (IHS) transform and the generalized IHS (GIHS), which may cause serious spectral distortion. Spectral distortion in the GIHS is proven to result from changes in saturation during fusion. Therefore, reducing such changes can achieve high spectral fidelity. A GIHS-based spectral preservation fusion method that can theoretically reduce spectral distortion is proposed in this study. The proposed algorithm consists of two steps. The first step is spectral modulation (SM), which uses the Gaussian function to extract spatial details and conduct SM of multispectral (MS) images. This method yields a desirable visual effect without requiring histogram matching between the panchromatic image and the intensity of the MS image. The second step uses the Gaussian convolution function to restore lost edge details during SM. The proposed method is proven effective and shown to provide better results compared with other GIHS-based methods.

  10. Automated method for RNFL segmentation in spectral domain OCT

    NASA Astrophysics Data System (ADS)

    Paranjape, Amit S.; Elmaanaoui, Badr; Dewelle, Jordan; Rylander, H. Grady; Milner, Thomas E.

    2008-02-01

    We introduce a method based on optical reflectivity changes to segment the retinal nerve fiber layer (RNFL) in images recorded using swept source spectral domain optical coherence tomography (OCT). The segmented image is used to determine the RNFL thickness. Simple filtering followed by edge detecting techniques can successfully be applied to segment the RNFL from recorded images and estimate RNFL thickness. The method is computationally more efficient than previously reported approaches. Higher computational efficiency allows faster segmentation and provides the ophthalmologist segmented retinal images that better utilize advantages of spectral domain OCT instrumentation. OCT B-scan and fundus images of the retina are recorded for 5 patients. The segmentation method is applied on B-scan images recorded from all patients. An expert ophthalmologist separately demarcates the RNFL layer in the OCT images from the same patients in each B-scan image. Results from automated image processing software are compared to the boundary demarcated by the expert ophthalmologist. The absolute error between the boundaries demarcated by the expert and the algorithm is expressed in terms of area and is used as an error metric. Ability of the algorithm to accurately segment the RNFL in comparison with an expert ophthalmologist is reported.

  11. Semi-spectral method for the Wigner equation

    NASA Astrophysics Data System (ADS)

    Furtmaier, O.; Succi, S.; Mendoza, M.

    2016-01-01

    We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into L2 (Rd) basis functions in momentum-space to obtain a system of first-order advection-reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations. The method is validated for the case of particles subject to a one-dimensional (an-)harmonic and Morse potential using finite-differences for the advection part. Thereby, we verify the second order of convergence and observe non-classical behavior in the evolution of the Wigner function.

  12. Global seismic waveform tomography based on the spectral element method.

    NASA Astrophysics Data System (ADS)

    Capdeville, Y.; Romanowicz, B.; Gung, Y.

    2003-04-01

    Because seismogram waveforms contain much more information on the earth structure than body wave time arrivals or surface wave phase velocities, inversion of complete time-domain seismograms should allow much better resolution in global tomography. In order to achieve this, accurate methods for the calculation of forward propagation of waves in a 3D earth need to be utilized, which presents theoretical as well as computational challenges. In the past 8 years, we have developed several global 3D S velocity models based on long period waveform data, and a normal mode asymptotic perturbation formalism (NACT, Li and Romanowicz, 1996). While this approach is relatively accessible from the computational point of view, it relies on the assumption of smooth heterogeneity in a single scattering framework. Recently, the introduction of the spectral element method (SEM) has been a major step forward in the computation of seismic waveforms in a global 3D earth with no restrictions on the size of heterogeneities (Chaljub, 2000). While this method is computationally heavy when the goal is to compute large numbers of seismograms down to typical body wave periods (1-10 sec), it is much more accessible when restricted to low frequencies (T>150sec). When coupled with normal modes (e.g. Capdeville et al., 2000), the numerical computation can be restricted to a spherical shell within which heterogeneity is considered, further reducing the computational time. Here, we present a tomographic method based on the non linear least square inversion of time domain seismograms using the coupled method of spectral elements and modal solution. SEM/modes are used for both the forward modeling and to compute partial derivatives. The parametrisation of the model is also based on the spectral element mesh, the "cubed sphere" (Sadourny, 1972), which leads to a 3D local polynomial parametrization. This parametrization, combined with the excellent earth coverage resulting from the full 3D theory used

  13. Application of spectral subtraction method on enhancement of electrolarynx speech.

    PubMed

    Liu, Hanjun; Zhao, Qin; Wan, Mingxi; Wang, Supin

    2006-07-01

    Although electrolarynx (EL) serves as an important method of phonation for the laryngectomees, the resulting speech is of poor intelligibility due to the presence of a steady background noise caused by the instrument, even worse in the case of additive noise. This paper investigates the problem of EL speech enhancement by taking into account the frequency-domain masking properties of the human auditory system. One approach is incorporating an auditory masking threshold (AMT) for parametric adaptation in a subtractive-type enhancement process. The other is the supplementary AMT (SAMT) algorithm, which applies a cross-correlation spectral subtraction (CCSS) approach as a post-processing scheme to enhancing EL speech dealt with the AMT method. The performance of these two algorithms was evaluated as compared to the power spectral subtraction (PSS) algorithm. The best performance of EL speech enhancement was associated with the SAMT algorithm, followed by the AMT algorithm and the PSS algorithm. Acoustic and perceptual analyses indicated that the AMT and SAMT algorithms achieved the better performances of noise reduction and the enhanced EL speech was more pleasant to human listeners as compared to the PSS algorithm. PMID:16875235

  14. 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.

  15. 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.

  16. Fourier time spectral method for subsonic and transonic flows

    NASA Astrophysics Data System (ADS)

    Zhan, Lei; Liu, Feng; Papamoschou, Dimitri

    2016-06-01

    The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

  17. Fourier time spectral method for subsonic and transonic flows

    NASA Astrophysics Data System (ADS)

    Zhan, Lei; Liu, Feng; Papamoschou, Dimitri

    2016-01-01

    The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

  18. 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.

  19. 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

  20. 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.

  1. Multi-Dimensional Spectral Difference Method for Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Liu, Yen; Vinokur, Marcel

    2005-01-01

    A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

  2. 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

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

    PubMed

    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

  4. How Accurately Do Spectral Methods Estimate Effective Elastic Thickness?

    NASA Astrophysics Data System (ADS)

    Perez-Gussinye, M.; Lowry, A. R.; Watts, A. B.; Velicogna, I.

    2002-12-01

    The effective elastic thickness, Te, is an important parameter that has the potential to provide information on the long-term thermal and mechanical properties of the the lithosphere. Previous studies have estimated Te using both forward and inverse (spectral) methods. While there is generally good agreement between the results obtained using these methods, spectral methods are limited because they depend on the spectral estimator and the window size chosen for analysis. In order to address this problem, we have used a multitaper technique which yields optimal estimates of the bias and variance of the Bouguer coherence function relating topography and gravity anomaly data. The technique has been tested using realistic synthetic topography and gravity. Synthetic data were generated assuming surface and sub-surface (buried) loading of an elastic plate with fractal statistics consistent with real data sets. The cases of uniform and spatially varying Te are examined. The topography and gravity anomaly data consist of 2000x2000 km grids sampled at 8 km interval. The bias in the Te estimate is assessed from the difference between the true Te value and the mean from analyzing 100 overlapping windows within the 2000x2000 km data grids. For the case in which Te is uniform, the bias and variance decrease with window size and increase with increasing true Te value. In the case of a spatially varying Te, however, there is a trade-off between spatial resolution and variance. With increasing window size the variance of the Te estimate decreases, but the spatial changes in Te are smeared out. We find that for a Te distribution consisting of a strong central circular region of Te=50 km (radius 600 km) and progressively smaller Te towards its edges, the 800x800 and 1000x1000 km window gave the best compromise between spatial resolution and variance. Our studies demonstrate that assumed stationarity of the relationship between gravity and topography data yields good results even in

  5. 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

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

    SciTech Connect

    David W. Freeman

    2000-06-04

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

  7. 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.

  8. Spectral finite-element methods for parametric constrained optimization problems.

    SciTech Connect

    Anitescu, M.; Mathematics and Computer Science

    2009-01-01

    We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.

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

    DOEpatents

    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.

  10. 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.

  11. 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.

  12. Tracking discontinuities in hyperbolic conservation laws with spectral accuracy

    NASA Astrophysics Data System (ADS)

    Touil, H.; Hussaini, M. Y.; Sussman, M.

    2007-08-01

    It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite-order convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New York, 2001; C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin Heidelberg, 2006]). If a discontinuity or a shock is present in the solution, this advantage is lost. There have been attempts to recover exponential convergence in such cases with rather limited success. The aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure, which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space. Spectral convergence is demonstrated in the case of the inviscid Burgers equation and the one-dimensional Euler equations.

  13. Magnetic depths to basalts: extension of spectral depths method

    NASA Astrophysics Data System (ADS)

    Clifton, Roger

    2015-11-01

    Although spectral depth determination has played a role in magnetic interpretation for over four decades, automating the procedure has been inhibited by the need for manual intervention. This paper introduces the concept of a slope spectrum of an equivalent layer, to be used in an automated depth interpretation algorithm suitable for application to very large datasets such as the complete Northern Territory aeromagnetic grid. In order to trace the extensive basalts across the Northern Territory, profiles of spectral depths have been obtained at 5 km intervals across the NT stitched grid of total magnetic intensity (TMI). Each profile is a graph from 0 to 1000 m of the probability of a magnetic layer occurring at each depth. Automating the collection of the 50 000 profiles required the development of a formula that relates slopes along the power spectrum to depths to an equivalent magnetic layer. Model slabs were populated with a large number of randomly located dipoles and their power spectra correlated with modelled depth to provide the formula. Depth profiles are too noisy to be used singly, but when a series of depth profiles are lined up side-by-side as a transect, significant magnetic layers can be traced for large distances. Transects frequently show a second layer. The formula is quite general in its derivation and would apply to any mid-latitude area where significant magnetic bodies can be modelled as extensive layers. Because the method requires a radial power spectrum, it fails to provide signal at depths much shallower than the flight line spacing. The method is convenient for a fast first pass at depth estimation, but its horizontal resolution is rather coarse and errors can be quite large.

  14. 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.

  15. Calculation of infrared system operating distance by spectral bisection method

    NASA Astrophysics Data System (ADS)

    Zhao, Yu; Wu, Ping; Sun, Wenfang

    2014-03-01

    During the transmission of infrared radiation, the atmospheric transmittance could be a complex parameter due to the absorbing and scattering of atmosphere, as well as the influences from the environment and transmission distance. With the help of a spectral bisection method, a new assessing formula and solution is raised by calculating the operating distance of infrared system. In the small segments, MODTRAN can be used to figure out the percentage of penetration, which is called by advanced program, so as to get the infrared radiation in those segments. The calculated data of the segments were summed up and used to calculate the operating distance of the infrared system. Compared with the conventional calculation methods that the transmittance was used as a constant or a average, The calculation precise of the operating distance is highly increased by this method the results of all small segments by comparing with the traditional methods. The whole computing process becomes more clear and effective by taking the influences from visibility of atmosphere, altitude, targets zenith angle and spatial frequency into consideration, and by building an instant monitoring system of the operating distance. The final computing result and real effecting distance are based on the general simulation for penetration rate and the tendency of operating distance in all conditions.

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

    NASA Astrophysics Data System (ADS)

    Pinault, Jean Louis

    1991-07-01

    A general deconvolution method applicable to X and gamma ray spectrometry is proposed. Using new spectral analysis methods, it is applied to an actual case: the accurate on-line analysis of three elements (Ca, Si, Fe) in a cement plant using neutron capture gamma rays. Neutrons are provided by a low activity (5 μg) 252Cf source; the detector is a BGO 3 in. × 8 in. scintillator. The principle of the method rests on the Fourier transform of the spectrum. The search for peaks and determination of peak areas are worked out in the Fourier representation, which enables separation of background and peaks and very efficiently discriminates peaks, or elements represented by several peaks. First the spectrum is transformed so that in the new representation the full width at half maximum (FWHM) is independent of energy. Thus, the spectrum is arranged symmetrically and transformed into the Fourier representation. The latter is multiplied by a function in order to transform original Gaussian into Lorentzian peaks. An autoregressive filter is calculated, leading to a characteristic polynomial whose complex roots represent both the location and the width of each peak, provided that the absolute value is lower than unit. The amplitude of each component (the area of each peak or the sum of areas of peaks characterizing an element) is fitted by the weighted least squares method, taking into account that errors in spectra are independent and follow a Poisson law. Very accurate results are obtained, which would be hard to achieve by other methods. The DECO FORTRAN code has been developed for compatible PC microcomputers. Some features of the code are given.

  17. Gravitational collapse of scalar fields via spectral methods

    SciTech Connect

    Oliveira, H. P. de; Rodrigues, E. L.; Skea, J. E. F.

    2010-11-15

    In this paper we present a new numerical code based on the Galerkin method to integrate the field equations for the spherical collapse of massive and massless scalar fields. By using a spectral decomposition in terms of the radial coordinate, the field equations were reduced to a finite set of ordinary differential equations in the space of modes associated with the Galerkin expansion of the scalar field, together with algebraic sets of equations connecting modes associated with the metric functions. The set of ordinary differential equations with respect to the null coordinate is then integrated using an eighth-order Runge-Kutta method. The numerical tests have confirmed the high accuracy and fast convergence of the code. As an application we have evaluated the whole spectrum of black hole masses which ranges from infinitesimal to large values obtained after varying the amplitude of the initial scalar field distribution. We have found strong numerical evidence that this spectrum is described by a nonextensive distribution law.

  18. Extraction of sea ice concentration based on spectral unmixing method

    NASA Astrophysics Data System (ADS)

    Zhang, Dong; Ke, Changqing; Sun, Bo; Lei, Ruibo; Tang, Xueyuan

    2011-01-01

    The traditional methods to derive sea ice concentration are mainly from low resolution microwave data, which is disadvantageous to meet the grid size requirement of high resolution climate models. In this paper, moderate resolution imaging spectroradiometer (MODIS)/Terra calibrated radiances Level-1B (MOD02HKM) data with 500 m resolution in the vicinity of the Abbot Ice Shelf, Antarctica, is unmixed, respectively, by two neural networks to extract the sea ice concentration. After two different neural network models and MODIS potential open water algorithm (MPA) are introduced, a MOD02HKM image is unmixed using these neural networks and sea ice concentration maps are derived. At the same time, sea ice concentration for the same area is extracted by MPA from MODIS/Terra sea ice extent (MOD29) data with 1 km resolution. Comparisons among sea ice concentration results of the three algorithms showed that a spectral unmixing method is suitable for the extraction of sea ice concentration with high resolution and the accuracy of radial basis function neural network is better than that of backpropagation.

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

    NASA Technical Reports Server (NTRS)

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

    2005-01-01

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

  20. 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.

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

    PubMed

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

    2015-04-01

    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. PMID:25659478

  2. 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.

  3. Method and apparatus for measuring film spectral properties

    DOEpatents

    Forrest, Stephen R.; Burrows, Paul E.; Garbuzov, Dmitri Z.; Bulovic, Vladimir

    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.

  4. A comparison of spectral estimation methods for the analysis of sibilant fricatives

    PubMed Central

    Reidy, Patrick F.

    2015-01-01

    It has been argued that, to ensure accurate spectral feature estimates for sibilants, the spectral estimation method should include a low-variance spectral estimator; however, no empirical evaluation of estimation methods in terms of feature estimates has been given. The spectra of /s/ and /ʃ/ were estimated with different methods that varied the pre-emphasis filter and estimator. These methods were evaluated in terms of effects on two features (centroid and degree of sibilance) and on the detection of four linguistic contrasts within these features. Estimation method affected the spectral features but none of the tested linguistic contrasts. PMID:25920873

  5. Finite Frequency Upper Mantle Tomography Using the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Lekic, V.; Romanowicz, B.

    2007-12-01

    In the past quarter century, global tomography based on ray theory and first-order perturbation methods has imaged long-wavelength velocity heterogeneities of the Earth's mantle. While these models have contributed significantly to our understanding of mantle circulation, the development of higher resolution images of the Earth's interior holds tremendous promise for understanding the nature of the observed heterogeneities. This endeavor confronts us with two challenges. First, it requires extracting a far greater amount of information from the available seismograms than is generally used. Second, the approximate techniques upon which global tomographers have traditionally relied become inadequate when dealing with short-wavelength heterogeneity. We have developed a novel hybrid approach to long-period waveform tomography in which forward-modeling is performed using the Coupled Spectral Element Method (CSEM: Capdeville et al., 2003), which can accurately model seismic wave propagation in a 3D earth with both short and long wavelength structure, while in the inversion step, the sensitivity kernels are calculated using an approximate, non-linear normal mode summation approach (NACT: Li and Romanowicz, 1995). Our dataset consists of complete 3-component time domain seismograms filtered at periods greater than 80 s for 100 earthquakes observed at well over 100 stations of the IRIS/GSN, GEOSCOPE, GEOFON and various regional broadband networks. Modeling is performed in an iterative fashion, and convergence is achieved as long as the sign of the sensitivity kernels is correct. A further advantage of this hybrid approach is that it allows us - for the first time in global tomography - to accurately account for the effects of crustal structure on the observed seismograms. We illustrate these effects and the consequences of common assumptions such as linear crustal corrections. We present a preliminary model of velocity and radial anisotropy variations in the upper 800 km of

  6. Towards spectral geometric methods for Euclidean quantum gravity

    NASA Astrophysics Data System (ADS)

    Panine, Mikhail; Kempf, Achim

    2016-04-01

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

  7. Global mantle waveform tomography using the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Romanowicz, B. A.; French, S.; Masson, Y.; Jiménez-Pérez, H.

    2015-12-01

    In the past 20 years, we developed several generations of global mantle shear velocity models based entirely on time domain waveform inversion. This implies computations of synthetics in 3D earth models. Initially, the method of choice relied on normal mode perturbation theory, within which we built the framework of our inversion methodology. The latter includes, among others, windowing of waveforms to bring out contribution of weak amplitude phases, (e,g, Sdiff), and a fast converging quasi-Newton inversion with an approximate Hessian calculated using non-linear asymptotic coupling theory (NACT, Li and Romanowicz, 1995). Recently, the Spectral Element Method (SEM) was introduced in global seismology as a powerful numerical method to compute the seismic wavefield accurately in arbitrary 3D models (Komatitsch and Vilotte, 1998; Komatitsch and Tromp, 2002). Implementing the numerical SEM synthetics was straightforward, albeit with significantly increased cost of computation. In order to advance mantle imaging at the global scale, we introduced computational efficiencies, such as (1) substituting a fine layered crustal model by an equivalent, smooth, "homogeneized" crust designed to fit a global surface wave dispersion dataset, (2) continuing quasi-Newton inversion using NACT rather than adjoints, which involved the development of an efficient matrix assembly method (French et al., 2015), and (3) stepping progressively from long to short periods. The resulting models (Lekic and Romanowicz, 2011; French et al., 2013; French and Romanowicz, 2014), in particular, confirm the presence of deep mantle plumes beneath many major hotspots (French and Romanowicz, 2015). We discuss the choice of inverse approach, and illustrate the stability of our global models, in view of the use of NACT kernels, with respect to the choice of the starting model. Global inversion remains a challenge as higher resolution implies reaching higher frequencies to capture more of the scattered

  8. Instrumentation considerations in spectral imaging for tissue demarcation: comparing three methods of spectral resolution

    NASA Astrophysics Data System (ADS)

    Gebhart, Steven C.; Stokes, David L.; Vo-Dinh, Tuan; Mahadevan-Jansen, Anita

    2005-03-01

    Multiple methodologies exist to implement spectral imaging for tissue demarcation and disease diagnosis. In this paper, benchtop acousto-optic tunable filter (AOTF), liquid-crystal tunable filter (LCTF) and Fourier interferometric spectral imaging systems were quantitatively compared in terms of imaging speed of soft tissue autofluorescence. Optical throughput, image signal-to-noise ratio (SNR), and collagen autofluorescence imaging in chicken breast were assessed. Within this comparison, the Fourier system possessed the largest optical throughput (~50%) relative to the tunable-filter imaging systems; however, its throughput advantage failed to correlate to improved image SNR over the LCTF system. Further, while the autofluorescence imaging capability of the Fourier system exceeded that of the LCTF system for comparable total image integration times, the LCTF is capable of producing equivalent autofluorescence SNR with superior SNR when interrogations at only a few wavelengths are required and the random access filter tuning of the LCTF can be exploited. Therefore, the simple, rugged design and random-access filter-tuning capability of LCTF-based spectral imaging makes it best-suited for clinical development of soft tissue autofluorescence imaging.

  9. 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.

  10. 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.

  11. 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.

  12. Assessing Mantle Models with the Spectral-Element Method

    NASA Astrophysics Data System (ADS)

    Tromp, J.; Komatitsch, D.; Ritsema, J.; Allen, R.

    2001-12-01

    We have developed and implemented a spectral-element method (SEM) to simulate seismic wave propagation throughout the entire globe. Our SEM incorporates the effects of fluid-solid boundaries, attenuation, anisotropy, the oceans, rotation, self-gravitation and 3-D mantle and crustal heterogeneity. The method is implemented on a massively parallel PC cluster computer using message-passing software (MPI). The effects of crustal thickness, anisotropy, and attenuation on surface waves are quite dramatic. Self-gravitation and, in particular, the presence of a water layer slow the Rayleigh wave down. For spherically symmetric Earth models the SEM is in excellent agreement with normal-mode synthetics at periods greater than 20~seconds. We use the SEM to assess the quality of mantle model S20RTS, developed by Ritsema and colleagues, and Iceland model ICEMAN, developed by Allen and colleagues. The effects of 3-D heterogeneity can be spectacular. For example, along oceanic paths from Fiji-Tonga to Western North America or Japan the Rayleigh wave arrives more than a minute earlier than in PREM, and the Love wave exhibits very little dispersion, unlike in PREM. These effects are largely due to the fact that the oceanic crust is much thinner than in PREM. For a set of well-recorded earthquakes we use the SEM to determine how well model S20RTS fits the travel-time data. Because the SEM synthetics are essentially exact at periods greater than 20~seconds, this facilitates a difficult test for a 3-D model. For Iceland we are investigating whether or not a narrow plume can explain the differential travel-time data used to constrain the model. The width of the plume is so small that standard ray theory may be inadequate for waves with periods greater than 20~seconds. Due to finite-frequency effects, a ray that `misses' the plume can still be significantly affected by its presence. The question is whether a thin plume, which is preferred in geodynamic models, can explain the data as

  13. Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

    SciTech Connect

    Fang Jiannong; Diebold, Marc; Higgins, Chad; Parlange, Marc B.

    2011-09-10

    Highlights: {yields} A radial basis function based smoothing technique is introduced. {yields} It is more general and easier to implement compared to other techniques. {yields} With this technique, a combined immersed boundary and spectral method is developed. {yields} It is shown that the proposed method works better in terms of reducing the non-physical Gibbs oscillation. - Abstract: It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.

  14. Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1

    NASA Astrophysics Data System (ADS)

    Deckers, Karl; van Deun, Joris; Bultheel, Adhemar

    2008-06-01

    In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1] . The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1] .

  15. 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).

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

    SciTech Connect

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

    2011-05-04

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

  17. New method for evaluation of finite-energy few-electron spectral function expressions

    NASA Astrophysics Data System (ADS)

    Carmelo, J. M. P.; Penc, K.; Sacramento, P. D.; Claessen, R.

    2004-04-01

    We present a method for the calculation of few-electron spectral functions of the one-dimen- sional Hubbard model which relies on a pseudofermion description introduced recently in Ref. [6]. The spectral functions are expressed as a convolution of pseudofermion dynamical correlation functions. Our general method involves the direct evaluation of the matrix elements of pseudofermion operators between the ground state and the excited states. We briefly discuss the application of our general method to the study of the unusual finite-energy spectral properties observed in the quasi-one-dimensional organic conductor TTF-TCNQ. Key words. correlation effects spectral properties organic conductors

  18. 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.

  19. 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.

  20. Spectral imaging method for material classification and inspection of printed circuit boards

    NASA Astrophysics Data System (ADS)

    Ibrahim, Abdelhameed; Tominaga, Shoji; Horiuchi, Takahiko

    2010-05-01

    We propose a spectral imaging method for material classification and inspection of raw printed circuit boards (PCBs). The method is composed of two steps (1) estimation the PCB surface-spectral reflectances and (2) unsupervised classification of the reflectance data to make the inspection of PCB easy and efficient. First, we develop a spectral imaging system that captures high dynamic range images of a raw PCB with spatially and spectrally high resolutions in the region of visible wavelength. The surface-spectral reflectance is then estimated at every pixel point from multiple spectral images, based on the reflection characteristics of different materials. Second, the surface-spectral reflectance data are classified into several groups, according to the number of PCB materials. We develop an unsupervised classification algorithm incorporating both spectral information and spatial information, based on the Nyström approximation of the normalized cut method. The initial seeds for the Nyström procedure are effectively chosen using a guidance module based on the K-means algorithm. Low-dimensional spectral features are efficiently extracted from the original high-dimensional spectral reflectance data. The feasibility of the proposed method is examined in experiments using real PCBs in detail.

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

    PubMed

    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. 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

  3. [Comparison among remotely sensed image fusion methods based on spectral response function].

    PubMed

    Dou, Wen; Sun, Hong-quan; Chen, Yun-hao

    2011-03-01

    Remotely sensed image fusion is a critical issue, and many methods have been developed to inject features from a high spatial resolution panchromatic sensor into low spatial resolution multi-spectral images, trying to preserve spectral signatures while improving spatial resolution of multi-spectral images. However, no explicit physical information of the detection system has been taken into account in usual methods, which might lead to undesirable effects such as severe spectral distortion. Benefiting from the proper decomposition of the image fusion problem by a concise image fusion mathematical model, the present paper focuses on comparing reasonable modulation coefficient of spatial details based on analysis of the spectral response function (SRF). According to the classification of former methods, three modulation coefficients based on SRF of sensors were concluded, which lead to three image fusion methods incorporating spatial detail retrieved by Gaussian high-pass filter. All these methods were validated on Ikonos data compared to GS and HPM method. PMID:21595232

  4. 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.

  5. Comparison of spectral CT imaging methods based a photon-counting detector: Experimental study

    NASA Astrophysics Data System (ADS)

    Lee, Youngjin; Lee, Seungwan; Kim, Hee-Joung

    2016-04-01

    Photon-counting detectors allow spectral computed tomography (CT) imaging using energy-resolved information from a polychromatic X-ray spectrum. The spectral CT images based on the photon-counting detectors are dependent on the energy ranges defined by energy bins for image acquisition. In this study, K-edge and energy weighting imaging methods were experimentally implemented by using a spectral CT system with a cadmium zinc telluride (CZT)-based photon-counting detector. The spectral CT images were obtained by various energy bins and compared in terms of CNR improvement for investigating the effect of energy bins and the efficiency of the spectral CT imaging methods. The results showed that the spectral CT image quality was improved by using the particular energy bins, which were optimized for each spectral CT imaging method and target material. The CNR improvement was different for the spectral CT imaging methods and target materials. It can be concluded that an appropriate selection of imaging method for each target material and the optimization of energy bin can maximize the quality of spectral CT images.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Low-bit-rate representation of cylindrical volume grids using Chebyshev bases: direct section computation, synthesis, and reconstruction

    NASA Astrophysics Data System (ADS)

    Desai, Ranjit P.; Menon, Jai P.

    1998-12-01

    A large class of high-speed visualization applications use image acquisition and 3D volume reconstruction techniques in cylindrical sampling grids; these include real-time 3D medical reconstruction, and reverse engineering. This paper presents the novel use of Chebyshev bases in such cylindrical grid- based volume applications, to allow efficient computation of cross-sectional planes of interest and partial volumes without the computationally expensive step of volume rendering, for subsequent transmission in constrained bitrate environments. This has important consequences for low-bitrate applications such as video-conferencing and internet-based visualization environments, where interaction and fusion between independently sampled heterogenous data streams (images, video and 3D volumes) from multiple sources is beginning to play an important part. Volumes often embody widely varying physical signals such as those acquired by X-rays, ultrasound sensors in addition to standard c.c.d. cameras. Several benefits of Chebyshev expansions such as fast convergence, bounded error, computational efficiency, and their optimality for cylindrical grids are taken into account. In addition, our method exploits knowledge about the sampling strategy (e.g. position and trajectory of the sensor) used to acquire the original ensemble of images, which in turn makes the overall approach very amenable to internet-based low-bitrate applications.

  11. [Correction method for infrared spectral emissivity measurement system based on integrating sphere reflectometer].

    PubMed

    Zhang, Yu-Feng; Dai, Jing-Min; Zhang, Yu; Pan, Wei-Dong; Zhang, Lei

    2013-08-01

    In view of the influence of non-ideal reference standard on spectral emissivity measurement, by analyzing the principle of infrared emissivity measurement system based on integrating sphere reflectometer, a calibration method suitable for measuring spectral emissivity system using the reflection measurement was proposed. By fitting a spectral reflectance curve of the reference standard sample to the given reflectance data, the correction coefficient of measurement system was computed. Then the output voltage curve of reference standard sample was corrected by this coefficient. The system error caused by the imperfection of reference standard was eliminated. The correction method was applied to the spectral emissivity measurement system based on integrating sphere reflectometer. The results measured by the corrected system and the results measured by energy comparison measurement were compared to verify the feasibility and effectivity of this correction method in improving the accuracy of spectral emissivity measurement. PMID:24159891

  12. 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...

  13. 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.

  14. 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.

  15. 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

  16. 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

    2015-01-01

    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

  17. Analysis of spectral radiative heat transfer using discrete exchange factor method

    NASA Astrophysics Data System (ADS)

    Zhang, Yinqiu; Naraghi, M. H. N.

    1993-09-01

    A solution technique is developed for spectral radiative heat-transfer problems. The formulation is based on the discrete exchange factor (DEF) method and uses Edward's (1976) wide band model to obtain spectral data. The results of the analyses of three cases were found to be in excellent agreement with those of the zonal method and differ by less than 5 percent from those of the discrete-ordinates method.

  18. 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.

  19. 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

  20. [Method of Remote Sensing Identification for Mineral Types Based on Multiple Spectral Characteristic Parameters Matching].

    PubMed

    Wei, Jing; Ming, Yan-fang; Han, Liu-sheng; Ren, Zhong-liang; Guo, Ya-min

    2015-10-01

    The traditional mineral mapping methods with remote sensing data, based on spectral reflectance matching techniques, shows low accuracy, for obviously being affected by the image quality, atmospheric and other factors. A new mineral mapping method based on multiple types of spectral characteristic parameters is presented in this paper. Various spectral characteristic parameters are used together to enhanced the stability in the situation of atmosphere and environment background affecting. AVIRIS (Airborne Visible Infrared Imaging Spectrometer) data of Nevada Cuprite are selected to determine the mineral types with this method. Typical mineral spectral data are also obtained from USGS (United States Geological Survey) spectral library to calculate the spectral characteristic parameters. A mineral identification model based on multiple spectral characteristic parameters is built by analyzing the various characteristic parameters, and is applied in the mineral mapping experiment in Cuprite area. The mineral mapping result produced by Clark et al. in 1995 is used to evaluate the effect of this method, results show, that mineral mapping results with this method can obtain a high precision, the overall mineral identification accuracy is 78.96%. PMID:26904833

  1. 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.

  2. 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.

  3. An empirical method for correcting the detector spectral response in energy-resolved CT

    NASA Astrophysics Data System (ADS)

    Schmidt, Taly Gilat

    2012-03-01

    Energy-resolving photon-counting detectors have the potential for improved material decomposition compared to dual-kVp approaches. However, material decomposition accuracy is limited by the nonideal spectral response of the detectors. This work proposes an empirical method for correcting the nonideal spectral response, including spectrum-tailing effects. Unlike previous correction methods which relied on synchrotron measurements, the proposed method can be performed on the scanner. The proposed method estimates a spectral-response matrix by performing x-ray projection measurements through a range of known thicknesses of two or more calibration materials. Once estimated, the spectral-response matrix is incorporated into conventional material decomposition algorithms. A simulation study investigated preliminary feasibility of the proposed method. The spectral-response matrix was estimated using simulated projection measurements through PMMA, aluminum, and gadolinium. An energy-resolved acquisition of a thorax phantom with gadolinium in the blood pool was simulated assuming a five-bin detector with realistic spectral response. Energy-bin data was decomposed into Compton, photoelectric, and gadolinium basis projections with and without the proposed correction method. Basis images were reconstructed by filtered backprojection. Results demonstrated that the nonideal spectral response reduced the ability to distinguish gadolinium from materials such as bone, while images reconstructed with the proposed correction method successfully depicted the contrast agent. The proposed correction method reduced errors from 9% to 0.6% in the Compton image, 90% to 0.6% in the photoelectric image and from 40% to 6% in the gadolinium image when using a three-material calibration. Overall, results support feasibility of the proposed spectral-response correction method.

  4. [Calculation of spectral shifts of the mutants of bacteriorhodopsin by QM/MM methods].

    PubMed

    Orekhov, F S; Shaĭtan, A K; Shaĭtan, K V

    2012-01-01

    In the present work spectral shifts of adsorption maxima for the number of mutants of bacteriorhodopsin have been calculated using QM/MM hybrid methodology. Along with this calculation an analysis of possible mechanisms of spectral modulation has been performed. Also we have carried out a comparative analysis of modern quantum chemical methods in respect of the level of optical spectra predictability they allow. We have shown that modern hybrid quantum chemical methods reach an acceptable level of preciseness when applied in the calculation of spectral shifts even if the absolute values of adsorption maxima predicted by these methods are underestimated. The number of rules has been found linking the value of spectral shift with the structural rearrangement in the apoprotein. The methods we were using as well as those rules we have found out both may be useful for development of nanoelectronical devices based on mutant species of bacteriorhodopsin (memory elements, optical triggers etc.). PMID:22594277

  5. 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.

    2016-06-01

    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.

  6. A method to correct for spectral artifacts in optical-CT dosimetry

    PubMed Central

    Pierquet, Michael; Jordan, Kevin; Oldham, Mark

    2011-01-01

    The recent emergence of radiochromic dosimeters with low inherent light-scattering presents the possibility of fast 3D dosimetry using broad-beam optical computed tomography (optical-CT). Current broad beam scanners typically employ either a single or a planar array of light-emitting diodes (LED) for the light source. The spectrum of light from LED sources is polychromatic and this, in combination with the non-uniform spectral absorption of the dosimeter, can introduce spectral artifacts arising from preferential absorption of photons at the peak absorption wavelengths in the dosimeter. Spectral artifacts can lead to large errors in the reconstructed attenuation coefficients, and hence dose measurement. This work presents an analytic method for correcting for spectral artifacts which can be applied if the spectral characteristics of the light source, absorbing dosimeter, and imaging detector are known or can be measured. The method is implemented here for a PRESAGE® dosimeter scanned with the DLOS telecentric scanner (Duke Large field-of-view Optical-CT Scanner). Emission and absorption profiles were measured with a commercial spectrometer and spectrophotometer, respectively. Simulations are presented that show spectral changes can introduce errors of 8% for moderately attenuating samples where spectral artifacts are less pronounced. The correction is evaluated by application to a 16 cm diameter PRESAGE® cylindrical dosimeter irradiated along the axis with two partially overlapping 6 × 6 cm fields of different doses. The resulting stepped dose distribution facilitates evaluation of the correction as each step had different spectral contributions. The spectral artifact correction was found to accurately correct the reconstructed coefficients to within ~1.5%, improved from ~7.5%, for normalized dose distributions. In conclusion, for situations where spectral artifacts cannot be removed by physical filters, the method shown here is an effective correction. Physical

  7. 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. PMID:25314714

  8. Detection and correction of spectral and spatial misregistrations for hyperspectral data using phase correlation method.

    PubMed

    Yokoya, Naoto; Miyamura, Norihide; Iwasaki, Akira

    2010-08-20

    Hyperspectral imaging sensors suffer from spectral and spatial misregistrations due to optical-system aberrations and misalignments. These artifacts distort spectral signatures that are specific to target objects and thus reduce classification accuracy. The main objective of this work is to detect and correct spectral and spatial misregistrations of hyperspectral images. The Hyperion visible near-infrared subsystem is used as an example. An image registration method based on phase correlation demonstrates the accurate detection of the spectral and spatial misregistrations. Cubic spline interpolation using estimated properties makes it possible to modify the spectral signatures. The accuracy of the proposed postlaunch estimation of the Hyperion characteristics is comparable to that of the prelaunch measurements, which enables the accurate onboard calibration of hyperspectral sensors. PMID:20733628

  9. 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.

  10. 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.

  11. Daniell method for power spectral density estimation in atomic force microscopy.

    PubMed

    Labuda, Aleksander

    2016-03-01

    An alternative method for power spectral density (PSD) estimation--the Daniell method--is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion--the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum. PMID:27036781

  12. Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

    NASA Astrophysics Data System (ADS)

    Auteri, F.; Quartapelle, L.; Vigevano, L.

    2002-08-01

    This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

  13. 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.

  14. 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.

  15. Daniell method for power spectral density estimation in atomic force microscopy

    NASA Astrophysics Data System (ADS)

    Labuda, Aleksander

    2016-03-01

    An alternative method for power spectral density (PSD) estimation—the Daniell method—is revisited and compared to the most prevalent method used in the field of atomic force microscopy for quantifying cantilever thermal motion—the Bartlett method. Both methods are shown to underestimate the Q factor of a simple harmonic oscillator (SHO) by a predictable, and therefore correctable, amount in the absence of spurious deterministic noise sources. However, the Bartlett method is much more prone to spectral leakage which can obscure the thermal spectrum in the presence of deterministic noise. By the significant reduction in spectral leakage, the Daniell method leads to a more accurate representation of the true PSD and enables clear identification and rejection of deterministic noise peaks. This benefit is especially valuable for the development of automated PSD fitting algorithms for robust and accurate estimation of SHO parameters from a thermal spectrum.

  16. 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

  17. 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).

  18. 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.

  19. 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.

  20. A method for fast selecting feature wavelengths from the spectral information of crop nitrogen

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Research on a method for fast selecting feature wavelengths from the nitrogen spectral information is necessary, which can determine the nitrogen content of crops. Based on the uniformity of uniform design, this paper proposed an improved particle swarm optimization (PSO) method. The method can ch...

  1. 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.

  2. Laser pulse transient method for measuring the normal spectral emissivity of samples with arbitrary surface quality

    NASA Astrophysics Data System (ADS)

    Jeromen, A.; Grabec, I.; Govekar, E.

    2008-09-01

    A laser pulse transient method for measuring normal spectral emissivity is described. In this method, a laser pulse ( λ=1064 nm) irradiates the top surface of a flat specimen. A two-dimensional temperature response of the bottom surface is measured with a calibrated thermographic camera. By solving an axisymmetric boundary value heat conduction problem, the normal spectral emissivity at 1064 nm is determined by using an iterative nonlinear least-squares estimation procedure. The method can be applied to arbitrary sample surface quality. The method is tested on a nickel specimen and used to determine the normal spectral emissivity of AISI 304 stainless steel. The expanded combined uncertainty of the method has been estimated to be 18%.

  3. 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.

  4. Spectral Methods for Determining the Stability and Noise Performance of Passively Modelocked Lasers

    NASA Astrophysics Data System (ADS)

    Menyuk, Curtis R.; Wang, Shaokang

    2016-06-01

    We describe spectral or dynamical methods that can be used to determine the stability and noise performance of modelocked lasers.We first review methods that have been used to date to theoretically and computationally study passively modelocked lasers, contrasting evolutionary and dynamical approaches and their application to full, averaged, and reduced models. We then develop the spectral methods and show how they can be used to determine the stability and to calculate the timing jitter and power spectral density for any averaged model with any equilibrium pulse shape. We review work that has been done on soliton lasers using soliton perturbation theory from this dynamical perspective, and we contrast the simplicity and generality of our methods to prior work. We close with a discussion of how to extend our approach from averaged models to full models.

  5. 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.

  6. Spectrally-accurate algorithm for the analysis of flows in two-dimensional vibrating channels

    NASA Astrophysics Data System (ADS)

    Zandi, S.; Mohammadi, A.; Floryan, J. M.

    2015-11-01

    A spectral algorithm based on the immersed boundary conditions (IBC) concept has been developed for the analysis of flows in channels bounded by vibrating walls. The vibrations take the form of travelling waves of arbitrary profile. The algorithm uses a fixed computational domain with the flow domain immersed in its interior. Boundary conditions enter the algorithm in the form of constraints. The spatial discretization uses a Fourier expansion in the stream-wise direction and a Chebyshev expansion in the wall-normal direction. Use of the Galileo transformation converts the unsteady problem into a steady one. An efficient solver which takes advantage of the structure of the coefficient matrix has been used. It is demonstrated that the method can be extended to more extreme geometries using the overdetermined formulation. Various tests confirm the spectral accuracy of the algorithm.

  7. 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.

  8. The effect of mutual coupling on the side lobe performance of Chebyshev arrays, volume 1

    NASA Astrophysics Data System (ADS)

    Gierard, Robert A.

    1989-03-01

    This computer analysis assessed the impact of mutual coupling on the side lobe performance of Chebyshev linear arrays as a function array size, scan condition, and the severity of Chebyshev taper. Array elements were horizontal parallel dipoles over a ground plane. Three simple compensation schemes to account for coupling were investigated. A FORTRAN computer program, based upon King-Middleton's modified, zero-order, two-term theory for cylindrical dipoles, was written to calculate the generalized impedance matrix for the linear array, dipole current distributions and the far-field H-plane pattern in the presence of coupling. It is sufficiently general to allow the user of specify, number of dipoles, dipole length and radius, dipole spacing, height above ground plane, frequency, and complex generator voltages driving the array. The results relate side lobe degradation (growth) to array size, scan condition, and desired Chebyshev side lobe level. Additional programs were written to reverse the matrix solution, and solve for generator voltages, which after coupling, produce a base current distribution with a Chebyshev taper. Three simpler compensation schemes then used approximations of the compensated (complex) voltages to drive the array.

  9. Performance of fluorescence retrieval methods and fluorescence spectrum reconstruction under various sensor spectral configurations

    NASA Astrophysics Data System (ADS)

    Li, Rong; Zhao, Feng

    2015-10-01

    Solar-induced chlorophyll fluorescence is closely related to photosynthesis and can serve as an indicator of plant status. Several methods have been proposed to retrieve fluorescence signal (Fs) either at specific spectral bands or within the whole fluorescence emission region. In this study, we investigated the precision of the fluorescence signal obtained through these methods under various sensor spectral characteristics. Simulated datasets generated by the SCOPE (Soil Canopy Observation, Photochemistry and Energy fluxes) model with known `true' Fs as well as an experimental dataset are exploited to investigate four commonly used Fs retrieval methods, namely the original Fraunhofer Line Discriminator method (FLD), the 3 bands FLD (3FLD), the improved FLD (iFLD), and the Spectral Fitting Methods (SFMs). Fluorescence Spectrum Reconstruction (FSR) method is also investigated using simulated datasets. The sensor characteristics of spectral resolution (SR) and signal-to-noise ratio (SNR) are taken into account. According to the results, finer SR and SNR both lead to better accuracy. Lowest precision is obtained for the FLD method with strong overestimation. Some improvements are made by the 3FLD method, but it still tends to overestimate. Generally, the iFLD method and the SFMs provide better accuracy. As to FSR, the shape and magnitude of reconstructed Fs are generally consistent with the `true' Fs distributions when fine SR is exploited. With coarser SR, however, though R2 of the retrieved Fs may be high, large bias is likely to be obtained as well.

  10. 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.

  11. 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].

  12. Acquisition of multi-spectral flash image using optimization method via weight map

    NASA Astrophysics Data System (ADS)

    Choi, Bong-Seok; Kim, Dae-Chul; Kwon, Oh-Seol; Ha, Yeong-Ho

    2013-02-01

    To acquire images in low-light environments, it is usually necessary to adopt long exposure times or to resort to flashes. Flashes, however, often induce color distortion, cause the red-eye effect and can be disturbing to the subjects. On the other hand, long-exposure shots are susceptible to subject-motion, as well as motion-blur due to camera shake when performed with a hand-held camera. A recently introduced technique to overcome the limitations of the traditional lowlight photography is the use of the multi-spectral flash. Multi-spectral flash images are a combination of UV/IR and visible spectrum information. The general idea is to retrieve the details from the UV/IR spectrum and the color from the visible spectrum. Multi-spectral flash images, however, are themselves subject to color distortion and noise. In this work, a method of computing multi-spectral flash images so as to reduce the noise and to improve the color accuracy is presented. The proposed method is a previously seen optimization method, improved by introducing a weight map used to discriminate the uniform regions from the detail regions. The optimization target function takes into account the output likelihood with respect to the ambient light image, the sparsity of image gradients, and the spectral constraints for the IR-red and UV-blue channels. The performance of the proposed method was objectively evaluated using longexposure shots as references.

  13. 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.

  14. 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.

  15. Automated endmember determination and adaptive spectral mixture analysis using kernel methods

    NASA Astrophysics Data System (ADS)

    Rand, Robert S.; Banerjee, Amit; Broadwater, Joshua

    2013-09-01

    Various phenomena occur in geographic regions that cause pixels of a scene to contain spectrally mixed pixels. The mixtures may be linear or nonlinear. It could simply be that the pixel size of a sensor is too large so many pixels contain patches of different materials within them (linear), or there could be microscopic mixtures and multiple scattering occurring within pixels (non-linear). Often enough, scenes may contain cases of both linear and non-linear mixing on a pixel-by-pixel basis. Furthermore, appropriate endmembers in a scene are not always easy to determine. A reference spectral library of materials may or may not be available, yet, even if a library is available, using it directly for spectral unmixing may not always be fruitful. This study investigates a generalized kernel-based method for spectral unmixing that attempts to determine if each pixel in a scene is linear or non-linear, and adapts to compute a mixture model at each pixel accordingly. The effort also investigates a kernel-based support vector method for determining spectral endmembers in a scene. Two scenes of hyperspectral imagery calibrated to reflectance are used to validate the methods. We test the approaches using a HyMAP scene collected over the Waimanalo Bay region in Oahu, Hawaii, as well as an AVIRIS scene collected over the oil spill region in the Gulf of Mexico during the Deepwater Horizon oil incident.

  16. Dual window method for processing spectroscopic optical coherence tomography signals with high spectral and spatial resolution

    NASA Astrophysics Data System (ADS)

    Robles, Francisco E.; Graf, Robert N.; Wax, Adam

    2009-02-01

    The generation of spectroscopic optical coherence tomography (SOCT) signals suffers from an inherent trade off between spatial and spectral resolution. Here, we present a dual window (DW) method that uses two Gaussian windows to simultaneously obtain high spectral and spatial resolution. We show that the DW method probes the Winger time-frequency distribution (TFD) with two orthogonal windows set by the standard deviation of the Gaussian windows used for processing. We also show that in the limit of an infinitesimally narrow window, combined with a large window, this method is equivalent to the Kirkwood & Richaczek TFD and, if the real part is taken, it is equivalent to the Margenau & Hill (MH) TFD. We demonstrate the effectiveness of the method by simulating a signal with four components separated in depth or center frequency. Six TFD are compared: the ideal, the Wigner, the MH, narrow window short time Fourier transform (STFT), wide window STFT, and the DW. The results show that the DW method contains features of the Wigner TFD, and that it contains the highest spatial and spectral resolution that is free of artifacts. This method can enable powerful applications, including accurate acquisition of the spectral information for cancer diagnosis.

  17. 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.

  18. Data processing method applying principal component analysis and spectral angle mapper for imaging spectroscopic sensors

    NASA Astrophysics Data System (ADS)

    García-Allende, P. B.; Conde, O. M.; Mirapeix, J.; Cubillas, A. M.; López-Higuera, J. M.

    2007-07-01

    A data processing method for hyperspectral images is presented. Each image contains the whole diffuse reflectance spectra of the analyzed material for all the spatial positions along a specific line of vision. This data processing method is composed of two blocks: data compression and classification unit. Data compression is performed by means of Principal Component Analysis (PCA) and the spectral interpretation algorithm for classification is the Spectral Angle Mapper (SAM). This strategy of classification applying PCA and SAM has been successfully tested on the raw material on-line characterization in the tobacco industry. In this application case the desired raw material (tobacco leaves) should be discriminated from other unwanted spurious materials, such as plastic, cardboard, leather, candy paper, etc. Hyperspectral images are recorded by a spectroscopic sensor consisting of a monochromatic camera and a passive Prism- Grating-Prism device. Performance results are compared with a spectral interpretation algorithm based on Artificial Neural Networks (ANN).

  19. Rapid screening of anti-infective drug products for counterfeits using Raman spectral library-based correlation methods.

    PubMed

    Loethen, Yvette L; Kauffman, John F; Buhse, Lucinda F; Rodriguez, Jason D

    2015-11-01

    A new spectral library-based approach that is capable of screening a diverse set of finished drug products using only an active pharmaceutical ingredient spectral library is described in this paper. This approach obviates the need for a comprehensive drug product library, thereby streamlining the use of spectral library-based tests for anti-counterfeiting efforts, specifically to target finished drug products containing the wrong active ingredient or no active ingredient at all. Both laboratory-based and portable spectrometers are used in the study to demonstrate the usefulness and transferability of the spectral correlation method for field screening. The spectral correlation between the active pharmaceutical ingredient and finished drug product spectra is calculated using both full spectral analysis and targeted spectral regions analysis of six types of antimalarial, antibiotic and antiviral products. The spectral regions were determined using a moving window spectral correlation algorithm, and the use of specific spectral regions is shown to be crucial in screening finished drug products using only the active pharmaceutical ingredient spectrum. This comprehensive screening spectral correlation method is tested on seven different validation samples from different manufacturers as those used to develop the method, as well as simulated counterfeits which were prepared to mimic falsified drugs containing no active ingredient. The spectral correlation method is successful in correctly identifying 100% of the authentic products and simulated counterfeit samples tested. PMID:26401527

  20. 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.

  1. Computing the period of light variability in blazar objects using the periodogram spectral analysis method

    NASA Astrophysics Data System (ADS)

    Tang, J.; Zhang, X.; Wu, L.

    2007-10-01

    The periodogram spectral analysis method for equally spaced data is discussed and the method is tested with modeling signals. The effectiveness of the periodogram spectral analysis is confirmed by applications in noise series. The method has been applied to analyze the period of the Blazar 3C 279,3C 345 and BL Lac Objects OJ 287,ON 231.Their periods are 7.14yr, 10.00yr, 11.76 yr and 6.80yr, which are consistent with other documents in Jurkevich method. The results are satisfying. The obtained periods are helpful to understand physical mechanisms of Blazars. The paper analyzes the influence of window function. Moreover, their advantages and disadvantages are discussed for the practical applications. The application results also indicate that in comparison to other traditional prediction methods, the prediction method used in this paper has a higher prediction accuracy. Thus it has theoretical meaning and practical value for the period of light variation prediction.

  2. 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

  3. A combined spatial-spectral method for automated white blood cells segmentation

    NASA Astrophysics Data System (ADS)

    Li, Qingli; Wang, Yiting; Liu, Hongying; Wang, Jianbiao; Guo, Fangmin

    2013-12-01

    To overcome the shortcomings in the traditional white blood cells (WBCs) identification methods based on the color or gray images captured by light microscopy, a microscopy hyperspectral imaging system was used to analyze the blood smears. The system was developed by coupling an acousto-optic tunable filter (AOTF) adapter to a microscopy and driven by a SPF Model AOTF controller, which can capture hyperspectral images from 550 nm to 1000 nm with the spectral resolution 2-5 nm. Moreover, a combined spatial-spectral algorithm is proposed to segment the nuclei and cytoplasm of WBCs from the microscopy hyperspectral images. The proposed algorithm is based on the pixel-wise improved spectral angle mapper (ISAM) segmentation, followed by the majority voting within the active contour model regions. Experimental results show that the accuracy of the proposed algorithm is 91.06% (nuclei) and 85.59% (cytoplasm), respectively, which is higher than that of the spectral information divergence (SID) algorithm because the new method can jointly use both the spectral and spatial information of blood cells.

  4. 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.

  5. High-Order Spectral Volume Method for 2D Euler Equations

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    The Spectral Volume (SV) method is extended to the 2D Euler equations. The focus of this paper is to study the performance of the SV method on multidimensional non-linear systems. Implementation details including total variation diminishing (TVD) and total variation bounded (TVB) limiters are presented. Solutions with both smooth features and discontinuities are utilized to demonstrate the overall capability of the SV method.

  6. Spectral approximation to advection-diffusion problems by the fictitious interface method

    NASA Astrophysics Data System (ADS)

    Frati, A.; Pasquarelli, F.; Quarteroni, A.

    1993-08-01

    The algorithmic aspects of the 'fictitious interface' method used in numerical approximations of convection-dominated flows are discussed. The solution algorithm presented alternates the advection-equation solution with that of the advection-diffusion equation within complementary subdomains. For the problems presently considered, spatial discretization is obtained by the spectral collocation method via Legendre-Gaussian modes. Attention is given to the the fictitious interface method's application to the Burgers equation.

  7. 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

  8. 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.

  9. 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.

  10. Application of the quasi-spectral fourier method to soliton equations

    NASA Astrophysics Data System (ADS)

    Popov, S. P.

    2010-12-01

    A numerical approach combining the quasi-spectral Fourier method and the Runge-Kutta technique is proposed for the numerical study of the long wavelength regularized equation and the Camassa-Holm and Holm-Hone equations. Test results are presented for soliton and peakon solutions.

  11. Quantitative evaluation of the sensitivity of library-based Raman spectral correlation methods.

    PubMed

    Rodriguez, Jason D; Westenberger, Benjamin J; Buhse, Lucinda F; Kauffman, John F

    2011-06-01

    Library-based Raman spectral correlation methods are widely used in surveillance applications in multiple areas including the pharmaceutical industry, where Raman spectroscopy is commonly used in verification screening of incoming raw materials. While these spectral correlation methods are rapid and require little or no sample preparation, their sensitivity to the presence of contaminants has not been adequately evaluated. This is particularly important when dealing with pharmaceutical excipients, which are susceptible to economically motivated adulteration by substances having similar physical/chemical/spectroscopic properties. We report a novel approach to evaluating the sensitivity of library-based Raman spectral correlation methods to contaminants in binary systems using a hit-quality index model. We examine three excipient/contaminant systems, glycerin/diethylene glycol, propylene glycol/diethylene glycol, and lactose/melamine and find that the sensitivity to contaminant for each system is 18%, 32%, and 4%, respectively. These levels are well-correlated to the minimum contaminant composition that can be detected by both verification and identification methods. Our studies indicate that the most important factor that determines the sensitivity of a spectral correlation measurement to the presence of contaminant is the relative Raman scattering cross section of the contaminant. PMID:21548558

  12. Computing the Light Periods of Blazars with the Periodogram Spectral Analysis Method

    NASA Astrophysics Data System (ADS)

    Tang, Jie; Zhang, Xiong; Wu, Lin

    2008-04-01

    The periodogram spectral analysis method applicable to equallyspaced time series is discussed, and the method is tested first with a simulated data series. It is confirmed that this method is effective for noisy series. Then, applying this method to the analysis of the light periods of the quasars 3C 279 and 3C 345 as well as the BL Lac objects OJ 287 and ON 231, we obtain their light periods to be 7.14 yr, 10.00 yr, 11.76 yr and 6.80 yr, respectively. These results obtained by periodogram spectral analysis are consistent with those obtained by the Jurkevich method in the literature. We have analyzed the effects of different window functions, and commented on their correct selection in practical applications.

  13. 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.

  14. Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

    DOE PAGESBeta

    Smallwood, D. O.

    1996-01-01

    It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

  15. 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.

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

    DOE PAGESBeta

    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

  17. 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.

  18. 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 polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore, the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO{sub 2}, and compared to previous calculations.

  19. [A spectral unmixing method of estimating main minerals abundance of lunar soils].

    PubMed

    Yan, Bo-Kun; Li, Jian-Zhong; Gan, Fu-Ping; Yang, Su-Ming; Wang, Run-Sheng

    2012-12-01

    Estimating minerals abundance from reflectance spectra is one of the fundamental goals of remote sensing lunar exploration, and the main difficulties are the complicated mixing law of minerals spectrum and spectral features being sensitive to several kinds of factors such as topography, particle size and roughness etc. A method based on spectral unmixing was put forward and tested in the present paper. Before spectra are unmixed the spectral continuum is removed for clarifying and strengthening spectral features. The absorption features and reflectance features (the upward curving parts of spectra between absorption features) are integrated for unmixing to improve the unmixing performance. The Hapke model was used to correct unmixing error due to nonlinear mixing of minerals spectra. Forty three mixed spectra of olivine, clinopyroxene, hypersthene and plagioclase were used to validate the above method. The four minerals abundance was estimated under the conditions of being unaware of endmember spectra used to mix, granularity and chemical composition of minerals. Residual error, abundance error and correlation coefficient between retrieved and true abundance were 5.0 Vol%, 14.4 Vol% and 0.92 respectively. The method and result of this paper could be referred in the lunar minerals mapping of imaging spectrometer data such as M3. PMID:23427563

  20. 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.

  1. 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.

  2. Split-operator spectral method for solving the time-dependent Schroedinger equation in spherical coordinates

    SciTech Connect

    Hermann, M.R.; Fleck J.A. Jr.

    1988-12-15

    A spectral method previously developed for solving the time-dependent Schroedinger equation in Cartesian coordinates is generalized to spherical polar coordinates. The solution is implemented by repeated application of a unitary evolution operator in symmetrically split form. The wave function is expanded as a Fourier series in the radial coordinate and in terms of Legendre functions in the polar angle. The use of appropriate quadrature sets makes the expansion exact for band-limited functions. The method is appropriate for solving explicitly time-dependent problems, or for determining stationary states by a spectral method. The accuracy of the method is established by computing the Stark shift and lifetime of the 1s state in hydrogen, the low-lying energy levels for hydrogen in a uniform magnetic field, and the 2p-nd dipole transition spectrum for hydrogen.

  3. Obtaining the real profile of self-absorbed copper spectral line by regularization method

    NASA Astrophysics Data System (ADS)

    Vučeljić, M.; Brajović, S.; Šćepanović, M.; Mijović, S.

    2016-03-01

    Spectroscopic methods, as non-invasive, offer many possibilities to diagnose plasmas in the laboratory and in the space. Spectral line shapes carry information about plasma characteristics and deriving these parameters of line shapes with sufficient accuracy is the primary task in this work. The intrinsic problem in these methods is, the derivation of plasma characteristics from the measured spectrum: a characteristic of plasma plays a role of "cause", and the observed data-"effect". Therefore, to obtain the characteristic from the experimental data is an inverse and ill posed problem from the point of mathematical physics. The spectroscopic studies of the low voltage DC arc, used for excitation of free-burning cuprum-vapor plasmas at atmospheric pressure, were conducted. The true profile of Cu I 324.754 nm, self-absorbed spectral line, was obtained by deconvolution from experimental results by Tikhonov regularization method. Accuracy, reproducibility and limitation of the method were analyzed. Satisfactory results are obtained.

  4. On spectral methods for Volterra-type integro-differential equations

    NASA Astrophysics Data System (ADS)

    Jiang, Ying-Jun

    2009-08-01

    This paper considers the spectral methods for a Volterra-type integro-differential equation. Firstly, the Volterra-type integro-differential equation is equivalently restated as two integral equations of the second kind. Secondly, a Legendre-collocation method is used to solve them. Then the error analysis is conducted based on the L[infinity]-norm. In addition, numerical results are presented to confirm our analysis.

  5. Cross-spectral recognition method of bridge deck aerodynamic admittance function

    NASA Astrophysics Data System (ADS)

    Zhao, Lin; Ge, Yaojun

    2015-12-01

    This study proposes a new identification algorithm about the admittance function, which can estimate the full set of six aerodynamic admittance functions considering cross power spectral density functions about the forces and the turbulence components. The method was first numerically validated through Monte Carlo simulations, and then adopted to estimate the aerodynamic admittance of a streamlined bridge deck. The identification method was further validated through a comparison between the numerical calculation and wind tunnel tests on a moving bridge section.

  6. 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

  7. 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.

  8. An Augmented Classical Least Squares Method for Quantitative Raman Spectral Analysis against Component Information Loss

    PubMed Central

    Zhou, Yan; Cao, Hui

    2013-01-01

    We propose an augmented classical least squares (ACLS) calibration method for quantitative Raman spectral analysis against component information loss. The Raman spectral signals with low analyte concentration correlations were selected and used as the substitutes for unknown quantitative component information during the CLS calibration procedure. The number of selected signals was determined by using the leave-one-out root-mean-square error of cross-validation (RMSECV) curve. An ACLS model was built based on the augmented concentration matrix and the reference spectral signal matrix. The proposed method was compared with partial least squares (PLS) and principal component regression (PCR) using one example: a data set recorded from an experiment of analyte concentration determination using Raman spectroscopy. A 2-fold cross-validation with Venetian blinds strategy was exploited to evaluate the predictive power of the proposed method. The one-way variance analysis (ANOVA) was used to access the predictive power difference between the proposed method and existing methods. Results indicated that the proposed method is effective at increasing the robust predictive power of traditional CLS model against component information loss and its predictive power is comparable to that of PLS or PCR. PMID:23956689

  9. Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals

    NASA Astrophysics Data System (ADS)

    Figueras, Jordi-Lluís; Tucker, Warwick; Villadelprat, Jordi

    We develop techniques for the verification of the Chebyshev property of Abelian integrals. These techniques are a combination of theoretical results, analysis of asymptotic behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply this approach to tackle a conjecture formulated by Dumortier and Roussarie in [F. Dumortier, R. Roussarie, Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009) 723-781], which we are able to prove for q≤2.

  10. Optimization Of Conformal Cartographic Projections For The Slovak Republic According To Chebyshev's Theorem

    NASA Astrophysics Data System (ADS)

    Szatmári, Daniel

    2015-12-01

    Disadvantages of the currently used Křovák's map projection in the Slovak Republic, such as large scale distortion, became evident after the division of Czechoslovakia. The aim of this paper is to show the results of the optimization of cartographic projections using Chebyshev's theorem for conformal projections and its application to the territory of the Slovak Republic. The calculus used, the scale distortions achieved and their comparison with the scale distortions of currently used map projections will be demonstrated.

  11. Analysis of graded-index optical fibers by the spectral parameter power series method

    NASA Astrophysics Data System (ADS)

    Castillo-Pérez, Raúl; Kravchenko, Vladislav V.; Torba, Sergii M.

    2015-02-01

    The spectral parameter power series (SPPS) method is a recently introduced technique (Kravchenko 2008 Complex Var. Elliptic Equ. 53 775-89, Kravchenko and Porter 2010 Math. Methods Appl. Sci. 33 459-68) for solving linear differential equations and related spectral problems. In this work we develop an approach based on the SPPS for analysis of graded-index optical fibers. The characteristic equation of the eigenvalue problem for calculation of guided modes is obtained in an analytical form in terms of SPPS. Truncation of the series and consideration in this way of the approximate characteristic equation gives us a simple and efficient numerical method for solving the problem. Comparison with the results obtained by other available techniques reveals clear advantages for the SPPS approach, in particular, with regards to accuracy. Based on the solution of the eigenvalue problem, parameters describing the dispersion are analyzed as well.

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

    PubMed

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

    2016-01-25

    Guar gum is a well-known inactive ingredient (excipient) used in a variety of oral pharmaceutical dosage forms as a thickener and stabilizer of suspensions and as a binder of powders. It is also widely used as a food ingredient in which case alternatives with similar properties, including chemically similar gums, are readily available. Recent supply shortages and price fluctuations have caused guar gum to come under increasing scrutiny for possible adulteration by substitution of cheaper alternatives. One way that the U.S. FDA is attempting to screen pharmaceutical ingredients at risk for adulteration or substitution is through field-deployable spectroscopic screening. Here we report a comprehensive approach to evaluate two field-deployable Raman methods--spectral correlation and principal component analysis--to differentiate guar gum from other gums. We report a comparison of the sensitivity of the spectroscopic screening methods with current compendial identification tests. The ability of the spectroscopic methods to perform unambiguous identification of guar gum compared to other gums makes them an enhanced surveillance alternative to the current compendial identification tests, which are largely subjective in nature. Our findings indicate that Raman spectral identification methods perform better than compendial identification methods and are able to distinguish guar gum from other gums with 100% accuracy for samples tested by spectral correlation and principal component analysis. PMID:26609678

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  14. A new spectral finite volume method for elastic wave modelling on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.

    2016-04-01

    In this paper, we consider a new spectral finite volume method for the elastic wave equations. Our new finite volume method is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order finite volume method and the spectral finite volume method. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles, and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an over-determined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2D problems, but the same methodology can be applied to 3D.

  15. 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

  16. 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.

  17. Spectral inverse quantum (Spectral-IQ) method for modeling mesoporous systems: application on silica films by FTIR.

    PubMed

    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

  18. [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

  19. Spectral and angular responses of microbolometer IR FPA: a characterization method using a FTIR

    NASA Astrophysics Data System (ADS)

    Touvignon, Aurélie; Durand, Alain; Romanens, Fabien; Favreau, Julien; Gravrand, Olivier; Tisse, Christel-Loïc.

    2014-05-01

    In order to evaluate the impact of technological evolutions on the spectral responsivity of microbolometer FPAs (Focal Plane Arrays) as well as to find out a way to estimate the mechanical stability of microbolometric pixel membranes, ULIS is proposing a new method to measuring the spectral response of the detector array over a large region (area of pixels) simultaneously. This is done by tweaking the standard protocol of a commercial FTIR (Fourier Transform InfraRed) spectrometer where the IR detector is replaced by the array to be measured. All the calculations (i.e. interferogram processing) are taken care of externally. We use this new set up to measure the angular spectral response of the detector array and to analyse the relationship between spectral response and mechanical behaviour of the pixel. Firstly the setup of this measurement is presented and some preliminary technical issues are outlined. Then we focus on the results obtained from the measurements on 17μm pitch pixels over a wide range of angles of incidence (from normal to 45° incidence). Finally, we share some theoretical insights on both those results and the inherent limitations of this protocol using a simple optical cavity model.

  20. Analytical calculation of spectral phase of grism pairs by the geometrical ray tracing method

    NASA Astrophysics Data System (ADS)

    Rahimi, L.; Askari, A. A.; Saghafifar, H.

    2016-07-01

    The most optimum operation of a grism pair is practically approachable when an analytical expression of its spectral phase is in hand. In this paper, we have employed the accurate geometrical ray tracing method to calculate the analytical phase shift of a grism pair, at transmission and reflection configurations. As shown by the results, for a great variety of complicated configurations, the spectral phase of a grism pair is in the same form of that of a prism pair. The only exception is when the light enters into and exits from different facets of a reflection grism. The analytical result has been used to calculate the second-order dispersions of several examples of grism pairs in various possible configurations. All results are in complete agreement with those from ray tracing method. The result of this work can be very helpful in the optimal design and application of grism pairs at various configurations.

  1. Control of dispersed-phase temperature in plasma flows by the spectral-brightness pyrometry method

    NASA Astrophysics Data System (ADS)

    Dolmatov, A. V.; Gulyaev, I. P.; Gulyaev, P. Yu; Iordan, V. I.

    2016-02-01

    In the present work, we propose a new method for measuring the distribution of temperature in the ensembles of condensed-phase particles in plasma spray flows. Interrelation between the spectral temperature of the particles and the distribution of camera brightness signal is revealed. The established inter-relation enables an in-situ calibration of measuring instruments using the objects under study. The spectral-brightness pyrometry method was approbated on a Plazer plasma-arc wire spraying facility at the Paton Institute of Electrical Welding (Ukrainian Academy of Sciences, Kiev) and on the Thermoplasma 50-1 powder spraying facility at the Institute of Theoretical and Applied Mechanics (Russian Academy of Sciences, Siberian Branch, Novosibirsk). The work was supported by the Russian Foundation for Basic Research (Grants Nos. 14-08-90428 and 15-48-00100).

  2. 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.

  3. Implicit spectrally-accurate method for moving boundary problems using immersed boundary conditions concept

    NASA Astrophysics Data System (ADS)

    Husain, S. Z.; Floryan, J. M.

    2008-04-01

    A fully implicit, spectral algorithm for the analysis of moving boundary problem is described. The algorithm is based on the concept of immersed boundary conditions (IBC), i.e., the computational domain is fixed while the time dependent physical domain is submerged inside the computational domain, and is described in the context of the diffusion-type problems. The physical conditions along the edges of the physical domain are treated as internal constraints. The method eliminates the need for adaptive grid generation that follows evolution of the physical domain and provides sharp resolution of the location of the boundary. Various tests confirm the spectral accuracy in space and the first- and second-order accuracy in time. The computational cost advantage of the IBC method as compared with the more traditional algorithm based on the mapping concept is demonstrated.

  4. 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

  5. Numerical simulation of core convection by a multi-layer semi-implicit spherical spectral method

    NASA Astrophysics Data System (ADS)

    Cai, Tao; Chan, Kwing L.; Deng, Licai

    2011-10-01

    A semi-implicit multi-layer spherical spectral method for simulating stellar core convection is described. The fully compressible three-dimensional hydrodynamic equations with rotation and energy generation are solved. Prognostic variables are expressed as finite sums of spherical harmonics in the horizontal directions and handled by the finite difference method in the radial direction. The stratified approximation is used to simplify the nonlinearity to quadratic. A multi-layer scheme is employed to overcome the time step problem arising from shrinking grid sizes in the physical space near the center of the star. Despite of the different spectral truncations in different layers, round-off conservation of the total mass and total angular momentum of the whole domain can be maintained, and were confirmed numerically. The code is parallelized; with 12 processors the speedup factor is about 9. The solutions of model core convection with and without rotation are discussed.

  6. Galerkin Spectral Method for the 2D Solitary Waves of Boussinesq Paradigm Equation

    SciTech Connect

    Christou, M. A.; Christov, C. I.

    2009-10-29

    We consider the 2D stationary propagating solitary waves of the so-called Boussinesq Paradigm equation. The fourth- order elliptic boundary value problem on infinite interval is solved by a Galerkin spectral method. An iterative procedure based on artificial time ('false transients') and operator splitting is used. Results are obtained for the shapes of the solitary waves for different values of the dispersion parameters for both subcritical and supercritical phase speeds.

  7. A spectral method for action-angle representation of linear waves in plasmas

    SciTech Connect

    Hirota, M.

    2009-11-10

    Hamiltonian aspects of linear waves in plasmas are generally reviewed and discussed. Action-angle representation of linear waves is a fundamental problem, but it requires a careful mathematical consideration in the presence of continuum mode (continuous spectrum). We introduce a novel spectral technique that can treat continuous spectrum as well as discrete spectrum in a unified manner. Our method facilitates the derivation of action-angle variables, which is demonstrated for the Van Kampen mode in electrostatic plasma.

  8. Comparative analysis of combined spectral and optical tomography methods for detection of skin and lung cancers

    NASA Astrophysics Data System (ADS)

    Zakharov, Valery P.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Myakinin, Oleg O.; Kornilin, Dmitry V.; Kozlov, Sergey V.; Moryatov, Alexander A.

    2015-02-01

    Malignant skin tumors of different types were studied in vivo using optical coherence tomography (OCT), backscattering (BS), and Raman spectroscopy (RS). A multimodal method is proposed for early cancer detection based on complex analysis of OCT images by their relative alteration of scattered-radiation spectral intensities between malignant and healthy tissues. An increase in average accuracy of diagnosis was observed for a variety of cancer types (9% sensitivity, 8% specificity) by a multimodal RS-BS-OCT system in comparison with any of the three methods used separately. The proposed approach equalizes the processing rates for all methods and allows for simultaneous imaging and classification of tumors.

  9. Spectral method for the Cornell and screened Cornell potentials in momentum space

    NASA Astrophysics Data System (ADS)

    Chen, Jiao-Kai

    2013-10-01

    We employ the Landé subtraction method and the spectral method to solve numerically the Schrödinger equation in momentum space with the Cornell and screened Cornell potentials in a unified approach. The calculated results are excellent, because singularities, especially the double-pole singularity, possessed by potentials are handled completely. Besides, we notice that the eigenvalues yielded by numerical methods have definite convergence directions. The convergence directions of the calculated eigenvalues are abnormal when potentials are singular and become normal as singularities are manipulated properly.

  10. CoreSVM: a generalized high-order spectral volume method bearing Conservative Order RElease

    NASA Astrophysics Data System (ADS)

    Lamouroux, Raphael; Gressier, Jeremie; Joly, Laurent; Grondin, Gilles

    2014-11-01

    The spectral volume method (SVM) introduced by Wang in 2002 is based on a compact polynomial reconstruction where the interpolation's degree is driven by the partition of the spectral volumes. We propose a generalization of the SVM which releases the polynomial degree from this constraint and more importantly that allows to resort to any polynomial order inferior to the regular stencil order without changing the original spectral volume partition. Using one-dimensional advection and Burgers equation, we prove that the proposed extended method exhibits versatile high-order convergence together with conservativity properties. This new method is thus named the CoreSVM for Conservative Order-REleased SVM and we therefore explore its potential towards the numerical simulation of stiff problems. It is stressed that CoreSVM is indeed particularly suited to handle discontinuities, as the order-reduction serves to damp the numerical oscillations due to Runge's phenomenon. To ensure computational stability, local p-coarsening is used to obtain the highest adequate polynomial degree. It is advocated finally that, since the CoreSVM sets the polynomial order adaptation free from any stencil changes, these features do not come at the expense of any extra remeshing or data adaptation cost. Part of this research was funded by the French DGA.

  11. On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions

    NASA Astrophysics Data System (ADS)

    Le Penven, Lionel; Buffat, Marc

    2012-10-01

    This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of Lagrange multipliers in relation to a discrete set of boundary constraints. For one-dimensional elliptic problems, this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth-order algebraic convergence rate. In this paper, a spectrally accurate formulation is presented for multi-dimensional applications. Instead of being specified locally, the forcing function is defined as a convolution of a mollifier (smooth bump function) and a Lagrange multiplier function (the amplitude of the bump). The multiplier function is then approximated by Fourier series. Using a Fourier Galerkin approximation, the spectral accuracy is demonstrated on a two-dimensional Laplacian problem and on a Stokes flow around a periodic array of cylinders. In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.

  12. Low-order mathematical modelling of electric double layer supercapacitors using spectral methods

    NASA Astrophysics Data System (ADS)

    Drummond, Ross; Howey, David A.; Duncan, Stephen R.

    2015-03-01

    This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity is accounted for, while in the other model it is not. A spectral element method is used to discretise the model equations and it is found that the error convergence rate with respect to the number of elements is faster compared to a finite difference method. The increased accuracy of the spectral element approach means that, for a similar level of solution accuracy, the model simulation computing time is approximately 50% of that of the finite difference method. This suggests that the spectral element model could be used for control and state estimation purposes. For a typical supercapacitor charging profile, the numerical solutions from both models closely match experimental voltage and current data. However, when the electrolyte is dilute or where there is a long charging time, a noticeable difference between the numerical solutions of the two models is observed. Electrical impedance spectroscopy simulations show that the capacitance of the two models rapidly decreases when the frequency of the perturbation current exceeds an upper threshold.

  13. 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.

  14. 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

  15. A new spectral finite volume method for elastic wave modelling on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.

    2016-07-01

    In this paper, we consider a new spectral finite volume method (FVM) for the elastic wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.

  16. A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations

    NASA Astrophysics Data System (ADS)

    Giraldo, F. X.; Perot, J. B.; Fischer, P. F.

    2003-09-01

    A spectral element semi-Lagrangian (SESL) method for the shallow water equations on the sphere is presented. The sphere is discretized using a hexahedral grid although any grid imaginable can be used as long as it is comprised of quadrilaterals. The equations are written in Cartesian coordinates to eliminate the pole singularity which plagues the equations in spherical coordinates. In a previous paper [Int. J. Numer. Methods Fluids 35 (2001) 869] we showed how to construct an explicit Eulerian spectral element (SE) model on the sphere; we now extend this work to a semi-Lagrangian formulation. The novelty of the Lagrangian formulation presented is that the high order SE basis functions are used as the interpolation functions for evaluating the values at the Lagrangian departure points. This makes the method not only high order accurate but quite general and thus applicable to unstructured grids and portable to distributed memory computers. The equations are discretized fully implicitly in time in order to avoid having to interpolate derivatives at departure points. By incorporating the Coriolis terms into the Lagrangian derivative, the block LU decomposition of the equations results in a symmetric positive-definite pseudo-Helmholtz operator which we solve using the generalized minimum residual method (GMRES) with a fast projection method [Comput. Methods Appl. Mech. Eng. 163 (1998) 193]. Results for eight test cases are presented to confirm the accuracy and stability of the method. These results show that SESL yields the same accuracy as an Eulerian spectral element semi-implicit (SESI) while allowing for time-steps 10 times as large and being up to 70% more efficient.

  17. 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.

  18. 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.

  19. 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. PMID:27140495

  20. 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.

  1. [Measurement of Mole Ratio for Alkali Metal Mixture by Using Spectral Absorption Method].

    PubMed

    Zou, Sheng; Zhang, Hong; Chen, Yao; Chen, Xi-yuan

    2015-08-01

    The ratio of alkali metal mixture is one of the most important parameters in gauge head belonging to the ultra-sensitivity inertial measurement equipment, which is required to detect precisely. According to the feature that ratio of alkali metal is related to alkali metal vapor density, the theory of optical depth is used to detect the ratio of alkali metal in the present article. The result shows that the data got by the theory of optical depth compared with empirical formula differs at three orders of magnitude, which can't ensure the accuracy. By changing the data processing method, model between spectral absorption rate and temperature in cell is established. The temperature in alkali metal cell is calibrated by spectral absorption rate. The ratio of alkali metal atoms in the cell is analyzed by calculating the alkali density with empirical formula. The computational error is less than 10%. PMID:26672309

  2. 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)

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

    NASA Astrophysics Data System (ADS)

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

    2007-07-01

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

  4. 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.

  5. 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. PMID:26257937

  6. 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.

  7. K-edge ratio method for identification of multiple nanoparticulate contrast agents by spectral CT imaging

    PubMed Central

    Ghadiri, H; Ay, M R; Shiran, M B; Soltanian-Zadeh, H

    2013-01-01

    Objective: Recently introduced energy-sensitive X-ray CT makes it feasible to discriminate different nanoparticulate contrast materials. The purpose of this work is to present a K-edge ratio method for differentiating multiple simultaneous contrast agents using spectral CT. Methods: The ratio of two images relevant to energy bins straddling the K-edge of the materials is calculated using an analytic CT simulator. In the resulting parametric map, the selected contrast agent regions can be identified using a thresholding algorithm. The K-edge ratio algorithm is applied to spectral images of simulated phantoms to identify and differentiate up to four simultaneous and targeted CT contrast agents. Results: We show that different combinations of simultaneous CT contrast agents can be identified by the proposed K-edge ratio method when energy-sensitive CT is used. In the K-edge parametric maps, the pixel values for biological tissues and contrast agents reach a maximum of 0.95, whereas for the selected contrast agents, the pixel values are larger than 1.10. The number of contrast agents that can be discriminated is limited owing to photon starvation. For reliable material discrimination, minimum photon counts corresponding to 140 kVp, 100 mAs and 5-mm slice thickness must be used. Conclusion: The proposed K-edge ratio method is a straightforward and fast method for identification and discrimination of multiple simultaneous CT contrast agents. Advances in knowledge: A new spectral CT-based algorithm is proposed which provides a new concept of molecular CT imaging by non-iteratively identifying multiple contrast agents when they are simultaneously targeting different organs. PMID:23934964

  8. A Gas Dynamics Method Based on The Spectral Deferred Corrections (SDC) Time Integration Technique and The Piecewise Parabolic Method (PPM)

    SciTech Connect

    Samet Y. Kadioglu

    2011-12-01

    We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge averaged quantities which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [17]. However, [17] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [17]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.

  9. 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.

  10. 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. PMID:23481673

  11. [Research of Outlier Samples Elimination Methods for Near-Infrared Spectral Analysis of Blood Glucose].

    PubMed

    Lin, Yongzhong; Li, Lina; Lin, Tianliang

    2015-12-01

    For the near-infrared (NIR) spectral analysis of the concentration of blood glucose, the calibration accuracy can be affected because of the existing of outlier samples. In this research, a Monte-Carlo cross validation (MCCV) method is constructed for eliminating outlier samples. The human blood plasma experiment in vitro and the human body experiment in vivo were introduced to evaluate the MCCV method for its application effect in NIR spectral analysis of blood glucose. And the uninformative sample elimination method based on modified uninformative variable elimination (MUVE-USE) was employed in this study for the comparison with MCCV. The results indicated that, like the MUVE-USE method, the outlier samples elimination method based on MCCV could be used to eliminate the outlier samples which came from gross errors (such as bad sample) or system errors (such as baseline drift). In addition, the outlier samples from the random errors of uncertain causes which affect model accuracy can be eliminated simultaneously by MCCV. The elimination of multiple outlier samples is beneficial to the improvement of prediction accuracy of calibration model. PMID:27079108

  12. Spectral residual method of saliency detection based on the two-dimensional fractional Fourier transform domain

    NASA Astrophysics Data System (ADS)

    Tian, Jiangxue; Qi, Lin; Wang, Yaxing

    2015-12-01

    As one of classic methods of frequency domain based saliency detection, Spectral residual (SR) method has shown several advantages. However, it usually produces higher saliency values at object edges instead of generating maps that uniformly cover the whole object, which results from failing to exploit all the spatial frequency content of the original image. The Two-Dimensional Fractional Fourier transform (2D-FRFT) is a generalized form of the traditional Fourier Transform (FT) which can abstract more meaningful information of the image under certain conditions. Based on this property, we propose a new method which detects the salient region based on 2D-FRFT domain. Moreover, we also use Hough transform detection and a band-pass filter to refine the saliency map. We conduct experiments on a common used dataset: MSRA. The proposed method is compared with several other saliency detection methods and shown to achieve superior result.

  13. 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.

  14. Hybrid spectral difference/embedded finite volume method for conservation laws

    NASA Astrophysics Data System (ADS)

    Choi, Jung J.

    2015-08-01

    Recently, interests have been increasing towards applying the high-order methods to various engineering applications with complex geometries [30]. As a result, a family of discontinuous high-order methods, such as Discontinuous Galerkin (DG), Spectral Volume (SV) and Spectral Difference (SD) methods, is under active development. These methods provide high-order accurate solutions and are highly parallelizable due to the local solution reconstruction within each element. But, these methods suffer from the Gibbs phenomena when discontinuities are present in the flow fields. Various types of limiters [43-45] and artificial viscosity [46,48] have been employed to overcome this problem. A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method [56]. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities

  15. The Laurdan spectral phasor method to explore membrane micro-heterogeneity and lipid domains in live cells.

    PubMed

    Golfetto, Ottavia; Hinde, Elizabeth; Gratton, Enrico

    2015-01-01

    In this method paper we describe the spectral phasor analysis applied to Laurdan emission for the assessment of the fluidity of different membranes in live cells. We first introduce the general context and then we show how to obtain the spectral phasor from data acquired using a commercial microscope. PMID:25331141

  16. Method for generating fractal mountains with controllable macroscopic shapes by spectral synthesis

    NASA Astrophysics Data System (ADS)

    Wang, Humin

    1996-03-01

    Let a 2D random function X(x,y) to denote fBm with exponent 0 < H < 1, then its spectral density Sx(u,v) has relation: Sx(u,v) 1/(u2 + v2)H+1. Such algorithm based on fBm has shown us beautiful pictures of fractal mountains. But the mountains (fractal surfaces) were produced naturally by random process. As a result, the macroscopic shapes and global positions of fractal mounts are not controllable. This paper presents a method that generates fractal mountains with controllable macroscopic shapes and positions using spectral synthesis. First, the discrete data of Y(x,y) on finite grids are inputted, and FFT is employed to produce discrete spectral F(u,v). Second, by InvFFT, low frequency components of F(u,v) together with high frequency components of F(u,v) are transformed to produce Z(x,y)--fractal surface. The macroscopic shapes are controlled by low frequency; meanwhile, the high frequency describes texture of fractal mountains.

  17. 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.

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

    DOE PAGESBeta

    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

  19. 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.

  20. Comparison of contrast enhancement methods using photon counting detector in spectral mammography

    NASA Astrophysics Data System (ADS)

    Kim, Hyemi; Park, Su-Jin; Jo, Byungdu; Kim, Dohyeon; Kim, Hee-Joung

    2016-03-01

    The photon counting detector with energy discrimination capabilities provides the spectral information and energy of each photon with single exposure. The energy-resolved photon counting detector makes it possible to improve the visualization of contrast agent by selecting the appropriate energy window. In this study, we simulated the photon counting spectral mammography system using a Monte Carlo method and compared three contrast enhancement methods (K-edge imaging, projection-based energy weighting imaging, and dual energy subtraction imaging). For the quantitative comparison, we used the homogeneous cylindrical breast phantom as a reference and the heterogeneous XCAT breast phantom. To evaluate the K-edge imaging methods, we obtained images by increasing the energy window width based on K-edge absorption energy of iodine. The iodine which has the K-edge discontinuity in the attenuation coefficient curve can be separated from the background. The projection-based energy weighting factor was defined as the difference in the transmissions between the contrast agent and the background. Each weighting factor as a function of photon energy was calculated and applied to the each energy bin. For the dual energy subtraction imaging, we acquired two images with below and above the iodine K-edge energy using single exposure. To suppress the breast tissue in high energy images, the weighting factor was applied as the ratio of the linear attenuation coefficients of the breast tissue at high and low energies. Our results demonstrated the CNR improvement of the K-edge imaging was the highest among the three methods. These imaging techniques based on the energy-resolved photon counting detector improved image quality with the spectral information.

  1. Evaluation of spectral CT data acquisition methods via non-stochastic variance maps

    NASA Astrophysics Data System (ADS)

    Sanchez, Adrian A.; Sidky, Emil Y.; Gilat Schmidt, Taly; Pan, Xiaochuan

    2015-03-01

    Recently, photon counting detectors capable of extracting spectral information have received much attention in CT, with promise of using spectral information to construct material basis images, correct beam-hardening artifacts, or provide improved imaging of K-edge contrast agents.1, 2 In this work, we focus on the goal of constructing images of basis material maps, and investigate the feasibility of analytically computing pixel variance maps for these images, so that alternative data acquisition and reconstruction methods can be compared and evaluated with respect to their noise properties. Our approach is based on linearization of the basis material decomposition and reconstruction operations, and we therefore demonstrate the method using the ubiquitous filtered back-projection algorithm, which is linear. We then performed preliminary investigation of the method by comparing basis material variance maps for two data acquisition methods that were previously found to have different noise properties:3 two-sided bin measurements acquired from separate, independent data realizations and two-sided bin measurements acquired from a single data realization.

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

    PubMed Central

    Pearman, Charles M.

    2014-01-01

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

  3. 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.

  4. 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.

  5. 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.

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

    SciTech Connect

    Xu, Jin; Yu, Yaming; Van Dyk, David A.; Kashyap, Vinay L.; Siemiginowska, Aneta; Drake, Jeremy; Ratzlaff, Pete; Connors, Alanna; Meng, Xiao-Li E-mail: yamingy@ics.uci.edu E-mail: vkashyap@cfa.harvard.edu E-mail: jdrake@cfa.harvard.edu E-mail: meng@stat.harvard.edu

    2014-10-20

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

  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. 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

  9. 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.

  10. [A New Method of Accurately Extracting Spectral Values for Discrete Sampling Points].

    PubMed

    Lü, Zhen-zhen; Liu, Guang-ming; Yang, Jin-song

    2015-08-01

    In the establishment of remote sensing information inversion model, the actual measured data of discrete sampling points and the corresponding spectrum data to pixels of remote sensing image, are used to establish the relation, thus to realize the goal of information retrieval. Accurate extraction of spectrum value is very important to establish the remote sensing inversion mode. Converting target spot layer to ROI (region of interest) and then saving the ROI as ASCII is one of the methods that researchers often used to extract the spectral values. Analyzing the coordinate and spectrum values extracted using original coordinate in ENVI, we found that the extracted and original coordinate were not inconsistent and part of spectrum values not belong to the pixel containing the sampling point. The inversion model based on the above information cannot really reflect relationship between the target properties and spectral values; so that the model is meaningless. We equally divided the pixel into four parts and summed up the law. It was found that only when the sampling points distributed in the upper left corner of pixels, the extracted values were correct. On the basis of the above methods, this paper systematically studied the principle of extraction target coordinate and spectral values, and summarized the rule. A new method for extracting spectral parameters of the pixel that sampling point located in the environment of ENVI software. Firstly, pixel sampling point coordinates for any of the four corner points were extracted by the sample points with original coordinate in ENVI. Secondly, the sampling points were judged in which partition of pixel by comparing the absolute values of difference longitude and latitude of the original and extraction coordinates. Lastly, all points were adjusted to the upper left corner of pixels by symmetry principle and spectrum values were extracted by the same way in the first step. The results indicated that the extracted spectrum

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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)

  17. A weighted polynomial based material decomposition method for spectral x-ray CT imaging.

    PubMed

    Wu, Dufan; Zhang, Li; Zhu, Xiaohua; Xu, Xiaofei; Wang, Sen

    2016-05-21

    Currently in photon counting based spectral x-ray computed tomography (CT) imaging, pre-reconstruction basis materials decomposition is an effective way to reconstruct densities of various materials. The iterative maximum-likelihood method requires precise spectrum information and is time-costly. In this paper, a novel non-iterative decomposition method based on polynomials is proposed for spectral CT, whose aim was to optimize the noise performance when there is more energy bins than the number of basis materials. Several subsets were taken from all the energy bins and conventional polynomials were established for each of them. The decomposition results from each polynomial were summed with pre-calculated weighting factors, which were designed to minimize the overall noises. Numerical studies showed that the decomposition noise of the proposed method was close to the Cramer-Rao lower bound under Poisson noises. Furthermore, experiments were carried out with an XCounter Filte X1 photon counting detector for two-material decomposition and three-material decomposition for validation. PMID:27082291

  18. A weighted polynomial based material decomposition method for spectral x-ray CT imaging

    NASA Astrophysics Data System (ADS)

    Wu, Dufan; Zhang, Li; Zhu, Xiaohua; Xu, Xiaofei; Wang, Sen

    2016-05-01

    Currently in photon counting based spectral x-ray computed tomography (CT) imaging, pre-reconstruction basis materials decomposition is an effective way to reconstruct densities of various materials. The iterative maximum-likelihood method requires precise spectrum information and is time-costly. In this paper, a novel non-iterative decomposition method based on polynomials is proposed for spectral CT, whose aim was to optimize the noise performance when there is more energy bins than the number of basis materials. Several subsets were taken from all the energy bins and conventional polynomials were established for each of them. The decomposition results from each polynomial were summed with pre-calculated weighting factors, which were designed to minimize the overall noises. Numerical studies showed that the decomposition noise of the proposed method was close to the Cramer–Rao lower bound under Poisson noises. Furthermore, experiments were carried out with an XCounter Filte X1 photon counting detector for two-material decomposition and three-material decomposition for validation.

  19. Investigation of molecular interaction between cefpodoxime acid and human mixtard insulin by ultrasonic and spectral methods.

    PubMed

    Ganesh, T; Kannappan, V; Mohamed Kamil, M G; Kumar, R

    2016-09-10

    This paper deals with the extensive investigation of molecular interaction between third generation cephalosporin antibiotic, Cefpodoxime Acid (CA) and Human Mixtard Insulin (HMI) in an aqueous medium through ultrasonic, dilute solution viscometric (DSV) and spectral [UV-vis, Attenuated total reflection (ATR)-FT IR] methods at various blend compositions of the drug and insulin at three different (303K, 310K and 313K) temperatures. This is an attempt to unravel the possibility of drug induced hypoglycemic effect. The existence of solute-solute interaction in aqueous solutions of CA and HMI is established from the variation of ultrasonic velocity and other acoustical parameters with blend composition. DSV method is used to confirm the range of blend composition at which the molecular interaction is significant. The conclusions drawn from ultrasonic and DSV methods are further established by the UV-vis and ATR- FT IR spectral studies of ternary mixtures at different blend compositions. Further, the existing interactions suggest the possibility of cefpodoxime acid induced hypoglycemia which is discussed based on the structural aspects of the two components. PMID:27442885

  20. Spectral analysis method and sample generation for real time visualization of speech

    NASA Astrophysics Data System (ADS)

    Hobohm, Klaus

    A method for translating speech signals into optical models, characterized by high sound discrimination and learnability and designed to provide to deaf persons a feedback towards control of their way of speaking, is presented. Important properties of speech production and perception processes and organs involved in these mechanisms are recalled in order to define requirements for speech visualization. It is established that the spectral representation of time, frequency and amplitude resolution of hearing must be fair and continuous variations of acoustic parameters of speech signal must be depicted by a continuous variation of images. A color table was developed for dynamic illustration and sonograms were generated with five spectral analysis methods such as Fourier transformations and linear prediction coding. For evaluating sonogram quality, test persons had to recognize consonant/vocal/consonant words and an optimized analysis method was achieved with a fast Fourier transformation and a postprocessor. A hardware concept of a real time speech visualization system, based on multiprocessor technology in a personal computer, is presented.

  1. 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. PMID:27257878

  2. 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.

  3. 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

  4. 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

  5. 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

  6. An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows.

    SciTech Connect

    Fischer, P.F.; Miller, N.I.; Tufo, H.M.

    1998-10-29

    As the sound speed is infinite for incompressible flows, computation of the pressure constitutes the stiffest component in the time advancement of unsteady simulations. For complex geometries, efficient solution is dependent upon the availability of fast solvers for sparse linear systems. In this paper we develop a Schwarz preconditioner for the spectral element method using overlapping subdomains for the pressure. These local subdomain problems are derived from tensor products of one-dimensional finite element discretizations and admit use of fast diagonalization methods based upon matrix-matrix products. In addition, we use a coarse grid projection operator whose solution is computed via a fast parallel direct solver. The combination of overlapping Schwarz preconditioning and fast coarse grid solver provides as much as a fourfold reduction in simulation time over previously employed methods based upon deflation for parallel solution of multi-million grid point flow problems.

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

    PubMed Central

    Samimi, Kayvan; Varghese, Tomy

    2015-01-01

    Estimation of frequency-dependent ultrasonic attenuation is an important aspect of tissue characterization. Along with other acoustic parameters studied in quantitative ultrasound, the attenuation coefficient can be used to differentiate normal and pathological tissue. The spectral centroid downshift (CDS) method is one the most common frequency-domain approaches applied to this problem. In this study, a statistical analysis of this method’s performance was carried out based on a parametric model of the signal power spectrum in the presence of electronic noise. The parametric model used for the power spectrum of received RF data assumes a Gaussian spectral profile for the transmit pulse, and incorporates effects of attenuation, windowing, and electronic noise. Spectral moments were calculated and used to estimate second-order centroid statistics. A theoretical expression for the variance of a maximum likelihood estimator of attenuation coefficient was derived in terms of the centroid statistics and other model parameters, such as transmit pulse center frequency and bandwidth, RF data window length, SNR, and number of regression points. Theoretically predicted estimation variances were compared with experimentally estimated variances on RF data sets from both computer-simulated and physical tissue-mimicking phantoms. Scan parameter ranges for this study were electronic SNR from 10 to 70 dB, transmit pulse standard deviation from 0.5 to 4.1 MHz, transmit pulse center frequency from 2 to 8 MHz, and data window length from 3 to 17 mm. Acceptable agreement was observed between theoretical predictions and experimentally estimated values with differences smaller than 0.05 dB/cm/MHz across the parameter ranges investigated. This model helps predict the best attenuation estimation variance achievable with the CDS method, in terms of said scan parameters. PMID:25965681

  8. 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.

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

    NASA Astrophysics Data System (ADS)

    Kornet, Kacper; Pothérat, Alban

    2015-10-01

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

  10. Solution of a singularly perturbed Cauchy problem for linear systems of ordinary differential equations by the method of spectral decomposition

    NASA Astrophysics Data System (ADS)

    Shaldanbayev, Amir; Shomanbayeva, Manat; Kopzhassarova, Asylzat

    2016-08-01

    This paper proposes a fundamentally new method of investigation of a singularly perturbed Cauchy problem for a linear system of ordinary differential equations based on the spectral theory of equations with deviating argument.

  11. Immersed boundary smooth extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

    NASA Astrophysics Data System (ADS)

    Stein, David B.; Guy, Robert D.; Thomases, Becca

    2016-01-01

    The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.

  12. A hybrid radial basis function-pseudospectral method for thermal convection in a 3-D spherical shell

    NASA Astrophysics Data System (ADS)

    Wright, G. B.; Flyer, N.; Yuen, D. A.

    2010-07-01

    A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth's mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 103 and 105. Results from a Ra = 106 simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature.

  13. Spectral method for efficient computation of time-dependent phenomena in complex lasers

    NASA Astrophysics Data System (ADS)

    Malik, O.; Makris, K. G.; Türeci, H. E.

    2015-12-01

    Studying time-dependent behavior in lasers is analytically difficult due to the saturating nonlinearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time and space in conventional finite-difference time-domain approaches. We describe here an efficient spectral method to overcome these shortcomings in complex lasers of arbitrary shape, gain medium distribution, and pumping profile. We apply this approach to a quasidegenerate two-mode laser in different dynamical regimes and compare the results in the long-time limit to the steady-state ab initio laser theory (SALT), which is also built on a spectral method but makes a more specific ansatz about the long-time dynamical evolution of the semiclassical laser equations. Analyzing a parameter regime outside the known domain of validity of the stationary inversion approximation, we find that for only a narrow regime of pump powers the inversion is not stationary, and that this, as pump power is further increased, triggers a synchronization transition upon which the inversion becomes stationary again. We provide a detailed analysis of mode synchronization (also known as cooperative frequency locking), revealing interesting dynamical features of such a laser system in the vicinity of the synchronization threshold.

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

    SciTech Connect

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

    1985-01-01

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

  15. 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.

  16. On estimating frequency response function envelopes using the spectral element method and fuzzy sets

    NASA Astrophysics Data System (ADS)

    Nunes, R. F.; Klimke, A.; Arruda, J. R. F.

    2006-04-01

    The influence of uncertain input data on response spectra of dynamic structures is considered. Traditionally, frequency response analyses are based on finite or boundary element models of the objective structure. In the case of the mid-frequency range problem, however, a very fine mesh is required to correctly approximate the frequency response. This is particularly problematic in uncertainty modeling where the computational effort is usually increased significantly by the need for multiple runs (e.g. when conducting a Monte Carlo analysis) to achieve reliable results. In this paper, the spectral element method, combined with a fuzzy set-based uncertainty modeling approach, is presented as an appealing alternative, provided that the models are simple enough to yield a spectral element representation. To conduct the fuzzy analysis part, three different implementations of the extension principle of fuzzy arithmetic are applied and compared. The suitability of each method depends on the number of uncertain parameters, the problem characteristics, and the required accuracy of the results. The performance of the proposed approach is illustrated by two test problems, a simple coupled rod and a reinforced plate model. To verify the fuzzy-valued results, a Monte Carlo simulation has also been included.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

    Uhe, P.; Thatcher, M.

    2014-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Uhe, P.; Thatcher, M.

    2015-06-01

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

  20. 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.

  1. On-line signature verification method by Laplacian spectral analysis and dynamic time warping

    NASA Astrophysics Data System (ADS)

    Li, Changting; Peng, Liangrui; Liu, Changsong; Ding, Xiaoqing

    2013-12-01

    As smartphones and touch screens are more and more popular, on-line signature verification technology can be used as one of personal identification means for mobile computing. In this paper, a novel Laplacian Spectral Analysis (LSA) based on-line signature verification method is presented and an integration framework of LSA and Dynamic Time Warping (DTW) based methods for practical application is proposed. In LSA based method, a Laplacian matrix is constructed by regarding the on-line signature as a graph. The signature's writing speed information is utilized in the Laplacian matrix of the graph. The eigenvalue spectrum of the Laplacian matrix is analyzed and used for signature verification. The framework to integrate LSA and DTW methods is further proposed. DTW is integrated at two stages. First, it is used to provide stroke matching results for the LSA method to construct the corresponding graph better. Second, the on-line signature verification results by DTW are fused with that of the LSA method. Experimental results on public signature database and practical signature data on mobile phones proved the effectiveness of the proposed method.

  2. Large Eddy Simulation of Compressible Flow past an Oscillating Cylinder using the Spectral Difference Method

    NASA Astrophysics Data System (ADS)

    Cox, Christopher; Liang, Chunlei

    2011-11-01

    In this investigation, we implement a high-order three-dimensional spectral difference (SD) method to solve the compressible Navier-Stokes equations on an unstructured moving deformable grid. Presently, the SD method is used to perform simulations of compressible flow past an oscillating circular cylinder. Oscillations parallel and normal to the free stream are considered at a fixed Reynolds number of 4000, oscillation frequency of 1 Hz , and oscillation amplitude of 20% cylinder diameter. We extend this study to large eddy simulations with the integration of a Smagorinsky-type subgrid-scale (SGS) model. Computational results will be compared to experimental data. The effectiveness of the large eddy simulation in capturing the vortex dynamics in the wake is analyzed. This work is funded by the Mechanical & Aerospace Engineering Department at George Washington University

  3. Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates

    NASA Astrophysics Data System (ADS)

    Novak, Jérôme; Bonazzola, Silvano

    2004-06-01

    We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary condition is simply written as a perturbation of the usual Sommerfeld radiation boundary condition. It is very easily implemented using spectral methods in spherical coordinates. Numerical tests of the method show that very good accuracy can be achieved and that this boundary condition has the same efficiency for dipolar and quadrupolar waves as the usual Sommerfeld boundary condition for monopolar ones. This is of particular importance for the simulation of gravitational waves, which have dominant quadrupolar terms, in General Relativity.

  4. An AC constant-response method for electrophysiological measurements of spectral sensitivity functions.

    PubMed

    de Souza, J M; DeVoe, R D; Schoeps, C; Ventura, D F

    1996-10-01

    A number of methods have been used in the past to measure spectral sensitivity (S(lambda)) functions of electric responses in the visual system. We present here a microcomputer based, AC, constant-response method for automatic on-line measurement of S(lambda) in cells with or without a sustained tonic response. It is based on feedback adjustment of light intensity to obtain constant peak-to-peak amplitudes of response to a flickering stimulus as the spectrum is scanned between 300 and 700 nm in 4 nm steps. It combines the advantages of: (1) on-line presentation of S(lambda) curves; (2) constant light adaptation; (3) sampling of many points; and (4) fast data collection time. The system can be applied to sensitivity or threshold (e.g., S(lambda), dark adaptation, receptive field) measurements of any electrically recorded visual response. PMID:8912193

  5. On the numerical dispersion and the spectral fidelity of the Particle-In-Cell method

    NASA Astrophysics Data System (ADS)

    Huang, Chengkun; Meyers, M. D.; Zeng, Y.; Yi, S.; Albright, B. J.

    2015-11-01

    The Particle-In-Cell (PIC) method is widely used in plasma modeling. However, the PIC method exhibits grid type numerical instabilities, including the finite grid instability and the numerical Cherenkov instability that can render unphysical simulation results or disrupt the simulation. A faithful numerical dispersion of the electromagnetic PIC algorithm is obtained and analyzed to obtain the insight about the numerical instabilities inherent in such a computation model. Using this dispersion, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. Compared with the gridless model, we show that the lack of spectral fidelity relative to the real system due to the aliasing effect is a major cause of the numerical instabilities in the PIC model. Work supported by the U.S. Department of Energy through the LDRD program at Los Alamos National Laboratory.

  6. 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.

  7. Performance of short-time spectral parametric methods for reducing the variance of the Doppler ultrasound mean instantaneous frequency estimation.

    PubMed

    Sava, H; Durand, L G; Cloutier, G

    1999-05-01

    To achieve an accurate estimation of the instantaneous turbulent velocity fluctuations downstream of prosthetic heart valves in vivo, the variability of the spectral method used to measure the mean frequency shift of the Doppler signal (i.e. the Doppler velocity) should be minimised. This paper investigates the performance of various short-time spectral parametric methods such as the short-time Fourier transform, autoregressive modelling based on two different approaches, autoregressive moving average modelling based on the Steiglitz-McBride method, and Prony's spectral method. A simulated Doppler signal was used to evaluate the performance of the above mentioned spectral methods and Gaussian noise was added to obtain a set of signals with various signal-to-noise ratios. Two different parameters were used to evaluate the performance of each method in terms of variability and accurate matching of the theoretical Doppler mean instantaneous frequency variation within the cardiac cycle. Results show that autoregressive modelling outperforms the other investigated spectral techniques for window lengths varying between 1 and 10 ms. Among the autoregressive algorithms implemented, it is shown that the maximum entropy method based on a block data processing technique gives the best results for a signal-to-noise ratio of 20 dB. However, at 10 and 0 dB, the Levinson-Durbin algorithm surpasses the performance of the maximum entropy method. It is expected that the intrinsic variance of the spectral methods can be an important source of error for the estimation of the turbulence intensity. The range of this error varies from 0.38% to 24% depending on the parameters of the spectral method and the signal-to-noise ratio. PMID:10505377

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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.

  15. A multi-similarity spectral clustering method for community detection in dynamic networks.

    PubMed

    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

  16. 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.

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

    NASA Astrophysics Data System (ADS)

    Schöll, Micha; Dudok de Wit, Thierry; Kretzschmar, Matthieu; Haberreiter, Margit

    2016-03-01

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

  18. 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.

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

    PubMed

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

    2014-03-01

    The aim of this study was to investigate the feasibility of using visible near-infrared (VisNIR) diffuse reflectance spectroscopy (DRS) as an easy, inexpensive, and rapid method to predict compost enzymatic activity, which traditionally measured by fluorescein diacetate hydrolysis (FDA-HR) assay. Compost samples representative of five different compost facilities were scanned by DRS, and the raw reflectance spectra were preprocessed using seven spectral transformations for predicting compost FDA-HR with six multivariate algorithms. Although principal component analysis for all spectral pretreatments satisfactorily identified the clusters by compost types, it could not separate different FDA contents. Furthermore, the artificial neural network multilayer perceptron (residual prediction deviation=3.2, validation r(2)=0.91 and RMSE=13.38 μg g(-1) h(-1)) outperformed other multivariate models to capture the highly non-linear relationships between compost enzymatic activity and VisNIR reflectance spectra after Savitzky-Golay first derivative pretreatment. This work demonstrates the efficiency of VisNIR DRS for predicting compost enzymatic as well as microbial activity. PMID:24398221

  20. 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.

  1. 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.

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

    SciTech Connect

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

    2015-04-15

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

  3. A recursive method for updating apple firmness prediction models based on spectral scattering images

    NASA Astrophysics Data System (ADS)

    Peng, Yankun; Lu, Renfu

    2007-09-01

    Multispectral scattering is effective for nondestructive prediction of fruit firmness. However, the established prediction models for multispectral scattering are variety specific and may not perform appropriately for fruit harvested from different orchards or at different times. In this research, a recursive least squares method was proposed to update the existing prediction model by adding samples from a new population to assure good performance of the model for predicting fruit from the new population. Multispectral scattering images acquired by a multispectral imaging system from Golden Delicious apples that were harvested at the same time but had different postharvest storage time periods were used to develop the updating method. Radial scattering profiles were described by the modified Lorentzian distribution (MLD) function with four profile parameters for eight wavelengths. Multi-linear regression was performed on MLD parameters to establish prediction models for fruit firmness for each group. The prediction model established in the first group was then updated by using selected samples from the second group, and four different sampling methods were compared and validated with the rest apples. The prediction model corrected by the model-updating method gave good firmness predictions with the correlation coefficient (r) of 0.86 and the standard error of prediction (SEP) of 6.11 N. This model updating method is promising for implementing the spectral scattering technique for real-time prediction of apple fruit firmness.

  4. A new method to probe the thermal electron content of the Galaxy through spectral analysis of background sources

    NASA Astrophysics Data System (ADS)

    Jones, D. I.; Igoshev, A. P.; Haverkorn, M.

    2016-08-01

    We present a new method for probing the thermal electron content of the Galaxy by spectral analysis of background point sources in the absorption-only limit to the radiative transfer equation. In this limit, calculating the spectral index, $\\alpha$, of these sources using a natural logarithm results in an additive factor, which we denote $\\alpha_\\mathrm{EM}$, resulting from the absorption of radiation due to the Galactic thermal electron population. We find that this effect is important at very low frequencies ($\

  5. 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.

  6. 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.

  7. An efficient method for computing spectral line profiles in stellar envelopes

    NASA Astrophysics Data System (ADS)

    Bertout, C.

    1984-10-01

    A computational technique is presented for calculating line-profiles from astronomical envelopes with complex velocity regions. The velocity field is assumed to accelerate outward through an envelope with no continuous opacity source. The emergent intensity is integrated numerically from the source to its maximum radius after evaluating a set of impact parameters at all locations on the outward bound rays. Account is taken of the interactions experienced by the photons and the optical depth at which the emergent intensity is measured. A method for separating out and integrating the fast-varying part of the emergent intensity is defined. The resultant code is demonstrated with calculations of power-law velocities. The model, written in FORTRAN77, is recommended for a variety of spectral line calculations, including static chromospheres and extended envelopes.

  8. 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.

  9. Spectral and network methods in the analysis of correlation matrices of stock returns

    NASA Astrophysics Data System (ADS)

    Heimo, Tapio; Saramäki, Jari; Onnela, Jukka-Pekka; Kaski, Kimmo

    2007-09-01

    Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: (i) spectral analysis, i.e. investigation of the eigenvalue-eigenvector pairs of the correlation matrix, (ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and (iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.

  10. A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

    NASA Astrophysics Data System (ADS)

    Balan, Aravind; May, Georg; Schöberl, Joachim

    2012-03-01

    Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not linearly stable on triangles. In this paper we present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart-Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. We demonstrate viability of the concept by showing linear stability both in the semi-discrete sense and for time stepping schemes of the SSP Runge-Kutta type. Furthermore, we present convergence studies, as well as case studies in compressible flow simulation using the Euler equations.

  11. Models of Lithospheric Flexure and Outer Trench Wall Fracturing using an Iterative Spectral Method

    NASA Astrophysics Data System (ADS)

    Garcia, E. S. M.; Sandwell, D. T.

    2014-12-01

    We have developed and tested an iterative spectral solution technique for flexure of thin elastic plates having continuously varying rigidity in both horizontal directions. This novel method was used to model oceanic lithosphere bending seaward of deep-sea trenches. In our formulation, the various mechanical loads that lead to plate flexure are simulated as applied bending moments and vertical forces acting on an arbitrary trench planform. Another input required by our model is a grid of flexural rigidity covering the plate domain laterally. We developed a procedure for estimating the rigidity from the plate age and curvature. With the loading and rigidity as input, the iterative spectral method gives the plate deflection as output. The plate curvature is then recalculated to obtain updated values of the rigidity, from which a new deflection grid is produced. These computations proceed iteratively until convergence is achieved. For our parameter estimation problem, we sought to find values of applied moments and vertical loads that produce a plate deflection surface which matches the seafloor bathymetry from ship soundings and marine gravity from satellite altimetry. By referring to a yield strength envelope formulation, we can take the modeled deflection surface and predict the lateral distribution of brittle failure at the bent areas of the plate. If we consider optimally-oriented faults according to an assumed value of the friction coefficient, we find that the upper layer of the plate undergoing brittle failure deepens with increasing proximity to the trench. We conducted tests for our modeling approach on an outer rise region adjacent to the South American Trench. Our preliminary results suggest a correspondence between the prevalence of surface fractures observed in high-resolution bathymetry with model predictions of brittle failure extending more than 10 kilometers deep into the plate.

  12. Revising the spectral method as applied to the mantle dynamics modeling.

    NASA Astrophysics Data System (ADS)

    Petrunin, A. G.; Kaban, M. K.; Rogozhina, I.; Trubytsyn, V. P.

    2012-04-01

    The spectral method is widely used for modeling instantaneous flow and stress field distribution in a spherical shell. This method provides a high accuracy semi-analytical solution of the Navier-Stokes and Poisson equations when the viscosity is only depth- (radial-) dependent. However, the distribution of viscosity in the real Earth is essentially three-dimensional. In this case, non-linear coupling of different spherical harmonic modes does not allow obtaining a straightforward semi-analytical solution. In this study, we present a numerical approach, built on substantially revised method originally proposed by Zhang and Christensen (1993) for solving the Navier-Stokes equation in a spectral domain in case if lateral variations of viscosity (LVV) are present. We demonstrate a number of numerical algorithms allowing to efficiently calculate instantaneous Stokes flow in a sphere taking into account the effects of LVV, self-gravitation and compressibility. In particular, the Newton-Raphson procedure applied to the shooting method shows the ability to solve the boundary value problem, necessary for cross-linking solutions on spheres. In contrast to the traditionally used propagator method, our approach suggests continuous integration over depth without introducing internal interfaces. The Clenshaw-based recursion algorithms for computing associated Legendre functions and the Horner's scheme for computing partial sums allow avoiding the problems in the Poles vicinity typical for the spherical harmonic methods and obtaining a fast and robust solution on a sphere for high degree and order. Since the benchmarking technique of 3-D spherical codes is not developed substantially, we employ different approaches to test the proposed numerical algorithm. First, we show that the algorithm produces correct results for radially symmetric viscosity distribution. Second, an iterative scheme for the LVV case is validated by comparing the solution for the tetrahedral symmetric (l=3,m

  13. 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

  14. 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.

  15. 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.

  16. A NOVEL SPECTRAL METHOD FOR INFERRING GENERAL DIPLOID SELECTION FROM TIME SERIES GENETIC DATA

    PubMed Central

    Steinrücken, Matthias; Bhaskar, Anand; Song, Yun S.

    2014-01-01

    The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of non-neutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote-advantage form of balancing selection may have been acting on these loci. PMID:25598858

  17. A new spectral difference method using hierarchical polynomial bases for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Liang, Xie; Min, Xu; Bin, Zhang; Zihua, Qiu

    2015-03-01

    To solve hyperbolic conservation laws, a new method is developed based on the spectral difference (SD) algorithm. The new scheme adopts hierarchical polynomials to represent the solution in each cell instead of Lagrange interpolation polynomials used by the original one. The degrees of freedom (DOFs) of the present scheme are the coefficients of these polynomials, which do not represent the states at the solution points like the original method. Therefore, the solution points defined in the original SD scheme are discarded, while the flux points are preserved to construct a Lagrange interpolation polynomial to approximate flux function in each cell. To update the DOFs, differential operators are applied to the governing equation as well as the Lagrange interpolation polynomial of flux function to evaluate first and higher order derivatives of both solution and flux at the centroid of the cell. The stability property of the current scheme is proved to be the same as the original SD method when the same solution space is adopted. One dimensional methods are always stable by the use of zeros of Legendre polynomials as inner flux points. For two dimensional problems, the introduction of Raviart-Thomas spaces for the interpolation of flux function proves stable schemes for triangles. Accuracy studies are performed with one- and two-dimensional problems. p-Multigrid algorithm is implemented with orthogonal hierarchical bases. The results verify the high efficiency and low memory requirements of implementation of p-multigrid algorithm with the proposed scheme.

  18. Towards a segregated time spectral solution method for incompressible viscous flows

    NASA Astrophysics Data System (ADS)

    Sabine, Baumbach

    2016-06-01

    Considering the growth of interest in understanding flow phenomena in rotational machines, computational fluid dynamics (CFD) is a powerful tool to reach this goal. Especially unsteady simulations are becoming a focus of interest. Nevertheless, unsteady simulations require huge computational times and ressources, thus it is necessary to investigate other methods to find more appropriate approaches to model time-periodic cases. For time-periodic flows the time spectral method (TSM) presents an interesting alternative to the regular time marching solvers. The TSM is well-known for computation of compressible time-periodic flows, but applications to incompressible cases are limited. This paper presents an extension of the TSM to incompressible flows. While there have been previous implementations using pressure correction method with an explicit treatment of time coupling, here an implicit treatment is chosen. To increase efficiency and employ a more robust coupling of the individual time instances the momentum equations are solved in block-coupled fashion. The pressure correction term is solved segregatedly. To consider cases with dynamic mesh motion an arbitrary lagrange Euler (ALE) formulation is also used in the solver. The efficiency of the method is demonstrated using a basic 2D aerodynamic test case and the results are compared to traditional time-stepping approaches.

  19. 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.

  20. 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.

  1. An oil film information retrieval method overcoming the influence of sun glitter, based on AISA+ airborne hyper-spectral image

    NASA Astrophysics Data System (ADS)

    Zhan, Yuanzeng; Mao, Tianming; Gong, Fang; Wang, Difeng; Chen, Jianyu

    2010-10-01

    As an effective survey tool for oil spill detection, the airborne hyper-spectral sensor affords the potentiality for retrieving the quantitative information of oil slick which is useful for the cleanup of spilled oil. But many airborne hyper-spectral images are affected by sun glitter which distorts radiance values and spectral ratios used for oil slick detection. In 2005, there's an oil spill event leaking at oil drilling platform in The South China Sea, and an AISA+ airborne hyper-spectral image recorded this event will be selected for studying in this paper, which is affected by sun glitter terribly. Through a spectrum analysis of the oil and water samples, two features -- "spectral rotation" and "a pair of fixed points" can be found in spectral curves between crude oil film and water. Base on these features, an oil film information retrieval method which can overcome the influence of sun glitter is presented. Firstly, the radiance of the image is converted to normal apparent reflectance (NormAR). Then, based on the features of "spectral rotation" (used for distinguishing oil film and water) and "a pair of fixed points" (used for overcoming the effect of sun glitter), NormAR894/NormAR516 is selected as an indicator of oil film. Finally, by using a threshold combined with the technologies of image filter and mathematic morphology, the distribution and relative thickness of oil film are retrieved.

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

    NASA Astrophysics Data System (ADS)

    Sidler, Rolf; Carcione, José M.; Holliger, Klaus

    2013-02-01

    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.

  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. 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

  5. Time Reversal Imaging of Seismic Sources by the Spectral Element Method.

    NASA Astrophysics Data System (ADS)

    Larmat, C.; Montagner, J.; Fink, M.; Capdeville, Y.; Clevede, E.; Tourin, A.

    2005-12-01

    The increasing power of computers and numerical methods (such as spectral elements methods) makes it possible to simulate more and more accurately the propagation of seismic waves in heterogeneous media and even to conceive new applications such as time reversal experiments within the three--dimensional Earth. These latter use the time reversal invariance and the spatial reciprocity of the wave equation. The idea is to construct a reverse movie of the propagation by sending the time--reversed recorded signals back from the receivers. The energy refocuses back at the location and the time of the original source. The concept of time-reversal has previously been successfully applied for acoustic waves in many fields such as medical imaging, oceanography and non destructive testing. For simulating the propagation of waves in the Earth as well as their time-reversed propagation, we used 2 different techniques, the normal mode summation technique (Gilbert and Dziewonski, 1975) and the spectral element method coupled with the modal solution (Capdeville et al., 2003). The first method is very accurate for 1D-earth models such as PREM whereas the second method is required for general heterogeneous 3D-models. For the first time, we have performed several synthetic and real data time-reversal experiments for seismic waves until the time of focalisation at the source. These tests show that sources are successfully localized in time and in space (though less accurately at depth), especially at very long period (> 200s) where the seismic properties of the Earth are well constrained. The corresponding movies are visible at the following address: http://www.gps.caltech.edu/~carene. We collect and send back the seismograms of the Global network of broadband seismic stations of the Federation of Digital Seismic Network (FDSN). We first consider a moderately large earthquake which can be considered as a point source in both time and space (Peru, June 23, 2001, Mw = 8.4). The

  6. Time domain spectral method and its application on antenna array and PCB trace with periodic roughness

    NASA Astrophysics Data System (ADS)

    Wang, Minshen

    The primary interest of the electromagnetic behavior of a periodic structure is in its near field and far field. However, it is still numerically difficult to analyze either one in the time domain. The primary goal of this dissertation is to develop corresponding time domain technique to analyze two topics. The first one is to evaluate the far field of a realistic, large antenna array using an efficient method. The second one is to evaluate the propagation characteristic of a commercially available printed circuit board (PCB) with intentional roughness. Both of which are hot topics in the antenna and signal integrity (SI) society respectively; however, none of them have ever been solved in the time domain. To efficiently evaluate the far field pattern of a realistically large antenna array, the spectral domain method and the reciprocity theorem are implemented in the finite difference time domain (FDTD) technique to avoid the simulation of the near field. By taking advantage of the periodic boundary condition (PBC), the proposed method demonstrates its capability to speed up far field evaluation from hours to minutes. Good agreement of the results is provided for various cases: circular antenna array, arbitrary feeding array, and highly directional leaky wave antenna, etc. Periodic structure modeling with finite sized feedings is developed by the array scanning method (ASM) implemented in the FDTD technique. The minimally coupled electric and magnetic co-mingled antenna array is evaluated by the method. Moreover, a commercially available PCB with very small roughness is modeled by the ASM-FDTD and the propagation characteristic is evaluated. Both are evaluated by time domain method for the first time. Efficiency in terms of memory and computing time is shown for this method and parallelization in the future is proposed.

  7. Calibration method for spectral responsivity of infrared detector based on blackbody at multiple temperature

    NASA Astrophysics Data System (ADS)

    Zhang, Y. F.; Shao, Z. F.; Wu, Y. Q.

    2015-08-01

    The spectral responsivity is one of the most important technical indicators of infrared detector which has an important significance for radiation thermometry and emissivity measurement. Using a blackbody radiation at multiple temperatures, the calibration for spectral responsivity of the infrared detector is proposed. With the Planck's law, the spectral radiance of blackbody at the different temperature is calculated. The detector captures the radiation and generates output values each of those is the function of spectral responsivity, spectral radiance and environmental radiation. Calibration equation is established by means of the calculated radiance and output values. By solving the equations based on principle of least squares, the calibration of spectral responsivity is implemented. From the comparison experiment of measuring the radiance of blackbody at 850K, radiance value measured by the MCT detector has a good consistency with the theoretical data.

  8. Analysis of Vibration and Noise of Construction Machinery Based on Ensemble Empirical Mode Decomposition and Spectral Correlation Analysis Method

    NASA Astrophysics Data System (ADS)

    Chen, Yuebiao; Zhou, Yiqi; Yu, Gang; Lu, Dan

    In order to analyze the effect of engine vibration on cab noise of construction machinery in multi-frequency bands, a new method based on ensemble empirical mode decomposition (EEMD) and spectral correlation analysis is proposed. Firstly, the intrinsic mode functions (IMFs) of vibration and noise signals were obtained by EEMD method, and then the IMFs which have the same frequency bands were selected. Secondly, we calculated the spectral correlation coefficients between the selected IMFs, getting the main frequency bands in which engine vibration has significant impact on cab noise. Thirdly, the dominated frequencies were picked out and analyzed by spectral analysis method. The study result shows that the main frequency bands and dominated frequencies in which engine vibration have serious impact on cab noise can be identified effectively by the proposed method, which provides effective guidance to noise reduction of construction machinery.

  9. 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

  10. 3D Multi-spectral Image-guided Near-infrared Spectroscopy using Boundary Element Method

    PubMed Central

    Srinivasan, Subhadra; Pogue, Brian W.; Paulsen, Keith D.

    2010-01-01

    Image guided (IG) Near-Infrared spectroscopy (NIRS) has the ability to provide high-resolution metabolic and vascular characterization of tissue, with clinical applications in diagnosis of breast cancer. This method is specific to multimodality imaging where tissue boundaries obtained from alternate modalities such as MRI/CT, are used for NIRS recovery. IG-NIRS is severely limited in 3D by challenges such as volumetric meshing of arbitrary anatomical shapes and computational burden encountered by existing models which use finite element method (FEM). We present an efficient and feasible alternative to FEM using boundary element method (BEM). The main advantage is the use of surface discretization which is reliable and more easily generated than volume grids in 3D and enables automation for large number of clinical data-sets. The BEM has been implemented for the diffusion equation to model light propagation in tissue. Image reconstruction based on BEM has been tested in a multi-threading environment using four processors which provides 60% improvement in computational time compared to a single processor. Spectral priors have been implemented in this framework and applied to a three-region problem with mean error of 6% in recovery of NIRS parameters. PMID:21179380

  11. A New Method for Spectral Decomposition Using a Bilinear Bayesian Approach

    NASA Astrophysics Data System (ADS)

    Ochs, M. F.; Stoyanova, R. S.; Arias-Mendoza, F.; Brown, T. R.

    1999-03-01

    A frequent problem in analysis is the need to find two matrices, closely related to the underlying measurement process, which when multiplied together reproduce the matrix of data points. Such problems arise throughout science, for example, in imaging where both the calibration of the sensor and the true scene may be unknown and in localized spectroscopy where multiple components may be present in varying amounts in any spectrum. Since both matrices are unknown, such a decomposition is a bilinear problem. We report here a solution to this problem for the case in which the decomposition results in matrices with elements drawn from positive additive distributions. We demonstrate the power of the methodology on chemical shift images (CSI). The new method, Bayesian spectral decomposition (BSD), reduces the CSI data to a small number of basis spectra together with their localized amplitudes. We apply this new algorithm to a19F nonlocalized study of the catabolism of 5-fluorouracil in human liver,31P CSI studies of a human head and calf muscle, and simulations which show its strengths and limitations. In all cases, the dataset, viewed as a matrix with rows containing the individual NMR spectra, results from the multiplication of a matrix of generally nonorthogonal basis spectra (the spectral matrix) by a matrix of the amplitudes of each basis spectrum in the the individual voxels (the amplitude matrix). The results show that BSD can simultaneously determine both the basis spectra and their distribution. In principle, BSD should solve this bilinear problem for any dataset which results from multiplication of matrices representing positive additive distributions if the data overdetermine the solutions.

  12. Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks.

    PubMed

    Patra, J C; Kot, A C

    2002-01-01

    A computationally efficient artificial neural network (ANN) for the purpose of dynamic nonlinear system identification is proposed. The major drawback of feedforward neural networks, such as multilayer perceptrons (MLPs) trained with the backpropagation (BP) algorithm, is that they require a large amount of computation for learning. We propose a single-layer functional-link ANN (FLANN) in which the need for a hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials. The novelty of this network is that it requires much less computation than that of a MLP. We have shown its effectiveness in the problem of nonlinear dynamic system identification. In the presence of additive Gaussian noise, the performance of the proposed network is found to be similar or superior to that of a MLP. A performance comparison in terms of computational complexity has also been carried out. PMID:18238146

  13. A simple model-free method for direct assessment of fluorescent ligand binding by linear spectral summation.

    PubMed

    Gasymov, Oktay K; Abduragimov, Adil R; Glasgow, Ben J

    2014-01-01

    Fluorescent tagged ligands are commonly used to determine binding to proteins. However, bound and free ligand concentrations are not directly determined. Instead the response in a fluorescent ligand titration experiment is considered to be proportional to the extent of binding and, therefore, the maximum value of binding is scaled to the total protein concentration. Here, a simple model-free method is presented to be performed in two steps. In the first step, normalized bound and free spectra of the ligand are determined. In the second step, these spectra are used to fit composite spectra as the sum of individual components or linear spectral summation. Using linear spectral summation, free and bound 1-Anilinonaphthalene-8-Sulfonic Acid (ANS) fluorescent ligand concentrations are directly calculated to determine ANS binding to tear lipocalin (TL), an archetypical ligand binding protein. Error analysis shows that the parameters that determine bound and free ligand concentrations were recovered with high certainty. The linear spectral summation method is feasible when fluorescence intensity is accompanied by a spectral shift upon protein binding. Computer simulations of the experiments of ANS binding to TL indicate that the method is feasible when the fluorescence spectral shift between bound and free forms of the ligand is just 8 nm. Ligands tagged with environmentally sensitive fluorescent dyes, e.g., dansyl chromophore, are particularly suitable for this method. PMID:24043458

  14. A Simple Model-Free Method for Direct Assessment of Fluorescent Ligand Binding by Linear Spectral Summation

    PubMed Central

    Gasymov, Oktay K.; Abduragimov, Adil R.; Glasgow, Ben J.

    2013-01-01

    Fluorescent tagged ligands are commonly used to determine binding to proteins. However, bound and free ligand concentrations are not directly determined. Instead the response in a fluorescent ligand titration experiment is considered to be proportional to the extent of binding and, therefore, the maximum value of binding is scaled to the total protein concentration. Here, a simple model-free method is presented to be performed in two steps. In the first step, normalized bound and free spectra of the ligand are determined. In the second step, these spectra are used to fit composite spectra as the sum of individual components or linear spectral summation. Using linear spectral summation, free and bound 1-Anilinonaphthalene-8-Sulfonic Acid (ANS) fluorescent ligand concentrations are directly calculated to determine ANS binding to tear lipocalin (TL), an archetypical ligand binding protein. Error analysis shows that the parameters that determine bound and free ligand concentrations were recovered with high certainty. The linear spectral summation method is feasible when fluorescence intensity is accompanied by a spectral shift upon protein binding. Computer simulations of the experiments of ANS binding to TL indicate that the method is feasible when the fluorescence spectral shift between bound and free forms of the ligand is just 8 nm. Ligands tagged with environmentally sensitive fluorescent dyes, e.g., dansyl chromophore, are particularly suitable for this method. PMID:24043458

  15. 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.

  16. 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

  17. Are spectral or spatial methods better for pansharpening? An evaluation for four sample methods based on spatial modulation of pixel spectra

    NASA Astrophysics Data System (ADS)

    Alparone, Luciano; Garzelli, Andrea; Vivone, Gemine

    2015-10-01

    The majority of pansharpening methods can be classified as spectral or spatial methods, depending on whether they are based on component substitution (CS) or multiresolution analysis (MRA). So far, the suitability of one class or methods rather than another has been seldom discussed. In this paper, through experiments on IKONOS and simulated Pléiades datasets, the authors demonstrate that the performances of spectral methods depend on the extent of spectral matching, measured by the coefficient of determination (CD) of the multivariate regression between MS and P. For data with simulated P, CD is very close to one and all methods perform almost identically. For true IKONOS datasets, the CD is few percent lower and spatial methods, once they have been optimized through the knowledge of the modulation transfer function (MTF) of the imaging system, are always more performing than spectral methods. Since spatial methods are unaffected by the spectral matching, they are preferable whenever such an issue is critical, e.g., for hyperspectral pansharpening.

  18. 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).

  19. 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.

  20. Density and atomic number measurements with spectral x-ray attenuation method

    NASA Astrophysics Data System (ADS)

    Heismann, B. J.; Leppert, J.; Stierstorfer, K.

    2003-08-01

    X-ray attenuation measurements are widely used in medical and industrial applications. The usual results are one- to three-dimensional representations of the attenuation coefficient μ(r). In this paper, we present the ρZ projection algorithm for obtaining the density ρ(r) and atomic number Z(r) with an energy-resolving x-ray method. As input data the algorithm uses at least two measurements μ1,μ2,… with different spectral weightings of the source spectrum S(E) and/or detector sensitivity D(E). Analytically, ρ is a function of μ1-cμ2, c=const, and Z is a function of μ1/μ2. The full numerical treatment yields ρ(μ1,μ2) and Z(μ1,μ2) with S(E) and D(E) as commutative parametric functions. We tested the method with dual-energy computed tomography measurements of an organic sample and a set of chemical solutions with predefined ρ and Z. The resulting images show ρ and Z as complementary information: The density ρ reflects the morphology of the objects, whereas the atomic number Z=number of electrons/atom describes the material distribution. For our experimental setup we obtain an absolute precision of 0.1 for Z and 20 mg/cm3 for ρ. The ρZ projection can potentially lead to these classes of quantitative information for various scientific, industrial, and medical applications.

  1. Development of a rapid method for the automatic classification of biological agents' fluorescence spectral signatures

    NASA Astrophysics Data System (ADS)

    Carestia, Mariachiara; Pizzoferrato, Roberto; Gelfusa, Michela; Cenciarelli, Orlando; Ludovici, Gian Marco; Gabriele, Jessica; Malizia, Andrea; Murari, Andrea; Vega, Jesus; Gaudio, Pasquale

    2015-11-01

    Biosecurity and biosafety are key concerns of modern society. Although nanomaterials are improving the capacities of point detectors, standoff detection still appears to be an open issue. Laser-induced fluorescence of biological agents (BAs) has proved to be one of the most promising optical techniques to achieve early standoff detection, but its strengths and weaknesses are still to be fully investigated. In particular, different BAs tend to have similar fluorescence spectra due to the ubiquity of biological endogenous fluorophores producing a signal in the UV range, making data analysis extremely challenging. The Universal Multi Event Locator (UMEL), a general method based on support vector regression, is commonly used to identify characteristic structures in arrays of data. In the first part of this work, we investigate fluorescence emission spectra of different simulants of BAs and apply UMEL for their automatic classification. In the second part of this work, we elaborate a strategy for the application of UMEL to the discrimination of different BAs' simulants spectra. Through this strategy, it has been possible to discriminate between these BAs' simulants despite the high similarity of their fluorescence spectra. These preliminary results support the use of SVR methods to classify BAs' spectral signatures.

  2. Accurate PSF-matched photometry and photometric redshifts for the extreme deep field with the Chebyshev-Fourier functions

    NASA Astrophysics Data System (ADS)

    Jiménez-Teja, Y.; Benítez, N.; Molino, A.; Fernandes, C. A. C.

    2015-10-01

    Photometric redshifts, which have become the cornerstone of several of the largest astronomical surveys like PanStarrs, DES, J-PAS and LSST, require precise measurements of galaxy photometry in different bands using a consistent physical aperture. This is not trivial, due to the variation in the shape and width of the point spread function (PSF) introduced by wavelength differences, instrument positions and atmospheric conditions. Current methods to correct for this effect rely on a detailed knowledge of PSF characteristics as a function of the survey coordinates, which can be difficult due to the relative paucity of stars tracking the PSF behaviour. Here we show that it is possible to measure accurate, consistent multicolour photometry without knowing the shape of the PSF. The Chebyshev-Fourier functions (CHEFs) can fit the observed profile of each object and produce high signal-to-noise integrated flux measurements unaffected by the PSF. These total fluxes, which encompass all the galaxy populations, are much more useful for galaxy evolution studies than aperture photometry. We compare the total magnitudes and colours obtained using our software to traditional photometry with SEXTRACTOR, using real data from the COSMOS survey and the Hubble Ultra-Deep Field (HUDF). We also apply the CHEF technique to the recently published eXtreme Deep Field (XDF) and compare the results to those from COLORPRO on the HUDF. We produce a photometric catalogue with 35 732 sources (10 823 with signal-to-noise ratio ≥5), reaching a photometric redshift precision of 2 per cent due to the extraordinary depth and wavelength coverage of the eXtreme Deep Field images.

  3. Validating 3D Seismic Velocity Models Using the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Maceira, M.; Rowe, C. A.; Allen, R. M.; Obrebski, M. J.

    2010-12-01

    As seismic instrumentation, data storage and dissemination and computational power improve, seismic velocity models attempt to resolve smaller structures and cover larger areas. However, it is unclear how accurate these velocity models are and, while the best models available are used for event determination, it is difficult to put uncertainties on seismic event parameters. Model validation is typically done using resolution tests that assume the imaging theory used is accurate and thus only considers the impact of the data coverage on resolution. We present the results of a more rigorous approach to model validation via full three-dimensional waveform propagation using Spectral Element Methods (SEM). This approach makes no assumptions about the theory used to generate the models but require substantial computational resources. We first validate 3D tomographic models for the Western USA generated using both ray-theoretical and finite-frequency methods. The Dynamic North America (DNA) Models of P- and S- velocity structure (DNA09-P and DNA09-S) use teleseismic body-wave traveltime residuals recorded at over 800 seismic stations provided by the Earthscope USArray and regional seismic networks. We performed systematic computations of synthetics for the dataset used to generate the DNA models. Direct comparison of these synthetic seismograms to the actual observations allows us to accurately assess and validate the models. Implementation of the method for a densely instrumented region such as that covered by the DNA model provides a useful testbed for the validation methods that we will subsequently apply to other, more challenging study areas.

  4. Investigation of the spectral reflectance and bidirectional reflectance distribution function of sea foam layer by the Monte Carlo method.

    PubMed

    Ma, L X; Wang, F Q; Wang, C A; Wang, C C; Tan, J Y

    2015-11-20

    Spectral properties of sea foam greatly affect ocean color remote sensing and aerosol optical thickness retrieval from satellite observation. This paper presents a combined Mie theory and Monte Carlo method to investigate visible and near-infrared spectral reflectance and bidirectional reflectance distribution function (BRDF) of sea foam layers. A three-layer model of the sea foam is developed in which each layer is composed of large air bubbles coated with pure water. A pseudo-continuous model and Mie theory for coated spheres is used to determine the effective radiative properties of sea foam. The one-dimensional Cox-Munk surface roughness model is used to calculate the slope density functions of the wind-blown ocean surface. A Monte Carlo method is used to solve the radiative transfer equation. Effects of foam layer thickness, bubble size, wind speed, solar zenith angle, and wavelength on the spectral reflectance and BRDF are investigated. Comparisons between previous theoretical results and experimental data demonstrate the feasibility of our proposed method. Sea foam can significantly increase the spectral reflectance and BRDF of the sea surface. The absorption coefficient of seawater near the surface is not the only parameter that influences the spectral reflectance. Meanwhile, the effects of bubble size, foam layer thickness, and solar zenith angle also cannot be obviously neglected. PMID:26836550

  5. 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.

  6. Moments of spectral functions: Monte Carlo evaluation and verification.

    PubMed

    Predescu, Cristian

    2005-11-01

    The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval . The algorithmic detail that leads to robust numerical approximations is the fact that the path-integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is nonlinear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed. PMID:16383787

  7. Global Upper Mantle Radially Anisotropic Model Developed Using the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Lekic, V.; Romanowicz, B.

    2008-12-01

    Improving the resolution of global upper mantle tomographic models of shear wavespeed and anisotropy is crucial for understanding the nature and morphology of upper mantle heterogeneities. Traditional methods of global tomography that rely on infinite-frequency and first-order perturbation theory become increasingly inadequate as shorter-wavelength heterogeneities are investigated. The spectral element method, on the other hand, permits accurate calculation of wave propagation through highly heterogeneous structures, and is computationally economical when coupled with a normal mode solution and applied to a restricted region of the earth such as the upper mantle (cSEM: Capdeville et al., 2003). Importantly, cSEM allows a dramatic improvement in accounting for the effects of crustal structure. We have implemented a new method for global tomography, which uses cSEM for forward modeling in conjunction with approximate 2D finite frequency kernels for the inversion step, calculated using non-linear asymptotic coupling theory (NACT: Li and Romanowicz, 1995). In order to avoid biasing our results toward existing 3D upper mantle models, we start our iterative inversion procedure with a 1D model. We verify that the use of approximate kernels does not prevent our iterative procedure from converging. With each iteration, we include additional waveforms that would be rejected based on a comparison with the 1D starting model. We obtain the first global model of upper mantle velocity and radial anisotropy developed by applying the SEM to modeling 3-component long- period (corner frequency : 80s) fundamental- and higher-mode waveforms. Our model confirms the large- scale features observed by previous researchers. In particular, we retrieve the relatively shallow, seismically slow velocities beneath volcanic arcs and mid-ocean ridges, the deeper fast roots underlying cratons, slow velocities in the central Pacific below 250km depth, and enhanced fast velocities anomalies

  8. A method to compute the n-dimensional solid spectral angle between vectors and its use for band selection in hyperspectral data

    NASA Astrophysics Data System (ADS)

    Tian, M.; Feng, J.; Rivard, B.; Zhao, C.

    2016-08-01

    This study presents the calculation of spectral angle beyond two endmember vectors to the n-dimensional solid spectral angle (NSSA). The calculation of the NSSA is used to characterize the local spectral shape difference among a set of endmembers, leading to a methodology for band selection based on spectral shape variations of more than two spectra. Equidistributed sequences used in the quasi-Monte Carlo method (ESMC) for numerical simulations are shown to expedite the calculation of the NSSA. We develop a band selection method using the computation of NSSA(ϑn) in the context of a sliding window. By sliding the window over all bands available for varying band intervals, the calculated solid spectral angle values can capture the similarity of the endmembers over all spectral regions available and for spectral features of varying widths. By selecting a subset of spectral bands with largest solid spectral angles, a methodology can be developed to capture the most important spectral information for the separation or mapping of endmembers. We provide an example of the merits of the NSSA-ESMC method for band selection as applied to linear spectral unmixing. Specifically, we examine the endmember abundance errors resulting from the NSSA band selection method as opposed to using the full spectral dimensionality available.

  9. Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

    NASA Astrophysics Data System (ADS)

    Chassaing, J.-C.; Lucor, D.; Trégon, J.

    2012-01-01

    An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.

  10. 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.

  11. 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.

  12. 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.

  13. 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).

  14. 3D simulation of seismic wave propagation around a tunnel using the spectral element method

    NASA Astrophysics Data System (ADS)

    Lambrecht, L.; Friederich, W.

    2010-05-01

    We model seismic wave propagation in the environment of a tunnel for later application to reconnaissance. Elastic wave propagation can be simulated by different numerical techniques such as finite differences and pseudospectral methods. Their disadvantage is the lack of accuracy on free surfaces, numerical dispersion and inflexibility of the mesh. Here we use the software package SPECFEM3D_SESAME in an svn development version, which is based on the spectral element method (SEM) and can handle complex mesh geometries. A weak form of the elastic wave equation leads to a linear system of equations with a diagonal mass matrix, where the free surface boundary of the tunnel can be treated under realistic conditions and can be effectively implemented in parallel. We have designed a 3D external mesh including a tunnel and realistic features such as layers and holes to simulate elastic wave propagation in the zone around the tunnel. The source is acting at the tunnel surface so that we excite Rayleigh waves which propagate to the front face of the tunnel. A conversion takes place and a high amplitude S-wave is radiated in the direction of the tunnel axis. Reflections from perturbations in front of the tunnel can be measured by receivers implemented on the tunnel face. For a shallow tunnel the land surface has high influence on the wave propagation. By implementing additional receivers at this surface we intent to improve the prediction. It shows that the SEM is very capable to handle the complex geometry of the model and especially incorporates the free surfaces of the model.

  15. 3D Spectral Element Method Simulations Of The Seismic Response of Caracas (Venezuela) Basin

    NASA Astrophysics Data System (ADS)

    Delavaud, E.; Vilotte, J.; Festa, G.; Cupillard, P.

    2007-12-01

    We present here 3D numerical simulations of the response of the Caracas (Venezuela) valley up to 5 Hz for different scenarios of plane wave excitation based on the regional seismicity. Attention is focused on the effects of the 3D basin geometry and of the adjacent regional topography. The simulations are performed using Spectral Element method (SEM) together with an unstructured hexahedral mesh discretization and perfectly matched layers (PML). These simulations show 3D amplification phenomena associated with complex wave reflexion, diffraction and focalisation patterns linked to the geometry of the basin. Time and frequency analysis reveal some interesting features both in terms of amplification and energy residence in the basin. The low frequency amplification pattern is mainly controlled by the early response of the basin to the incident plane wave while the high frequency amplification patterns result mainly from late arrivals where complex 3D wave diffraction phenomena are dominating and the memory of the initial excitation is lost. Interestingly enough, it is shown that H/V method correctly predict the low frequency amplification pattern when apply to the late part of the recorded seismograms. The complex high frequency amplification pattern is shown to be associated with surface wave generation at, and propagation from, sharp edges of the basin. Importance of 3D phenomena is assessed by comparison with simple 2D simulations. Significant differences in terms of time of residence, energy and amplification levels point out the interest of complete 3D modeling. In conclusions some of the limitations associated with the use of unstructured hexahedral meshes will be adressed. Despite the use of unstructured meshing tool, modeling the geometry of geological basins remain a complex and time consuming task. Possible extensions using more elaborate techniques like non conforming domain decomposition will be also discussed in conclusion.

  16. A method for analysis of stability of flows in ribbed annuli

    NASA Astrophysics Data System (ADS)

    Moradi, H. V.; Floryan, J. M.

    2016-06-01

    A spectrally-accurate algorithm for the linear stability analysis of pressure-gradient-driven flows in corrugated annuli is presented. The algorithm is suitable to analyze three-dimensional disturbances in the form of spiral traveling waves as well as in the form of streamwise vortices. A separate algorithm for the analysis of axisymmetric disturbances is presented. The discretization method relies on Fourier expansions in the streamwise and circumferential directions and on Chebyshev expansions in the radial direction. The Immersed Boundary Conditions (IBC) method is used to enforce the physical boundary conditions at the corrugated walls. Numerous tests confirm the spectral accuracy of the results. The performance of the algorithm is consistent with the theoretical predictions.

  17. 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...

  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. don...

  19. MapReduce Implementation of a Hybrid Spectral Library-Database Search Method for Large-Scale Peptide Identification

    SciTech Connect

    Kalyanaraman, Anantharaman; Cannon, William R.; Latt, Benjamin K.; Baxter, Douglas J.

    2011-11-01

    A MapReduce-based implementation called MR- MSPolygraph for parallelizing peptide identification from mass spectrometry data is presented. The underlying serial method, MSPolygraph, uses a novel hybrid approach to match an experimental spectrum against a combination of a protein sequence database and a spectral library. Our MapReduce implementation can run on any Hadoop cluster environment. Experimental results demonstrate that, relative to the serial version, MR-MSPolygraph reduces the time to solution from weeks to hours, for processing tens of thousands of experimental spectra. Speedup and other related performance studies are also reported on a 400-core Hadoop cluster using spectral datasets from environmental microbial communities as inputs.

  20. Classification method, spectral diversity, band combination and accuracy assessment evaluation for urban feature detection

    NASA Astrophysics Data System (ADS)

    Erener, A.

    2013-04-01

    Automatic extraction of urban features from high resolution satellite images is one of the main applications in remote sensing. It is useful for wide scale applications, namely: urban planning, urban mapping, disaster management, GIS (geographic information systems) updating, and military target detection. One common approach to detecting urban features from high resolution images is to use automatic classification methods. This paper has four main objectives with respect to detecting buildings. The first objective is to compare the performance of the most notable supervised classification algorithms, including the maximum likelihood classifier (MLC) and the support vector machine (SVM). In this experiment the primary consideration is the impact of kernel configuration on the performance of the SVM. The second objective of the study is to explore the suitability of integrating additional bands, namely first principal component (1st PC) and the intensity image, for original data for multi classification approaches. The performance evaluation of classification results is done using two different accuracy assessment methods: pixel based and object based approaches, which reflect the third aim of the study. The objective here is to demonstrate the differences in the evaluation of accuracies of classification methods. Considering consistency, the same set of ground truth data which is produced by labeling the building boundaries in the GIS environment is used for accuracy assessment. Lastly, the fourth aim is to experimentally evaluate variation in the accuracy of classifiers for six different real situations in order to identify the impact of spatial and spectral diversity on results. The method is applied to Quickbird images for various urban complexity levels, extending from simple to complex urban patterns. The simple surface type includes a regular urban area with low density and systematic buildings with brick rooftops. The complex surface type involves almost all

  1. Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

    NASA Astrophysics Data System (ADS)

    Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

    2014-12-01

    Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

  2. Spectral domain analysis of conducting patches of arbitrary geometry in multilayer media using the CG-FFT method

    NASA Astrophysics Data System (ADS)

    Catedra, Manuel F.; Gago, Emilio

    1990-10-01

    A conjugate-gradient fast-Fourier-transform (CG-FFT) scheme for analyzing finite flat metallic patches in multilayer structures is presented. Rooftop and razor-blade functions are considered as basis and testing functions, respectively. An equivalent periodic problem in both domains (real and spectral) is obtained and solved. Aliasing problems are avoided by performing a window on the Green's function. The spectral domain periodicity makes it feasible to take into account almost all the harmonics and to reduce the ripple in the computed current distributions. Nearly all the operations are performed in the spectral domain, including Green's function computations. Several results of convergence rates, current distributions and radar cross-section values are given and compare favorably with measurements or results obtained by other methods.

  3. Prediction of the spectral reflectance of laser-generated color prints by combination of an optical model and learning methods.

    PubMed

    Nébouy, David; Hébert, Mathieu; Fournel, Thierry; Larina, Nina; Lesur, Jean-Luc

    2015-09-01

    Recent color printing technologies based on the principle of revealing colors on pre-functionalized achromatic supports by laser irradiation offer advanced functionalities, especially for security applications. However, for such technologies, the color prediction is challenging, compared to classic ink-transfer printing systems. The spectral properties of the coloring materials modified by the lasers are not precisely known and may strongly vary, depending on the laser settings, in a nonlinear manner. We show in this study, through the example of the color laser marking (CLM) technology, based on laser bleaching of a mixture of pigments, that the combination of an adapted optical reflectance model and learning methods to get the model's parameters enables prediction of the spectral reflectance of any printable color with rather good accuracy. Even though the pigment mixture is formulated from three colored pigments, an analysis of the dimensionality of the spectral space generated by CLM printing, thanks to a principal component analysis decomposition, shows that at least four spectral primaries are needed for accurate spectral reflectance predictions. A polynomial interpolation is then used to relate RGB laser intensities with virtual coordinates of new basis vectors. By studying the influence of the number of calibration patches on the prediction accuracy, we can conclude that a reasonable number of 130 patches are enough to achieve good accuracy in this application. PMID:26367434

  4. A general spectral method for the numerical simulation of one-dimensional interacting fermions

    NASA Astrophysics Data System (ADS)

    Clason, Christian; von Winckel, Gregory

    2012-08-01

    This software implements a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient Matlab program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. The new version includes a Python implementation of the presented approach. New version program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 332 No. of bytes in distributed program, including test data, etc.: 5418 Distribution format: tar.gz Programming language: MATLAB/GNU Octave, Python Computer: Any architecture supported by MATLAB, GNU Octave or Python Operating system: Any supported by MATLAB, GNU Octave or Python RAM: Depends on the data Classification: 4.3, 2.2. External routines: Python 2.7+, NumPy 1.3+, SciPy 0.10+ Catalogue identifier of previous version: AEKO_v1_0 Journal reference of previous version: Comput. Phys. Commun. 183 (2012) 405 Does the new version supersede the previous version?: Yes Nature of problem: The direct numerical

  5. Estimation of Field-scale Aquifer Hydraulic and Sorption Parameters Based on Borehole Spectral Gamma Methods

    NASA Astrophysics Data System (ADS)

    Ward, A. L.; Draper, K.; Hasan, N.

    2010-12-01

    Knowledge of spatially variable aquifer hydraulic and sorption parameters is a pre-requisite for an improved understanding of the transport and spreading of sorbing solutes and for the development of effective strategies for remediation. Local-scale estimates of these parameters are often derived from core measurements but are typically not representative of field values. Fields-scale estimates are typically derived from pump and tracer tests but often lack the spatial resolution necessary to deconvolve the effects of fine-scale heterogeneities. Geophysical methods have the potential to bridge this gap both in terms of coverage and resolution, provided meaningful petrophysical relationships can be developed. The objective of this study was to develop a petrophysical relationship between soil textural attributes and the gamma-energy response of natural sediments. Measurements from Hanford’s 300 Area show the best model to be a linear relationship between 232Th concentration and clay content (R2 = 94%). This relationship was used to generate a 3-D distribution of clay mass fraction based on borehole spectral gamma logs. The distribution of clay was then used to predict distributions of permeability, porosity, bubbling pressure, and the pore-size distribution index, all of which are required for predicting variably saturated flow, as well as the specific surface area and cation exchange capacity needed for reactive transport predictions. With this approach, it is possible to obtain reliable estimates of hydraulic properties in zones that could not be characterized by field or laboratory measurements. The spatial distribution of flow properties is consistent with lithologic transitions inferred from geologist’s logs. A preferential flow path, identified from solute and heat tracer experiments and attributed to an erosional incision in the low-permeability Ringold Formation, is also evident. The resulting distributions can be used as a starting model for the

  6. Modeling of acoustic and gravity waves propagation through the atmosphere with spectral element method

    NASA Astrophysics Data System (ADS)

    Brissaud, Q.; Garcia, R.; Martin, R.; Komatitsch, D.

    2014-12-01

    Low-frequency events such as tsunamis generate acoustic and gravity waves which quickly propagate in the atmosphere. Since the atmospheric density decreases exponentially as the altitude increases and from the conservation of the kinetic energy, those waves see their amplitude raise (to the order of 105 at 200km of altitude), allowing their detection in the upper atmosphere. Various tools have been developed through years to model this propagation, such as normal modes modeling or to a greater extent time-reversal techniques, but none offer a low-frequency multi-dimensional atmospheric wave modelling.A modeling tool is worthy interest since there are many different phenomena, from quakes to atmospheric explosions, able to propagate acoustic and gravity waves. In order to provide a fine modeling of the precise observations of these waves by GOCE satellite data, we developed a new numerical modeling tool.Starting from the SPECFEM program that already propagate waves in solid, porous or fluid media using a spectral element method, this work offers a tool with the ability to model acoustic and gravity waves propagation in a stratified attenuating atmosphere with a bottom forcing or an atmospheric source.Atmospheric attenuation is required in a proper modeling framework since it has a crucial impact on acoustic wave propagation. Indeed, it plays the role of a frequency filter that damps high-frequency signals. The bottom forcing feature has been implemented due to its ability to easily model the coupling with the Earth's or ocean's surface (that vibrates when a surface wave go through it) but also huge atmospheric events.

  7. Numerical modeling of acoustic and gravity waves propagation in the atmosphere using a spectral element method

    NASA Astrophysics Data System (ADS)

    Martin, Roland; Brissaud, Quentin; Garcia, Raphael; Komatitsch, Dimitri

    2015-04-01

    During low-frequency events such as tsunamis, acoustic and gravity waves are generated and quickly propagate in the atmosphere. Due to the exponential decrease of the atmospheric density with the altitude, the conservation of the kinetic energy imposes that the amplitude of those waves increases (to the order of 105 at 200km of altitude), which allows their detection in the upper atmosphere. This propagation bas been modelled for years with different tools, such as normal modes modeling or to a greater extent time-reversal techniques, but a low-frequency multi-dimensional atmospheric wave modelling is still crucially needed. A modeling tool is worth of interest since there are many different sources, as earthquakes or atmospheric explosions, able to propagate acoustic and gravity waves. In order to provide a fine modeling of the precise observations of these waves by GOCE satellite data, we developed a new numerical modeling tool. By adding some developments to the SPECFEM package that already models wave propagation in solid, porous or fluid media using a spectral element method, we show here that acoustic and gravity waves propagation can now be modelled in a stratified attenuating atmosphere with a bottom forcing or an atmospheric source. The bottom forcing feature has been implemented to easily model the coupling with the Earth's or ocean's vibrating surfaces but also huge atmospheric events. Atmospheric attenuation is also introduced since it has a crucial impact on acoustic wave propagation. Indeed, it plays the role of a frequency filter that damps high-frequency signals.

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

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  9. A new method to predict the evolution of the power spectral density for a finite-amplitude sound wave

    NASA Astrophysics Data System (ADS)

    Menounou, Penelope; Blackstock, David T.

    2004-02-01

    A method to predict the effect of nonlinearity on the power spectral density of a plane wave traveling in a thermoviscous fluid is presented. As opposed to time-domain methods, the method presented here is based directly on the power spectral density of the signal, not the signal itself. The Burgers equation is employed for the mathematical description of the combined effects of nonlinearity and dissipation. The Burgers equation is transformed into an infinite set of linear equations that describe the evolution of the joint moments of the signal. A method for solving this system of equations is presented. Only a finite number of equations is appropriately selected and solved by numerical means. For the method to be applied all appropriate joint moments must be known at the source. If the source condition has Gaussian characteristics (it is a Gaussian noise signal or a Gaussian stationary and ergodic stochastic process), then all the joint moments can be computed from the power spectral density of the signal at the source. Numerical results from the presented method are shown to be in good agreement with known analytical solutions in the preshock region for two benchmark cases: (i) sinusoidal source signal and (ii) a Gaussian stochastic process as the source condition.

  10. Advanced Spectral Analysis Methods for Quantification of Coherent Ultrasound Scattering: Applications in the Breast

    NASA Astrophysics Data System (ADS)

    Rosado-Mendez, Ivan M.

    The goal of this dissertation was to improve the diagnostic value of parametric images generated from Quantitative Ultrasound (QUS) methods based on the power spectral density (PSD) of radiofrequency echo signals. This was achieved by testing for local adherence to conventional QUS assumptions that echo signals originate from incoherent scattering, and that signals are stationary over PSD estimation windows. For this purpose, we designed a novel algorithm that empirically evaluates the statistical significance of coherent-scattering signatures in the echo signals. Signatures are quantified through a set of optimized metrics describing the stationary or non-stationary features of the echo signals. We compared Nakagami-model based metrics and model-free metrics of the statistics of the echo signal amplitude for analyzing stationary features. For non-stationary features, we advanced the use of the echo-signal generalized spectrum by comparing single- and multi-taper estimators of this spectrum to the time-domain singular spectrum analysis method. Tests of statistical significance were done through empirical comparisons with values of the same metrics estimated from a uniform reference material exhibiting incoherent scattering. The metrics that quantify these features were selected after simulation- and phantom-based optimizations centered on the task of creating parametric images, where tradeoffs must be made between spatial resolution and detection performance. The connection of the analyses of the stationary and the non-stationary features provided a way to estimate descriptors of the tissue organization scales below and above the resolution limit imposed by the size of the acoustic pulse. A preliminary application of the developed algorithm was done on echo data from human breast lesions scanned in vivo. Results supported the idea of a more homogeneously random distribution of subresolution scatterers within invasive ductal carcinomas than within fibroadenomas

  11. A neural network-based method for spectral distortion correction in photon counting x-ray CT.

    PubMed

    Touch, Mengheng; Clark, Darin P; Barber, William; Badea, Cristian T

    2016-08-21

    Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables both 4 energy bins acquisition, as well as full-spectrum mode in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical effects in the detector and can be very noisy due to photon starvation in narrow energy bins. To address spectral distortions, we propose and demonstrate a novel artificial neural network (ANN)-based spectral distortion correction mechanism, which learns to undo the distortion in spectral CT, resulting in improved material decomposition accuracy. To address noise, post-reconstruction denoising based on bilateral filtration, which jointly enforces intensity gradient sparsity between spectral samples, is used to further improve the robustness of ANN training and material decomposition accuracy. Our ANN-based distortion correction method is calibrated using 3D-printed phantoms and a model of our spectral CT system. To enable realistic simulations and validation of our method, we first modeled the spectral distortions using experimental data acquired from (109)Cd and (133)Ba radioactive sources measured with our PCXD. Next, we trained an ANN to learn the relationship between the distorted spectral CT projections and the ideal, distortion-free projections in a calibration step. This required knowledge of the ground truth, distortion-free spectral CT projections, which were obtained by simulating a spectral CT scan of the digital version of a 3D-printed phantom. Once the training was completed, the trained ANN was used to perform

  12. A neural network-based method for spectral distortion correction in photon counting x-ray CT

    NASA Astrophysics Data System (ADS)

    Touch, Mengheng; Clark, Darin P.; Barber, William; Badea, Cristian T.

    2016-08-01

    Spectral CT using a photon counting x-ray detector (PCXD) shows great potential for measuring material composition based on energy dependent x-ray attenuation. Spectral CT is especially suited for imaging with K-edge contrast agents to address the otherwise limited contrast in soft tissues. We have developed a micro-CT system based on a PCXD. This system enables both 4 energy bins acquisition, as well as full-spectrum mode in which the energy thresholds of the PCXD are swept to sample the full energy spectrum for each detector element and projection angle. Measurements provided by the PCXD, however, are distorted due to undesirable physical effects in the detector and can be very noisy due to photon starvation in narrow energy bins. To address spectral distortions, we propose and demonstrate a novel artificial neural network (ANN)-based spectral distortion correction mechanism, which learns to undo the distortion in spectral CT, resulting in improved material decomposition accuracy. To address noise, post-reconstruction denoising based on bilateral filtration, which jointly enforces intensity gradient sparsity between spectral samples, is used to further improve the robustness of ANN training and material decomposition accuracy. Our ANN-based distortion correction method is calibrated using 3D-printed phantoms and a model of our spectral CT system. To enable realistic simulations and validation of our method, we first modeled the spectral distortions using experimental data acquired from 109Cd and 133Ba radioactive sources measured with our PCXD. Next, we trained an ANN to learn the relationship between the distorted spectral CT projections and the ideal, distortion-free projections in a calibration step. This required knowledge of the ground truth, distortion-free spectral CT projections, which were obtained by simulating a spectral CT scan of the digital version of a 3D-printed phantom. Once the training was completed, the trained ANN was used to perform

  13. A spectrally accurate boundary-layer code for infinite swept wings

    NASA Technical Reports Server (NTRS)

    Pruett, C. David

    1994-01-01

    This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

  14. Spectral analysis of the Chandler wobble: comparison of the discrete Fourier analysis and the maximum entropy method

    NASA Astrophysics Data System (ADS)

    Brzezinski, A.

    2014-12-01

    The methods of spectral analysis are applied to solve the following two problems concerning the free Chandler wobble (CW): 1) to estimate the CW resonance parameters, the period T and the quality factor Q, and 2) to perform the excitation balance of the observed free wobble. It appears, however, that the results depend on the algorithm of spectral analysis applied. Here we compare the following two algorithms which are frequently applied for analysis of the polar motion data, the classical discrete Fourier analysis and the maximum entropy method corresponding to the autoregressive modeling of the input time series. We start from general description of both methods and of their application to the analysis of the Earth orientation observations. Then we compare results of the analysis of the polar motion and the related excitation data.

  15. Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport Systems

    SciTech Connect

    Spata, Michael

    2012-08-01

    An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.

  16. On uniform constants of strong uniqueness in Chebyshev approximations and fundamental results of N. G. Chebotarev

    NASA Astrophysics Data System (ADS)

    Marinov, Anatolii V.

    2011-06-01

    In the problem of the best uniform approximation of a continuous real-valued function f\\in C(Q) in a finite-dimensional Chebyshev subspace M\\subset C(Q), where Q is a compactum, one studies the positivity of the uniform strong uniqueness constant \\gamma(N)=\\inf\\{\\gamma(f)\\colon f\\in N\\}. Here \\gamma(f) stands for the strong uniqueness constant of an element f_M\\in M of best approximation of f, that is, the largest constant \\gamma>0 such that the strong uniqueness inequality \\Vert f-\\varphi\\Vert\\ge\\Vert f-f_M\\Vert+\\gamma\\Vert f_M-\\varphi\\Vert holds for any \\varphi\\in M. We obtain a characterization of the subsets N\\subset C(Q) for which there is a neighbourhood O(N) of N satisfying the condition \\gamma(O(N))>0. The pioneering results of N. G. Chebotarev were published in 1943 and concerned the sharpness of the minimum in minimax problems and the strong uniqueness of algebraic polynomials of best approximation. They seem to have been neglected by the specialists, and we discuss them in detail.

  17. Systems and methods for selective detection and imaging in coherent Raman microscopy by spectral excitation shaping

    DOEpatents

    Xie, Xiaoliang Sunney; Freudiger, Christian; Min, Wei

    2016-03-15

    A microscopy imaging system is disclosed that includes a light source system, a spectral shaper, a modulator system, an optics system, an optical detector and a processor. The light source system is for providing a first train of pulses and a second train of pulses. The spectral shaper is for spectrally modifying an optical property of at least some frequency components of the broadband range of frequency components such that the broadband range of frequency components is shaped producing a shaped first train of pulses to specifically probe a spectral feature of interest from a sample, and to reduce information from features that are not of interest from the sample. The modulator system is for modulating a property of at least one of the shaped first train of pulses and the second train of pulses at a modulation frequency. The optical detector is for detecting an integrated intensity of substantially all optical frequency components of a train of pulses of interest transmitted or reflected through the common focal volume. The processor is for detecting a modulation at the modulation frequency of the integrated intensity of substantially all of the optical frequency components of the train of pulses of interest due to the non-linear interaction of the shaped first train of pulses with the second train of pulses as modulated in the common focal volume, and for providing an output signal for a pixel of an image for the microscopy imaging system.

  18. Spectral convergence of the quadrature discretization method in the solution of the Schrodinger and Fokker-Planck equations: comparison with sinc methods.

    PubMed

    Lo, Joseph; Shizgal, Bernie D

    2006-11-21

    Spectral methods based on nonclassical polynomials and Fourier basis functions or sinc interpolation techniques are compared for several eigenvalue problems for the Fokker-Planck and Schrodinger equations. A very rapid spectral convergence of the eigenvalues versus the number of quadrature points is obtained with the quadrature discretization method (QDM) and the appropriate choice of the weight function. The QDM is a pseudospectral method and the rate of convergence is compared with the sinc method reported by Wei [J. Chem. Phys., 110, 8930 (1999)]. In general, sinc methods based on Fourier basis functions with a uniform grid provide a much slower convergence. The paper considers Fokker-Planck equations (and analogous Schrodinger equations) for the thermalization of electrons in atomic moderators and for a quartic potential employed to model chemical reactions. The solution of the Schrodinger equation for the vibrational states of I2 with a Morse potential is also considered. PMID:17129090

  19. Estimation of the effective elastic thickness of the lithosphere using inverse spectral methods: The state of the art

    NASA Astrophysics Data System (ADS)

    Kirby, Jon F.

    2014-09-01

    The effective elastic thickness (Te) is a geometric measure of the flexural rigidity of the lithosphere, which describes the resistance to bending under the application of applied, vertical loads. As such, it is likely that its magnitude has a major role in governing the tectonic evolution of both continental and oceanic plates. Of the several ways to estimate Te, one has gained popularity in the 40 years since its development because it only requires gravity and topography data, both of which are now readily available and provide excellent coverage over the Earth and even the rocky planets and moons of the solar system. This method, the ‘inverse spectral method’, develops measures of the relationship between observed gravity and topography data in the spatial frequency (wavenumber) domain, namely the admittance and coherence. The observed measures are subsequently inverted against the predictions of thin, elastic plate models, giving estimates of Te and other lithospheric parameters. This article provides a review of inverse spectral methodology and the studies that have used it. It is not, however, concerned with the geological or geodynamic significance or interpretation of Te, nor does it discuss and compare Te results from different methods in different provinces. Since the three main aspects of the subject are thin elastic plate flexure, spectral analysis, and inversion methods, the article broadly follows developments in these. The review also covers synthetic plate modelling, and concludes with a summary of the controversy currently surrounding inverse spectral methods, whether or not the large Te values returned in cratonic regions are artefacts of the method, or genuine observations.

  20. Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

    SciTech Connect

    Gamba, Irene M. Tharkabhushanam, Sri Harsha

    2009-04-01

    We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ()]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst