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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. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  4. Efficient rational Chebyshev pseudo-spectral method with domain decomposition for optical waveguides modal analysis.

    PubMed

    Abdrabou, Amgad; Heikal, A M; Obayya, S S A

    2016-05-16

    We propose an accurate and computationally efficient rational Chebyshev multi-domain pseudo-spectral method (RC-MDPSM) for modal analysis of optical waveguides. For the first time, we introduce rational Chebyshev basis functions to efficiently handle semi-infinite computational subdomains. In addition, the efficiency of these basis functions is enhanced by employing an optimized algebraic map; thus, eliminating the use of PML-like absorbing boundary conditions. For leaky modes, we derived a leaky modes boundary condition at the guide-substrate interface providing an efficient technique to accurately model leaky modes with very small refractive index imaginary part. The efficiency and numerical precision of our technique are demonstrated through the analysis of high-index contrast dielectric and plasmonic waveguides, and the highly-leaky ARROW structure; where finding ARROW leaky modes using our technique clearly reflects its robustness.

  5. Solution of nonlinear partial differential equations using the Chebyshev spectral method

    NASA Astrophysics Data System (ADS)

    Kapania, R. K.; Eldred, L. B.

    1991-05-01

    The spectral method is a powerful numerical technique for solving engineering differential equations. The method is a specialization of the method of weighted residuals. Trial functions that are easily and exactly differentiable are used. Often the functions used also satisfy an orthogonality equation, which can improve the efficiency of the approximation. Generally, the entire domain is modeled, but multiple sub-domains may be used. A Chebyshev-Collocation Spectral method is used to solve a two-dimensional, highly nonlinear, two parameter Bratu's equation. This equation previously assumed to have only symmetric solutions are shown to have regions where solutions that are non-symmetric in x and y are valid. Away from these regions an accurate and efficient technique for tracking the equation's multi-valued solutions was developed. It is found that the accuracy of the present method is very good, with a significant improvement in computer time.

  6. 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

  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.

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

    PubMed

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

    2014-01-01

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

    NASA Astrophysics Data System (ADS)

    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

  12. 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

  13. The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations

    NASA Astrophysics Data System (ADS)

    Che, Cheng-Xuan; Wang, Xiu-Ming; Lin, Wei-Jun

    2010-06-01

    Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method (SEM) using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient (PCG)-element by element (EBE) method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method (FDM) for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.

  14. 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.

  15. Schur-decomposition for 3D matrix equations and its application in solving radiative discrete ordinates equations discretized by Chebyshev collocation spectral method

    SciTech Connect

    Li Benwen Tian Shuai; Sun Yasong; Hu, Zhang-Mao

    2010-02-20

    The Schur-decomposition for three-dimensional matrix equations is developed and used to directly solve the radiative discrete ordinates equations which are discretized by Chebyshev collocation spectral method. Three methods, say, the spectral methods based on 2D and 3D matrix equation solvers individually, and the standard discrete ordinates method, are presented. The numerical results show the good accuracy of spectral method based on direct solvers. The CPU time cost comparisons against the resolutions between these three methods are made using MATLAB and FORTRAN 95 computer languages separately. The results show that the CPU time cost of Chebyshev collocation spectral method with 3D Schur-decomposition solver is the least, and almost only one thirtieth to one fiftieth CPU time is needed when using the spectral method with 3D Schur-decomposition solver compared with the standard discrete ordinates method.

  16. 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.

  17. 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.

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

    SciTech Connect

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

    2012-07-01

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

  19. 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.

  20. 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.

  1. Parallel implementation of a Fourier-Chebyshev spectral method for the three-dimensional Navier-Stokes equations and application to transitional flow in cylindrical geometries

    NASA Astrophysics Data System (ADS)

    Hill, Roger Wayne

    1998-12-01

    A Fourier-Chebyshev collocation spectral method is parallelized to solve the incompressible and unsteady three dimensional Navier-Stokes equations using distributed memory and shared memory computing platforms. Two temporal discretization approaches using different techniques for treating the diffusive terms, determining the pressure field, and enforcing mass conservation are applied to study transitional flow in three types of enclosed cylindrical geometries. The first type is between counter rotating disks, the second is between corotating disks, and the third is in a differentially heated vertical annulus. Matrix diagonalization is employed for solving the pressure Poisson equation and the Helmholtz equations for the velocity components, providing a fast and efficient solution scheme. The parallelization approach is described and scaling results are presented for both shared memory and distributed memory parallel computing platform types. Numerical results are also presented for both axisymmetric and fully three dimensional simulations and compared with selected experimental data to demonstrate the accuracy of the method and the importance of properly capturing the unsteady three dimensional effects even though the geometry under consideration is two dimensional. For the counter rotating disk geometry, three dimensional simulations reveal that the initial transition is to unsteady three dimensional flow and the onset of unsteady flow occurs at much lower disk spin speeds than predicted with two dimensional simulations. The three dimensional simulations also closely match experimental velocity profiles whereas two dimensional simulations agree poorly. The initial transition in the corotating disk geometry is also to an unsteady three dimensional flow and occurs at much lower disk spin speeds than indicated by two dimensional simulations. Agreement with experimental data is not particularly good, but it is shown that the discrepancy may be attributed to a boundary

  2. 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.

  3. Mappings and accuracy for Chebyshev pseudo-spectral approximations

    NASA Technical Reports Server (NTRS)

    Bayliss, Alvin; Turkel, Eli

    1992-01-01

    The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.

  4. Mappings and accuracy for Chebyshev pseudo-spectral approximations

    NASA Technical Reports Server (NTRS)

    Bayliss, Alvin; Turkel, Eli

    1990-01-01

    The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Liu, Yi-Xin; Zhang, Hong-Dong

    2014-06-01

    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.

  7. 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.

  8. 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.

  9. 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

  10. Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions

    NASA Astrophysics Data System (ADS)

    Boyd, John P.; Yu, Fu

    2011-02-01

    We compare seven different strategies for computing spectrally-accurate approximations or differential equation solutions in a disk. Separation of variables for the Laplace operator yields an analytic solution as a Fourier-Bessel series, but this usually converges at an algebraic (sub-spectral) rate. The cylindrical Robert functions converge geometrically but are horribly ill-conditioned. The Zernike and Logan-Shepp polynomials span the same space, that of Cartesian polynomials of a given total degree, but the former allows partial factorization whereas the latter basis facilitates an efficient algorithm for solving the Poisson equation. The Zernike polynomials were independently rediscovered several times as the product of one-sided Jacobi polynomials in radius with a Fourier series in θ. Generically, the Zernike basis requires only half as many degrees of freedom to represent a complicated function on the disk as does a Chebyshev-Fourier basis, but the latter has the great advantage of being summed and interpolated entirely by the Fast Fourier Transform instead of the slower matrix multiplication transforms needed in radius by the Zernike basis. Conformally mapping a square to the disk and employing a bivariate Chebyshev expansion on the square is spectrally accurate, but clustering of grid points near the four singularities of the mapping makes this method less efficient than the rest, meritorious only as a quick-and-dirty way to adapt a solver-for-the-square to the disk. Radial basis functions can match the best other spectral methods in accuracy, but require slow non-tensor interpolation and summation methods. There is no single “best” basis for the disk, but we have laid out the merits and flaws of each spectral option.

  11. Spectral methods for partial differential equations

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

    Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid-dynamical applications are emphasized.

  12. Spectral methods for partial differential equations

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed. Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type. Fluid dynamical applications are emphasized.

  13. 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.

  14. 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.

  15. Membrane covered duct lining for high-frequency noise attenuation: prediction using a Chebyshev collocation method.

    PubMed

    Huang, Lixi

    2008-11-01

    A spectral method of Chebyshev collocation with domain decomposition is introduced for linear interaction between sound and structure in a duct lined with flexible walls backed by cavities with or without a porous material. The spectral convergence is validated by a one-dimensional problem with a closed-form analytical solution, and is then extended to the two-dimensional configuration and compared favorably against a previous method based on the Fourier-Galerkin procedure and a finite element modeling. The nonlocal, exact Dirichlet-to-Neumann boundary condition is embedded in the domain decomposition scheme without imposing extra computational burden. The scheme is applied to the problem of high-frequency sound absorption by duct lining, which is normally ineffective when the wavelength is comparable with or shorter than the duct height. When a tensioned membrane covers the lining, however, it scatters the incident plane wave into higher-order modes, which then penetrate the duct lining more easily and get dissipated. For the frequency range of f=0.3-3 studied here, f=0.5 being the first cut-on frequency of the central duct, the membrane cover is found to offer an additional 0.9 dB attenuation per unit axial distance equal to half of the duct height.

  16. 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.

  17. Recent applications of spectral methods in fluid dynamics

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    Origins of spectral methods, especially their relation to the method of weighted residuals, are surveyed. Basic Fourier and Chebyshev spectral concepts are reviewed and demonstrated through application to simple model problems. Both collocation and tau methods are considered. These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic and mixzed type. Fluid dynamical applications are emphasized.

  18. 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.

  19. The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

    NASA Technical Reports Server (NTRS)

    Boyd, J. P.

    1982-01-01

    Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

  20. 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.

  1. 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

  2. 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.

  3. Spectral methods for the Euler equations

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

    Spectral methods for compressible flows are introduced in relation to finite difference and finite element techniques within the framework of the method of weighted residuals. Current spectral collocation methods are put in historical context. The basic concepts of both Fourier and Chebyshev spectral collocation methods are provided. Filtering strategies for both shock-fitting and shock-capturing approaches are also presented. Fourier shock capturing techniques are evaluated using a one-dimensional, periodic astrophysical 'nozzle' problem. Examples of shock-fitting approaches include a shock/acoustic wave interaction, shock/vortex interaction, and the classical blunt body problem. While the shock capturing spectral method does not yet show a clear advantage over second-order finite differences, equivalent accuracy can be obtained using shock fitting with far fewer grid points.

  4. 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.

  5. 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.

  6. 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.

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

    NASA Astrophysics Data System (ADS)

    Kaporin, I. E.

    2012-02-01

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

  8. Convergence of spectral methods for hyperbolic initial-boundary value systems

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

    A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods.

  9. 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.

  10. 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.

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

    NASA Astrophysics Data System (ADS)

    Mahmood, Asad; Chen, Bin; Ghaffari, Abuzar

    2016-10-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

    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.

  13. 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.

  14. 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.

  15. Spectral collocation methods

    NASA Technical Reports Server (NTRS)

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

    1987-01-01

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

  16. 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

  17. 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.

  18. Milling Stability Analysis Based on Chebyshev Segmentation

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  19. 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.

  20. 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.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  3. 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.

  4. Spectral methods for discontinuous problems

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

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

  5. 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.

  6. 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).

  7. 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.

  8. Spectral methods in time for a class of parabolic partial differential equations

    SciTech Connect

    Ierley, G. ); Spencer, B. ); Worthing, R. )

    1992-09-01

    In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time. 14 refs., 9 figs.

  9. A spectral element method for fluid dynamics - Laminar flow in a channel expansion

    NASA Technical Reports Server (NTRS)

    Patera, A. T.

    1984-01-01

    A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.

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

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. Method of photon spectral analysis

    DOEpatents

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

    1993-01-01

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

  18. 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.

  19. Spectral methods for exterior elliptic problems

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  20. 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.

  1. Spectral methods for problems in complex geometries

    NASA Technical Reports Server (NTRS)

    Orszag, S. A.

    1979-01-01

    Techniques that permit the efficient application of spectral methods to solve problems in nearly arbitrary geometries are presented. These methods were found to be viable alternatives to finite difference and finite element processes. The spectral methods applied are extensions of the standard techniques of separation of variables to the solution of arbitrarily complicated problems.

  2. 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.

  3. 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.

  4. Some recent developments in spectral methods

    NASA Technical Reports Server (NTRS)

    Hussaini, M. Y.

    1986-01-01

    This paper is solely devoted to spectral iterative methods including spectral multigrid methods. These techniques are explained with reference to simple model problems. Some Navier-Stokes algorithms based on these techniques are mentioned. Results on transition simulation using these algorithms are presented.

  5. 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

  6. 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

  7. IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory.

    PubMed

    Romero, M; de Madrid, A P; Mañoso, C; Vinagre, B M

    2013-07-01

    This paper deals with the use of Chebyshev polynomials theory to achieve accurate discrete-time approximations to the fractional-order differentiator/integrator in terms of IIR filters. These filters are obtained using the Chebyshev-Padé and the Rational Chebyshev approximations, two highly accurate numerical methods that can be computed with ease using available software. They are compared against other highly accurate approximations proposed in the literature. It is also shown how the frequency response of the fractional-order integrator approximations can be easily improved at low frequencies. PMID:23507506

  8. Spectral element methods - Algorithms and architectures

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

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

  9. Spectral element methods: Algorithms and architectures

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

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

  10. 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.

  11. 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.

  12. Spectral methods for compressible reactive flows

    NASA Astrophysics Data System (ADS)

    Gottlieb, David; Gottlieb, Sigal

    2005-01-01

    High order simulations are necessary in order to capture fine details in resolving supersonic reactive flows. However, high Mach number compressible flows feature sharp gradients and discontinuities, which present a challenge to successful simulations using high order methods. Spectral methods have proven a powerful tool in simulation of incompressible turbulent flows, and recent advances allow the application of spectral methods to compressible reactive flows. We review the recent advances in the theory and application of spectral methods which allow stable computations of discontinuous phenomena, and the recovery of high order information via postprocessing, and present applications of high Mach number reactive flows. To cite this article: D. Gottlieb, S. Gottlieb, C. R. Mecanique 333 (2005).

  13. Novel methods for spectral analysis

    NASA Astrophysics Data System (ADS)

    Roy, R.; Sumpter, B. G.; Pfeffer, G. A.; Gray, S. K.; Noid, D. W.

    1991-06-01

    In this review article, various techniques for obtaining estimates of parameters related to the spectrum of an underlying process are discussed. These techniques include the conventional nonparametric FFT approach and more recently developed parametric techniques such as maximum entropy, MUSIC, and ESPRIT, the latter two being classified as signal-subspace or eigenvector techniques. These estimators span the spectrum of possible estimators in that extremes of a priori knowledge are assumed (nonparametric versus parametric) and extremes in the underlying model of the observed process (deterministic versus stochastic) are involved. The advantage of parametric techniques is their ability to provide very accurate estimates using data from extremely short time intervals. Several applications of these novel methods for frequency analysis of very short time data are presented. These include calculation of dispersion curves, and the density of vibrational states g(ω) for many-body systems, semiclassical transition frequencies, overtone linewidths, and resonance energies of the time-dependent Schrödinger equation for few-body problems.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. A spectral mimetic least-squares method

    DOE PAGES

    Bochev, Pavel; Gerritsma, Marc

    2014-09-01

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

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Application of Collocation Spectral Method for Irregular Convective-Radiative Fins with Temperature-Dependent Internal Heat Generation and Thermal Properties

    NASA Astrophysics Data System (ADS)

    Sun, Ya-Song; Ma, Jing; Li, Ben-Wen

    2015-11-01

    A collocation spectral method (CSM) is developed to solve the fin heat transfer in triangular, trapezoidal, exponential, concave parabolic, and convex geometries. In the thermal process of fin heat transfer, fin dissipates heat to environment by convection and radiation; internal heat generation, thermal conductivity, heat transfer coefficient, and surface emissivity are functions of temperature; ambient fluid temperature and radiative sink temperature are considered to be nonzero. The temperature in the fin is approximated by Chebyshev polynomials and spectral collocation points. Thus, the differential form of energy equation is transformed into the matrix form of algebraic equation. In order to test efficiency and accuracy of the developed method, five types of convective-radiative fins are examined. Results obtained by the CSM are assessed by comparing available results in references. These comparisons indicate that the CSM can be recommended as a good option to simulate and predict thermal performance of the convective-radiative fins.

  6. Relaxation schemes for spectral multigrid methods

    NASA Technical Reports Server (NTRS)

    Phillips, Timothy N.

    1987-01-01

    The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.

  7. 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

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

    NASA Astrophysics Data System (ADS)

    Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas; Galgon, Martin; Fehske, Holger; Hager, Georg; Lang, Bruno; Wellein, Gerhard

    2016-11-01

    We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 102 innermost eigenpairs of a topological insulator matrix with dimension 109 derived from quantum physics applications.

  9. Spectral method for a kinetic swarming model

    DOE PAGES

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

    2015-04-28

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

  10. Black Hole Scattering via Spectral Methods

    NASA Astrophysics Data System (ADS)

    Clemente, P. C. M.; de Oliveira, H. P.; Rodrigues, E. L.

    2013-12-01

    We present an alternative method to solve the problem of scattering by a black hole by adapting the spectral code originally developed by Boyd (Comp Phys 4:83, 1990). In order to show the effectiveness and versatility of the algorithm, we solve the scattering by Schwarzschild, standard acoustic, and charged black holes. We recover the partial and total absorption cross sections and, in the case of charged black holes, the conversion factor of eletromagnetic and gravitational waves. We also study the exponential decay of the reflection coefficient, which is a general feature of any scattering problem.

  11. 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.

  12. Parallel algorithms for the spectral transform method

    SciTech Connect

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

    1997-05-01

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

  13. Research on how to enhance the Chebyshev DC/DC filter's performance 1

    NASA Astrophysics Data System (ADS)

    Lixia, Zhang; Jianting, Gui; Xing, Chen; He, Zhang; Guangxing, Zhan

    To enhance the response speed of the battery pack testing system, the principle of damping-control algorithm and pole-shifting method are analyzed. There steady characteristic and dynamic response abilities that applied to Chebyshev filter are deduced and compared. Based on the optimized equivalent battery model, The Battery testing system is established by MATLAB7.01 to test the characteristics of the three amended Chebyshev filter. Tests were also carried out to proof the scheme. Researches showed that the pole-shifting method possesses batter combination property.

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

    NASA Technical Reports Server (NTRS)

    Deprit, A.

    1975-01-01

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

  15. 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.

  16. Can time-spectral methods improve turbulence modelling?

    NASA Astrophysics Data System (ADS)

    Scheffel, Jan

    2014-10-01

    In computational fusion physics, the widely separated time and space scales often demand extremely long computer simulations and vast memory resources, using finite time steps. Gyrokinetic turbulence modelling at high Reynolds or Lundquist numbers may be allocated millions of CPU hours for parallel processing on supercomputers. It is thus worthwhile to explore new avenues that may alleviate requirements on computer power. Indeed, time-stepping may be completely avoided for initial-value problems. In the recently developed Generalized Weighted Residual Method GWRM, temporal, spatial and parameter domains are all handled using a solution ansatz in the form of a sum of Chebyshev polynomials. The coefficients of the ansatz are determined using a weighted residual method for which a new efficient equation solver has been developed. In addition, the temporal and spatial computational region has been successfully treated using subdomain methods in a number of test problems, more efficiently than relevant finite difference methods. The GWRM, however, relies on solution of linear systems of equations in each subdomain, and memory requirement is an issue. In this presentation we will discuss recent subdomain approaches for efficient and convergent modelling of drift-wave turbulence.

  17. 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.

  18. 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.

  19. 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.

  20. Spectral element methods for the incompressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Maday, Yvon; Patera, Anthony T.

    1989-01-01

    Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.

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

    NASA Technical Reports Server (NTRS)

    Wiscombe, W. J.; Mugnai, A.

    1986-01-01

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

  2. Spectral element method and the delayed feedback control of chaos.

    PubMed

    Tweten, Dennis J; Mann, Brian P

    2012-10-01

    A spectral element approach is introduced to determine the Floquet exponents (FEs) of unstable periodic orbits (UPOs) stabilized by extended delayed feedback control (EDFC). The spectral approach does not require solving time-dependent eigenproblems that existing methods require. Instead, the spectral approach determines the stability of the delay differential equations of the system by numerical approximation. The method is capable of analyzing systems whose UPOs arise from bifurcations other than period-doubling. Results are presented for stabilizing UPOs in Duffing systems. The FEs calculated by the spectral approach are compared to published results for two examples. In both cases, the spectral method results agree well with those determined by previous methods. In addition, the spectral method was used to analyze a high-dimensional, asymmetrical system with a UPO in chaos arising from tori doubling following a Hopf bifurcation. PMID:23214670

  3. 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.

  4. [Standardization of technical methods for apple fluorescence canopy spectral detection].

    PubMed

    Zhu, Xi-Cun; Zhao, Geng-Xing; Lei, Tong; Wang, Ling; Dong, Fang; Wang, Jing-An

    2010-06-01

    Aiming at spectral detection of apple fluorescence canopy, the present paper carried out spectral detection tests under different weather conditions, different detection times, and different detection heights and angles to apple canopy in the two years of 2008 and 2009, so as to analyze impacts of these factors on apple canopy spectral characteristics and explore standardized spectral detection methods for apple fluorescence canopy. The results indicated the regularity in spectral reflectance of apple fluorescence canopy to a certain degree under different conditions, especially in the 760-1 350 nm near-infrared bands. The authors found that canopy spectral reflectance declined along with the decrease in sunshine and it is appropriate to detect canopy spectrum in sunny days with few clouds. In addition, spectral reflectance tended to be stable when the wind scale was below grade 2. The discrepancy of canopy spectra is small during the time period from 10:00 to 15:00 of a day compared to that of other times. For maintaining stable spectral curves, the height of detector to apple canopy needed to be adjusted to cover the whole canopy within the field of view according to detection angle of the detector. The vertical or approximately vertical detection was the best for canopy spectral reflectance acquisition. The standardization of technical methods of spectral detection for apple fluorescence canopy was proposed accordingly, which provided theoretical references for spectral detection and information extraction of apple tree canopy.

  5. 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.

  6. 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.

  7. 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.

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

    NASA Astrophysics Data System (ADS)

    Skerovic, V.; Zarubica, V.; Zekovic, L.; Belca, I.; Aleksić, M.

    2010-10-01

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

  9. Design of Chebyshev microstrip low-pass filter using defected ground structure

    NASA Astrophysics Data System (ADS)

    Yadav, Narendar S.; Chouhan, V. S.

    2013-01-01

    A method to design microstrip low pass filter having defected ground structure (DGS) is proposed. The difference between standard asymmetric microstrip technique and DGS is in using the structures etched in the microwave substrate ground plane. The DGS resonant characteristics are then used in filter design. The equivalent circuit for the proposed defected ground unit structure is derived by means of three-dimensional field analysis methods. The equivalent-circuit parameters are extracted by using a simple circuit analysis method. Filters of various orders and resonator configurations are designed and simulated. A combination of the DGS and five order low pass Chebyshev microstrip filter is designed as well realized and measurement results are compared with simulations. The experimental results show excellent agreements with theoretical results and the validity of the modeling method for the proposed defected ground unit structure. Finally, enhanced cut off frequency 2.715GHz of microstrip low pass chebyshev filter using DGS is observed.

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  11. 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.

  12. 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.

  13. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. Non-Equilibrium Allele Frequency Spectra Via Spectral Methods

    PubMed Central

    Hey, Jody; Chen, Kevin

    2011-01-01

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

  5. [Physical meaning of temperature measured by spectral line intensity method].

    PubMed

    Zhao, Wen-Hua; Tang, Huang-Zai; Shen, Yan; Shi, Yong; Hou, Ling-Yun

    2007-11-01

    The difference between electron temperature and excitation temperature is analyzed in the aspect of statistics thermodynamics. It is presented clearly that the temperature acquired by spectral line intensity method is not free electron temperature, but internal electronic excitation temperature of heavy particle. Under thermal equilibrium condition, the excitation temperature is equal to the electron temperature, while under non-thermal equilibrium condition, the excitation temperature is not equal to the electron temperature. In the study of arc jet plume in vacuum chamber, spectral line intensity method was employed to measure the apparent excitation temperature of arc jet plume, and Langmuir probe was employed to measure the electron temperature of arcjet plume. The big difference between the excitation temperature and the electron temperature proved that the temperature acquired by spectral line intensity method is not free electron temperature.

  6. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

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

  9. 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.

  10. 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.

  11. Comparison of multivariate calibration methods for quantitative spectral analysis

    SciTech Connect

    Thomas, E.V.; Haaland, D.M. )

    1990-05-15

    The quantitative prediction abilities of four multivariate calibration methods for spectral analyses are compared by using extensive Monte Carlo simulations. The calibration methods compared include inverse least-squares (ILS), classical least-squares (CLS), partial least-squares (PLS), and principal component regression (PCR) methods. ILS is a frequency-limited method while the latter three are capable of full-spectrum calibration. The simulations were performed assuming Beer's law holds and that spectral measurement errors and concentration errors associated with the reference method are normally distributed. Eight different factors that could affect the relative performance of the calibration methods were varied in a two-level, eight-factor experimental design in order to evaluate their effect on the prediction abilities of the four methods. It is found that each of the three full-spectrum methods has its range of superior performance. The frequency-limited ILS method was never the best method, although in the presence of relatively large concentration errors it sometimes yields comparable analysis precision to the full-spectrum methods for the major spectral component. The importance of each factor in the absolute and relative performances of the four methods is compared.

  12. Direct inversion methods for spectral amplitude modulation of femtosecond pulses.

    PubMed

    Delgado-Aguillón, Jesús; Garduño-Mejía, Jesús; López-Téllez, Juan Manuel; Bruce, Neil C; Rosete-Aguilar, Martha; Román-Moreno, Carlos Jesús; Ortega-Martínez, Roberto

    2014-04-01

    In the present work, we applied an amplitude-spatial light modulator to shape the spectral amplitude of femtosecond pulses in a single step, without an iterative algorithm, by using an inversion method defined as the generalized retardance function. Additionally, we also present a single step method to shape the intensity profile defined as the influence matrix. Numerical and experimental results are presented for both methods.

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

    PubMed

    Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen

    2002-11-29

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

  14. 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.

  15. 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.

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

    PubMed

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

    2013-10-01

    Aiming at the spectral distortion produced in PCA fusion process, the present paper proposes an improved low spectral distortion PCA fusion method. This method uses NCUT (normalized cut) image segmentation algorithm to make a complex hyperspectral remote sensing image into multiple sub-images for increasing the separability of samples, which can weaken the spectral distortions of traditional PCA fusion; Pixels similarity weighting matrix and masks were produced by using graph theory and clustering theory. These masks are used to cut the hyperspectral image and high-resolution image into some sub-region objects. All corresponding sub-region objects between the hyperspectral image and high-resolution image are fused by using PCA method, and all sub-regional integration results are spliced together to produce a new image. In the experiment, Hyperion hyperspectral data and Rapid Eye data were used. And the experiment result shows that the proposed method has the same ability to enhance spatial resolution and greater ability to improve spectral fidelity performance. PMID:24409735

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Experimental comparison of empirical material decomposition methods for spectral CT.

    PubMed

    Zimmerman, Kevin C; Schmidt, Taly Gilat

    2015-04-21

    Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a neural network estimator and a linearized maximum likelihood estimator with correction (A-table method). The two investigated methods differ in how they model the nonlinear relationship between the spectral measurements and material decomposition estimates. The bias and standard deviation of material decomposition estimates were compared for the two methods, using both simulations and experiments with a photon-counting x-ray detector. Both the neural network and A-table methods demonstrated a similar performance for the simulated data. The neural network had lower standard deviation for nearly all thicknesses of the test materials in the collimated (low scatter) and uncollimated (higher scatter) experimental data. In the experimental study of Teflon thicknesses, non-ideal detector effects demonstrated a potential bias of 11-28%, which was reduced to 0.1-11% using the proposed empirical methods. Overall, the results demonstrated preliminary experimental feasibility of empirical material decomposition for spectral CT using photon-counting detectors.

  2. Experimental comparison of empirical material decomposition methods for spectral CT

    NASA Astrophysics Data System (ADS)

    Zimmerman, Kevin C.; Gilat Schmidt, Taly

    2015-04-01

    Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a neural network estimator and a linearized maximum likelihood estimator with correction (A-table method). The two investigated methods differ in how they model the nonlinear relationship between the spectral measurements and material decomposition estimates. The bias and standard deviation of material decomposition estimates were compared for the two methods, using both simulations and experiments with a photon-counting x-ray detector. Both the neural network and A-table methods demonstrated a similar performance for the simulated data. The neural network had lower standard deviation for nearly all thicknesses of the test materials in the collimated (low scatter) and uncollimated (higher scatter) experimental data. In the experimental study of Teflon thicknesses, non-ideal detector effects demonstrated a potential bias of 11-28%, which was reduced to 0.1-11% using the proposed empirical methods. Overall, the results demonstrated preliminary experimental feasibility of empirical material decomposition for spectral CT using photon-counting detectors.

  3. Experimental Comparison of Empirical Material Decomposition Methods for Spectral CT

    PubMed Central

    Zimmerman, Kevin C.; Schmidt, Taly Gilat

    2015-01-01

    Material composition can be estimated from spectral information acquired using photon counting x-ray detectors with pulse height analysis. Non-ideal effects in photon counting x-ray detectors such as charge-sharing, k-escape, and pulse-pileup distort the detected spectrum, which can cause material decomposition errors. This work compared the performance of two empirical decomposition methods: a neural network estimator and a linearized maximum likelihood estimator with correction (A-table method). The two investigated methods differ in how they model the nonlinear relationship between the spectral measurements and material decomposition estimates. The bias and standard deviation of material decomposition estimates were compared for the two methods, using both simulations and experiments with a photon-counting x-ray detector. Both the neural network and A-table methods demonstrated similar performance for the simulated data. The neural network had lower standard deviation for nearly all thicknesses of the test materials in the collimated (low scatter) and uncollimated (higher scatter) experimental data. In the experimental study of Teflon thicknesses, non-ideal detector effects demonstrated a potential bias of 11–28%, which was reduced to 0.1–11% using the proposed empirical methods. Overall, the results demonstrated preliminary experimental feasibility of empirical material decomposition for spectral CT using photon-counting detectors. PMID:25813054

  4. 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.

  5. 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.

  6. A Spectral Elastodynamic Method for Bi-material Interface Problems

    NASA Astrophysics Data System (ADS)

    Kunnath, R.

    2013-12-01

    A computational method is proposed for modeling spontaneous propagation of dynamic cracks and slip ruptures at a planar interface between two dissimilar elastic half-spaces. It is based on a spectral formulation of the boundary integral equation method and is suited to parallel computing. The boundary integral equation can be written in two equivalent forms: (a) The tractions can be written as a space-time convolution of the displacement continuities at the interface (b) The displacement discontinuities can be written as a space-time convolution of the tractions on the interface. Prior work on spectral formulation of the boundary integral equation has adopted the former as the starting point. The present work has for its basis the latter form based on a space-time convolution of the tractions. The radiation damping term is then explicitly extracted to avoid singularities in the convolution kernels. Stress and displacement components are given a spectral representation as finite Fourier series in the spatial coordinate along the interface. With the spectral forms introduced, the space-time convolutions are converted to convolutions in time for each Fourier mode. The distinguishing feature of the method is that elastodynamic convolutions are performed over the history of tractions on the interface. Due the continuity of tractions across the interface, this leads to a simpler formulation and form of the convolution kernels, as compared to existing methods. When coupled with a cohesive law or a friction law, the method is of wide applicability for studying spontaneous crack or slip rupture propagation. The limitations of the method are that it is restricted to planar interfaces and semi-infinite geometries.

  7. 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

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

    NASA Technical Reports Server (NTRS)

    Freund, Roland

    1989-01-01

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

  9. 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.

  10. 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.

  11. A transform involving Chebyshev polynomials and its inversion formula

    NASA Astrophysics Data System (ADS)

    Ciaurri, Oscar; Navas, Luis M.; Varona, Juan L.

    2006-11-01

    We define a functional analytic transform involving the Chebyshev polynomials Tn(x), with an inversion formula in which the Mobius function [mu](n) appears. If with Re(s)>1, then given a bounded function from [-1,1] into , or from into itself, the following inversion formula holds: if and only if Some other similar results are given.

  12. SAR imaging via modern 2-D spectral estimation methods.

    PubMed

    DeGraaf, S R

    1998-01-01

    This paper discusses the use of modern 2D spectral estimation algorithms for synthetic aperture radar (SAR) imaging. The motivation for applying power spectrum estimation methods to SAR imaging is to improve resolution, remove sidelobe artifacts, and reduce speckle compared to what is possible with conventional Fourier transform SAR imaging techniques. This paper makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2D spectral estimation methods for SAR imaging. It provides a synopsis of the algorithms available, discusses their relative merits for SAR imaging, and illustrates their performance on simulated and collected SAR imagery. Some of the algorithms presented or their derivations are new, as are some of the insights into or analyses of the algorithms. Second, this work develops multichannel variants of four related algorithms, minimum variance method (MVM), reduced-rank MVM (RRMVM), adaptive sidelobe reduction (ASR) and space variant apodization (SVA) to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. All of these interferometric variants are new. In the interferometric contest, adaptive spectral estimation can improve the height estimates through a combination of adaptive nulling and averaging. Examples illustrate that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, ASR, and SVA interferometric height estimates.

  13. New fast spectral analysis method for solid materials

    NASA Astrophysics Data System (ADS)

    Bel'Kov, M. V.; Burakov, V. S.; Kiris, V. V.; Raikov, S. N.

    2007-05-01

    We propose a new fast method for direct spectral analysis of solid materials based on laser ablation of the sample in deionized water and real-time transport of the aqueous suspension of nanoparticles into the inductively coupled plasma of an emission spectrometer. As a result, we have all the instrumental and methodological advantages of standard equipment, along with calibration of the spectrometer using standard aqueous solutions.

  14. Spectral methods and sum acceleration algorithms. Final report

    SciTech Connect

    Boyd, J.

    1995-03-01

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

  15. 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.

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

    SciTech Connect

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

    1996-12-31

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

  17. Atomic spectral methods for molecular electronic structure calculations.

    PubMed

    Langhoff, P W; Boatz, J A; Hinde, R J; Sheehy, J A

    2004-11-15

    Theoretical methods are reported for ab initio calculations of the adiabatic (Born-Oppenheimer) electronic wave functions and potential energy surfaces of molecules and other atomic aggregates. An outer product of complete sets of atomic eigenstates familiar from perturbation-theoretical treatments of long-range interactions is employed as a representational basis without prior enforcement of aggregate wave function antisymmetry. The nature and attributes of this atomic spectral-product basis are indicated, completeness proofs for representation of antisymmetric states provided, convergence of Schrodinger eigenstates in the basis established, and strategies for computational implemention of the theory described. A diabaticlike Hamiltonian matrix representative is obtained, which is additive in atomic-energy and pairwise-atomic interaction-energy matrices, providing a basis for molecular calculations in terms of the (Coulombic) interactions of the atomic constituents. The spectral-product basis is shown to contain the totally antisymmetric irreducible representation of the symmetric group of aggregate electron coordinate permutations once and only once, but to also span other (non-Pauli) symmetric group representations known to contain unphysical discrete states and associated continua in which the physically significant Schrodinger eigenstates are generally embedded. These unphysical representations are avoided by isolating the physical block of the Hamiltonian matrix with a unitary transformation obtained from the metric matrix of the explicitly antisymmetrized spectral-product basis. A formal proof of convergence is given in the limit of spectral closure to wave functions and energy surfaces obtained employing conventional prior antisymmetrization, but determined without repeated calculations of Hamiltonian matrix elements as integrals over explicitly antisymmetric aggregate basis states. Computational implementations of the theory employ efficient recursive

  18. 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.

  19. Fast numerical treatment of nonlinear wave equations by spectral methods

    SciTech Connect

    Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.

    2011-02-15

    A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.

  20. Orbital tori construction using trajectory following spectral methods

    NASA Astrophysics Data System (ADS)

    Bordner, Ralph E.

    By assuming the motion of a satellite about the earth's geopotential mimics the known Kolmogorov-Arnold-Moser (KAM) solution of a lightly perturbed integrable Hamiltonian system, this research focused on applying trajectory following spectral methods to estimate orbital tori from sampled orbital data. From an estimated basis frequency set, orbital data was decomposed into multi-periodic Fourier series, essentially compressing ephemerides for long-term use. Real-world Global Positioning System (GPS) orbital tracks were decomposed and reconstructed with error from as low as few kilometers per coordinate axis over a 10-week span to tens of kilometers per coordinate axis over the same time period, depending on the method chosen. These less-than-precision-level results were due primarily to the resonant orbits of the GPS constellation. Additionally, the trajectory following spectral methods chosen experienced difficulties converging on a complete basis set when using data time spans much smaller than the period of the slowest system frequency. However, the lessons learned from GPS led to a new orbital tori construction method. This approach focused on fitting local spectral structures, denoted as frequency clusters, within the sampled orbital data to the analytical form of the windowed, truncated, continuous Fourier transform. Methods employing direct use of the observed spectrum as well as least squares fitting techniques were developed with considerable success. For portions of the low-earth-orbit regime, maximum errors per coordinate axis in orbital tori fits were kept below 5 meters over a time period of 1 year. Simulations using the Hubble Space Telescope yielded 1-dimensional root mean square errors of less than 2 meters in each coordinate axis in the initial and predicted ephemeris fits, both of which used 1-year-long tracks of numerically integrated data.

  1. 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.

  2. 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.

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

    SciTech Connect

    Solomon, Jr, O M

    1991-12-01

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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. A spectral method for the computation of propeller acoustics

    NASA Astrophysics Data System (ADS)

    Schulten, J. B. H. M.

    1987-10-01

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

  17. 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.

  18. 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.

  19. A spectral method for the computation of propeller acoustics

    NASA Astrophysics Data System (ADS)

    Schulten, J. B. H. M.

    1987-10-01

    In the present study an analytical description of the acoustic field of a propeller in a uniform flow is derived. Instead of applying the usual Ffowcs Williams-Hawkings (1969) version of the acoustic analogy, sources on a surface enclosing the propeller and its adjacent nonlinear flow field are formulated. This approach, which avoids the laborious evaluation of quadrupole source terms, is to be considered as a generalization of the Kirchhoff-Helmholtz theorem of acoustics. By describing the fundamental solution as a spectral Fourier-Bessel decomposition, the resulting sound field is readily given in the appropriate series of harmonic amplitudes. The method is validated by a comparison of numerical results with experimental data of a propeller in an acoustic wind tunnel. A good agreement, both in amplitude and phase, is found between theory and experiment.

  20. 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.

  1. 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.

  2. 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.

  3. A hybrid Pseudo-spectral Immersed-Boundary Method for Applications to Aquatic Locomotion

    NASA Astrophysics Data System (ADS)

    Ren, Zheng; Hall, David; Mohseni, Kamran

    2011-11-01

    A hybrid pseudo-spectral immersed boundary method is developed for application in marine locomotion. Spatial derivatives are calculated using pseudo-spectral method while a 2nd-order Runge-Kutta scheme is used for time integration. The singular force applied on the immersed boundary is obtained using a direct forcing method. To avoid Gibb's phenomenon in the spectral method, we regularize the force by smoothing it over several grid cells. This method has the advantage of spectral accuracy and the flexibility to model irregular, moving boundaries on a Cartesian coordinate without complex mesh generation. The method is applied to examine locomotion of jellyfish for both jetting and paddling jellyfish.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. Kernel polynomial approximations for densities of states and spectral functions

    SciTech Connect

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

    1996-03-01

    Chebyshev polynomial approximations are an efficient and numerically stable way to calculate properties of the very large Hamiltonians important in computational condensed matter physics. The present paper derives an optimal kernal polynomial which enforces positivity of density of states and spectral estimates, achieves the best energy resolution, and preserves normalization. This kernel polynomial method (KPM) is demonstrated for electronic structure and dynamic magnetic susceptibility calculations. For tight binding Hamiltonians of Si, we show how to achieve high precision and rapid convergence of the cohesive energy and vacancy formation energy by careful attention to the order of approximation. For disordered XXZ-magnets, we show that the KPM provides a simpler and more reliable procedure for calculating spectral functions than Lanczos recursion methods. Polynomial approximations to Fermi projection operators are also proposed. 26 refs., 10 figs.

  9. 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.

  10. 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

  11. 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.

  12. [The Research of Spectral Dimension Reduction Method Based on Human Visual Characteristics].

    PubMed

    He, Song-hua; Chen, Qiao; Duan, Jiang

    2015-06-01

    The traditional spectral dimension reduction methods are usually carried out by matching the reconstructed spectra to the original spectra mathematically, which will often result in reconstructed spectra of small spectral reconstruction errors but very poor colorimetric accuracy when compared with the original one. In order to minimize both the spectral and colorimetric errors more efficiently, we proposed three spectral dimension reduction methods by introducing the characteristics of human vision. The first method is VPCA, in which we apply spectral luminous efficiency function to the original spectra before reduction; The Second method (LMSPCA) uses a matrix derived from LMS cone sensitivity to weight the original spectra before reduction, and the matrix can be form by two methods, in which the L, M, S cones response offset is calculated by in two different ways: one is computed as the absolute value of each corresponding wave length offset, and the other is calculated as the square of each corresponding wave length offset. The third method is LMSPCAs, which is based on the second method LMSPCA by further applying PCA to the residual spectra. The result shows that the VPCA method produces the poorest perfomance. The two cones response weighted matrixes of LMSPCA method have similar performances by presenting better colorimetric accuracy and low spectral accuracy, while LMSPCAs method which compensates for the spectral loss of LMSPCA method can produce higher spectral and colorimetric reconstruction accuracy and color stability under different light source, and satisfies the requirements of spectral color reproduction. PMID:26601347

  13. Preconditioning for first-order spectral discretization

    NASA Technical Reports Server (NTRS)

    Streett, C. L.; Macaraeg, M. G.

    1986-01-01

    Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized. Direct solution of these equations is rarely feasible, thus iterative techniques are required. A preconditioning scheme for first-order Chebyshev collocation operators is proposed herein, in which the central finite difference mesh is finer than the collocation mesh. Details of the proper techniques for transferring information between the meshes are given here, and the scheme is analyzed by examination of the eigenvalue spectra of the preconditioned operators. The effect of artificial viscosity required in the inversion of the finite difference operator is examined. A second preconditioning scheme, involving a high-order upwind finite difference operator of the van Leer type is also analyzed to provide a comparison with the present scheme. Finally, the performance of the present scheme is verified by application to several test problems.

  14. 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.

  15. Time-spectral modelling of drift wave turbulence

    NASA Astrophysics Data System (ADS)

    Scheffel, Jan

    2013-10-01

    Time spectral methods for initial-value partial differential equations avoid the time stepping being characteristic for temporal finite difference schemes. Large gains in efficiency should then be within reach for problems in plasma physics with widely separated time scales. In the recently developed Generalized Weighted Residual Method GWRM, temporal, spatial and parameter domains are all handled using a Chebyshev polynomial solution ansatz. The coefficients of the ansatz are determined using a generalized weighted residual method, for which a new efficient equation system solver has been applied. In addition, subdomain methods for the temporal and spatial domains have been developed and employed successfully in a number of test problems. We will here also present a related method, being based on least square minimization of the residual rather than on the Galerkin method. Both methods are applied to problems in drift wave turbulence from which results will be presented.

  16. 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.

  17. Spectral Methods for Detecting Periodicity in Library Circulation Data: A Case Study.

    ERIC Educational Resources Information Center

    Decroos, Francis; And Others

    1997-01-01

    Describes an investigation that was conducted to show the feasibility of spectral methods in information science, particularly for analyzing academic library circulation data. Signal analysis methods were used to detect periodicity, and spectral methods show promise for analyzing time series and other signals in information science. (Author/LRW)

  18. 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.

  19. Characterizing Intra-Die Spatial Correlation Using Spectral Density Fitting Method

    NASA Astrophysics Data System (ADS)

    Fu, Qiang; Luk, Wai-Shing; Tao, Jun; Yan, Changhao; Zeng, Xuan

    In this paper, a spectral domain method named the SDF (Spectral Density Fitting) method for intra-die spatial correlation function extraction is presented. Based on theoretical analysis of random field, the spectral density, as the spectral domain counterpart of correlation function, is employed to estimate the parameters of the correlation function effectively in the spectral domain. Compared with the existing extraction algorithm in the original spatial domain, the SDF method can obtain the same quality of results in the spectral domain. In actual measurement process, the unavoidable measurement error with arbitrary frequency components would greatly confound the extraction results. A filtering technique is further developed to diminish the high frequency components of the measurement error and recover the data from noise contamination for parameter estimation. Experimental results have shown that the SDF method is practical and stable.

  20. 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

  1. 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.

  2. 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.

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

    PubMed

    Bayındır, Cihan

    2016-02-25

    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.

  4. 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

  5. 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

  6. A new fractional Chebyshev FDM: an application for solving the fractional differential equations generated by optimisation problem

    NASA Astrophysics Data System (ADS)

    Khader, M. M.

    2015-10-01

    In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method. The algorithm is based on a combination of the useful properties of Chebyshev polynomial approximation and finite difference method. We implement this technique to solve numerically the non-linear programming problem which are governed by fractional differential equations (FDEs). The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the Caputo fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The application of the method to the generated FDEs leads to algebraic systems which can be solved by an appropriate method. Two numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method. A comparison with the fourth-order Runge-Kutta method is given.

  7. 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.

  8. Uniform high order spectral methods for one and two dimensional Euler equations

    NASA Technical Reports Server (NTRS)

    Cai, Wei; Shu, Chi-Wang

    1991-01-01

    Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

  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. Color constancy - A method for recovering surface spectral reflectance

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

  11. 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.

  12. 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).

  13. 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.

  14. 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.

  15. Spectral methods in quantum field theory and quantum cosmology

    NASA Astrophysics Data System (ADS)

    Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

    2012-09-01

    We review the application of the spectral zeta function to the one-loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some time ago, the only boundary conditions that are completely invariant under infinitesimal diffeomorphisms on metric perturbations suffer from a drawback, i.e. lack of strong ellipticity of the resulting boundary-value problem. Nevertheless, at least on the Euclidean 4-ball background, it remains possible to evaluate the ζ(0) value, which describes in this case a universe which, in the limit of small 3-geometry, has vanishing probability of approaching the cosmological singularity. An assessment of this result is performed here, discussing its physical and mathematical implications. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

  16. [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.

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

    PubMed

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

    2013-04-01

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

  18. Extraction of spectral functions from Dyson-Schwinger studies via the maximum entropy method

    SciTech Connect

    Nickel, Dominik . E-mail: dominik.nickel@physik.tu-darmstadt.de

    2007-08-15

    It is shown how to apply the Maximum Entropy Method (MEM) to numerical Dyson-Schwinger studies for the extraction of spectral functions of correlators from their corresponding Euclidean propagators. Differences to the application in lattice QCD are emphasized and, as an example, the spectral functions of massless quarks in cold and dense matter are presented.

  19. 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.

  20. A nodal spectral stiffness matrix for the finite-element method

    NASA Astrophysics Data System (ADS)

    Bittencourt, Marco L.; Vazquez, Thais G.

    2008-12-01

    In this paper, shape functions are proposed for the spectral finite-element method aiming to finding a nodal spectral stiffness matrix. The proposed shape functions obtain a nearly diagonal 1D stiffness matrix with better conditioning than using the Lagrange and Jacobi bases.

  1. 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...

  2. Performance assessment of onboard and scene-based methods for Airborne Prism Experiment spectral characterization.

    PubMed

    D'Odorico, Petra; Guanter, Luis; Schaepman, Michael E; Schläpfer, Daniel

    2011-08-20

    Accurate spectral calibration of airborne and spaceborne imaging spectrometers is essential for proper preprocessing and scientific exploitation of high spectral resolution measurements of the land and atmosphere. A systematic performance assessment of onboard and scene-based methods for in-flight monitoring of instrument spectral calibration is presented for the first time in this paper. Onboard and ground imaging data were collected at several flight altitudes using the Airborne Prism Experiment (APEX) imaging spectrometer. APEX is equipped with an in-flight characterization (IFC) facility allowing the evaluation of radiometric, spectral, and geometric system properties, both in-flight and on-ground for the full field of view. Atmospheric and onboard filter spectral features present in at-sensor radiances are compared with the same features in reference transmittances convolved to varying instrument spectral configurations. A spectrum-matching algorithm, taking advantage of the high sensitivity of measurements around sharp spectral features toward spectrometer spectral performance, is used to retrieve channel center wavelength and bandwidth parameters. Results showed good agreement between spectral parameters estimated using onboard IFC and ground imaging data. The average difference between estimates obtained using the O(2) and H(2)O features and those obtained using the corresponding filter features amounted to about 0.3 nm (0.05 of a spectral pixel). A deviation from the nominal laboratory instrument spectral calibration and an altitude-dependent performance was additionally identified. The relatively good agreement between estimates obtained by the two approaches in similar spectral windows suggests they can be used in a complementary fashion: while the method relying on atmospheric features can be applied without the need for dedicated calibration acquisitions, the IFC allows assessment at user-selectable wavelength positions by custom filters as well as for

  3. 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.

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

    PubMed

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

    2015-07-03

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

  5. 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

  6. On the spectral methods for population balance problems

    NASA Astrophysics Data System (ADS)

    Solsvik, J.; Jakobsen, H. A.

    2013-10-01

    Numerical methods in the weighted residual framework have been evaluated for three population balance (PB) problems. Based on the present solution results, the orthogonal collocation method is recommended above the tau and least-squares methods. The orthogonal collocation method holds the simplest algebra theory, obtains high accuracy, and is more computational efficient compared to the other methods evaluated.

  7. 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.

  8. 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

  9. [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%.

  10. 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.

  11. [Research on the method for rapid detection of soil moisture content using spectral data].

    PubMed

    Song, Tao; Bao, Yi-Dan; He, Yong

    2009-03-01

    Spectroscopy technique is one of the qualitative and quantitative analytical techniques developed quickly in recent years. The spectral analysis is a fast and non-destructive method and has been used in many fields such as oil industry, food industry and so on. In the present paper, the spectral band sensitive to soil moisture content was found from the visible/near infrared spectra and a monadic linear regression model based on the data of sensitive spectral band was applied to develop a method for rapid detection of soil moisture content. The spectral data of 52 soil samples were collected by using FieldSpec HandHeld spectroradiometer made by ASD (Analytical Spectral Device) company in the US, and the data of soil moisture content were obtained by experiment. The spectral band sensitive to soil moisture content was achieved by correlation coefficient method. Then, the data of sensitive spectral band were used to build monadic linear regression model of soil moisture content. Finally, the model was employed for the prediction of soil moisture content. Correlation coefficient (r) of prediction and root mean square error of prediction (RMSEP) were used as the evaluation standards. The results indicated that the r and RMSEP for the prediction of soil moisture content were 0.966 5 and 0.012 1 respectively. Thus, it is concluded that the method used in this paper is an available method for the rapid detection of soil moisture content based on the visible/near-infrared spectra.

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

    NASA Astrophysics Data System (ADS)

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

    2008-10-01

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

  13. 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.

  14. 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

  15. Characterization of structure and properties of bone by spectral measure method.

    PubMed

    Cherkaev, Elena; Bonifasi-Lista, Carlos

    2011-01-11

    Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.

  16. Contourlet Filter Design Based on Chebyshev Best Uniform Approximation

    NASA Astrophysics Data System (ADS)

    Yang, Guoan; Fang, Xiaofeng; Jing, Mingli; Zhang, Songjun; Hou, Ming

    2010-12-01

    The contourlet transform can deal effectively with images which have directional information such as contour and texture. In contrast to wavelets for which there exists many good filters, the contourlet filter design for image processing applications is still an ongoing work. Therefore, this paper presents an approach for designing the contourlet filter based on the Chebyshev best uniform approximation for achieving an efficient image denoising applications using hidden Markov tree models in the contourlet domain. Here, we design both the optimal 9/7 wavelet filter banks with rational coefficients and new pkva 12 filter. In this paper, the Laplacian pyramid followed by the direction filter banks decomposition in the contourlet transform using the two filter banks above and the image denoising applications in the contourlet hidden Markov tree model are implemented, respectively. The experimental results show that the denoising performance of the test image Zelda in terms of peak signal-to-noise ratio is improved by 0.33 dB than using CDF 9/7 filter banks with irrational coefficients on the JPEG2000 standard and standard pkva 12 filter, and visual effects are as good as compared with the research results of Duncan D.-Y. Po and Minh N. Do.

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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

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

    PubMed

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

    2013-05-01

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

  3. 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.

  4. 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.

  5. [Study of the Detecting System of CH4 and SO2 Based on Spectral Absorption Method and UV Fluorescence Method].

    PubMed

    Wang, Shu-tao; Wang, Zhi-fang; Liu, Ming-hua; Wei, Meng; Chen, Dong-ying; Wang, Xing-long

    2016-01-01

    According to the spectral absorption characteristics of polluting gases and fluorescence characteristics, a time-division multiplexing detection system is designed. Through this system we can detect Methane (CH4) and sulfur dioxide (SO2) by using spectral absorption method and the SO2 can be detected by using UV fluorescence method. The system consists of four parts: a combination of a light source which could be switched, the common optical path, the air chamber and the signal processing section. The spectral absorption characteristics and fluorescence characteristics are measured first. Then the experiment of detecting CH4 and SO2 through spectral absorption method and the experiment of detecting SO2 through UV fluorescence method are conducted, respectively. Through measuring characteristics of spectral absorption and fluorescence, we get excitation wavelengths of SO2 and CH4 measured by spectral absorption method at the absorption peak are 280 nm and 1.64 μm, respectively, and the optimal excitation wavelength of SO2 measured by UV fluorescence method is 220 nm. we acquire the linear relation between the concentration of CH4 and relative intensity and the linear relation between the concentration of SO2 and output voltage after conducting the experiment of spectral absorption method, and the linearity are 98.7%, 99.2% respectively. Through the experiment of UV fluorescence method we acquire that the relation between the concentration of SO2 and the voltage is linear, and the linearity is 99.5%. Research shows that the system is able to be applied to detect the polluted gas by absorption spectrum method and UV fluorescence method. Combing these two measurement methods decreases the costing and the volume, and this system can also be used to measure the other gases. Such system has a certain value of application. PMID:27228784

  6. [Study of the Detecting System of CH4 and SO2 Based on Spectral Absorption Method and UV Fluorescence Method].

    PubMed

    Wang, Shu-tao; Wang, Zhi-fang; Liu, Ming-hua; Wei, Meng; Chen, Dong-ying; Wang, Xing-long

    2016-01-01

    According to the spectral absorption characteristics of polluting gases and fluorescence characteristics, a time-division multiplexing detection system is designed. Through this system we can detect Methane (CH4) and sulfur dioxide (SO2) by using spectral absorption method and the SO2 can be detected by using UV fluorescence method. The system consists of four parts: a combination of a light source which could be switched, the common optical path, the air chamber and the signal processing section. The spectral absorption characteristics and fluorescence characteristics are measured first. Then the experiment of detecting CH4 and SO2 through spectral absorption method and the experiment of detecting SO2 through UV fluorescence method are conducted, respectively. Through measuring characteristics of spectral absorption and fluorescence, we get excitation wavelengths of SO2 and CH4 measured by spectral absorption method at the absorption peak are 280 nm and 1.64 μm, respectively, and the optimal excitation wavelength of SO2 measured by UV fluorescence method is 220 nm. we acquire the linear relation between the concentration of CH4 and relative intensity and the linear relation between the concentration of SO2 and output voltage after conducting the experiment of spectral absorption method, and the linearity are 98.7%, 99.2% respectively. Through the experiment of UV fluorescence method we acquire that the relation between the concentration of SO2 and the voltage is linear, and the linearity is 99.5%. Research shows that the system is able to be applied to detect the polluted gas by absorption spectrum method and UV fluorescence method. Combing these two measurement methods decreases the costing and the volume, and this system can also be used to measure the other gases. Such system has a certain value of application.

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

    NASA Technical Reports Server (NTRS)

    Irvine, Tom; Larsen, Curtis

    2016-01-01

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

  8. 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.

  9. Extension of a spectral time-stepping domain decomposition method for dispersive and dissipative wave propagation.

    PubMed

    Botts, Jonathan; Savioja, Lauri

    2015-04-01

    For time-domain modeling based on the acoustic wave equation, spectral methods have recently demonstrated promise. This letter presents an extension of a spectral domain decomposition approach, previously used to solve the lossless linear wave equation, which accommodates frequency-dependent atmospheric attenuation and assignment of arbitrary dispersion relations. Frequency-dependence is straightforward to assign when time-stepping is done in the spectral domain, so combined losses from molecular relaxation, thermal conductivity, and viscosity can be approximated with little extra computation or storage. A mode update free from numerical dispersion is derived, and the model is confirmed with a numerical experiment.

  10. 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

  11. Tracking perturbations in Boolean networks with spectral methods.

    PubMed

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

    2005-08-01

    In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks. PMID:16196674

  12. 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.

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

    PubMed Central

    Xu, Zhenli; Cai, Wei

    2009-01-01

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

  14. 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.

  15. 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...

  16. 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.

  17. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-08-01

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

  20. 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.

  1. A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity

    SciTech Connect

    Feng, W. M.; Yu, P.; Hu, Shenyang Y.; Liu, Z. K.; Du, Q.; Chen , L.Q.

    2009-02-01

    In recent years, Fourier spectral methods have emerged as competitive numerical methods for large-scale phase field simulations of microstructures in computational materials sciences. To further improve their effectiveness, we recently developed a new adaptive Fourier-spectral semi-implicit method (AFSIM) for solving the phase field equation by combining an adaptive moving mesh method and the semi-implicit Fourier spectral algorithm. In this paper, we present the application of AFSIM to the Cahn-Hilliard equation with inhomogeneous, anisotropic elasticity. Numerical implementations and test examples in both two and three dimensions are considered with a particular illustration using the well-studied example of mis-fitting particles in a solid as they approach to their equilibrium shapes. It is shown that significant savings in memory and computational time is achieved while accurate solutions are preserved.

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

    SciTech Connect

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

    2013-06-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

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

  4. 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.

  5. 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.

  6. 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.

  7. A semi-Lagrangian model incorporating a spectral method for pollutant transport and diffusion

    SciTech Connect

    Lee, H.N.

    1994-12-31

    To improve the semi-Lagrangian model, a spectral method was incorporated in the numerical calculations. This spectral method for solving nonperiodic boundary problems was based on a technique of decomposing a variable (i.e. pollutant concentration) into a polynomial and a periodic Fourier residual. A fifth-order polynomial was proposed. When performing the semi-Lagrangian calculation, the spectral intrapolation for estimating the transport of material between grid points was used. From this, a method for removing small negative masses without lossing mass conservation was developed. The numerical tests of the semi-Lagrangian scheme with the spectral interpolation on the advective transport of a mass under nonuniform and uniform winds in a limited computational domain were performed previously and published. In this study, the scheme was applied to solve the two-dimensional time-dependent advection-diffusion equation describing the transport and dispersion of atmospheric pollutants. The calculations demonstrated the efficiency and accuracy of the numerical solutions in a limited region by using this semi-Lagrangian technique incorporated with the spectral method. The main objective of this present study was to develop an advanced numerical modelling technique for air pollution studies on a regional scale.

  8. 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.

  9. 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.

  10. Deconvolution methods based on φHL regularization for spectral recovery.

    PubMed

    Zhu, Hu; Deng, Lizhen; Bai, Xiaodong; Li, Meng; Cheng, Zhao

    2015-05-10

    The recorded spectra often suffer noise and band overlapping, and deconvolution methods are always used for spectral recovery. However, during the process of spectral recovery, the details cannot always be preserved. To solve this problem, two regularization terms are introduced and proposed. First, the conditions on the regularization term are analyzed for smoothing noise and preserving detail, and according to these conditions, φHL regularization is introduced into the spectral deconvolution model. In view of the deficiency of φHL under noisy condition, adaptive φHL regularization (φAHL) is proposed. Then semi-blind deconvolution methods based on φHL regularization (SBD-HL) and based on adaptive φHL regularization (SBD-AHL) are proposed, respectively. The simulation experimental results indicate that the proposed SBD-HL and SBD-AHL methods have better recovery, and SBD-AHL is superior to SBD-HL, especially in the noisy case.

  11. 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.

  12. 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

  13. 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.

  14. A NEW METHOD OF PULSE-WISE SPECTRAL ANALYSIS OF GAMMA-RAY BURSTS

    SciTech Connect

    Basak, Rupal; Rao, A. R. E-mail: arrao@tifr.res.in

    2013-05-10

    Time-resolved spectral analysis, though a very promising method to understand the emission mechanism of gamma-ray bursts (GRBs), is difficult to implement in practice because of poor statistics. We present a new method for pulse-wise time-resolved spectral study of the individual pulses of GRBs, using the fact that many spectral parameters are either constants or smooth functions of time. We use this method for the two pulses of GRB 081221, the brightest GRB with separable pulses. We choose, from the literature, a set of possible models that includes the Band model, blackbody with a power law (BBPL), and a collection of blackbodies with a smoothly varying temperature profile, along with a power law (mBBPL), and two blackbodies with a power law (2BBPL). First, we perform a time-resolved study to confirm the spectral parameter variations, and then we construct the new model to perform a joint spectral fit. We find that any photospheric emission in terms of blackbodies is required mainly in the rising parts of the pulses and the falling part can be adequately explained in terms of the Band model, with the low-energy photon index within the regime of synchrotron model. Interestingly, we find that 2BBPL is comparable or sometimes even better, though marginally, than the Band model, in all episodes. Consistent results are also obtained for the brightest GRB of Fermi era-GRB 090618. We point out that the method is generic enough to test any spectral model with well-defined parameter variations.

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

    NASA Technical Reports Server (NTRS)

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

    2013-01-01

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

  16. 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.

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

    PubMed

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

    2013-01-01

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

  18. 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.

  19. 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.

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

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

  1. 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.

  2. 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.

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

    DOE PAGES

    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.

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

    NASA Technical Reports Server (NTRS)

    Mcmurtry, Patrick A.; Givi, Peyman

    1992-01-01

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

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

    SciTech Connect

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

    2009-10-20

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

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

    SciTech Connect

    Yu, Hua-Gen

    2014-12-28

    A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.

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

    DOE PAGES

    Yu, Hua-Gen

    2014-12-28

    A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the originalmore » Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.« less

  8. 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.

  9. 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.

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

    PubMed

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

    2008-05-01

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

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

    PubMed

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

    2011-04-01

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

  12. 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.

  13. Spectral methods for the wave equation in second-order form

    SciTech Connect

    Taylor, Nicholas W.; Teukolsky, Saul A.; Kidder, Lawrence E.

    2010-07-15

    Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semidiscrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multidomain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.

  14. 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.

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

    NASA Technical Reports Server (NTRS)

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

    1974-01-01

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

  16. Improvements in the method of radiation anomaly detection by spectral comparison ratios.

    PubMed

    Pfund, D M; Anderson, K K; Detwiler, R S; Jarman, K D; McDonald, B S; Milbrath, B D; Myjak, M J; Paradis, N C; Robinson, S M; Woodring, M L

    2016-04-01

    We present a new procedure for configuring the Nuisance-rejection Spectral Comparison Ratio Anomaly Detection (N-SCRAD) method. The procedure minimizes detectable count rates of source spectra at a specified false positive rate using simulated annealing. We also present a new method for correcting the estimates of background variability used in N-SCRAD to current conditions of the total count rate. The correction lowers detection thresholds for a specified false positive rate, enabling greater sensitivity to targets. PMID:26807839

  17. A two-dimensional adaptive spectral element method for the direct simulation of incompressible flow

    NASA Astrophysics Data System (ADS)

    Hsu, Li-Chieh

    The spectral element method is a high order discretization scheme for the solution of nonlinear partial differential equations. The method draws its strengths from the finite element method for geometrical flexibility and spectral methods for high accuracy. Although the method is, in theory, very powerful for complex phenomena such as transitional flows, its practical implementation is limited by the arbitrary choice of domain discretization. For instance, it is hard to estimate the appropriate number of elements for a specific case. Selection of regions to be refined or coarsened is difficult especially as the flow becomes more complex and memory limits of the computer are stressed. We present an adaptive spectral element method in which the grid is automatically refined or coarsened in order to capture underresolved regions of the domain and to follow regions requiring high resolution as they develop in time. The objective is to provide the best and most efficient solution to a time-dependent nonlinear problem by continually optimizing resource allocation. The adaptivity is based on an error estimator which determines which regions need more resolution. The solution strategy is as follows: compute an initial solution with a suitable initial mesh, estimate errors in the solution locally in each element, modify the mesh according to the error estimators, interpolate old mesh solutions onto the new elements, and resume the numerical solution process. A two-dimensional adaptive spectral element method for the direct simulation of incompressible flows has been developed. The adaptive algorithm effectively diagnoses and refines regions of the flow where complexity of the solution requires increased resolution. The method has been demonstrated on two-dimensional examples in heat conduction, Stokes and Navier-Stokes flows.

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

    NASA Technical Reports Server (NTRS)

    Vanel, Florence O.

    1995-01-01

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

  19. 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.

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

    PubMed Central

    Putz, Ana-Maria; Putz, Mihai V.

    2012-01-01

    The present work advances the inverse quantum (IQ) structural criterion for ordering and characterizing the porosity of the mesosystems based on the recently advanced ratio of the particle-to-wave nature of quantum objects within the extended Heisenberg uncertainty relationship through employing the quantum fluctuation, both for free and observed quantum scattering information, as computed upon spectral identification of the wave-numbers specific to the maximum of absorption intensity record, and to left-, right- and full-width at the half maximum (FWHM) of the concerned bands of a given compound. It furnishes the hierarchy for classifying the mesoporous systems from more particle-related (porous, tight or ionic bindings) to more wave behavior (free or covalent bindings). This so-called spectral inverse quantum (Spectral-IQ) particle-to-wave assignment was illustrated on spectral measurement of FT-IR (bonding) bands’ assignment for samples synthesized within different basic environment and different thermal treatment on mesoporous materials obtained by sol-gel technique with n-dodecyl trimethyl ammonium bromide (DTAB) and cetyltrimethylammonium bromide (CTAB) and of their combination as cosolvents. The results were analyzed in the light of the so-called residual inverse quantum information, accounting for the free binding potency of analyzed samples at drying temperature, and were checked by cross-validation with thermal decomposition techniques by endo-exo thermo correlations at a higher temperature. PMID:23443102

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  2. 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.

  3. [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

  4. 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.

  5. 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.

  6. Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

    NASA Astrophysics Data System (ADS)

    Mao, Zhiping; Shen, Jie

    2016-02-01

    Efficient spectral-Galerkin algorithms are developed to solve multi-dimensional fractional elliptic equations with variable coefficients in conserved form as well as non-conserved form. These algorithms are extensions of the spectral-Galerkin algorithms for usual elliptic PDEs developed in [24]. More precisely, for separable FPDEs, we construct a direct method by using a matrix diagonalization approach, while for non-separable FPDEs, we employ a preconditioned BICGSTAB method with a suitable separable FPDE with constant-coefficients as preconditioner. The cost of these algorithms is of O (N d + 1) flops where d is the space dimension. We derive rigorous weighted error estimates which provide more precise convergence rate for problems with singularities at boundaries. We also present ample numerical results to validate the algorithms and error estimates.

  7. Vibration band-gap properties of three-dimensional Kagome lattices using the spectral element method

    NASA Astrophysics Data System (ADS)

    Wu, Zhi-Jing; Li, Feng-Ming; Zhang, Chuanzeng

    2015-04-01

    The spectral element method (SEM) is extended to investigate the vibration band-gap properties of three-dimensional (3D) Kagome lattices. The dynamic stiffness matrix of the 3D element which contains bending, tensional and torsional components is derived. The spectral equations of motion of the whole 3D Kagome lattice are then established. Comparing with frequency-domain solutions calculated by the finite element method (FEM), the accuracy and the feasibility of the SEM solutions are verified. It can be shown that the SEM is suitable for analyzing the vibration band-gap properties. Due to the band-gap characteristics, the periodic 3D Kagome lattice has the performance of vibration isolation. The influences of the structural and material parameters on the vibration band-gaps are discussed and a new type of 3D Kagome lattice is designed to obtain the improved vibration isolation capability.

  8. 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).

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

    NASA Technical Reports Server (NTRS)

    Maday, Yvon; Ronquist, Einar M.

    1989-01-01

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

  10. The core-saturation method with partial redistribution. [for solving spectral line radiative transfer equations

    NASA Technical Reports Server (NTRS)

    Stenholm, L. G.; Wehrse, R.

    1984-01-01

    The core-saturation technique for calculating the radiation field in spectral lines (Rybicki, 1971) is extended to cases where partial redistribution is important. The frequency space is discretized and a general vector equation relating the source function S to the mean intensities is derived. The components of S are then used in a lambda iteration to determine the specific intensities. Numerical tests show that the efficiency and accuracy of this method are maintained.

  11. Fast calculation method for computer-generated cylindrical hologram based on wave propagation in spectral domain.

    PubMed

    Jackin, Boaz Jessie; Yatagai, Toyohiko

    2010-12-01

    A fast calculation method for computer generation of cylindrical holograms is proposed. The calculation method is based on wave propagation in spectral domain and in cylindrical co-ordinates, which is otherwise similar to the angular spectrum of plane waves in cartesian co-ordinates. The calculation requires only two FFT operations and hence is much faster. The theoretical background of the calculation method, sampling conditions and simulation results are presented. The generated cylindrical hologram has been tested for reconstruction in different view angles and also in plane surfaces.

  12. Stray light errors in spectral colour measurement and two rejection methods

    NASA Astrophysics Data System (ADS)

    Shen, Haiping; Pan, Jiangen; Feng, Huajun; Liu, Muqing

    2009-02-01

    The measurement errors caused by stray light of array spectrometers in the spectral colour measurement for light emitting diodes (LEDs) are studied. A stray light correction method and a filter-wheel stray light blocking technology are compared both by simulation and by experiment. The results show that the stray light may cause unacceptable measurement errors. Both the correction method and the filter-wheel technology are very effective in correcting the stray light errors for all the LEDs. The correction method needs infrared filters for white LEDs. An optimized design of the filter wheel is given.

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  14. 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.

  15. 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.

  16. Introduction to the spectral element method for three-dimensional seismic wave propagation

    NASA Astrophysics Data System (ADS)

    Komatitsch, Dimitri; Tromp, Jeroen

    1999-12-01

    We present an introduction to the spectral element method, which provides an innovative numerical approach to the calculation of synthetic seismograms in 3-D earth models. The method combines the flexibility of a finite element method with the accuracy of a spectral method. One uses a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements that is adapted to the free surface and to the main internal discontinuities of the model. The wavefield on the elements is discretized using high-degree Lagrange interpolants, and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix, which greatly simplifies the algorithm. We illustrate the great potential of the method by comparing it to a discrete wavenumber/reflectivity method for layer-cake models. Both body and surface waves are accurately represented, and the method can handle point force as well as moment tensor sources. For a model with very steep surface topography we successfully benchmark the method against an approximate boundary technique. For a homogeneous medium with strong attenuation we obtain excellent agreement with the analytical solution for a point force.

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

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  18. A COMPARISON OF FOUR METHODS FOR DETERMINING PRECIPITABLE WATER VAPOR CONTENT FROM MULTI-SPECTRAL DATA

    SciTech Connect

    K. HIRSCH; ET AL

    2001-03-01

    Determining columnar water vapor is a fundamental problem in remote sensing. This measurement is important both for understanding atmospheric variability and also from removing atmospheric effects from remotely sensed data. Therefore discovering a reliable and if possible automated method for determining water vapor column abundance is important. There are two standard methods for determining precipitable water vapor during the daytime from multi-spectral data. The first method is the Continuum Interpolated Band Ratio (CIBR) (see for example King et al. 1996). This method assumes a baseline and measures the depth of a water vapor feature as compared to this baseline. The second method is the Atmospheric Pre-corrected Differential Absorption technique (APDA) (see Schlaepfer et al. 1998); this method accounts for the path radiance contribution to the top of atmosphere radiance measurement which is increasingly important at lower and lower reflectance values. We have also developed two methods of modifying CIBR. We use a simple curve fitting procedure to account for and remove any systematic errors due to low reflectance while still preserving the random spread of the CIBR values as a function of surface reflectance. We also have developed a two-dimensional look-up table for CIBR; CIBR using this technique is a function of both water vapor (as with all CIBR techniques) and surface reflectance. Here we use data recently acquired with the Multi-spectral Thermal Imager spacecraft (MTI) to compare these four methods of determining columnar water vapor content.

  19. 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.

  20. [Study on a method of selecting calibration samples in NIR spectral analysis].

    PubMed

    Qin, Chong; Chen, Wen-Wen; He, Xiong-Kui; Zhang, Lu-Da; Ma, Xiang

    2009-10-01

    In the present paper, a simple but novel method based on maximum linearly independent group was introduced into near-infrared (NIR) spectral analysis for selecting representative calibration samples. The experiment materials contained 2,652 tobacco powder samples, with 1,001 samples randomly selected as prediction set, and the others as representative sample candidate set from which calibration sample set was selected. The method of locating maximum linearly independent vectors was used to select representative samples from the spectral vectors of representative samples candidate set. The arithmetic was accomplished by function rref(X,q) in Matlab. The maximum linearly independent spectral vectors were treated as calibration samples set. When different calculating precision q was given, different amount of representative samples were acquired. The selected calibration sample set was used to build regression model to predict the total sugar of tobacco powder samples by PLS. The model was used to analyze 1001 samples in the prediction set. When selecting 32 representative samples, the model presented a good predictive veracity, whose predictive mean relative error was 3.6210%, and correlation coefficient was 0.9643. By paired-samples t-test, we found that the difference between the predicting result of model obtained by 32 samples and that obtained by 146 samples was not significant (alpha=0.05). Also, we compared the methods of randomly selecting calibration samples and maximum linearly independent selection by their predicting effects of models. In the experiment, correspondingly, six calibration sample sets were selected, one of which included 28 samples, while the others included 32, 41, 76, 146 and 163 samples respectively. The method of maximum linearly independent selecting samples turned out to be obviously better than that of randomly selecting. The result indicated that the proposed method can not only effectively enhance the cost-effectiveness of NIR

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

    NASA Astrophysics Data System (ADS)

    Luo, Ma

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

  2. 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.

  3. Existence of a Lipschitz selection of the Chebyshev-centre map

    SciTech Connect

    Druzhinin, Yuri Yu

    2013-05-31

    The paper is concerned with the existence of a Lipschitz selection for the operator T{sub C} (the Chebyshev-centre map) that assigns to any bounded subset M of a Banach space X the set T{sub C}(M) of its Chebyshev centres. It is proved that if the unit sphere S(X) of X has an exposed smooth point, then T{sub C} does not have a Lipschitz selection. It is also proved that if X is finite dimensional the operator T{sub C} has a Lipschitz selection if and only if X is polyhedral. The operator T{sub C} is also shown to have a Lipschitz selection in the space c{sub 0}(K) and c-spaces. Bibliography: 4 titles.

  4. 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

  5. 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.

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

    NASA Astrophysics Data System (ADS)

    Ng, R.; Polet, J.

    2015-12-01

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

  7. 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

  8. 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)

  9. 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.

  10. 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.

  11. 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.

  12. Some illustrative examples of the use of a spectral-element method in ocean acoustics.

    PubMed

    Cristini, Paul; Komatitsch, Dimitri

    2012-03-01

    Some numerical results in the time domain obtained with the spectral-element method are presented in order to illustrate the high potential of this technique for modeling the propagation of acoustic waves in the ocean in complex configurations. A validation for a simple configuration with a known solution is shown, followed by some simulations of the propagation of acoustic waves over different types of ocean bottoms (fluid, elastic, and porous) to emphasize the wide variety of media that can be considered within the framework of this method. Finally, a movie illustrating upslope propagation over a viscoelastic wedge is presented and discussed.

  13. Brake squeal analysis by coupling spectral linearization and modal identification methods

    NASA Astrophysics Data System (ADS)

    Grange, P.; Clair, D.; Baillet, L.; Fogli, M.

    2009-11-01

    Brake squeal is induced by self-excited vibrations, consequences of local nonlinearities at the contact interface. This paper deals with a new way to analyze the brake squeal behavior. The proposed method is based on a spectral linearization of the brake nonlinear dynamic response with unilateral contact and friction conditions. The approach enables to identify modal parameters of an equivalent linear system by a combination of the random decrement technique and the Ibrahim time domain method. It is applied to the analysis of a pad/beam squealing contact. The obtained results are compared to the classical complex eigenvalues analysis and nonlinear temporal dynamic finite element analysis ones.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

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

    PubMed

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

    2014-05-21

    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 (1)H and (13)C 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.

  19. 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

  20. 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.

  1. 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.

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

    DOE PAGES

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

    2015-09-08

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Cai, Wenjun; Zhang, Huai

    2016-04-01

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

  5. 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.

  6. 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.

  7. 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.

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

    NASA Astrophysics Data System (ADS)

    Kent, Erin B.; Shipman, Steven

    2014-06-01

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

  9. 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.

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

    PubMed

    Pearman, Charles M

    2014-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Pindza, Edson; Owolabi, Kolade M.

    2016-11-01

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

  12. 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.

  13. 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.

  14. A Fully Bayesian Method for Jointly Fitting Instrumental Calibration and X-Ray Spectral Models

    NASA Astrophysics Data System (ADS)

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

    2014-10-01

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

  15. 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

  16. Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

    NASA Technical Reports Server (NTRS)

    Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

    2016-01-01

    The perfectly matched layer (PML) technique is developed in the context of a high- order spectral-element Discontinuous-Galerkin (DG) method. The technique is applied to a range of test cases and is shown to be superior compared to other approaches, such as those based on using characteristic boundary conditions and sponge layers, for treating the inflow and outflow boundaries of computational domains. In general, the PML technique improves the quality of the numerical results for simulations of practical flow configurations, but it also exhibits some instabilities for large perturbations. A preliminary analysis that attempts to understand the source of these instabilities is discussed.

  17. [A 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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)

  5. 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.

  6. A novel nonstationary deconvolution method based on spectral modeling and variable-step sampling hyperbolic smoothing

    NASA Astrophysics Data System (ADS)

    Li, Fang; Wang, Shoudong; Chen, Xiaohong; Liu, Guochang; Zheng, Qiang

    2014-04-01

    Deconvolution is an important part of seismic processing tool for improving the resolution. One of the key assumptions made in most deconvolutional methods is that the seismic data is stationary. However, due to the anelastic absorption, the seismic data is usually nonstationary. In this paper, a novel nonstationary deconvolution approach is proposed based on spectral modeling and variable-step sampling (VSS) hyperbolic smoothing. To facilitate our method, firstly, we apply the Gabor transform to perform a time-frequency decomposition of the nonstationary seismic trace. Secondly, we estimate the source wavelet amplitude spectrum by spectral modeling. Thirdly, smoothing the Gabor magnitude spectrum of seismic data along hyperbolic paths with VSS can obtain the magnitude of the attenuation function, and can also eliminate the effect of source wavelet. Fourthly, by assuming that the source wavelet and attenuation function are minimum phase, their phases can be determined by Hilbert transform. Finally, the estimated two factors are removed by dividing them into the Gabor spectrum of the trace to estimate the Gabor spectrum of the reflectivity. An inverse Gabor transform gives the time-domain reflectivity estimate. Tests on synthetic and field data show that the presented method is an effective tool that not only has the advantages of stationary deconvolution, but also can compensate for the energy absorption, without knowing or estimating the quality factor Q.

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

    PubMed

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

    2014-06-27

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

  8. 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

  9. 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

  10. 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.

  11. 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.

  12. 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

  13. 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

  14. 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.

  15. 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%.

  16. Spectral and structural studies of the anti-cancer drug Flutamide by density functional theoretical method

    NASA Astrophysics Data System (ADS)

    Mariappan, G.; Sundaraganesan, N.

    2014-01-01

    A comprehensive screening of the more recent DFT theoretical approach to structural analysis is presented in this section of theoretical structural analysis. The chemical name of 2-methyl-N-[4-nitro-3-(trifluoromethyl)phenyl]-propanamide is usually called as Flutamide (In the present study it is abbreviated as FLT) and is an important and efficacious drug in the treatment of anti-cancer resistant. The molecular geometry, vibrational spectra, electronic and NMR spectral interpretation of Flutamide have been studied with the aid of density functional theory method (DFT). The vibrational assignments of the normal modes were performed on the basis of the PED calculations using the VEDA 4 program. Comparison of computational results with X-ray diffraction results of Flutamide allowed the evaluation of structure predictions and confirmed B3LYP/6-31G(d,p) as accurate for structure determination. Application of scaling factors for IR and Raman frequency predictions showed good agreement with experimental values. This is supported the assignment of the major contributors of the vibration modes of the title compound. Stability of the molecule arising from hyperconjugative interactions leading to its bioactivity, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. NMR chemical shifts of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. The comparison of measured FTIR, FT-Raman, and UV-Visible data to calculated values allowed assignment of major spectral features of the title molecule. Besides, Frontier molecular orbital analyze was also investigated using theoretical calculations.

  17. 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.

  18. Spectral Analysis Methods for the Robust Measurement of the Flexural Rigidity of Biopolymers

    PubMed Central

    Valdman, David; Atzberger, Paul J.; Yu, Dezhi; Kuei, Steve; Valentine, Megan T.

    2012-01-01

    The mechanical properties of biopolymers can be determined from a statistical analysis of the ensemble of shapes they exhibit when subjected to thermal forces. In practice, extracting information from fluorescence microscopy images can be challenging due to low signal/noise ratios and other artifacts. To address these issues, we develop a suite of tools for image processing and spectral data analysis that is based on a biopolymer contour representation expressed in a spectral basis of orthogonal polynomials. We determine biopolymer shape and stiffness using global fitting routines that optimize a utility function measuring the amount of fluorescence intensity overlapped by such contours. This approach allows for filtering of high-frequency noise and interpolation over sporadic gaps in fluorescence. We use benchmarking to demonstrate the validity of our methods, by analyzing an ensemble of simulated images generated using a simulated biopolymer with known stiffness and subjected to various types of image noise. We then use these methods to determine the persistence lengths of taxol-stabilized microtubules. We find that single microtubules are well described by the wormlike chain polymer model, and that ensembles of chemically identical microtubules show significant heterogeneity in bending stiffness, which cannot be attributed to sampling or fitting errors. We expect these approaches to be useful in the study of biopolymer mechanics and the effects of associated regulatory molecules. PMID:22404937

  19. Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique

    NASA Astrophysics Data System (ADS)

    Wang, Li; Sun, Xiaogang; Xing, Jian

    2012-04-01

    Retrieval of spheroidal particle size distribution using an approximate method in spectral extinction technique is proposed. The combined approximate method, which is the combination of Mie method and generalized eikonal approximation (GEA) method, is used as an alternative to the rigorous solutions to calculate the averaging extinction efficiency of spheroid. Based on the averaging extinction efficiency, the accuracy and limitations of the retrieval are then investigated. Moreover, the validity range and effect of the refractive index are also examined. The Johnson's SB function in this paper is used as a versatile function to fit the commonly used particle size distribution functions in the dependent model. Simulations and experimental results show that the combined approximate method can be successfully applied to retrieval of spheroidal particle size distribution. In certain constraint conditions, the retrieval results demonstrate the high reliability and stability of the method. By using the combined approximate method, the complexity and computation time of the retrieval are significantly reduced, which is more suitable for quick and easy measurement. The method can also be used as a replacement when the rigorous solutions suffer computationally intractable difficulties.

  20. [A method of object detection for remote sensing-imagery based on spectral space transformation].

    PubMed

    Wu, Gui-Ping; Xiao, Peng-Feng; Feng, Xue-Zhi; Wang, Ke

    2013-03-01

    Object detection is an intermediate link for remote sensing image processing, which is an important guarantee of remote sensing application and services aspects. In view of the characteristics of remotely sensed imagery in frequency domain, a novel object detection algorithm based on spectral space transformation was proposed in the present paper. Firstly, the Fourier transformation method was applied to transform the image in spatial domain into frequency domain. Secondly, the wedge-shaped sample and overlay analysis methods for frequency energy were used to decompose signal into different frequency spectrum zones, and the center frequency values of object's features were acquired as detection marks in frequency domain. Finally, object information was detected with the matched Gabor filters which have direction and frequency selectivity. The results indicate that the proposed algorithm here performs better and it has good detection capability in specific direction as well.

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

    SciTech Connect

    Tamarchenko, T.

    1996-12-31

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

  2. Electrochemical method for improving the spectral response of CdS/Cu 2S heterojunctions

    NASA Astrophysics Data System (ADS)

    Garcia-Camarero, E.; Arjona, F.; Fatas, E.

    The effect on the stoichiometry of a copper sulphide electrode of short-circuiting the Cu/Cu aq2+/Cu 2-δS/In galvanic cell for different times has been studied. This treatment has been carried out on the copper sulphide layer of CdS/Cu 2S solar cells prepared by different methods. The resulting changes of the spectral short circuit current and the I-V characteristics of the cells have been recorded. Remarkable increases in open circuit voltage, short circuit current, and fill factor have been observed as a consequence of any transformation that increases the proportion of copper in the copper sulphide films. Thus, this treatment could be a suitable method of improving the efficiency of CdS/Cu 2S solar cells.

  3. 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

  4. Spectral element-Fourier method for unsteady conjugate heat transfer in complex geometry flows

    NASA Astrophysics Data System (ADS)

    Amon, Cristina H.

    1995-04-01

    A spectral-element Fourier method (SEFM) is presented for the direct numerical simulation of forced convective heat transfer and conjugate conduction/convection in transitional internal flows in complex geometries. The SEFM is employed for the spatial discretization of the unsteady, incompressible, three-dimensional Navier-Stokes and energy equations. The resulting discrete equations are solved by a semi-implicit method in time treating explicitly the convection operator and implicitly the remaining pressure and viscous contributions. This methodology is illustrated by performing direct numerical simulations to investigate forced convective heat transfer in supercritical self-sustained oscillatory flows and conjugate effects in multimaterial domains. Highly unsteady flows in complex geometries are considered, including modified channels with periodic inhomogeneities such as spanwise rectangular and triangular grooves encountered in electronic equipment and compact heat exchangers.

  5. A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

    NASA Astrophysics Data System (ADS)

    Delgado-Vences, Francisco; Flandoli, Franco

    2016-08-01

    We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.

  6. 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

  7. 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.

  8. 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

  9. 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

  10. 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

  11. 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.

  12. [An improved characteristic spectral selection method for multicomponent gas quantitative analysis based on Tikhonov regularization].

    PubMed

    Tang, Xiao-Jun; Zhang, Lei; Wang, Er-Zhen; Li, Zhe-Bu; Meng, Yong-Peng; Liu, Jun-Hua

    2012-10-01

    In the present paper, an improved approach to the TR characteristic spectral selection is presented. For this approach, two ideas of TR1-norm and TR2-norm are used, two constraint items, spectral line distance and minimizing absolute value of coefficient are introduced, and a general formula of ill-posed optimization problem is established. The formula can reduce effectively the errors caused by experienced and experimental method when used in determining the regular matrix and parameter. Finally, the improved approach presented in the paper was used in the analysis of alkane gas mixture, with methane, ethane, propane, n-butane, iso-butane, n-pentane and iso-pentane included. The concentration range is 0.01%-20%. The experimental results show that the predicting error square is only 2.6 x 10(-4), and the coefficient of determination is 0. 959 2, which means that preceding accuracy is high, and that the practicability of TR regularization has been enhanced. PMID:23285876

  13. 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

  14. 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.

  15. Post-earthquake relaxation using a spectral element method: 2.5-D case

    USGS Publications Warehouse

    Pollitz, Fred

    2014-01-01

    The computation of quasi-static deformation for axisymmetric viscoelastic structures on a gravitating spherical earth is addressed using the spectral element method (SEM). A 2-D spectral element domain is defined with respect to spherical coordinates of radius and angular distance from a pole of symmetry, and 3-D viscoelastic structure is assumed to be azimuthally symmetric with respect to this pole. A point dislocation source that is periodic in azimuth is implemented with a truncated sequence of azimuthal order numbers. Viscoelasticity is limited to linear rheologies and is implemented with the correspondence principle in the Laplace transform domain. This leads to a series of decoupled 2-D problems which are solved with the SEM. Inverse Laplace transform of the independent 2-D solutions leads to the time-domain solution of the 3-D equations of quasi-static equilibrium imposed on a 2-D structure. The numerical procedure is verified through comparison with analytic solutions for finite faults embedded in a laterally homogeneous viscoelastic structure. This methodology is applicable to situations where the predominant structure varies in one horizontal direction, such as a structural contrast across (or parallel to) a long strike-slip fault.

  16. 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.

  17. 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

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

    NASA Astrophysics Data System (ADS)

    Qin, Xuanmei; Dai, Weidi; Jiao, Pengfei; Wang, Wenjun; Yuan, Ning

    2016-08-01

    Community structure is one of the fundamental characteristics of complex networks. Many methods have been proposed for community detection. However, most of these methods are designed for static networks and are not suitable for dynamic networks that evolve over time. Recently, the evolutionary clustering framework was proposed for clustering dynamic data, and it can also be used for community detection in dynamic networks. In this paper, a multi-similarity spectral (MSSC) method is proposed as an improvement to the former evolutionary clustering method. To detect the community structure in dynamic networks, our method considers the different similarity metrics of networks. First, multiple similarity matrices are constructed for each snapshot of dynamic networks. Then, a dynamic co-training algorithm is proposed by bootstrapping the clustering of different similarity measures. Compared with a number of baseline models, the experimental results show that the proposed MSSC method has better performance on some widely used synthetic and real-world datasets with ground-truth community structure that change over time.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. Novel image encryption scheme based on Chebyshev polynomial and Duffing map.

    PubMed

    Stoyanov, Borislav; Kordov, Krasimir

    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 10(113) key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. IR spectrum of FHF- and FDF- revisited using a spectral method in four dimensions.

    PubMed

    Pérez-Hernández, Guillermo; González-Vázquez, Jesús; González, Leticia

    2012-11-26

    A four dimensional (4D) time-dependent calculation to obtain the first vibrational states of the hydrogen bifluoride ion, FHF(-), and its deuterated counterpart, FDF(-), has been performed using a spectral method in Cartesian coordinates. The corresponding potential energy surfaces have been computed at the CCSD(T)/aug-cc-pVTZ level of theory. The obtained values for the fundamental vibrational bands ν(1) = 589 cm(-1), ν(2) = 1305 cm(-1), and ν(3) = 1372 cm(-1) assigned to the symmetric stretch, bend, and asymmetric stretch modes, respectively (598, 943, and 972 cm(-1) for FDF(-), respectively) are in good agreement with available experimental and theoretical values. Selected overtones and mixed modes are also calculated. Infrared spectra have been simulated using the dipole approximation for two different polarization directions of the incident light.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Enhanced plasmonic light absorption engineering of graphene: simulation by boundary-integral spectral element method.

    PubMed

    Niu, Jun; Luo, Ma; Zhu, Jinfeng; Liu, Qing Huo

    2015-02-23

    Graphene's relatively poor absorption is an essential obstacle for designing graphene-based photonic devices with satisfying photo-responsivity. To enhance the tunable light absorption of graphene, appropriate excitation of localized surface plasmon resonance is considered as a promising approach. In this work, the strategy of incorporating periodic cuboid gold nanoparticle (NP) cluster arrays and cylindrical gold NP arrays with Bragg reflectors into graphene-based photodetectors are theoretically studied by the boundary-integral spectral element method (BI-SEM). With the BI-SEM, the models can be numerically analyzed with excellent accuracy and efficiency. Numerical simulation shows that the proposed structures can effectively engineer the light absorption in graphene by tuning plasmon resonance. In the spectra of 300 nm to 1000 nm, a maximum light absorption of 67.54% is observed for the graphene layer with optimal parameters of the photodetector model.

  16. 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

  17. 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.

  18. Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

    NASA Astrophysics Data System (ADS)

    Kreeft, Jasper; Gerritsma, Marc

    2013-05-01

    In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in Kreeft et al. [51] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential k-forms with k-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions.

  19. 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

  20. 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.

  1. Investigations of spectral resolution and angle dependency in a 2-D tracking Doppler method.

    PubMed

    Fredriksen, Tonje D; Avdal, Jorgen; Ekroll, Ingvild K; Dahl, Torbjorn; Lovstakken, Lasse; Torp, Hans

    2014-07-01

    An important source of error in velocity measurements from conventional pulsed wave (PW) Doppler is the angle used for velocity calibration. Because there are great uncertainties and interobserver variability in the methods used for Doppler angle correction in the clinic today, it is desirable to develop new and more robust methods. In this work, we have investigated how a previously presented method, 2-D tracking Doppler, depends on the tracking angle. A signal model was further developed to include tracking along any angle, providing velocity spectra which showed good agreement with both experimental data and simulations. The full-width at half-maximum (FWHM) bandwidth and the peak value of predicted power spectra were calculated for varying tracking angles. It was shown that the spectra have lowest bandwidth and maximum power when the tracking angle is equal to the beam-to-flow angle. This may facilitate new techniques for velocity calibration, e.g., by manually adjusting the tracking angle, while observing the effect on the spectral display. An in vitro study was performed in which the Doppler angles were predicted by the minimum FWHM and the maximum power of the 2-D tracking Doppler spectra for 3 different flow angles. The estimated Doppler angles had an overall error of 0.24° ± 0.75° when using the minimum FWHM. With an in vivo example, it was demonstrated that the 2-D tracking Doppler method is suited for measurements in a patient with carotid stenosis.

  2. 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.

  3. 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.

  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. 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.

  6. Comparison between two methods for forward calculation of ambient noise H/V spectral ratios

    NASA Astrophysics Data System (ADS)

    Garcia-Jerez, A.; Luzón, F.; Sanchez-Sesma, F. J.; Santoyo, M. A.; Albarello, D.; Lunedei, E.; Campillo, M.; Iturrarán-Viveros, U.

    2011-12-01

    The analysis of horizontal-to-vertical spectral ratios of ambient noise (NHVSR) is a valuable tool for seismic prospecting, particularly if both a dense spatial sampling and a low-cost procedure are required. Unfortunately, the computation method still lacks of a unanimously accepted theoretical basis and different approaches are currently being used for inversion of the ground structure from the measured H/V curves. Two major approaches for forward calculation of NHVSRs in a layered medium are compared in this work. The first one was developed by Arai and Tokimatsu (2004) and recently improved by Albarello and Lunedei (2011). It consists of a description of the wavefield as generated by Far Surface point Forces (FSF method). The second one is based on the work of Sánchez-Sesma et al. (2011) who consider ambient noise as a Diffuse WaveField (DWF method), taking advantage of the proportionality between its Fourier-transformed autocorrelation (power spectrum) and the imaginary part of the Green function when source and receiver are the same. In both methods, the NHVSR is written as (PH/PV)1/2, where PH and PV are the horizontal and vertical power spectra. In the FSF method these quantities are given by PV∝⊙m(1+1/2χm2α2)(ARm/kRm)2 PH∝⊙m{(1+1/2χm2α2)(ARm/kRm)2χm2+1/2α2(ALm/kLm)2} where kRm, χm and ARm are wavenumber, ellipticity and medium response of the m-th Rayleigh wave mode; kLm and ALm correspond to the m-th Love wave mode and α is the horizontal-to-vertical load ratio of the ambient noise sources. Some common factors are omitted in the expressions of PV and PH. On the other hand, the DWF method deals with the full wavefield including both surface and body waves. In order to make the comparison easier, and taking into account that surface waves are often the dominant components in wide spectral ranges, body wave contributions are neglected here. In this case, the PH and PV power spectra for the DWF method are reduced to the simple expressions: PV

  7. 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

  8. Methods of foreign fiber detecting based on PCA analyzing of infrared spectral images

    NASA Astrophysics Data System (ADS)

    Tian, LiXun; Fu, WeiSen; Liu, JieYu; Zhang, HongBo; Pan, Jin; Wang, YaPeng; Tong, Fei

    2014-02-01

    A set of near infrared high resolution spectral imaging system is set up, the infrared absorption properties of raw cotton and colorless foreign are analyzed through the system, and scheme of polypropylene fiber detection based on the near infrared spectral image is proposed; On this basis, reduce dimensions the spectral images through the principal component analysis, further improve the efficiency of colorless foreign detection. The experimental results show that the spectral images after reducing dimensions can be used to detect colorless or light color raw cotton fiber effectively.

  9. 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.

  10. A nonlinear spectral unmixing method for abundance retrieval of mineral mixtures

    NASA Astrophysics Data System (ADS)

    Zhang, Xia; Lin, Honglei; Cen, Yi; Yang, Hang

    2016-05-01

    Minerals are generally present as intimate mixtures. The spectra of intimate mixtures in visible-infrared are complex function of abundance, grain size, and optical constants et.al, making the linear spectral unmixing model inapplicable. In this paper, we presented a nonlinear unmixing method by combining Shkuratov model (SK99) and Hapke model (H81) to unmix the mineral mixtures. For obtaining the abundances of mineral endmembers, we built up a look-up table (LUT) in the following steps: First, the optical constants were derived by SK99 model and then single scattering albedos of endmembers were computed. Second, the approximation of multiple scattering was derived by the Chandrasekhar H-function. Finally, LUT was established using H81 model. The root-mean-square error (RMSE) was calculated to find the best match between the reflectance of mixtures and LUT. We used the laboratory mineral mixtures to verify the accuracy of abundance estimation. The results show that RMSEs are less than 1% and the absolute errors of abundance retrieval are within 5%. The presented method can retrieve mineral abundance effectively and rapidly. It can be a potential method applying for hyperspectral images of the earth and planetary.

  11. Boundary integral spectral element method analyses of extreme ultraviolet multilayer defects.

    PubMed

    Niu, Jun; Luo, Ma; Fang, Yuan; Liu, Qing Huo

    2014-10-01

    Extreme ultraviolet (EUV) lithography is an emerging technology for high-density semiconductor patterning. Multilayer distortion caused by mask defects is regarded as one of the critical challenges of EUV lithography. To simulate the influence of the defected nanoscale structures with high accuracy and efficiency, we have developed a boundary integral spectral element method (BI-SEM) that combines the SEM with a set of surface integral equations. The SEM is used to solve the interior computational domain, while the open boundaries are truncated by the surface integral equations. Both two-dimensional (2D) and three-dimensional (3D) EUV cases are simulated. Through comparing the performance of this method with the conventional finite element method (FEM), it is shown that the proposed BI-SEM can greatly decrease both the memory cost and the computation time. For typical 2D problems, we show that the BI-SEM is 11 and 1.25 times more efficient than the FEM in terms of memory and CPU time, respectively, while for 3D problems, these factors are over 14 and 2, respectively, for smaller problems; realistic 3D problems that cannot be solved by the conventional FEM can be accurately simulated by the BI-SEM. PMID:25401246

  12. SEDEBLEND: a new method for deblending spectral energy distributions in confused imaging

    NASA Astrophysics Data System (ADS)

    MacKenzie, Todd P.; Scott, Douglas; Swinbank, Mark

    2016-11-01

    For high-redshift submillimetre or millimetre sources detected with single-dish telescopes, interferometric follow-up has shown that many are multiple submillimetre galaxies blended together. Confusion-limited Herschel observations of such targets are also available, and these sample the peak of their spectral energy distribution (SED) in the far-infrared. Many methods for analysing these data have been adopted, but most follow the traditional approach of extracting fluxes before model SEDs are fit, which has the potential to erase important information on degeneracies among fitting parameters and glosses over the intricacies of confusion noise. Here, we adapt the forward-modelling method that we originally developed to disentangle a high-redshift strongly lensed galaxy group, in order to tackle this general problem in a more statistically rigorous way, by combining source deblending and SED fitting into the same procedure. We call this method `SEDeblend'. As an application, we derive constraints on far-infrared luminosities and dust temperatures for sources within the ALMA follow-up of the LABOCA Extended Chandra Deep Field South Submillimetre Survey. We find an average dust temperature for an 870-μm-selected sample of (33.9 ± 2.4) K for the full survey. When selection effects of the sample are considered, we find no evidence that the average dust temperature evolves with redshift for sources with redshifts greater than about 1.5, when compared to those with redshifts between 0.1 and 1.5.

  13. Spectral methods to detect cometary minerals with OSIRIS on board Rosetta

    NASA Astrophysics Data System (ADS)

    Oklay, N.; Vincent, J.-B.; Sierks, H.

    2013-09-01

    Comet 67P/Churyumov-Gerasimenko is going to be observed by the OSIRIS scientific imager (Keller et al. 2007) on board ESA's spacecraft Rosetta in the wavelength range of 250-1000 nm with a combination of 12 filters for the narrow angle camera (NAC) and 14 combination of 12 filters for the narrow angle camera (NAC) and 14 filters in the wavelength range of 240-720 nm for the wide angle camera (WAC). NAC filters are suitable to surface composition studies, while WAC filters are designed for gas and radical emission studies. In order to investigate the composition of the comet surface from the observed images, we need to understand how to detect different minerals and which compositional information can be derived from the NAC filters. Therefore, the most common cometary silicates e.g. enstatite, forsterite are investigated with two hydrated silicates (serpentine and smectite) for the determina- tion of the spectral methods. Laboratory data of those selected minerals are collected from RELAB database (http://www.planetary.brown.edu/relabdocs/relab.htm) and absolute spectra of the minerals observed by OSIRIS NAC filters are calculated. Due to the limited spectral range of the laboratory data, Far-UV and Neutral density filters of NAC are excluded from this analysis. Considered NAC filters in this study are represented in Table 1 and the number of collected laboratory data are presented in Table 2. Detection and separation of the minerals will not only allow us to study the surface composition but also to study observed composition changes due to the cometary activity during the mission.

  14. A Comparison Between Deterministic and Stochastic Methods for Inverting Spectral Induced Polarization Data

    NASA Astrophysics Data System (ADS)

    Chen, J.; Kemna, A.; Hubbard, S.

    2007-12-01

    Cole-Cole model parameters (e.g., chargeability and time constant), extracted from spectral induced polarization (SIP) data, are being increasingly used to characterize subsurface properties. However, fitting Cole-Cole models (especially nested Cole-Cole models) to SIP data is challenging because of nonlinearity and non-uniqueness of the Cole-Cole models. This study compares conventional deterministic approaches (i.e., iterative based estimation methods) with Markov chain Monte Carlo (MCMC) based stochastic approaches for estimating Cole- Cole model parameters. The results of those case studies show that although deterministic methods are able to provide single optimal solutions under certain criteria (e.g., the least squares of misfit) and require minimal computing power, they suffer from two main limitations. The first limitation is that the optimal solutions heavily depend on the choice of the initial values. Different initial values may yield different inversion results, and in many cases, the deterministic methods even cannot converge for the chosen initial values. The second limitation is that those methods provide inadequate or inaccurate information about uncertainty in the estimation. On the contrary, the MCMC-based stochastic approaches are insensitive to the choice of the initial values and can provide extensive information about uncertainty in the estimation. From the drawn large number of samples, we can obtain exhaustive information about unknown parameters, such as the mean, the median, the mode, and even entire probability distribution of each unknown Cole-Cole model parameter. Although MCMC-based stochastic methods typically require that the forward models be run for thousands of times, this is not an issue given the current computer power. Through presentation of extensive synthetic and laboratory case studies, we will illustrate the benefits of the different methods when used individually and in combination with each other.

  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. A smile insensitive method for spectral linewidth narrowing on high power laser diode arrays

    NASA Astrophysics Data System (ADS)

    Yang, Zining; Wang, Hongyan; Li, Yuandong; Lu, Qisheng; Hua, Weihong; Xu, Xiaojun; Chen, Jinbao

    2011-10-01

    To eliminate the smile effect in spectral linewidth narrowing on high power laser diode arrays, we have introduced a plane reflective mirror into a common Littrow configuration external cavity to enhance the correlation among emitters. By this way, we obtained uniform spectral distribution among emitters of a 64-elements laser diode array with 35 GHz linewidth and 41 W output laser power.

  17. Iterative method for optimal design of flat-spectral-response arrayed waveguide gratings.

    PubMed

    Park, Shin-Woong; Park, Yohan; Yi, Yun; Kim, Hwi

    2013-10-20

    A novel iterative projection-type optimal design algorithm of arrayed waveguide gratings (AWGs) with a flat spectral response is proposed based on the Fourier optics model of AWG. The enhancement of the spectral-response flatness of the AWG is demonstrated, with an analysis on the trade-off relationship between band flatness and crosstalk.

  18. 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.

  19. 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).

  20. 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.

  1. 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

  2. Centaur feedline dynamics study using power spectral methods. [fundamental mode resonant frequencies of RL-10 oxygen and hydrogen feed lines

    NASA Technical Reports Server (NTRS)

    Lorenzo, C. F.

    1974-01-01

    Tests were conducted to determine the dynamic characteristics of the Centaur/RL-10 oxygen and hydrogen feedlines. The fundamental-mode resonant frequencies were determined by applying power spectral methods to noise-generated data from hot firings of the RL-10 engine. The effect of net positive suction pressure of the main feed pumps on resonant frequency characteristics was determined to be a straight-line relation. Power spectral methods were also used to determine the dynamic characteristics of the boost pumps.

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

    NASA Astrophysics Data System (ADS)

    Clason, Christian; von Winckel, Gregory

    2012-02-01

    This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. Program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 102 No. of bytes in distributed program, including test data, etc.: 2294 Distribution format: tar.gz Programming language: MATLAB Computer: Any architecture supported by MATLAB Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6) RAM: Depends on the data Classification: 4.3, 2.2 Nature of problem: The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Solution method: A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave

  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. 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.

  7. Inferring upper-mantle structure by full waveform tomography with the spectral element method

    NASA Astrophysics Data System (ADS)

    Lekić, V.; Romanowicz, B.

    2011-05-01

    Mapping the elastic and anelastic structure of the Earth's mantle is crucial for understanding the temperature, composition and dynamics of our planet. In the past quarter century, global tomography based on ray theory and first-order perturbation methods has imaged long-wavelength elastic velocity heterogeneities of the Earth's mantle. However, the approximate techniques upon which global tomographers have traditionally relied become inadequate when dealing with crustal structure, as well as short-wavelength or large amplitude mantle heterogeneity. 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 (SEM). Importantly, SEM allows a dramatic improvement in accounting for the effects of crustal structure. Here, we develop and apply a new hybrid method of tomography, which allows us to leverage the accuracy of SEM to model fundamental and higher-mode long period (>60 s) waveforms. We then present the first global model of upper-mantle velocity and radial anisotropy developed using SEM. Our model, SEMum, confirms that the long-wavelength mantle structure imaged using approximate semi-analytic techniques is robust and representative of the Earth's true structure. Furthermore, it reveals structures in the upper mantle that were not clearly seen in previous global tomographic models. We show that SEMum favourably compares to and rivals the resolving power of continental-scale studies. This new hybrid approach to tomography can be applied to a larger and higher-frequency data set in order to gain new insights into the structure of the lower mantle and more robustly map seismic structure at the regional and smaller scales.

  8. 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.

  9. 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.

  10. 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.

  11. 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).

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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

  19. Modeling the Tohoku, 2011, ionospheric acoustic-gravity waves with the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Khelfi, K.; Lognonne, P. H.; Komatitsch, D.; Astafyeva, E.

    2013-12-01

    After the Tohoku earthquake (Japan March 2011), several types of waves have been observed in the ionosphere. These waves are generated from different sources located at the Earth surface, either associated to the rupture and co-seismic ground uplift or to remote uplift associated to waves internal to the ocean-ground system, e.g. tsunami and seismic body and surface waves. These waves were densely observed by the Japanese GEONET network but also in several locations of the Pacific ocean e.g., Hawaii, Chile, California, etc..., enabling in depth studies and requesting therefore modeling integrating all the complexity and tri-dimensional structure of the atmosphere-ionosphere system. In this work, we present preliminary results obtained by the spectral element method, in order to perform 3D modeling of the propagation of the gravito-acoustic waves in the neutral atmosphere, by taking not only into account the coupling between the ionosphere and the neutral atmosphere which generate an anisotropic attenuation associated to the magnetic field, in addition to the isotropic attenuation due to viscosity, but also the complexity of the acoustic waves, which are originating from a complex structure with variable depth ocean. We first present the typical lateral variation of the propagation parameters, e.g . acoustic velocities and densities and local wave damping with respect to atmospheric viscosity, heat transfer and magnetic field used from the IGRF model, and we use also the IRI model for the ionospheric parameters We then show first results of wave simulations in 2D and 3D geometries. In this first step, the interaction between the neutral and ionosphere is assumed to be instantaneous, due to the large gyro frequency of ions and electrons as compared to the typical frequency of waves, but take into account the interaction with magnetic field and further diffusion. As this first steps focus on the propagation, results are illustrated for simple sources. The

  20. Modeling the Tohoku, 2011, ionospheric acoustic-gravity waves with the Spectral Element Method

    NASA Astrophysics Data System (ADS)

    Khelfi, K.; Lognonne, P. H.; Komatitsch, D.

    2012-12-01

    After the Tohoku earthquake (Japan March 2011), several types of waves have been observed in the ionosphere. These waves are generated from different sources located at the Earth surface, either associated to the rupture and co-seismic ground uplift or to remote uplift associated to waves internal to the ocean-ground system, e.g. tsunami and seismic body and surface waves. These waves were densely observed by the Japanese GEONET network but also in several locations of the Pacific ocean e.g., Hawaii, Chile, California, etc…, enabling in depth studies and requesting therefore modeling integrating all the complexity and tri-dimensional structure of the atmosphere-ionosphere system. In this work, we present preliminary results obtained by the spectral element method, in order to perform 3D modeling of the propagation of the gravito-acoustic waves in the neutral atmosphere, by taking into account the coupling between the ionosphere and the neutral atmosphere which generate an anisotropic attenuation associated to the magnetic field, in addition to the isotropic attenuation due to viscosity. We first present the typical lateral variation of the propagation parameters, e.g . acoustic velocities and densities and local wave damping with respect to atmospheric viscosity, heat transfer and magnetic field. We then show first results of wave simulations. In this first step, the interaction between the neutral and ionosphere is assumed to be instantaneous, due to the large gyro frequency of ions and electrons as compared to the typical frequency of waves. As this first steps focus on the propagation, results are illustrated for simple sources. The generalization for the more complex Tohoku signal is presented theoretically.

  1. Inferring the elastic structure of the Earth's mantle using the spectral element method

    NASA Astrophysics Data System (ADS)

    Lekic, Vedran

    Mapping the elastic and anelastic structure of the Earth's mantle is crucial for understanding the temperature, composition and dynamics of our planet. Extracting the information contained in seismic waveforms is the key to constraining the elastic and anelastic structure within the Earth, and is the goal of our work. 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. However, the approximate techniques upon which global tomographers have traditionally relied become inadequate when dealing with crustal structure, as well as short-wavelength or large amplitude mantle heterogeneity. 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 (SEM: Capdeville et al., 2003). Importantly, SEM allows a dramatic improvement in accounting for the effects of crustal structure. Here, we develop and apply a new hybrid method of tomography, which allows us to leverage the accuracy of SEM to model fundamental and high-mode long period (>60s) waveforms. We then present the first global model of upper mantle velocity and radial anisotropy developed using SEM. Our model, SEMum, confirms that the long-wavelength mantle structure imaged using approximate semi-analytic techniques is robust and representative of the Earth's true structure. Furthermore, it reveals structures in the upper mantle that were not clearly seen in previous global tomographic models, providing new constraints on the temperature, composition as well as flow in the mantle. We show that applying a clustering analysis to the absolute shear wave-speed profiles offers a powerful new way of exploring the relationship between surface expressions of tectonics and their

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Verification of a non-hydrostatic dynamical core using horizontally spectral element vertically finite difference method: 2-D aspects

    NASA Astrophysics Data System (ADS)

    Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

    2014-06-01

    The non-hydrostatic (NH) compressible Euler equations of dry atmosphere are solved in a simplified two dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative terms and quadrature. The Euler equations used here are in a flux form based on the hydrostatic pressure vertical coordinate, which are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate is implemented in this model. We verified the model by conducting widely used standard benchmark tests: the inertia-gravity wave, rising thermal bubble, density current wave, and linear hydrostatic mountain wave. The results from those tests demonstrate that the horizontally spectral element vertically finite difference model is accurate and robust. By using the 2-D slice model, we effectively show that the combined spatial discretization method of the spectral element and finite difference method in the horizontal and vertical directions, respectively, offers a viable method for the development of a NH dynamical core.

  8. 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.

  9. 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.

  10. 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

  11. Quality assurance of solar spectral UV-measurements: methods and use of the SHICrivm software tool

    NASA Astrophysics Data System (ADS)

    Williams, J. E.; den Outer, P. N.; Slaper, H.

    2003-04-01

    Ground-based UV-irradiance measurements are crucial for determining the long-term changes and trends in biologically and/or photo-chemically relevant solar UV-radiation reaching the Earth's surface. Such changes in UV-radiation levels have probably occurred and/or are expected due to ozone depletion and climate change. In order to analyse UV-irradiation levels in relation to atmospheric parameters and to facilitate an assessment of the European UV-climate a European database (EUVDatabase) has been set up within the EDUCE-project (EC-contract EVK2-CT-1999-00028). High quality UV-data-sets from across the continent are assessable from the EUVDatabase (http://uv.fmi.fi/uvdb/). An accurate analysis of the UV-climate and long term changes therein requires quality assurance of the spectral data. The SHICrivm software tool (http://www.rivm.nl/shicrivm) is developed to analyse several quality aspects of measured UV-spectra. The SHICrivm tool is applied to over one million spectra from the EUVDatabase and detects for each measured spectrum: the accuracy of the wavelength calibration from 290 up to 500 nm, the lowest detectable irradiance level, the occurrence of non-natural spikes in spectra, deviations in spectral shape, and identifies possible irradiance scale errors in the UV-range. In addition the SHIC-package can be used to correct wavelength scale errors and non-natural spectral spikes. A deconvolution and convolution algorithm is included to improve the comparibility of spectra obtained with different instruments, and to allow a fully comparable analysis of biologically weighted UV-dose for instruments with various spectral characteristics. Within the context of the EDUCE-project data from over 20 UV-monitoring stations are retrieved from the database and a quality assessment is performed using the SHIC-tool. The quality parameters are presented by means of a simple scheme of coloured quality flags. Spectra that meet the WMO-criteria for spectral measurements are

  12. Method for optimizing output in ultrashort-pulse multipass laser amplifiers with selective use of a spectral filter

    DOEpatents

    Backus, Sterling J.; Kapteyn, Henry C.

    2007-07-10

    A method for optimizing multipass laser amplifier output utilizes a spectral filter in early passes but not in later passes. The pulses shift position slightly for each pass through the amplifier, and the filter is placed such that early passes intersect the filter while later passes bypass it. The filter position may be adjust offline in order to adjust the number of passes in each category. The filter may be optimized for use in a cryogenic amplifier.

  13. A pseudo-spectral method for a non-local KdV-Burgers equation posed on R

    NASA Astrophysics Data System (ADS)

    de la Hoz, Francisco; Cuesta, Carlota M.

    2016-04-01

    In this paper, we present a new pseudo-spectral method to solve the initial value problem associated to a non-local KdV-Burgers equation involving a Caputo-type fractional derivative. The basic idea is, using an algebraic map, to transform the whole real line into a bounded interval where we can apply a Fourier expansion. Special attention is given to the correct computation of the fractional derivative in this setting.

  14. Methods of spectral estimation in local nuclear quadrupole resonance with a dispersion

    NASA Astrophysics Data System (ADS)

    Grechishkin, V. S.; Grechishkina, R. V.; Persichkin, A. A.; Shpilevoi, A. A.

    2002-10-01

    The spectral estimation in local nuclear quadrupole resonance at a high noise level is performed for the first time using the modern techniques of linear prediction (LPSVD) and matrix pencil (ITMPM). The fast Fourier transform with signal accumulation does not ensure the required sensitivity in the case of weak signals when the object and the receiver of the spectrometer are spaced widely apart or when there is an effect of adverse factors (screening, interference, random disturbance, etc.), which is typical of remote monitoring in actual practice. It is demonstrated that the use of the proposed techniques considerably increases the efficiency of spectral estimation in this field of solid-state spectroscopy and, in particular, avoids the phase errors arising in usual experiments at a signal-to-noise ratio of less than 0.5.

  15. An investigation of the 'Overlap' between the Statistical-Discrete-Gust and the Power-Spectral-Density analysis methods

    NASA Technical Reports Server (NTRS)

    Perry, Boyd, III; Pototzky, Anthony S.; Woods, Jessica A.

    1989-01-01

    This paper presents the results of a NASA investigation of a claimed 'Overlap' between two gust response analysis methods: the Statistical Discrete Gust (SDG) method and the Power Spectral Density (PSD) method. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented in this paper for several different airplanes at several different flight conditions indicate that such an 'Overlap' does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

  16. An Investigation of the Overlap Between the Statistical Discrete Gust and the Power Spectral Density Analysis Methods

    NASA Technical Reports Server (NTRS)

    Perry, Boyd, III; Pototzky, Anthony S.; Woods, Jessica A.

    1989-01-01

    The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

  17. The optimized gradient method for full waveform inversion and its spectral implementation

    NASA Astrophysics Data System (ADS)

    Wu, Zedong; Alkhalifah, Tariq

    2016-06-01

    At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.

  18. A new method to retrieve spectral absorption coefficient of highly-scattering and weakly-absorbing materials

    NASA Astrophysics Data System (ADS)

    Dombrovsky, Leonid A.

    2016-03-01

    A significant uncertainty in the absorption coefficient of highly scattering dispersed materials is typical in the spectral ranges of very weak absorption. The traditional way to identify the main absorption and scattering characteristics of semi-transparent materials is based on spectral measurements of normal-hemispherical reflectance and transmittance for the material sample. Unfortunately this way cannot be used in the case of in vivo measurements of optical properties of biological tissues. A method suggested in the present paper is based on thermal response to the periodic radiative heating of the open surface of a semi-transparent material. It is shown that the period of a variation of the surface temperature is sensitive to the value of an average absorption coefficient in the surface layer. As a result, the monochromatic external irradiation combined with the surface temperature measurements can be used to retrieve the spectral values of absorption coefficient. Possible application of this method to porous semi-transparent ceramics is considered. An example problem is also solved to illustrate the applicability of this method to human skin. The approach suggested enables one to estimate an average absorption coefficient of human skin of a patient just before the thermal processing.

  19. NEW METHOD FOR REMOVAL OF SPECTRAL INTERFERENCES FOR BERYLLIUM ASSAY USING INDUCTIVELY COUPLED PLASMA ATOMIC EMISSION SPECTROMETRY

    SciTech Connect

    Maxwell, S; Matthew Nelson, M; Linda Youmans, L; Maureen Bernard, M

    2008-01-14

    Beryllium has been used widely in specific areas of nuclear technology. Frequent monitoring of air and possible contaminated surfaces in U.S Department of Energy (DOE) facilities is required to identify potential health risks and to protect DOE workers from beryllium-contaminated dust. A new method has been developed to rapidly remove spectral interferences prior to beryllium (Be) measurement by inductively-coupled plasma atomic emission spectrometry (ICP-AES). The ion exchange separation removes uranium (U), thorium (Th), niobium (Nb), vanadium (V), molybdenum (Mo), zirconium (Zr), tungsten (W), iron (Fe), chromium (Cr), cerium (Ce), erbium (Er) and titanium (Ti). A stacked column consisting of Diphonix Resin{reg_sign} and TEVA Resin{reg_sign} reduces the levels of the spectral interferences so that low level Be measurements can be performed accurately. If necessary, an additional anion exchange separation can be used for further removal of interferences, particularly chromium. The method has been tested using spiked filters, spiked wipe samples and certified reference material standards with high levels of interferences added. The method provides very efficient removal of spectral interferences with very good accuracy and precision for beryllium on filters or wipes. A vacuum box system is employed to reduce analytical time and reduce labor costs.

  20. Spectral simulation of thermocapillary convection with a deformable free surface using boundary-fitted coordinates

    NASA Astrophysics Data System (ADS)

    Ahmed, Ikramuddin

    A Chebyshev-spectral collocation scheme has been developed to simulate thermocapillary convection processes in a differentially heated cavity with and without buoyancy effects. The time-dependent Navier- Stokes equations in primitive variables were solved with a semi-implicit scheme using the influence matrix technique. The deformable free surface was incorporated by means of a boundary-fitted coordinate (BFC) system. The BFC grid was generated by solving a system of elliptic equations. An iterative scheme based on finite difference methods was found to be sufficient for calculating a smooth distribution of grid-points for relatively low degrees of deformation of the free surface. The metrics of transformation, however, were calculated spectrally in order to achieve a high order of accuracy in the a posteriori mapping of the physical grid to the computational grid. The overall scheme was found to be efficient, economical, and capable of resolving the complex hydrodynamic and thermal structures in thermocapillarity driven flows with deformable free surfaces. The scheme was also modified to study problems with very high Marangoni numbers and non-deformable free surfaces, and later extended to three dimensions with periodic boundary conditions in order to explore the transitions to fully three dimensional phenomena that are anticipated in industrially relevant flow configurations.