B-spline Collocation with Domain Decomposition Method

International Nuclear Information System (INIS)

Hidayat, M I P; Parman, S; Ariwahjoedi, B

2013-01-01

A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C 0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.

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

KAUST Repository

Wang, Zhiheng

2015-01-01

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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

International Nuclear Information System (INIS)

Lee, Yoon Hee; Cho, Nam Zin

2016-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-05-15

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

Meshfree Local Radial Basis Function Collocation Method with Image Nodes

Energy Technology Data Exchange (ETDEWEB)

Baek, Seung Ki; Kim, Minjae [Pukyong National University, Busan (Korea, Republic of)

2017-07-15

We numerically solve two-dimensional heat diffusion problems by using a simple variant of the meshfree local radial-basis function (RBF) collocation method. The main idea is to include an additional set of sample nodes outside the problem domain, similarly to the method of images in electrostatics, to perform collocation on the domain boundaries. We can thereby take into account the temperature profile as well as its gradients specified by boundary conditions at the same time, which holds true even for a node where two or more boundaries meet with different boundary conditions. We argue that the image method is computationally efficient when combined with the local RBF collocation method, whereas the addition of image nodes becomes very costly in case of the global collocation. We apply our modified method to a benchmark test of a boundary value problem, and find that this simple modification reduces the maximum error from the analytic solution significantly. The reduction is small for an initial value problem with simpler boundary conditions. We observe increased numerical instability, which has to be compensated for by a sufficient number of sample nodes and/or more careful parameter choices for time integration.

Cosmographic analysis with Chebyshev polynomials

Science.gov (United States)

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

2018-05-01

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

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

KAUST Repository

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

2015-01-01

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

Chebyshev super spectral viscosity method for a fluidized bed model

International Nuclear Information System (INIS)

Sarra, Scott A.

2003-01-01

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

Derivation of reduced model for control system design using Chebyshev techniques

International Nuclear Information System (INIS)

Bistritz, Y.

1978-07-01

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

Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

Directory of Open Access Journals (Sweden)

Lee Ken Yap

2015-01-01

Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.

Pseudospectral collocation methods for fourth order differential equations

Science.gov (United States)

Malek, Alaeddin; Phillips, Timothy N.

1994-01-01

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

A spectral element-FCT method for the compressible Euler equations

International Nuclear Information System (INIS)

Giannakouros, J.; Karniadakis, G.E.

1994-01-01

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

Spectral methods for time dependent partial differential equations

Science.gov (United States)

Gottlieb, D.; Turkel, E.

1983-01-01

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

Superiority of legendre polynomials to Chebyshev polynomial in ...

African Journals Online (AJOL)

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

A collocation finite element method with prior matrix condensation

International Nuclear Information System (INIS)

Sutcliffe, W.J.

1977-01-01

For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-15

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

and chebyshev functions

Directory of Open Access Journals (Sweden)

Mohsen Razzaghi

2000-01-01

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

Application of collocation meshless method to eigenvalue problem

International Nuclear Information System (INIS)

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

2012-01-01

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

A Line-Tau Collocation Method for Partial Differential Equations ...

African Journals Online (AJOL)

This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...

Sinc-collocation method for solving the Blasius equation

International Nuclear Information System (INIS)

Parand, K.; Dehghan, Mehdi; Pirkhedri, A.

2009-01-01

Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

KAUST Repository

Babuška, Ivo; Nobile, Fabio; Tempone, Raul

2010-01-01

This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.

Antireflection coatings with Chebyshev or Butterworth response - Design

Science.gov (United States)

Baumeister, Philip

1986-12-01

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

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

Science.gov (United States)

Temel, Burcin; Mills, Greg; Metiu, Horia

2008-03-27

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

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

National Research Council Canada - National Science Library

Mitchell, Jason

2002-01-01

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

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

International Nuclear Information System (INIS)

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

2014-01-01

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

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

Science.gov (United States)

Cvitaš, Marko T; Althorpe, Stuart C

2013-08-14

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

Crosstalk statistics via collocation method

NARCIS (Netherlands)

Diouf, F.; Canavero, Flavio

2009-01-01

A probabilistic model for the evaluation of transmission lines crosstalk is proposed. The geometrical parameters are assumed to be unknown and the exact solution is decomposed into two functions, one depending solely on the random parameters and the other on the frequency. The stochastic collocation

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

Science.gov (United States)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

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

Science.gov (United States)

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

2018-06-12

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

Improvement of neutron kinetics module in TRAC-BF1code: one-dimensional nodal collocation method

Energy Technology Data Exchange (ETDEWEB)

Jambrina, Ana; Barrachina, Teresa; Miro, Rafael; Verdu, Gumersindo, E-mail: ajambrina@iqn.upv.es, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Universidade Politecnica de Valencia (UPV), Valencia (Spain); Soler, Amparo, E-mail: asoler@iberdrola.es [SEA Propulsion S.L., Madrid (Spain); Concejal, Alberto, E-mail: acbe@iberdrola.es [Iberdrola Ingenieria y Construcion S.A.U., Madrid (Spain)

2013-07-01

The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method. (author)

Geostationary satellites collocation

CERN Document Server

Li, Hengnian

2014-01-01

Geostationary Satellites Collocation aims to find solutions for deploying a safe and reliable collocation control. Focusing on the orbital perturbation analysis, the mathematical foundations for orbit and control of the geostationary satellite are summarized. The mathematical and physical principle of orbital maneuver and collocation strategies for multi geostationary satellites sharing with the same dead band is also stressed. Moreover, the book presents some applications using the above algorithms and mathematical models to help readers master the corrective method for planning station keeping maneuvers. Engineers and scientists in the fields of aerospace technology and space science can benefit from this book. Hengnian Li is the Deputy Director of State Key Laboratory of Astronautic Dynamics, China.

Numerical simulation of GEW equation using RBF collocation method

Directory of Open Access Journals (Sweden)

Hamid Panahipour

2012-08-01

Full Text Available The generalized equal width (GEW equation is solved numerically by a meshless method based on a global collocation with standard types of radial basis functions (RBFs. Test problems including propagation of single solitons, interaction of two and three solitons, development of the Maxwellian initial condition pulses, wave undulation and wave generation are used to indicate the efficiency and accuracy of the method. Comparisons are made between the results of the proposed method and some other published numerical methods.

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

Directory of Open Access Journals (Sweden)

M. Tavassoli Kajani

2012-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

An adaptive multi-element probabilistic collocation method for statistical EMC/EMI characterization

KAUST Repository

Yücel, Abdulkadir C.

2013-12-01

An adaptive multi-element probabilistic collocation (ME-PC) method for quantifying uncertainties in electromagnetic compatibility and interference phenomena involving electrically large, multi-scale, and complex platforms is presented. The method permits the efficient and accurate statistical characterization of observables (i.e., quantities of interest such as coupled voltages) that potentially vary rapidly and/or are discontinuous in the random variables (i.e., parameters that characterize uncertainty in a system\\'s geometry, configuration, or excitation). The method achieves its efficiency and accuracy by recursively and adaptively dividing the domain of the random variables into subdomains using as a guide the decay rate of relative error in a polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation/integration points determined by the adaptive ME-PC scheme. The adaptive ME-PC scheme requires far fewer (computationally costly) deterministic simulations than traditional polynomial chaos collocation and Monte Carlo methods for computing averages, standard deviations, and probability density functions of rapidly varying observables. The efficiency and accuracy of the method are demonstrated via its applications to the statistical characterization of voltages in shielded/unshielded microwave amplifiers and magnetic fields induced on car tire pressure sensors. © 2013 IEEE.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-03-28

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Multi-Index Stochastic Collocation for random PDEs

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations

Energy Technology Data Exchange (ETDEWEB)

Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)

1996-12-31

In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).

The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications

International Nuclear Information System (INIS)

Foo, Jasmine; Wan Xiaoliang; Karniadakis, George Em

2008-01-01

Stochastic spectral methods are numerical techniques for approximating solutions to partial differential equations with random parameters. In this work, we present and examine the multi-element probabilistic collocation method (ME-PCM), which is a generalized form of the probabilistic collocation method. In the ME-PCM, the parametric space is discretized and a collocation/cubature grid is prescribed on each element. Both full and sparse tensor product grids based on Gauss and Clenshaw-Curtis quadrature rules are considered. We prove analytically and observe in numerical tests that as the parameter space mesh is refined, the convergence rate of the solution depends on the quadrature rule of each element only through its degree of exactness. In addition, the L 2 error of the tensor product interpolant is examined and an adaptivity algorithm is provided. Numerical examples demonstrating adaptive ME-PCM are shown, including low-regularity problems and long-time integration. We test the ME-PCM on two-dimensional Navier-Stokes examples and a stochastic diffusion problem with various random input distributions and up to 50 dimensions. While the convergence rate of ME-PCM deteriorates in 50 dimensions, the error in the mean and variance is two orders of magnitude lower than the error obtained with the Monte Carlo method using only a small number of samples (e.g., 100). The computational cost of ME-PCM is found to be favorable when compared to the cost of other methods including stochastic Galerkin, Monte Carlo and quasi-random sequence methods

Collocations and collocation types in ESP textbooks: Quantitative pedagogical analysis

Directory of Open Access Journals (Sweden)

Bogdanović Vesna Ž.

2016-01-01

Full Text Available The term collocation, even though it is rather common in the English language grammar, it is not a well known or commonly used term in the textbooks and scientific papers written in the Serbian language. Collocating is usually defined as a natural appearance of two (or more words, which are usually one next to another even though they can be separated in the text, while collocations are defined as words with natural semantic and/or syntactic relations being joined together in a sentence. Collocations are naturally used in all English written texts, including scientific texts and papers. Using two textbooks for English for Specific Purposes (ESP for intermediate students' courses, this paper presents the frequency of collocations and their typology. The paper tries to investigate the relationship between lexical and grammatical collocations written in the ESP texts and the reasons for their presence. There is an overview of the most used subtypes of lexical collocations as well. Furthermore, on applying the basic corpus analysis based on the quantitative analysis, the paper presents the number of open, restricted and bound collocations in ESP texts, trying to draw conclusions on their frequency and hence the modes for their learning. There is also a section related to the number and usage of scientific collocations, both common scientific and narrow-professional ones. The conclusion is that the number of present collocations in the selected two textbooks imposes a demand for further analysis of these lexical connections, as well as new modes for their teaching and presentations to the English learning students.

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

International Nuclear Information System (INIS)

Benasser Algehawi, Mohammed; Samsudin, Azman

2010-01-01

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

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

Science.gov (United States)

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

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

Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

OpenAIRE

Choe, Hui-Chol; Kang, Yong-Suk

2013-01-01

We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

Directory of Open Access Journals (Sweden)

S.H. Nasseri

2011-07-01

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

CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

Directory of Open Access Journals (Sweden)

S.H. Nasseri

2009-10-01

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

A stochastic collocation method for the second order wave equation with a discontinuous random speed

KAUST Repository

Motamed, Mohammad

2012-08-31

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.

A Study on the Phenomenon of Collocations: Methodology of Teaching English and German Collocations to Russian Students

Science.gov (United States)

Varlamova, Elena V.; Naciscione, Anita; Tulusina, Elena A.

2016-01-01

Relevance of the issue stated in the article is determined by the fact that there is a lack of research devoted to the methods of teaching English and German collocations. The aim of our work is to determine methods of teaching English and German collocations to Russian university students studying foreign languages through experimental testing.…

A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains

Directory of Open Access Journals (Sweden)

Zhao-Qing Wang

2014-01-01

Full Text Available Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method.

Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

KAUST Repository

Bä ck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2010-01-01

Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods

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

Science.gov (United States)

Deprit, A.

1975-01-01

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

Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Multi-Index Stochastic Collocation (MISC) for random elliptic PDEs

KAUST Repository

Haji Ali, Abdul Lateef

2016-01-06

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. We propose an optimization procedure to select the most effective mixed differences to include in the MISC estimator: such optimization is a crucial step and allows us to build a method that, provided with sufficient solution regularity, is potentially more effective than other multi-level collocation methods already available in literature. We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one dimensional problem. We show the effectiveness of MISC with some computational tests, comparing it with other related methods available in the literature, such as the Multi-Index and Multilevel Monte Carlo, Multilevel Stochastic Collocation, Quasi Optimal Stochastic Collocation and Sparse Composite Collocation methods.

Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

Directory of Open Access Journals (Sweden)

Qinghai Zhao

2015-01-01

Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.

Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials

Directory of Open Access Journals (Sweden)

Tingting Wang

2015-01-01

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

Rectangular spectral collocation

KAUST Repository

Driscoll, Tobin A.; Hale, Nicholas

2015-01-01

Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon

On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

Directory of Open Access Journals (Sweden)

Paul Barry

2013-01-01

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

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

Science.gov (United States)

Khan, Sami Ullah; Ali, Ishtiaq

2018-03-01

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

Collocations in Marine Engineering English

Directory of Open Access Journals (Sweden)

Mirjana Borucinsky

2016-05-01

Full Text Available Collocations are very frequent in the English language (Hill, 2000, and they are probably the most common and most representative of English multi-word expressions (Lewis, 2000. Furthermore, as a subset of formulaic sequences, collocations are considered to be a central aspect of communicative competence (Nation, 2001. Hence, the importance of teaching collocations in General English (GE as well as in English for Specific Purposes (ESP is undeniable. Understanding and determining the relevant collocations and their mastery are of “utmost importance to a ME instructor” (Cole et al., 2007, p. 137, and collocations are one of the most productive ways of enriching vocabulary and terminology in modern ME. Vişan & Georgescu (2011 have undertaken a relevant study on  collocations and “collocational competence” on board ships, including mostly nautical terminology. However, no substantial work on collocations in Marine Engineering English as a sub-register of ME has been carried out. Hence, this paper tries to determine the most important collocations in Marine Engineering English, based on a small corpus of collected e-mails. After determining the most relevant collocations, we suggest how to implement these in the language classroom and how to improve the collocational competence of marine engineering students.

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

KAUST Repository

Hale, Nicholas

2014-02-06

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

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

Directory of Open Access Journals (Sweden)

Fakhrodin Mohammadi

2017-10-01

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

Mobile Collocated Interactions

DEFF Research Database (Denmark)

Lucero, Andrés; Clawson, James; Lyons, Kent

2015-01-01

Mobile devices such as smartphones and tablets were originally conceived and have traditionally been utilized for individual use. Research on mobile collocated interactions has been looking at situations in which collocated users engage in collaborative activities using their mobile devices, thus...... going from personal/individual toward shared/multiuser experiences and interactions. However, computers are getting smaller, more powerful, and closer to our bodies. Therefore, mobile collocated interactions research, which originally looked at smartphones and tablets, will inevitably include ever......-smaller computers, ones that can be worn on our wrists or other parts of the body. The focus of this workshop is to bring together a community of researchers, designers and practitioners to explore the potential of extending mobile collocated interactions to the use of wearable devices....

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

Directory of Open Access Journals (Sweden)

A. Karimi Dizicheh

2013-01-01

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

A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

Directory of Open Access Journals (Sweden)

Ali H. Bhrawy

2014-01-01

Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.

The Application of the Probabilistic Collocation Method to a Transonic Axial Flow Compressor

NARCIS (Netherlands)

Loeven, G.J.A.; Bijl, H.

2010-01-01

In this paper the Probabilistic Collocation method is used for uncertainty quantification of operational uncertainties in a transonic axial flow compressor (i.e. NASA Rotor 37). Compressor rotors are components of a gas turbine that are highly sensitive to operational and geometrical uncertainties.

Collocation Impact on Team Effectiveness

Directory of Open Access Journals (Sweden)

M Eccles

2010-11-01

Full Text Available The collocation of software development teams is common, specially in agile software development environments. However little is known about the impact of collocation on the team’s effectiveness. This paper explores the impact of collocating agile software development teams on a number of team effectiveness factors. The study focused on South African software development teams and gathered data through the use of questionnaires and interviews. The key finding was that collocation has a positive impact on a number of team effectiveness factors which can be categorised under team composition, team support, team management and structure and team communication. Some of the negative impact collocation had on team effectiveness relate to the fact that team members perceived that less emphasis was placed on roles, that morale of the group was influenced by individuals, and that collocation was invasive, reduced level of privacy and increased frequency of interruptions. Overall through it is proposed that companies should consider collocating their agile software development teams, as collocation might leverage overall team effectiveness.

Proxemic Mobile Collocated Interactions

DEFF Research Database (Denmark)

Porcheron, Martin; Lucero, Andrés; Quigley, Aaron

2016-01-01

and their digital devices (i.e. the proxemic relationships). Building on the ideas of proxemic interactions, this workshop is motivated by the concept of ‘proxemic mobile collocated interactions’, to harness new or existing technologies to create engaging and interactionally relevant experiences. Such approaches......Recent research on mobile collocated interactions has been looking at situations in which collocated users engage in collaborative activities using their mobile devices. However, existing practices fail to fully account for the culturally-dependent spatial relationships between people...... in exploring proxemics and mobile collocated interactions....

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

International Nuclear Information System (INIS)

Lee, Wei-Ming

2012-01-01

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.

A Survey of Symplectic and Collocation Integration Methods for Orbit Propagation

Science.gov (United States)

Jones, Brandon A.; Anderson, Rodney L.

2012-01-01

Demands on numerical integration algorithms for astrodynamics applications continue to increase. Common methods, like explicit Runge-Kutta, meet the orbit propagation needs of most scenarios, but more specialized scenarios require new techniques to meet both computational efficiency and accuracy needs. This paper provides an extensive survey on the application of symplectic and collocation methods to astrodynamics. Both of these methods benefit from relatively recent theoretical developments, which improve their applicability to artificial satellite orbit propagation. This paper also details their implementation, with several tests demonstrating their advantages and disadvantages.

A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra

International Nuclear Information System (INIS)

Avila, Gustavo; Carrington, Tucker

2015-01-01

In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates

Analysis of an upstream weighted collocation approximation to the transport equation

International Nuclear Information System (INIS)

Shapiro, A.; Pinder, G.F.

1981-01-01

The numerical behavior of a modified orthogonal collocation method, as applied to the transport equations, can be examined through the use of a Fourier series analysis. The necessity of such a study becomes apparent in the analysis of several techniques which emulate classical upstream weighting schemes. These techniques are employed in orthogonal collocation and other numerical methods as a means of handling parabolic partial differential equations with significant first-order terms. Divergent behavior can be shown to exist in one upstream weighting method applied to orthogonal collocation

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

International Nuclear Information System (INIS)

Javaloyes, J.; Balle, S.

2015-01-01

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

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

Science.gov (United States)

Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

2018-03-01

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

The Effect of Input Enhancement of Collocations in Reading on Collocation Learning and Retention of EFL Learners

Science.gov (United States)

Goudarzi, Zahra; Moini, M. Raouf

2012-01-01

Collocation is one of the most problematic areas in second language learning and it seems that if one wants to improve his or her communication in another language should improve his or her collocation competence. This study attempts to determine the effect of applying three different kinds of collocation on collocation learning and retention of…

Full-Wave Analysis of the Shielding Effectiveness of Thin Graphene Sheets with the 3D Unidirectionally Collocated HIE-FDTD Method

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Arne Van Londersele

2017-01-01

Full Text Available Graphene-based electrical components are inherently multiscale, which poses a real challenge for finite-difference time-domain (FDTD solvers due to the stringent time step upper bound. Here, a unidirectionally collocated hybrid implicit-explicit (UCHIE FDTD method is put forward that exploits the planar structure of graphene to increase the time step by implicitizing the critical dimension. The method replaces the traditional Yee discretization by a partially collocated scheme that allows a more accurate numerical description of the material boundaries. Moreover, the UCHIE-FDTD method preserves second-order accuracy even for nonuniform discretization in the direction of collocation. The auxiliary differential equation (ADE approach is used to implement the graphene sheet as a dispersive Drude medium. The finite grid is terminated by a uniaxial perfectly matched layer (UPML to permit open-space simulations. Special care is taken to elaborate on the efficient implementation of the implicit update equations. The UCHIE-FDTD method is validated by computing the shielding effectiveness of a typical graphene sheet.

Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

International Nuclear Information System (INIS)

Patra, A.; Saha Ray, S.

2014-01-01

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution

A stochastic collocation method for the second order wave equation with a discontinuous random speed

KAUST Repository

Motamed, Mohammad; Nobile, Fabio; Tempone, Raul

2012-01-01

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical

Multi-element probabilistic collocation method in high dimensions

International Nuclear Information System (INIS)

Foo, Jasmine; Karniadakis, George Em

2010-01-01

We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order μ and the effective dimension ν, with ν<< N, and N the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that ν≥μ for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.

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

Science.gov (United States)

Kaporin, I. E.

2012-02-01

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

Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

KAUST Repository

Ait-Haddou, Rachid

2013-08-01

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

Chebyshev blossoming in Müntz spaces: Toward shaping with Young diagrams

KAUST Repository

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

2013-01-01

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

Pseudo-random bit generator based on Chebyshev map

Science.gov (United States)

Stoyanov, B. P.

2013-10-01

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

An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis

KAUST Repository

Yücel, Abdulkadir C.

2010-07-01

The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a system\\'s excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.). To bound the probability of system malfunction, fast and accurate techniques to quantify the uncertainty in system observables (e.g., voltages across mission-critical circuit elements) are called for. Recently proposed stochastic frameworks [1-2] combine deterministic electromagnetic (EM) simulators with stochastic collocation (SC) methods that approximate system observables using generalized polynomial chaos expansion (gPC) [3] (viz. orthogonal polynomials spanning the entire random domain) to estimate their statistical moments and probability density functions (pdfs). When constructing gPC expansions, the EM simulator is used solely to evaluate system observables at collocation points prescribed by the SC-gPC scheme. The frameworks in [1-2] therefore are non-intrusive and straightforward to implement. That said, they become inefficient and inaccurate for system observables that vary rapidly or are discontinuous in the random variables (as their representations may require very high-order polynomials). © 2010 IEEE.

Application of a modified collocation method to the one dimensional, one group neutron transport equation

International Nuclear Information System (INIS)

Maschek, W.

1976-07-01

A modified collocation method is used for solving the one group criticality problem for a uniform multiplying slab. The critical parameters and the angular fluxes for a number of slabs are displayed and compared with previously published values. (orig.) [de

Bessel collocation approach for approximate solutions of Hantavirus infection model

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Suayip Yuzbasi

2017-11-01

Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

A fast collocation method for a variable-coefficient nonlocal diffusion model

Science.gov (United States)

Wang, Che; Wang, Hong

2017-02-01

We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N3) required by a commonly used direct solver to O (Nlog ⁡ N) per iteration and the memory requirement from O (N2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N2) to O (N). Numerical results are presented to show the utility of the fast method.

An empirical understanding of triple collocation evaluation measure

Science.gov (United States)

Scipal, Klaus; Doubkova, Marcela; Hegyova, Alena; Dorigo, Wouter; Wagner, Wolfgang

2013-04-01

Triple collocation method is an advanced evaluation method that has been used in the soil moisture field for only about half a decade. The method requires three datasets with an independent error structure that represent an identical phenomenon. The main advantages of the method are that it a) doesn't require a reference dataset that has to be considered to represent the truth, b) limits the effect of random and systematic errors of other two datasets, and c) simultaneously assesses the error of three datasets. The objective of this presentation is to assess the triple collocation error (Tc) of the ASAR Global Mode Surface Soil Moisture (GM SSM 1) km dataset and highlight problems of the method related to its ability to cancel the effect of error of ancillary datasets. In particular, the goal is to a) investigate trends in Tc related to the change in spatial resolution from 5 to 25 km, b) to investigate trends in Tc related to the choice of a hydrological model, and c) to study the relationship between Tc and other absolute evaluation methods (namely RMSE and Error Propagation EP). The triple collocation method is implemented using ASAR GM, AMSR-E, and a model (either AWRA-L, GLDAS-NOAH, or ERA-Interim). First, the significance of the relationship between the three soil moisture datasets was tested that is a prerequisite for the triple collocation method. Second, the trends in Tc related to the choice of the third reference dataset and scale were assessed. For this purpose the triple collocation is repeated replacing AWRA-L with two different globally available model reanalysis dataset operating at different spatial resolution (ERA-Interim and GLDAS-NOAH). Finally, the retrieved results were compared to the results of the RMSE and EP evaluation measures. Our results demonstrate that the Tc method does not eliminate the random and time-variant systematic errors of the second and the third dataset used in the Tc. The possible reasons include the fact a) that the TC

Quality Parameters Defined by Chebyshev Polynomials in Cold Rolling Process Chain

International Nuclear Information System (INIS)

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

2011-01-01

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

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

Science.gov (United States)

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

1998-01-01

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

Verb-Noun Collocation Proficiency and Academic Years

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Fatemeh Ebrahimi-Bazzaz

2014-01-01

Full Text Available Generally vocabulary and collocations in particular have significant roles in language proficiency. A collocation includes two words that are frequently joined concurrently in the memory of native speakers. There have been many linguistic studies trying to define, to describe, and to categorise English collocations. It contains grammatical collocations and lexical collocations which include nouns, adjectives, verbs, and adverb. In the context of a foreign language environment such as Iran, collocational proficiency can be useful because it helps the students improve their language proficiency. This paper investigates the possible relationship between verb-noun collocation proficiency among students from one academic year to the next. To reach this goal, a test of verb-noun collocations was administered to Iranian learners. The participants in the study were 212 Iranian students in an Iranian university. They were selected from the second term of freshman, sophomore, junior, and senior years. The students’ age ranged from 18 to 35.The results of ANOVA showed there was variability in the verb-noun collocations proficiency within each academic year and between the four academic years. The results of a post hoc multiple comparison tests demonstrated that the means are significantly different between the first year and the third and fourth years, and between the third and the fourth academic year; however, students require at least two years to show significant development in verb-noun collocation proficiency. These findings provided a vital implication that lexical collocations are learnt and developed through four academic years of university, but requires at least two years showing significant development in the language proficiency.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

Science.gov (United States)

Liu, L. H.; Tan, J. Y.

2007-02-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

International Nuclear Information System (INIS)

Liu, L.H.; Tan, J.Y.

2007-01-01

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media

Measuring receptive collocational competence across proficiency levels

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Déogratias Nizonkiza

2015-12-01

Full Text Available The present study investigates, (i English as Foreign Language (EFL learners’ receptive collocational knowledge growth in relation to their linguistic proficiency level; (ii how much receptive collocational knowledge is acquired as proficiency develops; and (iii the extent to which receptive knowledge of collocations of EFL learners varies across word frequency bands. A proficiency measure and a collocation test were administered to English majors at the University of Burundi. Results of the study suggest that receptive collocational competence develops alongside EFL learners’ linguistic proficiency; which lends empirical support to Gyllstad (2007, 2009 and Author (2011 among others, who reported similar findings. Furthermore, EFL learners’ collocations growth seems to be quantifiable wherein both linguistic proficiency level and word frequency occupy a crucial role. While more gains in terms of collocations that EFL learners could potentially add as a result of change in proficiency are found at lower levels of proficiency; collocations of words from more frequent word bands seem to be mastered first, and more gains are found at more frequent word bands. These results confirm earlier findings on the non-linearity nature of vocabulary growth (cf. Meara 1996 and the fundamental role played by frequency in word knowledge for vocabulary in general (Nation 1983, 1990, Nation and Beglar 2007, which are extended here to collocations knowledge.

A nonclassical Radau collocation method for solving the Lane-Emden equations of the polytropic index 4.75 ≤ α < 5

Science.gov (United States)

Tirani, M. D.; Maleki, M.; Kajani, M. T.

2014-11-01

A numerical method for solving the Lane-Emden equations of the polytropic index α when 4.75 ≤ α ≤ 5 is introduced. The method is based upon nonclassical Gauss-Radau collocation points and Freud type weights. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced and are utilized in the interval [0,1]. A smooth, strictly monotonic transformation is used to map the infinite domain x ∈ [0,∞) onto a half-open interval t ∈ [0,1). The resulting problem on the finite interval is then transcribed to a system of nonlinear algebraic equations using collocation. The method is easy to implement and yields very accurate results.

Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

Science.gov (United States)

Parand, Kourosh; Latifi, Sobhan; Delkhosh, Mehdi; Moayeri, Mohammad M.

2018-01-01

In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [0, ∞). Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y'(0), is obtained as -1.191790649719421734122828603800159364 for η = 0.5. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

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

International Nuclear Information System (INIS)

Jiménez-Teja, Y.; Benítez, N.

2012-01-01

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

Transport survey calculations using the spectral collocation method

International Nuclear Information System (INIS)

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

1989-01-01

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

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

Science.gov (United States)

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

2016-06-01

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

Classical solutions of two dimensional Stokes problems on non smooth domains. 2: Collocation method for the Radon equation

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-05-01

The non uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities. (author). 34 refs

Mobile Collocated Interactions With Wearables

DEFF Research Database (Denmark)

Lucero, Andrés; Wilde, Danielle; Robinson, Simon

2015-01-01

Research on mobile collocated interactions has been looking at situations in which collocated users engage in collaborative activities using their mobile devices, thus going from personal/individual toward shared/multiuser experiences and interactions. However, computers are getting smaller, more...

Fibonacci collocation method with a residual error Function to solve linear Volterra integro differential equations

Directory of Open Access Journals (Sweden)

Salih Yalcinbas

2016-01-01

Full Text Available In this paper, a new collocation method based on the Fibonacci polynomials is introduced to solve the high-order linear Volterra integro-differential equations under the conditions. Numerical examples are included to demonstrate the applicability and validity of the proposed method and comparisons are made with the existing results. In addition, an error estimation based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation.

Presenting collocates in a dictionary of computing and the Internet according to user needs

DEFF Research Database (Denmark)

Leroyer, Patrick; L'Homme, Marie-Claude; Jousse, Anne-Laure

2011-01-01

This paper presents a novel method for organizing and presenting collocations in a specialized dictionary of computing and the Internet. This work is undertaken in order to meet a specific user need, i.e. that of searching for a collocate (or a short list of collocates) that expresses a specific...

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

Czech Academy of Sciences Publication Activity Database

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

2010-01-01

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

The Effects of Input Flood and Consciousness-Raising Approach on Collocation Knowledge Development of Language Learners

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Elaheh Hamed Mahvelati

2012-11-01

Full Text Available Many researchers stress the importance of lexical coherence and emphasize the need for teaching collocations at all levels of language proficiency. Thus, this study was conducted to measure the relative effectiveness of explicit (consciousness-raising approach versus implicit (input flood collocation instruction with regard to learners’ knowledge of both lexical and grammatical collocations. Ninety-five upper-intermediate learners, who were randomly assigned to the control and experimental groups, served as the participants of this study. While one of the experimental groups was provided with input flood treatment, the other group received explicit collocation instruction. In contrast, the participants in the control group did not receive any instruction on learning collocations. The results of the study, which were collected through pre-test, immediate post-test and delayed post-test, revealed that although both methods of teaching collocations proved effective, the explicit method of consciousness-raising approach was significantly superior to the implicit method of input flood treatment.

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

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Winfried Auzinger

2006-01-01

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

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

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Chih-Hong Lin

2016-06-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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

Directory of Open Access Journals (Sweden)

Yu-Bo Jiao

2015-01-01

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

Slovene-English Contrastive Phraseology: Lexical Collocations

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Primož Jurko

2010-05-01

Full Text Available Phraseology is seen as one of the key elements and arguably the most productive part of any language. %e paper is focused on collocations and separates them from other phraseological units, such as idioms or compounds. Highlighting the difference between a monolingual and a bilingual (i.e. contrastive approach to collocation, the article presents two distinct classes of collocations: grammatical and lexical. %e latter, treated contrastively, represent the focal point of the paper, since they are an unending source of translation errors to both students of translation and professional translators. %e author introduces a methodology of systematic classification of lexical collocations applied on the Slovene-English language pair and based on structural (lexical congruence and semantic (translational predictability criteria.

Evaluating a new test of whole English collocations

DEFF Research Database (Denmark)

Revier, Robert Lee

2009-01-01

in their own right and, as such, feature formal, semantic, and usage properties similar to those borne by single words. Third, the semantic properties of the constituent words that combine to form collocations are likely to play a role in EFL learners' ability to 'produce' English collocations. Forth, testing...... of L2 collocation knowledge needs to focus on the recognition and production of whole collocations. It is this set of assumptions that the new collocation test presented in this chapter is desined to probe. More specifically, the test is designed to assess L2 learners' productive knowledge of whole...

Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

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Salih Yalcinbas

2016-01-01

Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

Rectangular spectral collocation

KAUST Repository

Driscoll, Tobin A.

2015-02-06

Boundary conditions in spectral collocation methods are typically imposed by removing some rows of the discretized differential operator and replacing them with others that enforce the required conditions at the boundary. A new approach based upon resampling differentiated polynomials into a lower-degree subspace makes differentiation matrices, and operators built from them, rectangular without any row deletions. Then, boundary and interface conditions can be adjoined to yield a square system. The resulting method is both flexible and robust, and avoids ambiguities that arise when applying the classical row deletion method outside of two-point scalar boundary-value problems. The new method is the basis for ordinary differential equation solutions in Chebfun software, and is demonstrated for a variety of boundary-value, eigenvalue and time-dependent problems.

The Presentation and Treatment of Collocations as Secondary ...

African Journals Online (AJOL)

Although the discussion primarily focuses on printed dictionaries proposals are also made for the presentation of collocations in online dictionaries. Keywords: Article structure, collocation, complex collocation, cotext, example sentences, integrated microstructure, non-grouped ordering, search zone, semi-integrated ...

Testing controlled productive knowledge of adverb-verb collocations ...

African Journals Online (AJOL)

A controlled productive test of adverb-verb collocations ..... The third approach to studying collocations, corpus analysis, ..... The collocation web model is thought to match Nation's (2001) psychological .... Theory, analysis, and applications. .... Canadian Modern ... Focus on vocabulary: Mastering the Academic Word List.

Semantic Analysis of Verbal Collocations with Lexical Functions

CERN Document Server

Gelbukh, Alexander

2013-01-01

This book is written for both linguists and computer scientists working in the field of artificial intelligence as well as to anyone interested in intelligent text processing. Lexical function is a concept that formalizes semantic and syntactic relations between lexical units. Collocational relation is a type of institutionalized lexical relations which holds between the base and its partner in a collocation. Knowledge of collocation is important for natural language processing because collocation comprises the restrictions on how words can be used together. The book shows how collocations can be annotated with lexical functions in a computer readable dictionary - allowing their precise semantic analysis in texts and their effective use in natural language applications including parsers, high quality machine translation, periphrasis system and computer-aided learning of lexica. The books shows how to extract collocations from corpora and annotate them with lexical functions automatically. To train algorithms,...

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Science.gov (United States)

Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.

2013-01-01

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Productive knowledge of collocations may predict academic literacy

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Van Dyk, Tobie

2016-12-01

Full Text Available The present study examines the relationship between productive knowledge of collocations and academic literacy among first year students at North-West University. Participants were administered a collocation test, the items of which were selected from Nation’s (2006 word frequency bands, i.e. the 2000-word, 3000-word, 5000-word bands; and the Academic Word List (Coxhead, 2000. The scores from the collocation test were compared to those from the Test of Academic Literacy Levels (version administered in 2012. The results of this study indicate that, overall, knowledge of collocations is significantly correlated with academic literacy, which is also observed at each of the frequency bands from which the items were selected. These results support Nizonkiza’s (2014 findings that a significant correlation between mastery of collocations of words from the Academic Word List and academic literacy exists; which is extended here to words from other frequency bands. They also confirm previous findings that productive knowledge of collocations increases alongside overall proficiency (cf. Gitsaki, 1999; Bonk, 2001; Eyckmans et al., 2004; Boers et al., 2006; Nizonkiza, 2011; among others. This study therefore concludes that growth in productive knowledge of collocations may entail growth in academic literacy; suggesting that productive use of collocations is linked to academic literacy to a considerable extent. In light of these findings, teaching strategies aimed to assist first year students meet academic demands posed by higher education and avenues to explore for further research are discussed. Especially, we suggest adopting a productive oriented approach to teaching collocations, which we believe may prove useful.

Testing controlled productive knowledge of adverb-verb collocations ...

African Journals Online (AJOL)

The study also reveals that controlled productive knowledge of adverbverb collocations is less problematic. Based on these results, teaching strategies aimed at improving the use of adverb-verb collocations among EFL users are proposed. Keywords: academic writing, adverb-verb collocations, productive knowledge of ...

Lexical and Grammatical Collocations in Writing Production of EFL Learners

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Maryam Bahardoust

2012-05-01

Full Text Available Lewis (1993 recognized significance of word combinations including collocations by presenting lexical approach. Because of the crucial role of collocation in vocabulary acquisition, this research set out to evaluate the rate of collocations in Iranian EFL learners' writing production across L1 and L2. In addition, L1 interference with L2 collocational use in the learner' writing samples was studied. To achieve this goal, 200 Persian EFL learners at BA level were selected. These participants were taking paragraph writing and essay writing courses in two successive semesters. As for the data analysis, mid-term, final exam, and also the assignments of L2 learners were evaluated. Because of the nominal nature of the data, chi-square test was utilized for data analysis. Then, the rate of lexical and grammatical collocations was calculated. Results showed that the lexical collocations outnumbered the grammatical collocations. Different categories of lexical collocations were also compared with regard to their frequencies in EFL writing production. The rate of the verb-noun and adjective-noun collocations appeared to be the highest and noun-verb collocations the lowest. The results also showed that L1 had both positive and negative effect on the occurrence of both grammatical and lexical collocations.

An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Webster, Clayton G [ORNL; Zhang, Guannan [ORNL; Gunzburger, Max D [ORNL

2012-10-01

Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.

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

International Nuclear Information System (INIS)

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

1990-01-01

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

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

KAUST Repository

Ait-Haddou, Rachid

2016-10-19

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

The relationship between productive knowledge of collocations and ...

African Journals Online (AJOL)

This research explores tertiary level L2 students' mastery of the collocations pertaining to the Academic Word List (AWL) and the extent to which their knowledge of collocations grows alongside their academic literacy. A collocation test modelled on Laufer and Nation (1999), with target words selected from Coxhead's (2000) ...

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

The present study investigates (i) English as Foreign Language (EFL) learners' receptive collocational knowledge growth in relation to their linguistic proficiency level; (ii) how much receptive collocational knowledge is acquired as linguistic proficiency develops; and (iii) the extent to which receptive knowledge of ...

An adaptive multi-element probabilistic collocation method for statistical EMC/EMI characterization

KAUST Repository

Yü cel, Abdulkadir C.; Bagci, Hakan; Michielssen, Eric

2013-01-01

polynomial chaos expansion of the observables. While constructing local polynomial expansions on each subdomain, a fast integral-equation-based deterministic field-cable-circuit simulator is used to compute the observable values at the collocation

High-frequency collocations of nouns in research articles across eight disciplines

Directory of Open Access Journals (Sweden)

Matthew Peacock

2012-04-01

Full Text Available This paper describes a corpus-based analysis of the distribution of the high-frequency collocates of abstract nouns in 320 research articles across eight disciplines: Chemistry, Computer Science, Materials Science, Neuroscience, Economics, Language and Linguistics, Management, and Psychology. Disciplinary variation was also examined – very little previous research seems to have investigated this. The corpus was analysed using WordSmith Tools. The 16 highest-frequency nouns across all eight disciplines were identified, followed by the highest-frequency collocates for each noun. Five disciplines showed over 50% variance from the overall results. Conclusions are that the differing patterns revealed are disciplinary norms and represent standard terminology within the disciplines arising from the topics discussed, research methods, and content of discussions. It is also concluded that the collocations are an important part of the meanings and functions of the nouns, and that this evidence of sharp discipline differences underlines the importance of discipline-specific collocation research.

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

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

1994-01-01

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

Teaching collocations

DEFF Research Database (Denmark)

Revier, Robert Lee; Henriksen, Birgit

2006-01-01

Very little pedadagoy has been made available to teachers interested in teaching collocations in foreign and/or second language classroom. This paper aims to contribute to and promote efforts in developing L2-based pedagogy for the teaching of phraseology. To this end, it presents pedagogical...

Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors

Czech Academy of Sciences Publication Activity Database

Musil, Tomáš; Jakl, Ondřej

2007-01-01

Roč. 1, č. 2 (2007), s. 555-564 ISSN 1802-680X. [Výpočtová mechanika 2007. Hrad Nečtiny, 05.11.2007-07.11.2007] Institutional research plan: CEZ:AV0Z20760514; CEZ:AV0Z30860518 Keywords : rotor system * trigonometric collocation * parallel computation Subject RIV: JR - Other Machinery

On Collocations and Their Interaction with Parsing and Translation

Directory of Open Access Journals (Sweden)

Violeta Seretan

2013-10-01

Full Text Available We address the problem of automatically processing collocations—a subclass of multi-word expressions characterized by a high degree of morphosyntactic flexibility—in the context of two major applications, namely, syntactic parsing and machine translation. We show that parsing and collocation identification are processes that are interrelated and that benefit from each other, inasmuch as syntactic information is crucial for acquiring collocations from corpora and, vice versa, collocational information can be used to improve parsing performance. Similarly, we focus on the interrelation between collocations and machine translation, highlighting the use of translation information for multilingual collocation identification, as well as the use of collocational knowledge for improving translation. We give a panorama of the existing relevant work, and we parallel the literature surveys with our own experiments involving a symbolic parser and a rule-based translation system. The results show a significant improvement over approaches in which the corresponding tasks are decoupled.

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

Directory of Open Access Journals (Sweden)

Imtiaz Wasim

2018-01-01

Full Text Available In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

Science.gov (United States)

Freund, Roland

1989-01-01

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

Verb-Noun Collocations in Written Discourse of Iranian EFL Learners

Directory of Open Access Journals (Sweden)

Fatemeh Ebrahimi-Bazzaz

2015-07-01

Full Text Available When native speakers of English write, they employ both grammatical rules and collocations. Collocations are words that are present in the memory of native speakers as ready-made prefabricated chunks. Non-native speakers who wish to acquire native-like fluency should give appropriate attention to collocations in writing in order not to produce sentences that native speakers may consider odd. The present study tries to explore the use of verb-noun collocations in written discourse of English as foreign language (EFL among Iranian EFL learners from one academic year to the next in Iran. To measure the use of verb-noun collocations in written discourse, there was a 60-minute task of writing story  based on a series of six pictures whereby for each picture, three verb-noun collocations were measured, and nouns were provided to limit the choice of collocations. The results of the statistical analysis of ANOVA for the research question indicated that there was a significant difference in the use of lexical verb-noun collocations in written discourse both between and within the four academic years. The results of a post hoc multiple comparison tests confirmed that the means are significantly different between the first year and the third and fourth years, between the second and the fourth, and between the third and the fourth academic year which indicate substantial development in verb-noun collocation proficiency.  The vital implication is that the learners could use verb-noun collocations in productive skill of writing.

A nodal collocation method for the calculation of the lambda modes of the P L equations

International Nuclear Information System (INIS)

Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.

2005-01-01

P L equations are classical approximations to the neutron transport equation admitting a diffusive form. Using this property, a nodal collocation method is developed for the P L approximations, which is based on the expansion of the flux in terms of orthonormal Legendre polynomials. This method approximates the differential lambda modes problem by an algebraic eigenvalue problem from which the fundamental and the subcritical modes of the system can be calculated. To test the performance of this method, two problems have been considered, a homogeneous slab, which admits an analytical solution, and a seven-region slab corresponding to a more realistic problem

Improving academic literacy by teaching collocations | Nizonkiza ...

African Journals Online (AJOL)

Stellenbosch Papers in Linguistics ... Abstract. This study explores the effect of teaching collocations on building academic vocabulary and hence improving academic writing abilities. ... They were presented with a completion task and an essay-writing task before and after being exposed to a collocation-based syllabus.

Application of the orthogonal collocation method to determination of temperature distribution in cylindrical conductors

International Nuclear Information System (INIS)

Fortini, Maria A.; Stamoulis, Michel N.; Ferreira, Angela F.M.; Pereira, Claubia; Costa, Antonella L.; Silva, Clarysson A.M.

2008-01-01

In this work, an analytical model for the determination of the temperature distribution in cylindrical heater components with characteristics of nuclear fuel rods, is presented. The heat conductor is characterized by an arbitrary number of solid walls and different types of materials, whose thermal properties are taken as function of temperature. The heat conduction fundamental equation is solved numerically with the method of weighted residuals (MWR) using a technique of orthogonal collocation. The results obtained with the proposed method are compared with the experimental data from tests performed in the TRIGA IPR-R1 research reactor localized at the CDTN/CNEN (Centro de Desenvolvimento da Tecnologia Nuclear/Comissao Nacional de Energia Nuclear) at Belo Horizonte in Brazil

An analytical investigation on unsteady motion of vertically falling spherical particles in non-Newtonian fluid by Collocation Method

Directory of Open Access Journals (Sweden)

M. Rahimi-Gorji

2015-06-01

Full Text Available An analytical investigation is applied for unsteady motion of a rigid spherical particle in a quiescent shear-thinning power-law fluid. The results were compared with those obtained from Collocation Method (CM and the established Numerical Method (Fourth order Runge–Kutta scheme. It was shown that CM gave accurate results. Collocation Method (CM and Numerical Method are used to solve the present problem. We obtained that the CM which was used to solve such nonlinear differential equation with fractional power is simpler and more accurate than series method such as HPM which was used in some previous works by others but the new method named Akbari-Ganji’s Method (AGM is an accurate and simple method which is slower than CM for solving such problems. The terminal settling velocity—that is the velocity at which the net forces on a falling particle eliminate—for three different spherical particles (made of plastic, glass and steel and three flow behavior index n, in three sets of power-law non-Newtonian fluids was investigated, based on polynomial solution (CM. Analytical results obtained indicated that the time of reaching the terminal velocity in a falling procedure is significantly increased with growing of the particle size that validated with Numerical Method. Further, with approaching flow behavior to Newtonian behavior from shear-thinning properties of flow (n → 1, the transient time to achieving the terminal settling velocity is decreased.

Testing knowledge of whole English collocations available for use in written production

DEFF Research Database (Denmark)

Revier, Robert Lee

2014-01-01

Testing knowledge of whole English collocations available for use in written production: Developing tests for use with intermediate and advanced Danish learners (dansk resume nedenfor) The present foreign language acquisition research derives its impetus from four assumptions regarding knowledge...... of English collocations. These are: (a) collocation knowledge can be conceptualized as an independent knowledge construct, (b) collocations are lexical items in their own right, (c) testing of collocation knowledge should also target knowledge of whole collocations, and (d) the learning burden of a whole...... the development of Danish EFL learners’ productive knowledge of whole English collocations. Five empirical studies were designed to generate information that would shed light on the reliability and validity of the CONTRIX as a measure of collocation knowledge available for use in written production. Study 1...

A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk

DEFF Research Database (Denmark)

Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan

2015-01-01

This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the for...

A review on the solution of Grad–Shafranov equation in the ...

Indian Academy of Sciences (India)

2017-02-10

Feb 10, 2017 ... coordinates based on the Chebyshev collocation technique. Z AMERIAN, M K SALEM, ... the power supply system. Any contact with ... often needed. Numerical .... Using composite differentiation (chain rule), and con- sidering ...

An efficient approach to numerical study of the coupled-BBM system with B-spline collocation method

Directory of Open Access Journals (Sweden)

khalid ali

2016-11-01

Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.

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

KAUST Repository

Hale, Nicholas; Townsend, Alex

2014-01-01

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

Supporting Collocation Learning with a Digital Library

Science.gov (United States)

Wu, Shaoqun; Franken, Margaret; Witten, Ian H.

2010-01-01

Extensive knowledge of collocations is a key factor that distinguishes learners from fluent native speakers. Such knowledge is difficult to acquire simply because there is so much of it. This paper describes a system that exploits the facilities offered by digital libraries to provide a rich collocation-learning environment. The design is based on…

"Minimum input, maximum output, indeed!" Teaching Collocations ...

African Journals Online (AJOL)

Fifty-nine EFL college students participated in the study, and they received two 75-minute instructions between pre- and post-tests: one on the definition of colloca-tion and its importance, and the other on the skill of looking up collocational information in the Naver Dictionary — an English–Korean online dictionary. During ...

A collocation--Galerkin finite element model of cardiac action potential propagation.

Science.gov (United States)

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

KAUST Repository

Farrell, Patricio; Wendland, Holger

2013-01-01

In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly

The structure of an Afrikaans collocation and phrase dictionary | Otto ...

African Journals Online (AJOL)

As one of the target groups is unsophisticated learners with a limited grammatical background, the ideal would be to enter lexical collocations both at their bases and at the collocators. To save space however, more information such as examples could then be provided at the bases only. Grammatical collocations should be ...

A Least Squares Collocation Method for Accuracy Improvement of Mobile LiDAR Systems

Directory of Open Access Journals (Sweden)

Qingzhou Mao

2015-06-01

Full Text Available In environments that are hostile to Global Navigation Satellites Systems (GNSS, the precision achieved by a mobile light detection and ranging (LiDAR system (MLS can deteriorate into the sub-meter or even the meter range due to errors in the positioning and orientation system (POS. This paper proposes a novel least squares collocation (LSC-based method to improve the accuracy of the MLS in these hostile environments. Through a thorough consideration of the characteristics of POS errors, the proposed LSC-based method effectively corrects these errors using LiDAR control points, thereby improving the accuracy of the MLS. This method is also applied to the calibration of misalignment between the laser scanner and the POS. Several datasets from different scenarios have been adopted in order to evaluate the effectiveness of the proposed method. The results from experiments indicate that this method would represent a significant improvement in terms of the accuracy of the MLS in environments that are essentially hostile to GNSS and is also effective regarding the calibration of misalignment.

47 CFR 51.323 - Standards for physical collocation and virtual collocation.

Science.gov (United States)

2010-10-01

... standards or any other performance standards. An incumbent LEC that denies collocation of a competitor's equipment, citing safety standards, must provide to the competitive LEC within five business days of the... incumbent LEC contends the competitor's equipment fails to meet. This affidavit must set forth in detail...

Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: A numerical comparison

KAUST Repository

Bäck, Joakim

2010-09-17

Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a suitable generalization of the classical sparse grid SC method, we are able to compare SG and SC on the same underlying multivariate polynomial space in terms of accuracy vs. computational work. The approximation spaces considered here include isotropic and anisotropic versions of Tensor Product (TP), Total Degree (TD), Hyperbolic Cross (HC) and Smolyak (SM) polynomials. Numerical results for linear elliptic SPDEs indicate a slight computational work advantage of isotropic SC over SG, with SC-SM and SG-TD being the best choices of approximation spaces for each method. Finally, numerical results corroborate the optimality of the theoretical estimate of anisotropy ratios introduced by the authors in a previous work for the construction of anisotropic approximation spaces. © 2011 Springer.

First-year University Students' Productive Knowledge of Collocations ...

African Journals Online (AJOL)

The present study examines productive knowledge of collocations of tertiary-level second language (L2) learners of English in an attempt to make estimates of the size of their knowledge. Participants involved first-year students at North-West University who sat a collocation test modelled on that developed by Laufer and ...

Corpus-Aided Business English Collocation Pedagogy: An Empirical Study in Chinese EFL Learners

Science.gov (United States)

Chen, Lidan

2017-01-01

This study reports an empirical study of an explicit instruction of corpus-aided Business English collocations and verifies its effectiveness in improving learners' collocation awareness and learner autonomy, as a result of which is significant improvement of learners' collocation competence. An eight-week instruction in keywords' collocations,…

RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

KAUST Repository

Farrell, Patricio

2013-01-01

In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.

Lexical richness and collocational competence in second-language writing

NARCIS (Netherlands)

Vedder, I.; Benigno, V.

2016-01-01

In this article we report on an experiment set up to investigate lexical richness and collocational competence in the written production of 39 low-intermediate and intermediate learners of Italian L2. Lexical richness was assessed by means of a lexical profiling method inspired by Laufer and Nation

Impact of WhatsApp on Learning and Retention of Collocation Knowledge among Iranian EFL Learners

Directory of Open Access Journals (Sweden)

Zahra Ashiyan

2016-10-01

Full Text Available During the recent technological years, language learning has been attempted to transform its path from the conventional methods to instrumental applications. Mobile phone provides people to reach and exchange information through chats (WhatsApp. It is a tool or mode that means the facilities are used for main purposes. The unique features of the application are its compatibility to exchange information, enhance communication and relationship. A mobile phone provides to download, upload and store learning materials and information files. The purpose of the current study was to investigate the use and effect of mobile applications such as WhatsApp on school work and out of school work. In this way, Oxford Placement Test (OPT was conducted among 80 learners in order to select intermediate EFL learners.  In total, 60 participants whose scores were 70 or higher were elected as the intermediate level and were divided into experimental and control groups. In order to control the reliability of the collocation pretest, the test was pilot studied on 15 learners. Then, the pretest was conducted to measure the learner’s collocation knowledge in both of the groups. The experimental group frequently installed WhatsApp application in order to learning and practicing new collocations in order to learning and practicing new collocations, while the control group did not use any tool for learning them. An immediate posttest after the treatment was administered. The results in each group were statistically evaluated and the findings manifested that the experimental group who used WhatsApp application in learning collocation significantly outperformed the control group in posttest. Thus usage of WhatsApp application to acquire collocations can reinforce and enhance the process of collocations acquisition and it can guarantee retention of collocations. This study also prepares pedagogical implications for utilizing mobile application as an influential instrument

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

Czech Academy of Sciences Publication Activity Database

Dzetkulič, Tomáš

2015-01-01

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

Adaptive collocation method for simultaneous heat and mass diffusion with phase change

International Nuclear Information System (INIS)

Chawla, T.C.; Leaf, G.; Minkowycz, W.J.; Pedersen, D.R.; Shouman, A.R.

1983-01-01

The present study is carried out to determine melting rates of a lead slab of various thicknesses by contact with sodium coolant and to evaluate the extent of penetration and the mixing rates of molten lead into liquid sodium by molecular diffusion alone. The study shows that these two calculations cannot be performed simultaneously without the use of adaptive coordinates which cause considerable stretching of the physical coordinates for mass diffusion. Because of the large difference in densities of these two liquid metals, the traditional constant density approximation for the calculation of mass diffusion cannot be used for studying their interdiffusion. The use of orthogonal collocation method along with adaptive coordinates produces extremely accurate results which are ascertained by comparing with the existing analytical solutions for concentration distribution for the case of constant density approximation and for melting rates for the case of infinite lead slab

THE INVESTIGATION OF PRODUCTIVE AND RECEPTIVE COMPETENCE IN V+N AND ADJ+N COLLOCATIONS AMONG INDONESIAN EFL LEARNERS

Directory of Open Access Journals (Sweden)

Saudin Saudin

2017-05-01

Full Text Available The important role of collocation in learners’ language proficiency has been acknowledged widely. In Systemic Functional Linguistics (SFL, collocation is known as one prominent member of the super-ordinate lexical cohesion, which contributes significantly to the textual coherence, together with grammatical cohesion and structural cohesion (Halliday & Hasan, 1985. Collocation is also viewed as the hallmark of truly advanced English learners since the higher the learners’ proficiency is, the more they tend to use collocation (Bazzaz & Samad, 2011; Hsu, 2007; Zhang, 1993. Further, knowledge of collocation is regarded as part of the native speakers’ communicative competence (Bazzaz & Samad, 2011; and lack of the knowledge is the most important sign of foreignness among foreign language learners (McArthur, 1992; McCarthy, 1990. Taking the importance of collocation into account, this study is aimed to shed light on Indonesian EFL learners’ levels of collocational competence. In the study, the collocational competence is restricted to v+n and adj+n of collocation but broken down into productive and receptive competence, about which little work has been done (Henriksen, 2013. For this purpose, 49 second-year students of an English department in a state polytechnic were chosen as the subjects. Two sets of tests (filling in the blanks and multiple-choice were administered to obtain the data of the subjects’ levels of productive and receptive competence and to gain information of which type was more problematic for the learners. The test instruments were designed by referring to Brashi’s (2006 test model, and Koya’s (2003. In the analysis of the data, interpretive-qualitative method was used primarily to obtain broad explanatory information. The data analysis showed that the scores of productive competence were lower than those of receptive competence in both v+n and adj+n collocation. The analysis also revealed that the scores of productive

Teachability of collocations: The role of word frequency counts ...

African Journals Online (AJOL)

... beginner/low-intermediate students and only exceed the 2 000-word band from the upper-intermediate learning stage onwards, a suggestion in line with Nation's (2006) discussion on how to teach vocabulary. Keywords: collocation size, controlled productive knowledge, teachability of collocations, word frequency counts, ...

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

Science.gov (United States)

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

2014-09-01

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

Collocations and Grammatical Patterns in a Multilingual Online Term ...

African Journals Online (AJOL)

This article considers the importance of including various types of collocations in a terminological database, with the aim of making this information available to the user via the user interface. We refer specifically to the inclusion of empirical and phraseological collocations, and information on grammatical patterning.

Developing and Evaluating a Web-Based Collocation Retrieval Tool for EFL Students and Teachers

Science.gov (United States)

Chen, Hao-Jan Howard

2011-01-01

The development of adequate collocational knowledge is important for foreign language learners; nonetheless, learners often have difficulties in producing proper collocations in the target language. Among the various ways of learning collocations, the DDL (data-driven learning) approach encourages independent learning of collocations and allows…

SOLUTION OF A MULTIVARIATE STRATIFIED SAMPLING PROBLEM THROUGH CHEBYSHEV GOAL PROGRAMMING

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Mohd. Vaseem Ismail

2010-12-01

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

A method for stochastic constrained optimization using derivative-free surrogate pattern search and collocation

International Nuclear Information System (INIS)

Sankaran, Sethuraman; Audet, Charles; Marsden, Alison L.

2010-01-01

Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.

Application of adaptive hierarchical sparse grid collocation to the uncertainty quantification of nuclear reactor simulators

Energy Technology Data Exchange (ETDEWEB)

Yankov, A.; Downar, T. [University of Michigan, 2355 Bonisteel Blvd, Ann Arbor, MI 48109 (United States)

2013-07-01

Recent efforts in the application of uncertainty quantification to nuclear systems have utilized methods based on generalized perturbation theory and stochastic sampling. While these methods have proven to be effective they both have major drawbacks that may impede further progress. A relatively new approach based on spectral elements for uncertainty quantification is applied in this paper to several problems in reactor simulation. Spectral methods based on collocation attempt to couple the approximation free nature of stochastic sampling methods with the determinism of generalized perturbation theory. The specific spectral method used in this paper employs both the Smolyak algorithm and adaptivity by using Newton-Cotes collocation points along with linear hat basis functions. Using this approach, a surrogate model for the outputs of a computer code is constructed hierarchically by adaptively refining the collocation grid until the interpolant is converged to a user-defined threshold. The method inherently fits into the framework of parallel computing and allows for the extraction of meaningful statistics and data that are not within reach of stochastic sampling and generalized perturbation theory. This paper aims to demonstrate the advantages of spectral methods-especially when compared to current methods used in reactor physics for uncertainty quantification-and to illustrate their full potential. (authors)

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

Directory of Open Access Journals (Sweden)

Fuqiang Zhao

2017-01-01

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

Examining Second Language Receptive Knowledge of Collocation and Factors That Affect Learning

Science.gov (United States)

Nguyen, Thi My Hang; Webb, Stuart

2017-01-01

This study investigated Vietnamese EFL learners' knowledge of verb-noun and adjective-noun collocations at the first three 1,000 word frequency levels, and the extent to which five factors (node word frequency, collocation frequency, mutual information score, congruency, and part of speech) predicted receptive knowledge of collocation. Knowledge…

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

Science.gov (United States)

Mireles James, J. D.; Murray, Maxime

2017-12-01

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

Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme

Directory of Open Access Journals (Sweden)

Şuayip Yüzbaşı

2015-02-01

Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.

Translating English Idioms and Collocations

Directory of Open Access Journals (Sweden)

Rochayah Machali

2004-01-01

Full Text Available Learners of English should be made aware of the nature, types, and use of English idioms. This paper disensses the nature of idioms and collocations and translation issues related to them

A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

KAUST Repository

Malenova, G.

2016-09-08

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.

A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty

KAUST Repository

Malenova, G.; Motamed, M.; Runborg, O.; Tempone, Raul

2016-01-01

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.

On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods

KAUST Repository

Beck, Joakim; Tempone, Raul; Nobile, Fabio; Tamellini, Lorenzo

2012-01-01

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.

On the optimal polynomial approximation of stochastic PDEs by galerkin and collocation methods

KAUST Repository

Beck, Joakim

2012-09-01

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials. We first consider the stochastic Galerkin method, and rely on sharp estimates for the decay of the Fourier coefficients of the spectral expansion of u on an orthogonal polynomial basis to build a sequence of polynomial subspaces that features better convergence properties, in terms of error versus number of degrees of freedom, than standard choices such as Total Degree or Tensor Product subspaces. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids. Numerical results show the effectiveness of the newly introduced polynomial spaces and sparse grids. © 2012 World Scientific Publishing Company.

Fourier Collocation Approach With Mesh Refinement Method for Simulating Transit-Time Ultrasonic Flowmeters Under Multiphase Flow Conditions.

Science.gov (United States)

Simurda, Matej; Duggen, Lars; Basse, Nils T; Lassen, Benny

2018-02-01

A numerical model for transit-time ultrasonic flowmeters operating under multiphase flow conditions previously presented by us is extended by mesh refinement and grid point redistribution. The method solves modified first-order stress-velocity equations of elastodynamics with additional terms to account for the effect of the background flow. Spatial derivatives are calculated by a Fourier collocation scheme allowing the use of the fast Fourier transform, while the time integration is realized by the explicit third-order Runge-Kutta finite-difference scheme. The method is compared against analytical solutions and experimental measurements to verify the benefit of using mapped grids. Additionally, a study of clamp-on and in-line ultrasonic flowmeters operating under multiphase flow conditions is carried out.

Learning and Teaching L2 Collocations: Insights from Research

Science.gov (United States)

Szudarski, Pawel

2017-01-01

The aim of this article is to present and summarize the main research findings in the area of learning and teaching second language (L2) collocations. Being a large part of naturally occurring language, collocations and other types of multiword units (e.g., idioms, phrasal verbs, lexical bundles) have been identified as important aspects of L2…

Application of a nodal collocation approximation for the multidimensional PL equations to the 3D Takeda benchmark problems

International Nuclear Information System (INIS)

Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdú, G.

2012-01-01

Highlights: ► The multidimensional P L approximation to the nuclear transport equation is reviewed. ► A nodal collocation method is developed for the spatial discretization of P L equations. ► Advantages of the method are lower dimension and good characterists of the associated algebraic eigenvalue problem. ► The P L nodal collocation method is implemented into the computer code SHNC. ► The SHNC code is verified with 2D and 3D benchmark eigenvalue problems from Takeda and Ikeda, giving satisfactory results. - Abstract: P L equations are classical approximations to the neutron transport equations, which are obtained expanding the angular neutron flux in terms of spherical harmonics. These approximations are useful to study the behavior of reactor cores with complex fuel assemblies, for the homogenization of nuclear cross-sections, etc., and most of these applications are in three-dimensional (3D) geometries. In this work, we review the multi-dimensional P L equations and describe a nodal collocation method for the spatial discretization of these equations for arbitrary odd order L, which is based on the expansion of the spatial dependence of the fields in terms of orthonormal Legendre polynomials. The performance of the nodal collocation method is studied by means of obtaining the k eff and the stationary power distribution of several 3D benchmark problems. The solutions are obtained are compared with a finite element method and a Monte Carlo method.

English collocations: A novel approach to teaching the language's last bastion

Directory of Open Access Journals (Sweden)

Rafe S. Zaabalawi

2017-01-01

Full Text Available Collocations are a class of idiomatic expressions comprised of a sequence of words which, for mostly arbitrary reasons, occur together in a prescribed order. Collocations are not necessarily grammatical and/or cannot be generated through knowledge of rules or formulae. Therefore, they are often not easily mastered by EFL learners and typically only dealt with during the latter phase of second language apprenticeship. Literature has mostly examined the phenomenon of collocations from one of two perspectives. First, there are studies focusing on error analysis and contingent pedagogical advice. Second, there is research concerned with theory development; a genre associated with a specific methodological limitations. This study reports on data pertaining to a novel approach to learning collocations; one based on a learner's incidental discovery of such structures in written texts. Our research question is: will students who have been introduced to and practiced specific collocations in reading texts be inclined to naturally use such exemplars appropriately in novel/unfamiliar subsequent contexts? Findings have implications for EFL teachers and those concerned with curriculum development.

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

Science.gov (United States)

Liang, Conghui; Ceccarelli, Marco; Takeda, Yukio

2012-12-01

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

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

International Nuclear Information System (INIS)

Flores-Lamas, H.

1994-01-01

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

The Use of English Collocations in Reader's Digest

OpenAIRE

Sinaga, Yudita Putri Nurani; Sinaga, Lidiman Sahat Martua

2014-01-01

This descriptive qualitative study is aimed at identifying and describing the types of free collocations found in the articles of Reader's Digest. By taking a sample of ten articles from different months for each year since 2003 up to 2012, it was found all the four productive free collocations were in the data. Type 4 (Determiner + Adjective + Noun) was the dominant type (53.92 %). This was possible because the adjective in the pattern included the present participle and past participle of v...

Corpora and Collocations in Chinese-English Dictionaries for Chinese Users

Science.gov (United States)

Xia, Lixin

2015-01-01

The paper identifies the major problems of the Chinese-English dictionary in representing collocational information after an extensive survey of nine dictionaries popular among Chinese users. It is found that the Chinese-English dictionary only provides the collocation types of "v+n" and "v+n," but completely ignores those of…

Collocational Relations in Japanese Language Textbooks and Computer-Assisted Language Learning Resources

Directory of Open Access Journals (Sweden)

Irena SRDANOVIĆ

2011-05-01

Full Text Available In this paper, we explore presence of collocational relations in the computer-assisted language learning systems and other language resources for the Japanese language, on one side, and, in the Japanese language learning textbooks and wordlists, on the other side. After introducing how important it is to learn collocational relations in a foreign language, we examine their coverage in the various learners’ resources for the Japanese language. We particularly concentrate on a few collocations at the beginner’s level, where we demonstrate their treatment across various resources. A special attention is paid to what is referred to as unpredictable collocations, which have a bigger foreign language learning-burden than the predictable ones.

A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion

Directory of Open Access Journals (Sweden)

Xiaokui Yue

2014-01-01

Full Text Available A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC method to search for the periodic solutions of an exact J2 nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W equations or Tschauner-Hempel (T-H equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO, which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.

Comparison of matrix exponential methods for fuel burnup calculations

International Nuclear Information System (INIS)

Oh, Hyung Suk; Yang, Won Sik

1999-01-01

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7. (author). 11 refs., 4 figs., 2 tabs

Collocations of High Frequency Noun Keywords in Prescribed Science Textbooks

Science.gov (United States)

Menon, Sujatha; Mukundan, Jayakaran

2012-01-01

This paper analyses the discourse of science through the study of collocational patterns of high frequency noun keywords in science textbooks used by upper secondary students in Malaysia. Research has shown that one of the areas of difficulty in science discourse concerns lexis, especially that of collocations. This paper describes a corpus-based…

GUESSING VERB-ADVERB COLLOCATIONS: ARAB EFL ...

African Journals Online (AJOL)

user

In the sections to follow, the concept and meaning of collocation is defined ... expressions (Alexander 1984); formulaic language or speech (Weinert 1995); multi- ... Two further studies reported Arab EFL learners' overall ignorance of col-.

Translating Legal Collocations in Contract Agreements by Iraqi EFL Students-Translators

Directory of Open Access Journals (Sweden)

Muntaha A. Abdulwahid

2017-01-01

Full Text Available Legal translation of contract agreements is a challenge to translators as it involves combining the literary translation with the technical terminological precision. In translating legal contract agreements, a legal translator must utilize the lexical or syntactic precision and, more importantly, the pragmatic awareness of the context. This will guarantee an overall communicative process and avoid inconsistency in legal translation. However, the inability of the translator to meet these two functions in translating the contract item not only affects the contractors’ comprehension of the contract item but also affects the parties’ contractual obligations. In light of this, the purpose of this study was to find out how legal collocations used in contract agreements are translated from Arabic into English by student-translators in terms of (1 purely technical, (2 semi-technical, and (3 everyday vocabulary collocations. For the data collection, a multiple-choice collocation test was used to be answered by 35 EFL Iraqi undergraduate translator-students to decide on the aspects of weaknesses and strengths of their translation, thus decide on the aspects of correction. The findings showed that these students had serious problems in translating legal collocations as they lack the linguistic knowledge and pragmatic awareness needed to achieve the legal meaning and effect. They were also unable to make a difference among the three categories of legal collocations, purely technical, semi-technical, and everyday vocabulary collocations. These students should be exposed to more legal translation practices to obtain the required experience needed for their future career.

Nested sparse grid collocation method with delay and transformation for subsurface flow and transport problems

Science.gov (United States)

Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi

2017-06-01

In numerical modeling of subsurface flow and transport problems, formation properties may not be deterministically characterized, which leads to uncertainty in simulation results. In this study, we propose a sparse grid collocation method, which adopts nested quadrature rules with delay and transformation to quantify the uncertainty of model solutions. We show that the nested Kronrod-Patterson-Hermite quadrature is more efficient than the unnested Gauss-Hermite quadrature. We compare the convergence rates of various quadrature rules including the domain truncation and domain mapping approaches. To further improve accuracy and efficiency, we present a delayed process in selecting quadrature nodes and a transformed process for approximating unsmooth or discontinuous solutions. The proposed method is tested by an analytical function and in one-dimensional single-phase and two-phase flow problems with different spatial variances and correlation lengths. An additional example is given to demonstrate its applicability to three-dimensional black-oil models. It is found from these examples that the proposed method provides a promising approach for obtaining satisfactory estimation of the solution statistics and is much more efficient than the Monte-Carlo simulations.

Let's collocate: student generated worksheets as a motivational tool

OpenAIRE

Simpson, Adam John

2006-01-01

This article discusses the process of producing collocation worksheets and the values of these worksheets as a motivational tool within a tertiary level preparatory English program. Firstly, the method by which these worksheets were produced is described, followed by an analysis of their effectiveness as a resource in terms of student motivation, personalisation, involvement in the development of the curriculum and in raising awareness of corpus linguistics and its applications.

Modified homotopy perturbation method for solving hypersingular integral equations of the first kind.

Science.gov (United States)

Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z

2016-01-01

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.

COLLOCATION PHRASES IN RELATION TO OTHER LEXICAL PHRASES IN CROATIAN

Directory of Open Access Journals (Sweden)

Goranka Blagus Bartolec

2012-01-01

Full Text Available The paper analyzes the semantic and lexicological aspects of collocation phrases in Croatian with tendency to separate them from other lexical phrases in Croatian (terms, idioms, names. The collocation phrase is defined as a special lexical phrase on a syntagmatic level, based on the semantic correlation of the two individual lexical components in which their meanings are specified.

Relation work in collocated and distributed collaboration

DEFF Research Database (Denmark)

Christensen, Lars Rune; Jensen, Rasmus Eskild; Bjørn, Pernille

2014-01-01

Creating social ties are important for collaborative work; however, in geographically distributed organizations e.g. global software development, making social ties requires extra work: Relation work. We find that characteristics of relation work as based upon shared history and experiences......, emergent in personal and often humorous situations. Relation work is intertwined with other activities such as articulation work and it is rhythmic by following the work patterns of the participants. By comparing how relation work is conducted in collocated and geographically distributed settings we...... in this paper identify basic differences in relation work. Whereas collocated relation work is spontaneous, place-centric, and yet mobile, relation work in a distributed setting is semi-spontaneous, technology-mediated, and requires extra efforts....

Age of Acquisition Effects in Chinese EFL learners’ Delexicalized Verb and Collocation Acquisition

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Miao Haiyan

2015-05-01

Full Text Available This paper investigates age of acquisition (AoA effects and the acquisition of delexicalized verbs and collocations in Chinese EFL learners, and explores the underlying reasons from the connectionist model for these learners’ acquisition characteristics. The data were collected through a translation test consisted of delexialized verb information section and English-Chinese and Chinese-English collocation parts, aiming to focus on Chinese EFL learners’ receptive and productive abilities respectively. As Chinese EFL is a nationally classroom-based practice beginning from early primary school, the pedagogical value and different phases of acquisition are thus taken into consideration in designing the translation test. Research results show that the effects of AoA are significant not only in the learners’ acquisition of individual delexicalized verbs but also in delexicalized collocations. Although learners have long begun to learn delexicalized verbs, their production indicates that early learning does not guarantee total acquisition, because their grasp of delexicalized verbs still stay at the senior middle school level. AoA effects significantly affect the recognition but not the production of collocations. Furthermore, a plateau effect occurs in learners’ acquisition of college-level delexicalized collocations, as their recognition and production have no processing advantages over earlier learned collocations.

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

DEFF Research Database (Denmark)

Nielsen, S.A.; Hesthaven, J.S.

2002-01-01

elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial...

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

KAUST Repository

Beck, Joakim; Nobile, F.; Tamellini, L.; Tempone, Raul

2011-01-01

We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.

Not Just "Small Potatoes": Knowledge of the Idiomatic Meanings of Collocations

Science.gov (United States)

Macis, Marijana; Schmitt, Norbert

2017-01-01

This study investigated learner knowledge of the figurative meanings of 30 collocations that can be both literal and figurative. One hundred and seven Chilean Spanish-speaking university students of English were asked to complete a meaning-recall collocation test in which the target items were embedded in non-defining sentences. Results showed…

Vocabulary and Receptive Knowledge of English Collocations among Swedish Upper Secondary School Students

OpenAIRE

Bergström, Kerstin

2008-01-01

The aim of this study is to examine the vocabulary and receptive collocation knowledge in English among Swedish upper secondary school students. The primary material consists of two vocabulary tests, one collocation test, and a background questionnaire. The first research question concerns whether the students who receive a major part of their education in English have a higher level of vocabulary and receptive collocation knowledge in English than those who are taught primarily in Swedish. T...

Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol

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Hong Lai

2012-01-01

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

NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

OpenAIRE

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

2017-01-01

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

Measuring receptive collocational competence across proficiency ...

African Journals Online (AJOL)

Kate H

frequency bands. A proficiency measure and a collocation test were administered to English ... battery may negatively impact the test-takers' performance. ..... examples. The major finding is that raising learners' awareness constitutes the best way forward ..... Amsterdam: John Benjamins Publishing Company. Green, R.

The treatment of lexical collocations in EFL coursebooks in the Estonian secondary school context

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Liina Vassiljev

2015-04-01

Full Text Available The article investigates lexical collocations encountered in English as a Foreign Language (EFL instruction in Estonian upper secondary schools. This is achieved through a statistical analysis of collocations featuring in three coursebooks where the collocations found are analysed in terms of their type, frequency and usefulness index by studying them through an online language corpus (Collins Wordbanks Online. The coursebooks are systematically compared and contrasted relying upon the data gathered. The results of the study reveal that the frequency and range of lexical collocations in a language corpus have not been regarded as an essential criterion for their selection and practice by any of the coursebook authors under discussion.

English Collocation Learning through Corpus Data: On-Line Concordance and Statistical Information

Science.gov (United States)

Ohtake, Hiroshi; Fujita, Nobuyuki; Kawamoto, Takeshi; Morren, Brian; Ugawa, Yoshihiro; Kaneko, Shuji

2012-01-01

We developed an English Collocations On Demand system offering on-line corpus and concordance information to help Japanese researchers acquire a better command of English collocation patterns. The Life Science Dictionary Corpus consists of approximately 90,000,000 words collected from life science related research papers published in academic…

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

Science.gov (United States)

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

2017-07-01

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

Multi-Index Monte Carlo and stochastic collocation methods for random PDEs

KAUST Repository

Nobile, Fabio; Haji Ali, Abdul Lateef; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

In this talk we consider the problem of computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a finite or countable sequence of terms in a suitable expansion. We describe and analyze a Multi-Index Monte Carlo (MIMC) and a Multi-Index Stochastic Collocation method (MISC). the former is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Instead of using firstorder differences as in MLMC, MIMC uses mixed differences to reduce the variance of the hierarchical differences dramatically. This in turn yields new and improved complexity results, which are natural generalizations of Giles s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence, O(TOL-2). On the same vein, MISC is a deterministic combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. Provided enough mixed regularity, MISC can achieve better complexity than MIMC. Moreover, we show that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one-dimensional spatial problem. We propose optimization procedures to select the most effective mixed differences to include in MIMC and MISC. Such optimization is a crucial step that allows us to make MIMC and MISC computationally effective. We finally show the effectiveness of MIMC and MISC with some computational tests, including tests with a infinite countable number of random parameters.

Multi-Index Monte Carlo and stochastic collocation methods for random PDEs

KAUST Repository

Nobile, Fabio

2016-01-09

In this talk we consider the problem of computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a finite or countable sequence of terms in a suitable expansion. We describe and analyze a Multi-Index Monte Carlo (MIMC) and a Multi-Index Stochastic Collocation method (MISC). the former is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Instead of using firstorder differences as in MLMC, MIMC uses mixed differences to reduce the variance of the hierarchical differences dramatically. This in turn yields new and improved complexity results, which are natural generalizations of Giles s MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence, O(TOL-2). On the same vein, MISC is a deterministic combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. Provided enough mixed regularity, MISC can achieve better complexity than MIMC. Moreover, we show that in the optimal case the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one-dimensional spatial problem. We propose optimization procedures to select the most effective mixed differences to include in MIMC and MISC. Such optimization is a crucial step that allows us to make MIMC and MISC computationally effective. We finally show the effectiveness of MIMC and MISC with some computational tests, including tests with a infinite countable number of random parameters.

Stochastic Collocation Applications in Computational Electromagnetics

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Dragan Poljak

2018-01-01

Full Text Available The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR, human exposure to electromagnetic fields, and buried lines and grounding systems.

The current strain distribution in the North China Basin of eastern China by least-squares collocation

Science.gov (United States)

Wu, J. C.; Tang, H. W.; Chen, Y. Q.; Li, Y. X.

2006-07-01

In this paper, the velocities of 154 stations obtained in 2001 and 2003 GPS survey campaigns are applied to formulate a continuous velocity field by the least-squares collocation method. The strain rate field obtained by the least-squares collocation method shows more clear deformation patterns than that of the conventional discrete triangle method. The significant deformation zones obtained are mainly located in three places, to the north of Tangshan, between Tianjing and Shijiazhuang, and to the north of Datong, which agree with the places of the Holocene active deformation zones obtained by geological investigations. The maximum shear strain rate is located at latitude 38.6°N and longitude 116.8°E, with a magnitude of 0.13 ppm/a. The strain rate field obtained can be used for earthquake prediction research in the North China Basin.

Runge-Kutta and Hermite Collocation for a biological invasion problem modeled by a generalized Fisher equation

International Nuclear Information System (INIS)

Athanasakis, I E; Papadopoulou, E P; Saridakis, Y G

2014-01-01

Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods

Improving academic literacy by teaching collocations

African Journals Online (AJOL)

Kate H

version of McCarthy and O'Dell's (2005) collocation web model were the techniques adopted ... both cued recall and essay writing, supporting earlier findings (cf. ..... from a 'holistic' representation of formulaic sequences in memory” (Boers et al. ... their study indicate that non-native speakers also retain words as they appear ...

On the hybrid stability of the collocated virtual holonomic constraints basedwalking design

Czech Academy of Sciences Publication Activity Database

Anderle, Milan; Čelikovský, Sergej

2017-01-01

Roč. 6, č. 2 (2017), s. 47-56 ISSN 2223-7038 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : Underactuated walking * Virtual holonomic constraints * Poincaré section method * collocated constraints Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems http://lib.physcon.ru/doc?id=60655c1961ed

Communication Collocations of the Lexeme Geld in General and Business German

Directory of Open Access Journals (Sweden)

Mirna Hocenski-Dreiseidl

2010-07-01

Full Text Available The authors aim to analyse and compare the lexeme Geld and its collocations on the grammatical and semantic levels in general and in business German. A special emphasis will be put on the importance of the communicative function that this lexeme and its collocations have in the language of banking. The paper also has a practical purpose. Its applicability in teaching is envisaged to improve the communicative competence of students of economics.

Adaptive probabilistic collocation based Kalman filter for unsaturated flow problem

Science.gov (United States)

Man, J.; Li, W.; Zeng, L.; Wu, L.

2015-12-01

The ensemble Kalman filter (EnKF) has gained popularity in hydrological data assimilation problems. As a Monte Carlo based method, a relatively large ensemble size is usually required to guarantee the accuracy. As an alternative approach, the probabilistic collocation based Kalman filter (PCKF) employs the Polynomial Chaos to approximate the original system. In this way, the sampling error can be reduced. However, PCKF suffers from the so called "cure of dimensionality". When the system nonlinearity is strong and number of parameters is large, PCKF is even more computationally expensive than EnKF. Motivated by recent developments in uncertainty quantification, we propose a restart adaptive probabilistic collocation based Kalman filter (RAPCKF) for data assimilation in unsaturated flow problem. During the implementation of RAPCKF, the important parameters are identified and active PCE basis functions are adaptively selected. The "restart" technology is used to alleviate the inconsistency between model parameters and states. The performance of RAPCKF is tested by unsaturated flow numerical cases. It is shown that RAPCKF is more efficient than EnKF with the same computational cost. Compared with the traditional PCKF, the RAPCKF is more applicable in strongly nonlinear and high dimensional problems.

Towards Improving the Efficiency of Bayesian Model Averaging Analysis for Flow in Porous Media via the Probabilistic Collocation Method

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Liang Xue

2018-04-01

Full Text Available The characterization of flow in subsurface porous media is associated with high uncertainty. To better quantify the uncertainty of groundwater systems, it is necessary to consider the model uncertainty. Multi-model uncertainty analysis can be performed in the Bayesian model averaging (BMA framework. However, the BMA analysis via Monte Carlo method is time consuming because it requires many forward model evaluations. A computationally efficient BMA analysis framework is proposed by using the probabilistic collocation method to construct a response surface model, where the log hydraulic conductivity field and hydraulic head are expanded into polynomials through Karhunen–Loeve and polynomial chaos methods. A synthetic test is designed to validate the proposed response surface analysis method. The results show that the posterior model weight and the key statistics in BMA framework can be accurately estimated. The relative errors of mean and total variance in the BMA analysis results are just approximately 0.013% and 1.18%, but the proposed method can be 16 times more computationally efficient than the traditional BMA method.

Versions of the Collocation and Least Residuals Method for Solving Problems of Mathematical Physics in the Convex Quadrangular Domains

Directory of Open Access Journals (Sweden)

Vasily A. Belyaev

2017-01-01

Full Text Available The new versions of the collocations and least residuals (CLR method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for PDE in the convex quadrangular domains. Their implementation and numerical experiments are performed by the examples of solving the biharmonic and Poisson equations. The solution of the biharmonic equation is used for simulation of the stress-strain state of an isotropic plate under the action of the transverse load. Differential problems are projected into the space of fourth-degree polynomials by the CLR method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLR method are implemented on the grids, which are constructed by two different ways. In the first version, a “quasiregular” grid is constructed in the domain, the extreme lines of this grid coincide with the boundaries of the domain. In the second version, the domain is initially covered by a regular grid with rectangular cells. Herewith, the collocation and matching points that are situated outside the domain are used for approximation of the differential equations in the boundary cells that had been crossed by the boundary. In addition the “small” irregular triangular cells that had been cut off by the domain boundary from rectangular cells of the initial regular grid are joined to adjacent quadrangular cells. This technique allowed to essentially reduce the conditionality of the system of linear algebraic equations of the approximate problem in comparison with the case when small irregular cells together with other cells were used as independent ones for constructing an approximate solution of the problem. It is shown that the approximate solution of problems converges with high order and matches with high accuracy with the analytical solution of the test problems in the case of the known solution in

Language Proficiency, Collocational Knowledge and the Role of L1 Transfer: A Correlational Study of Iranian EFL Learners

Directory of Open Access Journals (Sweden)

Mustapha Hajebi

2017-12-01

Full Text Available The present study investigates the correlation between language proficiency, collocations and the role of L1 transfer with collocations. This is a quantitative research. The research places more emphases on collecting data in the form of numbers. It is also experimental research in the sense that it tests participants to measure their variables. The participants of the study were 57 Persian B.A students, both male and female from Islamic Azad University of Bandar Abbas, Iran. The results showed that there is a significant relationship between Iranian subjects’ language proficiency, as measured by the Michigan proficiency test and their knowledge of collocations, as measured by their performance on a collocation test designed for the current study. The results obtained from the research indicate that Iranian EFL learners are more likely to use the right collocation in cases of L1 transfer. This suggests that positive transfer plays a major role when it comes to EFL learners’ ability to produce the right collocations in their L2. The findings of this study have some implications for language teaching. Teachers can put emphasis on the inclusion of selected grammatical and lexical collocations in reading comprehension passages.

Collocation methods for uncertainty quanti cation in PDE models with random data

KAUST Repository

Nobile, Fabio

2014-01-06

In this talk we consider Partial Differential Equations (PDEs) whose input data are modeled as random fields to account for their intrinsic variability or our lack of knowledge. After parametrizing the input random fields by finitely many independent random variables, we exploit the high regularity of the solution of the PDE as a function of the input random variables and consider sparse polynomial approximations in probability (Polynomial Chaos expansion) by collocation methods. We first address interpolatory approximations where the PDE is solved on a sparse grid of Gauss points in the probability space and the solutions thus obtained interpolated by multivariate polynomials. We present recent results on optimized sparse grids in which the selection of points is based on a knapsack approach and relies on sharp estimates of the decay of the coefficients of the polynomial chaos expansion of the solution. Secondly, we consider regression approaches where the PDE is evaluated on randomly chosen points in the probability space and a polynomial approximation constructed by the least square method. We present recent theoretical results on the stability and optimality of the approximation under suitable conditions between the number of sampling points and the dimension of the polynomial space. In particular, we show that for uniform random variables, the number of sampling point has to scale quadratically with the dimension of the polynomial space to maintain the stability and optimality of the approximation. Numerical results show that such condition is sharp in the monovariate case but seems to be over-constraining in higher dimensions. The regression technique seems therefore to be attractive in higher dimensions.

Fracture analysis of one-dimensional hexagonal quasicrystals: Researches of a finite dimension rectangular plate by boundary collocation method

Energy Technology Data Exchange (ETDEWEB)

Jiaxing, Cheng; Dongfa, Sheng [Southwest Forestry University, Yunnan (China)

2017-05-15

As an important supplement and development to crystallography, the applications about quasicrystal materials have played a core role in many fields, such as manufacturing and the space industry. Due to the sensitivity of quasicrystals to defects, the research on the fracture problem of quasicrystals has attracted a great deal of attention. We present a boundary collocation method to research fracture problems for a finite dimension rectangular one-dimensional hexagonal quasicrystal plate. Because mode I and mode II problems for one- dimensional hexagonal quasicrystals are like that for the classical elastic materials, only the anti-plane problem is discussed in this paper. The correctness of the present numerical method is verified through a comparison of the present results and the existing results. And then, the size effects on stress field, stress intensity factor and energy release rate are discussed in detail. The obtained results can provide valuable references for the fracture behavior of quasicrystals.

A fractional factorial probabilistic collocation method for uncertainty propagation of hydrologic model parameters in a reduced dimensional space

Science.gov (United States)

Wang, S.; Huang, G. H.; Huang, W.; Fan, Y. R.; Li, Z.

2015-10-01

In this study, a fractional factorial probabilistic collocation method is proposed to reveal statistical significance of hydrologic model parameters and their multi-level interactions affecting model outputs, facilitating uncertainty propagation in a reduced dimensional space. The proposed methodology is applied to the Xiangxi River watershed in China to demonstrate its validity and applicability, as well as its capability of revealing complex and dynamic parameter interactions. A set of reduced polynomial chaos expansions (PCEs) only with statistically significant terms can be obtained based on the results of factorial analysis of variance (ANOVA), achieving a reduction of uncertainty in hydrologic predictions. The predictive performance of reduced PCEs is verified by comparing against standard PCEs and the Monte Carlo with Latin hypercube sampling (MC-LHS) method in terms of reliability, sharpness, and Nash-Sutcliffe efficiency (NSE). Results reveal that the reduced PCEs are able to capture hydrologic behaviors of the Xiangxi River watershed, and they are efficient functional representations for propagating uncertainties in hydrologic predictions.

A fourth order spline collocation approach for a business cycle model

Science.gov (United States)

Sayfy, A.; Khoury, S.; Ibdah, H.

2013-10-01

A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.

THE CASE FOR VERB-ADJECTIVE COLLOCATIONS: CORPUS-BASED ANALYSIS AND LEXICOGRAPHICAL TREATMENT

Directory of Open Access Journals (Sweden)

Moisés Almela

2011-10-01

Full Text Available This article explores a type of co-occurrence pattern which cannot be adequately described by existing models of collocation, and for which combinatory dictionaries have yet failed to provide sufficient information. The phenomenon of “oblique inter-collocation”, as I propose to call it, is characterised by a concatenation of syntagmatic preferences which partially contravenes the habitual grammatical order of semantic selection. In particular, I will examine some of the effects which the verb cause exerts on the distribution of attributive adjectives in the context of specific noun classes. The procedure for detecting and describing patterns of oblique inter-collocation is illustrated by means of SketchEngine corpus query tools. Based on the data extracted from a large-scale corpus, this paper carries out a critical analysis of the micro-structure in Oxford Collocations Dictionary.

An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method

International Nuclear Information System (INIS)

Ma Xiang; Zabaras, Nicholas

2009-01-01

A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media

Composite multi-modal vibration control for a stiffened plate using non-collocated acceleration sensor and piezoelectric actuator

International Nuclear Information System (INIS)

Li, Shengquan; Li, Juan; Mo, Yueping; Zhao, Rong

2014-01-01

A novel active method for multi-mode vibration control of an all-clamped stiffened plate (ACSP) is proposed in this paper, using the extended-state-observer (ESO) approach based on non-collocated acceleration sensors and piezoelectric actuators. Considering the estimated capacity of ESO for system state variables, output superposition and control coupling of other modes, external excitation, and model uncertainties simultaneously, a composite control method, i.e., the ESO based vibration control scheme, is employed to ensure the lumped disturbances and uncertainty rejection of the closed-loop system. The phenomenon of phase hysteresis and time delay, caused by non-collocated sensor/actuator pairs, degrades the performance of the control system, even inducing instability. To solve this problem, a simple proportional differential (PD) controller and acceleration feed-forward with an output predictor design produce the control law for each vibration mode. The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the Smith Predictor technology. In order to improve the vibration control performance, the chaos optimization method based on logistic mapping is employed to auto-tune the parameters of the feedback channel. The experimental control system for the ACSP is tested using the dSPACE real-time simulation platform. Experimental results demonstrate that the proposed composite active control algorithm is an effective approach for suppressing multi-modal vibrations. (paper)

Multimodal interaction design in collocated mobile phone use

NARCIS (Netherlands)

El-Ali, A.; Lucero, A.; Aaltonen, V.

2011-01-01

In the context of the Social and Spatial Interactions (SSI) platform, we explore how multimodal interaction design (input and output) can augment and improve the experience of collocated, collaborative activities using mobile phones. Based largely on our prototype evaluations, we reflect on and

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

Energy Technology Data Exchange (ETDEWEB)

Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)

2012-07-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

International Nuclear Information System (INIS)

Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.

2012-01-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Extending Binary Collocations: (Lexicographical Implications of Going beyond the Prototypical a – b

Directory of Open Access Journals (Sweden)

Dušan Gabrovšek

2014-05-01

Full Text Available The paper focuses primarily on the Sinclairian concept of extended units of meaning in general and on extended collocations in particular, investigating their nature and types. Such extended units are extremely varied and diverse; they are regarded as instances of the functioning of the coselection principle. Some extended forms are used far more commonly that the corresponding prototypical (binary sequences. The final section delves into the ABCs of extended collocations in the context of lexicography, suggesting that dictionaries should make an effort to include a selection of such strings, especially for encoding tasks that are to be shown as examples of use. Most dictionaries incorporate very few such “loose” units, probably because of a powerful tradition to include as examples of use chiefly binary collocations and full sentences.

Entropy Stable Staggered Grid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier--Stokes Equations

KAUST Repository

Parsani, Matteo

2016-10-04

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Collocations and grammatical patterns in a Multilingual Online Term ...

African Journals Online (AJOL)

user

equivalents for key concepts in the African languages, but also additional con- ... for, inter alia, computational identification and extraction of collocations exist; .... sult' is to be followed by a prepositional phrase in which the preposition is.

Discrete Chebyshev nets and a universal permutability theorem

International Nuclear Information System (INIS)

Schief, W K

2007-01-01

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

Responding to Research Challenges Related to Studying L2 Collocational Use in Professional Academic Discourse

DEFF Research Database (Denmark)

Henriksen, Birgit; Westbrook, Pete

2017-01-01

and classifying collocations used by L2 speakers in advanced, domain-specific oral academic discourse. The main findings seem to suggest that to map an informant’s complete collocational use and to get an understanding of disciplinary differences, we need to not only take account of general, academic and domain...

Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank

DEFF Research Database (Denmark)

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

2013-01-01

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

An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems

Directory of Open Access Journals (Sweden)

Shuang Wang

2012-01-01

Full Text Available As an efficient tool, radial basis function (RBF has been widely used for the multivariate approximation, interpolating continuous, and the solution of the particle differential equations. However, ill-conditioned interpolation matrix may be encountered when the interpolation points are very dense or irregularly arranged. To avert this problem, RBFs with variable shape parameters are introduced, and several new variation strategies are proposed. Comparison with the RBF with constant shape parameters are made, and the results show that the condition number of the interpolation matrix grows much slower with our strategies. As an application, an improved collocation meshless method is formulated by employing the new RBF. In addition, the Hermite-type interpolation is implemented to handle the Neumann boundary conditions and an additional sine/cosine basis is introduced for the Helmlholtz equation. Then, two interior acoustic problems are solved with the presented method; the results demonstrate the robustness and effectiveness of the method.

Optimization of Low-Thrust Spiral Trajectories by Collocation

Science.gov (United States)

Falck, Robert D.; Dankanich, John W.

2012-01-01

As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.

The Challenge of English Language Collocation Learning in an ES/FL Environment: PRC Students in Singapore

Science.gov (United States)

Ying, Yang

2015-01-01

This study aimed to seek an in-depth understanding about English collocation learning and the development of learner autonomy through investigating a group of English as a Second Language (ESL) learners' perspectives and practices in their learning of English collocations using an AWARE approach. A group of 20 PRC students learning English in…

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

Science.gov (United States)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation

Energy Technology Data Exchange (ETDEWEB)

Alwan, Aravind; Aluru, N.R.

2013-12-15

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems.

Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation

International Nuclear Information System (INIS)

Alwan, Aravind; Aluru, N.R.

2013-01-01

This paper presents a data-driven framework for performing uncertainty quantification (UQ) by choosing a stochastic model that accurately describes the sources of uncertainty in a system. This model is propagated through an appropriate response surface function that approximates the behavior of this system using stochastic collocation. Given a sample of data describing the uncertainty in the inputs, our goal is to estimate a probability density function (PDF) using the kernel moment matching (KMM) method so that this PDF can be used to accurately reproduce statistics like mean and variance of the response surface function. Instead of constraining the PDF to be optimal for a particular response function, we show that we can use the properties of stochastic collocation to make the estimated PDF optimal for a wide variety of response functions. We contrast this method with other traditional procedures that rely on the Maximum Likelihood approach, like kernel density estimation (KDE) and its adaptive modification (AKDE). We argue that this modified KMM method tries to preserve what is known from the given data and is the better approach when the available data is limited in quantity. We test the performance of these methods for both univariate and multivariate density estimation by sampling random datasets from known PDFs and then measuring the accuracy of the estimated PDFs, using the known PDF as a reference. Comparing the output mean and variance estimated with the empirical moments using the raw data sample as well as the actual moments using the known PDF, we show that the KMM method performs better than KDE and AKDE in predicting these moments with greater accuracy. This improvement in accuracy is also demonstrated for the case of UQ in electrostatic and electrothermomechanical microactuators. We show how our framework results in the accurate computation of statistics in micromechanical systems

Finite Volume Methods for Incompressible Navier-Stokes Equations on Collocated Grids with Nonconformal Interfaces

DEFF Research Database (Denmark)

Kolmogorov, Dmitry

turbine computations, collocated grid-based SIMPLE-like algorithms are developed for computations on block-structured grids with nonconformal interfaces. A technique to enhance both the convergence speed and the solution accuracy of the SIMPLE-like algorithms is presented. The erroneous behavior, which...... versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail...... Block LU relaxation scheme is shown to possess several optimal conditions, which enables to preserve high efficiency of the multigrid solver on both conformal and nonconformal grids. The developments are done using a parallel MPI algorithm, which can handle multiple numbers of interfaces with multiple...

A Comparative Study of the Use of Collocation in Iranian High School Textbooks and American English File Books

Directory of Open Access Journals (Sweden)

Mohsen Shahrokhi

2014-05-01

Full Text Available The present study investigates the extent to which lexical and grammatical collocations are used in Iranian high school English textbooks, compared with the American English File books. To achieve the purposes of this study, this study had to be carried out in two phases. In the first phase, the content of the instructional textbooks, that is, American English File book series, Book 2 and Iranian high school English Book 3, were analyzed to find the frequencies and proportions of the collocations used in the textbooks. Since the instructional textbooks used in the two teaching environments (i.e., Iranian high schools and language institutes were not equal with regard to the density of texts, from each textbook just the first 6000 words, content words as well as function words, were considered. Then, the frequencies of the collocations among the first 6000 words in high school English Book 3 and American English File Book 2 were determined.The results of the statistical analyses revealed that the two text book series differ marginally in terms of frequency and type of collocations. Major difference existed between them when it came to lexical collocations in American English File book 2.

Performance evaluation of high rate space–time trellis-coded modulation using Gauss–Chebyshev quadrature technique

CSIR Research Space (South Africa)

Sokoya, O

2008-05-01

Full Text Available combines both simplicity and accuracy in finding the closed form expression of the PEP. The paper is organised as follows. In Section 2, we discuss the general transmission model of the HR-STTCM and the channel model. In Section 3, we describe... the derivation of the PEP using the Gauss–Chebyshev quadrature technique and also give a numerical example. In Section 4, we use the PEP obtained in Section 3 to estimate the average BEP for slow fading channels. Section 5 concludes the paper with discussion...

Using Small Parallel Corpora to Develop Collocation-Centred Activities in Specialized Translation Classes

Directory of Open Access Journals (Sweden)

Postolea Sorina

2016-12-01

Full Text Available The research devoted to special languages as well as the activities carried out in specialized translation classes tend to focus primarily on one-word or multi-word terminological units. However, a very important part in the making of specialist registers and texts is played by specialised collocations, i.e. relatively stable word combinations that do not designate concepts but are nevertheless of frequent use in a given field of activity. This is why helping students acquire competences relative to the identification and processing of collocations should become an important objective in specialised translation classes. An easily accessible and dependable resource that may be successfully used to this purpose is represented by corpora and corpus analysis tools, whose usefulness in translator training has been highlighted by numerous studies. This article proposes a series of practical, task-based activities-developed with the help of a small-size parallel corpus of specialised texts-that aim to raise the translation trainees′ awareness of the collocations present in specialised texts and to provide suggestions about their processing in translation.

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

Science.gov (United States)

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

2008-11-01

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

A nodal collocation approximation for the multi-dimensional PL equations - 2D applications

International Nuclear Information System (INIS)

Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.

2008-01-01

A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P L equations. In this work, the derivation of the P L equations for multi-dimensional geometries is reviewed and a nodal collocation method is developed to discretize these equations on a rectangular mesh based on the expansion of the neutronic fluxes in terms of orthogonal Legendre polynomials. The performance of the method and the dominant transport Lambda Modes are obtained for a homogeneous 2D problem, a heterogeneous 2D anisotropic scattering problem, a heterogeneous 2D problem and a benchmark problem corresponding to a MOX fuel reactor core

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

Science.gov (United States)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of

Collocational Networks Supporting Strategic Planning of Brand Communication: Analysis of Quarterly Reports of Telecommunication Companies

Directory of Open Access Journals (Sweden)

Pentti Järvi

2004-10-01

Full Text Available This study addresses analysing quarterly reports from a brandtheoretical viewpoint. The study addresses the issue through a method which introduces both a quantitative tool based on linguistic theory and qualitative decisions of the researchers. The research objects of this study are two quarterly reports each of three telecommunications companies: Ericsson, Motorola and Nokia. The method used is a collocational network. The analyses show that there are differences in communication and message strategies among investigated companies and also changes during a quite short period in each company

A numerical comparison between the spatially-growing and temporally-growing disturbance in a pipe

Energy Technology Data Exchange (ETDEWEB)

Pacheco, Rafael J. [Universidad de Guanajuato, Guanajuato (Mexico); Pacheco Vega, Arturo [University of Nortre Dame, IN (United States); Pacheco Vega, H. Raul [University of British Columbia, Vancouver (Canada)

2001-08-01

The linear stability of Poiseuille flow in a pipe is examined for the infinitesimal disturbances propagating in both, time and space. The numerical procedure for obtaining the eigenvalues of the linear problem and its adjoint is based on the spectral collocation method with shifted Chebyshev polynomials. The Fredholm alternative is then applied to determine the group velocity. We show that the temporal damping rates of axisymmetric infinitesimal perturbations are related to those in space by the group velocity in accord with the theory first developed by Gaster. [Spanish] Se examina la estabilidad lineal del flujo de Poiseuille en una tuberia para perturbaciones infinitesimales que se propagan en el tiempo y el espacio. El proceso numerico para obtener los valores caracteristicos del problema lineal y su adjunto se basa en el metodo espectral de colocacion con los polinomios de Chebyshev. La teoria de la alternativa de Fredholm se aplica a la determinacion de la velocidad de grupo. Se demuestra que las razones de decaimiento para las perturbaciones axisimetrias infinitesimales temporales estan relacionadas con las espaciales mediante la velocidad de grupo, de acuerdo con la teoria presentada por primera vez por Gaster.

POD for Real-Time Simulation of Hyperelastic Soft Biological Tissue Using the Point Collocation Method of Finite Spheres

Directory of Open Access Journals (Sweden)

Suleiman Banihani

2013-01-01

Full Text Available The point collocation method of finite spheres (PCMFS is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD model order reduction (MOR technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.

Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system for prediction of financial and energy market data

Directory of Open Access Journals (Sweden)

A.K. Parida

2016-09-01

Full Text Available In this paper Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system is presented for the prediction and analysis of financial and electrical energy market data. The normally used TSK-type feedforward fuzzy neural network is unable to take the full advantage of the use of the linear fuzzy rule base in accurate input–output mapping and hence the consequent part of the rule base is made nonlinear using polynomial or arithmetic basis functions. Further the Chebyshev polynomial functions provide an expanded nonlinear transformation to the input space thereby increasing its dimension for capturing the nonlinearities and chaotic variations in financial or energy market data streams. Also the locally recurrent neuro-fuzzy information system (LRNFIS includes feedback loops both at the firing strength layer and the output layer to allow signal flow both in forward and backward directions, thereby making the LRNFIS mimic a dynamic system that provides fast convergence and accuracy in predicting time series fluctuations. Instead of using forward and backward least mean square (FBLMS learning algorithm, an improved Firefly-Harmony search (IFFHS learning algorithm is used to estimate the parameters of the consequent part and feedback loop parameters for better stability and convergence. Several real world financial and energy market time series databases are used for performance validation of the proposed LRNFIS model.

Application of Computer Algebra Systems to the Construction of the Collocations and Least Residuals Method for Solving the 3D Navier–Stokes Equations

Directory of Open Access Journals (Sweden)

V. P. Shapeev

2014-01-01

Full Text Available The method of collocations and least residuals (CLR, which was proposed previously for the numerical solution of two-dimensional Navier–Stokes equations governing the stationary flows of a viscous incompressible fluid, is extended here for the three-dimensional case. The solution is sought in the implemented version of the method in the form of an expansion in the basis solenoidal functions. At all stages of the CLR method construction, a computer algebra system (CAS is applied for the derivation and verification of the formulas of the method and for their translation into arithmetic operators of the Fortran language. For accelerating the convergence of iterations a sufficiently universal algorithm is proposed, which is simple in its implementation and is based on the use of the Krylov’s subspaces. The obtained computational formulas of the CLR method were verified on the exact analytic solution of a test problem. Comparisons with the published numerical results of solving the benchmark problem of the 3D driven cubic cavity flow show that the accuracy of the results obtained by the CLR method corresponds to the known high-accuracy solutions.

A Fourier Collocation Approach for Transit-Time Ultrasonic Flowmeter Under Multi-Phase Flow Conditions

DEFF Research Database (Denmark)

Simurda, Matej; Lassen, Benny; Duggen, Lars

2017-01-01

A numerical model for a clamp-on transit-time ultrasonic flowmeter (TTUF) under multi-phase flow conditions is presented. The method solves equations of linear elasticity for isotropic heterogeneous materials with background flow where acoustic media are modeled by setting shear modulus to zero....... Spatial derivatives are calculated by a Fourier collocation method allowing the use of the fast Fourier transform (FFT) and time derivatives are approximated by a finite difference (FD) scheme. This approach is sometimes referred to as a pseudospectral time-domain method. Perfectly matched layers (PML......) are used to avoid wave-wrapping and staggered grids are implemented to improve stability and efficiency. The method is verified against exact analytical solutions and the effect of the time-staggering and associated lowest number of points per minimum wavelengths value is discussed. The method...

Hybrid Lanczos-type product methods

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals

Science.gov (United States)

Deimert, C.; Potter, M. E.; Okoniewski, M.

2016-12-01

The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

Science.gov (United States)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Gimme Context – towards New Domain-Specific Collocational Dictionaries

Directory of Open Access Journals (Sweden)

Sylvana Krausse

2011-04-01

Full Text Available The days of traditional drudgery-filled lexicography are long gone. Fortunately today, computers help in the enormous task of storing and analysing language in order to condense and store the found information in the form of dictionaries. In this paper, the way from a corpus to a small domain-specific collocational dictionary will be described and thus exemplified based on the example of the domain-specific language of mining reclamation, which can be duplicated for other specific languages too. So far, domain-specific dictionaries are mostly rare as their creation is very labour- and thus cost-effective and all too often they are just a collection of terms plus translation without any information on how to use them in speech. Particular small domains which do not involve a lot of users have been disregarded by lexicographers as there is also always the question of how well it sells afterwards. Following this, I will describe the creation of a small collocational dictionary on mining reclamation language which is based on the consequent use of corpus information. It is relatively quick to realize in the design phase and is thought to provide the sort of linguistic information engineering experts need when they communicate in English or read specialist texts in the specific domain.

Strategies in Translating Collocations in Religious Texts from Arabic into English

Science.gov (United States)

Dweik, Bader S.; Shakra, Mariam M. Abu

2010-01-01

The present study investigated the strategies adopted by students in translating specific lexical and semantic collocations in three religious texts namely, the Holy Quran, the Hadith and the Bible. For this purpose, the researchers selected a purposive sample of 35 MA translation students enrolled in three different public and private Jordanian…

Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations

KAUST Repository

Castrillon, Julio

2016-03-02

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remapped onto a corresponding PDE with a fixed deterministic domain. We show that the solution can be analytically extended to a well defined region in CN with respect to the random variables. A sparse grid stochastic collocation method is then used to compute the mean and variance of the QoI. Finally, convergence rates for the mean and variance of the QoI are derived and compared to those obtained in numerical experiments.

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

KAUST Repository

Beck, Joakim

2011-12-22

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce a new effective class of Sparse Grids, based on the idea of selecting a priori the most profitable hierarchical surpluses, that, again, features better convergence properties compared to standard Smolyak or tensor product grids.

Numerical Simulation of Entropy Generation with Thermal Radiation on MHD Carreau Nanofluid towards a Shrinking Sheet

Directory of Open Access Journals (Sweden)

Muhammad Mubashir Bhatti

2016-05-01

Full Text Available In this article, entropy generation with radiation on non-Newtonian Carreau nanofluid towards a shrinking sheet is investigated numerically. The effects of magnetohydrodynamics (MHD are also taken into account. Firstly, the governing flow problem is simplified into ordinary differential equations from partial differential equations with the help of similarity variables. The solution of the resulting nonlinear differential equations is solved numerically with the help of the successive linearization method and Chebyshev spectral collocation method. The influence of all the emerging parameters is discussed with the help of graphs and tables. It is observed that the influence of magnetic field and fluid parameters oppose the flow. It is also analyzed that thermal radiation effects and the Prandtl number show opposite behavior on temperature profile. Furthermore, it is also observed that entropy profile increases for all the physical parameters.

Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model

Science.gov (United States)

Dehghan, Mehdi; Mohammadi, Vahid

2017-03-01

As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

KAUST Repository

Farrell, Patricio

2015-04-30

© 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.

Spectral element method for wave propagation on irregular domains

Indian Academy of Sciences (India)

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

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

Science.gov (United States)

Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

2015-10-01

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

Teaching vocabulary using collocations versus using definitions in EFL classes

OpenAIRE

Altınok, Şerife İper

2000-01-01

Ankara : Institute of Economics and Social Sciences of Bilkent Univ., 2000. Thesis (Master's) -- Bilkent University, 2000. Includes bibliographical references leaves 40-43 Teaching words in collocations is a comparatively new technique and it is accepted as an effective one in vocabulary teaching. The purpose of this study was to find out whether teaching vocabulary would result in better learning and remembering vocabulary items. This study investigated the differences betw...

Spectral element method for wave propagation on irregular domains

Indian Academy of Sciences (India)

Yan Hui Geng

2018-03-14

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

Study on the Single Scattering of Elastic Waves by a Cylindrical Fiber with a Partially Imperfect Bonding Using the Collocation Point Method

Directory of Open Access Journals (Sweden)

Jun Zhang

2018-01-01

Full Text Available The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i the total scattering cross section (SCS is almost symmetric about the axis α=π/2 with respect to the location (α of the imperfect interface, (ii imperfect interfaces located at α=0 and α=π highly reduce the total SCS under a P-wave incidence and imperfect interfaces located at α=π/2 reduce the total SCS most significantly under SV-incidence, and (iii under a P-wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV-wave incidence.

The basis spline method and associated techniques

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1989-01-01

We outline the Basis Spline and Collocation methods for the solution of Partial Differential Equations. Particular attention is paid to the theory of errors, and the handling of non-self-adjoint problems which are generated by the collocation method. We discuss applications to Poisson's equation, the Dirac equation, and the calculation of bound and continuum states of atomic and nuclear systems. 12 refs., 6 figs

Study on dynamic behavior analysis of towed line array sensor

Directory of Open Access Journals (Sweden)

Hyun Kyoung Shin

2012-03-01

Full Text Available A set of equations of motion is derived for vibratory motions of an underwater cable connected to a moving vehicle at one end and with drogues at the other end. From the static analysis, cable configurations are obtained for different vehicle speeds and towing pretensions are determined by fluid resistance of drogues. Also the dynamic analysis is required to predict its vibratory motion. Nonlinear fluid drag forces greatly influence the dynamic tension. In this study, a numerical analysis program was developed to find out the characteristic of cable behaviour. The motion is described in terms of space and time coordinates based on Chebyshev polynomial expansions. For the spatial integration the collocation method is employed and the Newmark method is applied for the time integration. Dynamic tensions, displacements, velocities, accelerations were predicted in the time domain while natural frequencies and transfer functions were obtained in the frequency domain.

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

Science.gov (United States)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation

Directory of Open Access Journals (Sweden)

Hyung-Chu Lim

2008-12-01

Full Text Available Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

Parallel iterative solution of the Hermite Collocation equations on GPUs II

International Nuclear Information System (INIS)

Vilanakis, N; Mathioudakis, E

2014-01-01

Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation

Part 6. Internationalization and collocation of FBR fuel cycle facilities

International Nuclear Information System (INIS)

Stevenson, M.G.; Abramson, P.B.; LeSage, L.G.

1980-01-01

This report examines some of the non-proliferation, technical, and institutional aspects of internationalization and/or collocation of major facilities of the Fast Breeder Reactor (FBR) fuel cycle. The national incentives and disincentives for establishment of FBR Fuel Cycle Centers are enumerated. The technical, legal, and administrative considerations in determining the feasibility of FBR Fuel Cycle Centers are addressed by making comparisons with Light Water Reactor (LWR) centers which have been studied in detail by the IAEA and UNSRC

Unmanned aerial vehicle trajectory planning with direct methods

Science.gov (United States)

Geiger, Brian

A real-time method for trajectory optimization to maximize surveillance time of a fixed or moving ground target by one or more unmanned aerial vehicles (UAVs) is presented. The method accounts for performance limits of the aircraft, intrinsic properties of the camera, and external disturbances such as wind. Direct collocation with nonlinear programming is used to implement the method in simulation and onboard the Penn State/Applied Research Lab's testbed UAV. Flight test results compare well with simulation. Both stationary targets and moving targets, such as a low flying UAV, were successfully tracked in flight test. In addition, a new method using a neural network approximation is presented that removes the need for collocation and numerical derivative calculation. Neural networks are used to approximate the objective and dynamics functions in the optimization problem which allows for reduced computation requirements. The approximation reduces the size of the resulting nonlinear programming problem compared to direct collocation or pseudospectral methods. This method is shown to be faster than direct collocation and psuedospectral methods using numerical or automatic derivative techniques. The neural network approximation is also shown to be faster than analytical derivatives but by a lesser factor. Comparative results are presented showing similar accuracy for all methods. The method is modular and enables application to problems of the same class without network retraining.

Evolutionary optimization with data collocation for reverse engineering of biological networks.

Science.gov (United States)

Tsai, Kuan-Yao; Wang, Feng-Sheng

2005-04-01

Modern experimental biology is moving away from analyses of single elements to whole-organism measurements. Such measured time-course data contain a wealth of information about the structure and dynamic of the pathway or network. The dynamic modeling of the whole systems is formulated as a reverse problem that requires a well-suited mathematical model and a very efficient computational method to identify the model structure and parameters. Numerical integration for differential equations and finding global parameter values are still two major challenges in this field of the parameter estimation of nonlinear dynamic biological systems. We compare three techniques of parameter estimation for nonlinear dynamic biological systems. In the proposed scheme, the modified collocation method is applied to convert the differential equations to the system of algebraic equations. The observed time-course data are then substituted into the algebraic system equations to decouple system interactions in order to obtain the approximate model profiles. Hybrid differential evolution (HDE) with population size of five is able to find a global solution. The method is not only suited for parameter estimation but also can be applied for structure identification. The solution obtained by HDE is then used as the starting point for a local search method to yield the refined estimates.

Metaphors in terminological collocations in English language and their equivalents in Serbian

Directory of Open Access Journals (Sweden)

Orčić Lidija S.

2017-01-01

Full Text Available The framework of this paper is the theory of conceptual metaphor where metaphor is the transfer of a more concrete source domain into a more abstract target domain. Metaphor is a fundamental human ability to speak about abstract concepts using specific terms where the meaning of a term is transferred to another, thus achieving semantic extensions. Although it was thought that in terminology polysemantic expressions are not desirable, in recent decades this traditional view has been abandoned. Metaphor is used not only as a linguistic decoration in language, but as a means of argumentation. It may be noted that the metaphor, as a universal phenomenon, is also common in business English discourse. The subject of our interest is to investigate collocations made up of those nouns and adjectives, which, according to the Oxford Business English Dictionary for Learners of English, are most frequently used in this field. The main objective of this work is to identify and analyze the source and target domains in metaphors in English collocations that contain these nouns and adjectives, and detect mechanisms applied in translating into Serbian. We categorised metaphors in collocations into four groups. The first group consists of metaphors in which the source domain is expressed with the living beings: inanimate entities are described as if they were alive. In these examples, the personification is used to explain abstract concepts, forces and processes in order to present them in a more understandable way. The second group consists of metaphors in which animals are the source domain and their behavior and characteristics serve as a starting point. In business discourse people and institutions are described with such metaphors. In the third group we included the metaphors based on objects that users are familiar with in everyday life. The fourth group consists of metaphors in which the source domain are natural phenomena. When translating a metaphor we

ENGLISH COLLOCATIONS OF THE VERBS “TO BE”, “TO HAVE” AND “TO TAKE” AND THEIR EQUIVALENTS IN GERMAN, FRENCH AND ITALIAN LANGUAGES: LINGUISTIC–CULTURAL ASPECT

Directory of Open Access Journals (Sweden)

Anna Nikolaevna Panamaryova

2013-10-01

Full Text Available The aim of this research is to find out conceptual characteristics of English, German, French, Italian languages world image. The subject of this paper is English collocations with the verbs “to be”, “to have” and “to take” and their equivalents in German, French and Italian languages. The task of this paper is to compare English collocations of the verbs “to be”, “to have” and “to take” and their equivalents in German, French and Italian languages in linguistic–cultural aspect. In Russian language studies such word groups are called “synlexis”. This term was coined by G. I. Klimovskaya, the professor ofTomskStateUniversity. The main method of the research is a comparative study of linguistic units. The conclusions made in the research are essential in the further study of European linguistic world image and can be used in textbooks on Cultural Linguistics.The practical result of the research can be a cross-cultural collocation dictionary of some languages. Such a dictionary is important for linguists, translators and people studying foreign languages.DOI: http://dx.doi.org/10.12731/2218-7405-2013-8-32

Benchmarking the Collocation Stand-Alone Library and Toolkit (CSALT)

Science.gov (United States)

Hughes, Steven; Knittel, Jeremy; Shoan, Wendy; Kim, Youngkwang; Conway, Claire; Conway, Darrel J.

2017-01-01

This paper describes the processes and results of Verification and Validation (VV) efforts for the Collocation Stand Alone Library and Toolkit (CSALT). We describe the test program and environments, the tools used for independent test data, and comparison results. The VV effort employs classical problems with known analytic solutions, solutions from other available software tools, and comparisons to benchmarking data available in the public literature. Presenting all test results are beyond the scope of a single paper. Here we present high-level test results for a broad range of problems, and detailed comparisons for selected problems.

Comparing multiple model-derived aerosol optical properties to spatially collocated ground-based and satellite measurements

Science.gov (United States)

Ocko, Ilissa B.; Ginoux, Paul A.

2017-04-01

Anthropogenic aerosols are a key factor governing Earth's climate and play a central role in human-caused climate change. However, because of aerosols' complex physical, optical, and dynamical properties, aerosols are one of the most uncertain aspects of climate modeling. Fortunately, aerosol measurement networks over the past few decades have led to the establishment of long-term observations for numerous locations worldwide. Further, the availability of datasets from several different measurement techniques (such as ground-based and satellite instruments) can help scientists increasingly improve modeling efforts. This study explores the value of evaluating several model-simulated aerosol properties with data from spatially collocated instruments. We compare aerosol optical depth (AOD; total, scattering, and absorption), single-scattering albedo (SSA), Ångström exponent (α), and extinction vertical profiles in two prominent global climate models (Geophysical Fluid Dynamics Laboratory, GFDL, CM2.1 and CM3) to seasonal observations from collocated instruments (AErosol RObotic NETwork, AERONET, and Cloud-Aerosol Lidar with Orthogonal Polarization, CALIOP) at seven polluted and biomass burning regions worldwide. We find that a multi-parameter evaluation provides key insights on model biases, data from collocated instruments can reveal underlying aerosol-governing physics, column properties wash out important vertical distinctions, and improved models does not mean all aspects are improved. We conclude that it is important to make use of all available data (parameters and instruments) when evaluating aerosol properties derived by models.

A New Six-Parameter Model Based on Chebyshev Polynomials for Solar Cells

Directory of Open Access Journals (Sweden)

Shu-xian Lun

2015-01-01

Full Text Available This paper presents a new current-voltage (I-V model for solar cells. It has been proved that series resistance of a solar cell is related to temperature. However, the existing five-parameter model ignores the temperature dependence of series resistance and then only accurately predicts the performance of monocrystalline silicon solar cells. Therefore, this paper uses Chebyshev polynomials to describe the relationship between series resistance and temperature. This makes a new parameter called temperature coefficient for series resistance introduced into the single-diode model. Then, a new six-parameter model for solar cells is established in this paper. This new model can improve the accuracy of the traditional single-diode model and reflect the temperature dependence of series resistance. To validate the accuracy of the six-parameter model in this paper, five kinds of silicon solar cells with different technology types, that is, monocrystalline silicon, polycrystalline silicon, thin film silicon, and tripe-junction amorphous silicon, are tested at different irradiance and temperature conditions. Experiment results show that the six-parameter model proposed in this paper is an I-V model with moderate computational complexity and high precision.

An improved triple collocation algorithm for decomposing autocorrelated and white soil moisture retrieval errors

Science.gov (United States)

If not properly account for, auto-correlated errors in observations can lead to inaccurate results in soil moisture data analysis and reanalysis. Here, we propose a more generalized form of the triple collocation algorithm (GTC) capable of decomposing the total error variance of remotely-sensed surf...

A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

KAUST Repository

Bourantas, Georgios

2013-12-01

A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a collocated or a semi-staggered "grid" configuration. The developed numerical scheme approximates the unknown field functions using the Moving Least Squares approximation. A velocity, along with a pressure correction scheme is applied in the context of the meshless point collocation method. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it is a truly meshless method, (ii) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (iii) it incorporates simplicity and accuracy, (iv) results can be obtained using collocated or semi-staggered "grids", (v) there is no need for the usage of a curvilinear system of coordinates and (vi) it can solve steady and unsteady flows. The lid-driven cavity flow problem, for Reynolds numbers up to 5000, has been considered, by using both staggered and collocated grid configurations. Following, the Backward-Facing Step (BFS) flow problem was considered for Reynolds numbers up to 800 using a staggered grid. As a final example, the case of a laminar flow in a two-dimensional tube with an obstacle was examined. © 2013 Elsevier Ltd.

Computation of saddle-type slow manifolds using iterative methods

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall

2015-01-01

with respect to , appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples, including a model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables, and the computation of homoclinic connections in the Fitz......This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence...

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis-Menten kinetics and assessment of numerical methods.

Science.gov (United States)

Pereira, Félix Monteiro; Oliveira, Samuel Conceição

2016-11-01

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis-Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis-Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis-Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion-reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.

Corpus-Based Websites to Promote Learner Autonomy in Correcting Writing Collocation Errors

Directory of Open Access Journals (Sweden)

Pham Thuy Dung

2016-12-01

Full Text Available The recent yet powerful emergence of E-learning and using online resources in learning EFL (English as a Foreign Language has helped promote learner autonomy in language acquisition including self-correcting their mistakes. This pilot study despite conducted on a modest sample of 25 second year students majoring in Business English at Hanoi Foreign Trade University is an initial attempt to investigate the feasibility of using corpus-based websites to promote learner autonomy in correcting collocation errors in EFL writing. The data is collected using a pre-questionnaire and a post-interview aiming to find out the participants’ change in belief and attitude toward learner autonomy in collocation errors in writing, the extent of their success in using the corpus-based websites to self-correct the errors and the change in their confidence in self-correcting the errors using the websites. The findings show that a significant majority of students have shifted their belief and attitude toward a more autonomous mode of learning, enjoyed a fair success of using the websites to self-correct the errors and become more confident. The study also yields an implication that a face-to-face training of how to use these online tools is vital to the later confidence and success of the learners

ANALYSIS OF SPECIALISED COLLOCATIONS IN THE AREA OF REMOTE SENSING IN THE PERSPECTIVE OF PHRASEOLOGY

Directory of Open Access Journals (Sweden)

Diva Cardoso de CAMARGO

2013-12-01

Full Text Available The aim of this research is to build and analyze a parallel corpus in the field of remote sensing in order to identify, according to its frequency, specialized collocations in English and then search for their equivalents in Portuguese. The research is based on the interdisciplinary approach of Corpus-Based Translation Studies (BAKER, 1995; CAMARGO, 2007, Corpus Linguistics (BERBER SARDINHA, 2004; TOGNINI-BONELLI, 2001, Phraseology (ORENHA-OTTAIANO, 2009; PAVEL, 1993, and some principles of Terminology (BARROS, 2004. For manipulating the corpora, the program WordSmith Tools (SCOTT, 2012 version 6.0 is used. To support this study, two comparable corpora in English and Portuguese were also built from articles published in both national and international journals in remote sensing. The results show that the collocations in Portuguese seem to be still in the process of conventionalization, as the translators made use of greater variation in their translational options, which can be a way to make the text clearer for the reader.

Comparison of multiphase mixing simulations performed on a staggered and a collocated grid

International Nuclear Information System (INIS)

Leskovar, M.

2000-01-01

During a severe reactor accident following core meltdown when the molten fuel comes into contact with the coolant water a steam explosion may occur. The premixing phase of a steam explosion covers the interaction of the melt jet or droplets with the water prior to any steam explosion occurrence. To get a better insight of the hydrodynamic processes during the premixing phase beside hot premixing experiments, where the water evaporation is significant, also cold isothermal premixing experiments are performed. To analyze the cold premixing experiments the computer code ESE has been developed. The specialty of ESE is that it uses a combined single-multiphase flow model. Because of problems with the convergence of the momentum equation written in conservative form on a staggered grid, the development of a collocated grid version of ESE was planed. But since we obtained the commercial code CFX-4.3, which uses a collocated variable arrangement, we decided first to test the capabilities of CFX-4.3. With ESE and CFX-4.3 the cold premixing experiment Q08 has been simulated. In the paper the simulation results performed with both codes are presented and commented in comparison to experimental data. (author)

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

Science.gov (United States)

Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.

2015-01-01

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Collocation mismatch uncertainties in satellite aerosol retrieval validation

Science.gov (United States)

Virtanen, Timo H.; Kolmonen, Pekka; Sogacheva, Larisa; Rodríguez, Edith; Saponaro, Giulia; de Leeuw, Gerrit

2018-02-01

Satellite-based aerosol products are routinely validated against ground-based reference data, usually obtained from sun photometer networks such as AERONET (AEROsol RObotic NETwork). In a typical validation exercise a spatial sample of the instantaneous satellite data is compared against a temporal sample of the point-like ground-based data. The observations do not correspond to exactly the same column of the atmosphere at the same time, and the representativeness of the reference data depends on the spatiotemporal variability of the aerosol properties in the samples. The associated uncertainty is known as the collocation mismatch uncertainty (CMU). The validation results depend on the sampling parameters. While small samples involve less variability, they are more sensitive to the inevitable noise in the measurement data. In this paper we study systematically the effect of the sampling parameters in the validation of AATSR (Advanced Along-Track Scanning Radiometer) aerosol optical depth (AOD) product against AERONET data and the associated collocation mismatch uncertainty. To this end, we study the spatial AOD variability in the satellite data, compare it against the corresponding values obtained from densely located AERONET sites, and assess the possible reasons for observed differences. We find that the spatial AOD variability in the satellite data is approximately 2 times larger than in the ground-based data, and the spatial variability correlates only weakly with that of AERONET for short distances. We interpreted that only half of the variability in the satellite data is due to the natural variability in the AOD, and the rest is noise due to retrieval errors. However, for larger distances (˜ 0.5°) the correlation is improved as the noise is averaged out, and the day-to-day changes in regional AOD variability are well captured. Furthermore, we assess the usefulness of the spatial variability of the satellite AOD data as an estimate of CMU by comparing the

A Comparison of the Performance Improvement by Collocated and Noncollocated Active Damping in Motion Systems

NARCIS (Netherlands)

Babakhani, B.; de Vries, Theodorus J.A.; van Amerongen, J.

2012-01-01

In this paper, both collocated and noncollocated active vibration control (AVC) of a the vibrations in a motion system are considered. Pole-zero plots of both the AVC loop and the motion-control (MC) loop are used to analyze the effect of the applied active damping on the system dynamics. Using

Non-stationary covariance function modelling in 2D least-squares collocation

Science.gov (United States)

Darbeheshti, N.; Featherstone, W. E.

2009-06-01

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.

Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

KAUST Repository

Pestana, Reynam C.; Stoffa, Paul L.

2009-01-01

an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second

Comments on the comparison of global methods for linear two-point boundary value problems

International Nuclear Information System (INIS)

de Boor, C.; Swartz, B.

1977-01-01

A more careful count of the operations involved in solving the linear system associated with collocation of a two-point boundary value problem using a rough splines reverses results recently reported by others in this journal. In addition, it is observed that the use of the technique of ''condensation of parameters'' can decrease the computer storage required. Furthermore, the use of a particular highly localized basis can also reduce the setup time when the mesh is irregular. Finally, operation counts are roughly estimated for the solution of certain linear system associated with two competing collocation methods; namely, collocation with smooth splines and collocation of the equivalent first order system with continuous piecewise polynomials

The application of the Chebyshev-spectral method in transport phenomena

CERN Document Server

Guo, Weidong; Narayanan, Ranga

2012-01-01

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

A unified methodology for single- and multiobjective in-core fuel management optimisation based on augmented Chebyshev scalarisation and a harmony search algorithm

International Nuclear Information System (INIS)

Schlünz, E.B.; Bokov, P.M.; Prinsloo, R.H.; Vuuren, J.H. van

2016-01-01

Highlights: • Unified methodology for in-core fuel management optimisation (ICFMO). • Addresses single- and multiobjective constrained and unconstrained ICFMO problems. • Augmented Chebyshev scalarising objective function with additive penalty function. • Harmony search algorithm yields high-quality solution or approximate Pareto set. • Methodology provides cycle-to-cycle optimisation decision support capabilities. - Abstract: The in-core fuel management optimisation (ICFMO) problem is the problem of finding an optimal fuel reload configuration for a nuclear reactor core. ICFMO may involve the pursuit of a single or multiple objectives, while satisfying several constraints. Very little multiobjective ICFMO research involving the fundamental notion of Pareto optimality has, however, been performed. In this paper, a unified methodology is proposed for the modelling and solution of single- and multiobjective ICFMO problems, be they constrained or unconstrained. With this methodology, ICFMO problems incorporating a variety of objectives and/or constraints may be modelled and solved rapidly, thus providing a cycle-to-cycle optimisation decision support capability for nuclear reactors. An augmented Chebyshev scalarising objective function is incorporated in the methodology for modelling any number of objectives, while an additive penalty function handles potential constraints. Furthermore, an adapted harmony search algorithm is used to solve a given ICFMO problem. The algorithm is able to yield a single solution or a nondominated set of solutions as result (depending on the number of objectives in a problem). The applicability of the methodology is demonstrated by solving (approximately) a variety of ICFMO test problems for the SAFARI-1 nuclear research reactor. The results indicate that the methodology may be used as an effective decision support tool for reactor operators tasked with designing reload configurations from cycle to cycle.

Tau method approximation of the Hubbell rectangular source integral

International Nuclear Information System (INIS)

Kalla, S.L.; Khajah, H.G.

2000-01-01

The Tau method is applied to obtain expansions, in terms of Chebyshev polynomials, which approximate the Hubbell rectangular source integral:I(a,b)=∫ b 0 (1/(√(1+x 2 )) arctan(a/(√(1+x 2 )))) This integral corresponds to the response of an omni-directional radiation detector situated over a corner of a plane isotropic rectangular source. A discussion of the error in the Tau method approximation follows

Vs30 and spectral response from collocated shallow, active- and passive-source Vs data at 27 sites in Puerto Rico

Science.gov (United States)

Odum, Jack K.; Stephenson, William J.; Williams, Robert A.; von Hillebrandt-Andrade, Christa

2013-01-01

Shear‐wave velocity (VS) and time‐averaged shear‐wave velocity to 30 m depth (VS30) are the key parameters used in seismic site response modeling and earthquake engineering design. Where VS data are limited, available data are often used to develop and refine map‐based proxy models of VS30 for predicting ground‐motion intensities. In this paper, we present shallow VS data from 27 sites in Puerto Rico. These data were acquired using a multimethod acquisition approach consisting of noninvasive, collocated, active‐source body‐wave (refraction/reflection), active‐source surface wave at nine sites, and passive‐source surface‐wave refraction microtremor (ReMi) techniques. VS‐versus‐depth models are constructed and used to calculate spectral response plots for each site. Factors affecting method reliability are analyzed with respect to site‐specific differences in bedrock VS and spectral response. At many but not all sites, body‐ and surface‐wave methods generally determine similar depths to bedrock, and it is the difference in bedrock VS that influences site amplification. The predicted resonant frequencies for the majority of the sites are observed to be within a relatively narrow bandwidth of 1–3.5 Hz. For a first‐order comparison of peak frequency position, predictive spectral response plots from eight sites are plotted along with seismograph instrument spectra derived from the time series of the 16 May 2010 Puerto Rico earthquake. We show how a multimethod acquisition approach using collocated arrays compliments and corroborates VS results, thus adding confidence that reliable site characterization information has been obtained.

On the equivalence of spherical splines with least-squares collocation and Stokes's formula for regional geoid computation

Science.gov (United States)

Ophaug, Vegard; Gerlach, Christian

2017-11-01

This work is an investigation of three methods for regional geoid computation: Stokes's formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

Big Data and HPC collocation: Using HPC idle resources for Big Data Analytics

OpenAIRE

MERCIER , Michael; Glesser , David; Georgiou , Yiannis; Richard , Olivier

2017-01-01

International audience; Executing Big Data workloads upon High Performance Computing (HPC) infrastractures has become an attractive way to improve their performances. However, the collocation of HPC and Big Data workloads is not an easy task, mainly because of their core concepts' differences. This paper focuses on the challenges related to the scheduling of both Big Data and HPC workloads on the same computing platform. In classic HPC workloads, the rigidity of jobs tends to create holes in ...

Radiation budget studies using collocated observations from advanced Very High Resolution Radiometer, High-Resolution Infrared Sounder/2, and Earth Radiation Budget Experiment instruments

Science.gov (United States)

Ackerman, Steven A.; Frey, Richard A.; Smith, William L.

1992-01-01

Collocated observations from the Advanced Very High Resolution Radiometer (AVHRR), High-Resolution Infrared Sounder/2 (HIRS/2), and Earth Radiation Budget Experiment (ERBE) instruments onboard the NOAA 9 satellite are combined to describe the broadband and spectral radiative properties of the earth-atmosphere system. Broadband radiative properties are determined from the ERBE observations, while spectral properties are determined from the HIRS/2 and AVHRR observations. The presence of clouds, their areal coverage, and cloud top pressure are determined from a combination of the HIRS/2 and the AVHRR observations. The CO2 slicing method is applied to the HIRS/2 to determine the presence of upper level clouds and their effective emissivity. The AVHRR data collocated within the HIRS/2 field of view are utilized to determine the uniformity of the scene and retrieve sea surface temperature. Changes in the top of the atmosphere longwave and shortwave radiative energy budgets, and the spectral distribution of longwave radiation are presented as a function of cloud amount and cloud top pressure. The radiative characteristics of clear sky conditions over oceans are presented as a function of sea surface temperature and atmospheric water vapor structure.

Photodissociation of NaH using time-dependent Fourier grid method

Indian Academy of Sciences (India)

We have solved the time dependent Schrödinger equation by using the Chebyshev polynomial scheme and Fourier grid Hamiltonian method to calculate the dissociation cross section of NaH molecule by 1-photon absorption from the 1+ state to the 1 state. We have found that the results differ significantly from an ...

Preventing chatter vibrations in heavy-duty turning operations in large horizontal lathes

Science.gov (United States)

Urbikain, G.; Campa, F.-J.; Zulaika, J.-J.; López de Lacalle, L.-N.; Alonso, M.-A.; Collado, V.

2015-03-01

Productivity and surface finish are typical user manufacturer requirements that are restrained by chatter vibrations sooner or later in every machining operation. Thus, manufacturers are interested in knowing, before building the machine, the dynamic behaviour of each machine structure with respect to another. Stability lobe graphs are the most reliable approach to analyse the dynamic performance. During heavy rough turning operations a model containing (a) several modes, or (b) modes with non-conventional (Cartesian) orientations is necessary. This work proposes two methods which are combined with multimode analysis to predict chatter in big horizontal lathes. First, a traditional single frequency model (SFM) is used. Secondly, the modern collocation method based on the Chebyshev polynomials (CCM) is alternatively studied. The models can be used to identify the machine design features limiting lathe productivity, as well as the threshold values for choosing good cutting parameters. The results have been compared with experimental tests in a horizontal turning centre. Besides the model and approach, this work offers real worthy values for big lathes, difficult to be got from literature.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

Science.gov (United States)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

Science.gov (United States)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

A moving boundary problem and orthogonal collocation in solving a dynamic liquid surfactant membrane model including osmosis and breakage

Directory of Open Access Journals (Sweden)

E.C. Biscaia Junior

2001-06-01

Full Text Available A dynamic kinetic-diffusive model for the extraction of metallic ions from aqueous liquors using liquid surfactant membranes is proposed. The model incorporates undesirable intrinsic phenomena such as swelling and breakage of the emulsion globules that have to be controlled during process operation. These phenomena change the spatial location of the chemical reaction during the course of extraction, resulting in a transient moving boundary problem. The orthogonal collocation method was used to transform the partial differential equations into an ordinary differential equation set that was solved by an implicit numerical routine. The model was found to be numerically stable and reliable in predicting the behaviour of zinc extraction with acidic extractant for long residence times.

Investigating electro-mechanical signals from collocated piezoelectric wafers for the reference-free damage diagnosis of a plate

International Nuclear Information System (INIS)

Kim, Eun Jin; Park, Hyun Woo; Kim, Min Koo; Sohn, Hoon

2011-01-01

The electro-mechanical (EM) signals from piezoelectric (PZT) wafers are investigated for reference-free damage diagnosis so that a notch in a plate can be detected without requiring direct comparison with a baseline EM signal. Two identical PZT wafers collocated on both surfaces of a plate are utilized for extracting the mode-converted Lamb wave signals created by a notch. As harmonic input voltage signals are exerted on the collocated PZT wafers, the corresponding mode-converted Lamb wave signals become steady-state in the presence of damage. Applying fast Fourier transform to these mode-converted Lamb wave signals followed by a proper normalization, the EM signals associated with the mode conversion can be obtained. The theoretical finding of this paper is validated through spectral element simulations of a cantilever beam with a notch. The effects of the size and the location of the notch on the mode-converted EM signals are investigated as well. Finally, the applicability of the decomposed EM signals to reference-free damage diagnosis is discussed

A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line

Directory of Open Access Journals (Sweden)

D. Baleanu

2013-01-01

fractional derivatives is based on modified generalized Laguerre polynomials Li(α,β(x with x∈Λ=(0,∞, α>−1, and β>0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.

Continuous multistep methods for volterra integro-differential ...

African Journals Online (AJOL)

A new class of numerical methods for Volterra integro-differential equations of the second order is developed. The methods are based on interpolation and collocation of the shifted Legendre polynomial as basis function with Trapezoidal quadrature rules. The convergence analysis revealed that the methods are consistent ...

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

Energy Technology Data Exchange (ETDEWEB)

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn [School of Information Science and Technology, ShanghaiTech University, Shanghai 200031 (China); Lin, Guang, E-mail: guanglin@purdue.edu [Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States)

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks.

Science.gov (United States)

Zou, An-Min; Dev Kumar, Krishna; Hou, Zeng-Guang

2010-09-01

This paper investigates the problem of output feedback attitude control of an uncertain spacecraft. Two robust adaptive output feedback controllers based on Chebyshev neural networks (CNN) termed adaptive neural networks (NN) controller-I and adaptive NN controller-II are proposed for the attitude tracking control of spacecraft. The four-parameter representations (quaternion) are employed to describe the spacecraft attitude for global representation without singularities. The nonlinear reduced-order observer is used to estimate the derivative of the spacecraft output, and the CNN is introduced to further improve the control performance through approximating the spacecraft attitude motion. The implementation of the basis functions of the CNN used in the proposed controllers depends only on the desired signals, and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the CNN approximation errors and external disturbances. The adaptive NN controller-II can efficiently avoid the over-estimation problem (i.e., the bound of the CNNs output is much larger than that of the approximated unknown function, and hence, the control input may be very large) existing in the adaptive NN controller-I. Both adaptive output feedback controllers using CNN can guarantee that all signals in the resulting closed-loop system are uniformly ultimately bounded. For performance comparisons, the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed. Simulation studies are presented to show the advantages of the proposed CNN-based output feedback approach over the standard adaptive output feedback approach.

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

Energy Technology Data Exchange (ETDEWEB)

Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)

2012-08-01

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

Spectral methods in numerical plasma simulation

International Nuclear Information System (INIS)

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

1989-01-01

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

Trajectory Optimization Based on Multi-Interval Mesh Refinement Method

Directory of Open Access Journals (Sweden)

Ningbo Li

2017-01-01

Full Text Available In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.

FTA Corpus: a parallel corpus of English and Spanish Free Trade Agreements for the study of specialized collocations

Directory of Open Access Journals (Sweden)

Pedro Patiño García

2013-04-01

Full Text Available This paper describes the Corpus of Free Trade Agreements (henceforth FTA, a specialized parallel corpus in English and Spanish from Europe and America and a smaller subcorpus in English-Norwegian and Spanish-Norwegian that was prepared and then aligned with Translation Corpus Aligner 2 (Hofland & Johansson, 1998. The data was taken from Free Trade Agreements. These agreements are specialized texts officially signed and ratified by several countries and blocks of countries in the last twenty years. Thus, FTAs are a rich repository for terminology and phraseology that is used in different fields of business activity throughout the world. The corpus contains around 1.37 million words in the English section and 1.48 million words in its Spanish counterpart, plus 60,000 words each in the Spanish-Norwegian and English-Norwegian subcorpus. The corpus is being used primarily to study the terms and specialized collocations that include these terms in this kind of specialized texts.Keywords: specialized collocation, specialized parallel corpus, corpus linguistics, Free Trade Agreement

Extrapolated stabilized explicit Runge-Kutta methods

Science.gov (United States)

Martín-Vaquero, J.; Kleefeld, B.

2016-12-01

Extrapolated Stabilized Explicit Runge-Kutta methods (ESERK) are proposed to solve multi-dimensional nonlinear partial differential equations (PDEs). In such methods it is necessary to evaluate the function nt times per step, but the stability region is O (nt2). Hence, the computational cost is O (nt) times lower than for a traditional explicit algorithm. In that way stiff problems can be integrated by the use of simple explicit evaluations in which case implicit methods usually had to be used. Therefore, they are especially well-suited for the method of lines (MOL) discretizations of parabolic nonlinear multi-dimensional PDEs. In this work, first s-stages first-order methods with extended stability along the negative real axis are obtained. They have slightly shorter stability regions than other traditional first-order stabilized explicit Runge-Kutta algorithms (also called Runge-Kutta-Chebyshev codes). Later, they are used to derive nt-stages second- and fourth-order schemes using Richardson extrapolation. The stability regions of these fourth-order codes include the interval [ - 0.01nt2, 0 ] (nt being the number of total functions evaluations), which are shorter than stability regions of ROCK4 methods, for example. However, the new algorithms neither suffer from propagation of errors (as other Runge-Kutta-Chebyshev codes as ROCK4 or DUMKA) nor internal instabilities. Additionally, many other types of higher-order (and also lower-order) methods can be obtained easily in a similar way. These methods also allow adaptation of the length step with no extra cost. Hence, the stability domain is adapted precisely to the spectrum of the problem at the current time of integration in an optimal way, i.e., with minimal number of additional stages. We compare the new techniques with other well-known algorithms with good results in very stiff diffusion or reaction-diffusion multi-dimensional nonlinear equations.

UN Method For The Critical Slab Problem In One-Speed Neutron Transport Theory

International Nuclear Information System (INIS)

Oeztuerk, Hakan; Guengoer, Sueleyman

2008-01-01

The Chebyshev polynomial approximation (U N method) is used to solve the critical slab problem in one-speed neutron transport theory using Marshak boundary condition. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. Numerical results obtained by the U N method are presented in the tables together with the results obtained by the well-known P N method for comparison. It is shown that the method converges rapidly with its easily executable equations.

Study of a Biparametric Family of Iterative Methods

Directory of Open Access Journals (Sweden)

B. Campos

2014-01-01

Full Text Available The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. This biparametric family includes the c-iterative methods and the well-known Chebyshev-Halley family. We find the analytical expressions for the fixed and critical points by solving 6-degree polynomials. We use the free critical points to get the parameter planes and, by observing them, we specify some values of (α, c with clear stable and unstable behaviors.

Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

KAUST Repository

Haji Ali, Abdul Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raul

2016-01-01

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

Multi-index Stochastic Collocation Convergence Rates for Random PDEs with Parametric Regularity

KAUST Repository

Haji Ali, Abdul Lateef

2016-08-26

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data, and naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods, i.e., we use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDE in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Matérn model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis. © 2016 SFoCM

An estimation of the height system bias parameter N (0) using least squares collocation from observed gravity and GPS-levelling data

DEFF Research Database (Denmark)

Sadiq, Muhammad; Tscherning, Carl C.; Ahmad, Zulfiqar

2009-01-01

This paper deals with the analysis of gravity anomaly and precise levelling in conjunction with GPS-Levelling data for the computation of a gravimetric geoid and an estimate of the height system bias parameter N-o for the vertical datum in Pakistan by means of least squares collocation technique...... covariance parameters has facilitated to achieve gravimetric height anomalies in a global geocentric datum. Residual terrain modeling (RTM) technique has been used in combination with the EGM96 for the reduction and smoothing of the gravity data. A value for the bias parameter N-o has been estimated...... with reference to the local GPS-Levelling datum that appears to be 0.705 m with 0.07 m mean square error. The gravimetric height anomalies were compared with height anomalies obtained from GPS-Levelling stations using least square collocation with and without bias adjustment. The bias adjustment minimizes...

Instability of a binary liquid film flowing down a slippery heated plate

Science.gov (United States)

Ellaban, E.; Pascal, J. P.; D'Alessio, S. J. D.

2017-09-01

In this paper, we study the stability of a binary liquid film flowing down a heated slippery inclined surface. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier-Stokes equations governing the flow with equations for the concentration and temperature. A Navier slip condition is applied at the liquid-solid interface. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We use a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld-type equations. We also obtain an asymptotic solution that yields an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. A weighted residual approximation is employed to derive a reduced model that is used to analyse the nonlinear effects. Good agreement between the linear stability analysis and nonlinear simulations provided by the weighted residual model is found.

Non-collocated fuzzy logic and input shaping control strategy for elastic joint manipulator: vibration suppression and time response analysis

Energy Technology Data Exchange (ETDEWEB)

Rashidifar, Mohammed Amin [Faculty of Mechanical Engineering, Islamic Azad University, SHADEGAN (Iran, Islamic Republic of); Rashidifar, Ali Amin, E-mail: rashidifar_58@yahoo.com [Computer Science, Islamic Azad University, SHADEGAN (Iran, Islamic Republic of)

2014-07-01

Conventional model-based control strategies are very complex and difficult to synthesize due to high complexity of the dynamics of robots manipulator considering joint elasticity. This paper presents investigations into the development of hybrid control schemes for trajectory tracking and vibration control of a flexible joint manipulator. To study the effectiveness of the controllers, initially a collocated proportional-derivative (P D)-type Fuzzy Logic Controller (FLC) is developed for tip angular position control of a flexible joint manipulator. This is then extended to incorporate a non-collocated Fuzzy Logic Controller and input shaping scheme for vibration reduction of the flexible joint system. The positive zero-vibration-derivative-derivative (ZVDD) shaper is designed based on the properties of the system. Simulation results of the response of the flexible joint manipulator with the controllers are presented in time and frequency domains. The performances of the hybrid control schemes are examined in terms of input tracking capability, level of vibration reduction and time response specifications. Finally, a comparative assessment of the control techniques is presented and discussed. (Author)

Temporal gravity field modeling based on least square collocation with short-arc approach

Science.gov (United States)

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

Milestones in the Development of Iterative Solution Methods

Directory of Open Access Journals (Sweden)

Owe Axelsson

2010-01-01

Full Text Available Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.

Vibration suppression in cutting tools using collocated piezoelectric sensors/actuators with an adaptive control algorithm

Energy Technology Data Exchange (ETDEWEB)

Radecki, Peter P [Los Alamos National Laboratory; Farinholt, Kevin M [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory; Bement, Matthew T [Los Alamos National Laboratory

2008-01-01

The machining process is very important in many engineering applications. In high precision machining, surface finish is strongly correlated with vibrations and the dynamic interactions between the part and the cutting tool. Parameters affecting these vibrations and dynamic interactions, such as spindle speed, cut depth, feed rate, and the part's material properties can vary in real-time, resulting in unexpected or undesirable effects on the surface finish of the machining product. The focus of this research is the development of an improved machining process through the use of active vibration damping. The tool holder employs a high bandwidth piezoelectric actuator with an adaptive positive position feedback control algorithm for vibration and chatter suppression. In addition, instead of using external sensors, the proposed approach investigates the use of a collocated piezoelectric sensor for measuring the dynamic responses from machining processes. The performance of this method is evaluated by comparing the surface finishes obtained with active vibration control versus baseline uncontrolled cuts. Considerable improvement in surface finish (up to 50%) was observed for applications in modern day machining.

Numerical methods for stochastic partial differential equations with white noise

CERN Document Server

Zhang, Zhongqiang

2017-01-01

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

Collocation lists as instruments for metaphor detection in corpora Listas de colocações como instrumentos para detecção de metáforas em corpora

Directory of Open Access Journals (Sweden)

Tony Berber Sardinha

2006-01-01

Full Text Available This paper reports a study on the use of collocation lists as instruments for detecting metaphors in corpora. A collocation list contains the collocations for selected words in corpora together with concordances for those words. As corpora become more available to metaphor researchers, there is a growing need for developing ways to gain access to as much data as the corpus can offer. The research described here has hopefully come some way toward meeting the challenges of developing tools for metaphor corpus research. Results suggest that the collocation lists seem to be a good pre-processing instrument for corpus research of metaphor, despite accuracy problems.Este trabalho apresenta uma pesquisa sobre o uso de listas de colocações como instrumentos para detecção de metáforas em corpora. Uma lista de colocação contém as colocações de palavras selecionadas de corpora juntamente com as concordâncias dessas palavras. Na medida que os corpora se tornam mais acessíveis aos pesquisadores de metáfora, começa a surgir uma necessidade de desenvolver maneiras de acessar a maior quantidade possível de dados que um corpus oferece. A pesquisa descrita aqui tentou enfrentar esse desafio, criando e testando ferramentas para pesquisa de metáfora baseada em corpus. Os resultados sugerem que as listas de colocações podem ser um instrumento eficaz de pré-processamento de corpus com vistas à análise humana de metáforas, a despeito de alguns problemas de precisão.

A Comparative Study on Optimal Structural Dynamics Using Wavelet Functions

Directory of Open Access Journals (Sweden)

Seyed Hossein Mahdavi

2015-01-01

Full Text Available Wavelet solution techniques have become the focus of interest among researchers in different disciplines of science and technology. In this paper, implementation of two different wavelet basis functions has been comparatively considered for dynamic analysis of structures. For this aim, computational technique is developed by using free scale of simple Haar wavelet, initially. Later, complex and continuous Chebyshev wavelet basis functions are presented to improve the time history analysis of structures. Free-scaled Chebyshev coefficient matrix and operation of integration are derived to directly approximate displacements of the corresponding system. In addition, stability of responses has been investigated for the proposed algorithm of discrete Haar wavelet compared against continuous Chebyshev wavelet. To demonstrate the validity of the wavelet-based algorithms, aforesaid schemes have been extended to the linear and nonlinear structural dynamics. The effectiveness of free-scaled Chebyshev wavelet has been compared with simple Haar wavelet and two common integration methods. It is deduced that either indirect method proposed for discrete Haar wavelet or direct approach for continuous Chebyshev wavelet is unconditionally stable. Finally, it is concluded that numerical solution is highly benefited by the least computation time involved and high accuracy of response, particularly using low scale of complex Chebyshev wavelet.

A pseudospectral collocation time-domain method for diffractive optics

DEFF Research Database (Denmark)

Dinesen, P.G.; Hesthaven, J.S.; Lynov, Jens-Peter

2000-01-01

We present a pseudospectral method for the analysis of diffractive optical elements. The method computes a direct time-domain solution of Maxwell's equations and is applied to solving wave propagation in 2D diffractive optical elements. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights...

some generalized two-step block hybrid numerov method for solving ...

African Journals Online (AJOL)

Nwokem et al.

ABSTRACT. This paper proposes a class of generalized two-step Numerov methods, a block hybrid type for the direct solution of general second order ordinary differential equations. Both the main method and additional methods were derived via interpolation and collocation procedures. The basic properties of zero ...

Fully consistent CFD methods for incompressible flow computations

DEFF Research Database (Denmark)

Kolmogorov, Dmitry; Shen, Wen Zhong; Sørensen, Niels N.

2014-01-01

Nowadays collocated grid based CFD methods are one of the most e_cient tools for computations of the ows past wind turbines. To ensure the robustness of the methods they require special attention to the well-known problem of pressure-velocity coupling. Many commercial codes to ensure the pressure...

A comparison of companion matrix methods to find roots of a trigonometric polynomial

Science.gov (United States)

Boyd, John P.

2013-08-01

A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements

Well-posedness and exact controllability of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation

Directory of Open Access Journals (Sweden)

Ruili Wen

2016-08-01

Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.

Discretisation of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements

Directory of Open Access Journals (Sweden)

E. D. Resende

2007-09-01

Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

Directory of Open Access Journals (Sweden)

Hassan Saberi Nik

2014-01-01

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

Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations

KAUST Repository

Abdulle, Assyr

2013-01-01

We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.

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

KAUST Repository

Chu, Chunlei

2012-07-01

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

Prediction of Navigation Satellite Clock Bias Considering Clock's Stochastic Variation Behavior with Robust Least Square Collocation

Directory of Open Access Journals (Sweden)

WANG Yupu

2016-06-01

Full Text Available In order to better express the characteristic of satellite clock bias (SCB and further improve its prediction precision, a new SCB prediction model is proposed, which can take the physical feature, cyclic variation and stochastic variation behaviors of the space-borne atomic clock into consideration by using a robust least square collocation (LSC method. The proposed model firstly uses a quadratic polynomial model with periodic terms to fit and abstract the trend term and cyclic terms of SCB. Then for the residual stochastic variation part and possible gross errors hidden in SCB data, the model employs a robust LSC method to process them. The covariance function of the LSC is determined by selecting an empirical function and combining SCB prediction tests. Using the final precise IGS SCB products to conduct prediction tests, the results show that the proposed model can get better prediction performance. Specifically, the results' prediction accuracy can enhance 0.457 ns and 0.948 ns respectively, and the corresponding prediction stability can improve 0.445 ns and 1.233 ns, compared with the results of quadratic polynomial model and grey model. In addition, the results also show that the proposed covariance function corresponding to the new model is reasonable.

An hp symplectic pseudospectral method for nonlinear optimal control

Science.gov (United States)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Multi-fidelity stochastic collocation method for computation of statistical moments

Energy Technology Data Exchange (ETDEWEB)

Zhu, Xueyu, E-mail: xueyu-zhu@uiowa.edu [Department of Mathematics, University of Iowa, Iowa City, IA 52242 (United States); Linebarger, Erin M., E-mail: aerinline@sci.utah.edu [Department of Mathematics, University of Utah, Salt Lake City, UT 84112 (United States); Xiu, Dongbin, E-mail: xiu.16@osu.edu [Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)

2017-07-15

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

Collocated Dataglyphs for large-message storage and retrieval

Science.gov (United States)

Motwani, Rakhi C.; Breidenbach, Jeff A.; Black, John R.

2004-06-01

In contrast to the security and integrity of electronic files, printed documents are vulnerable to damage and forgery due to their physical nature. Researchers at Palo Alto Research Center utilize DataGlyph technology to render digital characteristics to printed documents, which provides them with the facility of tamper-proof authentication and damage resistance. This DataGlyph document is known as GlyphSeal. Limited DataGlyph carrying capacity per printed page restricted the application of this technology to a domain of graphically simple and small-sized single-paged documents. In this paper the authors design a protocol motivated by techniques from the networking domain and back-up strategies, which extends the GlyphSeal technology to larger-sized, graphically complex, multi-page documents. This protocol provides fragmentation, sequencing and data loss recovery. The Collocated DataGlyph Protocol renders large glyph messages onto multiple printed pages and recovers the glyph data from rescanned versions of the multi-page documents, even when pages are missing, reordered or damaged. The novelty of this protocol is the application of ideas from RAID to the domain of DataGlyphs. The current revision of this protocol is capable of generating at most 255 pages, if page recovery is desired and does not provide enough data density to store highly detailed images in a reasonable amount of page space.

Demonstration of non-collocated vibration control of a flexible manipulator using electrical dynamic absorbers

International Nuclear Information System (INIS)

Kim, Sang-Myeong; Kim, Heungseob; Boo, Kwangsuck; Brennan, Michael J

2013-01-01

This paper describes an experimental study into the vibration control of a servo system comprising a servo motor and a flexible manipulator. Two modes of the system are controlled by using the servo motor and an accelerometer attached to the tip of the flexible manipulator. The control system is thus non-collocated. It consists of two electrical dynamic absorbers, each of which consists of a modal filter and, in case of an out-of-phase mode, a phase inverter. The experimental results show that each absorber acts as a mechanical dynamic vibration absorber attached to each mode and significantly reduces the settling time for the system response to a step input. (technical note)

The collocated station Košetice - Kešín u Pacova, Czech Republic: an important research infrastructure in central Europe

Science.gov (United States)

Dvorska, Alice; Milan, Váňa; Vlastimil, Hanuš; Marian, Pavelka

2013-04-01

The collocated station Košetice - Křešín u Pacova, central Czech Republic, is a major research and monitoring infrastructure in the Czech Republic and central Europe. It consists of two basic components: the observatory Košetice run since 1988 by the Czech Hydrometeorological Institute and the atmospheric station (AS) Křešín u Pacova starting operation in 2013. The AS is built and run by CzechGlobe - Global Change Research Centre, Academy of Sciences of the Czech Republic and is situated 100 m far from the observatory. There are three research and monitoring activities at the collocated station providing data necessary for the research on climate and related changes. The AS Křešín u Pacova consists of a 250 m tall tower serving for ground-based and vertical gradient measurements of (i) concentrations of CO2, CO, CH4, total gaseous mercury and tropospheric ozone (continuously), (ii) elemental and organic carbon (semicontinuously), (iii) carbon and oxygen isotopes, radon, N2O, SF6 and other species (episodically), (iv) optical properties of atmospheric aerosols and (v) meteorological parameters and the boundary layer height. Further, eddy covariance measurements in the nearby agroecosystem provide data on CO2 and H2O fluxes between the atmosphere and the ecosystem. Finally, monitoring activities at the nearby small hydrological catchment Anenské povodí run under the GEOMON network enables studying local hydrological and biogeochemical cycles. These measurements are supported by the long-term monitoring of meteorological and air quality parameters at the observatory Košetice, that are representative for the central European background. The collocated station provides a big research opportunity and challenge due to (i) a broad spectra of monitored chemical species, meteorological, hydrological and other parameters, (ii) measurements in various environmental compartments and especially the atmosphere, (iii) provision of data suitable for conducting

Hybrid motion sensing and experimental modal analysis using collocated smartphone camera and accelerometers

International Nuclear Information System (INIS)

Ozer, Ekin; Feng, Dongming; Feng, Maria Q

2017-01-01

State-of-the-art multisensory technologies and heterogeneous sensor networks propose a wide range of response measurement opportunities for structural health monitoring (SHM). Measuring and fusing different physical quantities in terms of structural vibrations can provide alternative acquisition methods and improve the quality of the modal testing results. In this study, a recently introduced SHM concept, SHM with smartphones, is focused to utilize multisensory smartphone features for a hybridized structural vibration response measurement framework. Based on vibration testing of a small-scale multistory laboratory model, displacement and acceleration responses are monitored using two different smartphone sensors, an embedded camera and accelerometer, respectively. Double-integration or differentiation among different measurement types is performed to combine multisensory measurements on a comparative basis. In addition, distributed sensor signals from collocated devices are processed for modal identification, and performance of smartphone-based sensing platforms are tested under different configuration scenarios and heterogeneity levels. The results of these tests show a novel and successful implementation of a hybrid motion sensing platform through multiple sensor type and device integration. Despite the heterogeneity of motion data obtained from different smartphone devices and technologies, it is shown that multisensory response measurements can be blended for experimental modal analysis. Getting benefit from the accessibility of smartphone technology, similar smartphone-based dynamic testing methodologies can provide innovative SHM solutions with mobile, programmable, and cost-free interfaces. (paper)

Hybrid motion sensing and experimental modal analysis using collocated smartphone camera and accelerometers

Science.gov (United States)

Ozer, Ekin; Feng, Dongming; Feng, Maria Q.

2017-10-01

State-of-the-art multisensory technologies and heterogeneous sensor networks propose a wide range of response measurement opportunities for structural health monitoring (SHM). Measuring and fusing different physical quantities in terms of structural vibrations can provide alternative acquisition methods and improve the quality of the modal testing results. In this study, a recently introduced SHM concept, SHM with smartphones, is focused to utilize multisensory smartphone features for a hybridized structural vibration response measurement framework. Based on vibration testing of a small-scale multistory laboratory model, displacement and acceleration responses are monitored using two different smartphone sensors, an embedded camera and accelerometer, respectively. Double-integration or differentiation among different measurement types is performed to combine multisensory measurements on a comparative basis. In addition, distributed sensor signals from collocated devices are processed for modal identification, and performance of smartphone-based sensing platforms are tested under different configuration scenarios and heterogeneity levels. The results of these tests show a novel and successful implementation of a hybrid motion sensing platform through multiple sensor type and device integration. Despite the heterogeneity of motion data obtained from different smartphone devices and technologies, it is shown that multisensory response measurements can be blended for experimental modal analysis. Getting benefit from the accessibility of smartphone technology, similar smartphone-based dynamic testing methodologies can provide innovative SHM solutions with mobile, programmable, and cost-free interfaces.

Triple collocation-based estimation of spatially correlated observation error covariance in remote sensing soil moisture data assimilation

Science.gov (United States)

Wu, Kai; Shu, Hong; Nie, Lei; Jiao, Zhenhang

2018-01-01

Spatially correlated errors are typically ignored in data assimilation, thus degenerating the observation error covariance R to a diagonal matrix. We argue that a nondiagonal R carries more observation information making assimilation results more accurate. A method, denoted TC_Cov, was proposed for soil moisture data assimilation to estimate spatially correlated observation error covariance based on triple collocation (TC). Assimilation experiments were carried out to test the performance of TC_Cov. AMSR-E soil moisture was assimilated with a diagonal R matrix computed using the TC and assimilated using a nondiagonal R matrix, as estimated by proposed TC_Cov. The ensemble Kalman filter was considered as the assimilation method. Our assimilation results were validated against climate change initiative data and ground-based soil moisture measurements using the Pearson correlation coefficient and unbiased root mean square difference metrics. These experiments confirmed that deterioration of diagonal R assimilation results occurred when model simulation is more accurate than observation data. Furthermore, nondiagonal R achieved higher correlation coefficient and lower ubRMSD values over diagonal R in experiments and demonstrated the effectiveness of TC_Cov to estimate richly structuralized R in data assimilation. In sum, compared with diagonal R, nondiagonal R may relieve the detrimental effects of assimilation when simulated model results outperform observation data.

An introduction to meshfree methods and their programming

CERN Document Server

Liu, GR

2005-01-01

Friendly and straightforward presentation and beginner orientated Provides the fundamentals of numerical analysis that are particularly important to meshfree methods. Wide coverage of meshfree methods: EFG, RPIM, MLPG, LRPIM, MWS and collocation methods Detailed comparison case studies for many existing meshfree methods Well-tested computer source codes are attached with useful descriptions and readily test examples Soft copy of these source codes are available also at http://www.nus.edu.sg/ACES.

Evaluating the performance of collocated optical disdrometers: LPM and PARSIVEL

Science.gov (United States)

Angulo-Martinez, Marta; Begueria, Santiago; Latorre, Borja

2017-04-01

Optical disdrometers are present weather sensors with the ability of providing integrate information of precipitation like intensity and reflectivity together with discrete information of drop sizes and velocities distribution (DSVD) of the hydrometeors crossing the laser beam sampling area. These sensors constitute a step forward in comparison with pluviometers towards a more complete characterisation of precipitation. Their use is spreading in many research fields for several applications. Understanding the differences from one another helps in the election of the sensor and point out limitations to be fixed in future versions. Four collocated optical disdrometers, two Laser Precipitation Monitors (LPM-Thies Clima) and two PARSIVEL, 1-minute measurements of 800 natural rainfall events were compared. Results showed a general agreement in integrated variables, like intensity or liquid water content. Nevertheless, comparing raw data, as the number of particles and DSVD, great differences were found. LPM generally measures more and smaller drops than PARSIVEL and this difference increases with rainfall intensity. These results may affect especially the reflectivity value every disdrometer provide. A complete description of the measurements obtained, quantifiying the differences is provided, indicating their possible sources.

Between initial familiarity and future use – a case of Collocated Collaborative Writing

DEFF Research Database (Denmark)

Bødker, Susanne; Polli, Anna Maria

2014-01-01

these with the three above forms of practice. The initial familiarity leads to two different early practices that get in the way of each other, and the collaborative writing idea. They point instead towards a discursive sharing of individual feelings, a different kind of past experiences than anticipated in design.......This paper reports on a design experiment in an art gallery, where we explored visitor practices of commenting on art, and how they were shaped in interaction with a newly designed collocated, collaborative writing technology. In particular we investigate what potentials previous practices carry...... with them that may affect early use and further development of use. We base our analyses on interviews in the art gallery and on socio-cultural theories of artefactmediated learning and collaboration. The analyses help identify three forms of collaborative writing, which are placed in the space between...

Synergistic multi-sensor and multi-frequency retrieval of cloud ice water path constrained by CloudSat collocations

International Nuclear Information System (INIS)

Islam, Tanvir; Srivastava, Prashant K.

2015-01-01

The cloud ice water path (IWP) is one of the major parameters that have a strong influence on earth's radiation budget. Onboard satellite sensors are recognized as valuable tools to measure the IWP in a global scale. Albeit, active sensors such as the Cloud Profiling Radar (CPR) onboard the CloudSat satellite has better capability to measure the ice water content profile, thus, its vertical integral, IWP, than any passive microwave (MW) or infrared (IR) sensors. In this study, we investigate the retrieval of IWP from MW and IR sensors, including AMSU-A, MHS, and HIRS instruments on-board the N19 satellite, such that the retrieval is consistent with the CloudSat IWP estimates. This is achieved through the collocations between the passive satellite measurements and CloudSat scenes. Potential benefit of synergistic multi-sensor multi-frequency retrieval is investigated. Two modeling approaches are explored for the IWP retrieval – generalized linear model (GLM) and neural network (NN). The investigation has been carried out over both ocean and land surface types. The MW/IR synergy is found to be retrieved more accurate IWP than the individual AMSU-A, MHS, or HIRS measurements. Both GLM and NN approaches have been able to exploit the synergistic retrievals. - Highlights: • MW/IR synergy is investigated for IWP retrieval. • The IWP retrieval is modeled using CloudSat collocations. • Two modeling approaches are explored – GLM and ANN. • MW/IR synergy performs better than the MW or IR only retrieval

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

Science.gov (United States)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Orbiting Carbon Observatory-2 (OCO-2) cloud screening algorithms; validation against collocated MODIS and CALIOP data

Science.gov (United States)

Taylor, T. E.; O'Dell, C. W.; Frankenberg, C.; Partain, P.; Cronk, H. Q.; Savtchenko, A.; Nelson, R. R.; Rosenthal, E. J.; Chang, A. Y.; Fisher, B.; Osterman, G.; Pollock, R. H.; Crisp, D.; Eldering, A.; Gunson, M. R.

2015-12-01

The objective of the National Aeronautics and Space Administration's (NASA) Orbiting Carbon Observatory-2 (OCO-2) mission is to retrieve the column-averaged carbon dioxide (CO2) dry air mole fraction (XCO2) from satellite measurements of reflected sunlight in the near-infrared. These estimates can be biased by clouds and aerosols within the instrument's field of view (FOV). Screening of the most contaminated soundings minimizes unnecessary calls to the computationally expensive Level 2 (L2) XCO2 retrieval algorithm. Hence, robust cloud screening methods have been an important focus of the OCO-2 algorithm development team. Two distinct, computationally inexpensive cloud screening algorithms have been developed for this application. The A-Band Preprocessor (ABP) retrieves the surface pressure using measurements in the 0.76 μm O2 A-band, neglecting scattering by clouds and aerosols, which introduce photon path-length (PPL) differences that can cause large deviations between the expected and retrieved surface pressure. The Iterative Maximum A-Posteriori (IMAP) Differential Optical Absorption Spectroscopy (DOAS) Preprocessor (IDP) retrieves independent estimates of the CO2 and H2O column abundances using observations taken at 1.61 μm (weak CO2 band) and 2.06 μm (strong CO2 band), while neglecting atmospheric scattering. The CO2 and H2O column abundances retrieved in these two spectral regions differ significantly in the presence of cloud and scattering aerosols. The combination of these two algorithms, which key off of different features in the spectra, provides the basis for cloud screening of the OCO-2 data set. To validate the OCO-2 cloud screening approach, collocated measurements from NASA's Moderate Resolution Imaging Spectrometer (MODIS), aboard the Aqua platform, were compared to results from the two OCO-2 cloud screening algorithms. With tuning to allow throughputs of ≃ 30 %, agreement between the OCO-2 and MODIS cloud screening methods is found to be

An Analysis of Peak Wind Speed Data from Collocated Mechanical and Ultrasonic Anemometers

Science.gov (United States)

Short, David A.; Wells, Leonard; Merceret, Francis J.; Roeder, William P.

2007-01-01

This study compared peak wind speeds reported by mechanical and ultrasonic anemometers at Cape Canaveral Air Force Station and Kennedy Space Center (CCAFS/KSC) on the east central coast of Florida and Vandenberg Air Force Base (VAFB) on the central coast of California. Launch Weather Officers, forecasters, and Range Safety analysts need to understand the performance of wind sensors at CCAFS/KSC and VAFB for weather warnings, watches, advisories, special ground processing operations, launch pad exposure forecasts, user Launch Commit Criteria (LCC) forecasts and evaluations, and toxic dispersion support. The legacy CCAFS/KSC and VAFB weather tower wind instruments are being changed from propeller-and-vane (CCAFS/KSC) and cup-and-vane (VAFB) sensors to ultrasonic sensors under the Range Standardization and Automation (RSA) program. Mechanical and ultrasonic wind measuring techniques are known to cause differences in the statistics of peak wind speed as shown in previous studies. The 45th Weather Squadron (45 WS) and the 30th Weather Squadron (30 WS) requested the Applied Meteorology Unit (AMU) to compare data between the RSA ultrasonic and legacy mechanical sensors to determine if there are significant differences. Note that the instruments were sited outdoors under naturally varying conditions and that this comparison was not designed to verify either technology. Approximately 3 weeks of mechanical and ultrasonic wind data from each range from May and June 2005 were used in this study. The CCAFS/KSC data spanned the full diurnal cycle, while the VAFB data were confined to 1000-1600 local time. The sample of 1-minute data from numerous levels on five different towers on each range totaled more than 500,000 minutes of data (482,979 minutes of data after quality control). The ten towers were instrumented at several levels, ranging from 12 ft to 492 ft above ground level. The ultrasonic sensors were collocated at the same vertical levels as the mechanical sensors and

Continuous Groundwater Monitoring Collocated at USGS Streamgages

Science.gov (United States)

Constantz, J. E.; Eddy-Miller, C.; Caldwell, R.; Wheeer, J.; Barlow, J.

2012-12-01

USGS Office of Groundwater funded a 2-year pilot study collocating groundwater wells for monitoring water level and temperature at several existing continuous streamgages in Montana and Wyoming, while U.S. Army Corps of Engineers funded enhancement to streamgages in Mississippi. To increase spatial relevance with in a given watershed, study sites were selected where near-stream groundwater was in connection with an appreciable aquifer, and where logistics and cost of well installations were considered representative. After each well installation and surveying, groundwater level and temperature were easily either radio-transmitted or hardwired to existing data acquisition system located in streamgaging shelter. Since USGS field personnel regularly visit streamgages during routine streamflow measurements and streamgage maintenance, the close proximity of observation wells resulted in minimum extra time to verify electronically transmitted measurements. After field protocol was tuned, stream and nearby groundwater information were concurrently acquired at streamgages and transmitted to satellite from seven pilot-study sites extending over nearly 2,000 miles (3,200 km) of the central US from October 2009 until October 2011, for evaluating the scientific and engineering add-on value of the enhanced streamgage design. Examination of the four-parameter transmission from the seven pilot study groundwater gaging stations reveals an internally consistent, dynamic data suite of continuous groundwater elevation and temperature in tandem with ongoing stream stage and temperature data. Qualitatively, the graphical information provides appreciation of seasonal trends in stream exchanges with shallow groundwater, as well as thermal issues of concern for topics ranging from ice hazards to suitability of fish refusia, while quantitatively this information provides a means for estimating flux exchanges through the streambed via heat-based inverse-type groundwater modeling. In June

Numerical approaches to time evolution of complex quantum systems

International Nuclear Information System (INIS)

Fehske, Holger; Schleede, Jens; Schubert, Gerald; Wellein, Gerhard; Filinov, Vladimir S.; Bishop, Alan R.

2009-01-01

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank-Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner-Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron-phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

Development of three-dimensional transport code by the double finite element method

International Nuclear Information System (INIS)

Fujimura, Toichiro

1985-01-01

Development of a three-dimensional neutron transport code by the double finite element method is described. Both of the Galerkin and variational methods are adopted to solve the problem, and then the characteristics of them are compared. Computational results of the collocation method, developed as a technique for the vaviational one, are illustrated in comparison with those of an Ssub(n) code. (author)

FRBRization of a Library Catalog: Better Collocation of Records, Leading to Enhanced Search, Retrieval, and Display

Directory of Open Access Journals (Sweden)

Timothy J. Dickey

2008-03-01

Full Text Available The Functional Requirements for Bibliographic Records (FRBR’s hierarchical system defines families of bibliographic relationship between records and collocates them better than most extant bibliographic systems. Certain library materials (especially audio-visual formats pose notable challenges to search and retrieval; the first benefits of a FRBRized system would be felt in music libraries, but research already has proven its advantages for fine arts, theology, and literature—the bulk of the non-science, technology, and mathematics collections. This report will summarize the benefits of FRBR to nextgeneration library catalogs and OPACs, and will review the handful of ILS and catalog systems currently operating with its theoretical structure.

Numerical simulation methods for wave propagation through optical waveguides

International Nuclear Information System (INIS)

Sharma, A.

1993-01-01

The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs

Regularization and computational methods for precise solution of perturbed orbit transfer problems

Science.gov (United States)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these

A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

KAUST Repository

Bourantas, Georgios; Loukopoulos, Vassilios C.

2013-01-01

A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a

Evaluation of roundness error using a new method based on a small displacement screw

International Nuclear Information System (INIS)

Nouira, Hichem; Bourdet, Pierre

2014-01-01

In relation to industrial need and the progress of technology, LNE would like to improve the measurement of its primary pressure, spherical and flick standards. The spherical and flick standards are respectively used to calibrate the spindle motion error and the probe which equips commercial conventional cylindricity measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. To ensure such a level of uncertainty, both stability and performance of the machine are not sufficient, and the data processing should also be done with accuracy less than a nanometre. In this paper, a new method based on the small displacement screw (SDS) model is proposed. A first validation of this method is proposed on a theoretical dataset published by the European Community Bureau of Reference (BCR) in report no 3327. Then, an experiment is prepared in order to validate the new method on real datasets. Specific environment conditions are taken into account and many precautions are considered. The new method is applied to analyse the least-squares circle, minimum zone circle, maximum inscribed circle and minimum circumscribed circle. The results are compared to those done by the reference Chebyshev best-fit method and reveal perfect agreement. The sensibilities of the SDS and Chebyshev methodologies are investigated, and it is revealed that results remain unchanged when the value of the diameter exceeds 700 times the form error. (paper)

Feedback control of acoustic musical instruments: collocated control using physical analogs.

Science.gov (United States)

Berdahl, Edgar; Smith, Julius O; Niemeyer, Günter

2012-01-01

Traditionally, the average professional musician has owned numerous acoustic musical instruments, many of them having distinctive acoustic qualities. However, a modern musician could prefer to have a single musical instrument whose acoustics are programmable by feedback control, where acoustic variables are estimated from sensor measurements in real time and then fed back in order to influence the controlled variables. In this paper, theory is presented that describes stable feedback control of an acoustic musical instrument. The presentation should be accessible to members of the musical acoustics community who may have limited or no experience with feedback control. First, the only control strategy guaranteed to be stable subject to any musical instrument mobility is described: the sensors and actuators must be collocated, and the controller must emulate a physical analog system. Next, the most fundamental feedback controllers and the corresponding physical analog systems are presented. The effects that these controllers have on acoustic musical instruments are described. Finally, practical design challenges are discussed. A proof explains why changing the resonance frequency of a musical resonance requires much more control power than changing the decay time of the resonance. © 2012 Acoustical Society of America.

Leapfrog variants of iterative methods for linear algebra equations

Science.gov (United States)

Saylor, Paul E.

1988-01-01

Two iterative methods are considered, Richardson's method and a general second order method. For both methods, a variant of the method is derived for which only even numbered iterates are computed. The variant is called a leapfrog method. Comparisons between the conventional form of the methods and the leapfrog form are made under the assumption that the number of unknowns is large. In the case of Richardson's method, it is possible to express the final iterate in terms of only the initial approximation, a variant of the iteration called the grand-leap method. In the case of the grand-leap variant, a set of parameters is required. An algorithm is presented to compute these parameters that is related to algorithms to compute the weights and abscissas for Gaussian quadrature. General algorithms to implement the leapfrog and grand-leap methods are presented. Algorithms for the important special case of the Chebyshev method are also given.

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

Science.gov (United States)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

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

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

Science.gov (United States)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

Heat transfer study on convective–radiative semi-spherical fins with temperature-dependent properties and heat generation using efficient computational methods

International Nuclear Information System (INIS)

Atouei, S.A.; Hosseinzadeh, Kh.; Hatami, M.; Ghasemi, Seiyed E.; Sahebi, S.A.R.; Ganji, D.D.

2015-01-01

In this study, heat transfer and temperature distribution equations for semi-spherical convective–radiative porous fins are presented. Temperature-dependent heat generation, convection and radiation effects are considered and after deriving the governing equation, Least Square Method (LSM), Collocation Method (CM) and fourth order Runge-Kutta method (NUM) are applied for predicting the temperature distribution in the described fins. Results reveal that LSM has excellent agreement with numerical method, so can be suitable analytical method for solving the problem. Also, the effect of some physical parameters which are appeared in the mathematical formulation on fin surface temperature is investigated to show the effect of radiation and heat generation in a solid fin temperature. - Highlights: • Thermal analysis of a semi-spherical fin is investigated. • Collocation and Least Square Methods are applied on the problem. • Convection, radiation and heat generation is considered. • Physical results are compared to numerical outcomes.

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

Science.gov (United States)

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations

KAUST Repository

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

2014-01-01

main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization

Orbiting Carbon Observatory-2 (OCO-2) cloud screening algorithms: validation against collocated MODIS and CALIOP data

Science.gov (United States)

Taylor, Thomas E.; O'Dell, Christopher W.; Frankenberg, Christian; Partain, Philip T.; Cronk, Heather Q.; Savtchenko, Andrey; Nelson, Robert R.; Rosenthal, Emily J.; Chang, Albert Y.; Fisher, Brenden; Osterman, Gregory B.; Pollock, Randy H.; Crisp, David; Eldering, Annmarie; Gunson, Michael R.

2016-03-01

The objective of the National Aeronautics and Space Administration's (NASA) Orbiting Carbon Observatory-2 (OCO-2) mission is to retrieve the column-averaged carbon dioxide (CO2) dry air mole fraction (XCO2) from satellite measurements of reflected sunlight in the near-infrared. These estimates can be biased by clouds and aerosols, i.e., contamination, within the instrument's field of view. Screening of the most contaminated soundings minimizes unnecessary calls to the computationally expensive Level 2 (L2) XCO2 retrieval algorithm. Hence, robust cloud screening methods have been an important focus of the OCO-2 algorithm development team. Two distinct, computationally inexpensive cloud screening algorithms have been developed for this application. The A-Band Preprocessor (ABP) retrieves the surface pressure using measurements in the 0.76 µm O2 A band, neglecting scattering by clouds and aerosols, which introduce photon path-length differences that can cause large deviations between the expected and retrieved surface pressure. The Iterative Maximum A Posteriori (IMAP) Differential Optical Absorption Spectroscopy (DOAS) Preprocessor (IDP) retrieves independent estimates of the CO2 and H2O column abundances using observations taken at 1.61 µm (weak CO2 band) and 2.06 µm (strong CO2 band), while neglecting atmospheric scattering. The CO2 and H2O column abundances retrieved in these two spectral regions differ significantly in the presence of cloud and scattering aerosols. The combination of these two algorithms, which are sensitive to different features in the spectra, provides the basis for cloud screening of the OCO-2 data set.To validate the OCO-2 cloud screening approach, collocated measurements from NASA's Moderate Resolution Imaging Spectrometer (MODIS), aboard the Aqua platform, were compared to results from the two OCO-2 cloud screening algorithms. With tuning of algorithmic threshold parameters that allows for processing of ≃ 20-25 % of all OCO-2 soundings

Simulation of the acoustic wave propagation using a meshless method

Directory of Open Access Journals (Sweden)

Bajko J.

2017-01-01

Full Text Available This paper presents numerical simulations of the acoustic wave propagation phenomenon modelled via Linearized Euler equations. A meshless method based on collocation of the strong form of the equation system is adopted. Moreover, the Weighted least squares method is used for local approximation of derivatives as well as stabilization technique in a form of spatial ltering. The accuracy and robustness of the method is examined on several benchmark problems.

Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

Directory of Open Access Journals (Sweden)

Mahmoud Paripour

2014-08-01

Full Text Available In this paper, the Bernstein polynomials are used to approximatethe solutions of linear integral equations with multiple time lags (IEMTL through expansion methods (collocation method, partition method, Galerkin method. The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is carried out

Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

Directory of Open Access Journals (Sweden)

Baiyu Wang

2014-01-01

Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

Advances in iterative methods

International Nuclear Information System (INIS)

Beauwens, B.; Arkuszewski, J.; Boryszewicz, M.

1981-01-01

Results obtained in the field of linear iterative methods within the Coordinated Research Program on Transport Theory and Advanced Reactor Calculations are summarized. The general convergence theory of linear iterative methods is essentially based on the properties of nonnegative operators on ordered normed spaces. The following aspects of this theory have been improved: new comparison theorems for regular splittings, generalization of the notions of M- and H-matrices, new interpretations of classical convergence theorems for positive-definite operators. The estimation of asymptotic convergence rates was developed with two purposes: the analysis of model problems and the optimization of relaxation parameters. In the framework of factorization iterative methods, model problem analysis is needed to investigate whether the increased computational complexity of higher-order methods does not offset their increased asymptotic convergence rates, as well as to appreciate the effect of standard relaxation techniques (polynomial relaxation). On the other hand, the optimal use of factorization iterative methods requires the development of adequate relaxation techniques and their optimization. The relative performances of a few possibilities have been explored for model problems. Presently, the best results have been obtained with optimal diagonal-Chebyshev relaxation

New template family for the detection of gravitational waves from comparable-mass black hole binaries

International Nuclear Information System (INIS)

Porter, Edward K.

2007-01-01

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various resummation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on reexpressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all post-Newtonian orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the last stable orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates

On the security of a novel key agreement protocol based on chaotic maps

International Nuclear Information System (INIS)

Xiang Tao; Wong, K.-W.; Liao Xiaofeng

2009-01-01

Recently, Xiao et al. proposed a novel key agreement protocol based on Chebyshev chaotic map. In this paper, the security of the protocol is analyzed, and two attack methods can be found in different scenarios. The essential principle of Xiao et al.'s scheme is summarized. It is also pointed out with proof that any attempt along this line to improve the security of Chebyshev map is redundant.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

Science.gov (United States)

2016-10-17

the good performance of these schemes. In [4], we study spectral collocation methods for functions which are analytic in the open interval but have...the detailed detonation struc- ture. The efficient parallel AMR-WENO method provides a good tool for these detonation simulations. In [10], a...with his students a few years ago. This method has now found a wide usage in applications. In [11], we give a stability analysis, using both the GKS

Stable Numerical Approach for Fractional Delay Differential Equations

Science.gov (United States)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Solution of the Multigroup-Diffusion equation by the response matrix method

International Nuclear Information System (INIS)

Oliveira, C.R.E.

1980-10-01

A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt

Analysis of Piezoelectric Solids using Finite Element Method

Science.gov (United States)

Aslam, Mohammed; Nagarajan, Praveen; Remanan, Mini

2018-03-01

Piezoelectric materials are extensively used in smart structures as sensors and actuators. In this paper, static analysis of three piezoelectric solids is done using general-purpose finite element software, Abaqus. The simulation results from Abaqus are compared with the results obtained using numerical methods like Boundary Element Method (BEM) and meshless point collocation method (PCM). The BEM and PCM are cumbersome for complex shape and complicated boundary conditions. This paper shows that the software Abaqus can be used to solve the governing equations of piezoelectric solids in a much simpler and faster way than the BEM and PCM.

Thermoluminescence of SrAl_2O_4:Eu"2"+, Dy"3"+: dosimetric characteristics and evidence of glow-peak collocation

International Nuclear Information System (INIS)

Chithambo, M.L.

2016-01-01

The thermoluminescence of SrAl_2O_4:Eu"2"+, Dy"3"+ consists of collocated peaks whereby a dominant component subsumes subsidiary ones to such an extent that they appear as one; Qualitative and quantitative analysis of such cases will be described with suitable illustrative examples. The general features and qualitative kinetics properties of thermoluminescence from SrAl_2O_4:Eu"2"+, Dy"3"+ is reported. Measurements using X-ray excited optical luminescence show that stimulated luminescence from SrAl_2O_4:Eu"2"+, Dy"3"+ has two prominent emission bands, one at 475 nm and a more intense one near 575 nm, studied in this work. There are also weaker intensity emissions at 405, 510, 600 and 660 nm. The natural thermoluminescence measured at 1°C s"-"1 shows three peaks at 74, 170 and 340°C whereas 20 Gy beta-irradiation produces TL dominated by a single peak at 34°C. Analysis of this peak for its order of kinetics produces somewhat inconclusive results. The results of the partial heating procedure T_m - T_s_t_o_p are consistent with both first and second-order kinetics. On the other hand, the position of the peak is independent of dose for several ranges of doses implying that the apparently single peak consists of multiple first-order peaks. Complementary investigations using the fractional glow technique, resolution by isothermal heating and the effect of fading on the peak show that the glow-curve of SrAl_2O_4:Eu"2"+, Dy"3"+ comprises closely collocated thermoluminescence peaks. The implication of such complexity on kinetic analysis on this material and others that share this feature will be discussed. (author)

Study of the clinical utility and potential problems of quantitative phase analysis using multiple gated cardiac blood pool image

International Nuclear Information System (INIS)

Tabuchi, Hiromi

1987-01-01

The temporal Fourier fitting at the fundamental frequency (Fourier analysis) and the Chebyshev polynomials for order 9 (Chebyshev analysis) were performed in 24 patients with myocardial infarction (MI) and 10 normal subjects. Fourier analysis showed a significantly delayed regional phase values (RPV), only when corrected in R-R interval, in the MI group. In both Fourier and Chebyshev analyses, a significantly decreased regional ejection fraction was noted in the MI group. Regional ejection time calculated by Chebyshev analysis was significantly delayed as well in the MI group. Fourier and Chebyshev analyses were useful in early detecting and precisely analysing MI contraction abnormality, respectively, although the former method required the correction in R-R interval. The second series of Fourier analysis was made on 11 patients with right ventricular endocardial pacing (RVEP), 7 patients with left bundle branch block (LBBB), and 10 normal subjects. The LBBB group had markedly delayed RPV in the whole ventricular area. The RVEP group had initial contraction at the apex of right ventricle, with tendency for wave-like contraction spreading basal portions of both ventricles. Patients with type RS on QRS waves at pacing tended to have slight differences in RPV between the right and left ventricles. Fourier analysis was useful in evaluating ventricular contraction pattern in patients with miscellaneous cardiac diseases. (Namekawa, K.) 70 refs

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

KAUST Repository

Wright, G. B.

2010-07-01

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a "2 + 1" approach is presented for numerically simulating thermal convection in a 3-D spherical shell. This is the first study to apply RBFs to a full 3-D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface-based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be "scattered" over the surface of a sphere. In the radial direction, Chebyshev polynomials are used, which are also spectrally accurate and provide the necessary clustering near the boundaries to resolve boundary layers. Applications of this new hybrid methodology are given to the problem of convection in the Earth\\'s mantle, which is modeled by a Boussinesq fluid at infinite Prandtl number. To see whether this numerical technique warrants further investigation, the study limits itself to an isoviscous mantle. Benchmark comparisons are presented with other currently used mantle convection codes for Rayleigh number (Ra) 7 × 10³ and 10⁵. Results from a Ra = 10⁶ simulation are also given. The algorithmic simplicity of the code (mostly due to RBFs) allows it to be written in less than 400 lines of MATLAB and run on a single workstation. We find that our method is very competitive with those currently used in the literature. Copyright 2010 by the American Geophysical Union.

A Collocation Method by Moving Least Squares Applicable to European Option Pricing

Directory of Open Access Journals (Sweden)

M. Amirfakhrian

2016-05-01

Full Text Available The subject matter of the present inquiry is the pricing of European options in the actual form of numbers. To assess the numerical prices of European options, a scheme independent of any kind of mesh but rather powered by moving least squares (MLS estimation is made. In practical terms, first the discretion of time variable is implemented and then, an MLS-powered method is applied for spatial approximation. As, unlike other methods, these courses of action mentioned here don't rely on a mesh, one can firmly claim they are to be categorized under mesh-less methods. And, of course, at the end of the paper, various experiments are offered to prove how efficient and how powerful the introduced approach is.

ACORN—A new method for generating sequences of uniformly distributed Pseudo-random Numbers

Science.gov (United States)

Wikramaratna, R. S.

1989-07-01

A new family of pseudo-random number generators, the ACORN ( additive congruential random number) generators, is proposed. The resulting numbers are distributed uniformly in the interval [0, 1). The ACORN generators are defined recursively, and the ( k + 1)th order generator is easily derived from the kth order generator. Some theorems concerning the period length are presented and compared with existing results for linear congruential generators. A range of statistical tests are applied to the ACORN generators, and their performance is compared with that of the linear congruential generators and the Chebyshev generators. The tests show the ACORN generators to be statistically superior to the Chebyshev generators, while being statistically similar to the linear congruential generators. However, the ACORN generators execute faster than linear congruential generators for the same statistical faithfulness. The main advantages of the ACORN generator are speed of execution, long period length, and simplicity of coding.

Miniaturized dielectric waveguide filters

OpenAIRE

Sandhu, MY; Hunter, IC

2016-01-01

Design techniques for a new class of integrated monolithic high-permittivity ceramic waveguide filters are presented. These filters enable a size reduction of 50% compared to air-filled transverse electromagnetic filters with the same unloaded Q-factor. Designs for Chebyshev and asymmetric generalised Chebyshev filter and a diplexer are presented with experimental results for an 1800 MHz Chebyshev filter and a 1700 MHz generalised Chebyshev filter showing excellent agreement with theory.

CONTRIBUTIONS TO RATIONAL APPROXIMATION,

Science.gov (United States)

Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

Spline methods for conversation equations

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1991-01-01

The consider the numerical solution of physical theories, in particular hydrodynamics, which can be formulated as systems of conservation laws. To this end we briefly describe the Basis Spline and collocation methods, paying particular attention to representation theory, which provides discrete analogues of the continuum conservation and dispersion relations, and hence a rigorous understanding of errors and instabilities. On this foundation we propose an algorithm for hydrodynamic problems in which most linear and nonlinear instabilities are brought under control. Numerical examples are presented from one-dimensional relativistic hydrodynamics. 9 refs., 10 figs

Solving the Schroedinger equation using Smolyak interpolants

International Nuclear Information System (INIS)

Avila, Gustavo; Carrington, Tucker Jr.

2013-01-01

In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased

Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics.

Science.gov (United States)

Berti, Claudio; Gillespie, Dirk; Bardhan, Jaydeep P; Eisenberg, Robert S; Fiegna, Claudio

2012-07-01

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the

Parametric study on a collocated PZT beam vibration absorber and power harvester

Energy Technology Data Exchange (ETDEWEB)

Huang, Shyh Chin [Mechanical Engineering, Ming Chi University of Technology, New Taipei (China); Tsai, Chao Yang [Mechanical Engineering Army Academy, R.O.C., Taoyuan (China); Liao, Hsiao Hui [LNG Construction and Project Division, CPC Corp., Taipei (China)

2016-11-15

The parametric effects of a PZT beam that is simultaneously used as a vibration absorber and a power harvester were investigated in this study. A cantilever beam paved with PZT layers and with added tip mass has been widely used as a harvester or sometimes as a Dynamic vibration absorber (DVA). However, the beam is rarely considered a collocated device. In this study, the first step was theoretical derivation of a distributed beam covered with bimorph PZT layers. Then, the beam was attached to a 1DOF vibratory main system. Two indicators for vibration absorption and power harvesting were defined. Numerical results demonstrated that the lumped mass ratio favored both of the abilities, but that the DVA mass ratio influenced these two abilities in exactly the opposite way. The conjunction of a harvester circuit into a DVA shifted its resonance frequency up to 5 % (an extreme case of open circuit R→∞). Simultaneous power harvesting diminished the absorption capability up to 35 % for each set of mass ratios. To achieve the maximum degree of power harvesting, a corresponding load resistance that somewhat increases with the lumped mass ratio is applied. Experimental results verified the existence of the best load resistance, but the measured harvested curve was lower than the theoretical calculation because of structure damping and deviations of PZT material properties.

Parametric study on a collocated PZT beam vibration absorber and power harvester

International Nuclear Information System (INIS)

Huang, Shyh Chin; Tsai, Chao Yang; Liao, Hsiao Hui

2016-01-01

The parametric effects of a PZT beam that is simultaneously used as a vibration absorber and a power harvester were investigated in this study. A cantilever beam paved with PZT layers and with added tip mass has been widely used as a harvester or sometimes as a Dynamic vibration absorber (DVA). However, the beam is rarely considered a collocated device. In this study, the first step was theoretical derivation of a distributed beam covered with bimorph PZT layers. Then, the beam was attached to a 1DOF vibratory main system. Two indicators for vibration absorption and power harvesting were defined. Numerical results demonstrated that the lumped mass ratio favored both of the abilities, but that the DVA mass ratio influenced these two abilities in exactly the opposite way. The conjunction of a harvester circuit into a DVA shifted its resonance frequency up to 5 % (an extreme case of open circuit R→∞). Simultaneous power harvesting diminished the absorption capability up to 35 % for each set of mass ratios. To achieve the maximum degree of power harvesting, a corresponding load resistance that somewhat increases with the lumped mass ratio is applied. Experimental results verified the existence of the best load resistance, but the measured harvested curve was lower than the theoretical calculation because of structure damping and deviations of PZT material properties

Numerical modeling of bubble dynamics in viscoelastic media with relaxation

Science.gov (United States)

Warnez, M. T.; Johnsen, E.

2015-06-01

Cavitation occurs in a variety of non-Newtonian fluids and viscoelastic materials. The large-amplitude volumetric oscillations of cavitation bubbles give rise to high temperatures and pressures at collapse, as well as induce large and rapid deformation of the surroundings. In this work, we develop a comprehensive numerical framework for spherical bubble dynamics in isotropic media obeying a wide range of viscoelastic constitutive relationships. Our numerical approach solves the compressible Keller-Miksis equation with full thermal effects (inside and outside the bubble) when coupled to a highly generalized constitutive relationship (which allows Newtonian, Kelvin-Voigt, Zener, linear Maxwell, upper-convected Maxwell, Jeffreys, Oldroyd-B, Giesekus, and Phan-Thien-Tanner models). For the latter two models, partial differential equations (PDEs) must be solved in the surrounding medium; for the remaining models, we show that the PDEs can be reduced to ordinary differential equations. To solve the general constitutive PDEs, we present a Chebyshev spectral collocation method, which is robust even for violent collapse. Combining this numerical approach with theoretical analysis, we simulate bubble dynamics in various viscoelastic media to determine the impact of relaxation time, a constitutive parameter, on the associated physics. Relaxation time is found to increase bubble growth and permit rebounds driven purely by residual stresses in the surroundings. Different regimes of oscillations occur depending on the relaxation time.

Structure soil structure interaction effects: Seismic analysis of safety related collocated concrete structures

International Nuclear Information System (INIS)

Joshi, J.R.

2000-01-01

The Process, Purification and Stack Buildings are collocated safety related concrete shear wall structures with plan dimensions in excess of 100 feet. An important aspect of their seismic analysis was the determination of structure soil structure interaction (SSSI) effects, if any. The SSSI analysis of the Process Building, with one other building at a time, was performed with the SASSI computer code for up to 50 frequencies. Each combined model had about 1500 interaction nodes. Results of the SSSI analysis were compared with those from soil structure interaction (SSI) analysis of the individual buildings, done with ABAQUS and SASSI codes, for three parameters: peak accelerations, seismic forces and the in-structure floor response spectra (FRS). The results may be of wider interest due to the model size and the potential applicability to other deep soil layered sites. Results obtained from the ABAQUS analysis were consistently higher, as expected, than those from the SSI and SSSI analyses using the SASSI. The SSSI effect between the Process and Purification Buildings was not significant. The Process and Stack Building results demonstrated that under certain conditions a massive structure can have an observable effect on the seismic response of a smaller and less stiff structure

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

International Nuclear Information System (INIS)

Pasciak, J.E.

1982-01-01

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

Fast algorithms for evaluating the stress field of dislocation lines in anisotropic elastic media

Science.gov (United States)

Chen, C.; Aubry, S.; Oppelstrup, T.; Arsenlis, A.; Darve, E.

2018-06-01

In dislocation dynamics (DD) simulations, the most computationally intensive step is the evaluation of the elastic interaction forces among dislocation ensembles. Because the pair-wise interaction between dislocations is long-range, this force calculation step can be significantly accelerated by the fast multipole method (FMM). We implemented and compared four different methods in isotropic and anisotropic elastic media: one based on the Taylor series expansion (Taylor FMM), one based on the spherical harmonics expansion (Spherical FMM), one kernel-independent method based on the Chebyshev interpolation (Chebyshev FMM), and a new kernel-independent method that we call the Lagrange FMM. The Taylor FMM is an existing method, used in ParaDiS, one of the most popular DD simulation softwares. The Spherical FMM employs a more compact multipole representation than the Taylor FMM does and is thus more efficient. However, both the Taylor FMM and the Spherical FMM are difficult to derive in anisotropic elastic media because the interaction force is complex and has no closed analytical formula. The Chebyshev FMM requires only being able to evaluate the interaction between dislocations and thus can be applied easily in anisotropic elastic media. But it has a relatively large memory footprint, which limits its usage. The Lagrange FMM was designed to be a memory-efficient black-box method. Various numerical experiments are presented to demonstrate the convergence and the scalability of the four methods.

Cellular Neural Network Method for Critical Slab with Albedo Boundary Condition

International Nuclear Information System (INIS)

Pirouzmanda, A.; Hadada, K.; Suh, K. Y.

2010-01-01

The neutron transport problems have been studied theoretically and numerically for years. A number of researchers have studied the criticality problems of one-speed neutrons in homogeneous slabs and spheres using various methods. The Chebyshev polynomial approximation method (T N method) has lately been developed and improved for the neutron transport equation in slab geometry. The one-speed time-dependent neutron transport equation using the Cellular Neural Network (CNN) for the vacuum boundary condition has previously been solved. In this paper, we demonstrate the capacity of CNN in calculating the critical slab thickness for different boundary conditions and its variation with moments N. The architecture of the CNN has already been dealt with thoroughly. Essentially, the CNN is used to model a first-order system of the partial differential equations (PDEs). The original equations in the T N approximation are also a set of PDEs. The CNN approach lends itself to analog VLSI implementation. In this study, the CNN model is implemented using the HSpice software package

A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

Science.gov (United States)

Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

2017-11-01

The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

Magnetic field computations of the magnetic circuits with permanent magnets by infinite element method

International Nuclear Information System (INIS)

Hahn, Song Yop

1985-01-01

A method employing infinite elements is described for the magnetic field computations of the magnetic circuits with permanent magnet. The system stiffness matrix is derived by a variational approach, while the interfacial boundary conditions between the finite element regions and the infinite element regions are dealt with using collocation method. The proposed method is applied to a simple linear problems, and the numerical results are compared with those of the standard finite element method and the analytic solutions. It is observed that the proposed method gives more accurate results than those of the standard finite element method under the same computing efforts. (Author)

An ME-PC Enhanced HDMR Method for Efficient Statistical Analysis of Multiconductor Transmission Line Networks

KAUST Repository

Yucel, Abdulkadir C.

2015-05-05

An efficient method for statistically characterizing multiconductor transmission line (MTL) networks subject to a large number of manufacturing uncertainties is presented. The proposed method achieves its efficiency by leveraging a high-dimensional model representation (HDMR) technique that approximates observables (quantities of interest in MTL networks, such as voltages/currents on mission-critical circuits) in terms of iteratively constructed component functions of only the most significant random variables (parameters that characterize the uncertainties in MTL networks, such as conductor locations and widths, and lumped element values). The efficiency of the proposed scheme is further increased using a multielement probabilistic collocation (ME-PC) method to compute the component functions of the HDMR. The ME-PC method makes use of generalized polynomial chaos (gPC) expansions to approximate the component functions, where the expansion coefficients are expressed in terms of integrals of the observable over the random domain. These integrals are numerically evaluated and the observable values at the quadrature/collocation points are computed using a fast deterministic simulator. The proposed method is capable of producing accurate statistical information pertinent to an observable that is rapidly varying across a high-dimensional random domain at a computational cost that is significantly lower than that of gPC or Monte Carlo methods. The applicability, efficiency, and accuracy of the method are demonstrated via statistical characterization of frequency-domain voltages in parallel wire, interconnect, and antenna corporate feed networks.

A perturbation method to the tent map based on Lyapunov exponent and its application

Science.gov (United States)

Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu

2015-10-01

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

Fibonacci-regularization method for solving Cauchy integral equations of the first kind

Directory of Open Access Journals (Sweden)

Mohammad Ali Fariborzi Araghi

2017-09-01

Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.

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

Science.gov (United States)

Streett, C. L.

1987-01-01

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

Monolithic Integrated Ceramic Waveguide Filters

OpenAIRE

Hunter, IC; Sandhu, MY

2014-01-01

Design techniques for a new class of integrated monolithic high permittivity ceramic waveguide filters are presented. These filters enable a size reduction of 50% compared to air-filled TEM filters with the same unloaded Q-Factor. Designs for both chebyshev and asymmetric generalized chebyshev filter are presented, with experimental results for an 1800 MHz chebyshev filter showing excellent agreement with theory.

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

Science.gov (United States)

Behnabian, Behzad; Mashhadi Hossainali, Masoud; Malekzadeh, Ahad

2018-02-01

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization (II): Solution of Equation

International Nuclear Information System (INIS)

Wang Huaiyu; Long Yao; Chen Nanxian

2006-01-01

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green's function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Chebyshev Distance

OpenAIRE

Coghetto Roland

2016-01-01

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

Chebyshev Distance

Directory of Open Access Journals (Sweden)

Coghetto Roland

2016-06-01

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

Polarized atomic orbitals for linear scaling methods

Science.gov (United States)

Berghold, Gerd; Parrinello, Michele; Hutter, Jürg

2002-02-01

We present a modified version of the polarized atomic orbital (PAO) method [M. S. Lee and M. Head-Gordon, J. Chem. Phys. 107, 9085 (1997)] to construct minimal basis sets optimized in the molecular environment. The minimal basis set derives its flexibility from the fact that it is formed as a linear combination of a larger set of atomic orbitals. This approach significantly reduces the number of independent variables to be determined during a calculation, while retaining most of the essential chemistry resulting from the admixture of higher angular momentum functions. Furthermore, we combine the PAO method with linear scaling algorithms. We use the Chebyshev polynomial expansion method, the conjugate gradient density matrix search, and the canonical purification of the density matrix. The combined scheme overcomes one of the major drawbacks of standard approaches for large nonorthogonal basis sets, namely numerical instabilities resulting from ill-conditioned overlap matrices. We find that the condition number of the PAO overlap matrix is independent from the condition number of the underlying extended basis set, and consequently no numerical instabilities are encountered. Various applications are shown to confirm this conclusion and to compare the performance of the PAO method with extended basis-set calculations.

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Science.gov (United States)

Joslin, Ronald D.; Streett, Craig L.; Chang, Chau-Lyan

1992-01-01

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Ice particle production in mid-level stratiform mixed-phase clouds observed with collocated A-Train measurements

Directory of Open Access Journals (Sweden)

D. Zhang

2018-03-01

Full Text Available Collocated A-Train CloudSat radar and CALIPSO lidar measurements between 2006 and 2010 are analyzed to study primary ice particle production characteristics in mid-level stratiform mixed-phase clouds on a global scale. For similar clouds in terms of cloud top temperature and liquid water path, Northern Hemisphere latitude bands have layer-maximum radar reflectivity (ZL that is  ∼  1 to 8 dBZ larger than their counterparts in the Southern Hemisphere. The systematically larger ZL under similar cloud conditions suggests larger ice number concentrations in mid-level stratiform mixed-phase clouds over the Northern Hemisphere, which is possibly related to higher background aerosol loadings. Furthermore, we show that springtime northern mid- and high latitudes have ZL that is larger by up to 6 dBZ (a factor of 4 higher ice number concentration than other seasons, which might be related to more dust events that provide effective ice nucleating particles. Our study suggests that aerosol-dependent ice number concentration parameterizations are required in climate models to improve mixed-phase cloud simulations, especially over the Northern Hemisphere.

Spectral element method for vector radiative transfer equation

International Nuclear Information System (INIS)

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

2010-01-01

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

Rapid expansion method (REM) for time‐stepping in reverse time migration (RTM)

KAUST Repository

Pestana, Reynam C.

2009-01-01

We show that the wave equation solution using a conventional finite‐difference scheme, derived commonly by the Taylor series approach, can be derived directly from the rapid expansion method (REM). After some mathematical manipulation we consider an analytical approximation for the Bessel function where we assume that the time step is sufficiently small. From this derivation we find that if we consider only the first two Chebyshev polynomials terms in the rapid expansion method we can obtain the second order time finite‐difference scheme that is frequently used in more conventional finite‐difference implementations. We then show that if we use more terms from the REM we can obtain a more accurate time integration of the wave field. Consequently, we have demonstrated that the REM is more accurate than the usual finite‐difference schemes and it provides a wave equation solution which allows us to march in large time steps without numerical dispersion and is numerically stable. We illustrate the method with post and pre stack migration results.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

Science.gov (United States)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

A semi-analytical analysis of electro-thermo-hydrodynamic stability in dielectric nanofluids using Buongiorno's mathematical model together with more realistic boundary conditions

Science.gov (United States)

Wakif, Abderrahim; Boulahia, Zoubair; Sehaqui, Rachid

2018-06-01

The main aim of the present analysis is to examine the electroconvection phenomenon that takes place in a dielectric nanofluid under the influence of a perpendicularly applied alternating electric field. In this investigation, we assume that the nanofluid has a Newtonian rheological behavior and verifies the Buongiorno's mathematical model, in which the effects of thermophoretic and Brownian diffusions are incorporated explicitly in the governing equations. Moreover, the nanofluid layer is taken to be confined horizontally between two parallel plate electrodes, heated from below and cooled from above. In a fast pulse electric field, the onset of electroconvection is due principally to the buoyancy forces and the dielectrophoretic forces. Within the framework of the Oberbeck-Boussinesq approximation and the linear stability theory, the governing stability equations are solved semi-analytically by means of the power series method for isothermal, no-slip and non-penetrability conditions. In addition, the computational implementation with the impermeability condition implies that there exists no nanoparticles mass flux on the electrodes. On the other hand, the obtained analytical solutions are validated by comparing them to those available in the literature for the limiting case of dielectric fluids. In order to check the accuracy of our semi-analytical results obtained for the case of dielectric nanofluids, we perform further numerical and semi-analytical computations by means of the Runge-Kutta-Fehlberg method, the Chebyshev-Gauss-Lobatto spectral method, the Galerkin weighted residuals technique, the polynomial collocation method and the Wakif-Galerkin weighted residuals technique. In this analysis, the electro-thermo-hydrodynamic stability of the studied nanofluid is controlled through the critical AC electric Rayleigh number Rec , whose value depends on several physical parameters. Furthermore, the effects of various pertinent parameters on the electro

Initial Design and Quick Analysis of SAW Ultra–Wideband HFM Transducers

Directory of Open Access Journals (Sweden)

A. Janeliauskas

2017-09-01

Full Text Available This paper presents techniques for initial design and quick fundamental and harmonic operation analysis of surface acoustic waves ultra–wideband hyperbolically frequency modulated (HFM interdigital transducer (IDT. The primary analysis is based on the quasi–static method. Quasi–electrostatic charge's density distribution was approximated by Chebyshev polynomials and the method of Green’s function. It assesses the non uniform charge distribution of electrodes, electric field interaction and the end effects of a whole transducer. It was found that numerical integration (e.g. Romberg, Gauss–Chebyshev requires a lot of machine time for calculation of the Chebyshev polynomial and the Green’s function convolution when integration includes coordinates of a large number of neighboring electrodes. In order to accelerate the charge density calculation, the analytic expressions are derived. Evaluation of HFM transducer fundamental and harmonics' operation amplitude response with simulation single–dispersive interdigital chirp filter structure is presented. Elapsed time of HFM IDT with 589 electrodes simulations and 2000 frequency response point is only 54 seconds (0.027 s/point on PC with CPU Intel Core I7–4770S. Amplitude response is compared with linear frequency modulated (LFM IDT response. It was determined that the HFM transducer characteristic is less distorted in comparison with LFM transducer.

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

Science.gov (United States)

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Underground collocation of nuclear power plant reactors and repository to facilitate the post-renaissance expansion of nuclear power

Energy Technology Data Exchange (ETDEWEB)

Myers, Carl W [Los Alamos National Laboratory; Elkins, Ned Z [Los Alamos National Laboratory

2008-01-01

Underground collocation of nuclear power reactors and the nuclear waste management facilities supporting those reactors, termed an underground nuclear park (UNP), appears to have several advantages compared to the conventional approach to siting reactors and waste management facilities. These advantages include the potential to lower reactor capital and operating cost, lower nuclear waste management cost, and increase margins of physical security and safety. Envirorunental impacts related to worker health, facility accidents, waste transportation, and sabotage and terrorism appear to be lower for UNPs compared to the current approach. In-place decommissioning ofUNP reactors appears to have cost, safety, envirorunental and waste disposal advantages. The UNP approach has the potential to lead to greater public acceptance for the deployment of new power reactors. Use of the UNP during the post-nuclear renaissance time frame has the potential to enable a greater expansion of U.S. nuclear power generation than might otherwise result. Technical and economic aspects of the UNP concept need more study to determine the viability of the concept.

Computational Error Estimate for the Power Series Solution of Odes ...

African Journals Online (AJOL)

This paper compares the error estimation of power series solution with recursive Tau method for solving ordinary differential equations. From the computational viewpoint, the power series using zeros of Chebyshevpolunomial is effective, accurate and easy to use. Keywords: Lanczos Tau method, Chebyshev polynomial, ...

Inversion of the strain-life and strain-stress relationships for use in metal fatigue analysis

Science.gov (United States)

Manson, S. S.

1979-01-01

The paper presents closed-form solutions (collocation method and spline-function method) for the constants of the cyclic fatigue life equation so that they can be easily incorporated into cumulative damage analysis. The collocation method involves conformity with the experimental curve at specific life values. The spline-function method is such that the basic life relation is expressed as a two-part function, one applicable at strains above the transition strain (strain at intersection of elastic and plastic lines), the other below. An illustrative example is treated by both methods. It is shown that while the collocation representation has the advantage of simplicity of form, the spline-function representation can be made more accurate over a wider life range, and is simpler to use.

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Zhao, J.M., E-mail: jmzhao@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); Tan, J.Y., E-mail: tanjy@hit.edu.cn [School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China); Liu, L.H., E-mail: lhliu@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, People' s Republic of China (China); School of Auto Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road, Weihai 264209, People' s Republic of China (China)

2013-01-01

A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

Reduction of Linear Programming to Linear Approximation

OpenAIRE

Vaserstein, Leonid N.

2006-01-01

It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

Browse Title Index

African Journals Online (AJOL)

Items 151 - 200 of 985 ... Vol 15 (2009), Application of Neuro-Fuzzy to palm oil production ... the Strength of Users Passwords in Computing Systems in Nigeria, Abstract ... of the Chebyshev polynomials for the Tau numerical method, Abstract.

A Cartesian Adaptive Level Set Method for Two-Phase Flows

Science.gov (United States)

Ham, F.; Young, Y.-N.

2003-01-01

In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.

Possibility-based robust design optimization for the structural-acoustic system with fuzzy parameters

Science.gov (United States)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2018-03-01

The conventional engineering optimization problems considering uncertainties are based on the probabilistic model. However, the probabilistic model may be unavailable because of the lack of sufficient objective information to construct the precise probability distribution of uncertainties. This paper proposes a possibility-based robust design optimization (PBRDO) framework for the uncertain structural-acoustic system based on the fuzzy set model, which can be constructed by expert opinions. The objective of robust design is to optimize the expectation and variability of system performance with respect to uncertainties simultaneously. In the proposed PBRDO, the entropy of the fuzzy system response is used as the variability index; the weighted sum of the entropy and expectation of the fuzzy response is used as the objective function, and the constraints are established in the possibility context. The computations for the constraints and objective function of PBRDO are a triple-loop and a double-loop nested problem, respectively, whose computational costs are considerable. To improve the computational efficiency, the target performance approach is introduced to transform the calculation of the constraints into a double-loop nested problem. To further improve the computational efficiency, a Chebyshev fuzzy method (CFM) based on the Chebyshev polynomials is proposed to estimate the objective function, and the Chebyshev interval method (CIM) is introduced to estimate the constraints, thereby the optimization problem is transformed into a single-loop one. Numerical results on a shell structural-acoustic system verify the effectiveness and feasibility of the proposed methods.

Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation

International Nuclear Information System (INIS)

Sen, Oishik; Davis, Sean; Jacobs, Gustaaf; Udaykumar, H.S.

2015-01-01

The effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. This is done with the express purpose of using metamodels to bridge scales between micro- and macro-scale models in a multi-scale multimaterial simulation. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver

Time-variant random interval natural frequency analysis of structures

Science.gov (United States)

Wu, Binhua; Wu, Di; Gao, Wei; Song, Chongmin

2018-02-01

This paper presents a new robust method namely, unified interval Chebyshev-based random perturbation method, to tackle hybrid random interval structural natural frequency problem. In the proposed approach, random perturbation method is implemented to furnish the statistical features (i.e., mean and standard deviation) and Chebyshev surrogate model strategy is incorporated to formulate the statistical information of natural frequency with regards to the interval inputs. The comprehensive analysis framework combines the superiority of both methods in a way that computational cost is dramatically reduced. This presented method is thus capable of investigating the day-to-day based time-variant natural frequency of structures accurately and efficiently under concrete intrinsic creep effect with probabilistic and interval uncertain variables. The extreme bounds of the mean and standard deviation of natural frequency are captured through the embedded optimization strategy within the analysis procedure. Three particularly motivated numerical examples with progressive relationship in perspective of both structure type and uncertainty variables are demonstrated to justify the computational applicability, accuracy and efficiency of the proposed method.

A method for including external feed in depletion calculations with CRAM and implementation into ORIGEN

International Nuclear Information System (INIS)

Isotalo, A.E.; Wieselquist, W.A.

2015-01-01

Highlights: • A method for handling external feed in depletion calculations with CRAM. • Source term can have polynomial or exponentially decaying time-dependence. • CRAM with source term and adjoint capability implemented to ORIGEN in SCALE. • The new solver is faster and more accurate than the original solver of ORIGEN. - Abstract: A method for including external feed with polynomial time dependence in depletion calculations with the Chebyshev Rational Approximation Method (CRAM) is presented and the implementation of CRAM to the ORIGEN module of the SCALE suite is described. In addition to being able to handle time-dependent feed rates, the new solver also adds the capability to perform adjoint calculations. Results obtained with the new CRAM solver and the original depletion solver of ORIGEN are compared to high precision reference calculations, which shows the new solver to be orders of magnitude more accurate. Furthermore, in most cases, the new solver is up to several times faster due to not requiring similar substepping as the original one

Transport equation solving methods

International Nuclear Information System (INIS)

Granjean, P.M.

1984-06-01

This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

Geometrical effects on western intensification of wind-driven ocean currents: The rotated-channel Stommel model, coastal orientation, and curvature

Science.gov (United States)

Boyd, John P.; Sanjaya, Edwin

2014-03-01

We revisit early models of steady western boundary currents [Gulf Stream, Kuroshio, etc.] to explore the role of irregular coastlines on jets, both to advance the research frontier and to illuminate for education. In the framework of a steady-state, quasigeostrophic model with viscosity, bottom friction and nonlinearity, we prove that rotating a straight coastline, initially parallel to the meridians, significantly thickens the western boundary layer. We analyze an infinitely long, straight channel with arbitrary orientation and bottom friction using an exact solution and singular perturbation theory, and show that the model, though simpler than Stommel's, nevertheless captures both the western boundary jet (“Gulf Stream”) and the “orientation effect”. In the rest of the article, we restrict attention to the Stommel flow (that is, linear and inviscid except for bottom friction) and apply matched asymptotic expansions, radial basis function, Fourier-Chebyshev and Chebyshev-Chebyshev pseudospectral methods to explore the effects of coastal geometry in a variety of non-rectangular domains bounded by a circle, parabolas and squircles. Although our oceans are unabashedly idealized, the narrow spikes, broad jets and stationary points vividly illustrate the power and complexity of coastal control of western boundary layers.

Linear stability analysis of laminar flow near a stagnation point in the slip flow regime

Science.gov (United States)

Essaghir, E.; Oubarra, A.; Lahjomri, J.

2017-12-01

The aim of the present contribution is to analyze the effect of slip parameter on the stability of a laminar incompressible flow near a stagnation point in the slip flow regime. The analysis is based on the traditional normal mode approach and assumes parallel flow approximation. The Orr-Sommerfeld equation that governs the infinitesimal disturbance of stream function imposed to the steady main flow, which is an exact solution of the Navier-Stokes equation satisfying slip boundary conditions, is obtained by using the powerful spectral Chebyshev collocation method. The results of the effect of slip parameter K on the hydrodynamic characteristics of the base flow, namely the velocity profile, the shear stress profile, the boundary layer, displacement and momentum thicknesses are illustrated and discussed. The numerical data for these characteristics, as well as those of the eigenvalues and the corresponding wave numbers recover the results of the special case of no-slip boundary conditions. They are found to be in good agreement with previous numerical calculations. The effects of slip parameter on the neutral curves of stability, for two-dimensional disturbances in the Reynolds-wave number plane, are then obtained for the first time in the slip flow regime for stagnation point flow. Furthermore, the evolution of the critical Reynolds number against the slip parameter is established. The results show that the critical Reynolds number for instability is significantly increased with the slip parameter and the flow turn out to be more stable when the effect of rarefaction becomes important.

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

Science.gov (United States)

Hu, Jun; Hadid, Hamda Ben; Henry, Daniel; Mojtabi, Abdelkader

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, ) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (0), and oscillatory for =0 remains so for >0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

Global stability analysis of axisymmetric boundary layer over a circular cylinder

Science.gov (United States)

Bhoraniya, Ramesh; Vinod, Narayanan

2018-05-01

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.

The effect of strongly anisotropic scattering on the critical size of a slab in one-speed neutron transport theory: Modified UN method

International Nuclear Information System (INIS)

Öztürk, Hakan

2014-01-01

Highlights: • The criticality problem for one-speed neutrons in homogeneous slab is investigated. • A combination of forward–backward and linear anisotropy is used. • The effect of the strongly anisotropic scattering on the critical size is analyzed. - Abstract: The criticality problem for one-speed neutrons in a uniform finite slab is studied in the case of a combination of forward and backward scattering with linearly anisotropic scattering using U N method based on the Chebyshev polynomials of second kind. The effect of the linear anisotropy on the critical thickness of the slab is investigated. The critical slab thicknesses are calculated by using Marshak boundary condition for various values of the anisotropy parameters and they are presented in the tables. In comparison to the results obtained by other methods, the results of this study are in compatible with the former ones

Slavic Phraseology: A View Through Corpora

Directory of Open Access Journals (Sweden)

Zakharov Victor

2017-12-01

Full Text Available The study of word collocability is one of the main tasks of linguistics. The combinatory ability of language units, collocability, is one of the linguistic syntagmatic laws. This phenomenon is the main object of the phraseology and lexicography. The article deals with set phrases of different types in Russian, Czech and Slovak from the point of view of their quantitative evaluation. Corpus linguistics understand set phrases as statistically determined unities. This approach is the basic point of different automatic ways to extract idioms and collocations. The paper describes experiments which show how text corpora and corpus methods and tools can be used to expand the entries in existing dictionaries and how set phrases could be evaluated quantitatively. It is shown and maintained that corpus linguistics methods and tools allow to create dictionaries of new type which have to include a larger amount of set phrases and collocations than before.

Crack edge collocation for the direct computation of stress intensity factors using the displacement discontinuity method

CSIR Research Space (South Africa)

Napier, JAL

2002-09-01

Full Text Available The numerical solution of problems relating to crack fracture and failure can be accomplished using the displacement discontinuity boundary element method. This paper presents an extension to the normal formulation of this method to enable stress...

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

Science.gov (United States)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

Directory of Open Access Journals (Sweden)

Farshid Mirzaee

2014-06-01

Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.

Comparison of the method of classes and the quadrature of moment for the modelling of neodymium oxalate precipitation

Energy Technology Data Exchange (ETDEWEB)

Gaillard, J.P.; Lalleman, S.; Bertrand, M. [CEA, Centre de Marcoule, Nuclear Energy Division, RadioChemistry and Process Department, F-30207 Bagnols sur Ceze (France); Plasari, E. [Ecole Nationale Superieure des Industries Chimiques, Laboratoire Reactions et Genie des Procedes, Universite de Lorraine - CNRS,1 rue Grandville, BP 20451, 54001, Nancy Cedex (France)

2016-07-01

Oxalic precipitation is generally used in the nuclear industry to deal with radioactive waste and recover the actinides from a multicomponent solution. To facilitate the development of experimental methods and data acquisitions, actinides are often simulated using lanthanides, gaining experience more easily. The purpose of this article is to compare the results achieved by two methods for solving the population balance during neodymium oxalate precipitation in a continuous MSMPR (Mixed Suspension Mixed Product Removal). The method of classes, also called discretized population balance, used in this study is based on the method of Litster. Whereas, the Quadrature Method of Moment (QMOM) is written in terms of the transport equations of the moments of the number density function. All the integrals are solved through a quadrature approximation thanks to the product-difference algorithm or the Chebyshev algorithm. Primary nucleation, crystal growth and agglomeration are taken into account. Agglomeration phenomena have been found to be represented by a loose agglomerates model. Thermodynamic effects are modeled by activity coefficients which are calculated using the Bromley model. The sizes of particles predicted by the two methods are in good agreement with experimental measurements. (authors)

Michelson interferometer based interleaver design using classic IIR filter decomposition.

Science.gov (United States)

Cheng, Chi-Hao; Tang, Shasha

2013-12-16

An elegant method to design a Michelson interferometer based interleaver using a classic infinite impulse response (IIR) filter such as Butterworth, Chebyshev, and elliptic filters as a starting point are presented. The proposed design method allows engineers to design a Michelson interferometer based interleaver from specifications seamlessly. Simulation results are presented to demonstrate the validity of the proposed design method.

Application of polynomial preconditioners to conservation laws

NARCIS (Netherlands)

Geurts, Bernardus J.; van Buuren, R.; Lu, H.

2000-01-01

Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries

KAUST Repository

Williams-Rioux, Bertrand

2012-01-12

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

Seismic Noise Analysis and Reduction through Utilization of Collocated Seismic and Atmospheric Sensors at the GRO Chile Seismic Network

Science.gov (United States)

Farrell, M. E.; Russo, R. M.

2013-12-01

The installation of Earthscope Transportable Array-style geophysical observatories in Chile expands open data seismic recording capabilities in the southern hemisphere by nearly 30%, and has nearly tripled the number of seismic stations providing freely-available data in southern South America. Through the use of collocated seismic and atmospheric sensors at these stations we are able to analyze how local atmospheric conditions generate seismic noise, which can degrade data in seismic frequency bands at stations in the ';roaring forties' (S latitudes). Seismic vaults that are climate-controlled and insulated from the local environment are now employed throughout the world in an attempt to isolate seismometers from as many noise sources as possible. However, this is an expensive solution that is neither practical nor possible for all seismic deployments; and also, the increasing number and scope of temporary seismic deployments has resulted in the collection and archiving of terabytes of seismic data that is affected to some degree by natural seismic noise sources such as wind and atmospheric pressure changes. Changing air pressure can result in a depression and subsequent rebound of Earth's surface - which generates low frequency noise in seismic frequency bands - and even moderate winds can apply enough force to ground-coupled structures or to the surface above the seismometers themselves, resulting in significant noise. The 10 stations of the permanent Geophysical Reporting Observatories (GRO Chile), jointly installed during 2011-12 by IRIS and the Chilean Servicio Sismológico, include instrumentation in addition to the standard three seismic components. These stations, spaced approximately 300 km apart along the length of the country, continuously record a variety of atmospheric data including infrasound, air pressure, wind speed, and wind direction. The collocated seismic and atmospheric sensors at each station allow us to analyze both datasets together, to

Ocean Striations Detecting and Its Features

Science.gov (United States)

Guan, Y. P.; Zhang, Y.; Chen, Z.; Liu, H.; Yu, Y.; Huang, R. X.

2016-02-01

Over the past 10 years or so, ocean striations has been one of the research frontiers as reported in many investigators. With suitable filtering subroutines, striations can be revealed from many different types of ocean datasets. It is clear that striations are some types of meso-scale phenomena in the large-scale circulation system, which in the form of alternating band-like structure. We present a comprehensive study on the effectiveness of the different detection approaches to unveiling the striations. Three one-dimensional filtering methods: Gaussian smoothing, Hanning and Chebyshev high-pass filtering. Our results show that all three methods can reveal ocean banded structures, but the Chebyshev filtering is the best choice. The Gaussian smoothing is not a high pass filter, and it can merely bring regional striations, such as those in the Eastern Pacific, to light. The Hanning high pass filter can introduce a northward shifting of stripes, so it is not as good as the Chebyshev filter. On the other hand, striations in the open ocean are mostly zonally oriented; however, there are always exceptions. In particular, in coastal ocean, due to topography constraint and along shore currents, striations can titled in the meridional direction. We examined the band-like structure of striation for some selected regions of the open ocean and the semi-closed sub-basins, such as the South China sea, the Gulf of Mexico, the Mediterranean Sea and the Japan Sea. A reasonable interpretation is given here.

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

Directory of Open Access Journals (Sweden)

S. S. Motsa

2013-01-01

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

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

Science.gov (United States)

Woollands, Robyn M.; Read, Julie; Hernandez, Kevin; Probe, Austin; Junkins, John L.

2018-03-01

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require "shooting" but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational

Application of preconditioned conjugate gradient-like methods to reactor kinetics

International Nuclear Information System (INIS)

Yang, D.Y.; Chen, G.S.; Chou, H.P.

1993-01-01

Several conjugate gradient-like (CG-like) methods are applied to solve the nonsymmetric linear systems of equations derived from the time-dependent two-dimensional two-energy-group neutron diffusion equations by a finite difference approximation. The methods are: the generalized conjugate residual method; the generalized conjugate gradient least-square method; the generalized minimal residual method (GMRES); the conjugate gradient square method; and a variant of bi-conjugate gradient method (Bi-CGSTAB). In order to accelerate these methods, six preconditioning techniques are investigated. Two are based on pointwise incomplete factorization: the incomplete LU (ILU) and the modified incomplete LU (MILU) decompositions; two, based on the block tridiagonal structure of the coefficient matrix, are blockwise and modified blockwise incomplete factorizations, BILU and MBILU; two are the alternating-direction implicit and symmetric successive overrelaxation (SSOR) preconditioners, derived from the basic iterative schemes. Comparisons are made by using CG-like methods combined with different preconditioners to solve a sequence of time-step reactor transient problems. Numerical tests indicate that preconditioned BI-CGSTAB with the preconditioner MBILU requires less CPU time and fewer iterations than other methods. The preconditioned CG-like methods are less sensitive to the time-step size used than the Chebyshev semi-iteration method and line SOR method. The indication is that the CGS, Bi-CGSTAB and GMRES methods are, on average, better than the other methods in reactor kinetics computation and that a good preconditioner is more important than the choice of CG-like methods. The MILU decomposition based on the conventional row-sum criterion has difficulty yielding a convergent solution and an improved version is introduced. (author)

A novel algorithm for thermal image encryption.

Science.gov (United States)

Hussain, Iqtadar; Anees, Amir; Algarni, Abdulmohsen

2018-04-16

Thermal images play a vital character at nuclear plants, Power stations, Forensic labs biological research, and petroleum products extraction. Safety of thermal images is very important. Image data has some unique features such as intensity, contrast, homogeneity, entropy and correlation among pixels that is why somehow image encryption is trickier as compare to other encryptions. With conventional image encryption schemes it is normally hard to handle these features. Therefore, cryptographers have paid attention to some attractive properties of the chaotic maps such as randomness and sensitivity to build up novel cryptosystems. That is why, recently proposed image encryption techniques progressively more depends on the application of chaotic maps. This paper proposed an image encryption algorithm based on Chebyshev chaotic map and S8 Symmetric group of permutation based substitution boxes. Primarily, parameters of chaotic Chebyshev map are chosen as a secret key to mystify the primary image. Then, the plaintext image is encrypted by the method generated from the substitution boxes and Chebyshev map. By this process, we can get a cipher text image that is perfectly twisted and dispersed. The outcomes of renowned experiments, key sensitivity tests and statistical analysis confirm that the proposed algorithm offers a safe and efficient approach for real-time image encryption.

A new method of simulating fiber suspensions and applications to channel Flows

KAUST Repository

Yang, Wei

2012-06-01

A successive iteration method is proposed to numerically simulate fiber suspensions. The computational field is discretized with the collocated finite volume method, and an ergodic hypothesis is adopted to greatly accelerate the solution to the Fokker - Planck equation. The method is employed in channel flows with different fiber volume fractions and aspect ratios, and its effectiveness is proved. The numerical results show that the existence of fibers significantly changes the pressure distribution, and the fiber aspect ratio has a greater effect on the velocity profile than on the volume faction. At the center of the channel, the velocity increases along the streamwise direction, while the velocity near the wall decreases slightly. The uncoupling and coupling solutions of the additional stress of the fiber suspensions are quite different. © 2012 Chinese Physical Society and IOP Publishing Ltd.

A new method of simulating fiber suspensions and applications to channel Flows

KAUST Repository

Yang, Wei; Zhou, Kun

2012-01-01

A successive iteration method is proposed to numerically simulate fiber suspensions. The computational field is discretized with the collocated finite volume method, and an ergodic hypothesis is adopted to greatly accelerate the solution to the Fokker - Planck equation. The method is employed in channel flows with different fiber volume fractions and aspect ratios, and its effectiveness is proved. The numerical results show that the existence of fibers significantly changes the pressure distribution, and the fiber aspect ratio has a greater effect on the velocity profile than on the volume faction. At the center of the channel, the velocity increases along the streamwise direction, while the velocity near the wall decreases slightly. The uncoupling and coupling solutions of the additional stress of the fiber suspensions are quite different. © 2012 Chinese Physical Society and IOP Publishing Ltd.

A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

International Nuclear Information System (INIS)

Meyer, Chad D.; Balsara, Dinshaw S.; Aslam, Tariq D.

2014-01-01

Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s 2 times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very useful

A comparison of three time-dependent wave packet methods for calculating electron--atom elastic scattering cross sections

International Nuclear Information System (INIS)

Judson, R.S.; McGarrah, D.B.; Sharafeddin, O.A.; Kouri, D.J.; Hoffman, D.K.

1991-01-01

We compare three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials. The three methods are the time-dependent amplitude density method (TDADM), what we term a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, we propagate the time-dependent amplitude density, |ζ(t)right-angle=U|ψ(t)right-angle, where U is the interaction potential and |ψ(t)right-angle is the usual time-dependent wave function. In the other two, the wave function is propagated. As a numerical example, we calculate phase shifts and cross sections using a screened Coulomb, Yukawa type potential over the range 200--1000 eV. One of the major advantages of time-dependent methods such as these is that we get scattering information over this entire range of energies from one propagation. We find that in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l=0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

Science.gov (United States)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Algorithm for Compressing Time-Series Data

Science.gov (United States)

Hawkins, S. Edward, III; Darlington, Edward Hugo

2012-01-01

An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").

Controllable quantum private queries using an entangled Fibonacci-sequence spiral source

Energy Technology Data Exchange (ETDEWEB)

Lai, Hong, E-mail: honglaimm@163.com [School of Computer and Information Science, Southwest University, Chongqing 400715 (China); Department of Computing, Macquarie University, Sydney, NSW 2109 (Australia); School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Orgun, Mehmet A. [Department of Computing, Macquarie University, Sydney, NSW 2109 (Australia); Pieprzyk, Josef [School of Electrical Engineering and Computer Science, Queensland University of Technology, Brisbane, QLD 4000 (Australia); Xiao, Jinghua [School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Xue, Liyin [Corporate Analytics, The Australian Taxation Office, Sydney NSW 2000 (Australia); Jia, Zhongtian, E-mail: ise_jiazt@ujn.edu.cn [Provincial Key Laboratory for Network Based Intelligent Computing, University of Jinan, Jinan 250022 (China)

2015-10-23

Highlights: • Alice can easily control the size of a block by adjusting the parameter m rather than a high-dimension oracle. • The case of Alice knowing an exact multi-bit message can be realized deterministically. • Our protocol provides broad measures of protection against errors caused by the effect of noise. • Our protocol can greatly save both quantum and classical communication and exhibit some advantages in security. • Our protocol is scalable and flexible, and secure against quantum memory attacks by Alice. - Abstract: By changing the initial values in entangled Fibonacci-sequence spiral sources in Simon et al.'s (2013) experimental setup [13], we propose a controllable quantum private query protocol. Moreover, our protocol achieves flexible key expansion and even exhibits secure advantages during communications because of the following observations. We observe the close relationships between Lucas numbers and the first kind of Chebyshev maps, and the Chebyshev maps and k-Chebyshev maps; by adjusting the parameter m in k-Chebyshev maps, Alice and Bob can obtain their expected values of the key blocks and database respectively.

Controllable quantum private queries using an entangled Fibonacci-sequence spiral source

International Nuclear Information System (INIS)

Lai, Hong; Orgun, Mehmet A.; Pieprzyk, Josef; Xiao, Jinghua; Xue, Liyin; Jia, Zhongtian

2015-01-01

Highlights: • Alice can easily control the size of a block by adjusting the parameter m rather than a high-dimension oracle. • The case of Alice knowing an exact multi-bit message can be realized deterministically. • Our protocol provides broad measures of protection against errors caused by the effect of noise. • Our protocol can greatly save both quantum and classical communication and exhibit some advantages in security. • Our protocol is scalable and flexible, and secure against quantum memory attacks by Alice. - Abstract: By changing the initial values in entangled Fibonacci-sequence spiral sources in Simon et al.'s (2013) experimental setup [13], we propose a controllable quantum private query protocol. Moreover, our protocol achieves flexible key expansion and even exhibits secure advantages during communications because of the following observations. We observe the close relationships between Lucas numbers and the first kind of Chebyshev maps, and the Chebyshev maps and k-Chebyshev maps; by adjusting the parameter m in k-Chebyshev maps, Alice and Bob can obtain their expected values of the key blocks and database respectively

Temperature profile in a fix-bed reactor and with cylindrical geometry by the method of orthogonal collocation

International Nuclear Information System (INIS)

Basta, C.

1982-01-01

Using the method of orthogonal colocation the boundary problem for a fix bed with cylindrical geometry was solved. The axial disposal term was despicable and the results were compared with those the explicit finite difference method. (E.G.) [pt