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.

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.

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.

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.

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

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.

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

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 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.)

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.

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

Science.gov (United States)

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

2018-05-01

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

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.

Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

Directory of Open Access Journals (Sweden)

Olumuyiwa A. Agbolade

2017-01-01

Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

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

Science.gov (United States)

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

2018-06-01

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

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.

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.

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).

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.

Simulation of electrically driven jet using Chebyshev collocation method

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

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

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.

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...

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.

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.

A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method

Directory of Open Access Journals (Sweden)

Changqing Yang

2012-01-01

Full Text Available A numerical method to solve Lane-Emden equations as singular initial value problems is presented in this work. This method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The collocation method transforms the differential equation into a system of algebraic equations. It also has application in a wide area of differential equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

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

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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.

Collocations in Marine Engineering English

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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.

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

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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

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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

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

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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.

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.

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 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

Verb-Noun Collocation Proficiency and Academic Years

Directory of Open Access Journals (Sweden)

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.

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.

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

Multidomain spectral solution of compressible viscous flows

International Nuclear Information System (INIS)

Kopriva, D.A.

1994-01-01

We develop a nonoverlapping mutidomain spectral collocation method to solve compressible viscous flows. At the interfaces, the advection terms are treated with a characteristic correction method. The diffusion terms are treated with a penalty method. Spectral accuracy is demonstrated on linear model problems in one and two space dimensions. The method is applied to a subsonic and supersonic flow over a flat plate. The results are compared to solutions of the boundary-layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream Mach number of two. A second application is to a transonic flow in a two-dimensional converging-diverging nozzle, where the computed results are compared to experimental data

An embedded formula of the Chebyshev collocation method for stiff problems

Science.gov (United States)

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

2017-12-01

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

Measuring receptive collocational competence across proficiency levels

Directory of Open Access Journals (Sweden)

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 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.

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.

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...

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

Directory of Open Access Journals (Sweden)

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.

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

Directory of Open Access Journals (Sweden)

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.

Modelling and Simulation of a Packed Bed of Pulp Fibers Using Mixed Collocation Method

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Ishfaq Ahmad Ganaie

2013-01-01

Full Text Available A convenient computational approach for solving mathematical model related to diffusion dispersion during flow through packed bed is presented. The algorithm is based on the mixed collocation method. The method is particularly useful for solving stiff system arising in chemical and process engineering. The convergence of the method is found to be of order 2 using the roots of shifted Chebyshev polynomial. Model is verified using the literature data. This method has provided a convenient check on the accuracy of the results for wide range of parameters, namely, Peclet numbers. Breakthrough curves are plotted to check the effect of Peclet number on average and exit solute concentrations.

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,...

Productive knowledge of collocations may predict academic literacy

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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

2017-05-01

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

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 ...

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

International Nuclear Information System (INIS)

Kupka, F.

1997-11-01

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

Lexical and Grammatical Collocations in Writing Production of EFL Learners

Directory of Open Access Journals (Sweden)

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.

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.

Overdetermined shooting methods for computing standing water waves with spectral accuracy

International Nuclear Information System (INIS)

Wilkening, Jon; Yu Jia

2012-01-01

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

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

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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.

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.

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...

Spectral methods. Fundamentals in single domains

International Nuclear Information System (INIS)

Canuto, C.

2006-01-01

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

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.

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...

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

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.

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

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

KAUST Repository

Carpenter, Mark H.

2016-01-04

Nonlinearly stable finite element methods of arbitrary type and order, are currently unavailable for discretizations of the compressible Navier-Stokes equations. Summation-by-parts (SBP) entropy stability analysis provides a means of constructing nonlinearly stable discrete operators of arbitrary order, but is currently limited to simple element types. Herein, recent progress is reported, on developing entropy-stable (SS) discontinuous spectral collocation formulations for hexahedral elements. Two complementary efforts are discussed. The first effort generalizes previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort extends previous work on entropy stability to include p-refinement at nonconforming interfaces. A generalization of existing entropy stability theory is required to accommodate the nuances of fully multidimensional SBP operators. The entropy stability of the compressible Euler equations on nonconforming interfaces is demonstrated using the newly developed LG operators and multidimensional interface interpolation operators. Preliminary studies suggest design order accuracy at nonconforming interfaces.

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, ...

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…

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.

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…

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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.

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…

Spectral/hp element methods for CFD

CERN Document Server

Karniadakis, George Em

1999-01-01

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

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.

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.

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

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…

Spectral Methods in Numerical Plasma Simulation

DEFF Research Database (Denmark)

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

1989-01-01

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

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.

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

Directory of Open Access Journals (Sweden)

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.

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...

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.

Introduction to finite and spectral element methods using Matlab

CERN Document Server

Pozrikidis, Constantine

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

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…

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

Directory of Open Access Journals (Sweden)

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

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

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Science.gov (United States)

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

2016-01-01

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

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 ...

Chebyshev super spectral viscosity method for water hammer analysis

Directory of Open Access Journals (Sweden)

Hongyu Chen

2013-09-01

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

A divisive spectral method for network community detection

International Nuclear Information System (INIS)

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

2016-01-01

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

Chebyshev and Fourier spectral methods

CERN Document Server

Boyd, John P

2001-01-01

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

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.

[An improved low spectral distortion PCA fusion method].

Science.gov (United States)

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

2013-10-01

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

Digital spectral analysis parametric, non-parametric and advanced methods

CERN Document Server

Castanié, Francis

2013-01-01

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

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.)

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.

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

Science.gov (United States)

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

2018-02-01

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

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

Directory of Open Access Journals (Sweden)

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.

Stochastic Spectral and Conjugate Descent Methods

KAUST Repository

Kovalev, Dmitry

2018-02-11

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

Stochastic Spectral and Conjugate Descent Methods

KAUST Repository

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

2018-01-01

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

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

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 ...

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.

The spectral volume method as applied to transport problems

International Nuclear Information System (INIS)

McClarren, Ryan G.

2011-01-01

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

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.

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 ...

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

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-10-15

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

Spectral Analysis Methods of Social Networks

Directory of Open Access Journals (Sweden)

P. G. Klyucharev

2017-01-01

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

Spectral radiative property control method based on filling solution

International Nuclear Information System (INIS)

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

2014-01-01

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

A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Waleed M. Abd-Elhameed

2016-09-01

Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.

Evolutionary Computing Methods for Spectral Retrieval

Science.gov (United States)

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

2009-01-01

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

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

Logarithmic compression methods for spectral data

Science.gov (United States)

Dunham, Mark E.

2003-01-01

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

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.

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.

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...

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

KAUST Repository

Dia, Ben Mansour

2015-01-07

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

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

Energy Technology Data Exchange (ETDEWEB)

McKay, S.M.

1994-12-31

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

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

Science.gov (United States)

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

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

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

Directory of Open Access Journals (Sweden)

Yi Wang

2016-11-01

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

Numerical Methods for Stochastic Computations A Spectral Method Approach

CERN Document Server

Xiu, Dongbin

2010-01-01

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

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis; Mouhot, Clé ment

2011-01-01

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

Analysis of spectral methods for the homogeneous Boltzmann equation

KAUST Repository

Filbet, Francis

2011-04-01

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

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.

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...

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

1976-01-01

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

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

Indian Academy of Sciences (India)

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

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…

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.

The spectral cell method in nonlinear earthquake modeling

Science.gov (United States)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

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

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.

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

Science.gov (United States)

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

2017-08-01

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

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

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

A Spectral Conjugate Gradient Method for Unconstrained Optimization

International Nuclear Information System (INIS)

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

2001-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Spectral anomaly methods for aerial detection using KUT nuisance rejection

International Nuclear Information System (INIS)

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

2015-01-01

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

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

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

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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.

Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

Directory of Open Access Journals (Sweden)

Jinkui Liu

2012-01-01

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

Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Xuqing Zhang

2013-01-01

Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

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

Science.gov (United States)

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

2018-01-01

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

A stabilised nodal spectral element method for fully nonlinear water waves

DEFF Research Database (Denmark)

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

2016-01-01

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

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

Science.gov (United States)

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

2017-09-01

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

High order spectral volume and spectral difference methods on unstructured grids

Science.gov (United States)

Kannan, Ravishekar

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

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

Science.gov (United States)

Larsen, Curtis E.; Irvine, Tom

2013-01-01

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

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

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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.

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

KAUST Repository

Dia, Ben Mansour; Chá con-Rebollo, Tomas

2015-01-01

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

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...

Spectrally accurate initial data in numerical relativity

Science.gov (United States)

Battista, Nicholas A.

Einstein's theory of general relativity has radically altered the way in which we perceive the universe. His breakthrough was to realize that the fabric of space is deformable in the presence of mass, and that space and time are linked into a continuum. Much evidence has been gathered in support of general relativity over the decades. Some of the indirect evidence for GR includes the phenomenon of gravitational lensing, the anomalous perihelion of mercury, and the gravitational redshift. One of the most striking predictions of GR, that has not yet been confirmed, is the existence of gravitational waves. The primary source of gravitational waves in the universe is thought to be produced during the merger of binary black hole systems, or by binary neutron stars. The starting point for computer simulations of black hole mergers requires highly accurate initial data for the space-time metric and for the curvature. The equations describing the initial space-time around the black hole(s) are non-linear, elliptic partial differential equations (PDE). We will discuss how to use a pseudo-spectral (collocation) method to calculate the initial puncture data corresponding to single black hole and binary black hole systems.

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

International Nuclear Information System (INIS)

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

1987-01-01

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

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.

Convergence analysis of spectral element method for electromechanical devices

NARCIS (Netherlands)

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

2017-01-01

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

Convergence analysis of spectral element method for magnetic devices

NARCIS (Netherlands)

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

2018-01-01

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

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-04-27

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

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.

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

Science.gov (United States)

Irvine, Tom; Larsen, Curtis

2016-01-01

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

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.

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Spectral element method for elastic and acoustic waves in frequency domain

Energy Technology Data Exchange (ETDEWEB)

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

2016-12-15

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

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.

GOSAT and OCO-2 Inter-comparison on Measured Spectral Radiance and Retrieved Carbon Dioxide

Science.gov (United States)

Kataoka, F.; Kuze, A.; Shiomi, K.; Suto, H.; Crisp, D.; Bruegge, C. J.; Schwandner, F. M.

2016-12-01

TANSO-FTS onboard GOSAT and grating spectrometer on OCO-2 use different measurement techniques to measure carbon dioxide (CO2) and molecular oxygen (O2). Both instruments observe sunlight reflected from the Earth's surface in almost the same spectral range. As a first step in cross calibrating these two instruments, we compared spectral radiance observations within the three short wave infrared (SWIR) spectral bands centered on the O2 A-band (O2A), the weak CO2 band near 1.6 microns (Weak-CO2) and 2.06 micons (Strong-CO2) bands at temporally coincident and spatially collocated points. In this work, we reconciled the different size of the footprints and evaluated at various types of surface targets such as ocean, desert and forest. For radiometric inter-comparisons, we consider long term instrument sensitivity degradation in orbit and differences in viewing geometry and associated differences in surface bidirectional reflectance distribution function (BRDF). Measured spectral radiances agree very well within 5% for all bands. This presentation will summarize these comparisons of GOSAT and OCO-2 spectral radiance observations and associated estimates of carbon dioxide and related parameters retrieved with the same algorithm at matchup points. We will also discuss instrument related uncertainties from various target observations.

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

OpenAIRE

Male , Jean-Michel; Fezoui , Loula ,

1993-01-01

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

Sparse Generalized Fourier Series via Collocation-based Optimization

Science.gov (United States)

2014-11-01

Theory 51, 12 (2005) 4203– 4215. [6] P. CONSTANTINE , M. ELDRED AND E. PHIPPS, Sparse pseu- dospectral approximation method. Comput. Methods Appl. Mech...Visition XVI: Algorithms, Techniques, Active Vision , and Materials Handling, 224 (1997). [15] J. SHEN AND L. WANG, Some recent advances on spectral methods

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 analysis of mammographic images using a multitaper method

International Nuclear Information System (INIS)

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

2012-01-01

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

The analysis of toxic connections content in water by spectral methods

Science.gov (United States)

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

2017-08-01

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

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

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

Science.gov (United States)

Zhao, Peng-yuan; Huang, Xiao-ping

2018-03-01

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

Performance of spectral fitting methods for vegetation fluorescence quantification

NARCIS (Netherlands)

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

2010-01-01

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

Computation of High-Frequency Waves with Random Uncertainty

KAUST Repository

Malenova, Gabriela; Motamed, Mohammad; Runborg, Olof; Tempone, Raul

2016-01-01

or nonlinear functionals of the wave solution and its spatial/temporal derivatives. The numerical scheme combines two techniques: a high-frequency method based on Gaussian beams [2, 3], a sparse stochastic collocation method [4]. The fast spectral

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

Science.gov (United States)

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

2017-02-01

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

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...

Application of Least-Squares Spectral Element Methods to Polynomial Chaos

NARCIS (Netherlands)

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

2006-01-01

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

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.

A conjugate gradient method for the spectral partitioning of graphs

NARCIS (Netherlands)

Kruyt, Nicolaas P.

1997-01-01

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

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

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

Science.gov (United States)

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

2015-08-01

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

Convergence of spectral methods for nonlinear conservation laws. Final report

International Nuclear Information System (INIS)

Tadmor, E.

1987-08-01

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

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

Science.gov (United States)

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

2018-02-01

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

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

Science.gov (United States)

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

2016-11-01

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

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

Spectral calculations in magnetohydrodynamics using the Jacobi-Davidson method

NARCIS (Netherlands)

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

2001-01-01

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

Spectral analysis of an algebraic collapsing acceleration for the characteristics method

International Nuclear Information System (INIS)

Le Tellier, R.; Hebert, A.

2005-01-01

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

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

International Nuclear Information System (INIS)

Hopkins, A.T.

1984-01-01

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

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

Science.gov (United States)

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

2016-01-25

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

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

CERN Document Server

Shizgal, Bernard

2015-01-01

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

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.

International Conference on Spectral and High-Order Methods

CERN Document Server

Dumont, Ney; Hesthaven, Jan

2017-01-01

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

Sparse Pseudo Spectral Projection Methods with Directional Adaptation for Uncertainty Quantification

KAUST Repository

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

2015-01-01

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

Nonconforming h-p spectral element methods for elliptic problems

Indian Academy of Sciences (India)

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

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

The core spline method for solution of quantum-mechanical systems of differential equations for bound states

International Nuclear Information System (INIS)

Aleksandrov, L.; Drenska, M.; Karadzhov, D.

1986-01-01

A generalization of the core spline method is given in the case of solution of the general bound state problem for a system of M linear differential equations with coefficients depending on the spectral parameter. The recursion scheme for construction of basic splines is described. The wave functions are expressed as linear combinations of basic splines, which are approximate partial solutions of the system. The spectral parameter (the eigenvalue) is determined from the condition for existence of a nontrivial solution of a (MxM) linear algebraic system at the last collocation point. The nontrivial solutions of this system determine (M - 1) coefficients of the linear spans, expressing the wave functions. The last unknown coefficient is determined from a boundary (or normalization) condition for the system. The computational aspects of the method are discussed, in particular, its concrete algorithmic realization used in the RODSOL program. The numerical solution of the Dirac system for the bound states of a hydrogen atom is given is an example

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.

Spectral mimetic least-squares method for div-curl systems

NARCIS (Netherlands)

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

2018-01-01

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

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

A spectral measurement method for determining white OLED average junction temperatures

Science.gov (United States)

Zhu, Yiting; Narendran, Nadarajah

2016-09-01

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

Deconvolution of EPR spectral lines with an approximate method

International Nuclear Information System (INIS)

Jimenez D, H.; Cabral P, A.

1990-10-01

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

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

KAUST Repository

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

2014-01-01

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

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

International Nuclear Information System (INIS)

Yu, Hua-Gen

2014-01-01

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

Spectral decomposition in advection-diffusion analysis by finite element methods

International Nuclear Information System (INIS)

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

1978-01-01

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

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

KAUST Repository

Zou, Peng

2017-05-10

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

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

INTEGRATED FUSION METHOD FOR MULTIPLE TEMPORAL-SPATIAL-SPECTRAL IMAGES

Directory of Open Access Journals (Sweden)

H. Shen

2012-08-01

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

Nightside studies of coherent HF Radar spectral width behaviour

Directory of Open Access Journals (Sweden)

E. E. Woodfield

2002-09-01

Full Text Available A previous case study found a relationship between high spectral width measured by the CUTLASS Finland HF radar and elevated electron temperatures observed by the EISCAT and ESR incoherent scatter radars in the post-midnight sector of magnetic local time. This paper expands that work by briefly re-examining that interval and looking in depth at two further case studies. In all three cases a region of high HF spectral width (>200 ms-1 exists poleward of a region of low HF spectral width (<200 ms-1. Each case, however, occurs under quite different geomagnetic conditions. The original case study occurred during an interval with no observed electrojet activity, the second study during a transition from quiet to active conditions with a clear band of ion frictional heating indicating the location of the flow reversal boundary, and the third during an isolated sub-storm. These case studies indicate that the relationship between elevated electron temperature and high HF radar spectral width appears on closed field lines after 03:00 magnetic local time (MLT on the nightside. It is not clear whether the same relationship would hold on open field lines, since our analysis of this relationship is restricted in latitude. We find two important properties of high spectral width data on the nightside. Firstly the high spectral width values occur on both open and closed field lines, and secondly that the power spectra which exhibit high widths are both single-peak and multiple-peak. In general the regions of high spectral width (>200 ms-1 have more multiple-peak spectra than the regions of low spectral widths whilst still maintaining a majority of single-peak spectra. We also find that the region of ion frictional heating is collocated with many multiple-peak HF spectra. Several mechanisms for the generation of high spectral width have been proposed which would produce multiple-peak spectra, these are discussed in relation to the data presented here. Since the

Nightside studies of coherent HF Radar spectral width behaviour

Directory of Open Access Journals (Sweden)

E. E. Woodfield

Full Text Available A previous case study found a relationship between high spectral width measured by the CUTLASS Finland HF radar and elevated electron temperatures observed by the EISCAT and ESR incoherent scatter radars in the post-midnight sector of magnetic local time. This paper expands that work by briefly re-examining that interval and looking in depth at two further case studies. In all three cases a region of high HF spectral width (>200 ms^-1 exists poleward of a region of low HF spectral width (<200 ms^-1. Each case, however, occurs under quite different geomagnetic conditions. The original case study occurred during an interval with no observed electrojet activity, the second study during a transition from quiet to active conditions with a clear band of ion frictional heating indicating the location of the flow reversal boundary, and the third during an isolated sub-storm. These case studies indicate that the relationship between elevated electron temperature and high HF radar spectral width appears on closed field lines after 03:00 magnetic local time (MLT on the nightside. It is not clear whether the same relationship would hold on open field lines, since our analysis of this relationship is restricted in latitude. We find two important properties of high spectral width data on the nightside. Firstly the high spectral width values occur on both open and closed field lines, and secondly that the power spectra which exhibit high widths are both single-peak and multiple-peak. In general the regions of high spectral width (>200 ms^-1 have more multiple-peak spectra than the regions of low spectral widths whilst still maintaining a majority of single-peak spectra. We also find that the region of ion frictional heating is collocated with many multiple-peak HF spectra. Several mechanisms for the generation of high spectral width have been proposed which would produce multiple-peak spectra, these are discussed in relation to

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

DEFF Research Database (Denmark)

Larsén, Xiaoli Guo; Kruger, Andries C.

2014-01-01

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

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

Science.gov (United States)

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

2013-07-01

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

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.

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

KAUST Repository

Zou, Peng; Cheng, Jiubing

2017-01-01

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

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.

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...

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

Science.gov (United States)

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

2009-05-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1999-06-01

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

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.

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

Spectral gamuts and spectral gamut mapping

Science.gov (United States)

Rosen, Mitchell R.; Derhak, Maxim W.

2006-01-01

All imaging devices have two gamuts: the stimulus gamut and the response gamut. The response gamut of a print engine is typically described in CIE colorimetry units, a system derived to quantify human color response. More fundamental than colorimetric gamuts are spectral gamuts, based on radiance, reflectance or transmittance units. Spectral gamuts depend on the physics of light or on how materials interact with light and do not involve the human's photoreceptor integration or brain processing. Methods for visualizing a spectral gamut raise challenges as do considerations of how to utilize such a data-set for producing superior color reproductions. Recent work has described a transformation of spectra reduced to 6-dimensions called LabPQR. LabPQR was designed as a hybrid space with three explicit colorimetric axes and three additional spectral reconstruction axes. In this paper spectral gamuts are discussed making use of LabPQR. Also, spectral gamut mapping is considered in light of the colorimetric-spectral duality of the LabPQR space.

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

International Nuclear Information System (INIS)

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

2009-01-01

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

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

Science.gov (United States)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

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

Spectral Imaging by Upconversion

DEFF Research Database (Denmark)

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

2011-01-01

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

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...

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

International Nuclear Information System (INIS)

Gunnink, R.

1983-06-01

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

Testing the accuracy and stability of spectral methods in numerical relativity

International Nuclear Information System (INIS)

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

2007-01-01

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

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

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

Science.gov (United States)

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

2016-05-01

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

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)

Towards spectral geometric methods for Euclidean quantum gravity

Science.gov (United States)

Panine, Mikhail; Kempf, Achim

2016-04-01

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

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

Indian Academy of Sciences (India)

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

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

DEFF Research Database (Denmark)

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

2005-01-01

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

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

Spectral analysis methods for vehicle interior vibro-acoustics identification

Science.gov (United States)

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

2009-02-01

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

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

International Nuclear Information System (INIS)

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

1993-01-01

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

Finite length Taylor Couette flow

Science.gov (United States)

Streett, C. L.; Hussaini, M. Y.

1987-01-01

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.

Spectral Element Method for the Simulation of Unsteady Compressible Flows

Science.gov (United States)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

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

A Statistical study of the Doppler spectral width of high-latitude ionospheric F-region echoes recorded with SuperDARN coherent HF radars

Directory of Open Access Journals (Sweden)

J.-P. Villain

2002-11-01

Full Text Available The HF radars of the Super Dual Auroral Radar Network (SuperDARN provide measurements of the E × B drift of ionospheric plasma over extended regions of the high-latitude ionosphere. We have conducted a statistical study of the associated Doppler spectral width of ionospheric F-region echoes. The study has been conducted with all available radars from the Northern Hemisphere for 2 specific periods of time. Period 1 corresponds to the winter months of 1994, while period 2 covers October 1996 to March 1997. The distributions of data points and average spectral width are presented as a function of Magnetic Latitude and Magnetic Local Time. The databases are very consistent and exhibit the same features. The most stringent features are: a region of very high spectral width, collocated with the ionospheric LLBL/cusp/mantle region; an oval shaped region of high spectral width, whose equator-ward boundary matches the poleward limit of the Holzworth and Meng auroral oval. A simulation has been conducted to evaluate the geometrical and instrumental effects on the spectral width. It shows that these effects cannot account for the observed spectral features. It is then concluded that these specific spectral width characteristics are the signature of ionospheric/magnetospheric coupling phenomena.Key words. Ionosphere (auroral ionosphere; ionosphere-magnetosphere interactions; ionospheric irregularities

A Statistical study of the Doppler spectral width of high-latitude ionospheric F-region echoes recorded with SuperDARN coherent HF radars

Directory of Open Access Journals (Sweden)

J.-P. Villain

Full Text Available The HF radars of the Super Dual Auroral Radar Network (SuperDARN provide measurements of the E × B drift of ionospheric plasma over extended regions of the high-latitude ionosphere. We have conducted a statistical study of the associated Doppler spectral width of ionospheric F-region echoes. The study has been conducted with all available radars from the Northern Hemisphere for 2 specific periods of time. Period 1 corresponds to the winter months of 1994, while period 2 covers October 1996 to March 1997. The distributions of data points and average spectral width are presented as a function of Magnetic Latitude and Magnetic Local Time. The databases are very consistent and exhibit the same features. The most stringent features are: a region of very high spectral width, collocated with the ionospheric LLBL/cusp/mantle region; an oval shaped region of high spectral width, whose equator-ward boundary matches the poleward limit of the Holzworth and Meng auroral oval. A simulation has been conducted to evaluate the geometrical and instrumental effects on the spectral width. It shows that these effects cannot account for the observed spectral features. It is then concluded that these specific spectral width characteristics are the signature of ionospheric/magnetospheric coupling phenomena.

Key words. Ionosphere (auroral ionosphere; ionosphere-magnetosphere interactions; ionospheric irregularities

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.

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.

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

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Adaptive Spectral Doppler Estimation

DEFF Research Database (Denmark)

Gran, Fredrik; Jakobsson, Andreas; Jensen, Jørgen Arendt

2009-01-01

. The methods can also provide better quality of the estimated power spectral density (PSD) of the blood signal. Adaptive spectral estimation techniques are known to pro- vide good spectral resolution and contrast even when the ob- servation window is very short. The 2 adaptive techniques are tested......In this paper, 2 adaptive spectral estimation techniques are analyzed for spectral Doppler ultrasound. The purpose is to minimize the observation window needed to estimate the spectrogram to provide a better temporal resolution and gain more flexibility when designing the data acquisition sequence...... and compared with the averaged periodogram (Welch’s method). The blood power spectral capon (BPC) method is based on a standard minimum variance technique adapted to account for both averaging over slow-time and depth. The blood amplitude and phase estimation technique (BAPES) is based on finding a set...

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

KAUST Repository

Chacó n Rebollo, Tomá s; Dia, Ben Mansour

2015-01-01

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

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

KAUST Repository

Chacón Rebollo, Tomás

2015-03-01

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

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

Science.gov (United States)

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

2018-01-15

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

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

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2009-01-01

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

A spectral nudging method for the ACCESS1.3 atmospheric model

Science.gov (United States)

Uhe, P.; Thatcher, M.

2015-06-01

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

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

International Nuclear Information System (INIS)

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

1996-01-01

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

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

Directory of Open Access Journals (Sweden)

Martin Seilmayer

2017-01-01

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

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

International Nuclear Information System (INIS)

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

2003-01-01

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

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

International Nuclear Information System (INIS)

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

2004-01-01

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

High temperature spectral emissivity measurement using integral blackbody method

Science.gov (United States)

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

2016-10-01

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

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

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

Science.gov (United States)

Samimi, Kayvan; Varghese, Tomy

2015-05-01

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

Solution of the Schroedinger equation by a spectral method

International Nuclear Information System (INIS)

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

1982-01-01

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

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

Science.gov (United States)

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

2018-02-01

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

Spectrally accurate contour dynamics

International Nuclear Information System (INIS)

Van Buskirk, R.D.; Marcus, P.S.

1994-01-01

We present an exponentially accurate boundary integral method for calculation the equilibria and dynamics of piece-wise constant distributions of potential vorticity. The method represents contours of potential vorticity as a spectral sum and solves the Biot-Savart equation for the velocity by spectrally evaluating a desingularized contour integral. We use the technique in both an initial-value code and a newton continuation method. Our methods are tested by comparing the numerical solutions with known analytic results, and it is shown that for the same amount of computational work our spectral methods are more accurate than other contour dynamics methods currently in use

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

International Nuclear Information System (INIS)

Ostachowicz, W; Kudela, P

2010-01-01

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

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

CERN Document Server

American Society for Testing and Materials. Philadelphia

1971-01-01

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

The use of spectral methods in bidomain studies.

Science.gov (United States)

Trayanova, N; Pilkington, T

1992-01-01

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

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

Science.gov (United States)

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

2010-04-01

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

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

Digital Repository Service at National Institute of Oceanography (India)

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

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

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

NARCIS (Netherlands)

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

2002-01-01

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

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

CERN Document Server

American Society for Testing and Materials. Philadelphia

2010-01-01

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

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.

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

International Nuclear Information System (INIS)

Lisitsa, V.S.

2009-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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 ...

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

DEFF Research Database (Denmark)

Xu, Hui; Cantwell, Chris; Monteserin, Carlos

2018-01-01

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

A spectral nudging method for the ACCESS1.3 atmospheric model

Directory of Open Access Journals (Sweden)

P. Uhe

2015-06-01

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

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

NARCIS (Netherlands)

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

2016-01-01

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

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

International Nuclear Information System (INIS)

Miyoshi, Takahiro

2000-05-01

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

Visual Method for Spectral Energy Distribution Calculation of ...

Indian Academy of Sciences (India)

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

Spectral Karyotyping. An new method for chromosome analysis

International Nuclear Information System (INIS)

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

2006-01-01

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

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

KAUST Repository

Efendiev, Yalchin

2011-02-01

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

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

Science.gov (United States)

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

2018-01-01

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

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

Science.gov (United States)

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

2011-04-01

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

Spectral Learning for Supervised Topic Models.

Science.gov (United States)

Ren, Yong; Wang, Yining; Zhu, Jun

2018-03-01

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods have been applied to learn unsupervised topic models, such as latent Dirichlet allocation (LDA), with provable guarantees. This paper investigates the possibility of applying spectral methods to recover the parameters of supervised LDA (sLDA). We first present a two-stage spectral method, which recovers the parameters of LDA followed by a power update method to recover the regression model parameters. Then, we further present a single-phase spectral algorithm to jointly recover the topic distribution matrix as well as the regression weights. Our spectral algorithms are provably correct and computationally efficient. We prove a sample complexity bound for each algorithm and subsequently derive a sufficient condition for the identifiability of sLDA. Thorough experiments on synthetic and real-world datasets verify the theory and demonstrate the practical effectiveness of the spectral algorithms. In fact, our results on a large-scale review rating dataset demonstrate that our single-phase spectral algorithm alone gets comparable or even better performance than state-of-the-art methods, while previous work on spectral methods has rarely reported such promising performance.

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

Directory of Open Access Journals (Sweden)

Z. Pashazadeh Atabakan

2013-01-01

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

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 New Pansharpening Method Based on Spatial and Spectral Sparsity Priors.

Science.gov (United States)

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

2014-06-27

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

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

International Nuclear Information System (INIS)

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

2001-01-01

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

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

Science.gov (United States)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

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

Science.gov (United States)

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

2018-04-01

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

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

Science.gov (United States)

Pearman, Charles M.

2014-01-01

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

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

Science.gov (United States)

Djenidi, L.; Antonia, R. A.

2012-10-01

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

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

NARCIS (Netherlands)

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

2010-01-01

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

3D Spatial and Spectral Fusion of Terrestrial Hyperspectral Imagery and Lidar for Hyperspectral Image Shadow Restoration Applied to a Geologic Outcrop

Science.gov (United States)

Hartzell, P. J.; Glennie, C. L.; Hauser, D. L.; Okyay, U.; Khan, S.; Finnegan, D. C.

2016-12-01

Recent advances in remote sensing technology have expanded the acquisition and fusion of active lidar and passive hyperspectral imagery (HSI) from an exclusively airborne technique to terrestrial modalities. This enables high resolution 3D spatial and spectral quantification of vertical geologic structures for applications such as virtual 3D rock outcrop models for hydrocarbon reservoir analog analysis and mineral quantification in open pit mining environments. In contrast to airborne observation geometry, the vertical surfaces observed by horizontal-viewing terrestrial HSI sensors are prone to extensive topography-induced solar shadowing, which leads to reduced pixel classification accuracy or outright removal of shadowed pixels from analysis tasks. Using a precisely calibrated and registered offset cylindrical linear array camera model, we demonstrate the use of 3D lidar data for sub-pixel HSI shadow detection and the restoration of the shadowed pixel spectra via empirical methods that utilize illuminated and shadowed pixels of similar material composition. We further introduce a new HSI shadow restoration technique that leverages collocated backscattered lidar intensity, which is resistant to solar conditions, obtained by projecting the 3D lidar points through the HSI camera model into HSI pixel space. Using ratios derived from the overlapping lidar laser and HSI wavelengths, restored shadow pixel spectra are approximated using a simple scale factor. Simulations of multiple lidar wavelengths, i.e., multi-spectral lidar, indicate the potential for robust HSI spectral restoration that is independent of the complexity and costs associated with rigorous radiometric transfer models, which have yet to be developed for horizontal-viewing terrestrial HSI sensors. The spectral restoration performance is quantified through HSI pixel classification consistency between full sun and partial sun exposures of a single geologic outcrop.

An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property

KAUST Repository

Friedrich, Lucas

2017-12-29

This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented is that the nodal DG method is constructed with the collocated Legendre-Gauss-Lobatto nodes. This choice ensures that the derivative/mass matrix pair is a summation-by-parts (SBP) operator such that entropy stability proofs from the continuous analysis are discretely mimicked. Special attention is given to the coupling between nonconforming elements as we demonstrate that the standard mortar approach for DG methods does not guarantee entropy stability for non-linear problems, which can lead to instabilities. As such, we describe a precise procedure and modify the mortar method to guarantee entropy stability for general non-linear hyperbolic systems on h/p non-conforming meshes. We verify the high-order accuracy and the entropy conservation/stability of fully non-conforming approximation with numerical examples.

Calibrating spectral images using penalized likelihood

NARCIS (Netherlands)

Heijden, van der G.W.A.M.; Glasbey, C.

2003-01-01

A new method is presented for automatic correction of distortions and for spectral calibration (which band corresponds to which wavelength) of spectral images recorded by means of a spectrograph. The method consists of recording a bar-like pattern with an illumination source with spectral bands

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.

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

Science.gov (United States)

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

2017-11-01

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

Performance Evaluation of the Spectral Centroid Downshift Method for Attenuation Estimation

OpenAIRE

Samimi, Kayvan; Varghese, Tomy

2015-01-01

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

A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

Science.gov (United States)

Taneja, Ankur; Higdon, Jonathan

2018-01-01

A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

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

International Nuclear Information System (INIS)

Shen, Hua-Wei; Cheng, Xue-Qi

2010-01-01

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

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

Science.gov (United States)

Nagaev, S. V.

2017-12-01

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

A case study of forward calculations of the gravity anomaly by spectral method for a three-dimensional parameterised fault model

Science.gov (United States)

Xu, Weimin; Chen, Shi

2018-02-01

Spectral methods provide many advantages for calculating gravity anomalies. In this paper, we derive a kernel function for a three-dimensional (3D) fault model in the wave number domain, and present the full Fortran source code developed for the forward computation of the gravity anomalies and related derivatives obtained from the model. The numerical error and computing speed obtained using the proposed spectral method are compared with those obtained using a 3D rectangular prism model solved in the space domain. The error obtained using the spectral method is shown to be dependent on the sequence length employed in the fast Fourier transform. The spectral method is applied to some examples of 3D fault models, and is demonstrated to be a straightforward and alternative computational approach to enhance computational speed and simplify the procedures for solving many gravitational potential forward problems involving complicated geological models. The proposed method can generate a great number of feasible geophysical interpretations based on a 3D model with only a few variables, and can thereby improve the efficiency of inversion.

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

Science.gov (United States)

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

2017-09-01

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

Terahertz spectral unmixing based method for identifying gastric cancer

Science.gov (United States)

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

2018-02-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

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.

The spectral method and ergodic theorems for general Markov chains

International Nuclear Information System (INIS)

Nagaev, S V

2015-01-01

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

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

Science.gov (United States)

Pearman, Charles M

2014-12-01

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

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

International Nuclear Information System (INIS)

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

1991-06-01

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

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

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

Science.gov (United States)

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

2015-07-01

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

CRISS power spectral density

International Nuclear Information System (INIS)

Vaeth, W.

1979-04-01

The correlation of signal components at different frequencies like higher harmonics cannot be detected by a normal power spectral density measurement, since this technique correlates only components at the same frequency. This paper describes a special method for measuring the correlation of two signal components at different frequencies: the CRISS power spectral density. From this new function in frequency analysis, the correlation of two components can be determined quantitatively either they stem from one signal or from two diverse signals. The principle of the method, suitable for the higher harmonics of a signal as well as for any other frequency combinations is shown for the digital frequency analysis technique. Two examples of CRISS power spectral densities demonstrates the operation of the new method. (orig.) [de

Spacetime Discontinuous Galerkin FEM: Spectral Response

International Nuclear Information System (INIS)

Abedi, R; Omidi, O; Clarke, P L

2014-01-01

Materials in nature demonstrate certain spectral shapes in terms of their material properties. Since successful experimental demonstrations in 2000, metamaterials have provided a means to engineer materials with desired spectral shapes for their material properties. Computational tools are employed in two different aspects for metamaterial modeling: 1. Mircoscale unit cell analysis to derive and possibly optimize material's spectral response; 2. macroscale to analyze their interaction with conventional material. We compare two different approaches of Time-Domain (TD) and Frequency Domain (FD) methods for metamaterial applications. Finally, we discuss advantages of the TD method of Spacetime Discontinuous Galerkin finite element method (FEM) for spectral analysis of metamaterials

Diffusion in multicomponent systems: a free energy approach

International Nuclear Information System (INIS)

Emmanuel, Simon; Cortis, Andrea; Berkowitz, Brian

2004-01-01

This work examines diffusion in ternary non-ideal systems and derives coupled non-linear equations based on a non-equilibrium thermodynamic approach in which an explicit expression for the free energy is substituted into standard diffusion equations. For ideal solutions, the equations employ four mobility parameters (M aa , M ab , M ba , and M bb ), and uphill diffusion is predicted for certain initial conditions and combinations of mobilities. For the more complex case of ternary Simple Mixtures, two non-ideality parameters (χ ac and χ bc ) that are directly related to the excess free energy of mixing are introduced. The solution of the equations is carried out by means of two different numerical schemes: (1) spectral collocation and (2) finite element. An error minimization technique is coupled with the spectral collocation method and applied to diffusional profiles to extract the M and χ parameters. The model satisfactorily reproduces diffusional profiles from published data for silicate melts. Further improvements in numerical and experimental techniques are then suggested

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

International Nuclear Information System (INIS)

Fiebig, H. Rudolf

2002-01-01

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

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

KAUST Repository

Le Maitre, Olivier

2014-01-06

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